Finite Group Databasebeta

← #15676332

Subgroups — #15676332

Order 2944.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic
2#13092310C211yesmaximal, characteristic, complemented
3#13092304C211yesmaximal, characteristic, complemented
4#13092298C211yesmaximal, characteristic, complemented
5#13092293C211yesmaximal, characteristic
6#13092293C211yesmaximal, characteristic
7#13092284C211yesmaximal, characteristic, complemented
8#13092278C211yesmaximal, characteristic, complemented
9#13092274C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic23C211yesmaximal, characteristic, complemented
11C4×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
12#13092264C211yesmaximal, characteristic, complemented
13#13092263C211yesmaximal, characteristic, complemented
14#95×D23C211yesmaximal, characteristic, complemented
15C23×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D23C2211yescharacteristic
17C23×Dic23C2211yescharacteristic
18C22×C4×D23C2211yescharacteristic
19C22×C4×D23C2211yescharacteristic
20C22×C4×D23C2211yescharacteristic
21C2×C4⋊C4×C23C2211yescharacteristic
22C2×C22⋊C4×C23C2211yescharacteristic
23C2×C22⋊C4×C23C2211yescharacteristic
24C2×C22⋊C4×C23C2211yescharacteristic
25C2×C42×C23C2211yescharacteristic
26C2×C22⋊Dic23C2211yescharacteristic
27C2×C22⋊Dic23C2211yescharacteristic
28C2×(C2×D23)⋊C4C2211yescharacteristic
29C2×(C2×D23)⋊C4C2211yescharacteristic
30C2×(C2×D23)⋊C4C2211yescharacteristic
31C2×C4⋊Dic23C2211yescharacteristic
32C2×Dic23⋊C4C2211yescharacteristic
33C2×C4×Dic23C2211yescharacteristic
34C2×C4×Dic23C2211yescharacteristic
35C2×C4×Dic23C2211yescharacteristic
36C2×C4×Dic23C2211yescharacteristic
37(C22⋊D23)⋊C4C418yescomplemented
38C23×#95C2211yescharacteristic
39C23×#95C2211yescharacteristic
40C23⋊#95C2211yescharacteristic
41C23⋊#95C2211yescharacteristic
42C23⋊#95C2211yescharacteristic
43C23⋊#95C2211yescharacteristic
44C23⋊#95C2211yescharacteristic
45C23⋊#95C2211yescharacteristic
46C23⋊#95C2211yescharacteristic
47C23⋊#95C2211yescharacteristic
48C23⋊#95C2211yescharacteristic
49C23⋊#95C2211yescharacteristic
50C23⋊#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C24×C23C2311yescharacteristic
53C23×D23C2311yescharacteristic
54C22×C4×C23C2311yescharacteristic
55C22×C4×C23C2311yescharacteristic
56C22×C4×C23C2311yescharacteristic
57C22×C4×C23C2311yescharacteristic
58C22×C4×C23C2311yescharacteristic
59C22×C4×C23C2311yescharacteristic
60C2×C22⋊D23—22no—
61C2×C22⋊D23—22no—
62C2×C22⋊D23C2×C414yes—
63C22×Dic23—41no—
64C22×Dic23—41no—
65C22×Dic23C2×C414yescomplemented
66C22×Dic23C2311yescharacteristic
67C22×Dic23C2311yescharacteristic
68C22×Dic23C2311yescharacteristic
69C22×Dic23C2311yescharacteristic
70C22×Dic23C2311yescharacteristic
71C22×Dic23C2311yescharacteristic
72C22×Dic23C2311yescharacteristic
73C2×C4×D23—22no—
74C2×C4×D23—22no—
75C2×C4×D23—22no—
76C2×C4×D23—22no—
77C2×C4×D23—41no—
78C2×C4×D23—41no—
79C2×C4×D23—41no—
80C2×C4×D23—41no—
81C2×C4×D23C2×C414yes—
82C4⋊C4×C23—41no—
83C22⋊C4×C23—22no—
84C22⋊C4×C23—41no—
85C22⋊C4×C23C2×C414yescomplemented
86C42×C23—22no—
87C22⋊Dic23—22no—
88C22⋊Dic23—41no—
89(C2×D23)⋊C4—22no—
90(C2×D23)⋊C4—22no—
91(C2×D23)⋊C4C2×C414yes—
92C4⋊Dic23—41no—
93Dic23⋊C4C2×C414yescomplemented
94C4×Dic23—22no—
95C4×Dic23—41no—
96C4×Dic23—41no—
97C4×Dic23C2×C414yescomplemented
98C23×C23—21no—
99C23×C23—21no—
100C23×C23—21no—
101C23×C23—21no—
102C23×C23—21no—
103C23×C23—21no—
104C23×C23C22×C412yes—
105C23×C23C2411yescharacteristic
106C22×D23—21no—
107C22×D23—21no—
108C22×D23—21no—
109C22×D23—21no—
110C22×D23C22×C412yes—
111C22×D23#4112yes—
112C22×D23#4112yes—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×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×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23C22×C412yes—
129C2×C4×C23C22×C412yes—
130C2×C4×C23#4112yes—
131C22⋊D23—28no—
132C2×Dic23—21no—
133C2×Dic23—21no—
134C2×Dic23—21no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—21no—
138C2×Dic23—21no—
139C2×Dic23—21no—
140C2×Dic23—21no—
141C2×Dic23—21no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—44no—
150C2×Dic23C22×C412yes—
151C2×Dic23C22×C412yes—
152C2×Dic23C22×C412yes—
153C2×Dic23#4112yes—
154C4×D23—44no—
155C4×D23—44no—
156C4×D23—44no—
157#2353—231nomaximal, Sylow
158C22×C23—22no—
159C22×C23—22no—
160C22×C23—22no—
161C22×C23—41no—
162C22×C23—41no—
163C22×C23—41no—
164C22×C23—41no—
165C22×C23C23×C411yescharacteristic
166C22×C23C2×#4111yescharacteristic
167C22×C23C2×#4111yescharacteristic
168C22×C23C2×#4111yescharacteristic
169C22×C23C2×#4111yescharacteristic
170C22×C23H(5,𝔽2)11yescharacteristic
171C22×C23H(5,𝔽2)11yescharacteristic
172C2×D23—22no—
173C2×D23—22no—
174C2×D23—22no—
175C2×D23—22no—
176C2×D23—22no—
177C2×D23—22no—
178C2×D23#11714yes—
179C4×C23—22no—
180C4×C23—22no—
181C4×C23—22no—
182C4×C23—41no—
183C4×C23—41no—
184C4×C23—41no—
185Dic23—22no—
186Dic23—22no—
187Dic23—22no—
188Dic23—22no—
189Dic23—41no—
190Dic23—41no—
191Dic23—41no—
192C2×C4×D4—231no—
193#388—231no—
194#388D2311yescharacteristic, complemented
195#387—231no—
196#387—231no—
197#386—231no—
198#386—231no—
199#383—231no—
200#381—231no—
201#380—231no—
202C4×C22⋊C4—231no—
203C4×C22⋊C4—231no—
204C4×C22⋊C4—231no—
205#376—231no—
206C2×#95—231no—
207C2×C23—42no—
208C2×C23C2×#11711yescharacteristic
209C2×C23C4×#4111yescharacteristic
210C2×C23#51811yescharacteristic
211C2×C23#55111yescharacteristic
212C2×C23#55111yescharacteristic
213C2×C23#55311yescharacteristic
214C2×C23#55311yescharacteristic
215D23—24no—
216C22×D4—231no—
217C23×C4—231no—
218C23×C4—231no—
219C23×C4—231no—
220C23×C4—231no—
221C4×D4—238no—
222C2×C4⋊C4—231no—
223C2×C4⋊C4—231no—
224C2×C4⋊C4C2×D2311yescharacteristic
225C2×C22⋊C4—231no—
226C2×C22⋊C4—231no—
227C2×C22⋊C4—231no—
228C2×C22⋊C4—231no—
229C2×C22⋊C4—231no—
230C2×C22⋊C4C2×D2311yescharacteristic
231C2×C22⋊C4C2×D2311yescharacteristic
232C2×C22⋊C4C2×D2311yescharacteristic
233C2×C42—231no—
234C2×C42—231no—
235C2×C42—231no—
236C2×C42—231no—
237C2×C42C2×D2311yescharacteristic
238#95—231no—
239#95—231no—
240#95—231no—
241#95—231no—
242#95—231no—
243#95—231no—
244#95—231no—
245#95—231no—
246#95—231no—
247#95—231no—
248#95—231no—
249#95—231no—
250#95C2×D2311yescharacteristic
251#95C2×D2311yescharacteristic
252C23#235311yescharacteristic, complemented, Sylow
253C24—231no—
254C24C22×D2311yescharacteristic
255C2×D4—234no—
256C2×D4—462no—
257C2×D4—462no—
258C22×C4—231no—
259C22×C4—231no—
260C22×C4—231no—
261C22×C4—231no—
262C22×C4—234no—
263C22×C4—234no—
264C22×C4—231no—
265C22×C4—231no—
266C22×C4—231no—
267C22×C4—462no—
268C22×C4—462no—
269C22×C4—462no—
270C22×C4—462no—
271C22×C4—921no—
272C22×C4—921no—
273C22×C4—921no—
274C22×C4—921no—
275C22×C4—921no—
276C22×C4—921no—
277C22×C4C22×D2311yescharacteristic
278C22×C4C22×D2311yescharacteristic
279C22×C4C22×D2311yescharacteristic
280C22×C4C22×D2311yescharacteristic
281C22×C4C22×D2311yescharacteristic
282C22×C4C22×D2311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—234no—
285C4⋊C4—921no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—234no—
289C22⋊C4—462no—
290C22⋊C4—462no—
291C22⋊C4—462no—
292C22⋊C4—921no—
293C22⋊C4C4×D2314yescomplemented
294C42—22no—
295C42—234no—
296C42—462no—
297C42—921no—
298C42—921no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—232no—
306C23—232no—
307C23—232no—
308C23—461no—
309C23—461no—
310C23—461no—
311C23—461no—
312C23C2×C4×D2312yes—
313C23C23×D2311yescharacteristic
314D4—468no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—232no—
331C2×C4—232no—
332C2×C4—232no—
333C2×C4—232no—
334C2×C4—461no—
335C2×C4—461no—
336C2×C4—461no—
337C2×C4—461no—
338C2×C4—461no—
339C2×C4—461no—
340C2×C4—461no—
341C2×C4—461no—
342C2×C4—461no—
343C2×C4—461no—
344C2×C4—461no—
345C2×C4—461no—
346C2×C4—461no—
347C2×C4—461no—
348C2×C4—461no—
349C2×C4—461no—
350C2×C4—461no—
351C2×C4—924no—
352C2×C4—924no—
353C2×C4—924no—
354C2×C4—924no—
355C2×C4C2×C4×D2312yes—
356C2×C4C2×C4×D2312yes—
357C2×C4#6729012yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—234no—
366C22—462no—
367C22—462no—
368C22—462no—
369C22—462no—
370C22—462no—
371C22—462no—
372C22C22×C4×D2311yescharacteristic
373C22C2×#6729011yescharacteristic
374C22#1062515511yescharacteristic
375C22#41×D2311yescharacteristic
376C22#41×D2311yescharacteristic
377C22#41×D2311yescharacteristic
378C22#1062516011yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—462no—
386C4—462no—
387C4—462no—
388C4—462no—
389C4—921no—
390C4—921no—
391C4—921no—
392C2—42no—
393C2—464no—
394C2#117×D2311yescharacteristic
395C2C4×#6729011yescharacteristic
396C2#1309288911yescharacteristic
397C2#1309309011yescharacteristic
398C2#1309309711yescharacteristic
399C2#1309311411yescharacteristic
400C2#1309311811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#388C2
socle, cosocleC23×C23C24
prime radicalC22×C22⋊D23C22
hypercenter#388D23
hypocenterC23#2353
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #13092310C2semidirect
3. #13092304C2semidirect
4. #13092298C2semidirect
7. #13092284C2semidirect
8. #13092278C2semidirect
9. #13092274C2semidirect
10. C22⋊C4×Dic23C2semidirect
11. C4×(C2×D23)⋊C4C2semidirect
12. #13092264C2semidirect
13. #13092263C2semidirect
14. #95×D23C2semidirect
15. C23×#388C2semidirect
37. (C22⋊D23)⋊C4C4semidirect
65. C22×Dic23C2×C4semidirect
85. C22⋊C4×C23C2×C4semidirect
93. Dic23⋊C4C2×C4semidirect
97. C4×Dic23C2×C4semidirect
194. #388D23semidirect
252. C23#2353semidirect
293. C22⋊C4C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D23)⋊C42
#130923102
#130923042
#130922982
#130922932
#130922842
#130922782
#130922742
C22⋊C4×Dic232
C4×(C2×D23)⋊C42
#130922642
#130922632
#95×D232
C23×#3882
#235323