Finite Group Databasebeta

← #15676209

Subgroups — #15676209

Order 2944.

540 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625118C211yesmaximal, characteristic
2#13092324C211yesmaximal, characteristic, complemented
3#13092309C211yesmaximal, characteristic, complemented
4#13092308C211yesmaximal, characteristic, complemented
5#13092307C211yesmaximal, characteristic, complemented
6#13092306C211yesmaximal, characteristic, complemented
7#13092295C211yesmaximal, characteristic
8#13092295C211yesmaximal, characteristic
9#13092291C211yesmaximal, characteristic, complemented
10#13092288C211yesmaximal, characteristic, complemented
11#13092284C211yesmaximal, characteristic, complemented
12#13092268C211yesmaximal, characteristic, complemented
13C4×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
14#13092264C211yesmaximal, characteristic, complemented
15C23×#391C211yesmaximal, characteristic, complemented
16C22×Q8×C23C2211yescharacteristic
17C22×D92C2211yescharacteristic
18C22×C4×D23C2211yescharacteristic
19C22×C4×D23C2211yescharacteristic
20C2×C4⋊C4×C23C2211yescharacteristic
21C2×C42×C23C2211yescharacteristic
22#10625118C418yescomplemented
23C2×(C2×D23)⋊C4C2211yescharacteristic
24C2×(C2×D23)⋊C4C2211yescharacteristic
25C2×(C2×D23)⋊C4C2211yescharacteristic
26C2×(C2×D23)⋊C4C2211yescharacteristic
27C2×(C2×D23)⋊C4C2211yescharacteristic
28C2×(C2×D23)⋊C4C2211yescharacteristic
29C2×(C2×D23)⋊C4C2211yescharacteristic
30C2×(C2×D23)⋊C4C2211yescharacteristic
31C2×(C2×D23)⋊C4C2211yescharacteristic
32C2×(C2×D23)⋊C4C2211yescharacteristic
33C2×C4⋊Dic23C2211yescharacteristic
34C2×Dic23⋊C4C2211yescharacteristic
35C2×Dic23⋊C4C2211yescharacteristic
36C2×C4×Dic23C2211yescharacteristic
37C2×C4×Dic23C2211yescharacteristic
38C2×C4×Dic23C2211yescharacteristic
39C2×C4×Dic23C2211yescharacteristic
40C23×#95C2211yescharacteristic
41C23×#95C2211yescharacteristic
42C23×#95C2211yescharacteristic
43C23×#95C2211yescharacteristic
44C23⋊#95C2211yescharacteristic
45C23⋊#95C2211yescharacteristic
46C23⋊#95C2211yescharacteristic
47C23⋊#95C2211yescharacteristic
48C23⋊#95C2211yescharacteristic
49C23⋊#95C2211yescharacteristic
50C23⋊#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C23×D23C2311yescharacteristic
53C23×D23C2311yescharacteristic
54C2×Q8×C23—41no—
55C2×Q8×C23—41no—
56C2×Q8×C23C2×C414yescomplemented
57C22×C4×C23C2311yescharacteristic
58C22×C4×C23C2311yescharacteristic
59C22×C4×C23C2311yescharacteristic
60C22×C4×C23C2311yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C22×C4×C23C2311yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C22×Dic23C2311yescharacteristic
65C22×Dic23C2311yescharacteristic
66C22×Dic23C2311yescharacteristic
67C22×Dic23C2311yescharacteristic
68C22×Dic23C2311yescharacteristic
69C22×Dic23C2311yescharacteristic
70C2×D92—41no—
71C2×D92—41no—
72C2×D92C2×C414yes—
73C2×C4×D23—22no—
74C2×C4×D23—22no—
75C2×C4×D23—41no—
76C2×C4×D23—41no—
77C2×C4×D23—41no—
78C2×C4×D23—41no—
79C4⋊C4×C23—41no—
80C42×C23—41no—
81(C2×D23)⋊C4—22no—
82(C2×D23)⋊C4—22no—
83(C2×D23)⋊C4—41no—
84(C2×D23)⋊C4—41no—
85(C2×D23)⋊C4—41no—
86(C2×D23)⋊C4—41no—
87(C2×D23)⋊C4C2×C414yescomplemented
88(C2×D23)⋊C4C2×C414yescomplemented
89(C2×D23)⋊C4C2×C414yescomplemented
90(C2×D23)⋊C4C2×C414yescomplemented
91C4⋊Dic23—41no—
92Dic23⋊C4—22no—
93Dic23⋊C4—22no—
94C4×Dic23—41no—
95C4×Dic23—41no—
96C4×Dic23—41no—
97C4×Dic23C2×C414yescomplemented
98C23×C23C2411yescharacteristic
99C22×D23—21no—
100C22×D23—21no—
101C22×D23—21no—
102C22×D23—21no—
103C22×D23—21no—
104C22×D23—21no—
105C22×D23—21no—
106C22×D23—21no—
107C22×D23—21no—
108C22×D23—21no—
109C22×D23—21no—
110C22×D23—21no—
111C22×D23C22×C412yes—
112C22×D23C22×C412yes—
113Q8×C23—44no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23C22×C412yes—
132C2×C4×C23C22×C412yes—
133C2×C4×C23C22×C412yes—
134C2×C4×C23#4112yes—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—21no—
139C2×Dic23—21no—
140C2×Dic23—21no—
141C2×Dic23—21no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23C22×C412yes—
151C2×Dic23C22×C412yes—
152C2×Dic23#4112yes—
153D92—44no—
154C4×D23—44no—
155C4×D23—44no—
156#2337—231nomaximal, Sylow
157C22×C23C23×C411yescharacteristic
158C22×C23C2×#4111yescharacteristic
159C22×C23C2×#4111yescharacteristic
160C22×C23H(5,𝔽2)11yescharacteristic
161C22×C23H(5,𝔽2)11yescharacteristic
162C22×C23H(5,𝔽2)11yescharacteristic
163C22×C232−1+411yescharacteristic
164C2×D23—22no—
165C2×D23—22no—
166C2×D23—22no—
167C2×D23—22no—
168C2×D23—22no—
169C2×D23—22no—
170C2×D23—41no—
171C2×D23—41no—
172C2×D23—41no—
173C2×D23—41no—
174C2×D23—41no—
175C2×D23—41no—
176C2×D23—41no—
177C2×D23—41no—
178C4×C23—22no—
179C4×C23—22no—
180C4×C23—22no—
181C4×C23—22no—
182C4×C23—41no—
183C4×C23—41no—
184C4×C23—41no—
185Dic23—22no—
186Dic23—22no—
187Dic23—22no—
188Dic23—41no—
189Dic23—41no—
190Dic23—41no—
191C2×#124—231no—
192#391—231no—
193#391D2311yescharacteristic, complemented
194#388—231no—
195#388—231no—
196#388—231no—
197#388—231no—
198#386—231no—
199#386—231no—
200#385—231no—
201#385—231no—
202#383—231no—
203C4×C4⋊C4—231no—
204C4×C22⋊C4—231no—
205C4×C22⋊C4—231no—
206C2×C23C4×#4111yescharacteristic
207C2×C23#51811yescharacteristic
208C2×C23#52011yescharacteristic
209C2×C23#53811yescharacteristic
210C2×C23#53811yescharacteristic
211C2×C23#54211yescharacteristic
212C2×C23#54211yescharacteristic
213D23—42no—
214D23—42no—
215C22×Q8C2×D2311yescharacteristic
216C22×D4—231no—
217C23×C4—231no—
218C23×C4—231no—
219#124—238no—
220C2×C4⋊C4—231no—
221C2×C4⋊C4—231no—
222C2×C4⋊C4—231no—
223C2×C4⋊C4C2×D2311yescharacteristic
224C2×C22⋊C4—231no—
225C2×C22⋊C4—231no—
226C2×C22⋊C4—231no—
227C2×C22⋊C4—231no—
228C2×C22⋊C4—231no—
229C2×C22⋊C4—231no—
230C2×C22⋊C4—231no—
231C2×C22⋊C4—231no—
232C2×C22⋊C4—231no—
233C2×C22⋊C4—231no—
234C2×C42—231no—
235C2×C42—231no—
236C2×C42—231no—
237C2×C42—231no—
238C2×C42C2×D2311yescharacteristic
239#95—231no—
240#95—231no—
241#95—231no—
242#95—231no—
243#95—231no—
244#95—231no—
245#95—231no—
246#95—231no—
247#95C2×D2311yescharacteristic
248#95C2×D2311yescharacteristic
249#95C2×D2311yescharacteristic
250#95C2×D2311yescharacteristic
251C23#233711yescharacteristic, complemented, Sylow
252C24—231no—
253C24—231no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8C4×D2314yescomplemented
257C2×D4—234no—
258C2×D4—921no—
259C2×D4—921no—
260C22×C4—231no—
261C22×C4—231no—
262C22×C4—231no—
263C22×C4—231no—
264C22×C4—231no—
265C22×C4—231no—
266C22×C4—462no—
267C22×C4—462no—
268C22×C4—921no—
269C22×C4—921no—
270C22×C4—921no—
271C22×C4—921no—
272C22×C4C22×D2311yescharacteristic
273C22×C4C22×D2311yescharacteristic
274C22×C4C22×D2311yescharacteristic
275C22×C4C22×D2311yescharacteristic
276C22×C4C22×D2311yescharacteristic
277C22×C4C22×D2311yescharacteristic
278C22×C4C22×D2311yescharacteristic
279C4⋊C4—41no—
280C4⋊C4—462no—
281C4⋊C4—462no—
282C4⋊C4—921no—
283C22⋊C4—234no—
284C22⋊C4—234no—
285C22⋊C4—234no—
286C22⋊C4—234no—
287C22⋊C4—462no—
288C22⋊C4—462no—
289C22⋊C4—921no—
290C22⋊C4—921no—
291C22⋊C4—921no—
292C22⋊C4—921no—
293C42—41no—
294C42—234no—
295C42—921no—
296C42—921no—
297C42—921no—
298C23—232no—
299C23—232no—
300C23—461no—
301C23—461no—
302C23—461no—
303C23—461no—
304C23—461no—
305C23—461no—
306C23—461no—
307C23—461no—
308C23—461no—
309C23—461no—
310C23—461no—
311C23—461no—
312C23C23×D2311yescharacteristic
313Q8—44no—
314D4—924no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—232no—
333C2×C4—232no—
334C2×C4—232no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—461no—
338C2×C4—461no—
339C2×C4—461no—
340C2×C4—461no—
341C2×C4—461no—
342C2×C4—461no—
343C2×C4—461no—
344C2×C4—461no—
345C2×C4—461no—
346C2×C4—461no—
347C2×C4—461no—
348C2×C4—461no—
349C2×C4—461no—
350C2×C4—924no—
351C2×C4—924no—
352C2×C4C2×C4×D2312yes—
353C2×C4C2×C4×D2312yes—
354C2×C4C2×C4×D2312yes—
355C2×C4#6729212yes—
356C22—462no—
357C22—462no—
358C22—462no—
359C22—462no—
360C22—462no—
361C22—462no—
362C22—921no—
363C22—921no—
364C22—921no—
365C22—921no—
366C22—921no—
367C22—921no—
368C22—921no—
369C22—921no—
370C22C22×C4×D2311yescharacteristic
371C22#1062515511yescharacteristic
372C22#1062515511yescharacteristic
373C22C2×#6729211yescharacteristic
374C22#1062515811yescharacteristic
375C22#41×D2311yescharacteristic
376C22#1062516011yescharacteristic
377C4—22no—
378C4—22no—
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—462no—
385C4—462no—
386C4—462no—
387C4—921no—
388C4—921no—
389C4—921no—
390C2—922no—
391C2—922no—
392C2C4×#6729211yescharacteristic
393C2#1309289011yescharacteristic
394C2#1309289911yescharacteristic
395C2#1309300111yescharacteristic
396C2#1309300711yescharacteristic
397C2#1309303711yescharacteristic
398C2#1309304111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#391C2
socle, cosocleC23×C23C24
prime radicalC22×D92C22
hypercenter#391D23
hypocenterC23#2337
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #13092324C2semidirect
3. #13092309C2semidirect
4. #13092308C2semidirect
5. #13092307C2semidirect
6. #13092306C2semidirect
9. #13092291C2semidirect
10. #13092288C2semidirect
11. #13092284C2semidirect
12. #13092268C2semidirect
13. C4×(C2×D23)⋊C4C2semidirect
14. #13092264C2semidirect
15. C23×#391C2semidirect
22. #10625118C4semidirect
56. C2×Q8×C23C2×C4semidirect
87. (C2×D23)⋊C4C2×C4semidirect
88. (C2×D23)⋊C4C2×C4semidirect
89. (C2×D23)⋊C4C2×C4semidirect
90. (C2×D23)⋊C4C2×C4semidirect
97. C4×Dic23C2×C4semidirect
193. #391D23semidirect
251. C23#2337semidirect
256. C2×Q8C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251182
#130923242
#130923092
#130923082
#130923072
#130923062
#130922952
#130922912
#130922882
#130922842
#130922682
C4×(C2×D23)⋊C42
#130922642
C23×#3912
#233723