Finite Group Databasebeta

← #15684899

Subgroups — #15684899

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×#10625079C211yesmaximal, characteristic, complemented
2C2×SD16×D23C211yesmaximal, characteristic, complemented
3#13093077C211yesmaximal, characteristic, complemented
4#13093051C211yesmaximal, characteristic, complemented
5#13092803C211yesmaximal, characteristic, complemented
6#13092654C211yesmaximal, characteristic, complemented
7#13092635C211yesmaximal, characteristic, complemented
8#13092616C211yesmaximal, characteristic, complemented
9#13092567C211yesmaximal, characteristic, complemented
10#13092560C211yesmaximal, characteristic, complemented
11#13092557C211yesmaximal, characteristic, complemented
12#13092552C211yesmaximal, characteristic, complemented
13#13092516C211yesmaximal, characteristic, complemented
14#13092486C211yesmaximal, characteristic, complemented
15C23×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic, complemented
17C2×D4×D23—21no—
18C2×D4×D23C2211yescharacteristic
19C2×#67288C2211yescharacteristic, complemented
20C22×D92C2211yescharacteristic
21C2×SD16×C23C2211yescharacteristic, complemented
22C2×M16×C23C2211yescharacteristic, complemented
23C23×C22⋊Q8C2211yescharacteristic, complemented
24C23×#121C2211yescharacteristic
25#10625118C2211yescharacteristic, complemented
26C2×#67274C2211yescharacteristic
27C2×#67274C2211yescharacteristic, complemented
28#10625111C2211yescharacteristic
29#10625108—21no—
30C2×#67273C2211yescharacteristic, complemented
31C2×#67272C2211yescharacteristic, complemented
32C4×C22⋊D23C2211yescharacteristic
33SD16×D23—24no—
34#10625079—24no—
35C2×D184C2211yescharacteristic
36C2×D184C2211yescharacteristic, complemented
37C2×#67263C2211yescharacteristic
38C2×#67263C2211yescharacteristic, complemented
39C2×C8×D23C2211yescharacteristic, complemented
40#10625067—21no—
41#10625066C2211yescharacteristic
42#10625066C2211yescharacteristic, complemented
43#10625064—21no—
44#10625064C2211yescharacteristic
45#10625058C2211yescharacteristic, complemented
46#10625056—21no—
47#10625055—21no—
48#10625055—21no—
49#10625053—21no—
50C23×#107C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53C22⋊(C23⋊C8)C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic, complemented
55#10624997C2211yescharacteristic, complemented
56Dic23⋊C8C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic
59#10624991C2211yescharacteristic, complemented
60#10624991C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23—21no—
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23D411yescharacteristic
72Q8×D23—22no—
73Q8×D23—41no—
74D4×D23—22no—
75D4×D23—41no—
76D4×D23—44no—
77#67288—22no—
78#67288—41no—
79C2×D92—22no—
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×Dic46—21no—
92C2×Dic46C2311yescharacteristic
93SD16×C23—22no—
94M16×C23—22no—
95C2×C8×C23C2311yescharacteristic
96C2×C8×C23C2311yescharacteristic
97C4⋊C4×C23—21no—
98C4⋊C4×C23C2311yescharacteristic
99C4⋊C4×C23C2311yescharacteristic
100C22⋊C4×C23—21no—
101C22⋊C4×C23—21no—
102C22⋊Dic23D411yescharacteristic
103#67274—22no—
104#67274—41no—
105#67273—22no—
106#67272—41no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4—21no—
112(C2×D23)⋊C4D411yescharacteristic
113Dic23⋊C4—21no—
114Dic23⋊C4D411yescharacteristic
115C4×Dic23—21no—
116C4×Dic23C2311yescharacteristic
117C2×C23⋊C8C2311yescharacteristic
118C2×C23⋊C8C2311yescharacteristic
119D184—22no—
120D184—22no—
121#67263—22no—
122#67263D414yescomplemented
123C8×D23—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—
138D4×C23—21no—
139D4×C23—21no—
140D4×C23—42no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23C2×D411yescharacteristic
147C2×C4×C23C2411yescharacteristic
148C22⋊D23—22no—
149C22⋊D23—42no—
150C22⋊D23—42no—
151C22⋊D23—42no—
152C22⋊D23—81no—
153C2×Dic23—21no—
154C2×Dic23C2×D411yescharacteristic
155C2×Dic23C2×D411yescharacteristic
156C2×Dic23C2×D411yescharacteristic
157D92—21no—
158D92—21no—
159D92—21no—
160D92—21no—
161D92—21no—
162D92—42no—
163D92—42no—
164D92—42no—
165D92C2×D412yes—
166C4×D23—21no—
167C4×D23—21no—
168C4×D23—42no—
169C4×D23—42no—
170C4×D23—42no—
171Dic46—21no—
172Dic46—42no—
173Dic46C2×D412yescomplemented
174C8×C23—21no—
175C8×C23C2×D412yescomplemented
176C23⋊C8—21no—
177C23⋊C8—21no—
178#3265—231nomaximal, Sylow
179C22×C23—21no—
180C22×C23—21no—
181C22×C23—21no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23C22×D411yescharacteristic
186C2×D23—21no—
187C2×D23—21no—
188C2×D23—22no—
189C2×D23—41no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C2×D23—41no—
197C2×D23—84no—
198C2×D23—84no—
199C2×D23AGL(1,ℤ/8)12yescomplemented
200C4×C23—21no—
201C4×C23—41no—
202C4×C23—41no—
203C4×C23—41no—
204C4×C23C22×D411yescharacteristic
205C4×C23H(5,𝔽2)11yescharacteristic
206Dic23—22no—
207Dic23—21no—
208Dic23—21no—
209Dic23—21no—
210C2×AGL(1,ℤ/8)—231no—
211C22×SD16—231no—
212#548—231no—
213D42—231no—
214#496—231no—
215#468D2311yescharacteristic, complemented
216#466—231no—
217#463—231no—
218#460—231no—
219#450—231no—
220#449—231no—
221#448—231no—
222#447—231no—
223#440—231no—
224#435—231no—
225C2×C23—41no—
226C2×C23—81no—
227C2×C23D4211yescharacteristic
228C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
229C2×C23#57711yescharacteristic
230D23—22no—
231D23—42no—
232D23—81no—
233D23—81no—
234C2×#41—231no—
235C22×Q8—231no—
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—231no—
245C2×SD16—464no—
246C2×SD16C2×D2311yescharacteristic, complemented
247C2×D8—231no—
248C2×D8—231no—
249C2×D8—231no—
250C2×M16C2×D2311yescharacteristic, complemented
251C22×C8—231no—
252#127—231no—
253#124—231no—
254#124—461no—
255C22⋊Q8—461no—
256C22⋊Q8C2×D2311yescharacteristic, complemented
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#107C2×D2311yescharacteristic, complemented
269C4⋊C8—231no—
270#103—231no—
271#103C2×D2311yescharacteristic, complemented
272#102—231no—
273#102—231no—
274#102—231no—
275#102C2×D2311yescharacteristic, complemented
276C22⋊C8—231no—
277C22⋊C8—231no—
278#97—231no—
279C23#326511yescharacteristic, complemented, Sylow
280C24—461no—
281C24—461no—
282#41—462no—
283#41—921no—
284C2×Q8—231no—
285C2×Q8—461no—
286C2×Q8—462no—
287C2×Q8—921no—
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—231no—
308C22×C4—461no—
309C22×C4—461no—
310C22×C4—461no—
311C22×C4C22×D2311yescharacteristic
312SD16—22no—
313SD16—234no—
314SD16—462no—
315SD16—462no—
316SD16—462no—
317SD16—921no—
318D8—462no—
319D8—462no—
320D8—921no—
321M16—22no—
322C2×C8—231no—
323C2×C8—231no—
324C2×C8—462no—
325C2×C8C22×D2311yescharacteristic
326C2×C8C22×D2311yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—231no—
329C4⋊C4—461no—
330C4⋊C4C22×D2311yescharacteristic
331C4⋊C4C22×D2311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—231no—
335C22⋊C4—231no—
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—232no—
358Q8—461no—
359Q8—922no—
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—231no—
383C2×C4—231no—
384C2×C4—231no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—922no—
389C2×C4—922no—
390C2×C4—922no—
391C2×C4D4×D2311yescharacteristic
392C2×C4C23×D2311yescharacteristic
393C8—21no—
394C8—461no—
395C8—461no—
396C8D4×D2312yescomplemented
397C22—21no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—232no—
404C22—461no—
405C22—461no—
406C22—462no—
407C22—921no—
408C22—921no—
409C22—921no—
410C22—921no—
411C22—921no—
412C22—921no—
413C22—921no—
414C22—921no—
415C22—1844no—
416C22—1844no—
417C22C2×D4×D2311yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—461no—
423C4—461no—
424C4—461no—
425C4—462no—
426C4C2×D4×D2311yescharacteristic
427C4#1062516011yescharacteristic
428C2—41no—
429C2—81no—
430C2—462no—
431C2—922no—
432C2—1841no—
433C2—1841no—
434C2#1309305111yescharacteristic
435C2AGL(1,ℤ/8)×D2311yescharacteristic
436C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#468C2
socleC22×C23C22×D4
hypercenter#468D23
hypocenterC23#3265
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×SD16×D23C2semidirect
3. #13093077C2semidirect
4. #13093051C2semidirect
5. #13092803C2semidirect
6. #13092654C2semidirect
7. #13092635C2semidirect
8. #13092616C2semidirect
9. #13092567C2semidirect
10. #13092560C2semidirect
11. #13092557C2semidirect
12. #13092552C2semidirect
13. #13092516C2semidirect
14. #13092486C2semidirect
15. C23×#468C2semidirect
16. C2×Q8×D23C22semidirect
19. C2×#67288C22semidirect
21. C2×SD16×C23C22semidirect
22. C2×M16×C23C22semidirect
23. C23×C22⋊Q8C22semidirect
25. #10625118C22semidirect
27. C2×#67274C22semidirect
30. C2×#67273C22semidirect
31. C2×#67272C22semidirect
36. C2×D184C22semidirect
38. C2×#67263C22semidirect
39. C2×C8×D23C22semidirect
42. #10625066C22semidirect
45. #10625058C22semidirect
50. C23×#107C22semidirect
51. C23×#103C22semidirect
52. C23×#102C22semidirect
53. C22⋊(C23⋊C8)C22semidirect
54. (C2×D23)⋊C8C22semidirect
55. #10624997C22semidirect
56. Dic23⋊C8C22semidirect
57. #10624992C22semidirect
59. #10624991C22semidirect
60. #10624991C22semidirect
122. #67263D4semidirect
173. Dic46C2×D4semidirect
175. C8×C23C2×D4semidirect
199. C2×D23AGL(1,ℤ/8)semidirect
215. #468D23semidirect
246. C2×SD16C2×D23semidirect
250. C2×M16C2×D23semidirect
256. C22⋊Q8C2×D23semidirect
268. #107C2×D23semidirect
271. #103C2×D23semidirect
275. #102C2×D23semidirect
279. C23#3265semidirect
396. C8D4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
C2×SD16×D232
#130930772
#130930512
#130928032
#130926542
#130926352
#130926162
#130925672
#130925602
#130925572
#130925522
#130925162
#130924862
C23×#4682
#326523