Finite Group Databasebeta

← #15684928

Subgroups — #15684928

Order 2944.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625085C211yesmaximal, characteristic, complemented
2C2×#10625087C211yesmaximal, characteristic, complemented
3#13093070C211yesmaximal, characteristic, complemented
4#13093062C211yesmaximal, characteristic, complemented
5#13092809C211yesmaximal, characteristic, complemented
6#13092674C211yesmaximal, characteristic, complemented
7#13092649C211yesmaximal, characteristic, complemented
8#13092633C211yesmaximal, characteristic, complemented
9#13092582C211yesmaximal, characteristic, complemented
10#13092576C211yesmaximal, characteristic, complemented
11#13092566C211yesmaximal, characteristic, complemented
12#13092565C211yesmaximal, characteristic, complemented
13#13092527C211yesmaximal, characteristic, complemented
14#13092487C211yesmaximal, characteristic, complemented
15C23×#461C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×#67292C2211yescharacteristic, complemented
18C2×#67290C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic
20C2×SD16×C23C2211yescharacteristic
21C2×SD16×C23C2211yescharacteristic
22C23×C4⋊Q8C2211yescharacteristic, complemented
23C4×D4×C23C2211yescharacteristic
24#10625117C2211yescharacteristic
25#10625117C2211yescharacteristic, complemented
26C2×#67275C2211yescharacteristic, complemented
27C2×#67275C2211yescharacteristic, complemented
28C2×#67274C2211yescharacteristic
29C2×#67274C2211yescharacteristic
30C2×#67272C2211yescharacteristic
31#10625101—21no—
32C2×(C2×D23)⋊C4—21no—
33#10625087—24no—
34#10625085—24no—
35C2×D184C2211yescharacteristic
36C2×#67263C2211yescharacteristic, complemented
37C2×#67262C2211yescharacteristic
38C2×C8×D23C2211yescharacteristic, complemented
39#10625068C2211yescharacteristic
40#10625066—21no—
41#10625066C2211yescharacteristic
42#10625065—21no—
43#10625065—21no—
44C4⋊C4×D23—21no—
45#10625057—21no—
46#10625053—21no—
47#10625046C2211yescharacteristic
48C4×D92C2211yescharacteristic
49C4×D92C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#103C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic
54#10625003C2211yescharacteristic
55(C2×D23)⋊C8C2211yescharacteristic
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57#10624998C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic, complemented
59#10624990C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×Q8×C23C2311yescharacteristic
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C22×Dic23—21no—
69#67292—22no—
70#67292—22no—
71#67292—41no—
72#67292—41no—
73#67290—22no—
74#67290—41no—
75D4×D23—22no—
76D4×D23—41no—
77C2×D92—21no—
78C2×D92—21no—
79C2×D92—21no—
80C2×D92D411yescharacteristic
81C2×D92C2311yescharacteristic
82C2×D92C2311yescharacteristic
83C2×C4×D23—21no—
84C2×C4×D23—21no—
85C2×C4×D23—21no—
86C2×C4×D23C2311yescharacteristic
87C2×C4×D23C2311yescharacteristic
88C2×Dic46C2311yescharacteristic
89SD16×C23—22no—
90SD16×C23—22no—
91C2×C8×C23C2311yescharacteristic
92C2×C8×C23C2311yescharacteristic
93C4⋊C4×C23—21no—
94C4⋊C4×C23—21no—
95C4⋊C4×C23C2311yescharacteristic
96C22⋊C4×C23—21no—
97C42×C23C2311yescharacteristic
98#67275—22no—
99#67275—41no—
100#67274—22no—
101#67274—41no—
102#67272D414yescomplemented
103(C2×D23)⋊C4—21no—
104(C2×D23)⋊C4—21no—
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
111(C2×D23)⋊C4D411yescharacteristic
112C4⋊Dic23—21no—
113C4⋊Dic23D411yescharacteristic
114C4⋊Dic23C2311yescharacteristic
115Dic23⋊C4—21no—
116Dic23⋊C4—21no—
117C2×C23⋊C8C2311yescharacteristic
118C2×C23⋊C8C2311yescharacteristic
119D184—22no—
120#67263—22no—
121#67262—22no—
122C8×D23—22no—
123C23×C23—21no—
124C22×D23—21no—
125C22×D23—21no—
126C22×D23—42no—
127C22×D23—42no—
128C22×D23—81no—
129C22×D23C2×D411yescharacteristic
130C22×D23C2×D411yescharacteristic
131Q8×C23—21no—
132Q8×C23—21no—
133Q8×C23—21no—
134Q8×C23—21no—
135D4×C23—21no—
136D4×C23C2×D412yes—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—81no—
141C2×C4×C23C2×D411yescharacteristic
142C2×C4×C23C2×D411yescharacteristic
143C2×C4×C23C2411yescharacteristic
144C22⋊D23—42no—
145C22⋊D23—42no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—42no—
149C2×Dic23C2×D411yescharacteristic
150C2×Dic23C2×D411yescharacteristic
151D92—21no—
152D92—21no—
153D92—21no—
154D92—41no—
155D92—42no—
156D92—42no—
157D92—81no—
158D92C2×D412yes—
159C4×D23—21no—
160C4×D23—21no—
161C4×D23—21no—
162C4×D23—21no—
163C4×D23—42no—
164C4×D23—42no—
165C4×D23—42no—
166Dic46—21no—
167Dic46—21no—
168C8×C23—21no—
169C8×C23—21no—
170C23⋊C8—21no—
171C23⋊C8C2×D412yes—
172#3267—231nomaximal, Sylow
173C22×C23—22no—
174C22×C23—41no—
175C22×C23—41no—
176C22×C23C22×D411yescharacteristic
177C2×D23—21no—
178C2×D23—21no—
179C2×D23—22no—
180C2×D23—21no—
181C2×D23—21no—
182C2×D23—21no—
183C2×D23—21no—
184C2×D23—41no—
185C2×D23—41no—
186C2×D23—41no—
187C2×D23—41no—
188C2×D23—41no—
189C2×D23—84no—
190C4×C23—21no—
191C4×C23—21no—
192C4×C23—41no—
193C4×C23—41no—
194C4×C23—41no—
195C4×C23C22×D411yescharacteristic
196C4×C23H(5,𝔽2)11yescharacteristic
197Dic23—21no—
198Dic23—21no—
199Dic23—41no—
200Dic23—41no—
201C2×AGL(1,ℤ/8)—231no—
202C2×#135—231no—
203#547—231no—
204#546—231no—
205#497—231no—
206#470—231no—
207#465—231no—
208#463—231no—
209#461D2311yescharacteristic, complemented
210#452—231no—
211#452—231no—
212#450—231no—
213#449—231no—
214#442—231no—
215#435—231no—
216C2×C23—42no—
217C2×C23D4211yescharacteristic
218C2×C23#57511yescharacteristic
219C2×C23#57711yescharacteristic
220D23—41no—
221D23—41no—
222D23—42no—
223D23—81no—
224C2×#41—231no—
225C2×#41—231no—
226C2×#41—231no—
227C22×D4—231no—
228AGL(1,ℤ/8)—464no—
229#135—464no—
230C2×Q16—231no—
231C2×Q16—231no—
232C2×SD16—231no—
233C2×SD16—231no—
234C2×SD16—231no—
235C2×SD16C2×D2311yescharacteristic
236C2×SD16C2×D2311yescharacteristic
237C2×D8—231no—
238C2×D8—231no—
239C2×M16—231no—
240C22×C8—231no—
241C4⋊Q8C2×D2311yescharacteristic, complemented
242#124—231no—
243#123—461no—
244#123—461no—
245#123—461no—
246C22⋊Q8—231no—
247C22⋊Q8—231no—
248C22⋊Q8—231no—
249#121—231no—
250#121—461no—
251#121—461no—
252#120—461no—
253C4×D4—231no—
254C4×D4—231no—
255C4×D4C2×D2311yescharacteristic
256C2×C4⋊C4—461no—
257C2×C22⋊C4—461no—
258#106—231no—
259C4⋊C8C2×D2311yescharacteristic, complemented
260#103—231no—
261#103C2×D2311yescharacteristic, complemented
262#103C2×D2311yescharacteristic, complemented
263#102—231no—
264#102—231no—
265#102—231no—
266C22⋊C8—231no—
267C22⋊C8—231no—
268#97—231no—
269C23#326711yescharacteristic, complemented, Sylow
270C24—461no—
271#41—462no—
272#41—462no—
273#41—462no—
274#41—921no—
275#41—921no—
276#41—921no—
277C2×Q8—231no—
278C2×Q8C22×D2311yescharacteristic
279C2×Q8C22×D2311yescharacteristic
280C2×D4—231no—
281C2×D4—231no—
282C2×D4—231no—
283C2×D4—461no—
284C2×D4—461no—
285C2×D4—461no—
286C2×D4—461no—
287C2×D4—462no—
288C2×D4—461no—
289C2×D4—921no—
290C2×D4C22×D2311yescharacteristic
291C22×C4—21no—
292C22×C4—231no—
293C22×C4—231no—
294C22×C4—461no—
295C22×C4—461no—
296C22×C4—461no—
297C22×C4—461no—
298Q16—462no—
299Q16—921no—
300SD16—22no—
301SD16—22no—
302SD16—462no—
303SD16—462no—
304SD16—921no—
305D8—234no—
306D8—462no—
307M16—462no—
308C2×C8—231no—
309C2×C8—231no—
310C2×C8—462no—
311C2×C8C22×D2311yescharacteristic
312C2×C8C22×D2311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—231no—
316C4⋊C4—231no—
317C4⋊C4—461no—
318C4⋊C4—461no—
319C4⋊C4—461no—
320C4⋊C4C22×D2311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—231no—
323C22⋊C4—231no—
324C22⋊C4—461no—
325C22⋊C4—461no—
326C22⋊C4—461no—
327C22⋊C4—461no—
328C22⋊C4—461no—
329C22⋊C4—461no—
330C22⋊C4—461no—
331C42C22×D2311yescharacteristic
332C23—21no—
333C23—231no—
334C23—231no—
335C23—461no—
336C23—461no—
337C23—922no—
338C23—922no—
339C23—1841no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—461no—
345Q8—461no—
346D4—21no—
347D4—232no—
348D4—461no—
349D4—461no—
350D4—461no—
351D4—921no—
352D4—922no—
353D4—922no—
354D4—922no—
355D4—922no—
356D4—1841no—
357D4D4×D2312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—81no—
362C2×C4—231no—
363C2×C4—231no—
364C2×C4—461no—
365C2×C4—461no—
366C2×C4—461no—
367C2×C4—461no—
368C2×C4—461no—
369C2×C4—461no—
370C2×C4—922no—
371C2×C4—922no—
372C2×C4—922no—
373C2×C4—922no—
374C2×C4D4×D2311yescharacteristic
375C2×C4D4×D2311yescharacteristic
376C2×C4C23×D2311yescharacteristic
377C8—21no—
378C8—21no—
379C8—232no—
380C8—461no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—461no—
385C22—461no—
386C22—461no—
387C22—461no—
388C22—461no—
389C22—461no—
390C22—462no—
391C22—921no—
392C22—921no—
393C22—921no—
394C22—921no—
395C22—921no—
396C22—1844no—
397C22C2×D4×D2311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—461no—
404C4—461no—
405C4—921no—
406C4—921no—
407C4C2×D4×D2311yescharacteristic
408C4#1062516011yescharacteristic
409C2—42no—
410C2—921no—
411C2—921no—
412C2—922no—
413C2—1841no—
414C2#1309305111yescharacteristic
415C2#1309321611yescharacteristic
416C2#1309322311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#461C2
socleC22×C23C22×D4
hypercenter#461D23
hypocenterC23#3267
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C2×#10625087C2semidirect
3. #13093070C2semidirect
4. #13093062C2semidirect
5. #13092809C2semidirect
6. #13092674C2semidirect
7. #13092649C2semidirect
8. #13092633C2semidirect
9. #13092582C2semidirect
10. #13092576C2semidirect
11. #13092566C2semidirect
12. #13092565C2semidirect
13. #13092527C2semidirect
14. #13092487C2semidirect
15. C23×#461C2semidirect
17. C2×#67292C22semidirect
22. C23×C4⋊Q8C22semidirect
25. #10625117C22semidirect
26. C2×#67275C22semidirect
27. C2×#67275C22semidirect
36. C2×#67263C22semidirect
38. C2×C8×D23C22semidirect
49. C4×D92C22semidirect
50. C23×C4⋊C8C22semidirect
51. C23×#103C22semidirect
52. C23×#103C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. #10624998C22semidirect
58. #10624991C22semidirect
59. #10624990C22semidirect
60. #10624985C22semidirect
102. #67272D4semidirect
209. #461D23semidirect
241. C4⋊Q8C2×D23semidirect
259. C4⋊C8C2×D23semidirect
261. #103C2×D23semidirect
262. #103C2×D23semidirect
269. C23#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
C2×#106250872
#130930702
#130930622
#130928092
#130926742
#130926492
#130926332
#130925822
#130925762
#130925662
#130925652
#130925272
#130924872
C23×#4612
#326723