Finite Group Databasebeta

← #15685343

Subgroups — #15685343

Order 2944.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093130C211yesmaximal, characteristic, complemented
2#13093086C211yesmaximal, characteristic, complemented
3#13092762C211yesmaximal, characteristic, complemented
4#13092741C211yesmaximal, characteristic, complemented
5#13092739C211yesmaximal, characteristic, complemented
6#13092710C211yesmaximal, characteristic, complemented
7#13092653C211yesmaximal, characteristic, complemented
8#13092652C211yesmaximal, characteristic, complemented
9#13092611C211yesmaximal, characteristic, complemented
10#13092565C211yesmaximal, characteristic, complemented
11#13092562C211yesmaximal, characteristic, complemented
12#13092502C211yesmaximal, characteristic, complemented
13C8×C22⋊D23C211yesmaximal, characteristic, complemented
14#13092412C211yesmaximal, characteristic, complemented
15C23×#416C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C23×#117C2211yescharacteristic
20Q8×Dic23C2211yescharacteristic
21C2×#67274C2211yescharacteristic
22#10625111—21no—
23#10625111C2211yescharacteristic
24#10625109—21no—
25#10625109C2211yescharacteristic
26C2×#67272C2211yescharacteristic
27#10625101—21no—
28#10625101C2211yescharacteristic
29#10625101C2211yescharacteristic
30C4×C22⋊D23—21no—
31C4×C22⋊D23C2211yescharacteristic
32C2×D184C2211yescharacteristic
33C2×C8×D23C2211yescharacteristic
34#10625066C2211yescharacteristic
35#10625064C2211yescharacteristic
36#10625063C2211yescharacteristic
37#10625059C2211yescharacteristic
38#10625056—21no—
39#10625055—21no—
40#10625046—21no—
41#10625043—21no—
42C23×#103C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625014C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51(C2×D23)⋊C8C2211yescharacteristic
52#10625000C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624989C2211yescharacteristic
59#41×C23—22no—
60#41×C23—41no—
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C22×C4×C23C2311yescharacteristic
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23D411yescharacteristic
72#67292—22no—
73#67292—41no—
74C2×D92—21no—
75C2×D92—21no—
76C2×D92C2311yescharacteristic
77C2×D92C2311yescharacteristic
78C2×C4×D23—21no—
79C2×C4×D23—21no—
80C2×C4×D23C2311yescharacteristic
81C2×Dic46—21no—
82C2×C8×C23—41no—
83C2×C8×C23C2311yescharacteristic
84C2×C8×C23C2311yescharacteristic
85C4⋊C4×C23C2311yescharacteristic
86C4⋊C4×C23C2311yescharacteristic
87C22⋊C4×C23—21no—
88C42×C23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23D411yescharacteristic
91#67274—22no—
92#67272—41no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4—21no—
96(C2×D23)⋊C4—21no—
97(C2×D23)⋊C4—21no—
98(C2×D23)⋊C4D411yescharacteristic
99C4⋊Dic23—21no—
100C4⋊Dic23C2311yescharacteristic
101C4⋊Dic23C2311yescharacteristic
102Dic23⋊C4—21no—
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109D184—41no—
110C8×D23—41no—
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114C22×D23—21no—
115C22×D23C2×D411yescharacteristic
116Q8×C23—21no—
117Q8×C23#4112yes—
118D4×C23—21no—
119D4×C23—21no—
120D4×C23—42no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—42no—
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2411yescharacteristic
129C22⋊D23—22no—
130C22⋊D23—42no—
131C22⋊D23—81no—
132C22⋊D23—81no—
133C22⋊D23—81no—
134C22⋊D23—81no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23C2×D411yescharacteristic
138C2×Dic23C2×D411yescharacteristic
139C2×Dic23C2×D411yescharacteristic
140D92—21no—
141D92—21no—
142D92—21no—
143D92—21no—
144D92—42no—
145D92—81no—
146C4×D23—21no—
147C4×D23—21no—
148C4×D23—42no—
149C4×D23—42no—
150Dic46—81no—
151C8×C23—21no—
152C8×C23—21no—
153C23⋊C8—21no—
154C23⋊C8—21no—
155#3305—231nomaximal, Sylow
156C22×C23—21no—
157C22×C23—21no—
158C22×C23—21no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23C22×D411yescharacteristic
163C2×D23—21no—
164C2×D23—21no—
165C2×D23—21no—
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—41no—
169C2×D23—41no—
170C2×D23—41no—
171C2×D23—41no—
172C4×C23—22no—
173C4×C23—21no—
174C4×C23—41no—
175C4×C23—41no—
176C4×C23C2×#4111yescharacteristic
177C4×C23H(5,𝔽2)11yescharacteristic
178Dic23—21no—
179Dic23—21no—
180Dic23—41no—
181Dic23—41no—
182Dic23#13512yes—
183#555—231no—
184#550—231no—
185#486—231no—
186#482—231no—
187#482—231no—
188#477—231no—
189#466—231no—
190#466—231no—
191#459—231no—
192#449—231no—
193#449—231no—
194C4×SD16—231no—
195C8×D4—231no—
196#416—231no—
197#416D2311yescharacteristic, complemented
198C2×C23—41no—
199C2×C23—81no—
200C2×C23#54611yescharacteristic
201C2×C23C2×#13511yescharacteristic
202C2×C23#57611yescharacteristic
203D23—41no—
204D23—81no—
205D23—81no—
206C2×#41—231no—
207C2×#41C2×D2311yescharacteristic
208C2×SD16—231no—
209C2×D8—231no—
210C2×D8—231no—
211C22×C8—231no—
212C22×C8C2×D2311yescharacteristic
213C4⋊Q8—231no—
214#127—231no—
215#127—461no—
216#124—461no—
217#124—461no—
218#121—231no—
219#121—231no—
220#121—231no—
221#121—231no—
222#121—461no—
223#121—461no—
224#121—461no—
225C4×Q8—231no—
226C4×D4—231no—
227C4×D4—231no—
228C4×D4—461no—
229#117—231no—
230#117—461no—
231#117C2×D2311yescharacteristic
232#107—231no—
233#107—231no—
234#106—231no—
235C4⋊C8—231no—
236#103—231no—
237#103C2×D2311yescharacteristic
238#103C2×D2311yescharacteristic
239#102—231no—
240#102—231no—
241#102—231no—
242#102—231no—
243#102—231no—
244#102C2×D2311yescharacteristic
245#102C2×D2311yescharacteristic
246C22⋊C8—231no—
247C22⋊C8—231no—
248C4×C8—231no—
249C23#330511yescharacteristic, complemented, Sylow
250#41—22no—
251#41—41no—
252#41—462no—
253#41—921no—
254C2×Q8—461no—
255C2×Q8C22×D2311yescharacteristic
256C2×D4—21no—
257C2×D4—231no—
258C2×D4—231no—
259C2×D4—231no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4—461no—
264C2×D4—461no—
265C2×D4—461no—
266C2×D4—461no—
267C2×D4C22×D2311yescharacteristic
268C22×C4—21no—
269C22×C4—231no—
270C22×C4—461no—
271C22×C4—461no—
272C22×C4C22×D2311yescharacteristic
273SD16—462no—
274D8—921no—
275D8—921no—
276C2×C8—41no—
277C2×C8—231no—
278C2×C8—231no—
279C2×C8—921no—
280C2×C8C22×D2311yescharacteristic
281C2×C8C22×D2311yescharacteristic
282C4⋊C4—231no—
283C4⋊C4—231no—
284C4⋊C4—231no—
285C4⋊C4—461no—
286C4⋊C4—461no—
287C4⋊C4C22×D2311yescharacteristic
288C4⋊C4C22×D2311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—231no—
291C22⋊C4—231no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C22⋊C4—461no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C22⋊C4—461no—
298C42—21no—
299C42—231no—
300C42—461no—
301C42—461no—
302C23—21no—
303C23—231no—
304C23—461no—
305C23—461no—
306C23D4×D2311yescharacteristic
307Q8—21no—
308Q8—1841no—
309Q8#6728812yes—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—462no—
314D4—461no—
315D4—461no—
316D4—461no—
317D4—461no—
318D4—922no—
319D4—922no—
320D4—1841no—
321D4—1841no—
322D4—1841no—
323D4—1841no—
324D4—1841no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—231no—
332C2×C4—231no—
333C2×C4—231no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—461no—
338C2×C4—922no—
339C2×C4—922no—
340C2×C4D4×D2311yescharacteristic
341C2×C4C23×D2311yescharacteristic
342C8—21no—
343C8—21no—
344C8—461no—
345C8—461no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—461no—
353C22—461no—
354C22—461no—
355C22—921no—
356C22—921no—
357C22—921no—
358C22—921no—
359C22—921no—
360C22—921no—
361C22C2×D4×D2311yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—232no—
367C4—461no—
368C4—461no—
369C4—921no—
370C4—921no—
371C4C2×#6728811yescharacteristic
372C4#1062515511yescharacteristic
373C2—41no—
374C2—81no—
375C2—921no—
376C2—1841no—
377C2—1841no—
378C2#1309305711yescharacteristic
379C2#135×D2311yescharacteristic
380C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#416C2
socleC22×C23C22×D4
hypercenter#416D23
hypocenterC23#3305
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #13093130C2semidirect
2. #13093086C2semidirect
3. #13092762C2semidirect
4. #13092741C2semidirect
5. #13092739C2semidirect
6. #13092710C2semidirect
7. #13092653C2semidirect
8. #13092652C2semidirect
9. #13092611C2semidirect
10. #13092565C2semidirect
11. #13092562C2semidirect
12. #13092502C2semidirect
13. C8×C22⋊D23C2semidirect
14. #13092412C2semidirect
15. C23×#416C2semidirect
197. #416D23semidirect
249. C23#3305semidirect

Maximal subgroups

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

subgroupindex
#130931302
#130930862
#130927622
#130927412
#130927392
#130927102
#130926532
#130926522
#130926112
#130925652
#130925622
#130925022
C8×C22⋊D232
#130924122
C23×#4162
#330523