Finite Group Databasebeta

← #15684898

Subgroups — #15684898

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×#10625082C211yesmaximal, characteristic, complemented
2C2×SD16×D23C211yesmaximal, characteristic, complemented
3#13093075C211yesmaximal, characteristic, complemented
4D4×D92C211yesmaximal, characteristic, complemented
5#13092807C211yesmaximal, characteristic, complemented
6#13092666C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092618C211yesmaximal, characteristic, complemented
9#13092566C211yesmaximal, characteristic, complemented
10#13092563C211yesmaximal, characteristic, complemented
11#13092557C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092517C211yesmaximal, characteristic, complemented
14#13092487C211yesmaximal, characteristic, complemented
15C23×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic, complemented
17C2×#67290C2211yescharacteristic, complemented
18C2×D4×D23C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic
20C22×D92—21no—
21C2×SD16×C23C2211yescharacteristic
22C2×D8×C23C2211yescharacteristic
23C23×#124C2211yescharacteristic, complemented
24C4×D4×C23C2211yescharacteristic
25#10625117C2211yescharacteristic, complemented
26C2×#67274C2211yescharacteristic, complemented
27C2×#67274C2211yescharacteristic, complemented
28#10625109C2211yescharacteristic, complemented
29C2×#67273C2211yescharacteristic
30C2×#67272C2211yescharacteristic, complemented
31C2×#67272C2211yescharacteristic, complemented
32#10625101—21no—
33SD16×D23—24no—
34#10625082—24no—
35C2×#67263C2211yescharacteristic, complemented
36C2×#67263C2211yescharacteristic, complemented
37C2×#67262C2211yescharacteristic, complemented
38C2×C8×D23C2211yescharacteristic, complemented
39#10625066C2211yescharacteristic
40#10625066C2211yescharacteristic
41#10625056—21no—
42#10625055—21no—
43#10625053—21no—
44#10625053—21no—
45(C22⋊D23)⋊C4—21no—
46#10625049—21no—
47#10625045C2211yescharacteristic
48C4×D92C2211yescharacteristic
49C4×Dic46C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic
54#10625003C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic, complemented
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57(C2×D23)⋊C8C2211yescharacteristic, complemented
58#10624992C2211yescharacteristic, complemented
59#10624989C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C23×D23—21no—
62C23×D23—21no—
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C22×C4×C23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C22×Dic23—21no—
72Q8×D23—22no—
73Q8×D23—41no—
74#67290—22no—
75#67290—41no—
76D4×D23—22no—
77D4×D23—22no—
78D4×D23—41no—
79D4×D23—41no—
80C2×D92—21no—
81C2×D92—21no—
82C2×D92—21no—
83C2×D92—21no—
84C2×D92—44no—
85C2×D92D411yescharacteristic
86C2×D92C2311yescharacteristic
87C2×D92C2311yescharacteristic
88C2×C4×D23—21no—
89C2×C4×D23C2311yescharacteristic
90C2×C4×D23C2311yescharacteristic
91C2×Dic46—21no—
92C2×Dic46C2311yescharacteristic
93SD16×C23—22no—
94D8×C23—22no—
95C2×C8×C23C2311yescharacteristic
96C2×C8×C23C2311yescharacteristic
97C4⋊C4×C23C2311yescharacteristic
98C22⋊C4×C23—21no—
99C22⋊C4×C23—21no—
100C22⋊C4×C23—21no—
101C42×C23C2311yescharacteristic
102C22⋊Dic23—21no—
103#67274—22no—
104#67274—41no—
105#67273D414yescomplemented
106#67272—22no—
107#67272—41no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4D411yescharacteristic
112(C2×D23)⋊C4D411yescharacteristic
113C4⋊Dic23D411yescharacteristic
114C4⋊Dic23C2311yescharacteristic
115Dic23⋊C4—21no—
116Dic23⋊C4—21no—
117C4×Dic23—21no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120#67263—22no—
121#67263—22no—
122#67262—22no—
123C8×D23—22no—
124C23×C23—21no—
125C23×C23—21no—
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—42no—
129C22×D23—42no—
130C22×D23—42no—
131C22×D23—42no—
132C22×D23—81no—
133C22×D23—81no—
134C22×D23C2×D411yescharacteristic
135C22×D23C2×D411yescharacteristic
136Q8×C23—21no—
137Q8×C23—21no—
138D4×C23—21no—
139D4×C23—21no—
140D4×C23—21no—
141D4×C23C2×D412yes—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—42no—
145C2×C4×C23C2×D411yescharacteristic
146C2×C4×C23C2×D411yescharacteristic
147C2×C4×C23C2411yescharacteristic
148C22⋊D23—42no—
149C22⋊D23—42no—
150C22⋊D23—42no—
151C22⋊D23—42no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—42no—
155C2×Dic23C2×D411yescharacteristic
156C2×Dic23C2×D411yescharacteristic
157D92—22no—
158D92—21no—
159D92—21no—
160D92—21no—
161D92—21no—
162D92—42no—
163D92—42no—
164D92—42no—
165D92—81no—
166C4×D23—21no—
167C4×D23—21no—
168C4×D23—21no—
169C4×D23—21no—
170C4×D23—42no—
171Dic46—21no—
172Dic46—42no—
173Dic46C2×D412yescomplemented
174C8×C23—21no—
175C8×C23—21no—
176C23⋊C8—21no—
177C23⋊C8C2×D412yescomplemented
178#3265—231nomaximal, Sylow
179C22×C23—22no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23C22×D411yescharacteristic
186C2×D23—21no—
187C2×D23—21no—
188C2×D23—21no—
189C2×D23—21no—
190C2×D23—21no—
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—21no—
202C4×C23—41no—
203C4×C23—41no—
204C4×C23C22×D411yescharacteristic
205C4×C23H(5,𝔽2)11yescharacteristic
206Dic23—22no—
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#463D2311yescharacteristic, complemented
218#460—231no—
219#450—231no—
220#449—231no—
221#448—231no—
222#447—231no—
223#440—231no—
224#435—231no—
225C2×C23—42no—
226C2×C23—81no—
227C2×C23D4211yescharacteristic
228C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
229C2×C23#57711yescharacteristic
230D23—22no—
231D23—41no—
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
247C2×D8—231no—
248C2×D8—231no—
249C2×D8C2×D2311yescharacteristic
250C2×M16—231no—
251C22×C8—231no—
252#127—231no—
253#124—461no—
254#124C2×D2311yescharacteristic, complemented
255C22⋊Q8—231no—
256C22⋊Q8—461no—
257#121—231no—
258#121—231no—
259#121—231no—
260#121—461no—
261#121—461no—
262#120—461no—
263#120—461no—
264C4×Q8—231no—
265C4×D4—231no—
266C4×D4—461no—
267C4×D4C2×D2311yescharacteristic
268#107—231no—
269C4⋊C8C2×D2311yescharacteristic, complemented
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—231no—
290C2×D4—231no—
291C2×D4—231no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—462no—
297C2×D4—462no—
298C2×D4—461no—
299C2×D4—461no—
300C2×D4—461no—
301C2×D4—461no—
302C2×D4—924no—
303C2×D4—921no—
304C2×D4—921no—
305C2×D4C22×D2311yescharacteristic
306C2×D4C22×D2311yescharacteristic
307C22×C4—21no—
308C22×C4—231no—
309C22×C4—231no—
310C22×C4—461no—
311C22×C4—461no—
312SD16—22no—
313SD16—234no—
314SD16—462no—
315SD16—462no—
316SD16—462no—
317SD16—921no—
318D8—22no—
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—21no—
334C22⋊C4—21no—
335C22⋊C4—231no—
336C22⋊C4—231no—
337C22⋊C4—461no—
338C22⋊C4—461no—
339C22⋊C4—461no—
340C22⋊C4—461no—
341C42—461no—
342C42C22×D2311yescharacteristic
343C23—21no—
344C23—21no—
345C23—231no—
346C23—231no—
347C23—461no—
348C23—461no—
349C23—922no—
350C23—922no—
351C23—922no—
352C23—922no—
353C23—1841no—
354C23—1841no—
355Q8—21no—
356Q8—21no—
357Q8—232no—
358Q8—461no—
359Q8—922no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—462no—
364D4—461no—
365D4—461no—
366D4—461no—
367D4—461no—
368D4—922no—
369D4—922no—
370D4—922no—
371D4—922no—
372D4—922no—
373D4—922no—
374D4—922no—
375D4—1841no—
376D4D4×D2312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—231no—
381C2×C4—231no—
382C2×C4—461no—
383C2×C4—461no—
384C2×C4—461no—
385C2×C4—461no—
386C2×C4—461no—
387C2×C4—461no—
388C2×C4—922no—
389C2×C4—922no—
390C2×C4D4×D2311yescharacteristic
391C2×C4D4×D2311yescharacteristic
392C2×C4C23×D2311yescharacteristic
393C8—21no—
394C8—21no—
395C8—232no—
396C8—461no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—232no—
404C22—461no—
405C22—461no—
406C22—461no—
407C22—461no—
408C22—461no—
409C22—921no—
410C22—921no—
411C22—921no—
412C22—921no—
413C22—921no—
414C22—921no—
415C22—1844no—
416C22—1844no—
417C22C2×D4×D2311yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—461no—
423C4—461no—
424C4—462no—
425C4—921no—
426C4C2×D4×D2311yescharacteristic
427C4#1062516011yescharacteristic
428C2—42no—
429C2—81no—
430C2—462no—
431C2—921no—
432C2—1841no—
433C2—1841no—
434C2#1309305111yescharacteristic
435C2AGL(1,ℤ/8)×D2311yescharacteristic
436C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#463C2
socleC22×C23C22×D4
hypercenter#463D23
hypocenterC23#3265
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C2×SD16×D23C2semidirect
3. #13093075C2semidirect
4. D4×D92C2semidirect
5. #13092807C2semidirect
6. #13092666C2semidirect
7. #13092652C2semidirect
8. #13092618C2semidirect
9. #13092566C2semidirect
10. #13092563C2semidirect
11. #13092557C2semidirect
12. #13092549C2semidirect
13. #13092517C2semidirect
14. #13092487C2semidirect
15. C23×#463C2semidirect
16. C2×Q8×D23C22semidirect
17. C2×#67290C22semidirect
23. C23×#124C22semidirect
25. #10625117C22semidirect
26. C2×#67274C22semidirect
27. C2×#67274C22semidirect
28. #10625109C22semidirect
30. C2×#67272C22semidirect
31. C2×#67272C22semidirect
35. C2×#67263C22semidirect
36. C2×#67263C22semidirect
37. C2×#67262C22semidirect
38. C2×C8×D23C22semidirect
49. C4×Dic46C22semidirect
50. C23×C4⋊C8C22semidirect
51. C23×#103C22semidirect
52. C23×#102C22semidirect
54. #10625003C22semidirect
55. #10625003C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. (C2×D23)⋊C8C22semidirect
58. #10624992C22semidirect
59. #10624989C22semidirect
60. #10624985C22semidirect
105. #67273D4semidirect
173. Dic46C2×D4semidirect
177. C23⋊C8C2×D4semidirect
199. C2×D23AGL(1,ℤ/8)semidirect
217. #463D23semidirect
254. #124C2×D23semidirect
269. C4⋊C8C2×D23semidirect
271. #103C2×D23semidirect
275. #102C2×D23semidirect
279. C23#3265semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
C2×SD16×D232
#130930752
D4×D922
#130928072
#130926662
#130926522
#130926182
#130925662
#130925632
#130925572
#130925492
#130925172
#130924872
C23×#4632
#326523