Finite Group Databasebeta

← #15686107

Subgroups — #15686107

Order 2944.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093123C211yesmaximal, characteristic, complemented
2#13093088C211yesmaximal, characteristic, complemented
3#13092783C211yesmaximal, characteristic, complemented
4#13092780C211yesmaximal, characteristic, complemented
5#13092762C211yesmaximal, characteristic, complemented
6#13092720C211yesmaximal, characteristic, complemented
7#13092706C211yesmaximal, characteristic, complemented
8#13092613C211yesmaximal, characteristic, complemented
9#13092611C211yesmaximal, characteristic, complemented
10#13092611C211yesmaximal, characteristic, complemented
11#13092546C211yesmaximal, characteristic, complemented
12#13092528C211yesmaximal, characteristic, complemented
13#13092527C211yesmaximal, characteristic, complemented
14#13092499C211yesmaximal, characteristic, complemented
15C23×#478C211yesmaximal, characteristic, complemented
16C2×#67288—21no—
17C23×#125C2211yescharacteristic
18C4×D4×C23C2211yescharacteristic
19#10625111C2211yescharacteristic
20#10625111C2211yescharacteristic
21C2×#67272C2211yescharacteristic
22#10625101—21no—
23C2×D184C2211yescharacteristic
24C2×D184C2211yescharacteristic
25#10625068—21no—
26#10625067—21no—
27#10625067—21no—
28#10625064C2211yescharacteristic
29#10625064C2211yescharacteristic
30#10625064C2211yescharacteristic
31#10625064C2211yescharacteristic
32C4⋊C4×D23—21no—
33#10625061C2211yescharacteristic
34#10625059C2211yescharacteristic
35#10625055—21no—
36#10625055—21no—
37#10625045C2211yescharacteristic
38C4×D92C2211yescharacteristic
39C4×Dic46C2211yescharacteristic
40C23×#107C2211yescharacteristic
41C23×#106C2211yescharacteristic
42C23×C4⋊C8C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C23×#102C2211yescharacteristic
45#10625014C2211yescharacteristic
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10624997C2211yescharacteristic
49Dic23⋊C8C2211yescharacteristic
50Dic23⋊C8C2211yescharacteristic
51C8×Dic23C2211yescharacteristic
52#10624991C2211yescharacteristic
53#10624991C2211yescharacteristic
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×D4×C23C2311yescharacteristic
60C22×C4×C23—21no—
61C2×C22⋊D23—21no—
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64C2×C22⋊D23—21no—
65#67288—44no—
66C2×D92—21no—
67C2×D92—21no—
68C2×D92C2311yescharacteristic
69C2×D92C2311yescharacteristic
70C2×D92C2311yescharacteristic
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23—21no—
74C2×C4×D23—21no—
75C2×C4×D23—21no—
76C2×Dic46—21no—
77C2×Dic46D411yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C2×C8×C23C2311yescharacteristic
80C4⋊C4×C23—21no—
81C4⋊C4×C23—21no—
82C4⋊C4×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C42×C23C2311yescharacteristic
87#67272—22no—
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—
93C4⋊Dic23—21no—
94C4⋊Dic23D411yescharacteristic
95C4⋊Dic23C2311yescharacteristic
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4D411yescharacteristic
99Dic23⋊C4D411yescharacteristic
100C4×Dic23C2311yescharacteristic
101C4×Dic23C2311yescharacteristic
102C2×C23⋊C8C2311yescharacteristic
103C2×C23⋊C8C2311yescharacteristic
104D184—22no—
105D184—22no—
106C23×C23—21no—
107C22×D23—21no—
108C22×D23—21no—
109C22×D23—21no—
110D4×C23—21no—
111D4×C23—21no—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—42no—
116C2×C4×C23C2×D411yescharacteristic
117C2×C4×C23C2×D411yescharacteristic
118C2×C4×C23C2411yescharacteristic
119C22⋊D23—42no—
120C22⋊D23—42no—
121C22⋊D23—81no—
122C22⋊D23—81no—
123C2×Dic23—21no—
124C2×Dic23C2×D411yescharacteristic
125C2×Dic23C2×D411yescharacteristic
126C2×Dic23C2×D411yescharacteristic
127C2×Dic23C2×D411yescharacteristic
128D92—21no—
129D92—21no—
130D92—21no—
131D92—21no—
132D92—21no—
133D92—42no—
134D92—81no—
135D92#4112yescomplemented
136C4×D23—42no—
137C4×D23—42no—
138C4×D23—42no—
139C4×D23—81no—
140C4×D23—81no—
141Dic46—22no—
142Dic46—81no—
143C8×C23—21no—
144C8×C23—21no—
145C23⋊C8—21no—
146C23⋊C8—21no—
147#3366—231nomaximal, Sylow
148C22×C23—41no—
149C22×C23—41no—
150C22×C23—41no—
151C22×C23C22×D411yescharacteristic
152C2×D23—22no—
153C2×D23—41no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23—41no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C2×D23—41no—
161C4×C23—21no—
162C4×C23—21no—
163C4×C23—41no—
164C4×C23—41no—
165C4×C23—41no—
166C4×C23C2×#4111yescharacteristic
167C4×C232−1+411yescharacteristic
168Dic23—21no—
169Dic23—21no—
170Dic23—21no—
171Dic23—41no—
172Dic23AGL(1,ℤ/8)12yes—
173#554—231no—
174#550—231no—
175#490—231no—
176#490—231no—
177#486—231no—
178#478—231no—
179#478D2311yescharacteristic, complemented
180#476—231no—
181#459—231no—
182#459—231no—
183#459—231no—
184#446—231no—
185#442—231no—
186#442—231no—
187C4×D8—231no—
188C2×C23—81no—
189C2×C23#54811yescharacteristic
190C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C23#57611yescharacteristic
192D23—42no—
193D23—81no—
194D23—81no—
195C2×#41—461no—
196C2×D8—231no—
197C2×D8—231no—
198C2×D8—231no—
199C4⋊Q8—231no—
200#127—231no—
201#127—231no—
202#127—231no—
203#125—231no—
204#125C2×D2311yescharacteristic
205C22⋊Q8—461no—
206C22⋊Q8—461no—
207C22⋊Q8—461no—
208#121—461no—
209#121—461no—
210#121—461no—
211C4×Q8—231no—
212C4×D4—231no—
213C4×D4—231no—
214C4×D4—231no—
215C4×D4—231no—
216C4×D4—231no—
217C4×D4C2×D2311yescharacteristic
218C2×C4⋊C4—461no—
219#107C2×D2311yescharacteristic
220#106—231no—
221#106C2×D2311yescharacteristic
222C4⋊C8—231no—
223C4⋊C8—231no—
224C4⋊C8C2×D2311yescharacteristic
225#102—231no—
226#102—231no—
227#102—231no—
228#102—231no—
229#102—231no—
230#102—231no—
231#102—231no—
232#102—231no—
233#102C2×D2311yescharacteristic
234#102C2×D2311yescharacteristic
235#97—231no—
236#97—231no—
237C4×C8—231no—
238C23#336611yescharacteristic, complemented, Sylow
239#41—924no—
240C2×Q8—231no—
241C2×Q8—461no—
242C2×D4—231no—
243C2×D4—231no—
244C2×D4—231no—
245C2×D4—461no—
246C2×D4—461no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4—461no—
250C2×D4—461no—
251C2×D4C22×D2311yescharacteristic
252C22×C4—21no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256C22×C4—461no—
257C22×C4—461no—
258D8—462no—
259D8—462no—
260D8—462no—
261C2×C8—231no—
262C2×C8—231no—
263C2×C8C22×D2311yescharacteristic
264C2×C8C22×D2311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4—231no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4C22×D2311yescharacteristic
275C4⋊C4C22×D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C42—231no—
284C42—231no—
285C42C22×D2311yescharacteristic
286C23—21no—
287C23—461no—
288C23—461no—
289C23—461no—
290Q8—462no—
291Q8—1841no—
292D4—21no—
293D4—21no—
294D4—232no—
295D4—461no—
296D4—461no—
297D4—461no—
298D4—461no—
299D4—461no—
300D4—922no—
301D4—922no—
302D4—922no—
303D4—1841no—
304D4—1841no—
305D4—1841no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—231no—
311C2×C4—231no—
312C2×C4—231no—
313C2×C4—231no—
314C2×C4—461no—
315C2×C4—922no—
316C2×C4—922no—
317C2×C4—922no—
318C2×C4—1841no—
319C2×C4—1841no—
320C2×C4D4×D2311yescharacteristic
321C2×C4D4×D2311yescharacteristic
322C2×C4C23×D2311yescharacteristic
323C8—21no—
324C8—21no—
325C8—461no—
326C8—461no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—462no—
331C22—921no—
332C22—921no—
333C22—921no—
334C22—921no—
335C22—921no—
336C22—921no—
337C22—921no—
338C22—921no—
339C22C2×D4×D2311yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—232no—
346C4—461no—
347C4—461no—
348C4—461no—
349C4—921no—
350C4#1062515811yescharacteristic
351C4#41×D2311yescharacteristic
352C2—81no—
353C2—922no—
354C2—1841no—
355C2—1841no—
356C2#1309307711yescharacteristic
357C2AGL(1,ℤ/8)×D2311yescharacteristic
358C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#478C2
socleC22×C23C22×D4
hypercenter#478D23
hypocenterC23#3366
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #13093123C2semidirect
2. #13093088C2semidirect
3. #13092783C2semidirect
4. #13092780C2semidirect
5. #13092762C2semidirect
6. #13092720C2semidirect
7. #13092706C2semidirect
8. #13092613C2semidirect
9. #13092611C2semidirect
10. #13092611C2semidirect
11. #13092546C2semidirect
12. #13092528C2semidirect
13. #13092527C2semidirect
14. #13092499C2semidirect
15. C23×#478C2semidirect
135. D92#41semidirect
179. #478D23semidirect
238. C23#3366semidirect

Maximal subgroups

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

subgroupindex
#130931232
#130930882
#130927832
#130927802
#130927622
#130927202
#130927062
#130926132
#130926112
#130925462
#130925282
#130925272
#130924992
C23×#4782
#336623