Finite Group Databasebeta

← #15684944

Subgroups — #15684944

Order 2944.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625079C211yesmaximal, characteristic, complemented
2C2×#10625087C211yesmaximal, characteristic, complemented
3#13093085C211yesmaximal, characteristic, complemented
4#13093058C211yesmaximal, characteristic, complemented
5#13092803C211yesmaximal, characteristic, complemented
6#13092654C211yesmaximal, characteristic, complemented
7#13092642C211yesmaximal, characteristic, complemented
8#13092611C211yesmaximal, characteristic, complemented
9#13092577C211yesmaximal, characteristic, complemented
10#13092565C211yesmaximal, characteristic, complemented
11#13092563C211yesmaximal, characteristic, complemented
12#13092550C211yesmaximal, characteristic, complemented
13#13092516C211yesmaximal, characteristic, complemented
14#13092486C211yesmaximal, characteristic, complemented
15C23×#468C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×#67290C2211yescharacteristic, complemented
18C2×#67288C2211yescharacteristic
19C22×D92C2211yescharacteristic
20C2×SD16×C23C2211yescharacteristic, complemented
21C2×M16×C23C2211yescharacteristic
22C23×C22⋊Q8C2211yescharacteristic
23C23×#121C2211yescharacteristic
24#10625118C2211yescharacteristic
25C2×#67275C2211yescharacteristic, complemented
26C2×#67274C2211yescharacteristic, complemented
27#10625111—21no—
28#10625111C2211yescharacteristic, complemented
29#10625110—21no—
30C2×#67272C2211yescharacteristic
31C2×#67272C2211yescharacteristic
32C4×C22⋊D23C2211yescharacteristic
33#10625087—24no—
34#10625079—24no—
35C2×D184C2211yescharacteristic
36C2×D184C2211yescharacteristic
37C2×#67263C2211yescharacteristic
38C2×#67263C2211yescharacteristic
39C2×C8×D23C2211yescharacteristic, complemented
40#10625066—21no—
41#10625066C2211yescharacteristic
42#10625066C2211yescharacteristic, complemented
43#10625065—21no—
44#10625064C2211yescharacteristic
45#10625058C2211yescharacteristic, complemented
46#10625055—21no—
47#10625053—21no—
48(C22⋊D23)⋊C4—21no—
49C22⋊C4×D23—21no—
50C23×#107C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53C22⋊(C23⋊C8)C2211yescharacteristic
54(C2×D23)⋊C8C2211yescharacteristic, complemented
55#10624997C2211yescharacteristic, complemented
56Dic23⋊C8C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic
59#10624991C2211yescharacteristic
60#10624991C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23D411yescharacteristic
71C22×Dic23—21no—
72#67292—22no—
73#67292—41no—
74#67290—22no—
75#67290—41no—
76#67288—22no—
77#67288—41no—
78C2×D92—22no—
79C2×D92—21no—
80C2×D92—21no—
81C2×D92—21no—
82C2×D92—21no—
83C2×D92—41no—
84C2×D92C2311yescharacteristic
85C2×D92C2311yescharacteristic
86C2×D92C2311yescharacteristic
87C2×C4×D23—21no—
88C2×C4×D23—21no—
89C2×C4×D23—21no—
90C2×C4×D23C2311yescharacteristic
91C2×Dic46C2311yescharacteristic
92SD16×C23—22no—
93M16×C23—22no—
94C2×C8×C23C2311yescharacteristic
95C2×C8×C23C2311yescharacteristic
96C4⋊C4×C23—21no—
97C4⋊C4×C23C2311yescharacteristic
98C4⋊C4×C23C2311yescharacteristic
99C22⋊C4×C23—21no—
100C22⋊C4×C23—21no—
101C22⋊Dic23D411yescharacteristic
102#67275—22no—
103#67274—41no—
104#67272—22no—
105#67272—41no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4D411yescharacteristic
112Dic23⋊C4—21no—
113Dic23⋊C4D411yescharacteristic
114C4×Dic23—21no—
115C4×Dic23C2311yescharacteristic
116C2×C23⋊C8C2311yescharacteristic
117C2×C23⋊C8C2311yescharacteristic
118D184—22no—
119D184—22no—
120#67263—22no—
121#67263D414yescomplemented
122C8×D23—22no—
123C23×C23—21no—
124C23×C23C2×D411yescharacteristic
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—42no—
129C22×D23—42no—
130C22×D23—81no—
131C22×D23C2×D411yescharacteristic
132Q8×C23—21no—
133Q8×C23—21no—
134D4×C23—21no—
135D4×C23—21no—
136D4×C23—81no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23C2×D411yescharacteristic
143C2×C4×C23C2411yescharacteristic
144C22⋊D23—41no—
145C22⋊D23—42no—
146C22⋊D23—42no—
147C22⋊D23—42no—
148C22⋊D23—81no—
149C2×Dic23—21no—
150C2×Dic23—42no—
151C2×Dic23C2×D411yescharacteristic
152C2×Dic23C2×D411yescharacteristic
153C2×Dic23C2×D411yescharacteristic
154D92—21no—
155D92—21no—
156D92—21no—
157D92—21no—
158D92—21no—
159D92—42no—
160D92—42no—
161D92—81no—
162D92—81no—
163D92C2×D412yes—
164C4×D23—21no—
165C4×D23—21no—
166C4×D23—42no—
167C4×D23—42no—
168C4×D23—81no—
169Dic46—21no—
170Dic46C2×D412yes—
171C8×C23—21no—
172C8×C23C2×D412yes—
173C23⋊C8—21no—
174C23⋊C8—21no—
175#3268—231nomaximal, Sylow
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23—41no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23C22×D411yescharacteristic
183C2×D23—21no—
184C2×D23—22no—
185C2×D23—21no—
186C2×D23—21no—
187C2×D23—41no—
188C2×D23—41no—
189C2×D23—41no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—84no—
196C4×C23—21no—
197C4×C23—41no—
198C4×C23—41no—
199C4×C23—41no—
200C4×C23C22×D411yescharacteristic
201C4×C23H(5,𝔽2)11yescharacteristic
202Dic23—22no—
203Dic23—21no—
204Dic23—21no—
205Dic23—21no—
206C2×AGL(1,ℤ/8)—231no—
207C2×#135—231no—
208#550—231no—
209#546—231no—
210#496—231no—
211#468D2311yescharacteristic, complemented
212#466—231no—
213#464—231no—
214#459—231no—
215#452—231no—
216#449—231no—
217#449—231no—
218#447—231no—
219#440—231no—
220#435—231no—
221C2×C23—41no—
222C2×C23—81no—
223C2×C23D4211yescharacteristic
224C2×C23#57511yescharacteristic
225C2×C23#57611yescharacteristic
226D23—41no—
227D23—42no—
228D23—81no—
229D23—81no—
230C2×#41—231no—
231C2×#41—231no—
232C2×#41—231no—
233C22×D4—231no—
234AGL(1,ℤ/8)—464no—
235#135—464no—
236C2×Q16—231no—
237C2×SD16—231no—
238C2×SD16—231no—
239C2×SD16—231no—
240C2×SD16C2×D2311yescharacteristic, complemented
241C2×D8—231no—
242C2×D8—231no—
243C2×D8—231no—
244C2×D8—231no—
245C2×M16C2×D2311yescharacteristic
246C22×C8—231no—
247#127—231no—
248#127—461no—
249#124—231no—
250#123—461no—
251C22⋊Q8C2×D2311yescharacteristic
252#121—231no—
253#121—231no—
254#121—461no—
255#121—461no—
256#121—461no—
257#121C2×D2311yescharacteristic
258#120—461no—
259C4×Q8—231no—
260C4×D4—231no—
261C4×D4—231no—
262C4×D4—461no—
263C2×C22⋊C4—461no—
264#107C2×D2311yescharacteristic, complemented
265C4⋊C8—231no—
266#103—231no—
267#103C2×D2311yescharacteristic, complemented
268#102—231no—
269#102—231no—
270#102—231no—
271#102C2×D2311yescharacteristic, complemented
272C22⋊C8—231no—
273C22⋊C8—231no—
274#97—231no—
275C23#326811yescharacteristic, complemented, Sylow
276C24—461no—
277#41—462no—
278#41—462no—
279#41—462no—
280#41—921no—
281#41—921no—
282#41—921no—
283C2×Q8—231no—
284C2×Q8C22×D2311yescharacteristic
285C2×D4—21no—
286C2×D4—231no—
287C2×D4—231no—
288C2×D4—231no—
289C2×D4—231no—
290C2×D4—462no—
291C2×D4—461no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—921no—
300C2×D4C22×D2311yescharacteristic
301C22×C4—231no—
302C22×C4—461no—
303C22×C4—461no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4C22×D2311yescharacteristic
307Q16—462no—
308SD16—22no—
309SD16—234no—
310SD16—462no—
311SD16—921no—
312D8—462no—
313D8—462no—
314D8—462no—
315D8—921no—
316M16—22no—
317C2×C8—231no—
318C2×C8—231no—
319C2×C8—462no—
320C2×C8C22×D2311yescharacteristic
321C2×C8C22×D2311yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—231no—
324C4⋊C4—461no—
325C4⋊C4C22×D2311yescharacteristic
326C4⋊C4C22×D2311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—231no—
330C22⋊C4—231no—
331C22⋊C4—461no—
332C22⋊C4—461no—
333C22⋊C4—461no—
334C22⋊C4—461no—
335C22⋊C4—461no—
336C42—231no—
337C42—461no—
338C23—21no—
339C23—231no—
340C23—461no—
341C23—461no—
342C23—461no—
343C23—922no—
344C23—922no—
345C23—1841no—
346C23D4×D2311yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—232no—
350Q8—461no—
351D4—21no—
352D4—21no—
353D4—81no—
354D4—232no—
355D4—461no—
356D4—461no—
357D4—461no—
358D4—461no—
359D4—461no—
360D4—922no—
361D4—922no—
362D4—921no—
363D4—922no—
364D4—922no—
365D4—922no—
366D4—1841no—
367D4—1841no—
368D4—1841no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—231no—
375C2×C4—231no—
376C2×C4—231no—
377C2×C4—461no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—922no—
381C2×C4—922no—
382C2×C4—922no—
383C2×C4—1841no—
384C2×C4D4×D2311yescharacteristic
385C2×C4C23×D2311yescharacteristic
386C8—21no—
387C8—461no—
388C8—461no—
389C8D4×D2312yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—461no—
397C22—461no—
398C22—461no—
399C22—462no—
400C22—921no—
401C22—921no—
402C22—921no—
403C22—921no—
404C22—921no—
405C22—921no—
406C22—921no—
407C22—921no—
408C22—1844no—
409C22C2×D4×D2311yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—461no—
415C4—461no—
416C4—461no—
417C4—462no—
418C4C2×D4×D2311yescharacteristic
419C4#1062516011yescharacteristic
420C2—41no—
421C2—81no—
422C2—921no—
423C2—922no—
424C2—1841no—
425C2—1841no—
426C2#1309305111yescharacteristic
427C2#1309321611yescharacteristic
428C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#468C2
socleC22×C23C22×D4
hypercenter#468D23
hypocenterC23#3268
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. C2×#10625087C2semidirect
3. #13093085C2semidirect
4. #13093058C2semidirect
5. #13092803C2semidirect
6. #13092654C2semidirect
7. #13092642C2semidirect
8. #13092611C2semidirect
9. #13092577C2semidirect
10. #13092565C2semidirect
11. #13092563C2semidirect
12. #13092550C2semidirect
13. #13092516C2semidirect
14. #13092486C2semidirect
15. C23×#468C2semidirect
17. C2×#67290C22semidirect
20. C2×SD16×C23C22semidirect
25. C2×#67275C22semidirect
26. C2×#67274C22semidirect
28. #10625111C22semidirect
39. C2×C8×D23C22semidirect
42. #10625066C22semidirect
45. #10625058C22semidirect
50. C23×#107C22semidirect
51. C23×#103C22semidirect
52. C23×#102C22semidirect
54. (C2×D23)⋊C8C22semidirect
55. #10624997C22semidirect
56. Dic23⋊C8C22semidirect
57. #10624992C22semidirect
60. #10624991C22semidirect
121. #67263D4semidirect
211. #468D23semidirect
240. C2×SD16C2×D23semidirect
264. #107C2×D23semidirect
267. #103C2×D23semidirect
271. #102C2×D23semidirect
275. C23#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
C2×#106250872
#130930852
#130930582
#130928032
#130926542
#130926422
#130926112
#130925772
#130925652
#130925632
#130925502
#130925162
#130924862
C23×#4682
#326823