Finite Group Databasebeta

← #15685289

Subgroups — #15685289

Order 2944.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093108C211yesmaximal, characteristic, complemented
2#13093079C211yesmaximal, characteristic
3#13092772C211yesmaximal, characteristic, complemented
4#13092760C211yesmaximal, characteristic, complemented
5#13092732C211yesmaximal, characteristic, complemented
6#13092724C211yesmaximal, characteristic, complemented
7#13092657C211yesmaximal, characteristic, complemented
8#13092649C211yesmaximal, characteristic, complemented
9#13092639C211yesmaximal, characteristic, complemented
10#13092578C211yesmaximal, characteristic, complemented
11#13092571C211yesmaximal, characteristic, complemented
12C8×D92C211yesmaximal, characteristic, complemented
13#13092412C211yesmaximal, characteristic, complemented
14#103×D23C211yesmaximal, characteristic, complemented
15C4×Q16×C23C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic
18C2×Q16×C23C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic
20C4×Q8×C23C2211yescharacteristic
21#10625117C2211yescharacteristic
22#10625117C2211yescharacteristic
23C2×#67275C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25C2×C8×D23C2211yescharacteristic
26C2×C8×D23C2211yescharacteristic
27#10625068—21no—
28#10625068C2211yescharacteristic
29#10625066—21no—
30#10625066C2211yescharacteristic
31#10625065—21no—
32#10625063C2211yescharacteristic
33C4⋊C4×D23C2211yescharacteristic
34#10625060—21no—
35#10625047—21no—
36#10625046—21no—
37#10625046C2211yescharacteristic
38C4×D92—21no—
39C4×D92C2211yescharacteristic
40#10625043—21no—
41#10625041C2211yescharacteristic
42C23×#107C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×#103C2211yescharacteristic
45C4×C8×C23C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625017C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625003C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51(C2×D23)⋊C8C2211yescharacteristic
52#10624998C2211yescharacteristic
53#10624998C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61#67292—22no—
62#67292—41no—
63Q8×D23—22no—
64Q8×D23—41no—
65C2×D92—21no—
66C2×D92—21no—
67C2×D92D411yescharacteristic
68C2×D92C2311yescharacteristic
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23C2311yescharacteristic
73C2×C4×D23C2311yescharacteristic
74C2×Dic46—21no—
75C2×Dic46C2311yescharacteristic
76Q16×C23—22no—
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C42×C23—21no—
84C42×C23—21no—
85C42×C23C2311yescharacteristic
86#67275—41no—
87#67274—41no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4D411yescharacteristic
96(C2×D23)⋊C4D411yescharacteristic
97C4⋊Dic23—21no—
98C4⋊Dic23D411yescharacteristic
99C4⋊Dic23C2311yescharacteristic
100C4⋊Dic23C2311yescharacteristic
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105Dic23⋊C4—21no—
106C4×Dic23—21no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C8×D23—41no—
110C8×D23—41no—
111C22×D23—21no—
112C22×D23C2×D411yescharacteristic
113C22×D23C2×D411yescharacteristic
114Q8×C23—21no—
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23#4112yes—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23C2×D411yescharacteristic
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130D92—22no—
131D92—21no—
132D92—21no—
133D92—42no—
134D92—42no—
135C4×D23—21no—
136C4×D23—21no—
137C4×D23—21no—
138C4×D23—21no—
139C4×D23—42no—
140C4×D23—42no—
141C4×D23—42no—
142Dic46—21no—
143Dic46—21no—
144Dic46—42no—
145C8×C23—21no—
146C8×C23—21no—
147C23⋊C8—21no—
148C23⋊C8—21no—
149#3300—231nomaximal, Sylow
150C22×C23C22×D411yescharacteristic
151C2×D23—21no—
152C2×D23—21no—
153C2×D23—21no—
154C2×D23—21no—
155C2×D23—21no—
156C2×D23—41no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23#13512yes—
160C4×C23—22no—
161C4×C23—21no—
162C4×C23—21no—
163C4×C23—41no—
164C4×C23—41no—
165C4×C23—41no—
166C4×C23C2×#4111yescharacteristic
167C4×C23H(5,𝔽2)11yescharacteristic
168Dic23—21no—
169Dic23—21no—
170Dic23—41no—
171Dic23—41no—
172Dic23—41no—
173#552—231no—
174#548—231no—
175#488—231no—
176#485—231no—
177#480—231no—
178#479—231no—
179#467—231no—
180#465—231no—
181#464—231no—
182#452—231no—
183#451—231no—
184C4×Q16D2311yescharacteristic, complemented
185C8×D4—231no—
186#416—231no—
187C2×#103—231no—
188C2×C23#54611yescharacteristic
189C2×C23C2×#13511yescharacteristic
190C2×C23#57811yescharacteristic
191D23—22no—
192D23—41no—
193D23—81no—
194C2×#41—231no—
195C22×Q8—231no—
196C2×Q16—231no—
197C2×Q16C2×D2311yescharacteristic
198C2×SD16—231no—
199C22×C8—231no—
200C22×C8—231no—
201#126—461no—
202#125—231no—
203#125—461no—
204#124—231no—
205#124—461no—
206#123—461no—
207C22⋊Q8—231no—
208C22⋊Q8—231no—
209C22⋊Q8—231no—
210C22⋊Q8—461no—
211#121—231no—
212#121—461no—
213C4×Q8C2×D2311yescharacteristic
214C4×Q8C2×D2311yescharacteristic
215C4×D4—231no—
216C4×D4—461no—
217#117—231no—
218#117—461no—
219C2×C4⋊C4—231no—
220#107—231no—
221#107C2×D2311yescharacteristic
222#106—231no—
223C4⋊C8—231no—
224#103—231no—
225#103—231no—
226#103—231no—
227#103—231no—
228#103—231no—
229#103C2×D2311yescharacteristic
230#103C2×D2311yescharacteristic
231#102—231no—
232#102—231no—
233#102—231no—
234C22⋊C8—231no—
235C22⋊C8—231no—
236C4×C8C2×D2311yescharacteristic
237C23#330011yescharacteristic, complemented, Sylow
238#41—462no—
239#41—921no—
240C2×Q8—231no—
241C2×Q8—461no—
242C2×Q8—462no—
243C2×Q8—921no—
244C2×Q8C22×D2311yescharacteristic
245C2×Q8C22×D2311yescharacteristic
246C2×D4—231no—
247C2×D4—231no—
248C2×D4—461no—
249C2×D4—461no—
250C22×C4—231no—
251C22×C4—231no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255Q16—22no—
256Q16—921no—
257SD16—921no—
258C2×C8—231no—
259C2×C8—231no—
260C2×C8—921no—
261C2×C8—921no—
262C2×C8C22×D2311yescharacteristic
263C2×C8C22×D2311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4C22×D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—231no—
278C22⋊C4—231no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C42—21no—
287C42—21no—
288C42—461no—
289C42C22×D2311yescharacteristic
290C23—231no—
291C23—231no—
292C23—461no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—461no—
297Q8—461no—
298Q8—922no—
299Q8#6728812yes—
300D4—462no—
301D4—461no—
302D4—461no—
303D4—922no—
304D4—922no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—231no—
310C2×C4—231no—
311C2×C4—461no—
312C2×C4—461no—
313C2×C4—461no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—922no—
319C2×C4—922no—
320C2×C4—922no—
321C2×C4D4×D2311yescharacteristic
322C2×C4D4×D2311yescharacteristic
323C2×C4C23×D2311yescharacteristic
324C8—21no—
325C8—21no—
326C8—461no—
327C8—461no—
328C22—232no—
329C22—461no—
330C22—461no—
331C22—461no—
332C22—461no—
333C22—461no—
334C22—921no—
335C22—921no—
336C22—921no—
337C22C2×D4×D2311yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—461no—
345C4—461no—
346C4—921no—
347C4—921no—
348C4—921no—
349C4C2×#6728811yescharacteristic
350C4#1062516011yescharacteristic
351C2—462no—
352C2—921no—
353C2—1841no—
354C2#1309306311yescharacteristic
355C2#135×D2311yescharacteristic
356C2#1309323011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×Q16×C23C2
socleC22×C23C22×D4
prime radical#13093079C2
hypercenterC4×Q16D23
hypocenterC23#3300
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #13093108C2semidirect
3. #13092772C2semidirect
4. #13092760C2semidirect
5. #13092732C2semidirect
6. #13092724C2semidirect
7. #13092657C2semidirect
8. #13092649C2semidirect
9. #13092639C2semidirect
10. #13092578C2semidirect
11. #13092571C2semidirect
12. C8×D92C2semidirect
13. #13092412C2semidirect
14. #103×D23C2semidirect
15. C4×Q16×C23C2semidirect
184. C4×Q16D23semidirect
237. C23#3300semidirect

Maximal subgroups

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

subgroupindex
#130931082
#130930792
#130927722
#130927602
#130927322
#130927242
#130926572
#130926492
#130926392
#130925782
#130925712
C8×D922
#130924122
#103×D232
C4×Q16×C232
#330023