Finite Group Databasebeta

← D3×#127×AGL(1,𝔽7) #72244277

Subgroups — D3×#127×AGL(1,𝔽7) #72244277

Order 8064.

12498 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72244271C211yesmaximal, characteristic, complemented
2AGL(1,𝔽7)×#874C211yesmaximal, characteristic, complemented
3D3×#10620710C211yesmaximal, characteristic, complemented
4C42×D3×AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
5#72244257C216yesmaximal, complemented
6C4×(C3⋊AGL(1,𝔽7))⋊C4C2213yescomplemented
7D3×#6503⋊C3C216yesmaximal, complemented
8#72244254C2216yescomplemented
9C4×D3×ΓL(1,𝔽8)⋊C4C2213yescomplemented
10#127×C3⋊AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
11#72244251C2211yescharacteristic, complemented
12C42×C3⋊AGL(1,𝔽7)C2211yescharacteristic, complemented
13D3×ΓL(1,𝔽8)×#127C211yesmaximal, characteristic, complemented
14ΓL(1,𝔽8)×#874C2211yescharacteristic, complemented
15C42×D3×ΓL(1,𝔽8)C2211yescharacteristic, complemented
16AGL(1,𝔽7)×#940C216yesmaximal, complemented
17#72244245C22124yescomplemented
18#72244244C2216yescomplemented
19C4×Dic3×AGL(1,𝔽7)C2213yescomplemented
20#72244242C2216yescomplemented
21#72244241C2216yescomplemented
22ΓL(1,𝔽8)×#940C2216yescomplemented
23C3×#127×AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
24C3×#10620710C2211yescharacteristic, complemented
25C3×C42×AGL(1,𝔽7)C2211yescharacteristic, complemented
26C3×#6503⋊C3C2216yescomplemented
27C3×ΓL(1,𝔽8)×#127C2211yescharacteristic, complemented
28D3×D7×#127C311yesmaximal, characteristic, complemented
29C2×D3×D4×AGL(1,𝔽7)C216yesmaximal, complemented
30C2×#66681⋊C3C2216yescomplemented
31C2×D12×AGL(1,𝔽7)C2216yescomplemented
32C2×D3×C4⋊AGL(1,𝔽7)C2216yescomplemented
33C2×#66694⋊C3C22112yescomplemented
34C2×#67×AGL(1,𝔽7)C22112yescomplemented
35C2×D3×(C22⋊D7)⋊C3C22112yescomplemented
36C23×D3×AGL(1,𝔽7)C2214yes—
37C2×D4×C3⋊AGL(1,𝔽7)C2216yescomplemented
38C2×D3×D4×ΓL(1,𝔽8)C2216yescomplemented
39C2×C3×D4×AGL(1,𝔽7)C2216yescomplemented
40C2×#127×AGL(1,𝔽7)—31nomaximal
41D3×D4×AGL(1,𝔽7)—248no—
42C2×C4×D3×AGL(1,𝔽7)C2213yes—
43C2×D3×D4×D7C2×C316yescomplemented
44C22×D4×AGL(1,𝔽7)—36no—
45#127×D21C2×C311yescharacteristic, complemented
46D3×C7×#127C2×C311yescharacteristic, complemented
47C3×D7×#127C2×C311yescharacteristic, complemented
48C2×ΓL(1,𝔽8)×#127—31no—
49#13059944C2×C316yescomplemented
50D3×#6503C2×C316yescomplemented
51D7×#940C2×C316yescomplemented
52#13057978C2×C311yescharacteristic, complemented
53D3×#6437C2×C311yescharacteristic, complemented
54D7×#874C2×C311yescharacteristic, complemented
55C42×D3×D7C2×C311yescharacteristic, complemented
56C2×#6503⋊C3—36no—
57#127×AGL(1,𝔽7)—21no—
58#127×AGL(1,𝔽7)—31no—
59#127×AGL(1,𝔽7)—36no—
60#127×AGL(1,𝔽7)—36no—
61#127×AGL(1,𝔽7)—31no—
62#127×AGL(1,𝔽7)—31no—
63#127×AGL(1,𝔽7)D311yescharacteristic, direct product factor
64C2×#10620710—31no—
65C2×C42×AGL(1,𝔽7)—31no—
66C2×C3×D3×#127—71nomaximal, Hall
67C23×C3⋊AGL(1,𝔽7)C2314yes—
68C23×D3×ΓL(1,𝔽8)C2314yes—
69C23×C3×AGL(1,𝔽7)C2314yes—
70C22×D3×AGL(1,𝔽7)—248no—
71C22×D3×AGL(1,𝔽7)C2314yes—
72C22×D3×AGL(1,𝔽7)C2314yes—
73C22×D3×AGL(1,𝔽7)C2314yes—
74C22×D3×AGL(1,𝔽7)C2311yescharacteristic
75C2×C3×D4×ΓL(1,𝔽8)C2316yescomplemented
76C2×#4268⋊C3C23112yescomplemented
77D4×C3⋊AGL(1,𝔽7)—224no—
78C2×C4⋊(C3⋊AGL(1,𝔽7))C2316yescomplemented
79C2×C4×C3⋊AGL(1,𝔽7)C2313yes—
80C2×ΓL(1,𝔽8)×#67C23112yescomplemented
81D3×D4×ΓL(1,𝔽8)—224no—
82C2×ΓL(1,𝔽8)×D12C2316yescomplemented
83C2×C4×D3×ΓL(1,𝔽8)C2313yes—
84C2×C3×(C22⋊D7)⋊C3C23112yescomplemented
85C3×D4×AGL(1,𝔽7)—224no—
86C2×C3×C4⋊AGL(1,𝔽7)C2316yescomplemented
87C2×C3×C4×AGL(1,𝔽7)C2313yes—
88#66694⋊C3—248no—
89D3×(C22⋊D7)⋊C3—248no—
90#67×AGL(1,𝔽7)—248no—
91C2×#4247⋊C3C23112yescomplemented
92C2×#4246⋊C3C23112yescomplemented
93C2×#4245⋊C3C23112yescomplemented
94C2×(C3⋊AGL(1,𝔽7))⋊C4C2313yes—
95C2×D3×ΓL(1,𝔽8)⋊C4C2313yes—
96C2×Dic3×AGL(1,𝔽7)C2313yes—
97#66681⋊C3—224no—
98D3×C4⋊AGL(1,𝔽7)—224no—
99D12×AGL(1,𝔽7)—224no—
100C4×D3×AGL(1,𝔽7)D4124yescomplemented
101C3×C42×ΓL(1,𝔽8)C2311yescharacteristic, complemented
102C4×C3⋊(ΓL(1,𝔽8)⋊C4)C2313yescomplemented
103C4×Dic3×ΓL(1,𝔽8)C2313yescomplemented
104C3×C4×ΓL(1,𝔽8)⋊C4C2313yescomplemented
105Dic3×ΓL(1,𝔽8)⋊C4C2316yescomplemented
106C2×D7×#127—31noHall
107C23×D3×D7C22×C314yes—
108C24×AGL(1,𝔽7)—34no—
109C2×D4×D21C22×C316yescomplemented
110C2×D3×C7×D4C22×C316yescomplemented
111C2×C3×D4×D7C22×C316yescomplemented
112C22×D4×ΓL(1,𝔽8)—36no—
113C2×#66694C22×C3112yescomplemented
114C2×D3×C22⋊D7C22×C3112yescomplemented
115C2×D7×#67C22×C3112yescomplemented
116D3×D4×D7—248no—
117C2×#66681C22×C316yescomplemented
118C2×D3×D28C22×C316yescomplemented
119C2×D7×D12C22×C316yescomplemented
120C2×C4×D3×D7C22×C313yes—
121C22×(C22⋊D7)⋊C3—312no—
122C2×D4×AGL(1,𝔽7)—26no—
123C2×D4×AGL(1,𝔽7)—312no—
124C2×D4×AGL(1,𝔽7)—36no—
125C2×D4×AGL(1,𝔽7)—312no—
126C2×D4×AGL(1,𝔽7)—36no—
127C2×D4×AGL(1,𝔽7)—36no—
128C2×D4×AGL(1,𝔽7)—648no—
129C2×D4×AGL(1,𝔽7)C2×D316yescomplemented
130C22×C4⋊AGL(1,𝔽7)—36no—
131C22×C4×AGL(1,𝔽7)—33no—
132C3×C7×#127C22×C311yescharacteristic, complemented
133#10621423C22×C316yescomplemented
134#10621357C22×C311yescharacteristic, complemented
135C42×D21C22×C311yescharacteristic, complemented
136C7×#940C22×C316yescomplemented
137C7×#874C22×C311yescharacteristic, complemented
138C42×D3×C7C22×C311yescharacteristic, complemented
139C3×#6503C22×C316yescomplemented
140C3×#6437C22×C311yescharacteristic, complemented
141C3×C42×D7C22×C311yescharacteristic, complemented
142ΓL(1,𝔽8)×#127—21no—
143ΓL(1,𝔽8)×#127—36no—
144ΓL(1,𝔽8)×#127—31no—
145ΓL(1,𝔽8)×#127C2×D311yescharacteristic, complemented
146C2×C42×ΓL(1,𝔽8)—31no—
147#10621129C22×C3124yescomplemented
148#10621025C22×C316yescomplemented
149#10621020C22×C316yescomplemented
150#10621013C22×C316yescomplemented
151C4×D21⋊C4C22×C313yescomplemented
152C4×D3×Dic7C22×C313yescomplemented
153C4×Dic3×D7C22×C313yescomplemented
154#6503⋊C3—26no—
155#6503⋊C3—36no—
156#6503⋊C3—36no—
157#6503⋊C3—324no—
158#6503⋊C3—36no—
159#6503⋊C3C2×D316yescomplemented
160C2×C4×ΓL(1,𝔽8)⋊C4—33no—
161#10620710—21no—
162#10620710—36no—
163#10620710—31no—
164#10620710C2×D311yescharacteristic, complemented
165C42×AGL(1,𝔽7)—21no—
166C42×AGL(1,𝔽7)—33no—
167C42×AGL(1,𝔽7)—33no—
168C42×AGL(1,𝔽7)—31no—
169C42×AGL(1,𝔽7)C2×D311yescharacteristic, complemented
170C22×C3×D3×D4—76no—
171C2×C32×#127—71no—
172C2×C3×#940—76no—
173C3×D3×#127—71no—
174C3×D3×#127—71no—
175C3×D3×#127—71no—
176C3×D3×#127—76no—
177C3×D3×#127—76no—
178C3×D3×#127—141no—
179C2×C3×#874—71no—
180C2×C3×C42×D3—71no—
181C23×C3×ΓL(1,𝔽8)C2414yes—
182C22×C3⋊AGL(1,𝔽7)—224no—
183C22×C3⋊AGL(1,𝔽7)C2414yes—
184C22×C3⋊AGL(1,𝔽7)C2411yescharacteristic
185C22×D3×ΓL(1,𝔽8)—224no—
186C22×D3×ΓL(1,𝔽8)C2414yes—
187C22×D3×ΓL(1,𝔽8)C2411yescharacteristic
188C22×C3×AGL(1,𝔽7)—224no—
189C22×C3×AGL(1,𝔽7)C2414yes—
190C22×C3×AGL(1,𝔽7)C2411yescharacteristic
191C2×D3×AGL(1,𝔽7)—224no—
192C2×D3×AGL(1,𝔽7)—224no—
193C2×D3×AGL(1,𝔽7)—224no—
194C2×D3×AGL(1,𝔽7)—464no—
195C2×D3×AGL(1,𝔽7)C2×D4112yes—
196C3×D4×ΓL(1,𝔽8)—212no—
197C2×C3×C4×ΓL(1,𝔽8)C2413yes—
198#4268⋊C3—224no—
199C2×C3⋊(ΓL(1,𝔽8)⋊C4)C2413yes—
200C4⋊(C3⋊AGL(1,𝔽7))—212no—
201C4×C3⋊AGL(1,𝔽7)C2×D4112yescomplemented
202ΓL(1,𝔽8)×#67—224no—
203C2×Dic3×ΓL(1,𝔽8)C2413yes—
204ΓL(1,𝔽8)×D12—212no—
205C4×D3×ΓL(1,𝔽8)C2×D4112yescomplemented
206C3×(C22⋊D7)⋊C3—224no—
207C2×C3×ΓL(1,𝔽8)⋊C4C2413yes—
208C3×C4⋊AGL(1,𝔽7)—212no—
209C3×C4×AGL(1,𝔽7)C2×D4112yescomplemented
210#4247⋊C3—224no—
211#4246⋊C3—224no—
212#4245⋊C3—224no—
213(C3⋊AGL(1,𝔽7))⋊C4C2×D4112yescomplemented
214D3×ΓL(1,𝔽8)⋊C4C2×D4112yescomplemented
215Dic3×AGL(1,𝔽7)C2×D4112yescomplemented
216C22×D4×D7—36no—
217C2×C7×#127—31no—
218C2×#6503—36no—
219D7×#127—36no—
220D7×#127—31no—
221D7×#127—36no—
222D7×#127—31no—
223D7×#127—31no—
224D7×#127C3×D311yescharacteristic, complemented
225C2×#6437—31no—
226C2×C42×D7—31no—
227C22×C3×#127—211no—
228C2×D3×#127—71no—
229C23×D21C23×C314yes—
230C23×D3×C7C23×C314yes—
231C23×C3×D7C23×C314yes—
232C24×ΓL(1,𝔽8)—34no—
233C22×D3×D7—248no—
234C22×D3×D7C23×C314yes—
235C22×D3×D7C23×C314yes—
236C22×D3×D7C23×C314yes—
237C22×D3×D7C23×C311yescharacteristic
238C23×AGL(1,𝔽7)—24no—
239C23×AGL(1,𝔽7)—31no—
240C23×AGL(1,𝔽7)—34no—
241C23×AGL(1,𝔽7)—34no—
242C23×AGL(1,𝔽7)—34no—
243C23×AGL(1,𝔽7)—34no—
244C23×AGL(1,𝔽7)—648no—
245C23×AGL(1,𝔽7)C22×D314yes—
246C2×C3×C7×D4C23×C316yescomplemented
247C2×#4268C23×C3112yescomplemented
248D4×D21—224no—
249C2×D84C23×C316yescomplemented
250C2×C4×D21C23×C313yes—
251C2×C7×#67C23×C3112yescomplemented
252D3×C7×D4—224no—
253C2×C7×D12C23×C316yescomplemented
254C2×C4×D3×C7C23×C313yes—
255C2×C3×C22⋊D7C23×C3112yescomplemented
256C3×D4×D7—224no—
257C2×C3×D28C23×C316yescomplemented
258C2×C3×C4×D7C23×C313yes—
259C2×D4×ΓL(1,𝔽8)—26no—
260C2×D4×ΓL(1,𝔽8)—312no—
261C2×D4×ΓL(1,𝔽8)—36no—
262C2×D4×ΓL(1,𝔽8)—624no—
263C2×D4×ΓL(1,𝔽8)C22×D316yescomplemented
264C22×C4×ΓL(1,𝔽8)—33no—
265#66694—248no—
266D3×C22⋊D7—248no—
267D7×#67—248no—
268C2×#4247C23×C3112yescomplemented
269C2×#4246C23×C3112yescomplemented
270C2×#4245C23×C3112yescomplemented
271C2×D21⋊C4C23×C313yes—
272C2×D3×Dic7C23×C313yes—
273C2×Dic3×D7C23×C313yes—
274#66681—224no—
275D3×D28—224no—
276D7×D12—224no—
277C4×D3×D7C3×D4124yescomplemented
278C2×(C22⋊D7)⋊C3—212no—
279C2×(C22⋊D7)⋊C3—312no—
280C2×(C22⋊D7)⋊C3—312no—
281C2×(C22⋊D7)⋊C3—312no—
282C2×(C22⋊D7)⋊C3—648no—
283C2×(C22⋊D7)⋊C3C22×D3112yescomplemented
284C22×ΓL(1,𝔽8)⋊C4—33no—
285D4×AGL(1,𝔽7)—224no—
286D4×AGL(1,𝔽7)—424no—
287D4×AGL(1,𝔽7)—624no—
288D4×AGL(1,𝔽7)—648no—
289D4×AGL(1,𝔽7)—624no—
290D4×AGL(1,𝔽7)—648no—
291D4×AGL(1,𝔽7)—624no—
292C2×C4⋊AGL(1,𝔽7)—26no—
293C2×C4⋊AGL(1,𝔽7)—312no—
294C2×C4⋊AGL(1,𝔽7)—36no—
295C2×C4⋊AGL(1,𝔽7)—624no—
296C2×C4⋊AGL(1,𝔽7)C22×D316yescomplemented
297C2×C4×AGL(1,𝔽7)—23no—
298C2×C4×AGL(1,𝔽7)—33no—
299C2×C4×AGL(1,𝔽7)—33no—
300C2×C4×AGL(1,𝔽7)—33no—
301C2×C4×AGL(1,𝔽7)—324no—
302C2×C4×AGL(1,𝔽7)C22×D313yes—
303C3×C42×C7C23×C311yescharacteristic, complemented
304C4×Dic21C23×C313yescomplemented
305C4×C7×Dic3C23×C313yescomplemented
306C3×C4×Dic7C23×C313yescomplemented
307C42×ΓL(1,𝔽8)—21no—
308C42×ΓL(1,𝔽8)—33no—
309C42×ΓL(1,𝔽8)C22×D311yescharacteristic, complemented
310Dic3×Dic7C23×C316yescomplemented
311C4×ΓL(1,𝔽8)⋊C4—23no—
312C4×ΓL(1,𝔽8)⋊C4—33no—
313C4×ΓL(1,𝔽8)⋊C4—36no—
314C4×ΓL(1,𝔽8)⋊C4C22×D313yescomplemented
315C24×C3×D3—74no—
316C22×C32×D4—76no—
317C22×C3×#67—712no—
318C2×C3×D3×D4—76no—
319C2×C3×D3×D4—712no—
320C2×C3×D3×D4—76no—
321C2×C3×D3×D4—76no—
322C2×C3×D3×D4—712no—
323C2×C3×D3×D4—1448no—
324C2×C3×D3×D4—146no—
325C22×C3×D12—76no—
326C22×C3×C4×D3—73no—
327C32×#127—76no—
328C32×#127—71no—
329C32×#127—141no—
330C2×C32×C42—71no—
331C3×#940—76no—
332C3×#940—724no—
333C3×#940—76no—
334C3×#940—76no—
335C3×#940—146no—
336C2×C3×C4×Dic3—73no—
337C3×#874—76no—
338C3×#874—71no—
339C3×#874—141no—
340C3×C42×D3—73no—
341C3×C42×D3—71no—
342C3×C42×D3—73no—
343C3×C42×D3—141no—
344C22×C3×ΓL(1,𝔽8)—212no—
345C22×C3×ΓL(1,𝔽8)C2511yescharacteristic
346C2×C3⋊AGL(1,𝔽7)—212no—
347C2×C3⋊AGL(1,𝔽7)—416no—
348C2×C3⋊AGL(1,𝔽7)C22×D416yes—
349C2×D3×ΓL(1,𝔽8)—212no—
350C2×D3×ΓL(1,𝔽8)—416no—
351C2×D3×ΓL(1,𝔽8)C22×D416yes—
352C2×C3×AGL(1,𝔽7)—212no—
353C2×C3×AGL(1,𝔽7)—416no—
354C2×C3×AGL(1,𝔽7)C22×D416yes—
355D3×AGL(1,𝔽7)—416no—
356D3×AGL(1,𝔽7)—416no—
357D3×AGL(1,𝔽7)—416no—
358D3×AGL(1,𝔽7)#127116yesdirect product factor
359C3×C4×ΓL(1,𝔽8)C22×D416yescomplemented
360C3⋊(ΓL(1,𝔽8)⋊C4)C22×D416yescomplemented
361Dic3×ΓL(1,𝔽8)C22×D416yescomplemented
362C3×ΓL(1,𝔽8)⋊C4C22×D416yescomplemented
363C24×D7—34no—
364C22×C7×D4—36no—
365C22×C22⋊D7—312no—
366C2×D4×D7—312no—
367C2×D4×D7—36no—
368C2×D4×D7—312no—
369C2×D4×D7—36no—
370C2×D4×D7—36no—
371C2×D4×D7—648no—
372C2×D4×D7C2×C3×D316yescomplemented
373C22×D28—36no—
374C22×C4×D7—33no—
375C7×#127—36no—
376C7×#127—31no—
377C7×#127C2×C3×D311yescharacteristic, complemented
378C2×C42×C7—31no—
379#6503—36no—
380#6503—324no—
381#6503—36no—
382#6503—36no—
383#6503C2×C3×D316yescomplemented
384C2×C4×Dic7—33no—
385#6437—36no—
386#6437—31no—
387#6437C2×C3×D311yescharacteristic, complemented
388C42×D7—33no—
389C42×D7—31no—
390C42×D7—33no—
391C42×D7C2×C3×D311yescharacteristic, complemented
392C23×C3×D4—216no—
393C22×D3×D4—76no—
394C2×C3×#127—71no—
395C2×C3×#127—71no—
396C2×C3×#127—141no—
397C2×C3×#127—211no—
398C2×C3×#127—216no—
399C2×C3×#127—216no—
400C2×C3×#127—211no—
401C2×C3×#127—211no—
402C2×C3×#127—216no—
403C2×C3×#127—211no—
404C2×C3×#127—421no—
405C22×C3×C42—211no—
406C2×#940—76no—
407D3×#127—76no—
408D3×#127—71no—
409D3×#127—76no—
410D3×#127—71no—
411D3×#127—71no—
412D3×#127AGL(1,𝔽7)11yescharacteristic, direct product factor
413C2×#874—71no—
414C2×C42×D3—71no—
415C23×C3×C7C24×C314yes—
416C22×D21—224no—
417C22×D21C24×C314yes—
418C22×D21C24×C311yescharacteristic
419C22×D3×C7—224no—
420C22×D3×C7C24×C314yes—
421C22×D3×C7C24×C311yescharacteristic
422C22×C3×D7—224no—
423C22×C3×D7C24×C314yes—
424C22×C3×D7C24×C311yescharacteristic
425C23×ΓL(1,𝔽8)—24no—
426C23×ΓL(1,𝔽8)—31no—
427C23×ΓL(1,𝔽8)—34no—
428C23×ΓL(1,𝔽8)—624no—
429C23×ΓL(1,𝔽8)C23×D314yes—
430C2×D3×D7—224no—
431C2×D3×D7—224no—
432C2×D3×D7—224no—
433C2×D3×D7—464no—
434C2×D3×D7C2×C3×D4112yes—
435C22×AGL(1,𝔽7)—224no—
436C22×AGL(1,𝔽7)—21no—
437C22×AGL(1,𝔽7)—24no—
438C22×AGL(1,𝔽7)—31no—
439C22×AGL(1,𝔽7)—312no—
440C22×AGL(1,𝔽7)—34no—
441C22×AGL(1,𝔽7)—424no—
442C22×AGL(1,𝔽7)—624no—
443C22×AGL(1,𝔽7)—624no—
444C22×AGL(1,𝔽7)—624no—
445C22×AGL(1,𝔽7)—624no—
446C22×AGL(1,𝔽7)—1264no—
447C22×AGL(1,𝔽7)C23×D314yes—
448C22×AGL(1,𝔽7)C23×D311yescharacteristic
449C3×C7×D4—212no—
450C2×C3×C4×C7C24×C313yes—
451#4268—224no—
452C2×Dic21C24×C313yes—
453D84—212no—
454C4×D21C2×C3×D4112yescomplemented
455C7×#67—224no—
456C2×C7×Dic3C24×C313yes—
457C7×D12—212no—
458C4×D3×C7C2×C3×D4112yescomplemented
459C3×C22⋊D7—224no—
460C2×C3×Dic7C24×C313yes—
461C3×D28—212no—
462C3×C4×D7C2×C3×D4112yescomplemented
463D4×ΓL(1,𝔽8)—212no—
464D4×ΓL(1,𝔽8)—412no—
465D4×ΓL(1,𝔽8)—624no—
466D4×ΓL(1,𝔽8)—612no—
467C2×C4×ΓL(1,𝔽8)—23no—
468C2×C4×ΓL(1,𝔽8)—33no—
469C2×C4×ΓL(1,𝔽8)—312no—
470C2×C4×ΓL(1,𝔽8)C23×D313yes—
471#4247—224no—
472#4246—224no—
473#4245—224no—
474D21⋊C4C2×C3×D4112yescomplemented
475D3×Dic7C2×C3×D4112yescomplemented
476Dic3×D7C2×C3×D4112yescomplemented
477(C22⋊D7)⋊C3—224no—
478(C22⋊D7)⋊C3—424no—
479(C22⋊D7)⋊C3—624no—
480(C22⋊D7)⋊C3—624no—
481(C22⋊D7)⋊C3—624no—
482C2×ΓL(1,𝔽8)⋊C4—23no—
483C2×ΓL(1,𝔽8)⋊C4—33no—
484C2×ΓL(1,𝔽8)⋊C4—312no—
485C2×ΓL(1,𝔽8)⋊C4C23×D313yes—
486C4⋊AGL(1,𝔽7)—212no—
487C4⋊AGL(1,𝔽7)—412no—
488C4⋊AGL(1,𝔽7)—624no—
489C4⋊AGL(1,𝔽7)—612no—
490C4×AGL(1,𝔽7)—212no—
491C4×AGL(1,𝔽7)—312no—
492C4×AGL(1,𝔽7)—312no—
493C4×AGL(1,𝔽7)—312no—
494C4×AGL(1,𝔽7)D3×D4112yescomplemented
495C24×C32—74no—
496C23×C3×D3—71no—
497C23×C3×D3—74no—
498C23×C3×D3—74no—
499C23×C3×D3—74no—
500C23×C3×D3—74no—
501C23×C3×D3—1448no—
502C23×C3×D3—144no—
503C2×C32×D4—712no—
504C2×C32×D4—76no—
505C2×C32×D4—1424no—
506C2×C32×D4—146no—
507C22×C32×C4—73no—
508C2×C3×#67—712no—
509C2×C3×#67—712no—
510C2×C3×#67—712no—
511C2×C3×#67—1448no—
512C2×C3×#67—1412no—
513C22×C3×Dic3—73no—
514C3×D3×D4—1448no—
515C3×D3×D4—1424no—
516C3×D3×D4—1448no—
517C3×D3×D4—1424no—
518C3×D3×D4—1424no—
519C3×D3×D4—2824no—
520C2×C3×D12—712no—
521C2×C3×D12—76no—
522C2×C3×D12—1424no—
523C2×C3×D12—146no—
524C2×C3×C4×D3—73no—
525C2×C3×C4×D3—73no—
526C2×C3×C4×D3—73no—
527C2×C3×C4×D3—724no—
528C2×C3×C4×D3—143no—
529C32×C42—73no—
530C32×C42—141no—
531C3×C4×Dic3—73no—
532C3×C4×Dic3—76no—
533C3×C4×Dic3—143no—
534C22×#127—211noSylow
535C2×C3×ΓL(1,𝔽8)—44no—
536C2×C3×ΓL(1,𝔽8)C23×D413yes—
537C3⋊AGL(1,𝔽7)—44no—
538C3⋊AGL(1,𝔽7)C2×#12714yescomplemented
539D3×ΓL(1,𝔽8)—44no—
540D3×ΓL(1,𝔽8)C2×#12714yescomplemented
541C3×AGL(1,𝔽7)—44no—
542C3×AGL(1,𝔽7)C2×#12714yescomplemented
543C24×C7—34no—
544C23×D7—31no—
545C23×D7—34no—
546C23×D7—34no—
547C23×D7—34no—
548C23×D7—34no—
549C23×D7—648no—
550C23×D7C22×C3×D314yes—
551C2×C7×D4—312no—
552C2×C7×D4—36no—
553C2×C7×D4—624no—
554C2×C7×D4C22×C3×D316yescomplemented
555C22×C4×C7—33no—
556C2×C22⋊D7—312no—
557C2×C22⋊D7—312no—
558C2×C22⋊D7—312no—
559C2×C22⋊D7—648no—
560C2×C22⋊D7C22×C3×D3112yescomplemented
561C22×Dic7—33no—
562D4×D7—224no—
563D4×D7—624no—
564D4×D7—648no—
565D4×D7—624no—
566D4×D7—648no—
567D4×D7—624no—
568C2×D28—312no—
569C2×D28—36no—
570C2×D28—624no—
571C2×D28C22×C3×D316yescomplemented
572C2×C4×D7—33no—
573C2×C4×D7—33no—
574C2×C4×D7—33no—
575C2×C4×D7—324no—
576C2×C4×D7C22×C3×D313yes—
577C42×C7—33no—
578C42×C7C22×C3×D311yescharacteristic, complemented
579C4×Dic7—33no—
580C4×Dic7—36no—
581C4×Dic7C22×C3×D313yescomplemented
582C25×C3—214no—
583C24×D3—74no—
584C22×C3×D4—76no—
585C22×C3×D4—76no—
586C22×C3×D4—146no—
587C22×C3×D4—216no—
588C22×C3×D4—2112no—
589C22×C3×D4—2112no—
590C22×C3×D4—216no—
591C22×C3×D4—216no—
592C22×C3×D4—2112no—
593C22×C3×D4—216no—
594C22×C3×D4—426no—
595C22×C3×D4—4248no—
596C23×C3×C4—213no—
597C22×#67—712no—
598C2×D3×D4—712no—
599C2×D3×D4—76no—
600C2×D3×D4—712no—
601C2×D3×D4—76no—
602C2×D3×D4—76no—
603C2×D3×D4—1448no—
604C2×D3×D4C2×AGL(1,𝔽7)16yescomplemented
605C22×D12—76no—
606C22×C4×D3—73no—
607C3×#127—76no—
608C3×#127—76no—
609C3×#127—71no—
610C3×#127—71no—
611C3×#127—146no—
612C3×#127—141no—
613C3×#127—141no—
614C3×#127—216no—
615C3×#127—211no—
616C3×#127—2124no—
617C3×#127—216no—
618C3×#127—216no—
619C3×#127—216no—
620C3×#127—281no—
621C3×#127—421no—
622C3×#127—426no—
623C3×#127C2×AGL(1,𝔽7)11yescharacteristic, complemented
624C2×C3×C42—71no—
625C2×C3×C42—71no—
626C2×C3×C42—141no—
627C2×C3×C42—213no—
628C2×C3×C42—213no—
629C2×C3×C42—211no—
630C2×C3×C42—213no—
631C2×C3×C42—421no—
632#940—76no—
633#940—724no—
634#940—76no—
635#940—76no—
636#940C2×AGL(1,𝔽7)16yescomplemented
637C2×C4×Dic3—73no—
638#874—76no—
639#874—71no—
640#874C2×AGL(1,𝔽7)11yescharacteristic, complemented
641C42×D3—73no—
642C42×D3—71no—
643C42×D3—73no—
644C42×D3C2×AGL(1,𝔽7)11yescharacteristic, complemented
645C22×C3×C7—212no—
646C22×C3×C7C25×C311yescharacteristic
647C2×D21—212no—
648C2×D21—416no—
649C2×D21C22×C3×D416yes—
650C2×D3×C7—212no—
651C2×D3×C7—416no—
652C2×D3×C7C22×C3×D416yes—
653C2×C3×D7—212no—
654C2×C3×D7—416no—
655C2×C3×D7C22×C3×D416yes—
656C22×ΓL(1,𝔽8)—212no—
657C22×ΓL(1,𝔽8)—21no—
658C22×ΓL(1,𝔽8)—36no—
659C22×ΓL(1,𝔽8)—412no—
660C22×ΓL(1,𝔽8)—612no—
661C22×ΓL(1,𝔽8)—1216no—
662C22×ΓL(1,𝔽8)C24×D311yescharacteristic
663D3×D7—416no—
664D3×D7—416no—
665D3×D7—416no—
666D3×D7C3×#127116yescomplemented
667C2×AGL(1,𝔽7)—212no—
668C2×AGL(1,𝔽7)—26no—
669C2×AGL(1,𝔽7)—36no—
670C2×AGL(1,𝔽7)—316no—
671C2×AGL(1,𝔽7)—412no—
672C2×AGL(1,𝔽7)—416no—
673C2×AGL(1,𝔽7)—612no—
674C2×AGL(1,𝔽7)—816no—
675C2×AGL(1,𝔽7)—1216no—
676C2×AGL(1,𝔽7)—1216no—
677C2×AGL(1,𝔽7)—1216no—
678C2×AGL(1,𝔽7)—1216no—
679C2×AGL(1,𝔽7)C2×D3×D416yes—
680C3×C4×C7C22×C3×D416yescomplemented
681Dic21C22×C3×D416yescomplemented
682C3×Dic7C22×C3×D416yescomplemented
683C7×Dic3C22×C3×D416yescomplemented
684C4×ΓL(1,𝔽8)—26no—
685C4×ΓL(1,𝔽8)—36no—
686C4×ΓL(1,𝔽8)C2×D3×D416yescomplemented
687ΓL(1,𝔽8)⋊C4—26no—
688ΓL(1,𝔽8)⋊C4—36no—
689ΓL(1,𝔽8)⋊C4C2×D3×D416yescomplemented
690C23×C32—71no—
691C23×C32—74no—
692C23×C32—1424no—
693C23×C32—144no—
694C22×C3×D3—71no—
695C22×C3×D3—712no—
696C22×C3×D3—74no—
697C22×C3×D3—1424no—
698C22×C3×D3—1424no—
699C22×C3×D3—1424no—
700C22×C3×D3—1424no—
701C22×C3×D3—141no—
702C22×C3×D3—144no—
703C22×C3×D3—2824no—
704C22×C3×D3—2864no—
705C32×D4—1424no—
706C32×D4—1412no—
707C32×D4—2812no—
708C2×C32×C4—73no—
709C2×C32×C4—712no—
710C2×C32×C4—143no—
711C3×#67—1424no—
712C3×#67—1424no—
713C3×#67—1424no—
714C3×#67—2824no—
715C2×C3×Dic3—73no—
716C2×C3×Dic3—712no—
717C2×C3×Dic3—143no—
718C3×D12—1424no—
719C3×D12—1412no—
720C3×D12—2812no—
721C3×C4×D3—712no—
722C3×C4×D3—712no—
723C3×C4×D3—712no—
724C3×C4×D3—1412no—
725C23×D4—216no—
726C2×#127—31no—
727C2×#127—71no—
728C2×#127—211no—
729C2×#127—211no—
730C2×#127—216no—
731C2×#127—211no—
732C2×#127—216no—
733C2×#127—216no—
734C2×#127—211no—
735C22×C42—211no—
736C3×ΓL(1,𝔽8)C22×#12711yescharacteristic, complemented, Hall
737C23×C7—31no—
738C23×C7—34no—
739C23×C7—624no—
740C23×C7C23×C3×D314yes—
741C22×D7—224no—
742C22×D7—31no—
743C22×D7—312no—
744C22×D7—34no—
745C22×D7—624no—
746C22×D7—624no—
747C22×D7—624no—
748C22×D7—624no—
749C22×D7—1264no—
750C22×D7C23×C3×D314yes—
751C22×D7C23×C3×D311yescharacteristic
752C7×D4—212no—
753C7×D4—624no—
754C7×D4—612no—
755C2×C4×C7—33no—
756C2×C4×C7—312no—
757C2×C4×C7C23×C3×D313yes—
758C22⋊D7—224no—
759C22⋊D7—624no—
760C22⋊D7—624no—
761C22⋊D7—624no—
762C2×Dic7—33no—
763C2×Dic7—312no—
764C2×Dic7C23×C3×D313yes—
765D28—212no—
766D28—624no—
767D28—612no—
768C4×D7—312no—
769C4×D7—312no—
770C4×D7—312no—
771C4×D7C3×D3×D4112yescomplemented
772C24×C3—74no—
773C24×C3—74no—
774C24×C3—144no—
775C24×C3—211no—
776C24×C3—214no—
777C24×C3—214no—
778C24×C3—214no—
779C24×C3—214no—
780C24×C3—424no—
781C24×C3—4248no—
782C23×D3—71no—
783C23×D3—74no—
784C23×D3—74no—
785C23×D3—74no—
786C23×D3—74no—
787C23×D3—1448no—
788C23×D3C22×AGL(1,𝔽7)14yes—
789C2×C3×D4—712no—
790C2×C3×D4—712no—
791C2×C3×D4—76no—
792C2×C3×D4—76no—
793C2×C3×D4—1412no—
794C2×C3×D4—146no—
795C2×C3×D4—1424no—
796C2×C3×D4—1424no—
797C2×C3×D4—146no—
798C2×C3×D4—2112no—
799C2×C3×D4—216no—
800C2×C3×D4—2112no—
801C2×C3×D4—2112no—
802C2×C3×D4—2112no—
803C2×C3×D4—2824no—
804C2×C3×D4—286no—
805C2×C3×D4—426no—
806C2×C3×D4—4212no—
807C2×C3×D4—4224no—
808C2×C3×D4—4248no—
809C2×C3×D4—4248no—
810C2×C3×D4—4224no—
811C2×C3×D4—4224no—
812C2×C3×D4—4248no—
813C2×C3×D4—4224no—
814C2×C3×D4—8424no—
815C2×C3×D4C22×AGL(1,𝔽7)16yescomplemented
816C22×C3×C4—73no—
817C22×C3×C4—73no—
818C22×C3×C4—143no—
819C22×C3×C4—213no—
820C22×C3×C4—213no—
821C22×C3×C4—2124no—
822C22×C3×C4—213no—
823C22×C3×C4—213no—
824C22×C3×C4—423no—
825C2×#67—712no—
826C2×#67—712no—
827C2×#67—712no—
828C2×#67—1448no—
829C2×#67C22×AGL(1,𝔽7)112yescomplemented
830C22×Dic3—73no—
831D3×D4—224no—
832D3×D4—1424no—
833D3×D4—1448no—
834D3×D4—1424no—
835D3×D4—1448no—
836D3×D4—1424no—
837C2×D12—712no—
838C2×D12—76no—
839C2×D12—1424no—
840C2×D12C22×AGL(1,𝔽7)16yescomplemented
841C2×C4×D3—73no—
842C2×C4×D3—73no—
843C2×C4×D3—73no—
844C2×C4×D3—724no—
845C2×C4×D3C22×AGL(1,𝔽7)13yes—
846C3×C42—73no—
847C3×C42—73no—
848C3×C42—143no—
849C3×C42—141no—
850C3×C42—216no—
851C3×C42—213no—
852C3×C42—281no—
853C3×C42—423no—
854C3×C42C22×AGL(1,𝔽7)11yescharacteristic, complemented
855C4×Dic3—73no—
856C4×Dic3—76no—
857C4×Dic3C22×AGL(1,𝔽7)13yescomplemented
858C2×C3×C7—44no—
859C2×C3×C7C23×C3×D413yes—
860D21—44no—
861D21C2×C3×#12714yescomplemented
862C3×D7—44no—
863C3×D7C2×C3×#12714yescomplemented
864D3×C7—44no—
865D3×C7C2×C3×#12714yescomplemented
866C2×ΓL(1,𝔽8)—23no—
867C2×ΓL(1,𝔽8)—34no—
868C2×ΓL(1,𝔽8)—44no—
869C2×ΓL(1,𝔽8)—84no—
870C2×ΓL(1,𝔽8)—124no—
871C2×ΓL(1,𝔽8)C22×D3×D413yes—
872AGL(1,𝔽7)—24no—
873AGL(1,𝔽7)—34no—
874AGL(1,𝔽7)—44no—
875AGL(1,𝔽7)—84no—
876AGL(1,𝔽7)—124no—
877AGL(1,𝔽7)D3×#12714yesdirect product factor
878C22×C32—76no—
879C22×C32—1412no—
880C22×C32—141no—
881C22×C32—2812no—
882C22×C32—2816no—
883C2×C3×D3—76no—
884C2×C3×D3—716no—
885C2×C3×D3—1412no—
886C2×C3×D3—146no—
887C2×C3×D3—2812no—
888C2×C3×D3—2816no—
889C2×C3×D3—2816no—
890C2×C3×D3—2816no—
891C2×C3×D3—2816no—
892C2×C3×D3—5616no—
893C32×C4—76no—
894C32×C4—146no—
895C3×Dic3—76no—
896C3×Dic3—146no—
897C25—214no—
898C22×D4—36no—
899C22×D4—76no—
900C22×D4—216no—
901C22×D4—216no—
902C22×D4—2112no—
903C22×D4—216no—
904C22×D4—2112no—
905C22×D4—2112no—
906C22×D4—216no—
907C22×D4—4248no—
908C23×C4—213no—
909#127—36no—
910#127—31no—
911#127—76no—
912#127—71no—
913#127—216no—
914#127—216no—
915#127—2124no—
916#127—216no—
917#127—216no—
918#127—211no—
919#127D3×AGL(1,𝔽7)11yescharacteristic, direct product factor
920C2×C42—31no—
921C2×C42—71no—
922C2×C42—213no—
923C2×C42—213no—
924C2×C42—213no—
925C2×C42—211no—
926C22×C7—212no—
927C22×C7—36no—
928C22×C7—612no—
929C22×C7—1216no—
930C22×C7C24×C3×D311yescharacteristic
931C2×D7—212no—
932C2×D7—36no—
933C2×D7—316no—
934C2×D7—416no—
935C2×D7—612no—
936C2×D7—1216no—
937C2×D7—1216no—
938C2×D7—1216no—
939C2×D7—1216no—
940C2×D7C2×C3×D3×D416yes—
941C4×C7—36no—
942C4×C7C2×C3×D3×D416yescomplemented
943Dic7—36no—
944Dic7C2×C3×D3×D416yescomplemented
945C23×C3—71no—
946C23×C3—71no—
947C23×C3—74no—
948C23×C3—74no—
949C23×C3—141no—
950C23×C3—144no—
951C23×C3—1424no—
952C23×C3—1424no—
953C23×C3—144no—
954C23×C3—2112no—
955C23×C3—211no—
956C23×C3—214no—
957C23×C3—2824no—
958C23×C3—284no—
959C23×C3—421no—
960C23×C3—424no—
961C23×C3—4224no—
962C23×C3—4224no—
963C23×C3—4224no—
964C23×C3—4224no—
965C23×C3—8424no—
966C23×C3—8464no—
967C23×C3C23×AGL(1,𝔽7)14yes—
968C22×D3—224no—
969C22×D3—71no—
970C22×D3—712no—
971C22×D3—74no—
972C22×D3—1424no—
973C22×D3—1424no—
974C22×D3—1424no—
975C22×D3—1424no—
976C22×D3—2864no—
977C22×D3C23×AGL(1,𝔽7)14yes—
978C22×D3C23×AGL(1,𝔽7)11yescharacteristic
979C3×D4—212no—
980C3×D4—1424no—
981C3×D4—1424no—
982C3×D4—1412no—
983C3×D4—1412no—
984C3×D4—2812no—
985C3×D4—2824no—
986C3×D4—2812no—
987C3×D4—4224no—
988C3×D4—4212no—
989C3×D4—4224no—
990C3×D4—4224no—
991C3×D4—4224no—
992C3×D4—5612no—
993C3×D4—8412no—
994C3×D4—8424no—
995C2×C3×C4—73no—
996C2×C3×C4—73no—
997C2×C3×C4—712no—
998C2×C3×C4—712no—
999C2×C3×C4—143no—
1000C2×C3×C4—1412no—
1001C2×C3×C4—143no—
1002C2×C3×C4—2112no—
1003C2×C3×C4—2112no—
1004C2×C3×C4—2112no—
1005C2×C3×C4—213no—
1006C2×C3×C4—2112no—
1007C2×C3×C4—283no—
1008C2×C3×C4—4212no—
1009C2×C3×C4—423no—
1010C2×C3×C4C23×AGL(1,𝔽7)13yes—
1011#67—224no—
1012#67—1424no—
1013#67—1424no—
1014#67—1424no—
1015C2×Dic3—73no—
1016C2×Dic3—712no—
1017C2×Dic3C23×AGL(1,𝔽7)13yes—
1018D12—212no—
1019D12—1424no—
1020D12—1412no—
1021C4×D3—712no—
1022C4×D3—712no—
1023C4×D3—712no—
1024C4×D3D4×AGL(1,𝔽7)112yescomplemented
1025C3×C7C22×C3×#12711yescharacteristic, complemented
1026ΓL(1,𝔽8)—21no—
1027ΓL(1,𝔽8)C2×D3×#12711yescharacteristic, complemented
1028C2×C32—74no—
1029C2×C32—143no—
1030C2×C32—284no—
1031C2×C32—564no—
1032C3×D3—74no—
1033C3×D3—144no—
1034C3×D3—284no—
1035C3×D3—564no—
1036C24—34no—
1037C24—74no—
1038C24—211no—
1039C24—214no—
1040C24—214no—
1041C24—214no—
1042C24—214no—
1043C24—4248no—
1044C2×D4—312no—
1045C2×D4—36no—
1046C2×D4—624no—
1047C2×D4—712no—
1048C2×D4—76no—
1049C2×D4—1424no—
1050C2×D4—2112no—
1051C2×D4—2112no—
1052C2×D4—2112no—
1053C2×D4—2112no—
1054C2×D4—216no—
1055C2×D4—4224no—
1056C2×D4—4224no—
1057C2×D4—4224no—
1058C2×D4—4248no—
1059C2×D4—4224no—
1060C2×D4—4248no—
1061C2×D4—4248no—
1062C2×D4C2×D3×AGL(1,𝔽7)16yescomplemented
1063C22×C4—33no—
1064C22×C4—73no—
1065C22×C4—213no—
1066C22×C4—2124no—
1067C22×C4—213no—
1068C22×C4—213no—
1069C22×C4—213no—
1070C42—33no—
1071C42—73no—
1072C42—216no—
1073C42—213no—
1074C42C2×D3×AGL(1,𝔽7)11yescharacteristic, complemented
1075C2×C7—34no—
1076C2×C7—44no—
1077C2×C7—124no—
1078C2×C7C22×C3×D3×D413yes—
1079D7—34no—
1080D7—44no—
1081D7—124no—
1082D7C3×D3×#12714yescomplemented
1083C22×C3—212no—
1084C22×C3—76no—
1085C22×C3—76no—
1086C22×C3—146no—
1087C22×C3—1412no—
1088C22×C3—1412no—
1089C22×C3—141no—
1090C22×C3—2116no—
1091C22×C3—216no—
1092C22×C3—2812no—
1093C22×C3—2812no—
1094C22×C3—2816no—
1095C22×C3—2816no—
1096C22×C3—281no—
1097C22×C3—426no—
1098C22×C3—4212no—
1099C22×C3—5612no—
1100C22×C3—5616no—
1101C22×C3—8412no—
1102C22×C3—8416no—
1103C22×C3—8416no—
1104C22×C3—8416no—
1105C22×C3—8416no—
1106C22×C3—16816no—
1107C22×C3C24×AGL(1,𝔽7)11yescharacteristic
1108C2×D3—212no—
1109C2×D3—416no—
1110C2×D3—76no—
1111C2×D3—716no—
1112C2×D3—1412no—
1113C2×D3—2816no—
1114C2×D3—2816no—
1115C2×D3—2816no—
1116C2×D3—2816no—
1117C2×D3C2×D4×AGL(1,𝔽7)16yes—
1118C3×C4—76no—
1119C3×C4—76no—
1120C3×C4—146no—
1121C3×C4—146no—
1122C3×C4—216no—
1123C3×C4—286no—
1124C3×C4—426no—
1125C3×C4C2×D4×AGL(1,𝔽7)16yescomplemented
1126Dic3—76no—
1127Dic3C2×D4×AGL(1,𝔽7)16yescomplemented
1128C32—141noSylow
1129C23—31no—
1130C23—34no—
1131C23—624no—
1132C23—71no—
1133C23—74no—
1134C23—1424no—
1135C23—2112no—
1136C23—211no—
1137C23—214no—
1138C23—4224no—
1139C23—4224no—
1140C23—4224no—
1141C23—4224no—
1142C23—8464no—
1143C23C22×D3×AGL(1,𝔽7)14yes—
1144D4—212no—
1145D4—624no—
1146D4—612no—
1147D4—1424no—
1148D4—1412no—
1149D4—4224no—
1150D4—4224no—
1151D4—4224no—
1152D4—4224no—
1153D4—4212no—
1154C2×C4—33no—
1155C2×C4—312no—
1156C2×C4—73no—
1157C2×C4—712no—
1158C2×C4—2112no—
1159C2×C4—2112no—
1160C2×C4—2112no—
1161C2×C4—213no—
1162C2×C4—2112no—
1163C2×C4C22×D3×AGL(1,𝔽7)13yes—
1164C7C2×C3×D3×#12711yescharacteristic, complemented, Sylow
1165C2×C3—44no—
1166C2×C3—74no—
1167C2×C3—74no—
1168C2×C3—144no—
1169C2×C3—143no—
1170C2×C3—214no—
1171C2×C3—284no—
1172C2×C3—284no—
1173C2×C3—283no—
1174C2×C3—424no—
1175C2×C3—564no—
1176C2×C3—564no—
1177C2×C3—844no—
1178C2×C3—1124no—
1179C2×C3—1684no—
1180C2×C3C22×D4×AGL(1,𝔽7)13yes—
1181D3—44no—
1182D3—74no—
1183D3—284no—
1184D3#127×AGL(1,𝔽7)14yesdirect product factor
1185C22—212no—
1186C22—36no—
1187C22—612no—
1188C22—76no—
1189C22—1216no—
1190C22—1412no—
1191C22—2116no—
1192C22—216no—
1193C22—2816no—
1194C22—4212no—
1195C22—8416no—
1196C22—8416no—
1197C22—8416no—
1198C22—8416no—
1199C22C23×D3×AGL(1,𝔽7)11yescharacteristic
1200C4—36no—
1201C4—76no—
1202C4—216no—
1203C4D3×D4×AGL(1,𝔽7)16yescomplemented
1204C3—141no—
1205C3—281no—
1206C3C2×#127×AGL(1,𝔽7)11yescharacteristic, complemented
1207C2—34no—
1208C2—44no—
1209C2—74no—
1210C2—124no—
1211C2—214no—
1212C2—284no—
1213C2—844no—
1214C2C2×D3×D4×AGL(1,𝔽7)13yes—
subgroupG/H
center, FrattiniC22C23×D3×AGL(1,𝔽7)
commutator, socle, cosocleC22×C3×C7C25×C3
FittingC3×C7×#127C22×C3
hypercenter#127D3×AGL(1,𝔽7)
hypocenterC3×C7C22×C3×#127
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ #127

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #72244271C2semidirect
2. AGL(1,𝔽7)×#874C2semidirect
3. D3×#10620710C2semidirect
4. C42×D3×AGL(1,𝔽7)C2semidirect
5. #72244257C2semidirect
6. C4×(C3⋊AGL(1,𝔽7))⋊C4C22semidirect
7. D3×#6503⋊C3C2semidirect
8. #72244254C22semidirect
9. C4×D3×ΓL(1,𝔽8)⋊C4C22semidirect
10. #127×C3⋊AGL(1,𝔽7)C2semidirect
11. #72244251C22semidirect
12. C42×C3⋊AGL(1,𝔽7)C22semidirect
13. D3×ΓL(1,𝔽8)×#127C2semidirect
14. ΓL(1,𝔽8)×#874C22semidirect
15. C42×D3×ΓL(1,𝔽8)C22semidirect
16. AGL(1,𝔽7)×#940C2semidirect
17. #72244245C22semidirect
18. #72244244C22semidirect
19. C4×Dic3×AGL(1,𝔽7)C22semidirect
20. #72244242C22semidirect
21. #72244241C22semidirect
22. ΓL(1,𝔽8)×#940C22semidirect
23. C3×#127×AGL(1,𝔽7)C2semidirect
24. C3×#10620710C22semidirect
25. C3×C42×AGL(1,𝔽7)C22semidirect
26. C3×#6503⋊C3C22semidirect
27. C3×ΓL(1,𝔽8)×#127C22semidirect
28. D3×D7×#127C3semidirect
29. C2×D3×D4×AGL(1,𝔽7)C2semidirect
30. C2×#66681⋊C3C22semidirect
31. C2×D12×AGL(1,𝔽7)C22semidirect
32. C2×D3×C4⋊AGL(1,𝔽7)C22semidirect
33. C2×#66694⋊C3C22semidirect
34. C2×#67×AGL(1,𝔽7)C22semidirect
35. C2×D3×(C22⋊D7)⋊C3C22semidirect
37. C2×D4×C3⋊AGL(1,𝔽7)C22semidirect
38. C2×D3×D4×ΓL(1,𝔽8)C22semidirect
39. C2×C3×D4×AGL(1,𝔽7)C22semidirect
43. C2×D3×D4×D7C2×C3semidirect
45. #127×D21C2×C3semidirect
46. D3×C7×#127C2×C3semidirect
47. C3×D7×#127C2×C3semidirect
49. #13059944C2×C3semidirect
50. D3×#6503C2×C3semidirect
51. D7×#940C2×C3semidirect
52. #13057978C2×C3semidirect
53. D3×#6437C2×C3semidirect
54. D7×#874C2×C3semidirect
55. C42×D3×D7C2×C3semidirect
63. #127×AGL(1,𝔽7)D3direct (N × H)
75. C2×C3×D4×ΓL(1,𝔽8)C23semidirect
76. C2×#4268⋊C3C23semidirect
78. C2×C4⋊(C3⋊AGL(1,𝔽7))C23semidirect
80. C2×ΓL(1,𝔽8)×#67C23semidirect
82. C2×ΓL(1,𝔽8)×D12C23semidirect
84. C2×C3×(C22⋊D7)⋊C3C23semidirect
86. C2×C3×C4⋊AGL(1,𝔽7)C23semidirect
91. C2×#4247⋊C3C23semidirect
92. C2×#4246⋊C3C23semidirect
93. C2×#4245⋊C3C23semidirect
100. C4×D3×AGL(1,𝔽7)D4semidirect
101. C3×C42×ΓL(1,𝔽8)C23semidirect
102. C4×C3⋊(ΓL(1,𝔽8)⋊C4)C23semidirect
103. C4×Dic3×ΓL(1,𝔽8)C23semidirect
104. C3×C4×ΓL(1,𝔽8)⋊C4C23semidirect
105. Dic3×ΓL(1,𝔽8)⋊C4C23semidirect
109. C2×D4×D21C22×C3semidirect
110. C2×D3×C7×D4C22×C3semidirect
111. C2×C3×D4×D7C22×C3semidirect
113. C2×#66694C22×C3semidirect
114. C2×D3×C22⋊D7C22×C3semidirect
115. C2×D7×#67C22×C3semidirect
117. C2×#66681C22×C3semidirect
118. C2×D3×D28C22×C3semidirect
119. C2×D7×D12C22×C3semidirect
129. C2×D4×AGL(1,𝔽7)C2×D3semidirect
132. C3×C7×#127C22×C3semidirect
133. #10621423C22×C3semidirect
134. #10621357C22×C3semidirect
135. C42×D21C22×C3semidirect
136. C7×#940C22×C3semidirect
137. C7×#874C22×C3semidirect
138. C42×D3×C7C22×C3semidirect
139. C3×#6503C22×C3semidirect
140. C3×#6437C22×C3semidirect
141. C3×C42×D7C22×C3semidirect
145. ΓL(1,𝔽8)×#127C2×D3semidirect
147. #10621129C22×C3semidirect
148. #10621025C22×C3semidirect
149. #10621020C22×C3semidirect
150. #10621013C22×C3semidirect
151. C4×D21⋊C4C22×C3semidirect
152. C4×D3×Dic7C22×C3semidirect
153. C4×Dic3×D7C22×C3semidirect
159. #6503⋊C3C2×D3semidirect
164. #10620710C2×D3semidirect
169. C42×AGL(1,𝔽7)C2×D3semidirect
201. C4×C3⋊AGL(1,𝔽7)C2×D4semidirect
205. C4×D3×ΓL(1,𝔽8)C2×D4semidirect
209. C3×C4×AGL(1,𝔽7)C2×D4semidirect
213. (C3⋊AGL(1,𝔽7))⋊C4C2×D4semidirect
214. D3×ΓL(1,𝔽8)⋊C4C2×D4semidirect
215. Dic3×AGL(1,𝔽7)C2×D4semidirect
224. D7×#127C3×D3semidirect
246. C2×C3×C7×D4C23×C3semidirect
247. C2×#4268C23×C3semidirect
249. C2×D84C23×C3semidirect
251. C2×C7×#67C23×C3semidirect
253. C2×C7×D12C23×C3semidirect
255. C2×C3×C22⋊D7C23×C3semidirect
257. C2×C3×D28C23×C3semidirect
263. C2×D4×ΓL(1,𝔽8)C22×D3semidirect
268. C2×#4247C23×C3semidirect
269. C2×#4246C23×C3semidirect
270. C2×#4245C23×C3semidirect
277. C4×D3×D7C3×D4semidirect
283. C2×(C22⋊D7)⋊C3C22×D3semidirect
296. C2×C4⋊AGL(1,𝔽7)C22×D3semidirect
303. C3×C42×C7C23×C3semidirect
304. C4×Dic21C23×C3semidirect
305. C4×C7×Dic3C23×C3semidirect
306. C3×C4×Dic7C23×C3semidirect
309. C42×ΓL(1,𝔽8)C22×D3semidirect
310. Dic3×Dic7C23×C3semidirect
314. C4×ΓL(1,𝔽8)⋊C4C22×D3semidirect
358. D3×AGL(1,𝔽7)#127direct (N × H)
359. C3×C4×ΓL(1,𝔽8)C22×D4semidirect
360. C3⋊(ΓL(1,𝔽8)⋊C4)C22×D4semidirect
361. Dic3×ΓL(1,𝔽8)C22×D4semidirect
362. C3×ΓL(1,𝔽8)⋊C4C22×D4semidirect
372. C2×D4×D7C2×C3×D3semidirect
377. C7×#127C2×C3×D3semidirect
383. #6503C2×C3×D3semidirect
387. #6437C2×C3×D3semidirect
391. C42×D7C2×C3×D3semidirect
412. D3×#127AGL(1,𝔽7)direct (N × H)
454. C4×D21C2×C3×D4semidirect
458. C4×D3×C7C2×C3×D4semidirect
462. C3×C4×D7C2×C3×D4semidirect
474. D21⋊C4C2×C3×D4semidirect
475. D3×Dic7C2×C3×D4semidirect
476. Dic3×D7C2×C3×D4semidirect
494. C4×AGL(1,𝔽7)D3×D4semidirect
538. C3⋊AGL(1,𝔽7)C2×#127semidirect
540. D3×ΓL(1,𝔽8)C2×#127semidirect
542. C3×AGL(1,𝔽7)C2×#127semidirect
554. C2×C7×D4C22×C3×D3semidirect
560. C2×C22⋊D7C22×C3×D3semidirect
571. C2×D28C22×C3×D3semidirect
578. C42×C7C22×C3×D3semidirect
581. C4×Dic7C22×C3×D3semidirect
604. C2×D3×D4C2×AGL(1,𝔽7)semidirect
623. C3×#127C2×AGL(1,𝔽7)semidirect
636. #940C2×AGL(1,𝔽7)semidirect
640. #874C2×AGL(1,𝔽7)semidirect
644. C42×D3C2×AGL(1,𝔽7)semidirect
666. D3×D7C3×#127semidirect
680. C3×C4×C7C22×C3×D4semidirect
681. Dic21C22×C3×D4semidirect
682. C3×Dic7C22×C3×D4semidirect
683. C7×Dic3C22×C3×D4semidirect
686. C4×ΓL(1,𝔽8)C2×D3×D4semidirect
689. ΓL(1,𝔽8)⋊C4C2×D3×D4semidirect
736. C3×ΓL(1,𝔽8)C22×#127semidirect
771. C4×D7C3×D3×D4semidirect
815. C2×C3×D4C22×AGL(1,𝔽7)semidirect
829. C2×#67C22×AGL(1,𝔽7)semidirect
840. C2×D12C22×AGL(1,𝔽7)semidirect
854. C3×C42C22×AGL(1,𝔽7)semidirect
857. C4×Dic3C22×AGL(1,𝔽7)semidirect
861. D21C2×C3×#127semidirect
863. C3×D7C2×C3×#127semidirect
865. D3×C7C2×C3×#127semidirect
877. AGL(1,𝔽7)D3×#127direct (N × H)
919. #127D3×AGL(1,𝔽7)direct (N × H)
942. C4×C7C2×C3×D3×D4semidirect
944. Dic7C2×C3×D3×D4semidirect
1024. C4×D3D4×AGL(1,𝔽7)semidirect
1025. C3×C7C22×C3×#127semidirect
1027. ΓL(1,𝔽8)C2×D3×#127semidirect
1062. C2×D4C2×D3×AGL(1,𝔽7)semidirect
1074. C42C2×D3×AGL(1,𝔽7)semidirect
1082. D7C3×D3×#127semidirect
1125. C3×C4C2×D4×AGL(1,𝔽7)semidirect
1127. Dic3C2×D4×AGL(1,𝔽7)semidirect
1164. C7C2×C3×D3×#127semidirect
1184. D3#127×AGL(1,𝔽7)direct (N × H)
1203. C4D3×D4×AGL(1,𝔽7)semidirect
1206. C3C2×#127×AGL(1,𝔽7)semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#722442712
AGL(1,𝔽7)×#8742
D3×#106207102
C42×D3×AGL(1,𝔽7)2
#722442572
D3×#6503⋊C32
#127×C3⋊AGL(1,𝔽7)2
D3×ΓL(1,𝔽8)×#1272
AGL(1,𝔽7)×#9402
C3×#127×AGL(1,𝔽7)2
D3×D7×#1273
C2×D3×D4×AGL(1,𝔽7)2
C2×#127×AGL(1,𝔽7)3
C2×C3×D3×#1277