Finite Group Databasebeta

← #15684940

Subgroups — #15684940

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×#10625120C211yesmaximal, characteristic, complemented
2C2×#10625090C211yesmaximal, characteristic, complemented
3#13093086C211yesmaximal, characteristic, complemented
4#13093058C211yesmaximal, characteristic, complemented
5#13092803C211yesmaximal, characteristic, complemented
6#13092665C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092641C211yesmaximal, characteristic, complemented
9#13092611C211yesmaximal, characteristic, complemented
10#13092565C211yesmaximal, characteristic, complemented
11#13092561C211yesmaximal, characteristic, complemented
12#13092553C211yesmaximal, characteristic, complemented
13#13092520C211yesmaximal, characteristic, complemented
14#13092491C211yesmaximal, characteristic, complemented
15C23×#452C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×#67292C2211yescharacteristic, complemented
19C22×D92C2211yescharacteristic
20C2×Q16×C23C2211yescharacteristic, complemented
21C2×SD16×C23C2211yescharacteristic, complemented
22C23×C22⋊Q8C2211yescharacteristic
23#10625120—24no—
24#10625118C2211yescharacteristic
25Q8×Dic23C2211yescharacteristic, complemented
26C2×#67274C2211yescharacteristic
27C2×#67274C2211yescharacteristic
28C2×#67274C2211yescharacteristic, complemented
29#10625111—21no—
30#10625111C2211yescharacteristic, complemented
31#10625109—21no—
32#10625109C2211yescharacteristic, complemented
33C2×#67272C2211yescharacteristic
34C2×#67272C2211yescharacteristic
35#10625101—21no—
36#10625101C2211yescharacteristic
37C4×C22⋊D23—21no—
38C4×C22⋊D23C2211yescharacteristic
39C2×#67267C2211yescharacteristic
40#10625090—24no—
41C2×D184C2211yescharacteristic
42C2×D184C2211yescharacteristic
43C2×C8×D23C2211yescharacteristic, complemented
44#10625066—21no—
45#10625066C2211yescharacteristic
46#10625065—21no—
47#10625064C2211yescharacteristic
48#10625053—21no—
49C22⋊C4×D23—21no—
50C23×#103C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic, complemented
52C23×C22⋊C8C2211yescharacteristic
53#10625017C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic
55#10625003C2211yescharacteristic
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57#10624997C2211yescharacteristic, complemented
58Dic23⋊C8C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic, complemented
60#10624989C2211yescharacteristic, complemented
61C23×D23—21no—
62#41×C23—22no—
63#41×C23—41no—
64C2×Q8×C23C2311yescharacteristic
65C2×Q8×C23C2311yescharacteristic
66C2×D4×C23—21no—
67C2×D4×C23C2311yescharacteristic
68C22×C4×C23—21no—
69C22×C4×C23C2311yescharacteristic
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23D411yescharacteristic
75#67292—22no—
76#67292—22no—
77#67292—41no—
78#67292—41no—
79C2×D92—22no—
80C2×D92—21no—
81C2×D92—21no—
82C2×D92—21no—
83C2×D92—21no—
84C2×D92—41no—
85C2×D92C2311yescharacteristic
86C2×D92C2311yescharacteristic
87C2×D92C2311yescharacteristic
88C2×C4×D23—21no—
89C2×C4×D23—21no—
90C2×C4×D23—21no—
91C2×C4×D23C2311yescharacteristic
92Q16×C23—22no—
93SD16×C23—41no—
94C2×C8×C23C2311yescharacteristic
95C2×C8×C23C2311yescharacteristic
96C4⋊C4×C23—21no—
97C4⋊C4×C23C2311yescharacteristic
98C22⋊C4×C23—21no—
99C22⋊Dic23—21no—
100C22⋊Dic23D411yescharacteristic
101#67274—22no—
102#67274—22no—
103#67274D414yescomplemented
104#67272—22no—
105#67272—22no—
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
112C4⋊Dic23—21no—
113C4⋊Dic23C2311yescharacteristic
114Dic23⋊C4D411yescharacteristic
115C4×Dic23—21no—
116C4×Dic23C2311yescharacteristic
117#67267—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120D184—22no—
121D184—41no—
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—
134Q8×C23—21no—
135Q8×C23C2×D412yes—
136D4×C23—21no—
137D4×C23—21no—
138D4×C23—42no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—42no—
145C2×C4×C23C2×D411yescharacteristic
146C2×C4×C23C2411yescharacteristic
147C22⋊D23—41no—
148C22⋊D23—42no—
149C22⋊D23—81no—
150C22⋊D23—81no—
151C22⋊D23—81no—
152C2×Dic23—21no—
153C2×Dic23C2×D411yescharacteristic
154C2×Dic23C2×D411yescharacteristic
155C2×Dic23C2×D411yescharacteristic
156D92—21no—
157D92—21no—
158D92—21no—
159D92—21no—
160D92—21no—
161D92—42no—
162D92—42no—
163D92—42no—
164D92—81no—
165D92C2×D412yes—
166C4×D23—21no—
167C4×D23—21no—
168C4×D23—42no—
169C4×D23—42no—
170C4×D23—81no—
171C8×C23—21no—
172C8×C23—21no—
173C23⋊C8—21no—
174C23⋊C8C2×D412yes—
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—22no—
197C4×C23—21no—
198C4×C23—41no—
199C4×C23—41no—
200C4×C23C22×D411yescharacteristic
201C4×C23H(5,𝔽2)11yescharacteristic
202Dic23—21no—
203Dic23—21no—
204Dic23—21no—
205Dic23—41no—
206C2×AGL(1,ℤ/8)—231no—
207C2×#135—231no—
208#550—231no—
209#546—231no—
210#496—231no—
211#468—231no—
212#466—231no—
213#464—231no—
214#459—231no—
215#452D2311yescharacteristic, complemented
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×#41C2×D2311yescharacteristic
233C22×D4—231no—
234AGL(1,ℤ/8)—464no—
235#135—464no—
236C2×Q16C2×D2311yescharacteristic, complemented
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×M16—231no—
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—231no—
255#121—461no—
256#121—461no—
257#121—461no—
258#120—461no—
259C4×Q8—231no—
260C4×D4—231no—
261C4×D4—231no—
262C4×D4—461no—
263C2×C22⋊C4—461no—
264#107—231no—
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⋊C8C2×D2311yescharacteristic
274#97—231no—
275C23#326811yescharacteristic, complemented, Sylow
276C24—461no—
277#41—22no—
278#41—41no—
279#41—462no—
280#41—462no—
281#41—921no—
282#41—921no—
283C2×Q8C22×D2311yescharacteristic
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—21no—
302C22×C4—231no—
303C22×C4—461no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4C22×D2311yescharacteristic
307Q16—22no—
308SD16—41no—
309SD16—234no—
310SD16—462no—
311SD16—462no—
312D8—462no—
313D8—462no—
314D8—462no—
315D8—921no—
316M16—462no—
317C2×C8—231no—
318C2×C8—231no—
319C2×C8—462no—
320C2×C8C22×D2311yescharacteristic
321C2×C8C22×D2311yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—231no—
324C4⋊C4—231no—
325C4⋊C4—461no—
326C4⋊C4C22×D2311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—231no—
329C22⋊C4—231no—
330C22⋊C4—461no—
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—21no—
350Q8D4×D2312yes—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—232no—
355D4—461no—
356D4—461no—
357D4—461no—
358D4—461no—
359D4—461no—
360D4—922no—
361D4—922no—
362D4—922no—
363D4—921no—
364D4—922no—
365D4—1841no—
366D4—1841no—
367D4—1841no—
368D4—1841no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—231no—
376C2×C4—231no—
377C2×C4—231no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—461no—
381C2×C4—922no—
382C2×C4—922no—
383C2×C4—1841no—
384C2×C4D4×D2311yescharacteristic
385C2×C4C23×D2311yescharacteristic
386C8—21no—
387C8—21no—
388C8—232no—
389C8—461no—
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—22no—
412C4—41no—
413C4—41no—
414C4—461no—
415C4—461no—
416C4—461no—
417C4—921no—
418C4C2×D4×D2311yescharacteristic
419C4#1062515511yescharacteristic
420C2—41no—
421C2—81no—
422C2—921no—
423C2—922no—
424C2—1841no—
425C2—1841no—
426C2#1309304911yescharacteristic
427C2#1309321611yescharacteristic
428C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#452C2
socleC22×C23C22×D4
hypercenter#452D23
hypocenterC23#3268
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×#10625120C2semidirect
2. C2×#10625090C2semidirect
3. #13093086C2semidirect
4. #13093058C2semidirect
5. #13092803C2semidirect
6. #13092665C2semidirect
7. #13092652C2semidirect
8. #13092641C2semidirect
9. #13092611C2semidirect
10. #13092565C2semidirect
11. #13092561C2semidirect
12. #13092553C2semidirect
13. #13092520C2semidirect
14. #13092491C2semidirect
15. C23×#452C2semidirect
18. C2×#67292C22semidirect
20. C2×Q16×C23C22semidirect
21. C2×SD16×C23C22semidirect
25. Q8×Dic23C22semidirect
28. C2×#67274C22semidirect
30. #10625111C22semidirect
32. #10625109C22semidirect
43. C2×C8×D23C22semidirect
50. C23×#103C22semidirect
51. C23×#102C22semidirect
53. #10625017C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. #10624997C22semidirect
58. Dic23⋊C8C22semidirect
59. #10624991C22semidirect
60. #10624989C22semidirect
103. #67274D4semidirect
215. #452D23semidirect
236. C2×Q16C2×D23semidirect
240. C2×SD16C2×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×#106251202
C2×#106250902
#130930862
#130930582
#130928032
#130926652
#130926522
#130926412
#130926112
#130925652
#130925612
#130925532
#130925202
#130924912
C23×#4522
#326823