Finite Group Databasebeta

← #15676038

Subgroups — #15676038

Order 2944.

540 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic
2#13092317C211yesmaximal, characteristic
3#13092317C211yesmaximal, characteristic
4#13092314C211yesmaximal, characteristic, complemented
5#13092312C211yesmaximal, characteristic, complemented
6#13092310C211yesmaximal, characteristic, complemented
7#13092308C211yesmaximal, characteristic, complemented
8#13092306C211yesmaximal, characteristic, complemented
9#13092279C211yesmaximal, characteristic, complemented
10#13092278C211yesmaximal, characteristic, complemented
11#13092275C211yesmaximal, characteristic, complemented
12#13092274C211yesmaximal, characteristic, complemented
13C4×Dic23⋊C4C211yesmaximal, characteristic, complemented
14#13092262C211yesmaximal, characteristic, complemented
15C23×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D23C2211yescharacteristic
17C23×Dic23C2211yescharacteristic
18C22×C4×D23C2211yescharacteristic
19C2×C4⋊C4×C23C2211yescharacteristic
20C2×C22⋊C4×C23C2211yescharacteristic
21C2×C22⋊C4×C23C2211yescharacteristic
22C2×C22⋊C4×C23C2211yescharacteristic
23C2×C42×C23C2211yescharacteristic
24C2×C22⋊Dic23C2211yescharacteristic
25C2×C22⋊Dic23C2211yescharacteristic
26C2×(C2×D23)⋊C4C2211yescharacteristic
27C2×(C2×D23)⋊C4C2211yescharacteristic
28C2×(C2×D23)⋊C4C2211yescharacteristic
29C2×(C2×D23)⋊C4C2211yescharacteristic
30C2×(C2×D23)⋊C4C2211yescharacteristic
31C2×C4⋊Dic23C2211yescharacteristic
32C2×Dic23⋊C4C2211yescharacteristic
33C2×Dic23⋊C4C2211yescharacteristic
34C2×Dic23⋊C4C2211yescharacteristic
35C2×Dic23⋊C4C2211yescharacteristic
36C2×Dic23⋊C4C2211yescharacteristic
37C2×C4×Dic23C2211yescharacteristic
38C2×C4×Dic23C2211yescharacteristic
39C2×C4×Dic23C2211yescharacteristic
40C2×C4×Dic23C2211yescharacteristic
41(C22⋊D23)⋊C4C418yescomplemented
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×C414yes—
66C22×Dic23C2311yescharacteristic
67C22×Dic23C2311yescharacteristic
68C22×Dic23C2311yescharacteristic
69C22×Dic23C2311yescharacteristic
70C22×Dic23C2311yescharacteristic
71C22×Dic23C2311yescharacteristic
72C22×Dic23C2311yescharacteristic
73C2×C4×D23—41no—
74C2×C4×D23—41no—
75C2×C4×D23C2×C414yes—
76C4⋊C4×C23—41no—
77C22⋊C4×C23—41no—
78C22⋊C4×C23—41no—
79C22⋊C4×C23C2×C414yes—
80C42×C23—41no—
81C22⋊Dic23—41no—
82C22⋊Dic23—41no—
83(C2×D23)⋊C4—41no—
84(C2×D23)⋊C4—41no—
85(C2×D23)⋊C4—41no—
86(C2×D23)⋊C4—41no—
87(C2×D23)⋊C4C2×C414yes—
88C4⋊Dic23—41no—
89Dic23⋊C4—22no—
90Dic23⋊C4—22no—
91Dic23⋊C4—41no—
92Dic23⋊C4—41no—
93Dic23⋊C4C2×C414yes—
94C4×Dic23—22no—
95C4×Dic23—22no—
96C4×Dic23—41no—
97C4×Dic23C2×C414yes—
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×D23—21no—
111C22×D23—21no—
112C22×D23C22×C412yes—
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×C23—21no—
129C2×C4×C23C22×C412yes—
130C2×C4×C23C22×C412yes—
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—44no—
149C2×Dic23C22×C412yes—
150C2×Dic23C22×C412yes—
151C2×Dic23C22×C412yes—
152C2×Dic23#4112yes—
153C2×Dic23#4112yes—
154C4×D23—44no—
155#2319—231nomaximal, Sylow
156C22×C23—22no—
157C22×C23—22no—
158C22×C23—22no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23—41no—
163C22×C23C23×C411yescharacteristic
164C22×C23C2×#4111yescharacteristic
165C22×C23C2×#4111yescharacteristic
166C22×C23H(5,𝔽2)11yescharacteristic
167C22×C23H(5,𝔽2)11yescharacteristic
168C22×C23H(5,𝔽2)11yescharacteristic
169C22×C232−1+411yescharacteristic
170C2×D23—22no—
171C2×D23—22no—
172C2×D23—22no—
173C2×D23—41no—
174C2×D23—41no—
175C2×D23—41no—
176C2×D23—41no—
177C4×C23—22no—
178C4×C23—22no—
179C4×C23—41no—
180C4×C23—41no—
181C4×C23—41no—
182C4×C23—41no—
183Dic23—22no—
184Dic23—22no—
185Dic23—41no—
186Dic23—41no—
187Dic23—41no—
188Dic23—41no—
189Dic23#11714yes—
190C2×C4×D4—231no—
191#390—231no—
192#390—231no—
193#389—231no—
194#389—231no—
195#388—231no—
196#388—231no—
197#388—231no—
198#388D2311yescharacteristic, complemented
199#381—231no—
200#381—231no—
201#380—231no—
202#380—231no—
203C4×C4⋊C4—231no—
204#376—231no—
205C2×C23—42no—
206C2×C23C2×#11711yescharacteristic
207C2×C23#51811yescharacteristic
208C2×C23#52011yescharacteristic
209C2×C23#54011yescharacteristic
210C2×C23#54011yescharacteristic
211C2×C23#54211yescharacteristic
212C2×C23#54211yescharacteristic
213D23—42no—
214C22×D4—231no—
215C23×C4—231no—
216C23×C4—231no—
217C4×D4—238no—
218C2×C4⋊C4—231no—
219C2×C4⋊C4—231no—
220C2×C4⋊C4—231no—
221C2×C4⋊C4—231no—
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⋊C4—231no—
231C2×C22⋊C4—231no—
232C2×C22⋊C4C2×D2311yescharacteristic
233C2×C22⋊C4C2×D2311yescharacteristic
234C2×C22⋊C4C2×D2311yescharacteristic
235C2×C42—231no—
236C2×C42—231no—
237C2×C42—231no—
238C2×C42—231no—
239C2×C42C2×D2311yescharacteristic
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#95C2×D2311yescharacteristic
249#95C2×D2311yescharacteristic
250C23#231911yescharacteristic, complemented, Sylow
251C24—231no—
252C24C22×D2311yescharacteristic
253C2×D4—234no—
254C2×D4—462no—
255C2×D4—462no—
256C22×C4—231no—
257C22×C4—231no—
258C22×C4—231no—
259C22×C4—234no—
260C22×C4—234no—
261C22×C4—231no—
262C22×C4—231no—
263C22×C4—231no—
264C22×C4—231no—
265C22×C4—921no—
266C22×C4—921no—
267C22×C4—921no—
268C22×C4—921no—
269C22×C4C22×D2311yescharacteristic
270C22×C4C22×D2311yescharacteristic
271C22×C4C22×D2311yescharacteristic
272C22×C4C22×D2311yescharacteristic
273C22×C4C22×D2311yescharacteristic
274C22×C4C22×D2311yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—234no—
277C4⋊C4—462no—
278C4⋊C4—462no—
279C4⋊C4—921no—
280C4⋊C4—921no—
281C4⋊C4—921no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—234no—
285C22⋊C4—921no—
286C22⋊C4—921no—
287C22⋊C4—921no—
288C22⋊C4—921no—
289C22⋊C4—921no—
290C22⋊C4—921no—
291C22⋊C4C4×D2314yes—
292C42—41no—
293C42—234no—
294C42—462no—
295C42—462no—
296C42—921no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—232no—
304C23—461no—
305C23—461no—
306C23—461no—
307C23—461no—
308C23—461no—
309C23—461no—
310C23C2×C4×D2312yes—
311C23C23×D2311yescharacteristic
312D4—468no—
313C2×C4—21no—
314C2×C4—21no—
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—232no—
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—924no—
351C2×C4—924no—
352C2×C4C2×C4×D2312yes—
353C2×C4C2×C4×D2312yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—462no—
362C22—462no—
363C22—462no—
364C22—921no—
365C22—921no—
366C22—921no—
367C22—921no—
368C22C22×C4×D2311yescharacteristic
369C22#1062515511yescharacteristic
370C22#1062515511yescharacteristic
371C22#41×D2311yescharacteristic
372C22#41×D2311yescharacteristic
373C22#1062516011yescharacteristic
374C22#1062516111yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—234no—
382C4—462no—
383C4—462no—
384C4—921no—
385C4—921no—
386C4—921no—
387C4—921no—
388C2—42no—
389C2—922no—
390C2#117×D2311yescharacteristic
391C2#1309288911yescharacteristic
392C2#1309289611yescharacteristic
393C2#1309301711yescharacteristic
394C2#1309301911yescharacteristic
395C2#1309303111yescharacteristic
396C2#1309303311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#388C2
socle, cosocleC23×C23C24
prime radicalC22×C22⋊D23C22
hypercenter#388D23
hypocenterC23#2319
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. #13092314C2semidirect
5. #13092312C2semidirect
6. #13092310C2semidirect
7. #13092308C2semidirect
8. #13092306C2semidirect
9. #13092279C2semidirect
10. #13092278C2semidirect
11. #13092275C2semidirect
12. #13092274C2semidirect
13. C4×Dic23⋊C4C2semidirect
14. #13092262C2semidirect
15. C23×#388C2semidirect
41. (C22⋊D23)⋊C4C4semidirect
198. #388D23semidirect
250. C23#2319semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D23)⋊C42
#130923172
#130923142
#130923122
#130923102
#130923082
#130923062
#130922792
#130922782
#130922752
#130922742
C4×Dic23⋊C42
#130922622
C23×#3882
#231923