Finite Group Databasebeta

← C2×#67×#64424 #72246366

Subgroups — C2×#67×#64424 #72246366

Order 14112.

5390 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#72245929C211yesmaximal, characteristic, complemented
2C2×#72245938C211yesmaximal, characteristic, complemented
3C2×#72245919C211yesmaximal, characteristic, complemented
4C2×#67×#3861C211yesmaximal, characteristic, complemented
5C23×C3×#64424C211yesmaximal, characteristic, complemented
6C23×C3×#3861C2211yescharacteristic, complemented
7#67×#64424C218yesmaximal, direct product factor
8#72245938C2214yescomplemented
9#72245929C2214yescomplemented
10#72245919C2214yescomplemented
11#67×#3861C2214yescomplemented
12C2×Dic3×#64424C211yesmaximal, characteristic, complemented
13C2×C3⋊#10596874C2211yescharacteristic, complemented
14C2×Dic3×#3861C2211yescharacteristic, complemented
15Dic3×#64424C2214yescomplemented
16C2×#67×C7⋊D7C311yesmaximal, characteristic, complemented
17C2×#11924240C2×C311yescharacteristic, complemented
18C2×#11924241C2×C311yescharacteristic, complemented
19C2×#11924293C2×C311yescharacteristic, complemented
20C2×C72×#67C2×C311yescharacteristic, complemented
21C23×C3×C7⋊D7C2×C311yescharacteristic, complemented
22#67×C7⋊D7C2×C318yescomplemented
23C2×Dic3×C7⋊D7C2×C311yescharacteristic, complemented
24C2×#67×AGL(1,𝔽7)—71nomaximal
25C2×#67×AGL(1,𝔽7)—71nomaximal
26C2×#67×AGL(1,𝔽7)—76nomaximal
27C22×D3×#64424C211yesmaximal, characteristic, complemented
28C22×D3×C7⋊D7C2×C311yescharacteristic, complemented
29C22×C3⋊#64424C2211yescharacteristic, complemented
30C22×D3×#3861C2211yescharacteristic, complemented
31C22×C3×#64424—24no—
32C22×C3×#64424C2211yescharacteristic
33C22×C3×#64424C2214yescomplemented
34C22×C3×#64424C2211yescharacteristic, complemented
35C2×D3×#64424—24no—
36C2×D3×#64424C2214yescomplemented
37C2×D4×#64424—31nomaximal
38C2×C4×#64424—31no—
39C2×C4⋊#64424—31no—
40C2×#11924217—31no—
41C2×#11924217—31no—
42C2×D4×#3861—31no—
43D4×#64424—38no—
44C23×#64424—21no—
45C23×#64424—31no—
46C23×#64424D311yescharacteristic, complemented
47C22×C3×#3861—22no—
48C22×C3×#3861C2311yescharacteristic
49C22×C3×#3861C2312yescomplemented
50C2×D3×#3861—22no—
51C2×D3×#3861C2312yescomplemented
52C2×C3⋊#64424—22no—
53C2×C3⋊#64424C2312yescomplemented
54C2×C3×#64424—22no—
55C2×C3×#64424—28no—
56C2×C3×#64424D414yescomplemented
57C2×C3×#64424C2312yes—
58C2×C3×#64424C2312yescomplemented
59D3×#64424—28no—
60C3⋊#10596874C2312yescomplemented
61Dic3×#3861C2312yescomplemented
62C2×D4×C7⋊D7—31noHall
63C23×C3×C72C22×C311yescharacteristic, complemented
64C22×C3⋊(C7⋊D7)C22×C311yescharacteristic, complemented
65C22×D3×C72C22×C311yescharacteristic, complemented
66C22×C3×C7⋊D7—24no—
67C22×C3×C7⋊D7C22×C311yescharacteristic
68C22×C3×C7⋊D7C22×C314yescomplemented
69C22×C3×C7⋊D7C22×C311yescharacteristic, complemented
70C23×#3861—21no—
71C23×#3861—31no—
72C23×#3861C2×D311yescharacteristic, complemented
73C2×D3×C7⋊D7—24no—
74C2×D3×C7⋊D7C22×C314yescomplemented
75C22×#64424—24no—
76C22×#64424—24no—
77C22×#64424—21no—
78C22×#64424—24no—
79C22×#64424—24no—
80C22×#64424—21no—
81C22×#64424—31no—
82C22×#64424—34no—
83C22×#64424—64no—
84C22×#64424C2×D311yescharacteristic
85C22×#64424C2×D314yescomplemented
86C22×#64424C2×D311yescharacteristic, complemented
87#11924293C22×C314yescomplemented
88C2×C3⋊(C7⋊Dic7)C22×C311yescharacteristic, complemented
89C72×#67C22×C314yescomplemented
90C2×C72×Dic3C22×C311yescharacteristic, complemented
91D4×#3861—34no—
92C2×C4×#3861—31no—
93#11924241C22×C314yescomplemented
94#11924240C22×C314yescomplemented
95Dic3×C7⋊D7C22×C314yescomplemented
96#11924217—34no—
97#11924217—34no—
98C2×#10596874—31no—
99C4⋊#64424—34no—
100C4×#64424—34no—
101C23×C3×AGL(1,𝔽7)—71no—
102C23×C3×AGL(1,𝔽7)—71no—
103C23×C3×AGL(1,𝔽7)—76no—
104C22×D3×AGL(1,𝔽7)—71no—
105C22×D3×AGL(1,𝔽7)—71no—
106C22×D3×AGL(1,𝔽7)—76no—
107C2×#4268⋊C3—71no—
108C2×#4268⋊C3—71no—
109C2×#4268⋊C3—76no—
110C2×ΓL(1,𝔽8)×#67—71no—
111C2×ΓL(1,𝔽8)×#67—141no—
112C2×ΓL(1,𝔽8)×#67—146no—
113#67×AGL(1,𝔽7)—78no—
114#67×AGL(1,𝔽7)—78no—
115#67×AGL(1,𝔽7)—748no—
116C2×#4246⋊C3—71no—
117C2×#4246⋊C3—71no—
118C2×#4246⋊C3—76no—
119C2×#4245⋊C3—71no—
120C2×#4245⋊C3—71no—
121C2×#4245⋊C3—76no—
122C2×Dic3×AGL(1,𝔽7)—71no—
123C2×Dic3×AGL(1,𝔽7)—71no—
124C2×Dic3×AGL(1,𝔽7)—76no—
125C2×C3×#3861—22no—
126C2×C3×#3861C2×D412yescomplemented
127C2×C3×#3861C2411yescharacteristic
128C3⋊#64424—22no—
129D3×#3861—22no—
130C3×#64424—22no—
131C3×#64424C2×D414yescomplemented
132C23×C7⋊D7—31no—
133C23×C7⋊D7C3×D311yescharacteristic, complemented
134C2×C72×D4—31no—
135C2×C22⋊(C7⋊D7)—31no—
136C2×C22⋊(C7⋊D7)—31no—
137D4×C7⋊D7—38no—
138C2×C4⋊(C7⋊D7)—31no—
139C2×C4×C7⋊D7—31no—
140C2×D7×#67—71no—
141C2×D7×#67—71no—
142C2×D7×#67—76no—
143C2×D4×AGL(1,𝔽7)—211no—
144C2×D4×AGL(1,𝔽7)—211no—
145C2×D4×AGL(1,𝔽7)—216no—
146C22×C3×C72—22no—
147C22×C3×C72C23×C311yescharacteristic
148C22×C3×C72C23×C312yescomplemented
149C2×C3⋊(C7⋊D7)—22no—
150C2×C3⋊(C7⋊D7)C23×C312yescomplemented
151C2×D3×C72—22no—
152C2×D3×C72C23×C312yescomplemented
153C2×C3×C7⋊D7—22no—
154C2×C3×C7⋊D7—28no—
155C2×C3×C7⋊D7C3×D414yescomplemented
156C2×C3×C7⋊D7C23×C312yes—
157C2×C3×C7⋊D7C23×C312yescomplemented
158C22×#3861—22no—
159C22×#3861—22no—
160C22×#3861—22no—
161C22×#3861—21no—
162C22×#3861—22no—
163C22×#3861—32no—
164C22×#3861—62no—
165C22×#3861C22×D311yescharacteristic
166C22×#3861C22×D312yescomplemented
167D3×C7⋊D7—28no—
168C2×#64424—22no—
169C2×#64424—28no—
170C2×#64424—22no—
171C2×#64424—28no—
172C2×#64424—22no—
173C2×#64424—28no—
174C2×#64424—24no—
175C2×#64424—22no—
176C2×#64424—22no—
177C2×#64424—32no—
178C2×#64424—62no—
179C2×#64424—68no—
180C2×#64424#6714yesdirect product factor
181C2×#64424C22×D312yes—
182C2×#64424C22×D312yescomplemented
183C3⋊(C7⋊Dic7)C23×C312yescomplemented
184C72×Dic3C23×C312yescomplemented
185C4×#3861—32no—
186#10596874—32no—
187C23×C3×ΓL(1,𝔽8)—71no—
188C23×C3×ΓL(1,𝔽8)—141no—
189C23×C3×ΓL(1,𝔽8)—146no—
190C22×C3⋊AGL(1,𝔽7)—71no—
191C22×C3⋊AGL(1,𝔽7)—71no—
192C22×C3⋊AGL(1,𝔽7)—76no—
193C22×D3×ΓL(1,𝔽8)—71no—
194C22×D3×ΓL(1,𝔽8)—141no—
195C22×D3×ΓL(1,𝔽8)—146no—
196C22×C3×AGL(1,𝔽7)—71no—
197C22×C3×AGL(1,𝔽7)—71no—
198C22×C3×AGL(1,𝔽7)—76no—
199C22×C3×AGL(1,𝔽7)—71no—
200C22×C3×AGL(1,𝔽7)—74no—
201C22×C3×AGL(1,𝔽7)—71no—
202C22×C3×AGL(1,𝔽7)—76no—
203C22×C3×AGL(1,𝔽7)—74no—
204C22×C3×AGL(1,𝔽7)—724no—
205C22×C3×AGL(1,𝔽7)—144no—
206C22×C3×AGL(1,𝔽7)—144no—
207C22×C3×AGL(1,𝔽7)—1424no—
208C2×D3×AGL(1,𝔽7)—74no—
209C2×D3×AGL(1,𝔽7)—74no—
210C2×D3×AGL(1,𝔽7)—724no—
211C2×D3×AGL(1,𝔽7)—144no—
212C2×D3×AGL(1,𝔽7)—144no—
213C2×D3×AGL(1,𝔽7)—1424no—
214#4268⋊C3—74no—
215#4268⋊C3—74no—
216#4268⋊C3—724no—
217C2×C3⋊(ΓL(1,𝔽8)⋊C4)—71no—
218C2×C3⋊(ΓL(1,𝔽8)⋊C4)—71no—
219C2×C3⋊(ΓL(1,𝔽8)⋊C4)—76no—
220ΓL(1,𝔽8)×#67—74no—
221ΓL(1,𝔽8)×#67—144no—
222ΓL(1,𝔽8)×#67—1424no—
223C2×Dic3×ΓL(1,𝔽8)—71no—
224C2×Dic3×ΓL(1,𝔽8)—141no—
225C2×Dic3×ΓL(1,𝔽8)—146no—
226#4246⋊C3—74no—
227#4246⋊C3—74no—
228#4246⋊C3—724no—
229#4245⋊C3—74no—
230#4245⋊C3—74no—
231#4245⋊C3—724no—
232Dic3×AGL(1,𝔽7)—74no—
233Dic3×AGL(1,𝔽7)—74no—
234Dic3×AGL(1,𝔽7)—724no—
235C3×#3861C22×D411yescharacteristic, complemented, Hall
236C23×C72—31no—
237C23×C72C2×C3×D311yescharacteristic, complemented
238C22×C7⋊D7—24no—
239C22×C7⋊D7—31no—
240C22×C7⋊D7—34no—
241C22×C7⋊D7—64no—
242C22×C7⋊D7C2×C3×D311yescharacteristic
243C22×C7⋊D7C2×C3×D314yescomplemented
244C22×C7⋊D7C2×C3×D311yescharacteristic, complemented
245C72×D4—34no—
246C2×C4×C72—31no—
247C22⋊(C7⋊D7)—34no—
248C22⋊(C7⋊D7)—34no—
249C2×C7⋊Dic7—31no—
250C4⋊(C7⋊D7)—34no—
251C4×C7⋊D7—34no—
252C23×C3×D7—71no—
253C23×C3×D7—71no—
254C23×C3×D7—76no—
255C22×D3×D7—71no—
256C22×D3×D7—71no—
257C22×D3×D7—76no—
258C23×AGL(1,𝔽7)—71no—
259C23×AGL(1,𝔽7)—71no—
260C23×AGL(1,𝔽7)—76no—
261C23×AGL(1,𝔽7)—141no—
262C23×AGL(1,𝔽7)—141no—
263C23×AGL(1,𝔽7)—146no—
264C23×AGL(1,𝔽7)—211no—
265C23×AGL(1,𝔽7)—211no—
266C23×AGL(1,𝔽7)—216no—
267C2×#4268—71no—
268C2×#4268—71no—
269C2×#4268—76no—
270C2×C7×#67AGL(1,𝔽7)11yescharacteristic, complemented
271C2×C7×#67AGL(1,𝔽7)11yescharacteristic, complemented
272C2×C7×#67AGL(1,𝔽7)16yescomplemented
273C2×D4×ΓL(1,𝔽8)—211no—
274C2×D4×ΓL(1,𝔽8)—421no—
275C2×D4×ΓL(1,𝔽8)—426no—
276D7×#67—78no—
277D7×#67—78no—
278D7×#67—748no—
279C2×#4246—71no—
280C2×#4246—71no—
281C2×#4246—76no—
282C2×#4245—71no—
283C2×#4245—71no—
284C2×#4245—76no—
285C2×Dic3×D7—71no—
286C2×Dic3×D7—71no—
287C2×Dic3×D7—76no—
288C2×(C22⋊D7)⋊C3—211no—
289C2×(C22⋊D7)⋊C3—211no—
290C2×(C22⋊D7)⋊C3—216no—
291C2×(C22⋊D7)⋊C3—211no—
292C2×(C22⋊D7)⋊C3—211no—
293C2×(C22⋊D7)⋊C3—216no—
294D4×AGL(1,𝔽7)—218no—
295D4×AGL(1,𝔽7)—218no—
296D4×AGL(1,𝔽7)—2148no—
297C2×C4⋊AGL(1,𝔽7)—211no—
298C2×C4⋊AGL(1,𝔽7)—211no—
299C2×C4⋊AGL(1,𝔽7)—216no—
300C2×C4×AGL(1,𝔽7)—211no—
301C2×C4×AGL(1,𝔽7)—211no—
302C2×C4×AGL(1,𝔽7)—216no—
303C2×C3×C72—22no—
304C2×C3×C72C2×C3×D412yescomplemented
305C2×C3×C72C24×C311yescharacteristic
306C3⋊(C7⋊D7)—22no—
307D3×C72—22no—
308C3×C7⋊D7—22no—
309C3×C7⋊D7C2×C3×D414yescomplemented
310C2×#3861—22no—
311C2×#3861—22no—
312C2×#3861—22no—
313C2×#3861—21no—
314C2×#3861—22no—
315C2×#3861—62no—
316C2×#3861C2×#6712yescomplemented
317C2×#3861C23×D311yescharacteristic
318#64424—22no—
319#64424—22no—
320#64424—22no—
321#64424—24no—
322#64424—62no—
323#64424C2×#6714yesdirect product factor
324C22×C3×#67—491noHall
325C22×C3×ΓL(1,𝔽8)—71no—
326C22×C3×ΓL(1,𝔽8)—72no—
327C22×C3×ΓL(1,𝔽8)—141no—
328C22×C3×ΓL(1,𝔽8)—146no—
329C22×C3×ΓL(1,𝔽8)—142no—
330C22×C3×ΓL(1,𝔽8)—1412no—
331C22×C3×ΓL(1,𝔽8)—142no—
332C22×C3×ΓL(1,𝔽8)—282no—
333C22×C3×ΓL(1,𝔽8)—2812no—
334C2×C3⋊AGL(1,𝔽7)—72no—
335C2×C3⋊AGL(1,𝔽7)—72no—
336C2×C3⋊AGL(1,𝔽7)—712no—
337C2×C3⋊AGL(1,𝔽7)—142no—
338C2×C3⋊AGL(1,𝔽7)—142no—
339C2×C3⋊AGL(1,𝔽7)—1412no—
340C2×D3×ΓL(1,𝔽8)—72no—
341C2×D3×ΓL(1,𝔽8)—142no—
342C2×D3×ΓL(1,𝔽8)—1412no—
343C2×D3×ΓL(1,𝔽8)—142no—
344C2×D3×ΓL(1,𝔽8)—282no—
345C2×D3×ΓL(1,𝔽8)—2812no—
346C2×C3×AGL(1,𝔽7)—72no—
347C2×C3×AGL(1,𝔽7)—74no—
348C2×C3×AGL(1,𝔽7)—72no—
349C2×C3×AGL(1,𝔽7)—712no—
350C2×C3×AGL(1,𝔽7)—74no—
351C2×C3×AGL(1,𝔽7)—724no—
352C2×C3×AGL(1,𝔽7)—72no—
353C2×C3×AGL(1,𝔽7)—72no—
354C2×C3×AGL(1,𝔽7)—712no—
355C2×C3×AGL(1,𝔽7)—148no—
356C2×C3×AGL(1,𝔽7)—148no—
357C2×C3×AGL(1,𝔽7)—1448no—
358C2×C3×AGL(1,𝔽7)—142no—
359C2×C3×AGL(1,𝔽7)—142no—
360C2×C3×AGL(1,𝔽7)—1412no—
361D3×AGL(1,𝔽7)—148no—
362D3×AGL(1,𝔽7)—148no—
363D3×AGL(1,𝔽7)—1448no—
364C3⋊(ΓL(1,𝔽8)⋊C4)—72no—
365C3⋊(ΓL(1,𝔽8)⋊C4)—72no—
366C3⋊(ΓL(1,𝔽8)⋊C4)—712no—
367Dic3×ΓL(1,𝔽8)—72no—
368Dic3×ΓL(1,𝔽8)—142no—
369Dic3×ΓL(1,𝔽8)—1412no—
370C2×D4×D7—211no—
371C2×D4×D7—211no—
372C2×D4×D7—216no—
373C22×C72—22no—
374C22×C72—32no—
375C22×C72—62no—
376C22×C72C22×C3×D311yescharacteristic
377C22×C72C22×C3×D312yescomplemented
378C2×C7⋊D7—22no—
379C2×C7⋊D7—28no—
380C2×C7⋊D7—32no—
381C2×C7⋊D7—62no—
382C2×C7⋊D7—68no—
383C2×C7⋊D7C3×#6714yescomplemented
384C2×C7⋊D7C22×C3×D312yes—
385C2×C7⋊D7C22×C3×D312yescomplemented
386C4×C72—32no—
387C7⋊Dic7—32no—
388C23×C3×C7C2×AGL(1,𝔽7)11yescharacteristic, complemented
389C23×C3×C7C2×AGL(1,𝔽7)11yescharacteristic, complemented
390C23×C3×C7C2×AGL(1,𝔽7)16yescomplemented
391C22×D21—71no—
392C22×D21—71no—
393C22×D21—76no—
394C22×D3×C7C2×AGL(1,𝔽7)11yescharacteristic, complemented
395C22×D3×C7C2×AGL(1,𝔽7)11yescharacteristic, complemented
396C22×D3×C7C2×AGL(1,𝔽7)16yescomplemented
397C22×C3×D7—71no—
398C22×C3×D7—71no—
399C22×C3×D7—76no—
400C22×C3×D7—71no—
401C22×C3×D7—71no—
402C22×C3×D7—76no—
403C22×C3×D7—74no—
404C22×C3×D7—74no—
405C22×C3×D7—724no—
406C22×C3×D7—144no—
407C22×C3×D7—144no—
408C22×C3×D7—1424no—
409C23×ΓL(1,𝔽8)—71no—
410C23×ΓL(1,𝔽8)—141no—
411C23×ΓL(1,𝔽8)—146no—
412C23×ΓL(1,𝔽8)—141no—
413C23×ΓL(1,𝔽8)—211no—
414C23×ΓL(1,𝔽8)—281no—
415C23×ΓL(1,𝔽8)—286no—
416C23×ΓL(1,𝔽8)—421no—
417C23×ΓL(1,𝔽8)—426no—
418C2×D3×D7—74no—
419C2×D3×D7—74no—
420C2×D3×D7—724no—
421C2×D3×D7—144no—
422C2×D3×D7—144no—
423C2×D3×D7—1424no—
424C22×AGL(1,𝔽7)—71no—
425C22×AGL(1,𝔽7)—71no—
426C22×AGL(1,𝔽7)—76no—
427C22×AGL(1,𝔽7)—71no—
428C22×AGL(1,𝔽7)—74no—
429C22×AGL(1,𝔽7)—71no—
430C22×AGL(1,𝔽7)—76no—
431C22×AGL(1,𝔽7)—74no—
432C22×AGL(1,𝔽7)—724no—
433C22×AGL(1,𝔽7)—141no—
434C22×AGL(1,𝔽7)—141no—
435C22×AGL(1,𝔽7)—146no—
436C22×AGL(1,𝔽7)—141no—
437C22×AGL(1,𝔽7)—144no—
438C22×AGL(1,𝔽7)—141no—
439C22×AGL(1,𝔽7)—146no—
440C22×AGL(1,𝔽7)—144no—
441C22×AGL(1,𝔽7)—1424no—
442C22×AGL(1,𝔽7)—144no—
443C22×AGL(1,𝔽7)—144no—
444C22×AGL(1,𝔽7)—1424no—
445C22×AGL(1,𝔽7)—144no—
446C22×AGL(1,𝔽7)—144no—
447C22×AGL(1,𝔽7)—144no—
448C22×AGL(1,𝔽7)—1424no—
449C22×AGL(1,𝔽7)—144no—
450C22×AGL(1,𝔽7)—1424no—
451C22×AGL(1,𝔽7)—214no—
452C22×AGL(1,𝔽7)—214no—
453C22×AGL(1,𝔽7)—2124no—
454C22×AGL(1,𝔽7)—211no—
455C22×AGL(1,𝔽7)—211no—
456C22×AGL(1,𝔽7)—216no—
457C22×AGL(1,𝔽7)—424no—
458C22×AGL(1,𝔽7)—424no—
459C22×AGL(1,𝔽7)—4224no—
460#4268—74no—
461#4268—74no—
462#4268—724no—
463C2×Dic21—71no—
464C2×Dic21—71no—
465C2×Dic21—76no—
466C7×#67C2×AGL(1,𝔽7)14yescomplemented
467C7×#67C2×AGL(1,𝔽7)14yescomplemented
468C7×#67C2×AGL(1,𝔽7)124yescomplemented
469C2×C7×Dic3C2×AGL(1,𝔽7)11yescharacteristic, complemented
470C2×C7×Dic3C2×AGL(1,𝔽7)11yescharacteristic, complemented
471C2×C7×Dic3C2×AGL(1,𝔽7)16yescomplemented
472D4×ΓL(1,𝔽8)—214no—
473D4×ΓL(1,𝔽8)—424no—
474D4×ΓL(1,𝔽8)—4224no—
475C2×C4×ΓL(1,𝔽8)—211no—
476C2×C4×ΓL(1,𝔽8)—421no—
477C2×C4×ΓL(1,𝔽8)—426no—
478#4246—74no—
479#4246—74no—
480#4246—724no—
481#4245—74no—
482#4245—74no—
483#4245—724no—
484Dic3×D7—74no—
485Dic3×D7—74no—
486Dic3×D7—724no—
487(C22⋊D7)⋊C3—214no—
488(C22⋊D7)⋊C3—214no—
489(C22⋊D7)⋊C3—2124no—
490(C22⋊D7)⋊C3—214no—
491(C22⋊D7)⋊C3—214no—
492(C22⋊D7)⋊C3—2124no—
493C2×ΓL(1,𝔽8)⋊C4—211no—
494C2×ΓL(1,𝔽8)⋊C4—211no—
495C2×ΓL(1,𝔽8)⋊C4—216no—
496C4⋊AGL(1,𝔽7)—214no—
497C4⋊AGL(1,𝔽7)—214no—
498C4⋊AGL(1,𝔽7)—2124no—
499C4×AGL(1,𝔽7)—214no—
500C4×AGL(1,𝔽7)—214no—
501C4×AGL(1,𝔽7)—2124no—
502C3×C72C22×C3×D411yescharacteristic, complemented
503#3861—21no—
504#3861C22×#6711yescharacteristic, complemented
505C24×C32—491no—
506C23×C3×D3—491no—
507C2×C3×#67—491no—
508C2×C3×#67—491no—
509C2×C3×#67—498no—
510C2×C3×#67—491no—
511C2×C3×#67—981no—
512C22×C3×Dic3—491no—
513C2×C3×ΓL(1,𝔽8)—72no—
514C2×C3×ΓL(1,𝔽8)—71no—
515C2×C3×ΓL(1,𝔽8)—142no—
516C2×C3×ΓL(1,𝔽8)—141no—
517C2×C3×ΓL(1,𝔽8)—1412no—
518C2×C3×ΓL(1,𝔽8)—146no—
519C2×C3×ΓL(1,𝔽8)—142no—
520C2×C3×ΓL(1,𝔽8)—282no—
521C2×C3×ΓL(1,𝔽8)—2812no—
522C3⋊AGL(1,𝔽7)—142no—
523C3⋊AGL(1,𝔽7)—142no—
524C3⋊AGL(1,𝔽7)—1412no—
525D3×ΓL(1,𝔽8)—142no—
526D3×ΓL(1,𝔽8)—282no—
527D3×ΓL(1,𝔽8)—2812no—
528C3×AGL(1,𝔽7)—74no—
529C3×AGL(1,𝔽7)—74no—
530C3×AGL(1,𝔽7)—724no—
531C3×AGL(1,𝔽7)—142no—
532C3×AGL(1,𝔽7)—142no—
533C3×AGL(1,𝔽7)—1412no—
534C23×D7—71no—
535C23×D7—71no—
536C23×D7—76no—
537C23×D7—211no—
538C23×D7—211no—
539C23×D7—216no—
540C2×C7×D4—31no—
541C2×C7×D4—31no—
542C2×C7×D4—36no—
543C2×C22⋊D7—211no—
544C2×C22⋊D7—211no—
545C2×C22⋊D7—216no—
546C2×C22⋊D7—211no—
547C2×C22⋊D7—211no—
548C2×C22⋊D7—216no—
549D4×D7—218no—
550D4×D7—218no—
551D4×D7—2148no—
552C2×D28—211no—
553C2×D28—211no—
554C2×D28—216no—
555C2×C4×D7—211no—
556C2×C4×D7—211no—
557C2×C4×D7—216no—
558C2×C72—22no—
559C2×C72—62no—
560C2×C72C2×C3×#6712yescomplemented
561C2×C72C23×C3×D311yescharacteristic
562C7⋊D7—22no—
563C7⋊D7—62no—
564C7⋊D7C2×C3×#6714yescomplemented
565C22×C3×D4—1471no—
566C22×#67—491no—
567C22×C3×C7—22no—
568C22×C3×C7—22no—
569C22×C3×C7—212no—
570C22×C3×C7C22×AGL(1,𝔽7)11yescharacteristic
571C22×C3×C7C22×AGL(1,𝔽7)11yescharacteristic
572C22×C3×C7C22×AGL(1,𝔽7)16yes—
573C22×C3×C7C22×AGL(1,𝔽7)12yescomplemented
574C22×C3×C7C22×AGL(1,𝔽7)12yescomplemented
575C22×C3×C7C22×AGL(1,𝔽7)112yescomplemented
576C2×D21—72no—
577C2×D21—72no—
578C2×D21—712no—
579C2×D21—142no—
580C2×D21—142no—
581C2×D21—1412no—
582C2×D3×C7—22no—
583C2×D3×C7—22no—
584C2×D3×C7—212no—
585C2×D3×C7C22×AGL(1,𝔽7)12yescomplemented
586C2×D3×C7C22×AGL(1,𝔽7)12yescomplemented
587C2×D3×C7C22×AGL(1,𝔽7)112yescomplemented
588C2×C3×D7—74no—
589C2×C3×D7—74no—
590C2×C3×D7—724no—
591C2×C3×D7—72no—
592C2×C3×D7—72no—
593C2×C3×D7—712no—
594C2×C3×D7—72no—
595C2×C3×D7—72no—
596C2×C3×D7—712no—
597C2×C3×D7—148no—
598C2×C3×D7—148no—
599C2×C3×D7—1448no—
600C2×C3×D7—142no—
601C2×C3×D7—142no—
602C2×C3×D7—1412no—
603C22×ΓL(1,𝔽8)—71no—
604C22×ΓL(1,𝔽8)—72no—
605C22×ΓL(1,𝔽8)—141no—
606C22×ΓL(1,𝔽8)—146no—
607C22×ΓL(1,𝔽8)—142no—
608C22×ΓL(1,𝔽8)—1412no—
609C22×ΓL(1,𝔽8)—142no—
610C22×ΓL(1,𝔽8)—142no—
611C22×ΓL(1,𝔽8)—141no—
612C22×ΓL(1,𝔽8)—142no—
613C22×ΓL(1,𝔽8)—212no—
614C22×ΓL(1,𝔽8)—282no—
615C22×ΓL(1,𝔽8)—282no—
616C22×ΓL(1,𝔽8)—2812no—
617C22×ΓL(1,𝔽8)—282no—
618C22×ΓL(1,𝔽8)—282no—
619C22×ΓL(1,𝔽8)—2812no—
620C22×ΓL(1,𝔽8)—2812no—
621C22×ΓL(1,𝔽8)—281no—
622C22×ΓL(1,𝔽8)—286no—
623C22×ΓL(1,𝔽8)—282no—
624C22×ΓL(1,𝔽8)—2812no—
625C22×ΓL(1,𝔽8)—422no—
626C22×ΓL(1,𝔽8)—4212no—
627C22×ΓL(1,𝔽8)—422no—
628C22×ΓL(1,𝔽8)—842no—
629C22×ΓL(1,𝔽8)—8412no—
630D3×D7—148no—
631D3×D7—148no—
632D3×D7—1448no—
633C2×AGL(1,𝔽7)—74no—
634C2×AGL(1,𝔽7)—72no—
635C2×AGL(1,𝔽7)—74no—
636C2×AGL(1,𝔽7)—724no—
637C2×AGL(1,𝔽7)—72no—
638C2×AGL(1,𝔽7)—712no—
639C2×AGL(1,𝔽7)—72no—
640C2×AGL(1,𝔽7)—72no—
641C2×AGL(1,𝔽7)—712no—
642C2×AGL(1,𝔽7)—144no—
643C2×AGL(1,𝔽7)—142no—
644C2×AGL(1,𝔽7)—144no—
645C2×AGL(1,𝔽7)—1424no—
646C2×AGL(1,𝔽7)—142no—
647C2×AGL(1,𝔽7)—1412no—
648C2×AGL(1,𝔽7)—142no—
649C2×AGL(1,𝔽7)—142no—
650C2×AGL(1,𝔽7)—1412no—
651C2×AGL(1,𝔽7)—148no—
652C2×AGL(1,𝔽7)—148no—
653C2×AGL(1,𝔽7)—1448no—
654C2×AGL(1,𝔽7)—142no—
655C2×AGL(1,𝔽7)—142no—
656C2×AGL(1,𝔽7)—1412no—
657C2×AGL(1,𝔽7)—142no—
658C2×AGL(1,𝔽7)—148no—
659C2×AGL(1,𝔽7)—142no—
660C2×AGL(1,𝔽7)—148no—
661C2×AGL(1,𝔽7)—148no—
662C2×AGL(1,𝔽7)—1448no—
663C2×AGL(1,𝔽7)—142no—
664C2×AGL(1,𝔽7)—1412no—
665C2×AGL(1,𝔽7)—148no—
666C2×AGL(1,𝔽7)—1448no—
667C2×AGL(1,𝔽7)—142no—
668C2×AGL(1,𝔽7)—1412no—
669C2×AGL(1,𝔽7)—212no—
670C2×AGL(1,𝔽7)—212no—
671C2×AGL(1,𝔽7)—2112no—
672C2×AGL(1,𝔽7)—428no—
673C2×AGL(1,𝔽7)—428no—
674C2×AGL(1,𝔽7)—4248no—
675C2×AGL(1,𝔽7)—422no—
676C2×AGL(1,𝔽7)—422no—
677C2×AGL(1,𝔽7)—4212no—
678Dic21—72no—
679Dic21—72no—
680Dic21—712no—
681C7×Dic3C22×AGL(1,𝔽7)12yescomplemented
682C7×Dic3C22×AGL(1,𝔽7)12yescomplemented
683C7×Dic3C22×AGL(1,𝔽7)112yescomplemented
684C4×ΓL(1,𝔽8)—212no—
685C4×ΓL(1,𝔽8)—422no—
686C4×ΓL(1,𝔽8)—4212no—
687ΓL(1,𝔽8)⋊C4—212no—
688ΓL(1,𝔽8)⋊C4—212no—
689ΓL(1,𝔽8)⋊C4—2112no—
690C23×C32—491no—
691C23×C32—491no—
692C23×C32—494no—
693C23×C32—984no—
694C23×C32—981no—
695C22×C3×D3—491no—
696C22×C3×D3—494no—
697C22×C3×D3—984no—
698C22×C3×D3—981no—
699C3×#67—494no—
700C3×#67—494no—
701C3×#67—494no—
702C3×#67—984no—
703C2×C3×Dic3—491no—
704C2×C3×Dic3—494no—
705C2×C3×Dic3—981no—
706C3×ΓL(1,𝔽8)—71no—
707C3×ΓL(1,𝔽8)—141no—
708C3×ΓL(1,𝔽8)—146no—
709C23×C7—31no—
710C23×C7—31no—
711C23×C7—36no—
712C23×C7D3×AGL(1,𝔽7)11yescharacteristic, complemented
713C23×C7D3×AGL(1,𝔽7)11yescharacteristic, complemented
714C23×C7D3×AGL(1,𝔽7)16yescomplemented
715C22×D7—71no—
716C22×D7—71no—
717C22×D7—76no—
718C22×D7—71no—
719C22×D7—71no—
720C22×D7—76no—
721C22×D7—74no—
722C22×D7—74no—
723C22×D7—724no—
724C22×D7—144no—
725C22×D7—144no—
726C22×D7—1424no—
727C22×D7—214no—
728C22×D7—214no—
729C22×D7—2124no—
730C22×D7—211no—
731C22×D7—211no—
732C22×D7—216no—
733C22×D7—424no—
734C22×D7—424no—
735C22×D7—4224no—
736C7×D4—34no—
737C7×D4—34no—
738C7×D4—324no—
739C2×C4×C7—31no—
740C2×C4×C7—31no—
741C2×C4×C7—36no—
742C22⋊D7—214no—
743C22⋊D7—214no—
744C22⋊D7—2124no—
745C22⋊D7—214no—
746C22⋊D7—214no—
747C22⋊D7—2124no—
748C2×Dic7—211no—
749C2×Dic7—211no—
750C2×Dic7—216no—
751D28—214no—
752D28—214no—
753D28—2124no—
754C4×D7—214no—
755C4×D7—214no—
756C4×D7—2124no—
757C72C22×C3×#6711yescharacteristic, complemented, Sylow
758C24×C3—491no—
759C24×C3—491no—
760C24×C3—981no—
761C24×C3—1471no—
762C23×D3—491no—
763C2×C3×D4—2941no—
764C2×C3×D4—1471no—
765C2×C3×D4—1478no—
766C2×C3×D4—1471no—
767C2×C3×D4—1471no—
768C22×C3×C4—1471no—
769C2×#67—491no—
770C2×#67—491no—
771C2×#67—498no—
772C2×#67—491no—
773C2×#67#6442411yescharacteristic, direct product factor
774C22×Dic3—491no—
775C2×C3×C7—22no—
776C2×C3×C7—22no—
777C2×C3×C7—212no—
778C2×C3×C7D4×AGL(1,𝔽7)12yescomplemented
779C2×C3×C7D4×AGL(1,𝔽7)12yescomplemented
780C2×C3×C7D4×AGL(1,𝔽7)112yescomplemented
781C2×C3×C7C23×AGL(1,𝔽7)11yescharacteristic
782C2×C3×C7C23×AGL(1,𝔽7)11yescharacteristic
783C2×C3×C7C23×AGL(1,𝔽7)16yes—
784D21—142no—
785D21—142no—
786D21—1412no—
787C3×D7—74no—
788C3×D7—74no—
789C3×D7—724no—
790C3×D7—142no—
791C3×D7—142no—
792C3×D7—1412no—
793D3×C7—22no—
794D3×C7—22no—
795D3×C7—212no—
796C2×ΓL(1,𝔽8)—72no—
797C2×ΓL(1,𝔽8)—71no—
798C2×ΓL(1,𝔽8)—142no—
799C2×ΓL(1,𝔽8)—1412no—
800C2×ΓL(1,𝔽8)—141no—
801C2×ΓL(1,𝔽8)—146no—
802C2×ΓL(1,𝔽8)—142no—
803C2×ΓL(1,𝔽8)—142no—
804C2×ΓL(1,𝔽8)—142no—
805C2×ΓL(1,𝔽8)—141no—
806C2×ΓL(1,𝔽8)—282no—
807C2×ΓL(1,𝔽8)—2812no—
808C2×ΓL(1,𝔽8)—282no—
809C2×ΓL(1,𝔽8)—282no—
810C2×ΓL(1,𝔽8)—282no—
811C2×ΓL(1,𝔽8)—2812no—
812C2×ΓL(1,𝔽8)—2812no—
813C2×ΓL(1,𝔽8)—282no—
814C2×ΓL(1,𝔽8)—2812no—
815C2×ΓL(1,𝔽8)—281no—
816C2×ΓL(1,𝔽8)—286no—
817C2×ΓL(1,𝔽8)—422no—
818C2×ΓL(1,𝔽8)—842no—
819C2×ΓL(1,𝔽8)—8412no—
820AGL(1,𝔽7)—74no—
821AGL(1,𝔽7)—74no—
822AGL(1,𝔽7)—724no—
823AGL(1,𝔽7)—144no—
824AGL(1,𝔽7)—144no—
825AGL(1,𝔽7)—1424no—
826AGL(1,𝔽7)—142no—
827AGL(1,𝔽7)—142no—
828AGL(1,𝔽7)—1412no—
829AGL(1,𝔽7)—142no—
830AGL(1,𝔽7)—142no—
831AGL(1,𝔽7)—142no—
832AGL(1,𝔽7)—1412no—
833AGL(1,𝔽7)—142no—
834AGL(1,𝔽7)—1412no—
835AGL(1,𝔽7)—422no—
836AGL(1,𝔽7)—422no—
837AGL(1,𝔽7)—4212no—
838C22×C32—492no—
839C22×C32—494no—
840C22×C32—492no—
841C22×C32—988no—
842C22×C32—982no—
843C22×C32—981no—
844C22×C32—982no—
845C22×C32—1962no—
846C2×C3×D3—492no—
847C2×C3×D3—982no—
848C2×C3×D3—988no—
849C2×C3×D3—982no—
850C2×C3×D3—1962no—
851C3×Dic3—492no—
852C3×Dic3—982no—
853C22×D4—1471noSylow
854C22×C7—22no—
855C22×C7—22no—
856C22×C7—212no—
857C22×C7—32no—
858C22×C7—32no—
859C22×C7—312no—
860C22×C7—62no—
861C22×C7—62no—
862C22×C7—612no—
863C22×C7C2×D3×AGL(1,𝔽7)11yescharacteristic
864C22×C7C2×D3×AGL(1,𝔽7)11yescharacteristic
865C22×C7C2×D3×AGL(1,𝔽7)16yes—
866C22×C7C2×D3×AGL(1,𝔽7)12yescomplemented
867C22×C7C2×D3×AGL(1,𝔽7)12yescomplemented
868C22×C7C2×D3×AGL(1,𝔽7)112yescomplemented
869C2×D7—74no—
870C2×D7—74no—
871C2×D7—724no—
872C2×D7—72no—
873C2×D7—72no—
874C2×D7—712no—
875C2×D7—72no—
876C2×D7—72no—
877C2×D7—712no—
878C2×D7—148no—
879C2×D7—148no—
880C2×D7—1448no—
881C2×D7—142no—
882C2×D7—142no—
883C2×D7—1412no—
884C2×D7—212no—
885C2×D7—212no—
886C2×D7—2112no—
887C2×D7—428no—
888C2×D7—428no—
889C2×D7—4248no—
890C2×D7—422no—
891C2×D7—422no—
892C2×D7—4212no—
893C4×C7—32no—
894C4×C7—32no—
895C4×C7—312no—
896Dic7—212no—
897Dic7—212no—
898Dic7—2112no—
899C23×C3—2941no—
900C23×C3—2944no—
901C23×C3—491no—
902C23×C3—491no—
903C23×C3—491no—
904C23×C3—494no—
905C23×C3—491no—
906C23×C3—494no—
907C23×C3—981no—
908C23×C3—981no—
909C23×C3—984no—
910C23×C3—984no—
911C23×C3—984no—
912C23×C3—984no—
913C23×C3—984no—
914C23×C3—981no—
915C23×C3—1474no—
916C23×C3—1471no—
917C23×C3—1961no—
918C23×C3C2×#6442411yescharacteristic, complemented
919C22×D3—491no—
920C22×D3—494no—
921C22×D3—984no—
922C22×D3C2×#6442411yescharacteristic, complemented
923C3×D4—2944no—
924C3×D4—1474no—
925C3×D4—1474no—
926C3×D4—1474no—
927C2×C3×C4—2941no—
928C2×C3×C4—1474no—
929C2×C3×C4—1471no—
930#67—494no—
931#67—494no—
932#67—494no—
933#67C2×#6442414yesdirect product factor
934C2×Dic3—491no—
935C2×Dic3—494no—
936C2×Dic3C2×#6442411yescharacteristic, complemented
937C3×C7C2×D4×AGL(1,𝔽7)11yescharacteristic, complemented
938C3×C7C2×D4×AGL(1,𝔽7)11yescharacteristic, complemented
939C3×C7C2×D4×AGL(1,𝔽7)16yescomplemented
940ΓL(1,𝔽8)—71no—
941ΓL(1,𝔽8)—141no—
942ΓL(1,𝔽8)—146no—
943ΓL(1,𝔽8)—141no—
944ΓL(1,𝔽8)—281no—
945ΓL(1,𝔽8)—286no—
946C2×C32—494no—
947C2×C32—982no—
948C2×C32—981no—
949C2×C32—982no—
950C2×C32—1962no—
951C3×D3—982no—
952C3×D3—1962no—
953C24—491no—
954C24—1471no—
955C2×D4—31no—
956C2×D4—1471no—
957C2×D4—1478no—
958C2×D4—1471no—
959C2×D4—1471no—
960C22×C4—1471no—
961C2×C7—22no—
962C2×C7—22no—
963C2×C7—212no—
964C2×C7—62no—
965C2×C7—62no—
966C2×C7—612no—
967C2×C7#67×AGL(1,𝔽7)12yescomplemented
968C2×C7#67×AGL(1,𝔽7)12yescomplemented
969C2×C7#67×AGL(1,𝔽7)112yescomplemented
970C2×C7C22×D3×AGL(1,𝔽7)11yescharacteristic
971C2×C7C22×D3×AGL(1,𝔽7)11yescharacteristic
972C2×C7C22×D3×AGL(1,𝔽7)16yes—
973D7—74no—
974D7—74no—
975D7—724no—
976D7—142no—
977D7—142no—
978D7—1412no—
979D7—422no—
980D7—422no—
981D7—4212no—
982C22×C3—22no—
983C22×C3—2942no—
984C22×C3—2942no—
985C22×C3—2948no—
986C22×C3—492no—
987C22×C3—494no—
988C22×C3—492no—
989C22×C3—494no—
990C22×C3—492no—
991C22×C3—492no—
992C22×C3—5882no—
993C22×C3—982no—
994C22×C3—984no—
995C22×C3—982no—
996C22×C3—988no—
997C22×C3—988no—
998C22×C3—982no—
999C22×C3—988no—
1000C22×C3—982no—
1001C22×C3—988no—
1002C22×C3—982no—
1003C22×C3—982no—
1004C22×C3—981no—
1005C22×C3—982no—
1006C22×C3—1472no—
1007C22×C3—1962no—
1008C22×C3—1962no—
1009C22×C3—1962no—
1010C22×C3—1961no—
1011C22×C3—1962no—
1012C22×C3C22×#6442411yescharacteristic
1013C22×C3C22×#6442412yescomplemented
1014C2×D3—22no—
1015C2×D3—492no—
1016C2×D3—988no—
1017C2×D3—982no—
1018C2×D3C22×#6442412yescomplemented
1019C3×C4—2942no—
1020C3×C4—1472no—
1021Dic3—492no—
1022Dic3C22×#6442412yescomplemented
1023C32—981noSylow
1024C23—31no—
1025C23—2944no—
1026C23—491no—
1027C23—491no—
1028C23—494no—
1029C23—984no—
1030C23—1474no—
1031C23—1471no—
1032C23D3×#6442411yescharacteristic, complemented
1033D4—34no—
1034D4—1474no—
1035D4—1474no—
1036D4—1474no—
1037C2×C4—31no—
1038C2×C4—1474no—
1039C2×C4—1471no—
1040C7C2×#67×AGL(1,𝔽7)11yescharacteristic, complemented
1041C7C2×#67×AGL(1,𝔽7)11yescharacteristic, complemented
1042C7C2×#67×AGL(1,𝔽7)16yescomplemented
1043C2×C3—22no—
1044C2×C3—2942no—
1045C2×C3—494no—
1046C2×C3—494no—
1047C2×C3—5882no—
1048C2×C3—984no—
1049C2×C3—982no—
1050C2×C3—982no—
1051C2×C3—982no—
1052C2×C3—982no—
1053C2×C3—981no—
1054C2×C3—982no—
1055C2×C3—1962no—
1056C2×C3—1962no—
1057C2×C3—1962no—
1058C2×C3—1961no—
1059C2×C3—1962no—
1060C2×C3C23×#6442411yescharacteristic
1061C2×C3D4×#6442412yescomplemented
1062D3—22no—
1063D3—982no—
1064C22—22no—
1065C22—32no—
1066C22—62no—
1067C22—2948no—
1068C22—2942no—
1069C22—492no—
1070C22—494no—
1071C22—492no—
1072C22—988no—
1073C22—982no—
1074C22—1472no—
1075C22C2×D3×#6442411yescharacteristic
1076C22C2×D3×#6442412yescomplemented
1077C4—32no—
1078C4—1472no—
1079C3—981no—
1080C3—1961no—
1081C3C2×D4×#6442411yescharacteristic, complemented
1082C2—22no—
1083C2—62no—
1084C2—2942no—
1085C2—494no—
1086C2—982no—
1087C2C22×D3×#6442411yescharacteristic
1088C2#67×#6442412yesdirect product factor
subgroupG/H
centerC22C2×D3×#64424
commutator, cosocleC2×C3×C72C24×C3
FrattiniC2C22×D3×#64424
FittingC23×C3×C72C22×C3
socleC22×C3×C72C23×C3
hypercenterC23D3×#64424
hypocenterC3×C72C22×C3×D4
LCSG ▷ C2×C3×C72 ▷ C3×C72
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#72245929C2semidirect
2. C2×#72245938C2semidirect
3. C2×#72245919C2semidirect
4. C2×#67×#3861C2semidirect
5. C23×C3×#64424C2semidirect
6. C23×C3×#3861C22semidirect
7. #67×#64424C2direct (N × H)
8. #72245938C22semidirect
9. #72245929C22semidirect
10. #72245919C22semidirect
11. #67×#3861C22semidirect
12. C2×Dic3×#64424C2semidirect
13. C2×C3⋊#10596874C22semidirect
14. C2×Dic3×#3861C22semidirect
15. Dic3×#64424C22semidirect
16. C2×#67×C7⋊D7C3semidirect
17. C2×#11924240C2×C3semidirect
18. C2×#11924241C2×C3semidirect
19. C2×#11924293C2×C3semidirect
20. C2×C72×#67C2×C3semidirect
21. C23×C3×C7⋊D7C2×C3semidirect
22. #67×C7⋊D7C2×C3semidirect
23. C2×Dic3×C7⋊D7C2×C3semidirect
27. C22×D3×#64424C2semidirect
28. C22×D3×C7⋊D7C2×C3semidirect
29. C22×C3⋊#64424C22semidirect
30. C22×D3×#3861C22semidirect
33. C22×C3×#64424C22semidirect
34. C22×C3×#64424C22semidirect
36. C2×D3×#64424C22semidirect
46. C23×#64424D3semidirect
49. C22×C3×#3861C23semidirect
51. C2×D3×#3861C23semidirect
53. C2×C3⋊#64424C23semidirect
56. C2×C3×#64424D4semidirect
58. C2×C3×#64424C23semidirect
60. C3⋊#10596874C23semidirect
61. Dic3×#3861C23semidirect
63. C23×C3×C72C22×C3semidirect
64. C22×C3⋊(C7⋊D7)C22×C3semidirect
65. C22×D3×C72C22×C3semidirect
68. C22×C3×C7⋊D7C22×C3semidirect
69. C22×C3×C7⋊D7C22×C3semidirect
72. C23×#3861C2×D3semidirect
74. C2×D3×C7⋊D7C22×C3semidirect
85. C22×#64424C2×D3semidirect
86. C22×#64424C2×D3semidirect
87. #11924293C22×C3semidirect
88. C2×C3⋊(C7⋊Dic7)C22×C3semidirect
89. C72×#67C22×C3semidirect
90. C2×C72×Dic3C22×C3semidirect
93. #11924241C22×C3semidirect
94. #11924240C22×C3semidirect
95. Dic3×C7⋊D7C22×C3semidirect
126. C2×C3×#3861C2×D4semidirect
131. C3×#64424C2×D4semidirect
133. C23×C7⋊D7C3×D3semidirect
148. C22×C3×C72C23×C3semidirect
150. C2×C3⋊(C7⋊D7)C23×C3semidirect
152. C2×D3×C72C23×C3semidirect
155. C2×C3×C7⋊D7C3×D4semidirect
157. C2×C3×C7⋊D7C23×C3semidirect
166. C22×#3861C22×D3semidirect
180. C2×#64424#67direct (N × H)
182. C2×#64424C22×D3semidirect
183. C3⋊(C7⋊Dic7)C23×C3semidirect
184. C72×Dic3C23×C3semidirect
235. C3×#3861C22×D4semidirect
237. C23×C72C2×C3×D3semidirect
243. C22×C7⋊D7C2×C3×D3semidirect
244. C22×C7⋊D7C2×C3×D3semidirect
270. C2×C7×#67AGL(1,𝔽7)semidirect
271. C2×C7×#67AGL(1,𝔽7)semidirect
272. C2×C7×#67AGL(1,𝔽7)semidirect
304. C2×C3×C72C2×C3×D4semidirect
309. C3×C7⋊D7C2×C3×D4semidirect
316. C2×#3861C2×#67semidirect
323. #64424C2×#67direct (N × H)
377. C22×C72C22×C3×D3semidirect
383. C2×C7⋊D7C3×#67semidirect
385. C2×C7⋊D7C22×C3×D3semidirect
388. C23×C3×C7C2×AGL(1,𝔽7)semidirect
389. C23×C3×C7C2×AGL(1,𝔽7)semidirect
390. C23×C3×C7C2×AGL(1,𝔽7)semidirect
394. C22×D3×C7C2×AGL(1,𝔽7)semidirect
395. C22×D3×C7C2×AGL(1,𝔽7)semidirect
396. C22×D3×C7C2×AGL(1,𝔽7)semidirect
466. C7×#67C2×AGL(1,𝔽7)semidirect
467. C7×#67C2×AGL(1,𝔽7)semidirect
468. C7×#67C2×AGL(1,𝔽7)semidirect
469. C2×C7×Dic3C2×AGL(1,𝔽7)semidirect
470. C2×C7×Dic3C2×AGL(1,𝔽7)semidirect
471. C2×C7×Dic3C2×AGL(1,𝔽7)semidirect
502. C3×C72C22×C3×D4semidirect
504. #3861C22×#67semidirect
560. C2×C72C2×C3×#67semidirect
564. C7⋊D7C2×C3×#67semidirect
573. C22×C3×C7C22×AGL(1,𝔽7)semidirect
574. C22×C3×C7C22×AGL(1,𝔽7)semidirect
575. C22×C3×C7C22×AGL(1,𝔽7)semidirect
585. C2×D3×C7C22×AGL(1,𝔽7)semidirect
586. C2×D3×C7C22×AGL(1,𝔽7)semidirect
587. C2×D3×C7C22×AGL(1,𝔽7)semidirect
681. C7×Dic3C22×AGL(1,𝔽7)semidirect
682. C7×Dic3C22×AGL(1,𝔽7)semidirect
683. C7×Dic3C22×AGL(1,𝔽7)semidirect
712. C23×C7D3×AGL(1,𝔽7)semidirect
713. C23×C7D3×AGL(1,𝔽7)semidirect
714. C23×C7D3×AGL(1,𝔽7)semidirect
757. C72C22×C3×#67semidirect
773. C2×#67#64424direct (N × H)
778. C2×C3×C7D4×AGL(1,𝔽7)semidirect
779. C2×C3×C7D4×AGL(1,𝔽7)semidirect
780. C2×C3×C7D4×AGL(1,𝔽7)semidirect
866. C22×C7C2×D3×AGL(1,𝔽7)semidirect
867. C22×C7C2×D3×AGL(1,𝔽7)semidirect
868. C22×C7C2×D3×AGL(1,𝔽7)semidirect
918. C23×C3C2×#64424semidirect
922. C22×D3C2×#64424semidirect
933. #67C2×#64424direct (N × H)
936. C2×Dic3C2×#64424semidirect
937. C3×C7C2×D4×AGL(1,𝔽7)semidirect
938. C3×C7C2×D4×AGL(1,𝔽7)semidirect
939. C3×C7C2×D4×AGL(1,𝔽7)semidirect
967. C2×C7#67×AGL(1,𝔽7)semidirect
968. C2×C7#67×AGL(1,𝔽7)semidirect
969. C2×C7#67×AGL(1,𝔽7)semidirect
1013. C22×C3C22×#64424semidirect
1018. C2×D3C22×#64424semidirect
1022. Dic3C22×#64424semidirect
1032. C23D3×#64424semidirect
1040. C7C2×#67×AGL(1,𝔽7)semidirect
1041. C7C2×#67×AGL(1,𝔽7)semidirect
1042. C7C2×#67×AGL(1,𝔽7)semidirect
1061. C2×C3D4×#64424semidirect
1076. C22C2×D3×#64424semidirect
1081. C3C2×D4×#64424semidirect
1088. C2#67×#64424direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#722459292
C2×#722459382
C2×#722459192
C2×#67×#38612
C23×C3×#644242
#67×#644242
C2×Dic3×#644242
C2×#67×C7⋊D73
C2×#67×AGL(1,𝔽7)7
C22×D3×#644242
C2×D4×#644243