Finite Group Databasebeta

← #15685136

Subgroups — #15685136

Order 2944.

482 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625121C211yesmaximal, characteristic, complemented
2C2×Q16×D23C211yesmaximal, characteristic, complemented
3#13093077C211yesmaximal, characteristic, complemented
4#13093074C211yesmaximal, characteristic, complemented
5#13092798C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092641C211yesmaximal, characteristic, complemented
9#13092638C211yesmaximal, characteristic, complemented
10#13092581C211yesmaximal, characteristic, complemented
11#13092557C211yesmaximal, characteristic, complemented
12#13092554C211yesmaximal, characteristic, complemented
13#13092509C211yesmaximal, characteristic, complemented
14(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
15C23×#452C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic
18C2×Q8×D23C2211yescharacteristic
19C2×#67288C2211yescharacteristic
20C2×Q16×C23C2211yescharacteristic
21C2×SD16×C23C2211yescharacteristic
22C23×C22⋊Q8C2211yescharacteristic
23#10625121—24no—
24#10625118C2211yescharacteristic
25Q8×Dic23C2211yescharacteristic
26C2×#67275C2211yescharacteristic
27C2×#67275C2211yescharacteristic
28C2×#67274C2211yescharacteristic
29#10625109—21no—
30#10625109C2211yescharacteristic
31#10625107—21no—
32#10625107C2211yescharacteristic
33C2×#67273C2211yescharacteristic
34C2×#67272C2211yescharacteristic
35C4×C22⋊D23—21no—
36C4×C22⋊D23C2211yescharacteristic
37#10625095—21no—
38#10625095C2211yescharacteristic
39C22×C23⋊C8C2211yescharacteristic
40Q16×D23—24no—
41C2×Dic92C2211yescharacteristic
42C2×#67263C2211yescharacteristic
43C2×C8×D23C2211yescharacteristic
44#10625067—21no—
45#10625066C2211yescharacteristic
46#10625064—21no—
47#10625058C2211yescharacteristic
48#10625056—21no—
49#10625055—21no—
50C23×#103C2211yescharacteristic
51C23×#102C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic
53#10625017C2211yescharacteristic
54#10625003C2211yescharacteristic
55(C2×D23)⋊C8C2211yescharacteristic
56#10624998C2211yescharacteristic
57Dic23⋊C8C2211yescharacteristic
58C8×Dic23C2211yescharacteristic
59#10624992C2211yescharacteristic
60#10624989C2211yescharacteristic
61#41×C23—22no—
62#41×C23—41no—
63C2×Q8×C23C2311yescharacteristic
64C2×Q8×C23C2311yescharacteristic
65C2×D4×C23—21no—
66C2×D4×C23C2311yescharacteristic
67C22×C4×C23—21no—
68C22×C4×C23C2311yescharacteristic
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23D411yescharacteristic
72Q8×D23—22no—
73Q8×D23—22no—
74Q8×D23—41no—
75Q8×D23—41no—
76#67288—22no—
77#67288—41no—
78C2×D92—21no—
79C2×D92C2311yescharacteristic
80C2×C4×D23—21no—
81C2×C4×D23—21no—
82C2×C4×D23—21no—
83C2×C4×D23C2311yescharacteristic
84C2×Dic46—21no—
85C2×Dic46—21no—
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88Q16×C23—22no—
89SD16×C23—41no—
90C2×C8×C23C2311yescharacteristic
91C2×C8×C23C2311yescharacteristic
92C4⋊C4×C23—21no—
93C4⋊C4×C23C2311yescharacteristic
94C22⋊C4×C23—21no—
95C22⋊Dic23—21no—
96C22⋊Dic23—21no—
97C22⋊Dic23—21no—
98C22⋊Dic23—21no—
99C22⋊Dic23D411yescharacteristic
100#67275—22no—
101#67275D414yescomplemented
102#67274—22no—
103#67273—22no—
104#67272—22no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4D411yescharacteristic
109C4⋊Dic23—21no—
110C4⋊Dic23C2311yescharacteristic
111Dic23⋊C4—21no—
112Dic23⋊C4—21no—
113Dic23⋊C4D411yescharacteristic
114C4×Dic23—21no—
115C4×Dic23—21no—
116C4×Dic23C2311yescharacteristic
117C2×C23⋊C8—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120Dic92—22no—
121#67263—41no—
122C8×D23—22no—
123C23×C23—21no—
124C23×C23C2×D411yescharacteristic
125C22×D23—21no—
126C22×D23C2×D411yescharacteristic
127Q8×C23—21no—
128Q8×C23—21no—
129Q8×C23—21no—
130Q8×C23C2×D412yes—
131D4×C23—21no—
132D4×C23—21no—
133D4×C23—42no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—42no—
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—22no—
143C22⋊D23—42no—
144C22⋊D23—42no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23C2×D411yescharacteristic
149C2×Dic23C2×D411yescharacteristic
150C2×Dic23C2×D411yescharacteristic
151D92—21no—
152D92—21no—
153D92—42no—
154C4×D23—21no—
155C4×D23—21no—
156C4×D23—42no—
157C4×D23—42no—
158C4×D23—42no—
159Dic46—21no—
160Dic46—21no—
161Dic46—21no—
162Dic46—42no—
163Dic46—42no—
164Dic46C2×D412yes—
165C8×C23—21no—
166C8×C23—21no—
167C23⋊C8—21no—
168C23⋊C8C2×D412yes—
169#3285—231nomaximal, Sylow
170C22×C23—21no—
171C22×C23—21no—
172C22×C23—21no—
173C22×C23—41no—
174C22×C23—41no—
175C22×C23—41no—
176C22×C23C22×D411yescharacteristic
177C2×D23—21no—
178C2×D23—21no—
179C2×D23—41no—
180C2×D23—41no—
181C2×D23—41no—
182C2×D23#13512yescomplemented
183C4×C23—22no—
184C4×C23—21no—
185C4×C23—41no—
186C4×C23—41no—
187C4×C23C22×D411yescharacteristic
188C4×C23H(5,𝔽2)11yescharacteristic
189Dic23—22no—
190Dic23—21no—
191Dic23—21no—
192Dic23—21no—
193Dic23—41no—
194Dic23—41no—
195C2×#135—231no—
196C22×Q16—231no—
197#548—231no—
198#548—231no—
199#495—231no—
200#467—231no—
201#466—231no—
202#464—231no—
203#464—231no—
204#452—231no—
205#452D2311yescharacteristic, complemented
206#448—231no—
207#448—231no—
208C4×Q16—231no—
209C8×D4—231no—
210C2×C23—41no—
211C2×C23—81no—
212C2×C23D4211yescharacteristic
213C2×C23C2×#13511yescharacteristic
214C2×C23#57811yescharacteristic
215D23—22no—
216D23—81no—
217C2×#41—231no—
218C2×#41C2×D2311yescharacteristic
219C22×Q8—231no—
220C22×Q8—231no—
221#135—464no—
222C2×Q16—231no—
223C2×Q16—231no—
224C2×Q16—231no—
225C2×Q16—464no—
226C2×Q16C2×D2311yescharacteristic
227C2×SD16—231no—
228C2×SD16—231no—
229C2×SD16—231no—
230C2×SD16C2×D2311yescharacteristic
231C2×D8—231no—
232C22×C8—231no—
233C22×C8—231no—
234#124—231no—
235#124—231no—
236#124—461no—
237#124—461no—
238C22⋊Q8—231no—
239C22⋊Q8—461no—
240C22⋊Q8—461no—
241C22⋊Q8C2×D2311yescharacteristic
242#121—231no—
243#121—231no—
244#121—461no—
245#121—461no—
246C4×Q8—231no—
247C4×Q8—231no—
248C4×D4—231no—
249C4×D4—461no—
250C4×D4—461no—
251#107—231no—
252C4⋊C8—231no—
253#103—231no—
254#103—231no—
255#103—231no—
256#103C2×D2311yescharacteristic
257#102—231no—
258#102C2×D2311yescharacteristic
259C22⋊C8—231no—
260C22⋊C8C2×D2311yescharacteristic
261C4×C8—231no—
262C23#328511yescharacteristic, complemented, Sylow
263#41—22no—
264#41—41no—
265#41—462no—
266#41—921no—
267C2×Q8—231no—
268C2×Q8—231no—
269C2×Q8—461no—
270C2×Q8—461no—
271C2×Q8—462no—
272C2×Q8—462no—
273C2×Q8—921no—
274C2×Q8—921no—
275C2×Q8C22×D2311yescharacteristic
276C2×Q8C22×D2311yescharacteristic
277C2×D4—21no—
278C2×D4—231no—
279C2×D4—231no—
280C2×D4—461no—
281C2×D4—461no—
282C2×D4—461no—
283C2×D4C22×D2311yescharacteristic
284C22×C4—21no—
285C22×C4—231no—
286C22×C4—461no—
287C22×C4—461no—
288C22×C4—461no—
289C22×C4C22×D2311yescharacteristic
290Q16—22no—
291Q16—234no—
292Q16—462no—
293Q16—462no—
294SD16—41no—
295SD16—462no—
296SD16—462no—
297SD16—921no—
298D8—462no—
299C2×C8—231no—
300C2×C8—231no—
301C2×C8—462no—
302C2×C8—462no—
303C2×C8C22×D2311yescharacteristic
304C2×C8C22×D2311yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—231no—
307C4⋊C4—231no—
308C4⋊C4—461no—
309C4⋊C4—461no—
310C4⋊C4—461no—
311C4⋊C4C22×D2311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—231no—
314C22⋊C4—231no—
315C22⋊C4—461no—
316C22⋊C4—461no—
317C22⋊C4—461no—
318C22⋊C4—461no—
319C22⋊C4—461no—
320C22⋊C4—461no—
321C22⋊C4—461no—
322C42—231no—
323C42—461no—
324C42—461no—
325C23—21no—
326C23—231no—
327C23—461no—
328C23D4×D2311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—232no—
333Q8—461no—
334Q8—461no—
335Q8—461no—
336Q8—922no—
337Q8—922no—
338Q8D4×D2312yes—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—462no—
343D4—461no—
344D4—461no—
345D4—922no—
346D4—922no—
347D4—922no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—231no—
355C2×C4—231no—
356C2×C4—231no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—461no—
361C2×C4—461no—
362C2×C4—922no—
363C2×C4—922no—
364C2×C4—922no—
365C2×C4D4×D2311yescharacteristic
366C2×C4C23×D2311yescharacteristic
367C8—21no—
368C8—21no—
369C8—232no—
370C8—461no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—232no—
378C22—461no—
379C22—461no—
380C22—921no—
381C22—921no—
382C22—921no—
383C22C2×D4×D2311yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—461no—
389C4—461no—
390C4—461no—
391C4—462no—
392C4—921no—
393C4—921no—
394C4C2×D4×D2311yescharacteristic
395C4#1062515511yescharacteristic
396C2—41no—
397C2—81no—
398C2—462no—
399C2—1841no—
400C2#1309304911yescharacteristic
401C2#135×D2311yescharacteristic
402C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#452C2
socleC22×C23C22×D4
hypercenter#452D23
hypocenterC23#3285
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#10625121C2semidirect
2. C2×Q16×D23C2semidirect
3. #13093077C2semidirect
4. #13093074C2semidirect
5. #13092798C2semidirect
6. #13092656C2semidirect
7. #13092652C2semidirect
8. #13092641C2semidirect
9. #13092638C2semidirect
10. #13092581C2semidirect
11. #13092557C2semidirect
12. #13092554C2semidirect
13. #13092509C2semidirect
14. (C22⋊D23)⋊C8C2semidirect
15. C23×#452C2semidirect
101. #67275D4semidirect
182. C2×D23#135semidirect
205. #452D23semidirect
262. C23#3285semidirect

Maximal subgroups

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

subgroupindex
C2×#106251212
C2×Q16×D232
#130930772
#130930742
#130927982
#130926562
#130926522
#130926412
#130926382
#130925812
#130925572
#130925542
#130925092
(C22⋊D23)⋊C82
C23×#4522
#328523