Finite Group Databasebeta

← #15684935

Subgroups — #15684935

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×#10625103C211yesmaximal, characteristic, complemented
2C2×#10625083C211yesmaximal, characteristic, complemented
3#13093085C211yesmaximal, characteristic, complemented
4#13093061C211yesmaximal, characteristic, complemented
5#13092805C211yesmaximal, characteristic, complemented
6#13092661C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092638C211yesmaximal, characteristic, complemented
9#13092610C211yesmaximal, characteristic, complemented
10#13092581C211yesmaximal, characteristic, complemented
11#13092563C211yesmaximal, characteristic, complemented
12#13092559C211yesmaximal, characteristic, complemented
13#13092514C211yesmaximal, characteristic, complemented
14#13092491C211yesmaximal, characteristic, complemented
15C23×#447C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×#67290C2211yescharacteristic, complemented
19C2×#67288C2211yescharacteristic
20C2×D8×C23C2211yescharacteristic
21C2×D8×C23C2211yescharacteristic
22C23×#121C2211yescharacteristic
23#10625124—21no—
24C2×C22⋊Dic23—21no—
25#10625111—21no—
26#10625111C2211yescharacteristic, complemented
27#10625110—21no—
28#10625110—21no—
29#10625109C2211yescharacteristic
30#10625107C2211yescharacteristic
31#10625106—21no—
32D4×Dic23C2211yescharacteristic
33C2×#67273C2211yescharacteristic
34C2×#67273C2211yescharacteristic
35C2×#67273C2211yescharacteristic, complemented
36#10625103—24no—
37C2×#67272C2211yescharacteristic
38C2×#67272C2211yescharacteristic
39C4×C22⋊D23C2211yescharacteristic
40#10625095C2211yescharacteristic
41C2×#67267C2211yescharacteristic
42#10625083—24no—
43C2×Dic92C2211yescharacteristic, complemented
44C2×#67263C2211yescharacteristic, complemented
45C2×C8×D23C2211yescharacteristic, complemented
46#10625066C2211yescharacteristic, complemented
47#10625058C2211yescharacteristic, complemented
48#10625055—21no—
49(C22⋊D23)⋊C4—21no—
50C23×#102C2211yescharacteristic
51C23×#102C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic
53#10625014C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic, complemented
55(C2×D23)⋊C8C2211yescharacteristic, complemented
56#10624998C2211yescharacteristic, complemented
57#10624997C2211yescharacteristic, complemented
58Dic23⋊C8C2211yescharacteristic, complemented
59#10624992C2211yescharacteristic, complemented
60#10624989C2211yescharacteristic, complemented
61C24×C23—21no—
62C2×D4×C23—22no—
63C2×D4×C23—21no—
64C2×D4×C23—21no—
65C2×D4×C23—41no—
66C2×D4×C23C2311yescharacteristic
67C2×D4×C23C2311yescharacteristic
68C2×D4×C23C2311yescharacteristic
69C22×C4×C23C2311yescharacteristic
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C2×C22⋊D23D411yescharacteristic
77C22×Dic23—21no—
78C22×Dic23—21no—
79C22×Dic23—21no—
80#67290—22no—
81#67290—22no—
82#67290—41no—
83#67290—41no—
84#67288—22no—
85#67288—41no—
86C2×D92—21no—
87C2×D92C2311yescharacteristic
88C2×C4×D23—21no—
89C2×C4×D23C2311yescharacteristic
90C2×Dic46C2311yescharacteristic
91C2×Dic46C2311yescharacteristic
92D8×C23—22no—
93D8×C23—41no—
94C2×C8×C23C2311yescharacteristic
95C2×C8×C23C2311yescharacteristic
96C4⋊C4×C23C2311yescharacteristic
97C22⋊C4×C23—21no—
98C22⋊Dic23—21no—
99C22⋊Dic23—21no—
100C22⋊Dic23—21no—
101C22⋊Dic23—21no—
102C22⋊Dic23—21no—
103C22⋊Dic23D411yescharacteristic
104#67273—22no—
105#67273—22no—
106#67273D414yescomplemented
107#67272—22no—
108#67272—22no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4D411yescharacteristic
111C4⋊Dic23C2311yescharacteristic
112Dic23⋊C4—21no—
113Dic23⋊C4—21no—
114Dic23⋊C4D411yescharacteristic
115C4×Dic23—21no—
116C4×Dic23C2311yescharacteristic
117#67267—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120Dic92—22no—
121#67263—41no—
122C8×D23—22no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23—21no—
126C23×C23—42no—
127C23×C23—42no—
128C23×C23—81no—
129C23×C23C2×D411yescharacteristic
130C22×D23—21no—
131C22×D23C2×D411yescharacteristic
132D4×C23—21no—
133D4×C23—21no—
134D4×C23—21no—
135D4×C23—21no—
136D4×C23—21no—
137D4×C23—42no—
138D4×C23—81no—
139D4×C23C2×D412yes—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23C2×D411yescharacteristic
144C2×C4×C23C2411yescharacteristic
145C22⋊D23—41no—
146C22⋊D23—42no—
147C22⋊D23—42no—
148C22⋊D23—42no—
149C22⋊D23—42no—
150C22⋊D23—81no—
151C22⋊D23—81no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—42no—
156C2×Dic23—42no—
157C2×Dic23—81no—
158C2×Dic23C2×D411yescharacteristic
159C2×Dic23C2×D411yescharacteristic
160C2×Dic23C2×D411yescharacteristic
161D92—21no—
162D92—21no—
163D92—81no—
164C4×D23—21no—
165C4×D23—21no—
166C4×D23—42no—
167Dic46—21no—
168Dic46—21no—
169Dic46—21no—
170Dic46C2×D412yes—
171C8×C23—21no—
172C8×C23—21no—
173C23⋊C8—21no—
174C23⋊C8C2×D412yes—
175#3268—231nomaximal, Sylow
176C22×C23—22no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23—21no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—84no—
189C22×C23C22×D411yescharacteristic
190C2×D23—21no—
191C2×D23—21no—
192C2×D23—21no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C4×C23—21no—
197C4×C23—41no—
198C4×C23C22×D411yescharacteristic
199C4×C23H(5,𝔽2)11yescharacteristic
200Dic23—22no—
201Dic23—21no—
202Dic23—21no—
203Dic23—21no—
204Dic23—41no—
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#452—231no—
216#449—231no—
217#449—231no—
218#447D2311yescharacteristic, complemented
219#440—231no—
220#435—231no—
221C2×C23—41no—
222C2×C23—42no—
223C2×C23—81no—
224C2×C23—81no—
225C2×C23D4211yescharacteristic
226C2×C23#57511yescharacteristic
227C2×C23#57611yescharacteristic
228D23—41no—
229D23—81no—
230C2×#41—231no—
231C2×#41—231no—
232C2×#41—231no—
233C22×D4C2×D2311yescharacteristic
234AGL(1,ℤ/8)—464no—
235#135—464no—
236C2×Q16—231no—
237C2×SD16—231no—
238C2×SD16—231no—
239C2×SD16—231no—
240C2×SD16—231no—
241C2×D8—231no—
242C2×D8—231no—
243C2×D8C2×D2311yescharacteristic
244C2×D8C2×D2311yescharacteristic
245C2×M16—231no—
246C22×C8—231no—
247#127—231no—
248#127—461no—
249#124—231no—
250#123—461no—
251C22⋊Q8—231no—
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#107—231no—
265C4⋊C8—231no—
266#103—231no—
267#103—231no—
268#102—231no—
269#102—231no—
270#102C2×D2311yescharacteristic
271#102C2×D2311yescharacteristic
272C22⋊C8—231no—
273C22⋊C8C2×D2311yescharacteristic
274#97—231no—
275C23#326811yescharacteristic, complemented, Sylow
276C24—21no—
277#41—462no—
278#41—462no—
279#41—462no—
280#41—921no—
281#41—921no—
282#41—921no—
283C2×Q8—231no—
284C2×Q8—231no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—231no—
290C2×D4—231no—
291C2×D4—461no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4C22×D2311yescharacteristic
299C2×D4C22×D2311yescharacteristic
300C2×D4C22×D2311yescharacteristic
301C22×C4—231no—
302C22×C4—461no—
303C22×C4—461no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4C22×D2311yescharacteristic
307Q16—462no—
308SD16—234no—
309SD16—462no—
310SD16—462no—
311SD16—921no—
312D8—22no—
313D8—41no—
314D8—462no—
315D8—462no—
316M16—462no—
317C2×C8—231no—
318C2×C8—231no—
319C2×C8—462no—
320C2×C8C22×D2311yescharacteristic
321C2×C8C22×D2311yescharacteristic
322C4⋊C4—231no—
323C4⋊C4—231no—
324C4⋊C4—461no—
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—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—231no—
345C23—461no—
346C23D4×D2311yescharacteristic
347Q8—232no—
348Q8—461no—
349Q8—461no—
350Q8—461no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—461no—
359D4—461no—
360D4—921no—
361D4—922no—
362D4—922no—
363D4—922no—
364D4—922no—
365D4—1841no—
366D4—1841no—
367D4—1841no—
368D4D4×D2312yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—231no—
373C2×C4—231no—
374C2×C4—231no—
375C2×C4—461no—
376C2×C4—461no—
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—21no—
388C8—232no—
389C8—461no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—461no—
404C22—461no—
405C22—461no—
406C22—921no—
407C22—921no—
408C22—921no—
409C22C2×D4×D2311yescharacteristic
410C4—21no—
411C4—41no—
412C4—461no—
413C4—461no—
414C4—461no—
415C4—462no—
416C4—921no—
417C4—921no—
418C4C2×D4×D2311yescharacteristic
419C4#1062515511yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—921no—
425C2—1841no—
426C2#1309304911yescharacteristic
427C2#1309321311yescharacteristic
428C2#1309321811yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#447C2
socleC22×C23C22×D4
hypercenter#447D23
hypocenterC23#3268
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#10625103C2semidirect
2. C2×#10625083C2semidirect
3. #13093085C2semidirect
4. #13093061C2semidirect
5. #13092805C2semidirect
6. #13092661C2semidirect
7. #13092652C2semidirect
8. #13092638C2semidirect
9. #13092610C2semidirect
10. #13092581C2semidirect
11. #13092563C2semidirect
12. #13092559C2semidirect
13. #13092514C2semidirect
14. #13092491C2semidirect
15. C23×#447C2semidirect
18. C2×#67290C22semidirect
26. #10625111C22semidirect
35. C2×#67273C22semidirect
43. C2×Dic92C22semidirect
44. C2×#67263C22semidirect
45. C2×C8×D23C22semidirect
46. #10625066C22semidirect
47. #10625058C22semidirect
53. #10625014C22semidirect
54. #10625003C22semidirect
55. (C2×D23)⋊C8C22semidirect
56. #10624998C22semidirect
57. #10624997C22semidirect
58. Dic23⋊C8C22semidirect
59. #10624992C22semidirect
60. #10624989C22semidirect
106. #67273D4semidirect
218. #447D23semidirect
275. C23#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
C2×#106250832
#130930852
#130930612
#130928052
#130926612
#130926522
#130926382
#130926102
#130925812
#130925632
#130925592
#130925142
#130924912
C23×#4472
#326823