Finite Group Databasebeta

← #15676550

Subgroups — #15676550

Order 2944.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625055C211yesmaximal, characteristic
2#13092319C211yesmaximal, characteristic, complemented
3#13092317C211yesmaximal, characteristic, complemented
4#13092309C211yesmaximal, characteristic, complemented
5#13092304C211yesmaximal, characteristic, complemented
6#13092301C211yesmaximal, characteristic, complemented
7#13092295C211yesmaximal, characteristic, complemented
8#13092294C211yesmaximal, characteristic, complemented
9#13092294C211yesmaximal, characteristic, complemented
10#13092293C211yesmaximal, characteristic, complemented
11#13092292C211yesmaximal, characteristic, complemented
12#13092288C211yesmaximal, characteristic, complemented
13#13092279C211yesmaximal, characteristic, complemented
14#13092274C211yesmaximal, characteristic, complemented
15C23×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D23C2211yescharacteristic
17C22×C22⋊D23C2211yescharacteristic
18C23×Dic23C2211yescharacteristic
19C22×D92C2211yescharacteristic
20C22×C4×D23C2211yescharacteristic
21C22×C4×D23C2211yescharacteristic
22C2×C4⋊C4×C23C2211yescharacteristic
23C2×C22⋊C4×C23C2211yescharacteristic
24C2×C22⋊C4×C23C2211yescharacteristic
25C2×C22⋊C4×C23C2211yescharacteristic
26C2×C42×C23C2211yescharacteristic
27C2×C22⋊Dic23C2211yescharacteristic
28C2×(C2×D23)⋊C4C2211yescharacteristic
29C2×(C2×D23)⋊C4C2211yescharacteristic
30C2×(C2×D23)⋊C4C2211yescharacteristic
31C2×(C2×D23)⋊C4C2211yescharacteristic
32C2×(C2×D23)⋊C4C2211yescharacteristic
33C2×(C2×D23)⋊C4C2211yescharacteristic
34C2×(C2×D23)⋊C4C2211yescharacteristic
35C2×(C2×D23)⋊C4C2211yescharacteristic
36C2×C4⋊Dic23C2211yescharacteristic
37C2×C4⋊Dic23C2211yescharacteristic
38C2×Dic23⋊C4C2211yescharacteristic
39C2×Dic23⋊C4C2211yescharacteristic
40C2×C4×Dic23C2211yescharacteristic
41#10625055C418yescomplemented
42C23×#95C2211yescharacteristic
43C23×#95C2211yescharacteristic
44C23⋊#95C2211yescharacteristic
45C23⋊#95C2211yescharacteristic
46C23⋊#95C2211yescharacteristic
47C23⋊#95C2211yescharacteristic
48C23⋊#95C2211yescharacteristic
49C23⋊#95C2211yescharacteristic
50C23⋊#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C24×C23C2311yescharacteristic
53C23×D23C2311yescharacteristic
54C23×D23C2311yescharacteristic
55C22×C4×C23C2311yescharacteristic
56C22×C4×C23C2311yescharacteristic
57C22×C4×C23C2311yescharacteristic
58C22×C4×C23C2311yescharacteristic
59C22×C4×C23C2311yescharacteristic
60C22×C4×C23C2311yescharacteristic
61C2×C22⋊D23—41no—
62C2×C22⋊D23—41no—
63C2×C22⋊D23—41no—
64C2×C22⋊D23—41no—
65C2×C22⋊D23C2×C414yes—
66C2×C22⋊D23C2×C414yescomplemented
67C22×Dic23—41no—
68C22×Dic23—41no—
69C22×Dic23—41no—
70C22×Dic23C2311yescharacteristic
71C22×Dic23C2311yescharacteristic
72C22×Dic23C2311yescharacteristic
73C22×Dic23C2311yescharacteristic
74C22×Dic23C2311yescharacteristic
75C22×Dic23C2311yescharacteristic
76C2×D92—41no—
77C2×D92—41no—
78C2×D92C2×C414yescomplemented
79C2×C4×D23—41no—
80C2×C4×D23—41no—
81C2×C4×D23—41no—
82C2×C4×D23—41no—
83C2×C4×D23—41no—
84C2×C4×D23C2×C414yescomplemented
85C4⋊C4×C23—41no—
86C22⋊C4×C23—41no—
87C22⋊C4×C23—41no—
88C22⋊C4×C23C2×C414yescomplemented
89C42×C23—41no—
90C22⋊Dic23—41no—
91(C2×D23)⋊C4—41no—
92(C2×D23)⋊C4—41no—
93(C2×D23)⋊C4—41no—
94(C2×D23)⋊C4—41no—
95(C2×D23)⋊C4—41no—
96(C2×D23)⋊C4—41no—
97(C2×D23)⋊C4—41no—
98(C2×D23)⋊C4C2×C414yescomplemented
99C4⋊Dic23—41no—
100C4⋊Dic23—41no—
101Dic23⋊C4—41no—
102Dic23⋊C4C2×C414yescomplemented
103C4×Dic23—41no—
104C23×C23—21no—
105C23×C23—21no—
106C23×C23—21no—
107C23×C23—21no—
108C23×C23—21no—
109C23×C23—21no—
110C23×C23C22×C412yes—
111C23×C23C2411yescharacteristic
112C22×D23—21no—
113C22×D23—21no—
114C22×D23—21no—
115C22×D23—21no—
116C22×D23—21no—
117C22×D23—21no—
118C22×D23—21no—
119C22×D23—21no—
120C22×D23—21no—
121C22×D23—21no—
122C22×D23—21no—
123C22×D23—21no—
124C22×D23C22×C412yes—
125C22×D23C22×C412yes—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23C22×C412yes—
143C2×C4×C23C22×C412yes—
144C22⋊D23—44no—
145C22⋊D23—44no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—21no—
151C2×Dic23—21no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—21no—
157C2×Dic23—21no—
158C2×Dic23—21no—
159C2×Dic23—21no—
160C2×Dic23—21no—
161C2×Dic23—21no—
162C2×Dic23—44no—
163C2×Dic23C22×C412yes—
164C2×Dic23C22×C412yes—
165D92—44no—
166C4×D23—44no—
167C4×D23—44no—
168#2377—231nomaximal, Sylow
169C22×C23—22no—
170C22×C23—22no—
171C22×C23—22no—
172C22×C23—41no—
173C22×C23—41no—
174C22×C23—41no—
175C22×C23—41no—
176C22×C23C23×C411yescharacteristic
177C22×C23H(5,𝔽2)11yescharacteristic
178C22×C23H(5,𝔽2)11yescharacteristic
179C22×C23H(5,𝔽2)11yescharacteristic
180C22×C23H(5,𝔽2)11yescharacteristic
181C22×C23H(5,𝔽2)11yescharacteristic
182C22×C232−1+411yescharacteristic
183C2×D23—22no—
184C2×D23—22no—
185C2×D23—22no—
186C2×D23—22no—
187C2×D23—22no—
188C2×D23—22no—
189C2×D23—41no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C2×D23—41no—
197C4×C23—22no—
198C4×C23—22no—
199C4×C23—41no—
200C4×C23—41no—
201C4×C23—41no—
202C4×C23—41no—
203Dic23—22no—
204Dic23—22no—
205Dic23—41no—
206Dic23—41no—
207Dic23—41no—
208Dic23—41no—
209C2×#121—231no—
210#390—231no—
211#390—231no—
212#388—231no—
213#388D2311yescharacteristic, complemented
214#387—231no—
215#387—231no—
216#386—231no—
217#386—231no—
218#386—231no—
219#386—231no—
220#385—231no—
221#385—231no—
222#381—231no—
223#380—231no—
224C2×C23—42no—
225C2×C23#51811yescharacteristic
226C2×C23#51811yescharacteristic
227C2×C23#52011yescharacteristic
228C2×C23#56011yescharacteristic
229C2×C23#56011yescharacteristic
230C2×C23#56211yescharacteristic
231C2×C23#56211yescharacteristic
232D23—42no—
233D23—42no—
234C22×D4—231no—
235C22×D4—231no—
236C22×D4—231no—
237C23×C4—231no—
238C23×C4—231no—
239C23×C4—231no—
240#121—238no—
241C2×C4⋊C4—231no—
242C2×C4⋊C4—231no—
243C2×C4⋊C4—231no—
244C2×C4⋊C4—231no—
245C2×C4⋊C4C2×D2311yescharacteristic
246C2×C22⋊C4—231no—
247C2×C22⋊C4—231no—
248C2×C22⋊C4—231no—
249C2×C22⋊C4—231no—
250C2×C22⋊C4—231no—
251C2×C22⋊C4—231no—
252C2×C22⋊C4—231no—
253C2×C22⋊C4—231no—
254C2×C22⋊C4—231no—
255C2×C22⋊C4C2×D2311yescharacteristic
256C2×C22⋊C4C2×D2311yescharacteristic
257C2×C22⋊C4C2×D2311yescharacteristic
258C2×C42—231no—
259C2×C42C2×D2311yescharacteristic
260#95—231no—
261#95—231no—
262#95—231no—
263#95—231no—
264#95—231no—
265#95—231no—
266#95—231no—
267#95—231no—
268#95C2×D2311yescharacteristic
269#95C2×D2311yescharacteristic
270C23#237711yescharacteristic, complemented, Sylow
271C24—231no—
272C24—231no—
273C24C22×D2311yescharacteristic
274C2×D4—234no—
275C2×D4—234no—
276C2×D4—234no—
277C2×D4—921no—
278C2×D4—921no—
279C2×D4—921no—
280C2×D4—921no—
281C2×D4—921no—
282C2×D4—921no—
283C22×C4—231no—
284C22×C4—231no—
285C22×C4—234no—
286C22×C4—231no—
287C22×C4—231no—
288C22×C4—231no—
289C22×C4—231no—
290C22×C4—921no—
291C22×C4—921no—
292C22×C4—921no—
293C22×C4—921no—
294C22×C4—921no—
295C22×C4—921no—
296C22×C4—921no—
297C22×C4—921no—
298C22×C4C22×D2311yescharacteristic
299C22×C4C22×D2311yescharacteristic
300C22×C4C22×D2311yescharacteristic
301C22×C4C22×D2311yescharacteristic
302C22×C4C22×D2311yescharacteristic
303C22×C4C22×D2311yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—234no—
306C4⋊C4—921no—
307C4⋊C4—921no—
308C4⋊C4—921no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—234no—
312C22⋊C4—921no—
313C22⋊C4—921no—
314C22⋊C4—921no—
315C22⋊C4—921no—
316C22⋊C4—921no—
317C22⋊C4—921no—
318C22⋊C4—921no—
319C22⋊C4—921no—
320C22⋊C4C4×D2314yescomplemented
321C42—41no—
322C42—921no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—232no—
330C23—232no—
331C23—461no—
332C23—461no—
333C23—461no—
334C23—461no—
335C23—461no—
336C23—461no—
337C23—461no—
338C23—461no—
339C23—461no—
340C23—461no—
341C23—461no—
342C23—461no—
343C23C2×C4×D2312yes—
344C23C23×D2311yescharacteristic
345D4—924no—
346D4—924no—
347D4—924no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—232no—
365C2×C4—232no—
366C2×C4—461no—
367C2×C4—461no—
368C2×C4—461no—
369C2×C4—461no—
370C2×C4—461no—
371C2×C4—461no—
372C2×C4—461no—
373C2×C4—461no—
374C2×C4—461no—
375C2×C4—461no—
376C2×C4—461no—
377C2×C4—461no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—461no—
381C2×C4—461no—
382C2×C4—924no—
383C2×C4—924no—
384C2×C4—924no—
385C2×C4C2×C4×D2312yes—
386C2×C4C2×C4×D2312yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—462no—
395C22—462no—
396C22—462no—
397C22—462no—
398C22—462no—
399C22—462no—
400C22—921no—
401C22—921no—
402C22—921no—
403C22—921no—
404C22—921no—
405C22—921no—
406C22—921no—
407C22—921no—
408C22C22×C4×D2311yescharacteristic
409C22#1062515511yescharacteristic
410C22#1062515511yescharacteristic
411C22#1062516011yescharacteristic
412C22#1062516011yescharacteristic
413C22#1062516011yescharacteristic
414C22#1062516111yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—462no—
422C4—462no—
423C4—921no—
424C4—921no—
425C4—921no—
426C4—921no—
427C2—42no—
428C2—922no—
429C2—922no—
430C2#1309288911yescharacteristic
431C2#1309288911yescharacteristic
432C2#1309289711yescharacteristic
433C2#1309315511yescharacteristic
434C2#1309315811yescharacteristic
435C2#1309316111yescharacteristic
436C2#1309316411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#388C2
socle, cosocleC23×C23C24
prime radicalC2×#10625055C2
hypercenter#388D23
hypocenterC23#2377
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #13092319C2semidirect
3. #13092317C2semidirect
4. #13092309C2semidirect
5. #13092304C2semidirect
6. #13092301C2semidirect
7. #13092295C2semidirect
8. #13092294C2semidirect
9. #13092294C2semidirect
10. #13092293C2semidirect
11. #13092292C2semidirect
12. #13092288C2semidirect
13. #13092279C2semidirect
14. #13092274C2semidirect
15. C23×#388C2semidirect
41. #10625055C4semidirect
66. C2×C22⋊D23C2×C4semidirect
78. C2×D92C2×C4semidirect
84. C2×C4×D23C2×C4semidirect
88. C22⋊C4×C23C2×C4semidirect
98. (C2×D23)⋊C4C2×C4semidirect
102. Dic23⋊C4C2×C4semidirect
213. #388D23semidirect
270. C23#2377semidirect
320. C22⋊C4C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250552
#130923192
#130923172
#130923092
#130923042
#130923012
#130922952
#130922942
#130922932
#130922922
#130922882
#130922792
#130922742
C23×#3882
#237723