Finite Group Databasebeta

← #15684926

Subgroups — #15684926

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×#10625121C211yesmaximal, characteristic, complemented
3#13093069C211yesmaximal, characteristic, complemented
4#13093055C211yesmaximal, characteristic, complemented
5#13092810C211yesmaximal, characteristic, complemented
6#13092674C211yesmaximal, characteristic, complemented
7#13092648C211yesmaximal, characteristic, complemented
8#13092635C211yesmaximal, characteristic, complemented
9#13092620C211yesmaximal, characteristic, complemented
10#13092578C211yesmaximal, characteristic, complemented
11#13092569C211yesmaximal, characteristic, complemented
12#13092564C211yesmaximal, characteristic, complemented
13#13092526C211yesmaximal, characteristic, complemented
14#13092485C211yesmaximal, characteristic, complemented
15C23×#452C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C2×#67292C2211yescharacteristic
18C2×D4×D23C2211yescharacteristic
19C2×#67288C2211yescharacteristic, complemented
20C2×Q16×C23C2211yescharacteristic, complemented
21C2×SD16×C23C2211yescharacteristic
22C23×C22⋊Q8C2211yescharacteristic, complemented
23#10625121—24no—
24#10625118C2211yescharacteristic
25#10625117C2211yescharacteristic
26#10625115C2211yescharacteristic, complemented
27C2×#67275C2211yescharacteristic, complemented
28C2×#67274C2211yescharacteristic
29C2×#67274C2211yescharacteristic, complemented
30#10625110—21no—
31#10625108—21no—
32D4×Dic23C2211yescharacteristic
33C2×#67273C2211yescharacteristic
34C2×#67272C2211yescharacteristic
35#10625101C2211yescharacteristic
36#10625100—21no—
37C4×C22⋊D23C2211yescharacteristic
38C2×(C2×D23)⋊C4—21no—
39C22×C23⋊C8C2211yescharacteristic, complemented
40#10625085—24no—
41C2×D184C2211yescharacteristic
42C2×#67263C2211yescharacteristic
43C2×#67262C2211yescharacteristic
44#10625068C2211yescharacteristic
45#10625065—21no—
46#10625064C2211yescharacteristic, complemented
47C4⋊C4×D23—21no—
48#10625055—21no—
49#10625054—21no—
50C23×#103C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic, complemented
53#10625017C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic, complemented
55(C2×D23)⋊C8C2211yescharacteristic
56#10624998C2211yescharacteristic, complemented
57#10624997C2211yescharacteristic, complemented
58Dic23⋊C8C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic
60#10624990C2211yescharacteristic, complemented
61C23×D23—21no—
62#41×C23—22no—
63#41×C23—41no—
64C2×Q8×C23C2311yescharacteristic
65C2×Q8×C23C2311yescharacteristic
66C2×D4×C23—21no—
67C2×D4×C23C2311yescharacteristic
68C22×C4×C23—21no—
69C22×C4×C23C2311yescharacteristic
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23D411yescharacteristic
74C22×Dic23—21no—
75#67292—22no—
76#67292—41no—
77D4×D23—22no—
78D4×D23—41no—
79#67288—22no—
80#67288—41no—
81C2×D92—21no—
82C2×D92C2311yescharacteristic
83C2×D92C2311yescharacteristic
84C2×C4×D23—21no—
85C2×C4×D23—21no—
86C2×C4×D23—21no—
87C2×C4×D23C2311yescharacteristic
88C2×Dic46C2311yescharacteristic
89Q16×C23—41no—
90SD16×C23—22no—
91C2×C8×C23C2311yescharacteristic
92C2×C8×C23C2311yescharacteristic
93C4⋊C4×C23—21no—
94C4⋊C4×C23C2311yescharacteristic
95C22⋊C4×C23—21no—
96C22⋊Dic23—21no—
97C22⋊Dic23D411yescharacteristic
98#67275—22no—
99#67274—22no—
100#67274—22no—
101#67273—22no—
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)⋊C4D411yescharacteristic
110C4⋊Dic23—21no—
111C4⋊Dic23C2311yescharacteristic
112Dic23⋊C4—21no—
113Dic23⋊C4—21no—
114Dic23⋊C4—21no—
115Dic23⋊C4D411yescharacteristic
116C4×Dic23C2311yescharacteristic
117C2×C23⋊C8—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120D184—22no—
121#67263—41no—
122#67262—22no—
123C23×C23—21no—
124C23×C23C2×D411yescharacteristic
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—42no—
128C22×D23—42no—
129C22×D23—81no—
130C22×D23C2×D411yescharacteristic
131Q8×C23—21no—
132Q8×C23—21no—
133Q8×C23—21no—
134Q8×C23—21no—
135D4×C23—21no—
136D4×C23—42no—
137D4×C23C2×D412yes—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—42no—
144C2×C4×C23C2×D411yescharacteristic
145C2×C4×C23C2411yescharacteristic
146C22⋊D23—41no—
147C22⋊D23—42no—
148C22⋊D23—42no—
149C22⋊D23—81no—
150C2×Dic23—21no—
151C2×Dic23—21no—
152C2×Dic23—81no—
153C2×Dic23C2×D411yescharacteristic
154C2×Dic23C2×D411yescharacteristic
155C2×Dic23C2×D411yescharacteristic
156D92—21no—
157D92—21no—
158D92—21no—
159D92—42no—
160D92C2×D412yes—
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—21no—
174C22×C23—22no—
175C22×C23—21no—
176C22×C23—21no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23C22×D411yescharacteristic
180C2×D23—21no—
181C2×D23—22no—
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—41no—
192C4×C23—41no—
193C4×C23—41no—
194C4×C23C22×D411yescharacteristic
195C4×C23H(5,𝔽2)11yescharacteristic
196Dic23—21no—
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#461—231no—
210#452—231no—
211#452D2311yescharacteristic, complemented
212#450—231no—
213#449—231no—
214#442—231no—
215#435—231no—
216C2×C23—42no—
217C2×C23—41no—
218C2×C23D4211yescharacteristic
219C2×C23#57511yescharacteristic
220C2×C23#57711yescharacteristic
221D23—41no—
222D23—42no—
223D23—81no—
224C2×#41—231no—
225C2×#41—231no—
226C2×#41C2×D2311yescharacteristic
227C22×D4—231no—
228AGL(1,ℤ/8)—464no—
229#135—464no—
230C2×Q16—231no—
231C2×Q16C2×D2311yescharacteristic, complemented
232C2×SD16—231no—
233C2×SD16—231no—
234C2×SD16—231no—
235C2×SD16—231no—
236C2×SD16C2×D2311yescharacteristic
237C2×D8—231no—
238C2×D8—231no—
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⋊Q8C2×D2311yescharacteristic, complemented
249#121—231no—
250#121—461no—
251#121—461no—
252#120—461no—
253C4×D4—231no—
254C4×D4—231no—
255C4×D4—231no—
256C2×C4⋊C4—461no—
257C2×C22⋊C4—461no—
258#106—231no—
259C4⋊C8—231no—
260#103—231no—
261#103—231no—
262#103C2×D2311yescharacteristic, complemented
263#102—231no—
264#102—231no—
265#102C2×D2311yescharacteristic
266C22⋊C8—231no—
267C22⋊C8C2×D2311yescharacteristic, complemented
268#97—231no—
269C23#326711yescharacteristic, complemented, Sylow
270C24—461no—
271#41—22no—
272#41—41no—
273#41—462no—
274#41—462no—
275#41—921no—
276#41—921no—
277C2×Q8—231no—
278C2×Q8C22×D2311yescharacteristic
279C2×Q8C22×D2311yescharacteristic
280C2×D4—21no—
281C2×D4—231no—
282C2×D4—231no—
283C2×D4—231no—
284C2×D4—461no—
285C2×D4—461no—
286C2×D4—462no—
287C2×D4—461no—
288C2×D4—461no—
289C2×D4—921no—
290C2×D4C22×D2311yescharacteristic
291C22×C4—21no—
292C22×C4—231no—
293C22×C4—461no—
294C22×C4—461no—
295C22×C4—461no—
296C22×C4—461no—
297C22×C4C22×D2311yescharacteristic
298Q16—41no—
299Q16—462no—
300SD16—22no—
301SD16—462no—
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—231no—
315C4⋊C4—231no—
316C4⋊C4—461no—
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—
331C42—231no—
332C23—21no—
333C23—231no—
334C23—461no—
335C23—461no—
336C23—922no—
337C23—922no—
338C23—1841no—
339C23D4×D2311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—461no—
345Q8—461no—
346D4—21no—
347D4—42no—
348D4—232no—
349D4—461no—
350D4—461no—
351D4—461no—
352D4—922no—
353D4—921no—
354D4—922no—
355D4—922no—
356D4—1841no—
357D4D4×D2312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—231no—
365C2×C4—231no—
366C2×C4—231no—
367C2×C4—461no—
368C2×C4—461no—
369C2×C4—461no—
370C2×C4—461no—
371C2×C4—922no—
372C2×C4—922no—
373C2×C4—922no—
374C2×C4—1841no—
375C2×C4D4×D2311yescharacteristic
376C2×C4C23×D2311yescharacteristic
377C8—21no—
378C8—21no—
379C8—232no—
380C8—461no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
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—41no—
400C4—41no—
401C4—41no—
402C4—461no—
403C4—461no—
404C4—461no—
405C4—921no—
406C4—921no—
407C4C2×D4×D2311yescharacteristic
408C4#1062515511yescharacteristic
409C2—41no—
410C2—42no—
411C2—921no—
412C2—922no—
413C2—1841no—
414C2#1309304911yescharacteristic
415C2#1309321411yescharacteristic
416C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#452C2
socleC22×C23C22×D4
hypercenter#452D23
hypocenterC23#3267
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C2×#10625121C2semidirect
3. #13093069C2semidirect
4. #13093055C2semidirect
5. #13092810C2semidirect
6. #13092674C2semidirect
7. #13092648C2semidirect
8. #13092635C2semidirect
9. #13092620C2semidirect
10. #13092578C2semidirect
11. #13092569C2semidirect
12. #13092564C2semidirect
13. #13092526C2semidirect
14. #13092485C2semidirect
15. C23×#452C2semidirect
19. C2×#67288C22semidirect
20. C2×Q16×C23C22semidirect
22. C23×C22⋊Q8C22semidirect
26. #10625115C22semidirect
27. C2×#67275C22semidirect
29. C2×#67274C22semidirect
39. C22×C23⋊C8C22semidirect
46. #10625064C22semidirect
50. C23×#103C22semidirect
52. C23×C22⋊C8C22semidirect
53. #10625017C22semidirect
54. #10625003C22semidirect
56. #10624998C22semidirect
57. #10624997C22semidirect
58. Dic23⋊C8C22semidirect
60. #10624990C22semidirect
102. #67272D4semidirect
211. #452D23semidirect
231. C2×Q16C2×D23semidirect
248. C22⋊Q8C2×D23semidirect
262. #103C2×D23semidirect
267. C22⋊C8C2×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×#106251212
#130930692
#130930552
#130928102
#130926742
#130926482
#130926352
#130926202
#130925782
#130925692
#130925642
#130925262
#130924852
C23×#4522
#326723