Finite Group Databasebeta

← #16831022

Subgroups — #16831022

Order 3712.

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×#11745270C211yesmaximal, characteristic, complemented
2C2×#11745266C211yesmaximal, characteristic, complemented
3#14271818C211yesmaximal, characteristic, complemented
4#14271809C211yesmaximal, characteristic, complemented
5#14271557C211yesmaximal, characteristic, complemented
6#14271421C211yesmaximal, characteristic, complemented
7#14271392C211yesmaximal, characteristic, complemented
8#14271379C211yesmaximal, characteristic, complemented
9#14271369C211yesmaximal, characteristic, complemented
10#14271327C211yesmaximal, characteristic, complemented
11#14271327C211yesmaximal, characteristic, complemented
12#14271316C211yesmaximal, characteristic, complemented
13#14271310C211yesmaximal, characteristic, complemented
14#14271276C211yesmaximal, characteristic, complemented
15C29×#435C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C2×#90805C2211yescharacteristic, complemented
19C22×D116C2211yescharacteristic
20C2×M16×C29C2211yescharacteristic
21C22×C8×C29C2211yescharacteristic, complemented
22C4×D4×C29C2211yescharacteristic
23#11745300—21no—
24#11745299—21no—
25#11745292C2211yescharacteristic
26#11745286C2211yescharacteristic
27#11745286C2211yescharacteristic
28#11745286C2211yescharacteristic, complemented
29#11745270—24no—
30C2×Dic116C2211yescharacteristic, complemented
31C2×Dic116C2211yescharacteristic, complemented
32#11745266—24no—
33C2×D232C2211yescharacteristic
34C2×D232C2211yescharacteristic
35C2×#90773C2211yescharacteristic
36C2×#90773C2211yescharacteristic
37C2×#90773C2211yescharacteristic
38C2×#90773C2211yescharacteristic
39C2×#90773C2211yescharacteristic, complemented
40#11745256—21no—
41C4⋊C4×D29—21no—
42#11745246—21no—
43#11745245—21no—
44#11745245—21no—
45C22⋊C4×D29—21no—
46#11745237C2211yescharacteristic
47C4×D116C2211yescharacteristic
48C4×D116C2211yescharacteristic, complemented
49#11745231C2211yescharacteristic, complemented
50C29×C4⋊C8C2211yescharacteristic, complemented
51C29×C22⋊C8C2211yescharacteristic
52C29×C22⋊C8C2211yescharacteristic, complemented
53C29×#97C2211yescharacteristic, complemented
54#11745169C2211yescharacteristic
55#11745169C2211yescharacteristic
56#11745169C2211yescharacteristic, complemented
57#11745165C2211yescharacteristic, complemented
58#11745164C2211yescharacteristic, complemented
59#11745164C2211yescharacteristic, complemented
60#11745164C2211yescharacteristic, complemented
61C23×D29—21no—
62C2×D4×C29D411yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C22×C4×C29C2311yescharacteristic
65C2×C22⋊D29—21no—
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69#90805—22no—
70#90805—22no—
71#90805—22no—
72#90805—41no—
73#90805—41no—
74#90805—41no—
75C2×D116—22no—
76C2×D116—21no—
77C2×D116—41no—
78C2×D116C2311yescharacteristic
79C2×D116C2311yescharacteristic
80C2×D116C2311yescharacteristic
81C2×C4×D29—21no—
82C2×C4×D29—21no—
83C2×C4×D29—21no—
84C2×C4×D29—21no—
85C2×C4×D29—21no—
86C2×Dic58C2311yescharacteristic
87C2×Dic58C2311yescharacteristic
88C2×Dic58C2311yescharacteristic
89M16×C29—22no—
90C2×C8×C29—22no—
91C2×C8×C29C2311yescharacteristic
92C2×C8×C29C2311yescharacteristic
93C2×C8×C29C2311yescharacteristic
94C2×C8×C29C2311yescharacteristic
95C4⋊C4×C29D411yescharacteristic
96C22⋊C4×C29D411yescharacteristic
97C22⋊C4×C29D411yescharacteristic
98C42×C29C2311yescharacteristic
99C22⋊Dic29—21no—
100C22⋊Dic29—21no—
101C22⋊Dic29—21no—
102#90781—21no—
103#90781—21no—
104#90781—21no—
105#90781—21no—
106#90781—21no—
107C4⋊Dic29—21no—
108C4⋊Dic29—21no—
109C4⋊Dic29C2311yescharacteristic
110C4⋊Dic29C2311yescharacteristic
111#90779—21no—
112#90779—21no—
113#90779—21no—
114Dic116—22no—
115Dic116—41no—
116D232—22no—
117D232D414yescomplemented
118#90773—22no—
119#90773—22no—
120#90773—22no—
121#90773—22no—
122#90773—41no—
123C23×C29C2×D411yescharacteristic
124C23×C29C2×D411yescharacteristic
125C22×D29—21no—
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—42no—
129C22×D29—42no—
130C22×D29—81no—
131D4×C29—41no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2×D411yescharacteristic
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2×D411yescharacteristic
140C2×C4×C29C2411yescharacteristic
141C22⋊D29—42no—
142C22⋊D29—42no—
143C22⋊D29—42no—
144C22⋊D29—81no—
145C2×Dic29—21no—
146C2×Dic29—21no—
147C2×Dic29—21no—
148C2×Dic29—21no—
149C2×Dic29—21no—
150D116—21no—
151D116—21no—
152D116—21no—
153D116—21no—
154D116—42no—
155D116C2×D412yes—
156D116C2×D412yes—
157C4×D29—42no—
158C4×D29—42no—
159C4×D29—42no—
160C4×D29—42no—
161C4×D29—81no—
162Dic58—21no—
163Dic58—21no—
164Dic58—21no—
165Dic58—21no—
166Dic58—21no—
167Dic58—21no—
168C8×C29—21no—
169C8×C29—21no—
170C8×C29—21no—
171C8×C29C2×D412yes—
172#3267—291nomaximal, Sylow
173C22×C29—21no—
174C22×C29—21no—
175C22×C29—21no—
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29C22×D411yescharacteristic
180C2×D29—22no—
181C2×D29—22no—
182C2×D29—41no—
183C2×D29—41no—
184C2×D29—41no—
185C2×D29—41no—
186C2×D29—41no—
187C2×D29—41no—
188C2×D29—41no—
189C2×D29—84no—
190C4×C29—21no—
191C4×C29—21no—
192C4×C29—21no—
193C4×C29—21no—
194C4×C29C22×D411yescharacteristic
195C4×C29H(5,𝔽2)11yescharacteristic
196Dic29—41no—
197Dic29—41no—
198Dic29—41no—
199Dic29—41no—
200Dic29—41no—
201C2×AGL(1,ℤ/8)—291no—
202C2×#135—291no—
203#547—291no—
204#546—291no—
205#497—291no—
206#470—291no—
207#465—291no—
208#463—291no—
209#461—291no—
210#452—291no—
211#452—291no—
212#450—291no—
213#449—291no—
214#442—291no—
215#435D2911yescharacteristic, complemented
216C2×C29—41no—
217C2×C29—41no—
218C2×C29D4211yescharacteristic
219C2×C29#57511yescharacteristic
220C2×C29#57711yescharacteristic
221D29—42no—
222D29—42no—
223D29—81no—
224C2×#41—291no—
225C2×#41—291no—
226C2×#41—291no—
227C22×D4—291no—
228AGL(1,ℤ/8)—584no—
229#135—584no—
230C2×Q16—291no—
231C2×Q16—291no—
232C2×SD16—291no—
233C2×SD16—291no—
234C2×SD16—291no—
235C2×SD16—291no—
236C2×SD16—291no—
237C2×D8—291no—
238C2×D8—291no—
239C2×M16C2×D2911yescharacteristic
240C22×C8C2×D2911yescharacteristic, complemented
241C4⋊Q8—291no—
242#124—291no—
243#123—581no—
244#123—581no—
245#123—581no—
246C22⋊Q8—291no—
247C22⋊Q8—291no—
248C22⋊Q8—291no—
249#121—291no—
250#121—581no—
251#121—581no—
252#120—581no—
253C4×D4—291no—
254C4×D4—291no—
255C4×D4C2×D2911yescharacteristic
256C2×C4⋊C4—581no—
257C2×C22⋊C4—581no—
258#106—291no—
259C4⋊C8C2×D2911yescharacteristic, complemented
260#103—291no—
261#103—291no—
262#103—291no—
263#102—291no—
264#102—291no—
265#102—291no—
266C22⋊C8C2×D2911yescharacteristic
267C22⋊C8C2×D2911yescharacteristic, complemented
268#97C2×D2911yescharacteristic, complemented
269C29#326711yescharacteristic, complemented, Sylow
270C24—581no—
271#41—582no—
272#41—582no—
273#41—582no—
274#41—1161no—
275#41—1161no—
276#41—1161no—
277C2×Q8—291no—
278C2×Q8—291no—
279C2×Q8—291no—
280C2×D4—291no—
281C2×D4—291no—
282C2×D4—291no—
283C2×D4—582no—
284C2×D4—581no—
285C2×D4—581no—
286C2×D4—581no—
287C2×D4—581no—
288C2×D4—581no—
289C2×D4—1161no—
290C2×D4D11611yescharacteristic
291C22×C4—581no—
292C22×C4—581no—
293C22×C4—581no—
294C22×C4—581no—
295C22×C4—581no—
296C22×C4C22×D2911yescharacteristic
297C22×C4C22×D2911yescharacteristic
298Q16—582no—
299Q16—1161no—
300SD16—582no—
301SD16—582no—
302SD16—582no—
303SD16—582no—
304SD16—1161no—
305D8—294no—
306D8—582no—
307M16—22no—
308C2×C8—22no—
309C2×C8C22×D2911yescharacteristic
310C2×C8C22×D2911yescharacteristic
311C2×C8C22×D2911yescharacteristic
312C2×C8C22×D2911yescharacteristic
313C4⋊C4—291no—
314C4⋊C4—291no—
315C4⋊C4—581no—
316C4⋊C4—581no—
317C4⋊C4—581no—
318C4⋊C4—581no—
319C4⋊C4—581no—
320C4⋊C4D11611yescharacteristic
321C22⋊C4—581no—
322C22⋊C4—581no—
323C22⋊C4—581no—
324C22⋊C4—581no—
325C22⋊C4—581no—
326C22⋊C4—581no—
327C22⋊C4—581no—
328C22⋊C4—581no—
329C22⋊C4D11611yescharacteristic
330C22⋊C4D11611yescharacteristic
331C42C22×D2911yescharacteristic
332C23—581no—
333C23—581no—
334C23—581no—
335C23—1162no—
336C23—1162no—
337C23—2321no—
338C23C2×D11611yescharacteristic
339C23C2×D11611yescharacteristic
340Q8—581no—
341Q8—581no—
342Q8—581no—
343Q8—581no—
344Q8—581no—
345Q8—581no—
346D4—41no—
347D4—292no—
348D4—292no—
349D4—581no—
350D4—581no—
351D4—581no—
352D4—581no—
353D4—1162no—
354D4—1162no—
355D4—1162no—
356D4—1162no—
357D4—2321no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—581no—
363C2×C4—581no—
364C2×C4—581no—
365C2×C4—581no—
366C2×C4—581no—
367C2×C4—1162no—
368C2×C4—1162no—
369C2×C4—1162no—
370C2×C4—1162no—
371C2×C4—2321no—
372C2×C4C2×D11611yescharacteristic
373C2×C4C2×D11611yescharacteristic
374C2×C4C2×D11611yescharacteristic
375C2×C4C2×D11611yescharacteristic
376C2×C4C23×D2911yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D2912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—582no—
388C22—582no—
389C22—1161no—
390C22—1161no—
391C22—1161no—
392C22—1161no—
393C22—1161no—
394C22—1161no—
395C22—1161no—
396C22—2324no—
397C22C22×D11611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—1161no—
403C4—1161no—
404C4—1161no—
405C4—1161no—
406C4—1161no—
407C4C2×D4×D2911yescharacteristic
408C4#1174536411yescharacteristic
409C2—41no—
410C2—41no—
411C2—1162no—
412C2—1162no—
413C2—2321no—
414C2D4×D11611yescharacteristic
415C2#1427196311yescharacteristic
416C2#1427197511yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#435C2
socleC22×C29C22×D4
hypercenter#435D29
hypocenterC29#3267
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#11745270C2semidirect
2. C2×#11745266C2semidirect
3. #14271818C2semidirect
4. #14271809C2semidirect
5. #14271557C2semidirect
6. #14271421C2semidirect
7. #14271392C2semidirect
8. #14271379C2semidirect
9. #14271369C2semidirect
10. #14271327C2semidirect
11. #14271327C2semidirect
12. #14271316C2semidirect
13. #14271310C2semidirect
14. #14271276C2semidirect
15. C29×#435C2semidirect
18. C2×#90805C22semidirect
21. C22×C8×C29C22semidirect
28. #11745286C22semidirect
30. C2×Dic116C22semidirect
31. C2×Dic116C22semidirect
39. C2×#90773C22semidirect
48. C4×D116C22semidirect
49. #11745231C22semidirect
50. C29×C4⋊C8C22semidirect
52. C29×C22⋊C8C22semidirect
53. C29×#97C22semidirect
56. #11745169C22semidirect
57. #11745165C22semidirect
58. #11745164C22semidirect
59. #11745164C22semidirect
60. #11745164C22semidirect
117. D232D4semidirect
215. #435D29semidirect
240. C22×C8C2×D29semidirect
259. C4⋊C8C2×D29semidirect
267. C22⋊C8C2×D29semidirect
268. #97C2×D29semidirect
269. C29#3267semidirect

Maximal subgroups

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

subgroupindex
C2×#117452702
C2×#117452662
#142718182
#142718092
#142715572
#142714212
#142713922
#142713792
#142713692
#142713272
#142713162
#142713102
#142712762
C29×#4352
#326729