Finite Group Databasebeta

← #15684885

Subgroups — #15684885

Order 2944.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625085C211yesmaximal, characteristic, complemented
2C22×#67274C211yesmaximal, characteristic, complemented
3#13093078C211yesmaximal, characteristic, complemented
4#13093051C211yesmaximal, characteristic, complemented
5#13092803C211yesmaximal, characteristic, complemented
6#13092666C211yesmaximal, characteristic, complemented
7#13092651C211yesmaximal, characteristic, complemented
8#13092635C211yesmaximal, characteristic, complemented
9#13092615C211yesmaximal, characteristic, complemented
10#13092566C211yesmaximal, characteristic, complemented
11#13092565C211yesmaximal, characteristic, complemented
12#13092553C211yesmaximal, characteristic, complemented
13#13092520C211yesmaximal, characteristic, complemented
14#13092485C211yesmaximal, characteristic, complemented
15C23×#448C211yesmaximal, characteristic, complemented
16C22×Q8×C23C2211yescharacteristic, complemented
17C2×#67292C2211yescharacteristic, complemented
18C2×D4×D23—21no—
19C2×D4×D23C2211yescharacteristic
20C22×D92C2211yescharacteristic
21C2×SD16×C23C2211yescharacteristic, complemented
22C2×SD16×C23C2211yescharacteristic, complemented
23C23×#121C2211yescharacteristic
24#10625118—21no—
25#10625118C2211yescharacteristic, complemented
26#10625117—21no—
27#10625117C2211yescharacteristic, complemented
28Q8×Dic23C2211yescharacteristic, complemented
29C2×#67274—24no—
30C2×#67274C2211yescharacteristic
31C2×#67274C2211yescharacteristic
32C2×#67274C2211yescharacteristic, complemented
33C2×#67274C2211yescharacteristic, complemented
34#10625111C2211yescharacteristic
35#10625108—21no—
36C2×#67272C2211yescharacteristic, complemented
37#10625101—21no—
38#10625101C2211yescharacteristic, complemented
39C4×C22⋊D23—21no—
40C4×C22⋊D23C2211yescharacteristic
41C22×C23⋊C8C2211yescharacteristic, complemented
42#10625085—24no—
43C2×D184C2211yescharacteristic
44C2×D184C2211yescharacteristic, complemented
45C2×#67262C2211yescharacteristic, complemented
46#10625066C2211yescharacteristic
47#10625064C2211yescharacteristic
48#10625055—21no—
49#10625053—21no—
50C23×#103C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×C22⋊C8C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic
55#10625003C2211yescharacteristic, complemented
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57#10624997C2211yescharacteristic, complemented
58Dic23⋊C8C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic, complemented
60#10624989C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C2×Q8×C23—21no—
64C2×Q8×C23—22no—
65C2×Q8×C23—41no—
66C2×Q8×C23C2311yescharacteristic
67C2×Q8×C23C2311yescharacteristic
68C2×D4×C23—21no—
69C2×D4×C23C2311yescharacteristic
70C22×C4×C23—21no—
71C22×C4×C23C2311yescharacteristic
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C2×C22⋊D23D411yescharacteristic
77#67292—22no—
78#67292—41no—
79D4×D23—22no—
80D4×D23—41no—
81D4×D23—44no—
82C2×D92—22no—
83C2×D92—21no—
84C2×D92—21no—
85C2×D92—21no—
86C2×D92—41no—
87C2×D92C2311yescharacteristic
88C2×D92C2311yescharacteristic
89C2×D92C2311yescharacteristic
90C2×C4×D23—21no—
91C2×C4×D23—21no—
92C2×C4×D23C2311yescharacteristic
93SD16×C23—22no—
94SD16×C23—41no—
95C2×C8×C23C2311yescharacteristic
96C2×C8×C23C2311yescharacteristic
97C4⋊C4×C23C2311yescharacteristic
98C22⋊C4×C23—21no—
99C22⋊Dic23D411yescharacteristic
100#67274—22no—
101#67274—22no—
102#67274—22no—
103#67274D414yescomplemented
104#67272—22no—
105(C2×D23)⋊C4—21no—
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⋊C4—21no—
115Dic23⋊C4D411yescharacteristic
116C4×Dic23—21no—
117C4×Dic23C2311yescharacteristic
118C2×C23⋊C8—22no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121D184—22no—
122D184—41no—
123#67262—22no—
124C23×C23—21no—
125C23×C23C2×D411yescharacteristic
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—42no—
130C22×D23—42no—
131C22×D23—42no—
132C22×D23—42no—
133C22×D23—81no—
134C22×D23—81no—
135C22×D23C2×D411yescharacteristic
136Q8×C23—21no—
137Q8×C23—21no—
138Q8×C23—21no—
139Q8×C23—42no—
140Q8×C23C2×D412yescomplemented
141D4×C23—21no—
142D4×C23—21no—
143D4×C23—42no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—21no—
149C2×C4×C23—42no—
150C2×C4×C23C2×D411yescharacteristic
151C2×C4×C23C2411yescharacteristic
152C22⋊D23—22no—
153C22⋊D23—42no—
154C22⋊D23—42no—
155C22⋊D23—42no—
156C22⋊D23—81no—
157C2×Dic23—21no—
158C2×Dic23C2×D411yescharacteristic
159C2×Dic23C2×D411yescharacteristic
160C2×Dic23C2×D411yescharacteristic
161D92—21no—
162D92—21no—
163D92—21no—
164D92—21no—
165D92—21no—
166D92—42no—
167D92—42no—
168D92—42no—
169D92C2×D412yes—
170C4×D23—21no—
171C4×D23—21no—
172C4×D23—42no—
173C4×D23—42no—
174C8×C23—21no—
175C8×C23—21no—
176C23⋊C8—21no—
177C23⋊C8C2×D412yescomplemented
178#3265—231nomaximal, Sylow
179C22×C23—21no—
180C22×C23—21no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23AGL(1,ℤ/8)12yescomplemented
185C22×C23C22×D411yescharacteristic
186C2×D23—21no—
187C2×D23—22no—
188C2×D23—21no—
189C2×D23—21no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C2×D23—41no—
197C2×D23—41no—
198C2×D23—84no—
199C2×D23—84no—
200C4×C23—22no—
201C4×C23—21no—
202C4×C23—41no—
203C4×C23—41no—
204C4×C23C22×D411yescharacteristic
205C4×C23H(5,𝔽2)11yescharacteristic
206Dic23—21no—
207Dic23—21no—
208Dic23—21no—
209Dic23—41no—
210C2×AGL(1,ℤ/8)—231no—
211C22×SD16—231no—
212#548—231no—
213D42—231no—
214#496—231no—
215#468—231no—
216#466—231no—
217#463—231no—
218#460—231no—
219#450—231no—
220#449—231no—
221#448D2311yescharacteristic, complemented
222#447—231no—
223#440—231no—
224#435—231no—
225C2×C23—22no—
226C2×C23—81no—
227C2×C23D4211yescharacteristic
228C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
229C2×C23#57711yescharacteristic
230D23—41no—
231D23—42no—
232D23—81no—
233D23—81no—
234C2×#41—231no—
235C22×Q8C2×D2311yescharacteristic, complemented
236C22×D4—231no—
237C22×D4—231no—
238C22×D4—461no—
239AGL(1,ℤ/8)—464no—
240C2×SD16—231no—
241C2×SD16—231no—
242C2×SD16—231no—
243C2×SD16—231no—
244C2×SD16—464no—
245C2×SD16C2×D2311yescharacteristic, complemented
246C2×SD16C2×D2311yescharacteristic, complemented
247C2×D8—231no—
248C2×D8—231no—
249C2×D8—231no—
250C2×M16—231no—
251C22×C8—231no—
252#127—231no—
253#124—231no—
254#124—461no—
255C22⋊Q8—231no—
256C22⋊Q8—461no—
257#121—231no—
258#121—231no—
259#121—461no—
260#121—461no—
261#121C2×D2311yescharacteristic
262#120—461no—
263#120—461no—
264C4×Q8—231no—
265C4×D4—231no—
266C4×D4—231no—
267C4×D4—461no—
268#107—231no—
269C4⋊C8—231no—
270#103C2×D2311yescharacteristic, complemented
271#103C2×D2311yescharacteristic, complemented
272#102—231no—
273#102—231no—
274#102—231no—
275#102—231no—
276C22⋊C8—231no—
277C22⋊C8C2×D2311yescharacteristic, complemented
278#97—231no—
279C23#326511yescharacteristic, complemented, Sylow
280C24—461no—
281C24—461no—
282#41—462no—
283#41—921no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D2311yescharacteristic
288C2×Q8C22×D2311yescharacteristic
289C2×D4—21no—
290C2×D4—231no—
291C2×D4—231no—
292C2×D4—231no—
293C2×D4—231no—
294C2×D4—462no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—461no—
300C2×D4—462no—
301C2×D4—461no—
302C2×D4—461no—
303C2×D4—921no—
304C2×D4—921no—
305C2×D4—924no—
306C2×D4C22×D2311yescharacteristic
307C22×C4—21no—
308C22×C4—231no—
309C22×C4—461no—
310C22×C4—461no—
311C22×C4C22×D2311yescharacteristic
312SD16—22no—
313SD16—41no—
314SD16—234no—
315SD16—462no—
316SD16—462no—
317SD16—462no—
318D8—462no—
319D8—462no—
320D8—921no—
321M16—462no—
322C2×C8—231no—
323C2×C8—231no—
324C2×C8—462no—
325C2×C8C22×D2311yescharacteristic
326C2×C8C22×D2311yescharacteristic
327C4⋊C4—231no—
328C4⋊C4—231no—
329C4⋊C4—461no—
330C4⋊C4—461no—
331C4⋊C4C22×D2311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—231no—
334C22⋊C4—231no—
335C22⋊C4—461no—
336C22⋊C4—461no—
337C22⋊C4—461no—
338C22⋊C4—461no—
339C22⋊C4—461no—
340C22⋊C4—461no—
341C42—231no—
342C42—461no—
343C23—21no—
344C23—231no—
345C23—461no—
346C23—461no—
347C23—461no—
348C23—922no—
349C23—922no—
350C23—922no—
351C23—922no—
352C23—1841no—
353C23—1841no—
354C23D4×D2311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8D4×D2312yescomplemented
360D4—21no—
361D4—21no—
362D4—42no—
363D4—232no—
364D4—462no—
365D4—461no—
366D4—461no—
367D4—461no—
368D4—461no—
369D4—461no—
370D4—922no—
371D4—922no—
372D4—922no—
373D4—922no—
374D4—922no—
375D4—922no—
376D4—1841no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—231no—
384C2×C4—231no—
385C2×C4—231no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—461no—
389C2×C4—922no—
390C2×C4—922no—
391C2×C4D4×D2311yescharacteristic
392C2×C4C23×D2311yescharacteristic
393C8—21no—
394C8—21no—
395C8—232no—
396C8—461no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—461no—
403C22—461no—
404C22—461no—
405C22—462no—
406C22—921no—
407C22—921no—
408C22—921no—
409C22—921no—
410C22—921no—
411C22—921no—
412C22—921no—
413C22—921no—
414C22—1844no—
415C22—1844no—
416C22#1062508512yescomplemented
417C22C2×D4×D2311yescharacteristic
418C4—21no—
419C4—22no—
420C4—41no—
421C4—41no—
422C4—461no—
423C4—461no—
424C4—461no—
425C4—921no—
426C4C2×D4×D2311yescharacteristic
427C4#1062515511yescharacteristic
428C2—22no—
429C2—81no—
430C2—921no—
431C2—922no—
432C2—1841no—
433C2—1841no—
434C2#1309304911yescharacteristic
435C2C2×#1062508511yescharacteristic
436C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#448C2
socleC22×C23C22×D4
hypercenter#448D23
hypocenterC23#3265
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C22×#67274C2semidirect
3. #13093078C2semidirect
4. #13093051C2semidirect
5. #13092803C2semidirect
6. #13092666C2semidirect
7. #13092651C2semidirect
8. #13092635C2semidirect
9. #13092615C2semidirect
10. #13092566C2semidirect
11. #13092565C2semidirect
12. #13092553C2semidirect
13. #13092520C2semidirect
14. #13092485C2semidirect
15. C23×#448C2semidirect
16. C22×Q8×C23C22semidirect
17. C2×#67292C22semidirect
21. C2×SD16×C23C22semidirect
22. C2×SD16×C23C22semidirect
25. #10625118C22semidirect
27. #10625117C22semidirect
28. Q8×Dic23C22semidirect
32. C2×#67274C22semidirect
33. C2×#67274C22semidirect
36. C2×#67272C22semidirect
38. #10625101C22semidirect
41. C22×C23⋊C8C22semidirect
44. C2×D184C22semidirect
45. C2×#67262C22semidirect
50. C23×#103C22semidirect
51. C23×#103C22semidirect
52. C23×C22⋊C8C22semidirect
53. #10625014C22semidirect
55. #10625003C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. #10624997C22semidirect
58. Dic23⋊C8C22semidirect
59. #10624991C22semidirect
60. #10624989C22semidirect
103. #67274D4semidirect
140. Q8×C23C2×D4semidirect
177. C23⋊C8C2×D4semidirect
184. C22×C23AGL(1,ℤ/8)semidirect
221. #448D23semidirect
235. C22×Q8C2×D23semidirect
245. C2×SD16C2×D23semidirect
246. C2×SD16C2×D23semidirect
270. #103C2×D23semidirect
271. #103C2×D23semidirect
277. C22⋊C8C2×D23semidirect
279. C23#3265semidirect
359. Q8D4×D23semidirect
416. C22#10625085semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
C22×#672742
#130930782
#130930512
#130928032
#130926662
#130926512
#130926352
#130926152
#130925662
#130925652
#130925532
#130925202
#130924852
C23×#4482
#326523