Finite Group Databasebeta

← #15684941

Subgroups — #15684941

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×#10625082C211yesmaximal, characteristic, complemented
2C2×#10625121C211yesmaximal, characteristic, complemented
3#13093085C211yesmaximal, characteristic, complemented
4#13093055C211yesmaximal, characteristic, complemented
5#13092803C211yesmaximal, characteristic, complemented
6#13092666C211yesmaximal, characteristic, complemented
7#13092651C211yesmaximal, characteristic, complemented
8#13092642C211yesmaximal, characteristic, complemented
9#13092610C211yesmaximal, characteristic, complemented
10#13092576C211yesmaximal, characteristic, complemented
11#13092564C211yesmaximal, characteristic, complemented
12#13092552C211yesmaximal, characteristic, complemented
13#13092514C211yesmaximal, characteristic, complemented
14#13092485C211yesmaximal, characteristic, complemented
15C23×#449C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×D4×D23C2211yescharacteristic
19C2×#67288C2211yescharacteristic, complemented
20C2×SD16×C23C2211yescharacteristic, complemented
21C2×D8×C23C2211yescharacteristic
22C23×#121C2211yescharacteristic, complemented
23#10625121—24no—
24#10625118C2211yescharacteristic
25#10625117C2211yescharacteristic
26C2×#67275C2211yescharacteristic, complemented
27C2×#67274C2211yescharacteristic, complemented
28#10625111—21no—
29#10625111C2211yescharacteristic, complemented
30#10625110—21no—
31#10625110—21no—
32#10625108—21no—
33D4×Dic23C2211yescharacteristic
34C2×#67273C2211yescharacteristic
35C2×#67272C2211yescharacteristic
36C2×#67272C2211yescharacteristic
37#10625101C2211yescharacteristic
38#10625100—21no—
39C4×C22⋊D23C2211yescharacteristic
40C2×(C2×D23)⋊C4—21no—
41C22×C23⋊C8C2211yescharacteristic, complemented
42#10625082—24no—
43C2×D184C2211yescharacteristic
44C2×#67263C2211yescharacteristic
45C2×#67262C2211yescharacteristic
46#10625066C2211yescharacteristic
47#10625058C2211yescharacteristic, complemented
48#10625055—21no—
49(C22⋊D23)⋊C4—21no—
50C23×#103C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic, complemented
55(C2×D23)⋊C8C2211yescharacteristic
56#10624998C2211yescharacteristic, complemented
57#10624997C2211yescharacteristic, complemented
58Dic23⋊C8C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic
60#10624989C2211yescharacteristic, complemented
61C23×D23—21no—
62#41×C23—22no—
63#41×C23—41no—
64C2×Q8×C23C2311yescharacteristic
65C2×D4×C23—21no—
66C2×D4×C23—21no—
67C2×D4×C23C2311yescharacteristic
68C2×D4×C23C2311yescharacteristic
69C22×C4×C23—21no—
70C22×C4×C23C2311yescharacteristic
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C2×C22⋊D23—21no—
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C2×C22⋊D23D411yescharacteristic
78C22×Dic23—21no—
79C22×Dic23—21no—
80#67290—22no—
81#67290—41no—
82D4×D23—22no—
83D4×D23—41no—
84#67288—22no—
85#67288—41no—
86C2×D92—21no—
87C2×D92C2311yescharacteristic
88C2×D92C2311yescharacteristic
89C2×C4×D23—21no—
90C2×C4×D23C2311yescharacteristic
91C2×Dic46C2311yescharacteristic
92SD16×C23—41no—
93D8×C23—22no—
94C2×C8×C23C2311yescharacteristic
95C2×C8×C23C2311yescharacteristic
96C4⋊C4×C23C2311yescharacteristic
97C22⋊C4×C23—21no—
98C22⋊Dic23—21no—
99C22⋊Dic23D411yescharacteristic
100#67275—22no—
101#67274—22no—
102#67273D414yescomplemented
103#67272—22no—
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)⋊C4D411yescharacteristic
111C4⋊Dic23C2311yescharacteristic
112Dic23⋊C4—21no—
113Dic23⋊C4—21no—
114Dic23⋊C4D411yescharacteristic
115C4×Dic23—21no—
116C4×Dic23C2311yescharacteristic
117C2×C23⋊C8—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120D184—41no—
121#67263—22no—
122#67262—22no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23C2×D411yescharacteristic
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—42no—
129C22×D23—42no—
130C22×D23—81no—
131C22×D23C2×D411yescharacteristic
132Q8×C23—21no—
133Q8×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×C23—21no—
144C2×C4×C23—42no—
145C2×C4×C23C2×D411yescharacteristic
146C2×C4×C23C2411yescharacteristic
147C22⋊D23—41no—
148C22⋊D23—42no—
149C22⋊D23—42no—
150C22⋊D23—42no—
151C22⋊D23—42no—
152C22⋊D23—81no—
153C22⋊D23—81no—
154C2×Dic23—21no—
155C2×Dic23—21no—
156C2×Dic23—42no—
157C2×Dic23—81no—
158C2×Dic23C2×D411yescharacteristic
159C2×Dic23C2×D411yescharacteristic
160C2×Dic23C2×D411yescharacteristic
161D92—21no—
162D92—21no—
163D92—21no—
164D92—21no—
165D92—81no—
166C4×D23—21no—
167C4×D23—21no—
168C4×D23—42no—
169Dic46—21no—
170Dic46C2×D412yes—
171C8×C23—21no—
172C8×C23—21no—
173C23⋊C8—21no—
174C23⋊C8C2×D412yes—
175#3268—231nomaximal, Sylow
176C22×C23—21no—
177C22×C23—22no—
178C22×C23—21no—
179C22×C23—21no—
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—41no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—84no—
196C4×C23—21no—
197C4×C23—41no—
198C4×C23—41no—
199C4×C23C22×D411yescharacteristic
200C4×C23H(5,𝔽2)11yescharacteristic
201Dic23—22no—
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#452—231no—
216#449—231no—
217#449D2311yescharacteristic, complemented
218#447—231no—
219#440—231no—
220#435—231no—
221C2×C23—42no—
222C2×C23—41no—
223C2×C23—81no—
224C2×C23D4211yescharacteristic
225C2×C23#57511yescharacteristic
226C2×C23#57611yescharacteristic
227D23—41no—
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×Q16—231no—
237C2×SD16—231no—
238C2×SD16—231no—
239C2×SD16—231no—
240C2×SD16C2×D2311yescharacteristic, complemented
241C2×D8—231no—
242C2×D8—231no—
243C2×D8—231no—
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, complemented
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
272C22⋊C8—231no—
273C22⋊C8C2×D2311yescharacteristic, complemented
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×Q8—231no—
284C2×Q8C22×D2311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—231no—
288C2×D4—231no—
289C2×D4—231no—
290C2×D4—461no—
291C2×D4—461no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—462no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—921no—
299C2×D4C22×D2311yescharacteristic
300C2×D4C22×D2311yescharacteristic
301C22×C4—21no—
302C22×C4—231no—
303C22×C4—461no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4C22×D2311yescharacteristic
307Q16—462no—
308SD16—41no—
309SD16—234no—
310SD16—462no—
311SD16—462no—
312D8—22no—
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—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—231no—
341C23—461no—
342C23—461no—
343C23—922no—
344C23—922no—
345C23—1841no—
346C23D4×D2311yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—232no—
350Q8—461no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—81no—
356D4—461no—
357D4—461no—
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—21no—
373C2×C4—42no—
374C2×C4—231no—
375C2×C4—231no—
376C2×C4—231no—
377C2×C4—461no—
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—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—461no—
400C22—461no—
401C22—461no—
402C22—921no—
403C22—921no—
404C22—921no—
405C22—921no—
406C22—921no—
407C22—921no—
408C22—1844no—
409C22C2×D4×D2311yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—461no—
414C4—461no—
415C4—461no—
416C4—462no—
417C4—921no—
418C4C2×D4×D2311yescharacteristic
419C4#1062515511yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—921no—
424C2—1841no—
425C2—1841no—
426C2#1309304911yescharacteristic
427C2#1309321411yescharacteristic
428C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#449C2
socleC22×C23C22×D4
hypercenter#449D23
hypocenterC23#3268
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C2×#10625121C2semidirect
3. #13093085C2semidirect
4. #13093055C2semidirect
5. #13092803C2semidirect
6. #13092666C2semidirect
7. #13092651C2semidirect
8. #13092642C2semidirect
9. #13092610C2semidirect
10. #13092576C2semidirect
11. #13092564C2semidirect
12. #13092552C2semidirect
13. #13092514C2semidirect
14. #13092485C2semidirect
15. C23×#449C2semidirect
19. C2×#67288C22semidirect
20. C2×SD16×C23C22semidirect
22. C23×#121C22semidirect
26. C2×#67275C22semidirect
27. C2×#67274C22semidirect
29. #10625111C22semidirect
41. C22×C23⋊C8C22semidirect
47. #10625058C22semidirect
50. C23×#103C22semidirect
52. C23×C22⋊C8C22semidirect
53. #10625014C22semidirect
54. #10625003C22semidirect
56. #10624998C22semidirect
57. #10624997C22semidirect
58. Dic23⋊C8C22semidirect
60. #10624989C22semidirect
102. #67273D4semidirect
217. #449D23semidirect
240. C2×SD16C2×D23semidirect
257. #121C2×D23semidirect
267. #103C2×D23semidirect
273. C22⋊C8C2×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×#106250822
C2×#106251212
#130930852
#130930552
#130928032
#130926662
#130926512
#130926422
#130926102
#130925762
#130925642
#130925522
#130925142
#130924852
C23×#4492
#326823