Finite Group Databasebeta

← #15684927

Subgroups — #15684927

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×#10625079C211yesmaximal, characteristic, complemented
2C2×#10625075C211yesmaximal, characteristic, complemented
3#13093072C211yesmaximal, characteristic, complemented
4#13093063C211yesmaximal, characteristic, complemented
5#13092811C211yesmaximal, characteristic, complemented
6#13092675C211yesmaximal, characteristic, complemented
7#13092646C211yesmaximal, characteristic, complemented
8#13092633C211yesmaximal, characteristic, complemented
9#13092623C211yesmaximal, characteristic, complemented
10#13092581C211yesmaximal, characteristic, complemented
11#13092581C211yesmaximal, characteristic, complemented
12#13092570C211yesmaximal, characteristic, complemented
13#13092564C211yesmaximal, characteristic, complemented
14#13092530C211yesmaximal, characteristic, complemented
15C23×#435C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C2×#67288C2211yescharacteristic
18C2×#67288C2211yescharacteristic, complemented
19C22×D92C2211yescharacteristic
20C2×M16×C23C2211yescharacteristic
21C22×C8×C23C2211yescharacteristic, complemented
22C4×D4×C23C2211yescharacteristic
23#10625109—21no—
24#10625108—21no—
25#10625101C2211yescharacteristic
26#10625095C2211yescharacteristic
27#10625095C2211yescharacteristic
28#10625095C2211yescharacteristic, complemented
29#10625079—24no—
30C2×Dic92C2211yescharacteristic, complemented
31C2×Dic92C2211yescharacteristic, complemented
32#10625075—24no—
33C2×D184C2211yescharacteristic
34C2×D184C2211yescharacteristic
35C2×#67263C2211yescharacteristic
36C2×#67263C2211yescharacteristic
37C2×#67263C2211yescharacteristic
38C2×#67263C2211yescharacteristic
39C2×#67263C2211yescharacteristic, complemented
40#10625065—21no—
41C4⋊C4×D23—21no—
42#10625055—21no—
43#10625054—21no—
44#10625054—21no—
45C22⋊C4×D23—21no—
46#10625046C2211yescharacteristic
47C4×D92C2211yescharacteristic
48C4×D92C2211yescharacteristic, complemented
49#10625040C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×C22⋊C8C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic, complemented
53C23×#97C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic
55#10625003C2211yescharacteristic
56#10625003C2211yescharacteristic, complemented
57#10624999C2211yescharacteristic, complemented
58#10624998C2211yescharacteristic, complemented
59#10624998C2211yescharacteristic, complemented
60#10624998C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×D4×C23D411yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69#67288—22no—
70#67288—22no—
71#67288—22no—
72#67288—41no—
73#67288—41no—
74#67288—41no—
75C2×D92—22no—
76C2×D92—21no—
77C2×D92—41no—
78C2×D92C2311yescharacteristic
79C2×D92C2311yescharacteristic
80C2×D92C2311yescharacteristic
81C2×C4×D23—21no—
82C2×C4×D23—21no—
83C2×C4×D23—21no—
84C2×C4×D23—21no—
85C2×C4×D23—21no—
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88C2×Dic46C2311yescharacteristic
89M16×C23—22no—
90C2×C8×C23—22no—
91C2×C8×C23C2311yescharacteristic
92C2×C8×C23C2311yescharacteristic
93C2×C8×C23C2311yescharacteristic
94C2×C8×C23C2311yescharacteristic
95C4⋊C4×C23D411yescharacteristic
96C22⋊C4×C23D411yescharacteristic
97C22⋊C4×C23D411yescharacteristic
98C42×C23C2311yescharacteristic
99C22⋊Dic23—21no—
100C22⋊Dic23—21no—
101C22⋊Dic23—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—
107C4⋊Dic23—21no—
108C4⋊Dic23—21no—
109C4⋊Dic23C2311yescharacteristic
110C4⋊Dic23C2311yescharacteristic
111Dic23⋊C4—21no—
112Dic23⋊C4—21no—
113Dic23⋊C4—21no—
114Dic92—22no—
115Dic92—41no—
116D184—22no—
117D184D414yescomplemented
118#67263—22no—
119#67263—22no—
120#67263—22no—
121#67263—22no—
122#67263—41no—
123C23×C23C2×D411yescharacteristic
124C23×C23C2×D411yescharacteristic
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—42no—
129C22×D23—42no—
130C22×D23—81no—
131D4×C23—41no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23C2×D411yescharacteristic
137C2×C4×C23C2×D411yescharacteristic
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2411yescharacteristic
141C22⋊D23—42no—
142C22⋊D23—42no—
143C22⋊D23—42no—
144C22⋊D23—81no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150D92—21no—
151D92—21no—
152D92—21no—
153D92—21no—
154D92—42no—
155D92C2×D412yes—
156D92C2×D412yes—
157C4×D23—42no—
158C4×D23—42no—
159C4×D23—42no—
160C4×D23—42no—
161C4×D23—81no—
162Dic46—21no—
163Dic46—21no—
164Dic46—21no—
165Dic46—21no—
166Dic46—21no—
167Dic46—21no—
168C8×C23—21no—
169C8×C23—21no—
170C8×C23—21no—
171C8×C23C2×D412yes—
172#3267—231nomaximal, Sylow
173C22×C23—21no—
174C22×C23—21no—
175C22×C23—21no—
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23C22×D411yescharacteristic
180C2×D23—22no—
181C2×D23—22no—
182C2×D23—41no—
183C2×D23—41no—
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—21no—
193C4×C23—21no—
194C4×C23C22×D411yescharacteristic
195C4×C23H(5,𝔽2)11yescharacteristic
196Dic23—41no—
197Dic23—41no—
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#442—231no—
215#435D2311yescharacteristic, complemented
216C2×C23—41no—
217C2×C23—41no—
218C2×C23D4211yescharacteristic
219C2×C23#57511yescharacteristic
220C2×C23#57711yescharacteristic
221D23—42no—
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×SD16—231no—
236C2×SD16—231no—
237C2×D8—231no—
238C2×D8—231no—
239C2×M16C2×D2311yescharacteristic
240C22×C8C2×D2311yescharacteristic, complemented
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×D4—231no—
255C4×D4C2×D2311yescharacteristic
256C2×C4⋊C4—461no—
257C2×C22⋊C4—461no—
258#106—231no—
259C4⋊C8C2×D2311yescharacteristic, complemented
260#103—231no—
261#103—231no—
262#103—231no—
263#102—231no—
264#102—231no—
265#102—231no—
266C22⋊C8C2×D2311yescharacteristic
267C22⋊C8C2×D2311yescharacteristic, complemented
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—231no—
283C2×D4—462no—
284C2×D4—461no—
285C2×D4—461no—
286C2×D4—461no—
287C2×D4—461no—
288C2×D4—461no—
289C2×D4—921no—
290C2×D4D9211yescharacteristic
291C22×C4—461no—
292C22×C4—461no—
293C22×C4—461no—
294C22×C4—461no—
295C22×C4—461no—
296C22×C4C22×D2311yescharacteristic
297C22×C4C22×D2311yescharacteristic
298Q16—462no—
299Q16—921no—
300SD16—462no—
301SD16—462no—
302SD16—462no—
303SD16—462no—
304SD16—921no—
305D8—234no—
306D8—462no—
307M16—22no—
308C2×C8—22no—
309C2×C8C22×D2311yescharacteristic
310C2×C8C22×D2311yescharacteristic
311C2×C8C22×D2311yescharacteristic
312C2×C8C22×D2311yescharacteristic
313C4⋊C4—231no—
314C4⋊C4—231no—
315C4⋊C4—461no—
316C4⋊C4—461no—
317C4⋊C4—461no—
318C4⋊C4—461no—
319C4⋊C4—461no—
320C4⋊C4D9211yescharacteristic
321C22⋊C4—461no—
322C22⋊C4—461no—
323C22⋊C4—461no—
324C22⋊C4—461no—
325C22⋊C4—461no—
326C22⋊C4—461no—
327C22⋊C4—461no—
328C22⋊C4—461no—
329C22⋊C4D9211yescharacteristic
330C22⋊C4D9211yescharacteristic
331C42C22×D2311yescharacteristic
332C23—461no—
333C23—461no—
334C23—461no—
335C23—922no—
336C23—922no—
337C23—1841no—
338C23C2×D9211yescharacteristic
339C23C2×D9211yescharacteristic
340Q8—461no—
341Q8—461no—
342Q8—461no—
343Q8—461no—
344Q8—461no—
345Q8—461no—
346D4—41no—
347D4—232no—
348D4—232no—
349D4—461no—
350D4—461no—
351D4—461no—
352D4—461no—
353D4—922no—
354D4—922no—
355D4—922no—
356D4—922no—
357D4—1841no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—461no—
363C2×C4—461no—
364C2×C4—461no—
365C2×C4—461no—
366C2×C4—461no—
367C2×C4—922no—
368C2×C4—922no—
369C2×C4—922no—
370C2×C4—922no—
371C2×C4—1841no—
372C2×C4C2×D9211yescharacteristic
373C2×C4C2×D9211yescharacteristic
374C2×C4C2×D9211yescharacteristic
375C2×C4C2×D9211yescharacteristic
376C2×C4C23×D2311yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D2312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—462no—
388C22—462no—
389C22—921no—
390C22—921no—
391C22—921no—
392C22—921no—
393C22—921no—
394C22—921no—
395C22—921no—
396C22—1844no—
397C22C22×D9211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—921no—
403C4—921no—
404C4—921no—
405C4—921no—
406C4—921no—
407C4C2×D4×D2311yescharacteristic
408C4#1062516011yescharacteristic
409C2—41no—
410C2—41no—
411C2—922no—
412C2—922no—
413C2—1841no—
414C2D4×D9211yescharacteristic
415C2#1309321711yescharacteristic
416C2#1309322911yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#435C2
socleC22×C23C22×D4
hypercenter#435D23
hypocenterC23#3267
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. C2×#10625075C2semidirect
3. #13093072C2semidirect
4. #13093063C2semidirect
5. #13092811C2semidirect
6. #13092675C2semidirect
7. #13092646C2semidirect
8. #13092633C2semidirect
9. #13092623C2semidirect
10. #13092581C2semidirect
11. #13092581C2semidirect
12. #13092570C2semidirect
13. #13092564C2semidirect
14. #13092530C2semidirect
15. C23×#435C2semidirect
18. C2×#67288C22semidirect
21. C22×C8×C23C22semidirect
28. #10625095C22semidirect
30. C2×Dic92C22semidirect
31. C2×Dic92C22semidirect
39. C2×#67263C22semidirect
48. C4×D92C22semidirect
49. #10625040C22semidirect
50. C23×C4⋊C8C22semidirect
52. C23×C22⋊C8C22semidirect
53. C23×#97C22semidirect
56. #10625003C22semidirect
57. #10624999C22semidirect
58. #10624998C22semidirect
59. #10624998C22semidirect
60. #10624998C22semidirect
117. D184D4semidirect
215. #435D23semidirect
240. C22×C8C2×D23semidirect
259. C4⋊C8C2×D23semidirect
267. C22⋊C8C2×D23semidirect
268. #97C2×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×#106250792
C2×#106250752
#130930722
#130930632
#130928112
#130926752
#130926462
#130926332
#130926232
#130925812
#130925702
#130925642
#130925302
C23×#4352
#326723