Finite Group Databasebeta

← C2×C3⋊D3×(C22⋊D7)⋊C3 #72245698

Subgroups — C2×C3⋊D3×(C22⋊D7)⋊C3 #72245698

Order 6048.

3264 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094714C211yesmaximal, characteristic, complemented
2C2×#13094716C211yesmaximal, characteristic, complemented
3C2×#13094760C211yesmaximal, characteristic, complemented
4C2×C32×(C22⋊D7)⋊C3C211yesmaximal, characteristic, complemented
5C23×C3⋊D3×ΓL(1,𝔽8)C211yesmaximal, characteristic, complemented
6C3⋊D3×(C22⋊D7)⋊C3C218yesmaximal, direct product factor
7C2×C3⋊D3×ΓL(1,𝔽8)⋊C4C211yesmaximal, characteristic, complemented
8C2×C3⋊D3×C22⋊D7C311yesmaximal, characteristic, complemented
9C2×D3×(C22⋊D7)⋊C3—34nomaximal
10C22×C3⋊D3×AGL(1,𝔽7)C211yesmaximal, characteristic, complemented
11C23×C32×ΓL(1,𝔽8)C2211yescharacteristic, complemented
12C22×C3⋊(C3⋊AGL(1,𝔽7))C2211yescharacteristic, complemented
13C22×C3⋊D3×ΓL(1,𝔽8)—24no—
14C22×C3⋊D3×ΓL(1,𝔽8)C2211yescharacteristic
15C22×C3⋊D3×ΓL(1,𝔽8)C2211yescharacteristic, complemented
16C22×C3⋊D3×ΓL(1,𝔽8)C2214yescomplemented
17C22×C32×AGL(1,𝔽7)C2211yescharacteristic, complemented
18C2×C3⋊D3×AGL(1,𝔽7)—24no—
19C2×C3⋊D3×AGL(1,𝔽7)C2214yescomplemented
20#13094760C2214yescomplemented
21C2×C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C2211yescharacteristic, complemented
22C32×(C22⋊D7)⋊C3C2214yescomplemented
23C2×C32×ΓL(1,𝔽8)⋊C4C2211yescharacteristic, complemented
24#13094716C2214yescomplemented
25#13094714C2214yescomplemented
26C3⋊D3×ΓL(1,𝔽8)⋊C4C2214yescomplemented
27C23×C7×C3⋊D3C2×C311yescharacteristic, complemented
28C22×D7×C3⋊D3C2×C311yescharacteristic, complemented
29C23×D3×ΓL(1,𝔽8)—34no—
30C22×D3×AGL(1,𝔽7)—34no—
31C2×#92726C2×C311yescharacteristic, complemented
32C2×C32×C22⋊D7C2×C311yescharacteristic, complemented
33C3⋊D3×C22⋊D7C2×C318yescomplemented
34C2×#92678C2×C311yescharacteristic, complemented
35C2×#92676C2×C311yescharacteristic, complemented
36C2×C3⋊D3×Dic7C2×C311yescharacteristic, complemented
37C2×#4268⋊C3—34no—
38C2×C3×(C22⋊D7)⋊C3—24no—
39C2×C3×(C22⋊D7)⋊C3D314yescomplemented
40D3×(C22⋊D7)⋊C3—332no—
41C2×#4247⋊C3—34no—
42C2×#4245⋊C3—34no—
43C2×D3×ΓL(1,𝔽8)⋊C4—34no—
44C2×C3×D4×C3⋊D3—71nomaximal, Hall
45C22×C32×ΓL(1,𝔽8)—22no—
46C22×C32×ΓL(1,𝔽8)C2311yescharacteristic
47C22×C32×ΓL(1,𝔽8)C2312yescomplemented
48C2×C3⋊(C3⋊AGL(1,𝔽7))—22no—
49C2×C3⋊(C3⋊AGL(1,𝔽7))C2312yescomplemented
50C2×C3⋊D3×ΓL(1,𝔽8)—22no—
51C2×C3⋊D3×ΓL(1,𝔽8)—28no—
52C2×C3⋊D3×ΓL(1,𝔽8)D414yescomplemented
53C2×C3⋊D3×ΓL(1,𝔽8)C2312yes—
54C2×C3⋊D3×ΓL(1,𝔽8)C2312yescomplemented
55C2×C32×AGL(1,𝔽7)—22no—
56C2×C32×AGL(1,𝔽7)C2312yescomplemented
57C3⋊D3×AGL(1,𝔽7)—28no—
58C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C2312yescomplemented
59C32×ΓL(1,𝔽8)⋊C4C2312yescomplemented
60C2×D3×C22⋊D7—34no—
61C22×(C22⋊D7)⋊C3—91no—
62C23×C32×C7C22×C311yescharacteristic, complemented
63C22×C3⋊D21C22×C311yescharacteristic, complemented
64C22×C7×C3⋊D3—24no—
65C22×C7×C3⋊D3C22×C311yescharacteristic
66C22×C7×C3⋊D3C22×C314yescomplemented
67C22×C7×C3⋊D3C22×C311yescharacteristic, complemented
68C22×C32×D7C22×C311yescharacteristic, complemented
69C23×C3×ΓL(1,𝔽8)—24no—
70C23×C3×ΓL(1,𝔽8)C2×D314yescomplemented
71C2×D7×C3⋊D3—24no—
72C2×D7×C3⋊D3C22×C314yescomplemented
73C22×C3⋊AGL(1,𝔽7)—34no—
74C22×D3×ΓL(1,𝔽8)—34no—
75C22×D3×ΓL(1,𝔽8)—34no—
76C22×D3×ΓL(1,𝔽8)—316no—
77C22×D3×ΓL(1,𝔽8)—616no—
78C22×C3×AGL(1,𝔽7)—24no—
79C22×C3×AGL(1,𝔽7)C2×D314yescomplemented
80C2×D3×AGL(1,𝔽7)—316no—
81C2×D3×AGL(1,𝔽7)—616no—
82#92726C22×C314yescomplemented
83C2×C3⋊Dic21C22×C311yescharacteristic, complemented
84C32×C22⋊D7C22×C314yescomplemented
85C2×C32×Dic7C22×C311yescharacteristic, complemented
86#92678C22×C314yescomplemented
87#92676C22×C314yescomplemented
88C3⋊D3×Dic7C22×C314yescomplemented
89#4268⋊C3—316no—
90C2×C3⋊(ΓL(1,𝔽8)⋊C4)—34no—
91C3×(C22⋊D7)⋊C3—216no—
92C3×(C22⋊D7)⋊C3C2×D3116yescomplemented
93C2×C3×ΓL(1,𝔽8)⋊C4—24no—
94C2×C3×ΓL(1,𝔽8)⋊C4C2×D314yescomplemented
95#4247⋊C3—316no—
96#4245⋊C3—316no—
97D3×ΓL(1,𝔽8)⋊C4—316no—
98C23×C3×C3⋊D3—71no—
99C23×C3×C3⋊D3—71no—
100C2×C33×D4—71no—
101C2×C3×#638—71no—
102C2×C3×#638—71no—
103C3×D4×C3⋊D3—78no—
104C2×C3×C4⋊(C3⋊D3)—71no—
105C2×C3×C4×C3⋊D3—71no—
106C2×C32×ΓL(1,𝔽8)—22no—
107C2×C32×ΓL(1,𝔽8)C2×D412yescomplemented
108C2×C32×ΓL(1,𝔽8)C2411yescharacteristic
109C3⋊(C3⋊AGL(1,𝔽7))—22no—
110C3⋊D3×ΓL(1,𝔽8)—22no—
111C3⋊D3×ΓL(1,𝔽8)C2×D414yescomplemented
112C32×AGL(1,𝔽7)—22no—
113C23×D3×C7—34no—
114C24×ΓL(1,𝔽8)—91no—
115C22×D3×D7—34no—
116C23×AGL(1,𝔽7)—91no—
117C2×#4268—34no—
118C2×C3×C22⋊D7C3×D314yescomplemented
119D3×C22⋊D7—332no—
120C2×#4247—34no—
121C2×#4245—34no—
122C2×D3×Dic7—34no—
123C2×(C22⋊D7)⋊C3—24no—
124C2×(C22⋊D7)⋊C3—91no—
125C2×(C22⋊D7)⋊C3—91no—
126C2×(C22⋊D7)⋊C3—98no—
127C2×(C22⋊D7)⋊C3—91no—
128C2×(C22⋊D7)⋊C3C3⋊D311yescharacteristic, direct product factor
129C22×ΓL(1,𝔽8)⋊C4—91no—
130C2×D4×C3⋊D3—71no—
131C2×C3×D3×D4—214no—
132C22×C32×C7—22no—
133C22×C32×C7C23×C311yescharacteristic
134C22×C32×C7C23×C312yescomplemented
135C2×C3⋊D21—22no—
136C2×C3⋊D21C23×C312yescomplemented
137C2×C7×C3⋊D3—22no—
138C2×C7×C3⋊D3—28no—
139C2×C7×C3⋊D3C3×D414yescomplemented
140C2×C7×C3⋊D3C23×C312yes—
141C2×C7×C3⋊D3C23×C312yescomplemented
142C2×C32×D7—22no—
143C2×C32×D7C23×C312yescomplemented
144C22×C3×ΓL(1,𝔽8)—28no—
145C22×C3×ΓL(1,𝔽8)—24no—
146C22×C3×ΓL(1,𝔽8)—28no—
147C22×C3×ΓL(1,𝔽8)—48no—
148C22×C3×ΓL(1,𝔽8)C22×D314yes—
149C22×C3×ΓL(1,𝔽8)C22×D318yescomplemented
150D7×C3⋊D3—28no—
151C2×C3⋊AGL(1,𝔽7)—38no—
152C2×C3⋊AGL(1,𝔽7)—68no—
153C2×D3×ΓL(1,𝔽8)—316no—
154C2×D3×ΓL(1,𝔽8)—38no—
155C2×D3×ΓL(1,𝔽8)—38no—
156C2×D3×ΓL(1,𝔽8)—632no—
157C2×D3×ΓL(1,𝔽8)—68no—
158C2×C3×AGL(1,𝔽7)—28no—
159C2×C3×AGL(1,𝔽7)—28no—
160C2×C3×AGL(1,𝔽7)—48no—
161C2×C3×AGL(1,𝔽7)C22×D318yescomplemented
162D3×AGL(1,𝔽7)—632no—
163C3⋊Dic21C23×C312yescomplemented
164C32×Dic7C23×C312yescomplemented
165C3⋊(ΓL(1,𝔽8)⋊C4)—38no—
166C3×ΓL(1,𝔽8)⋊C4—28no—
167C3×ΓL(1,𝔽8)⋊C4C22×D318yescomplemented
168C22×C22⋊D7—91noHall
169C23×C33—71no—
170C23×C33—71no—
171C22×C3×C3⋊D3—71no—
172C22×C3×C3⋊D3—71no—
173C22×C3×C3⋊D3—74no—
174C22×C3×C3⋊D3—71no—
175C22×C3×C3⋊D3—74no—
176C22×C3×C3⋊D3—144no—
177C22×C3×C3⋊D3—144no—
178C33×D4—74no—
179C2×C33×C4—71no—
180C3×#638—74no—
181C3×#638—74no—
182C2×C3×C3⋊Dic3—71no—
183C3×C4⋊(C3⋊D3)—74no—
184C3×C4×C3⋊D3—74no—
185C32×ΓL(1,𝔽8)C22×D411yescharacteristic, complemented, Hall
186C23×C3×C7C2×C3×D314yescomplemented
187C22×D21—34no—
188C22×D3×C7—34no—
189C22×D3×C7—34no—
190C22×D3×C7—316no—
191C22×D3×C7—616no—
192C22×C3×D7C2×C3×D314yescomplemented
193C23×ΓL(1,𝔽8)—24no—
194C23×ΓL(1,𝔽8)—91no—
195C23×ΓL(1,𝔽8)—91no—
196C23×ΓL(1,𝔽8)—94no—
197C23×ΓL(1,𝔽8)—184no—
198C23×ΓL(1,𝔽8)C2×C3⋊D311yescharacteristic, complemented
199C2×D3×D7—316no—
200C2×D3×D7—616no—
201C22×AGL(1,𝔽7)—24no—
202C22×AGL(1,𝔽7)—91no—
203C22×AGL(1,𝔽7)—94no—
204C22×AGL(1,𝔽7)—184no—
205C22×AGL(1,𝔽7)C2×C3⋊D311yescharacteristic, complemented
206#4268—316no—
207C2×Dic21—34no—
208C3×C22⋊D7C2×C3×D3116yescomplemented
209C2×C3×Dic7C2×C3×D314yescomplemented
210#4247—316no—
211#4245—316no—
212D3×Dic7—316no—
213(C22⋊D7)⋊C3—216no—
214(C22⋊D7)⋊C3—94no—
215(C22⋊D7)⋊C3—94no—
216(C22⋊D7)⋊C3—94no—
217(C22⋊D7)⋊C3C2×C3⋊D314yesdirect product factor
218C2×ΓL(1,𝔽8)⋊C4—24no—
219C2×ΓL(1,𝔽8)⋊C4—91no—
220C2×ΓL(1,𝔽8)⋊C4—94no—
221C2×ΓL(1,𝔽8)⋊C4C2×C3⋊D311yescharacteristic, complemented
222C23×C3⋊D3—71no—
223C23×C3⋊D3AGL(1,𝔽7)11yescharacteristic, complemented
224C23×C3×D3—214no—
225C23×C3×D3—424no—
226C2×C32×D4—74no—
227C2×C32×D4—71no—
228C2×C32×D4—144no—
229C2×#638—71no—
230C2×#638—71no—
231D4×C3⋊D3—78no—
232C2×C4⋊(C3⋊D3)—71no—
233C2×C4×C3⋊D3—71no—
234C2×C3×#67—214no—
235C2×C3×#67—214no—
236C3×D3×D4—2132no—
237C2×C3×D12—214no—
238C2×C3×C4×D3—214no—
239C2×C32×C7—22no—
240C2×C32×C7C2×C3×D412yescomplemented
241C2×C32×C7C24×C311yescharacteristic
242C3⋊D21—22no—
243C7×C3⋊D3—22no—
244C7×C3⋊D3C2×C3×D414yescomplemented
245C32×D7—22no—
246C2×C3×ΓL(1,𝔽8)—28no—
247C2×C3×ΓL(1,𝔽8)—24no—
248C2×C3×ΓL(1,𝔽8)—28no—
249C2×C3×ΓL(1,𝔽8)—48no—
250C2×C3×ΓL(1,𝔽8)D3×D418yescomplemented
251C2×C3×ΓL(1,𝔽8)C23×D314yes—
252C3⋊AGL(1,𝔽7)—68no—
253D3×ΓL(1,𝔽8)—316no—
254D3×ΓL(1,𝔽8)—68no—
255C3×AGL(1,𝔽7)—28no—
256C3×AGL(1,𝔽7)—48no—
257C24×C7—91no—
258C23×D7—91no—
259C2×C22⋊D7—91no—
260C2×C22⋊D7—91no—
261C2×C22⋊D7—98no—
262C2×C22⋊D7—91no—
263C2×C22⋊D7C3×C3⋊D311yescharacteristic, complemented
264C22×Dic7—91no—
265C22×C33—71no—
266C22×C33—72no—
267C22×C33—72no—
268C22×C33—142no—
269C22×C33—142no—
270C2×C3×C3⋊D3—74no—
271C2×C3×C3⋊D3—72no—
272C2×C3×C3⋊D3—72no—
273C2×C3×C3⋊D3—72no—
274C2×C3×C3⋊D3—148no—
275C2×C3×C3⋊D3—148no—
276C2×C3×C3⋊D3—142no—
277C2×C3×C3⋊D3—142no—
278C33×C4—72no—
279C3×C3⋊Dic3—72no—
280C22×C3×D4—631no—
281C2×D3×D4—214no—
282C22×C3×C7—28no—
283C22×C3×C7C22×C3×D314yes—
284C22×C3×C7C22×C3×D318yescomplemented
285C2×D21—38no—
286C2×D21—68no—
287C2×D3×C7—38no—
288C2×D3×C7—316no—
289C2×D3×C7—38no—
290C2×D3×C7—632no—
291C2×D3×C7—68no—
292C2×C3×D7—28no—
293C2×C3×D7C22×C3×D318yescomplemented
294C22×ΓL(1,𝔽8)—22no—
295C22×ΓL(1,𝔽8)—24no—
296C22×ΓL(1,𝔽8)—28no—
297C22×ΓL(1,𝔽8)—48no—
298C22×ΓL(1,𝔽8)—92no—
299C22×ΓL(1,𝔽8)—94no—
300C22×ΓL(1,𝔽8)—92no—
301C22×ΓL(1,𝔽8)—188no—
302C22×ΓL(1,𝔽8)—182no—
303C22×ΓL(1,𝔽8)C22×C3⋊D311yescharacteristic
304C22×ΓL(1,𝔽8)C22×C3⋊D312yescomplemented
305D3×D7—632no—
306C2×AGL(1,𝔽7)—22no—
307C2×AGL(1,𝔽7)—28no—
308C2×AGL(1,𝔽7)—48no—
309C2×AGL(1,𝔽7)—92no—
310C2×AGL(1,𝔽7)—188no—
311C2×AGL(1,𝔽7)—182no—
312C2×AGL(1,𝔽7)C22×C3⋊D312yescomplemented
313Dic21—38no—
314C3×Dic7C22×C3×D318yescomplemented
315ΓL(1,𝔽8)⋊C4—28no—
316ΓL(1,𝔽8)⋊C4—92no—
317ΓL(1,𝔽8)⋊C4C22×C3⋊D312yescomplemented
318C23×C32—71no—
319C23×C32—74no—
320C23×C32—144no—
321C23×C32—144no—
322C23×C32—284no—
323C23×C32C2×AGL(1,𝔽7)11yescharacteristic, complemented
324C22×C3⋊D3—24no—
325C22×C3⋊D3—71no—
326C22×C3⋊D3—74no—
327C22×C3⋊D3—144no—
328C22×C3⋊D3C2×AGL(1,𝔽7)11yescharacteristic
329C22×C3⋊D3C2×AGL(1,𝔽7)14yescomplemented
330C22×C3⋊D3C2×AGL(1,𝔽7)11yescharacteristic, complemented
331C22×C3×D3—214no—
332C22×C3×D3—2116no—
333C22×C3×D3—424no—
334C22×C3×D3—424no—
335C22×C3×D3—4216no—
336C22×C3×D3—4216no—
337C22×C3×D3—4216no—
338C32×D4—74no—
339C32×D4—716no—
340C32×D4—1416no—
341C2×C32×C4—71no—
342C2×C32×C4—74no—
343C2×C32×C4—144no—
344#638—74no—
345#638—74no—
346C2×C3⋊Dic3—71no—
347C4⋊(C3⋊D3)—74no—
348C4×C3⋊D3—74no—
349C3×#67—2116no—
350C3×#67—2116no—
351C2×C3×Dic3—214no—
352C3×D12—2116no—
353C3×C4×D3—2116no—
354C32×C7C22×C3×D411yescharacteristic, complemented
355C3×ΓL(1,𝔽8)—24no—
356C3×ΓL(1,𝔽8)C2×D3×D414yescomplemented
357C23×C7—91no—
358C23×C7—91no—
359C23×C7—94no—
360C23×C7—184no—
361C23×C7C2×C3×C3⋊D311yescharacteristic, complemented
362C22×D7—91no—
363C22×D7—94no—
364C22×D7—184no—
365C22×D7C2×C3×C3⋊D311yescharacteristic, complemented
366C22⋊D7—94no—
367C22⋊D7—94no—
368C22⋊D7—94no—
369C22⋊D7C2×C3×C3⋊D314yescomplemented
370C2×Dic7—91no—
371C2×Dic7—94no—
372C2×Dic7C2×C3×C3⋊D311yescharacteristic, complemented
373C2×C33—72no—
374C2×C33—71no—
375C2×C33—142no—
376C2×C33—142no—
377C3×C3⋊D3—74no—
378C3×C3⋊D3—142no—
379C3×C3⋊D3—142no—
380C24×C3—631no—
381C24×C3—1261no—
382C23×D3—34no—
383C23×D3—214no—
384C2×C3×D4—71no—
385C2×C3×D4—74no—
386C2×C3×D4—144no—
387C2×C3×D4—631no—
388C2×C3×D4—638no—
389C2×C3×D4—631no—
390C2×C3×D4—631no—
391C22×C3×C4—631no—
392C2×#67—214no—
393C2×#67—214no—
394D3×D4—2132no—
395C2×D12—214no—
396C2×C4×D3—214no—
397C2×C3×C7—28no—
398C2×C3×C7C3×D3×D418yescomplemented
399C2×C3×C7C23×C3×D314yes—
400D21—68no—
401C3×D7—28no—
402D3×C7—316no—
403D3×C7—68no—
404C2×ΓL(1,𝔽8)—22no—
405C2×ΓL(1,𝔽8)—24no—
406C2×ΓL(1,𝔽8)—28no—
407C2×ΓL(1,𝔽8)—48no—
408C2×ΓL(1,𝔽8)—94no—
409C2×ΓL(1,𝔽8)—182no—
410C2×ΓL(1,𝔽8)D4×C3⋊D312yescomplemented
411C2×ΓL(1,𝔽8)C23×C3⋊D311yescharacteristic
412AGL(1,𝔽7)—22no—
413AGL(1,𝔽7)—48no—
414AGL(1,𝔽7)—182no—
415C22×C32—22no—
416C22×C32—72no—
417C22×C32—78no—
418C22×C32—148no—
419C22×C32—148no—
420C22×C32—142no—
421C22×C32—148no—
422C22×C32—144no—
423C22×C32—148no—
424C22×C32—288no—
425C22×C32—288no—
426C22×C32—284no—
427C22×C32—288no—
428C22×C32C22×AGL(1,𝔽7)11yescharacteristic
429C22×C32C22×AGL(1,𝔽7)12yescomplemented
430C2×C3⋊D3—22no—
431C2×C3⋊D3—28no—
432C2×C3⋊D3—72no—
433C2×C3⋊D3—142no—
434C2×C3⋊D3—148no—
435C2×C3⋊D3(C22⋊D7)⋊C314yesdirect product factor
436C2×C3⋊D3C22×AGL(1,𝔽7)12yes—
437C2×C3⋊D3C22×AGL(1,𝔽7)12yescomplemented
438C2×C3×D3—218no—
439C2×C3×D3—428no—
440C2×C3×D3—4216no—
441C2×C3×D3—428no—
442C2×C3×D3—4232no—
443C2×C3×D3—428no—
444C2×C3×D3—4232no—
445C2×C3×D3—428no—
446C32×C4—72no—
447C32×C4—78no—
448C32×C4—148no—
449C3⋊Dic3—72no—
450C3×Dic3—218no—
451C22×D4—631noSylow
452C22×C7—22no—
453C22×C7—92no—
454C22×C7—94no—
455C22×C7—92no—
456C22×C7—188no—
457C22×C7—182no—
458C22×C7C22×C3×C3⋊D311yescharacteristic
459C22×C7C22×C3×C3⋊D312yescomplemented
460C2×D7—22no—
461C2×D7—92no—
462C2×D7—188no—
463C2×D7—182no—
464C2×D7C22×C3×C3⋊D312yescomplemented
465Dic7—92no—
466Dic7C22×C3×C3⋊D312yescomplemented
467C33—71noSylow
468C23×C3—71no—
469C23×C3—74no—
470C23×C3—144no—
471C23×C3—141no—
472C23×C3—284no—
473C23×C3—634no—
474C23×C3—631no—
475C23×C3—1261no—
476C23×C3—1264no—
477C23×C3—1261no—
478C23×C3—1264no—
479C23×C3—1264no—
480C23×C3D3×AGL(1,𝔽7)14yescomplemented
481C22×D3—34no—
482C22×D3—34no—
483C22×D3—316no—
484C22×D3—616no—
485C22×D3—2116no—
486C22×D3—214no—
487C22×D3—4216no—
488C3×D4—74no—
489C3×D4—716no—
490C3×D4—1416no—
491C3×D4—634no—
492C3×D4—634no—
493C3×D4—634no—
494C2×C3×C4—71no—
495C2×C3×C4—74no—
496C2×C3×C4—144no—
497C2×C3×C4—634no—
498C2×C3×C4—631no—
499#67—2116no—
500#67—2116no—
501C2×Dic3—214no—
502D12—2116no—
503C4×D3—2116no—
504C3×C7C2×C3×D3×D414yescomplemented
505ΓL(1,𝔽8)—24no—
506ΓL(1,𝔽8)C2×D4×C3⋊D311yescharacteristic, complemented
507C2×C32—22no—
508C2×C32—148no—
509C2×C32—142no—
510C2×C32—148no—
511C2×C32—148no—
512C2×C32—144no—
513C2×C32—288no—
514C2×C32—288no—
515C2×C32—288no—
516C2×C32—284no—
517C2×C32C2×(C22⋊D7)⋊C312yescomplemented
518C2×C32C23×AGL(1,𝔽7)11yescharacteristic
519C3⋊D3—22no—
520C3⋊D3—142no—
521C3⋊D3C2×(C22⋊D7)⋊C314yesdirect product factor
522C3×D3—4216no—
523C3×D3—428no—
524C3×D3—428no—
525C24—91no—
526C24—631no—
527C2×D4—71no—
528C2×D4—631no—
529C2×D4—638no—
530C2×D4—631no—
531C2×D4—631no—
532C22×C4—631no—
533C2×C7—22no—
534C2×C7—94no—
535C2×C7—182no—
536C2×C7C3×D4×C3⋊D312yescomplemented
537C2×C7C23×C3×C3⋊D311yescharacteristic
538D7—22no—
539D7—182no—
540C22×C3—28no—
541C22×C3—72no—
542C22×C3—78no—
543C22×C3—142no—
544C22×C3—148no—
545C22×C3—142no—
546C22×C3—148no—
547C22×C3—141no—
548C22×C3—142no—
549C22×C3—288no—
550C22×C3—288no—
551C22×C3—284no—
552C22×C3—288no—
553C22×C3—632no—
554C22×C3—1262no—
555C22×C3—1262no—
556C22×C3—1264no—
557C22×C3—1268no—
558C22×C3—1262no—
559C22×C3—1268no—
560C22×C3—1262no—
561C22×C3C2×D3×AGL(1,𝔽7)14yes—
562C22×C3C2×D3×AGL(1,𝔽7)18yescomplemented
563C2×D3—316no—
564C2×D3—38no—
565C2×D3—38no—
566C2×D3—632no—
567C2×D3—68no—
568C2×D3—218no—
569C2×D3—4232no—
570C2×D3—428no—
571C3×C4—72no—
572C3×C4—78no—
573C3×C4—148no—
574C3×C4—632no—
575Dic3—218no—
576C32—144no—
577C32—284no—
578C32C22×(C22⋊D7)⋊C311yescharacteristic, complemented
579C23—71no—
580C23—91no—
581C23—91no—
582C23—94no—
583C23—184no—
584C23—634no—
585C23—631no—
586C23—1264no—
587C23C3⋊D3×AGL(1,𝔽7)11yescharacteristic, complemented
588D4—74no—
589D4—634no—
590D4—634no—
591D4—634no—
592C2×C4—71no—
593C2×C4—634no—
594C2×C4—631no—
595C7C2×C3×D4×C3⋊D311yescharacteristic, complemented, Sylow
596C2×C3—28no—
597C2×C3—142no—
598C2×C3—142no—
599C2×C3—148no—
600C2×C3—142no—
601C2×C3—141no—
602C2×C3—288no—
603C2×C3—288no—
604C2×C3—288no—
605C2×C3—284no—
606C2×C3—1264no—
607C2×C3—1262no—
608C2×C3—1262no—
609C2×C3D3×(C22⋊D7)⋊C318yescomplemented
610C2×C3C22×D3×AGL(1,𝔽7)14yes—
611D3—316no—
612D3—68no—
613D3—428no—
614C22—22no—
615C22—72no—
616C22—94no—
617C22—92no—
618C22—92no—
619C22—142no—
620C22—188no—
621C22—182no—
622C22—632no—
623C22—1268no—
624C22—1262no—
625C22C2×C3⋊D3×AGL(1,𝔽7)11yescharacteristic
626C22C2×C3⋊D3×AGL(1,𝔽7)12yescomplemented
627C4—72no—
628C4—632no—
629C3—141no—
630C3—284no—
631C3C2×D3×(C22⋊D7)⋊C314yescomplemented
632C2—22no—
633C2—94no—
634C2—142no—
635C2—182no—
636C2—1262no—
637C2C22×C3⋊D3×AGL(1,𝔽7)11yescharacteristic
638C2C3⋊D3×(C22⋊D7)⋊C312yesdirect product factor
subgroupG/H
centerC22C2×C3⋊D3×AGL(1,𝔽7)
commutator, cosocleC2×C32×C7C24×C3
FrattiniC2C22×C3⋊D3×AGL(1,𝔽7)
FittingC23×C32×C7C22×C3
socleC22×C32×C7C23×C3
hypercenterC23C3⋊D3×AGL(1,𝔽7)
hypocenterC32×C7C22×C3×D4
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#13094714C2semidirect
2. C2×#13094716C2semidirect
3. C2×#13094760C2semidirect
4. C2×C32×(C22⋊D7)⋊C3C2semidirect
5. C23×C3⋊D3×ΓL(1,𝔽8)C2semidirect
6. C3⋊D3×(C22⋊D7)⋊C3C2direct (N × H)
7. C2×C3⋊D3×ΓL(1,𝔽8)⋊C4C2semidirect
8. C2×C3⋊D3×C22⋊D7C3semidirect
10. C22×C3⋊D3×AGL(1,𝔽7)C2semidirect
11. C23×C32×ΓL(1,𝔽8)C22semidirect
12. C22×C3⋊(C3⋊AGL(1,𝔽7))C22semidirect
15. C22×C3⋊D3×ΓL(1,𝔽8)C22semidirect
16. C22×C3⋊D3×ΓL(1,𝔽8)C22semidirect
17. C22×C32×AGL(1,𝔽7)C22semidirect
19. C2×C3⋊D3×AGL(1,𝔽7)C22semidirect
20. #13094760C22semidirect
21. C2×C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C22semidirect
22. C32×(C22⋊D7)⋊C3C22semidirect
23. C2×C32×ΓL(1,𝔽8)⋊C4C22semidirect
24. #13094716C22semidirect
25. #13094714C22semidirect
26. C3⋊D3×ΓL(1,𝔽8)⋊C4C22semidirect
27. C23×C7×C3⋊D3C2×C3semidirect
28. C22×D7×C3⋊D3C2×C3semidirect
31. C2×#92726C2×C3semidirect
32. C2×C32×C22⋊D7C2×C3semidirect
33. C3⋊D3×C22⋊D7C2×C3semidirect
34. C2×#92678C2×C3semidirect
35. C2×#92676C2×C3semidirect
36. C2×C3⋊D3×Dic7C2×C3semidirect
39. C2×C3×(C22⋊D7)⋊C3D3semidirect
47. C22×C32×ΓL(1,𝔽8)C23semidirect
49. C2×C3⋊(C3⋊AGL(1,𝔽7))C23semidirect
52. C2×C3⋊D3×ΓL(1,𝔽8)D4semidirect
54. C2×C3⋊D3×ΓL(1,𝔽8)C23semidirect
56. C2×C32×AGL(1,𝔽7)C23semidirect
58. C3⋊(C3⋊(ΓL(1,𝔽8)⋊C4))C23semidirect
59. C32×ΓL(1,𝔽8)⋊C4C23semidirect
62. C23×C32×C7C22×C3semidirect
63. C22×C3⋊D21C22×C3semidirect
66. C22×C7×C3⋊D3C22×C3semidirect
67. C22×C7×C3⋊D3C22×C3semidirect
68. C22×C32×D7C22×C3semidirect
70. C23×C3×ΓL(1,𝔽8)C2×D3semidirect
72. C2×D7×C3⋊D3C22×C3semidirect
79. C22×C3×AGL(1,𝔽7)C2×D3semidirect
82. #92726C22×C3semidirect
83. C2×C3⋊Dic21C22×C3semidirect
84. C32×C22⋊D7C22×C3semidirect
85. C2×C32×Dic7C22×C3semidirect
86. #92678C22×C3semidirect
87. #92676C22×C3semidirect
88. C3⋊D3×Dic7C22×C3semidirect
92. C3×(C22⋊D7)⋊C3C2×D3semidirect
94. C2×C3×ΓL(1,𝔽8)⋊C4C2×D3semidirect
107. C2×C32×ΓL(1,𝔽8)C2×D4semidirect
111. C3⋊D3×ΓL(1,𝔽8)C2×D4semidirect
118. C2×C3×C22⋊D7C3×D3semidirect
128. C2×(C22⋊D7)⋊C3C3⋊D3direct (N × H)
134. C22×C32×C7C23×C3semidirect
136. C2×C3⋊D21C23×C3semidirect
139. C2×C7×C3⋊D3C3×D4semidirect
141. C2×C7×C3⋊D3C23×C3semidirect
143. C2×C32×D7C23×C3semidirect
149. C22×C3×ΓL(1,𝔽8)C22×D3semidirect
161. C2×C3×AGL(1,𝔽7)C22×D3semidirect
163. C3⋊Dic21C23×C3semidirect
164. C32×Dic7C23×C3semidirect
167. C3×ΓL(1,𝔽8)⋊C4C22×D3semidirect
185. C32×ΓL(1,𝔽8)C22×D4semidirect
186. C23×C3×C7C2×C3×D3semidirect
192. C22×C3×D7C2×C3×D3semidirect
198. C23×ΓL(1,𝔽8)C2×C3⋊D3semidirect
205. C22×AGL(1,𝔽7)C2×C3⋊D3semidirect
208. C3×C22⋊D7C2×C3×D3semidirect
209. C2×C3×Dic7C2×C3×D3semidirect
217. (C22⋊D7)⋊C3C2×C3⋊D3direct (N × H)
221. C2×ΓL(1,𝔽8)⋊C4C2×C3⋊D3semidirect
223. C23×C3⋊D3AGL(1,𝔽7)semidirect
240. C2×C32×C7C2×C3×D4semidirect
244. C7×C3⋊D3C2×C3×D4semidirect
250. C2×C3×ΓL(1,𝔽8)D3×D4semidirect
263. C2×C22⋊D7C3×C3⋊D3semidirect
284. C22×C3×C7C22×C3×D3semidirect
293. C2×C3×D7C22×C3×D3semidirect
304. C22×ΓL(1,𝔽8)C22×C3⋊D3semidirect
312. C2×AGL(1,𝔽7)C22×C3⋊D3semidirect
314. C3×Dic7C22×C3×D3semidirect
317. ΓL(1,𝔽8)⋊C4C22×C3⋊D3semidirect
323. C23×C32C2×AGL(1,𝔽7)semidirect
329. C22×C3⋊D3C2×AGL(1,𝔽7)semidirect
330. C22×C3⋊D3C2×AGL(1,𝔽7)semidirect
354. C32×C7C22×C3×D4semidirect
356. C3×ΓL(1,𝔽8)C2×D3×D4semidirect
361. C23×C7C2×C3×C3⋊D3semidirect
365. C22×D7C2×C3×C3⋊D3semidirect
369. C22⋊D7C2×C3×C3⋊D3semidirect
372. C2×Dic7C2×C3×C3⋊D3semidirect
398. C2×C3×C7C3×D3×D4semidirect
410. C2×ΓL(1,𝔽8)D4×C3⋊D3semidirect
429. C22×C32C22×AGL(1,𝔽7)semidirect
435. C2×C3⋊D3(C22⋊D7)⋊C3direct (N × H)
437. C2×C3⋊D3C22×AGL(1,𝔽7)semidirect
459. C22×C7C22×C3×C3⋊D3semidirect
464. C2×D7C22×C3×C3⋊D3semidirect
466. Dic7C22×C3×C3⋊D3semidirect
480. C23×C3D3×AGL(1,𝔽7)semidirect
504. C3×C7C2×C3×D3×D4semidirect
506. ΓL(1,𝔽8)C2×D4×C3⋊D3semidirect
517. C2×C32C2×(C22⋊D7)⋊C3semidirect
521. C3⋊D3C2×(C22⋊D7)⋊C3direct (N × H)
536. C2×C7C3×D4×C3⋊D3semidirect
562. C22×C3C2×D3×AGL(1,𝔽7)semidirect
578. C32C22×(C22⋊D7)⋊C3semidirect
587. C23C3⋊D3×AGL(1,𝔽7)semidirect
595. C7C2×C3×D4×C3⋊D3semidirect
609. C2×C3D3×(C22⋊D7)⋊C3semidirect
626. C22C2×C3⋊D3×AGL(1,𝔽7)semidirect
631. C3C2×D3×(C22⋊D7)⋊C3semidirect
638. C2C3⋊D3×(C22⋊D7)⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#130947142
C2×#130947162
C2×#130947602
C2×C32×(C22⋊D7)⋊C32
C23×C3⋊D3×ΓL(1,𝔽8)2
C3⋊D3×(C22⋊D7)⋊C32
C2×C3⋊D3×ΓL(1,𝔽8)⋊C42
C2×C3⋊D3×C22⋊D73
C2×D3×(C22⋊D7)⋊C33
C22×C3⋊D3×AGL(1,𝔽7)2
C2×C3×D4×C3⋊D37