Finite Group Databasebeta

← #15684924

Subgroups — #15684924

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×#10625082C211yesmaximal, characteristic, complemented
2C2×#10625083C211yesmaximal, characteristic, complemented
3#13093071C211yesmaximal, characteristic, complemented
4#13093062C211yesmaximal, characteristic, complemented
5#13092811C211yesmaximal, characteristic, complemented
6#13092676C211yesmaximal, characteristic, complemented
7#13092647C211yesmaximal, characteristic, complemented
8#13092632C211yesmaximal, characteristic, complemented
9#13092622C211yesmaximal, characteristic, complemented
10#13092580C211yesmaximal, characteristic, complemented
11#13092580C211yesmaximal, characteristic, complemented
12#13092569C211yesmaximal, characteristic, complemented
13#13092563C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#442C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×#67290C2211yescharacteristic, complemented
19C2×D4×D23C2211yescharacteristic
20C2×D8×C23C2211yescharacteristic
21C4×D4×C23C2211yescharacteristic
22C4×D4×C23C2211yescharacteristic, complemented
23C2×#67273C2211yescharacteristic
24C2×#67273C2211yescharacteristic
25C2×#67273C2211yescharacteristic, complemented
26C2×#67272C2211yescharacteristic
27#10625101—21no—
28#10625101—21no—
29C2×(C2×D23)⋊C4—21no—
30C2×C4⋊Dic23—21no—
31#10625083—24no—
32#10625082—24no—
33C2×Dic92C2211yescharacteristic, complemented
34C2×Dic92C2211yescharacteristic, complemented
35C2×#67263C2211yescharacteristic
36C2×#67263C2211yescharacteristic
37C2×#67262C2211yescharacteristic
38C2×C8×D23C2211yescharacteristic, complemented
39#10625068C2211yescharacteristic
40#10625068C2211yescharacteristic
41#10625068C2211yescharacteristic, complemented
42#10625066C2211yescharacteristic
43#10625057—21no—
44#10625057—21no—
45#10625057—21no—
46#10625053—21no—
47#10625046C2211yescharacteristic
48C4×D92C2211yescharacteristic
49#10625040C2211yescharacteristic, complemented
50C23×#106C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic
52C23×#102C2211yescharacteristic, complemented
53C23×#97C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic
55(C2×D23)⋊C8C2211yescharacteristic, complemented
56#10624992C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624992C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic
60C4⋊(C23⋊C8)C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×D4×C23C2311yescharacteristic
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C22×C4×C23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C22×Dic23—21no—
71C22×Dic23—21no—
72C22×Dic23—21no—
73#67290—22no—
74#67290—22no—
75#67290—22no—
76#67290—41no—
77#67290—41no—
78#67290—41no—
79D4×D23—22no—
80D4×D23—41no—
81C2×D92—21no—
82C2×D92D411yescharacteristic
83C2×D92C2311yescharacteristic
84C2×C4×D23C2311yescharacteristic
85C2×C4×D23C2311yescharacteristic
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88C2×Dic46C2311yescharacteristic
89D8×C23D414yescomplemented
90C2×C8×C23C2311yescharacteristic
91C2×C8×C23C2311yescharacteristic
92C4⋊C4×C23C2311yescharacteristic
93C4⋊C4×C23C2311yescharacteristic
94C22⋊C4×C23—21no—
95C22⋊C4×C23—21no—
96C42×C23C2311yescharacteristic
97#67273—22no—
98#67273—22no—
99#67273—22no—
100#67272—22no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104(C2×D23)⋊C4—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4D411yescharacteristic
108(C2×D23)⋊C4D411yescharacteristic
109C4⋊Dic23—21no—
110C4⋊Dic23—21no—
111C4⋊Dic23—21no—
112C4⋊Dic23—21no—
113C4⋊Dic23—21no—
114C4⋊Dic23D411yescharacteristic
115C2×C23⋊C8C2311yescharacteristic
116C2×C23⋊C8C2311yescharacteristic
117Dic92—22no—
118Dic92—41no—
119#67263—22no—
120#67263—41no—
121#67262—22no—
122C8×D23—22no—
123C23×C23—21no—
124C23×C23—21no—
125C22×D23—21no—
126C22×D23—42no—
127C22×D23—42no—
128C22×D23—81no—
129C22×D23C2×D411yescharacteristic
130C22×D23C2×D411yescharacteristic
131D4×C23—21no—
132D4×C23—21no—
133D4×C23C2×D412yes—
134D4×C23C2×D412yes—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—42no—
138C2×C4×C23—81no—
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—42no—
143C22⋊D23—42no—
144C22⋊D23—42no—
145C22⋊D23—42no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—42no—
150C2×Dic23—42no—
151C2×Dic23—42no—
152C2×Dic23C2×D411yescharacteristic
153C2×Dic23C2×D411yescharacteristic
154D92—21no—
155D92—21no—
156D92—41no—
157D92—81no—
158C4×D23—21no—
159C4×D23—21no—
160C4×D23—21no—
161C4×D23—21no—
162Dic46—21no—
163Dic46—21no—
164Dic46—21no—
165Dic46—21no—
166Dic46—21no—
167Dic46—21no—
168C8×C23—21no—
169C8×C23C2×D412yes—
170C23⋊C8—21no—
171C23⋊C8—21no—
172#3267—231nomaximal, Sylow
173C22×C23—22no—
174C22×C23—22no—
175C22×C23—41no—
176C22×C23—41no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23C22×D411yescharacteristic
180C2×D23—21no—
181C2×D23—21no—
182C2×D23—21no—
183C2×D23—21no—
184C2×D23—21no—
185C2×D23—21no—
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×C23C22×D411yescharacteristic
195C4×C23H(5,𝔽2)11yescharacteristic
196Dic23—21no—
197Dic23—21no—
198Dic23—41no—
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#461—231no—
210#452—231no—
211#452—231no—
212#450—231no—
213#449—231no—
214#442D2311yescharacteristic, complemented
215#435—231no—
216C2×C23—42no—
217C2×C23—42no—
218C2×C23D4211yescharacteristic
219C2×C23#57511yescharacteristic
220C2×C23#57711yescharacteristic
221D23—41no—
222D23—41no—
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×SD16—231no—
236C2×SD16—231no—
237C2×D8—231no—
238C2×D8C2×D2311yescharacteristic
239C2×M16—231no—
240C22×C8—231no—
241C4⋊Q8—231no—
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×D4C2×D2311yescharacteristic
255C4×D4C2×D2311yescharacteristic, complemented
256C2×C4⋊C4—461no—
257C2×C22⋊C4—461no—
258#106C2×D2311yescharacteristic, complemented
259C4⋊C8—231no—
260#103—231no—
261#103—231no—
262#103—231no—
263#102—231no—
264#102C2×D2311yescharacteristic
265#102C2×D2311yescharacteristic, complemented
266C22⋊C8—231no—
267C22⋊C8—231no—
268#97C2×D2311yescharacteristic, complemented
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×Q8—231no—
279C2×Q8—231no—
280C2×D4—231no—
281C2×D4—231no—
282C2×D4—461no—
283C2×D4—461no—
284C2×D4—462no—
285C2×D4—461no—
286C2×D4—461no—
287C2×D4—461no—
288C2×D4—921no—
289C2×D4C22×D2311yescharacteristic
290C2×D4C22×D2311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—231no—
294C22×C4—231no—
295C22×C4—461no—
296C22×C4—461no—
297C22×C4—461no—
298Q16—462no—
299Q16—921no—
300SD16—462no—
301SD16—462no—
302SD16—462no—
303SD16—462no—
304SD16—921no—
305D8—462no—
306D8D9214yescomplemented
307M16—462no—
308C2×C8—231no—
309C2×C8—231no—
310C2×C8—462no—
311C2×C8C22×D2311yescharacteristic
312C2×C8C22×D2311yescharacteristic
313C4⋊C4—231no—
314C4⋊C4—461no—
315C4⋊C4—461no—
316C4⋊C4—461no—
317C4⋊C4—461no—
318C4⋊C4—461no—
319C4⋊C4C22×D2311yescharacteristic
320C4⋊C4C22×D2311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—231no—
324C22⋊C4—231no—
325C22⋊C4—461no—
326C22⋊C4—461no—
327C22⋊C4—461no—
328C22⋊C4—461no—
329C22⋊C4—461no—
330C22⋊C4—461no—
331C42C22×D2311yescharacteristic
332C23—21no—
333C23—21no—
334C23—231no—
335C23—231no—
336C23—461no—
337C23—922no—
338C23—922no—
339C23—1841no—
340Q8—461no—
341Q8—461no—
342Q8—461no—
343Q8—461no—
344Q8—461no—
345Q8—461no—
346D4—21no—
347D4—21no—
348D4—461no—
349D4—461no—
350D4—921no—
351D4—922no—
352D4—922no—
353D4—922no—
354D4—922no—
355D4—1841no—
356D4C2×D9212yes—
357D4C2×D9212yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
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—461no—
371C2×C4—922no—
372C2×C4—922no—
373C2×C4—922no—
374C2×C4D4×D2311yescharacteristic
375C2×C4D4×D2311yescharacteristic
376C2×C4C23×D2311yescharacteristic
377C8—21no—
378C8—461no—
379C8—461no—
380C8C2×D9212yes—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—461no—
388C22—461no—
389C22—461no—
390C22—461no—
391C22—461no—
392C22—461no—
393C22—921no—
394C22—921no—
395C22—921no—
396C22—1844no—
397C22C2×D4×D2311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—461no—
403C4—461no—
404C4—921no—
405C4—921no—
406C4—921no—
407C4C22×D9211yescharacteristic
408C4#1062516011yescharacteristic
409C2—42no—
410C2—42no—
411C2—921no—
412C2—921no—
413C2—1841no—
414C2D4×D9211yescharacteristic
415C2#1309321311yescharacteristic
416C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#442C2
socleC22×C23C22×D4
hypercenter#442D23
hypocenterC23#3267
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C2×#10625083C2semidirect
3. #13093071C2semidirect
4. #13093062C2semidirect
5. #13092811C2semidirect
6. #13092676C2semidirect
7. #13092647C2semidirect
8. #13092632C2semidirect
9. #13092622C2semidirect
10. #13092580C2semidirect
11. #13092580C2semidirect
12. #13092569C2semidirect
13. #13092563C2semidirect
14. #13092490C2semidirect
15. C23×#442C2semidirect
18. C2×#67290C22semidirect
22. C4×D4×C23C22semidirect
25. C2×#67273C22semidirect
33. C2×Dic92C22semidirect
34. C2×Dic92C22semidirect
38. C2×C8×D23C22semidirect
41. #10625068C22semidirect
49. #10625040C22semidirect
50. C23×#106C22semidirect
52. C23×#102C22semidirect
53. C23×#97C22semidirect
55. (C2×D23)⋊C8C22semidirect
56. #10624992C22semidirect
57. #10624992C22semidirect
58. #10624992C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
89. D8×C23D4semidirect
214. #442D23semidirect
255. C4×D4C2×D23semidirect
258. #106C2×D23semidirect
265. #102C2×D23semidirect
268. #97C2×D23semidirect
269. C23#3267semidirect
306. D8D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
C2×#106250832
#130930712
#130930622
#130928112
#130926762
#130926472
#130926322
#130926222
#130925802
#130925692
#130925632
#130924902
C23×#4422
#326723