Finite Group Databasebeta

← #15682848

Subgroups — #15682848

Order 2944.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625121C211yesmaximal, characteristic, complemented
2#13092963C211yesmaximal, characteristic, complemented
3#41×Dic23C211yesmaximal, characteristic, complemented
4#13092641C211yesmaximal, characteristic, complemented
5#13092637C211yesmaximal, characteristic, complemented
6#13092634C211yesmaximal, characteristic, complemented
7#13092630C211yesmaximal, characteristic, complemented
8#13092625C211yesmaximal, characteristic, complemented
9#13092620C211yesmaximal, characteristic, complemented
10#13092615C211yesmaximal, characteristic, complemented
11#13092610C211yesmaximal, characteristic, complemented
12C2×Dic23⋊C8C211yesmaximal, characteristic, complemented
13#13092414C211yesmaximal, characteristic, complemented
14#13092413C211yesmaximal, characteristic, complemented
15C2×C23×#135C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#41×C23C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C23×#135—24no—
20C2×Q16×C23C2211yescharacteristic
21C2×SD16×C23C2211yescharacteristic
22C2×SD16×C23C2211yescharacteristic
23C2×D8×C23C2211yescharacteristic
24C22×C8×C23C2211yescharacteristic
25#10625121—24no—
26#10625118C2211yescharacteristic
27Q8×Dic23C2211yescharacteristic
28Q8×Dic23C2211yescharacteristic
29#10625115C2211yescharacteristic
30C2×#67275C2211yescharacteristic
31C2×#67274C2211yescharacteristic
32#10625111C2211yescharacteristic
33#10625110—21no—
34#10625110—21no—
35#10625107C2211yescharacteristic
36D4×Dic23—21no—
37D4×Dic23—21no—
38D4×Dic23C2211yescharacteristic
39D4×Dic23C2211yescharacteristic
40C2×#67273C2211yescharacteristic
41C2×#67272C2211yescharacteristic
42C4×C22⋊D23—21no—
43C4×C22⋊D23—21no—
44#10625097—21no—
45#10625097C2211yescharacteristic
46C2×C4×Dic23—21no—
47C2×C4×Dic23C2211yescharacteristic
48C22×C23⋊C8C2211yescharacteristic
49#10625017C2211yescharacteristic
50#10625017C2211yescharacteristic
51#10625014C2211yescharacteristic
52#10625014C2211yescharacteristic
53#10625003C2211yescharacteristic
54#10625003C2211yescharacteristic
55#10624998C2211yescharacteristic
56#10624998C2211yescharacteristic
57Dic23⋊C8C2211yescharacteristic
58Dic23⋊C8C2211yescharacteristic
59Dic23⋊C8C2211yescharacteristic
60Dic23⋊C8C2211yescharacteristic
61#41×C23—22no—
62#41×C23—22no—
63#41×C23—22no—
64#41×C23D414yescomplemented
65C2×Q8×C23C2311yescharacteristic
66C2×Q8×C23C2311yescharacteristic
67C2×D4×C23—21no—
68C2×D4×C23—21no—
69C2×D4×C23C2311yescharacteristic
70C2×D4×C23C2311yescharacteristic
71C22×C4×C23—21no—
72C22×C4×C23—21no—
73C22×C4×C23C2311yescharacteristic
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C22×Dic23—21no—
78C22×Dic23—21no—
79C22×Dic23D411yescharacteristic
80C22×Dic23D411yescharacteristic
81#67288—22no—
82#67288—22no—
83C2×D92C2311yescharacteristic
84C2×C4×D23—21no—
85C2×Dic46C2311yescharacteristic
86Q16×C23—22no—
87SD16×C23—22no—
88SD16×C23—22no—
89D8×C23—22no—
90C2×C8×C23—22no—
91C2×C8×C23C2311yescharacteristic
92C2×C8×C23C2311yescharacteristic
93C22⋊Dic23—21no—
94C22⋊Dic23—21no—
95C22⋊Dic23—21no—
96C22⋊Dic23—21no—
97C22⋊Dic23—21no—
98#67275—22no—
99#67274—22no—
100#67273—22no—
101#67272—22no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104C4⋊Dic23—21no—
105C4⋊Dic23—21no—
106C4⋊Dic23C2311yescharacteristic
107C4⋊Dic23C2311yescharacteristic
108Dic23⋊C4—21no—
109Dic23⋊C4—21no—
110C4×Dic23—21no—
111C4×Dic23—21no—
112C4×Dic23—21no—
113C4×Dic23D411yescharacteristic
114C4×Dic23D411yescharacteristic
115C4×Dic23C2311yescharacteristic
116C4×Dic23C2311yescharacteristic
117C2×C23⋊C8—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120C23×C23—21no—
121C23×C23—21no—
122C23×C23C2×D411yescharacteristic
123C22×D23—21no—
124Q8×C23—21no—
125Q8×C23—21no—
126Q8×C23—21no—
127Q8×C23C2×D412yes—
128D4×C23—24no—
129D4×C23—21no—
130D4×C23—21no—
131D4×C23—21no—
132D4×C23—42no—
133D4×C23C2×D412yes—
134C2×C4×C23—21no—
135C2×C4×C23—24no—
136C2×C4×C23—21no—
137C2×C4×C23—42no—
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D412yes—
140C2×C4×C23#4112yes—
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—42no—
143C22⋊D23—42no—
144C22⋊D23—42no—
145C2×Dic23—22no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—41no—
150C2×Dic23—42no—
151C2×Dic23—42no—
152C2×Dic23C2×D411yescharacteristic
153C2×Dic23C2×D411yescharacteristic
154C2×Dic23C2×D411yescharacteristic
155C2×Dic23C2×D411yescharacteristic
156D92—21no—
157D92—21no—
158C4×D23—42no—
159Dic46—21no—
160Dic46—21no—
161C8×C23—21no—
162C8×C23—21no—
163C23⋊C8—21no—
164C23⋊C8—21no—
165#3035—231nomaximal, Sylow
166C22×C23—21no—
167C22×C23—21no—
168C22×C23—22no—
169C22×C23—41no—
170C22×C23—41no—
171C22×C23—41no—
172C22×C23—41no—
173C22×C23—41no—
174C22×C23#12112yes—
175C22×C23C22×D411yescharacteristic
176C2×D23—41no—
177C2×D23—41no—
178C2×D23—41no—
179C4×C23—22no—
180C4×C23—41no—
181C4×C23#12112yes—
182C4×C23C22×D411yescharacteristic
183C4×C23C2×#4111yescharacteristic
184Dic23—21no—
185Dic23—21no—
186Dic23—21no—
187Dic23—41no—
188Dic23—41no—
189Dic23—41no—
190Dic23#13512yescomplemented
191C2×#135—231no—
192C2×#135D2311yescharacteristic, complemented
193#532—231no—
194C4×#41—231no—
195#464—231no—
196#464—231no—
197#463—231no—
198#463—231no—
199#462—231no—
200#461—231no—
201#460—231no—
202#459—231no—
203C2×C4⋊C8—231no—
204#416—231no—
205#416—231no—
206C2×C23—22no—
207C2×C23—42no—
208C2×C23—81no—
209C2×C23C2×#12111yescharacteristic
210C2×C23C2×#13511yescharacteristic
211C2×C23#57511yescharacteristic
212D23—81no—
213C2×#41—231no—
214C2×#41C2×D2311yescharacteristic
215C2×#41C2×D2311yescharacteristic
216#135—24no—
217#135—464no—
218C2×Q16—231no—
219C2×Q16C2×D2311yescharacteristic
220C2×SD16—231no—
221C2×SD16—231no—
222C2×SD16C2×D2311yescharacteristic
223C2×SD16C2×D2311yescharacteristic
224C2×D8—231no—
225C2×D8C2×D2311yescharacteristic
226C22×C8—231no—
227C22×C8C2×D2311yescharacteristic
228C4⋊Q8—231no—
229#127—231no—
230#124—231no—
231#124—231no—
232#121—461no—
233#121—461no—
234C4×Q8—231no—
235C4×Q8—231no—
236C4×D4—231no—
237C4×D4—231no—
238C4×D4—461no—
239C4×D4—461no—
240C4×D4—461no—
241C4×D4—461no—
242#117—231no—
243#117—461no—
244C2×C42—231no—
245C2×C42—461no—
246C4⋊C8—231no—
247C4⋊C8—231no—
248C4⋊C8—231no—
249C4⋊C8—231no—
250#103—231no—
251#103—231no—
252#103—231no—
253#103—231no—
254#102—231no—
255#102—231no—
256#102—231no—
257#102—231no—
258C23#303511yescharacteristic, complemented, Sylow
259#41—22no—
260#41—22no—
261#41—22no—
262#41—462no—
263#41—462no—
264#41C22⋊D2314yescomplemented
265C2×Q8—231no—
266C2×Q8C22×D2311yescharacteristic
267C2×Q8C22×D2311yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—231no—
271C2×D4—461no—
272C2×D4—461no—
273C2×D4—461no—
274C2×D4C22×D2311yescharacteristic
275C2×D4C22×D2311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—231no—
279C22×C4—231no—
280C22×C4—461no—
281C22×C4—461no—
282C22×C4—461no—
283C22×C4C22×D2311yescharacteristic
284Q16—22no—
285Q16—462no—
286SD16—22no—
287SD16—22no—
288SD16—462no—
289SD16—462no—
290D8—22no—
291D8—462no—
292C2×C8—22no—
293C2×C8—231no—
294C2×C8—231no—
295C2×C8—462no—
296C2×C8C22×D2311yescharacteristic
297C2×C8C22×D2311yescharacteristic
298C4⋊C4—231no—
299C4⋊C4—231no—
300C4⋊C4—461no—
301C4⋊C4—461no—
302C4⋊C4—461no—
303C4⋊C4—461no—
304C22⋊C4—461no—
305C22⋊C4—461no—
306C22⋊C4—461no—
307C22⋊C4—461no—
308C22⋊C4—461no—
309C22⋊C4—461no—
310C22⋊C4—461no—
311C42—231no—
312C42—231no—
313C42—231no—
314C42—231no—
315C42—461no—
316C42—461no—
317C42—461no—
318C23—21no—
319C23—21no—
320C23—461no—
321C23D4×D2311yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—461no—
326Q8—461no—
327Q8C2×C22⋊D2312yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—461no—
334D4—461no—
335D4—922no—
336D4—922no—
337D4—922no—
338D4C2×C22⋊D2312yes—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—231no—
344C2×C4—231no—
345C2×C4—231no—
346C2×C4—231no—
347C2×C4—462no—
348C2×C4—461no—
349C2×C4—461no—
350C2×C4—461no—
351C2×C4—922no—
352C2×C4—921no—
353C2×C4—922no—
354C2×C4—922no—
355C2×C4D4×D2311yescharacteristic
356C2×C4#6729012yes—
357C2×C4C2×C22⋊D2312yes—
358C2×C4C23×D2311yescharacteristic
359C8—21no—
360C8—21no—
361C8—461no—
362C8—461no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—921no—
372C22—921no—
373C22—921no—
374C22#1062511012yes—
375C22C2×D4×D2311yescharacteristic
376C4—22no—
377C4—41no—
378C4—232no—
379C4—461no—
380C4—461no—
381C4—461no—
382C4—921no—
383C4—921no—
384C4—921no—
385C4#1062511012yes—
386C4C2×#6729011yescharacteristic
387C4C22×C22⋊D2311yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—1841no—
392C2C2×#1062511011yescharacteristic
393C2#135×D2311yescharacteristic
394C2#1309321411yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#135C2
socleC22×C23C22×D4
hypercenterC2×#135D23
hypocenterC23#3035
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#10625121C2semidirect
2. #13092963C2semidirect
3. #41×Dic23C2semidirect
4. #13092641C2semidirect
5. #13092637C2semidirect
6. #13092634C2semidirect
7. #13092630C2semidirect
8. #13092625C2semidirect
9. #13092620C2semidirect
10. #13092615C2semidirect
11. #13092610C2semidirect
12. C2×Dic23⋊C8C2semidirect
13. #13092414C2semidirect
14. #13092413C2semidirect
15. C2×C23×#135C2semidirect
64. #41×C23D4semidirect
190. Dic23#135semidirect
192. C2×#135D23semidirect
258. C23#3035semidirect
264. #41C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251212
#130929632
#41×Dic232
#130926412
#130926372
#130926342
#130926302
#130926252
#130926202
#130926152
#130926102
C2×Dic23⋊C82
#130924142
#130924132
C2×C23×#1352
#303523