Finite Group Databasebeta

← #15685268

Subgroups — #15685268

Order 2944.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093125C211yesmaximal, characteristic
2#13093080C211yesmaximal, characteristic
3#13092766C211yesmaximal, characteristic, complemented
4#13092754C211yesmaximal, characteristic, complemented
5#13092750C211yesmaximal, characteristic, complemented
6#13092711C211yesmaximal, characteristic, complemented
7#13092657C211yesmaximal, characteristic, complemented
8#13092625C211yesmaximal, characteristic, complemented
9#13092572C211yesmaximal, characteristic, complemented
10#13092571C211yesmaximal, characteristic, complemented
11#13092509C211yesmaximal, characteristic, complemented
12C8×C22⋊D23C211yesmaximal, characteristic
13C2×#10624998C211yesmaximal, characteristic, complemented
14#103×D23C211yesmaximal, characteristic, complemented
15C23×#467C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C22×Dic46C2211yescharacteristic
18C2×Q16×C23C2211yescharacteristic
19C22×C8×C23C2211yescharacteristic
20C23×C22⋊Q8C2211yescharacteristic
21C23×C22⋊Q8C2211yescharacteristic
22#10625117C2211yescharacteristic
23Q8×Dic23C2211yescharacteristic
24#10625115C2211yescharacteristic
25C2×#67275C2211yescharacteristic
26C2×#67275C2211yescharacteristic
27C4×C22⋊D23C2211yescharacteristic
28C2×C4⋊Dic23C2211yescharacteristic
29C2×C8×D23C2211yescharacteristic
30#10625068—21no—
31#10625068C2211yescharacteristic
32#10625067—21no—
33C4⋊C4×D23C2211yescharacteristic
34#10625060—21no—
35#10625059—21no—
36#10625059C2211yescharacteristic
37#10625058C2211yescharacteristic
38(C22⋊D23)⋊C4—21no—
39(C22⋊D23)⋊C4—21no—
40#10625049—21no—
41#10625049—21no—
42C23×#107C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C23×#103C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47C22⋊(C23⋊C8)C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49#10624998C2211yescharacteristic
50#10624998C2211yescharacteristic
51#10624998C2211yescharacteristic
52#10624998C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624992C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624989C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C2×C22⋊D23D411yescharacteristic
63C22×Dic23—21no—
64C22×Dic23—21no—
65Q8×D23—22no—
66Q8×D23—41no—
67C2×C4×D23—21no—
68C2×C4×D23—21no—
69C2×C4×D23C2311yescharacteristic
70C2×Dic46—22no—
71C2×Dic46—21no—
72C2×Dic46—21no—
73C2×Dic46—21no—
74C2×Dic46—41no—
75C2×Dic46C2311yescharacteristic
76C2×Dic46C2311yescharacteristic
77Q16×C23—41no—
78C2×C8×C23—41no—
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23—21no—
82C4⋊C4×C23—21no—
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C22⋊Dic23D411yescharacteristic
88#67275—22no—
89#67275—41no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4D411yescharacteristic
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4D411yescharacteristic
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C8×D23—41no—
111C23×C23C2×D411yescharacteristic
112C22×D23C2×D411yescharacteristic
113Q8×C23—21no—
114Q8×C23—21no—
115Q8×C23—21no—
116Q8×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×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C22⋊D23Q1614yescomplemented
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—42no—
131C2×Dic23—81no—
132C2×Dic23C2×D411yescharacteristic
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135C4×D23—21no—
136C4×D23—21no—
137C4×D23—42no—
138C4×D23—81no—
139Dic46—21no—
140Dic46—21no—
141Dic46—21no—
142Dic46—42no—
143Dic46—42no—
144Dic46—81no—
145Dic46#4112yes—
146C8×C23—21no—
147C8×C23—21no—
148C23⋊C8—21no—
149C23⋊C8—21no—
150#3299—231nomaximal, Sylow
151C22×C23—21no—
152C22×C23—21no—
153C22×C23C2×Q1612yes—
154C22×C23C22×D411yescharacteristic
155C2×D23—21no—
156C2×D23—21no—
157C2×D23C2×Q1612yes—
158C4×C23—21no—
159C4×C23—41no—
160C4×C23—41no—
161C4×C23—41no—
162C4×C23—41no—
163C4×C23C2×#4111yescharacteristic
164C4×C23H(5,𝔽2)11yescharacteristic
165Dic23—22no—
166Dic23—21no—
167Dic23—21no—
168Dic23—41no—
169Dic23—41no—
170Dic23—41no—
171Dic23C2×Q1612yes—
172#554—231no—
173D4×Q8—231no—
174#487—231no—
175#484—231no—
176#484—231no—
177#477—231no—
178#467—231no—
179#467D2311yescharacteristic, complemented
180#462—231no—
181#451—231no—
182#451—231no—
183C4×Q16—231no—
184C8×D4—231no—
185C2×#103—231no—
186C2×#103—231no—
187C2×C23—22no—
188C2×C23#54611yescharacteristic
189C2×C23C22×Q1611yescharacteristic
190C2×C23#57711yescharacteristic
191D23—22no—
192C22×Q8—231no—
193C22×Q8—231no—
194C2×Q16—231no—
195C2×Q16—231no—
196C2×Q16C2×D2311yescharacteristic
197C22×C8—231no—
198C22×C8C2×D2311yescharacteristic
199C4⋊Q8—231no—
200C4⋊Q8—231no—
201C4⋊Q8—461no—
202#125—461no—
203C22⋊Q8—231no—
204C22⋊Q8—231no—
205C22⋊Q8—461no—
206C22⋊Q8—461no—
207C22⋊Q8—461no—
208C22⋊Q8—461no—
209C22⋊Q8C2×D2311yescharacteristic
210C22⋊Q8C2×D2311yescharacteristic
211C4×Q8—231no—
212C4×Q8—231no—
213C4×D4—231no—
214C4×D4—461no—
215C4×D4—461no—
216C2×C4⋊C4—231no—
217C2×C4⋊C4—231no—
218#107—231no—
219#107—231no—
220#107C2×D2311yescharacteristic
221C4⋊C8—231no—
222#103—231no—
223#103—231no—
224#103—231no—
225#103—231no—
226#103—231no—
227#103—231no—
228#103—231no—
229#103—231no—
230#103C2×D2311yescharacteristic
231#103C2×D2311yescharacteristic
232C22⋊C8—231no—
233C22⋊C8—231no—
234C4×C8—231no—
235C23#329911yescharacteristic, complemented, Sylow
236C2×Q8—231no—
237C2×Q8—231no—
238C2×Q8—461no—
239C2×Q8—461no—
240C2×Q8—462no—
241C2×Q8—461no—
242C2×Q8—462no—
243C2×Q8—921no—
244C2×Q8—921no—
245C2×Q8C22×D2311yescharacteristic
246C2×Q8C22×D2311yescharacteristic
247C2×D4—231no—
248C22×C4—231no—
249C22×C4—461no—
250C22×C4—461no—
251C22×C4—461no—
252C22×C4—461no—
253C22×C4C22×D2311yescharacteristic
254Q16—41no—
255Q16—462no—
256Q16—921no—
257C2×C8—41no—
258C2×C8—231no—
259C2×C8—231no—
260C2×C8—921no—
261C2×C8C22×D2311yescharacteristic
262C2×C8C22×D2311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—461no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4—461no—
276C4⋊C4—461no—
277C4⋊C4C22×D2311yescharacteristic
278C4⋊C4C22×D2311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—231no—
282C22⋊C4—231no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C42—231no—
286C42—461no—
287C42—461no—
288C23—231no—
289C23D4×D2311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—232no—
295Q8—461no—
296Q8—461no—
297Q8—461no—
298Q8—922no—
299Q8—922no—
300Q8—1841no—
301D4—234no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—231no—
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—922no—
318C2×C4—922no—
319C2×C4—1841no—
320C2×C4—1841no—
321C2×C4D4×D2311yescharacteristic
322C2×C4C23×D2311yescharacteristic
323C8—21no—
324C8—21no—
325C8—461no—
326C8—461no—
327C22—21no—
328C22—21no—
329C22—232no—
330C22—461no—
331C22—461no—
332C22Q16×D2312yes—
333C22C2×D4×D2311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—232no—
340C4—461no—
341C4—461no—
342C4—462no—
343C4—921no—
344C4—921no—
345C4—921no—
346C4#1062515511yescharacteristic
347C4#41×D2311yescharacteristic
348C2—22no—
349C2—462no—
350C2#1309305611yescharacteristic
351C2C2×Q16×D2311yescharacteristic
352C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#467C2
socleC22×C23C22×D4
prime radicalC2×C22⋊D23D4
hypercenter#467D23
hypocenterC23#3299
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #13092766C2semidirect
4. #13092754C2semidirect
5. #13092750C2semidirect
6. #13092711C2semidirect
7. #13092657C2semidirect
8. #13092625C2semidirect
9. #13092572C2semidirect
10. #13092571C2semidirect
11. #13092509C2semidirect
13. C2×#10624998C2semidirect
14. #103×D23C2semidirect
15. C23×#467C2semidirect
125. C22⋊D23Q16semidirect
179. #467D23semidirect
235. C23#3299semidirect

Maximal subgroups

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

subgroupindex
#130931252
#130930802
#130927662
#130927542
#130927502
#130927112
#130926572
#130926252
#130925722
#130925712
#130925092
C8×C22⋊D232
C2×#106249982
#103×D232
C23×#4672
#329923