Finite Group Databasebeta

← #16831427

Subgroups — #16831427

Order 3712.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271881C211yesmaximal, characteristic, complemented
2#14271832C211yesmaximal, characteristic
3#14271508C211yesmaximal, characteristic, complemented
4#14271487C211yesmaximal, characteristic, complemented
5#14271486C211yesmaximal, characteristic, complemented
6#14271446C211yesmaximal, characteristic, complemented
7#14271392C211yesmaximal, characteristic, complemented
8#14271391C211yesmaximal, characteristic, complemented
9#14271362C211yesmaximal, characteristic, complemented
10#14271328C211yesmaximal, characteristic, complemented
11#14271325C211yesmaximal, characteristic, complemented
12#14271255C211yesmaximal, characteristic, complemented
13C8×C22⋊D29C211yesmaximal, characteristic, complemented
14#14271158C211yesmaximal, characteristic, complemented
15C29×#416C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90809C2211yescharacteristic
18C22×C8×C29C2211yescharacteristic
19C29×#117C2211yescharacteristic
20Q8×Dic29C2211yescharacteristic
21C2×#90785C2211yescharacteristic
22#11745302—21no—
23#11745302C2211yescharacteristic
24#11745300—21no—
25#11745300C2211yescharacteristic
26C2×#90783C2211yescharacteristic
27#11745292—21no—
28#11745292C2211yescharacteristic
29C4×C22⋊D29—21no—
30C4×C22⋊D29C2211yescharacteristic
31#11745286C2211yescharacteristic
32C2×#90773C2211yescharacteristic
33C2×C8×D29C2211yescharacteristic
34#11745259C2211yescharacteristic
35#11745254C2211yescharacteristic
36#11745250C2211yescharacteristic
37#11745249C2211yescharacteristic
38#11745247—21no—
39#11745241—21no—
40#11745238—21no—
41C4×Dic58—21no—
42C29×#103C2211yescharacteristic
43C29×#103C2211yescharacteristic
44C29×#102C2211yescharacteristic
45C29×#102C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745180C2211yescharacteristic
48C22⋊#6597C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745165C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745162C2211yescharacteristic
54C8×Dic29C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic
58#11745155C2211yescharacteristic
59#41×C29—22no—
60#41×C29—41no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—21no—
63C2×D4×C29C2311yescharacteristic
64C22×C4×C29—21no—
65C22×C4×C29C2311yescharacteristic
66C2×C22⋊D29—21no—
67C2×C22⋊D29—21no—
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29D411yescharacteristic
71#90809—22no—
72#90809—41no—
73C2×D116—21no—
74C2×D116C2311yescharacteristic
75C2×C4×D29—21no—
76C2×C4×D29C2311yescharacteristic
77C2×Dic58—21no—
78C2×Dic58C2311yescharacteristic
79C2×C8×C29—41no—
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C42×C29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29D411yescharacteristic
89#90785—22no—
90#90783—41no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781D411yescharacteristic
95C4⋊Dic29—21no—
96C4⋊Dic29—21no—
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29—21no—
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109#90773—41no—
110C8×D29—41no—
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29C2×D411yescharacteristic
115Q8×C29—21no—
116Q8×C29#4112yes—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—42no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—42no—
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C22⋊D29—22no—
129C22⋊D29—42no—
130C22⋊D29—81no—
131C22⋊D29—81no—
132C22⋊D29—81no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139D116—21no—
140D116—21no—
141D116—42no—
142C4×D29—21no—
143C4×D29—21no—
144C4×D29—42no—
145Dic58—21no—
146Dic58—21no—
147Dic58—42no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3304—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—21no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C4×C29—22no—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29C2×#4111yescharacteristic
171C4×C29H(5,𝔽2)11yescharacteristic
172Dic29—21no—
173Dic29—21no—
174Dic29—41no—
175Dic29—41no—
176Dic29—41no—
177Dic29#13512yes—
178#556—291no—
179#550—291no—
180#486—291no—
181#482—291no—
182#482—291no—
183#475—291no—
184#465—291no—
185#465—291no—
186#460—291no—
187#452—291no—
188#452—291no—
189C4×Q16—291no—
190C8×D4—291no—
191#416—291no—
192#416D2911yescharacteristic, complemented
193C2×C29—41no—
194C2×C29—81no—
195C2×C29#54611yescharacteristic
196C2×C29C2×#13511yescharacteristic
197C2×C29#57711yescharacteristic
198D29—41no—
199D29—81no—
200C2×#41—291no—
201C2×#41C2×D2911yescharacteristic
202C2×Q16—291no—
203C2×SD16—291no—
204C2×SD16—291no—
205C22×C8—291no—
206C22×C8C2×D2911yescharacteristic
207C4⋊Q8—291no—
208#127—291no—
209#127—581no—
210#126—581no—
211#126—581no—
212#124—581no—
213C22⋊Q8—291no—
214C22⋊Q8—291no—
215#121—291no—
216#121—291no—
217#121—581no—
218#121—581no—
219C4×Q8—291no—
220C4×Q8—291no—
221C4×Q8—581no—
222C4×D4—291no—
223C4×D4—581no—
224#117—291no—
225#117C2×D2911yescharacteristic
226#107—291no—
227#106—291no—
228#106—291no—
229C4⋊C8—291no—
230#103—291no—
231#103—291no—
232#103C2×D2911yescharacteristic
233#103C2×D2911yescharacteristic
234#102—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102C2×D2911yescharacteristic
239#102C2×D2911yescharacteristic
240C22⋊C8—291no—
241C22⋊C8—291no—
242C4×C8—291no—
243C29#330411yescharacteristic, complemented, Sylow
244#41—22no—
245#41—41no—
246#41—582no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8—581no—
250C2×Q8C22×D2911yescharacteristic
251C2×D4—21no—
252C2×D4—291no—
253C2×D4—291no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—581no—
257C2×D4—581no—
258C2×D4—581no—
259C2×D4C22×D2911yescharacteristic
260C22×C4—21no—
261C22×C4—291no—
262C22×C4—581no—
263C22×C4C22×D2911yescharacteristic
264Q16—582no—
265SD16—1161no—
266SD16—1161no—
267C2×C8—41no—
268C2×C8—291no—
269C2×C8—291no—
270C2×C8—1161no—
271C2×C8C22×D2911yescharacteristic
272C2×C8C22×D2911yescharacteristic
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4C22×D2911yescharacteristic
282C4⋊C4C22×D2911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—291no—
285C22⋊C4—291no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C42—21no—
292C42—291no—
293C42—581no—
294C42—581no—
295C42—581no—
296C23—21no—
297C23—291no—
298C23—581no—
299C23D4×D2911yescharacteristic
300Q8—21no—
301Q8—581no—
302Q8—581no—
303Q8—1162no—
304Q8#9080512yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—582no—
309D4—581no—
310D4—581no—
311D4—1162no—
312D4—1162no—
313D4—2321no—
314D4—2321no—
315D4—2321no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—291no—
323C2×C4—291no—
324C2×C4—291no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—581no—
328C2×C4—581no—
329C2×C4—581no—
330C2×C4—1162no—
331C2×C4D4×D2911yescharacteristic
332C2×C4C23×D2911yescharacteristic
333C8—21no—
334C8—21no—
335C8—581no—
336C8—581no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—581no—
344C22—581no—
345C22—581no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22C2×D4×D2911yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—292no—
355C4—581no—
356C4—581no—
357C4—1161no—
358C4—1161no—
359C4—1161no—
360C4C2×#9080511yescharacteristic
361C4#1174535911yescharacteristic
362C2—41no—
363C2—81no—
364C2—1161no—
365C2—2321no—
366C2#1427180311yescharacteristic
367C2#135×D2911yescharacteristic
368C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#416C2
socleC22×C29C22×D4
prime radical#14271832C2
hypercenter#416D29
hypocenterC29#3304
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #14271881C2semidirect
3. #14271508C2semidirect
4. #14271487C2semidirect
5. #14271486C2semidirect
6. #14271446C2semidirect
7. #14271392C2semidirect
8. #14271391C2semidirect
9. #14271362C2semidirect
10. #14271328C2semidirect
11. #14271325C2semidirect
12. #14271255C2semidirect
13. C8×C22⋊D29C2semidirect
14. #14271158C2semidirect
15. C29×#416C2semidirect
192. #416D29semidirect
243. C29#3304semidirect

Maximal subgroups

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

subgroupindex
#142718812
#142718322
#142715082
#142714872
#142714862
#142714462
#142713922
#142713912
#142713622
#142713282
#142713252
#142712552
C8×C22⋊D292
#142711582
C29×#4162
#330429