Finite Group Databasebeta

← #16831381

Subgroups — #16831381

Order 3712.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271853C211yesmaximal, characteristic, complemented
2#14271822C211yesmaximal, characteristic
3#14271518C211yesmaximal, characteristic, complemented
4#14271505C211yesmaximal, characteristic, complemented
5#14271477C211yesmaximal, characteristic, complemented
6#14271471C211yesmaximal, characteristic, complemented
7#14271404C211yesmaximal, characteristic, complemented
8#14271392C211yesmaximal, characteristic, complemented
9#14271386C211yesmaximal, characteristic, complemented
10#14271327C211yesmaximal, characteristic, complemented
11#14271321C211yesmaximal, characteristic, complemented
12C4×Dic116C211yesmaximal, characteristic, complemented
13#14271160C211yesmaximal, characteristic, complemented
14C2×#11745164C211yesmaximal, characteristic, complemented
15C8×D4×C29C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C22×Dic58C2211yescharacteristic
18C22×C8×C29C2211yescharacteristic
19C22×C8×C29C2211yescharacteristic
20C4×D4×C29C2211yescharacteristic
21#11745301—21no—
22#11745297—21no—
23#11745292C2211yescharacteristic
24#11745288C2211yescharacteristic
25C2×C4⋊Dic29C2211yescharacteristic
26#11745286C2211yescharacteristic
27#11745286C2211yescharacteristic
28#11745286C2211yescharacteristic
29C2×Dic116C2211yescharacteristic
30C2×Dic116C2211yescharacteristic
31C2×#90773C2211yescharacteristic
32#11745258—21no—
33#11745251—21no—
34#11745247—21no—
35#11745243—21no—
36#11745241—21no—
37#11745239—21no—
38#11745237C2211yescharacteristic
39#11745232C2211yescharacteristic
40C4×Dic58C2211yescharacteristic
41C4×Dic58C2211yescharacteristic
42C29×C4⋊C8C2211yescharacteristic
43C29×C22⋊C8C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic
45C4×C8×C29C2211yescharacteristic
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745166C2211yescharacteristic
50#11745166C2211yescharacteristic
51#11745165C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745164C2211yescharacteristic
54#11745164C2211yescharacteristic
55#11745164C2211yescharacteristic
56#11745164C2211yescharacteristic
57#11745164C2211yescharacteristic
58#11745164C2211yescharacteristic
59C2×D4×C29D411yescharacteristic
60C22×C4×C29C2311yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C2×C22⋊D29—21no—
63C2×C22⋊D29—21no—
64C22×Dic29—21no—
65C22×Dic29—21no—
66#90805—22no—
67#90805—41no—
68C2×D116C2311yescharacteristic
69C2×C4×D29—21no—
70C2×Dic58—22no—
71C2×Dic58—21no—
72C2×Dic58—41no—
73C2×Dic58C2311yescharacteristic
74C2×Dic58C2311yescharacteristic
75C2×Dic58C2311yescharacteristic
76C2×C8×C29—41no—
77C2×C8×C29—41no—
78C2×C8×C29C2311yescharacteristic
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C4⋊C4×C29D411yescharacteristic
83C22⋊C4×C29D411yescharacteristic
84C22⋊C4×C29D411yescharacteristic
85C42×C29C2311yescharacteristic
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93C4⋊Dic29—21no—
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779—21no—
103#90779—21no—
104#90779—21no—
105C4×Dic29—21no—
106C4×Dic29—21no—
107C4×Dic29—21no—
108Dic116—22no—
109Dic116—41no—
110#90773—41no—
111C23×C29C2×D411yescharacteristic
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114D4×C29—22no—
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29C2×D411yescharacteristic
120C2×C4×C29C2×D411yescharacteristic
121C2×C4×C29C2×D411yescharacteristic
122C2×C4×C29C2×D411yescharacteristic
123C2×C4×C29C2411yescharacteristic
124C22⋊D29—42no—
125C22⋊D29—42no—
126C2×Dic29—21no—
127C2×Dic29—21no—
128C2×Dic29—21no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—42no—
134C2×Dic29—42no—
135D116—21no—
136D116—21no—
137C4×D29—42no—
138Dic58—21no—
139Dic58—21no—
140Dic58—21no—
141Dic58—21no—
142Dic58—21no—
143Dic58—42no—
144Dic58#4112yes—
145C8×C29—21no—
146C8×C29—21no—
147C8×C29—21no—
148C8×C29—21no—
149#3300—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29—21no—
154C22×C29—21no—
155C22×C29#13512yes—
156C22×C29C22×D411yescharacteristic
157C2×D29—41no—
158C2×D29—41no—
159C2×D29—41no—
160C4×C29—21no—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29C2×#4111yescharacteristic
165C4×C29H(5,𝔽2)11yescharacteristic
166Dic29—22no—
167Dic29—41no—
168Dic29—41no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172Dic29—41no—
173#552—291no—
174#548—291no—
175#488—291no—
176#485—291no—
177#480—291no—
178#479—291no—
179#467—291no—
180#465—291no—
181#464—291no—
182#452—291no—
183#451—291no—
184C4×Q16—291no—
185C8×D4D2911yescharacteristic, complemented
186#416—291no—
187C2×#103—291no—
188C2×C29—22no—
189C2×C29—41no—
190C2×C29#54611yescharacteristic
191C2×C29C2×#13511yescharacteristic
192C2×C29#57811yescharacteristic
193D29—81no—
194C2×#41—291no—
195C22×Q8—291no—
196C2×Q16—291no—
197C2×Q16—291no—
198C2×SD16—291no—
199C22×C8C2×D2911yescharacteristic
200C22×C8C2×D2911yescharacteristic
201#126—581no—
202#125—291no—
203#125—581no—
204#124—291no—
205#124—581no—
206#123—581no—
207C22⋊Q8—291no—
208C22⋊Q8—291no—
209C22⋊Q8—291no—
210C22⋊Q8—581no—
211#121—291no—
212#121—581no—
213C4×Q8—291no—
214C4×Q8—291no—
215C4×D4—581no—
216C4×D4C2×D2911yescharacteristic
217#117—291no—
218#117—581no—
219C2×C4⋊C4—291no—
220#107—291no—
221#107—291no—
222#106—291no—
223C4⋊C8C2×D2911yescharacteristic
224#103—291no—
225#103—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103—291no—
230#103—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234C22⋊C8C2×D2911yescharacteristic
235C22⋊C8C2×D2911yescharacteristic
236C4×C8C2×D2911yescharacteristic
237C29#330011yescharacteristic, complemented, Sylow
238#41—582no—
239#41—1161no—
240C2×Q8—291no—
241C2×Q8—291no—
242C2×Q8—291no—
243C2×Q8—582no—
244C2×Q8—581no—
245C2×Q8—1161no—
246C2×D4—291no—
247C2×D4—581no—
248C2×D4—581no—
249C2×D4D11611yescharacteristic
250C22×C4—581no—
251C22×C4—581no—
252C22×C4—581no—
253C22×C4C22×D2911yescharacteristic
254C22×C4C22×D2911yescharacteristic
255Q16—582no—
256Q16—1161no—
257SD16—1161no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22×D2911yescharacteristic
261C2×C8C22×D2911yescharacteristic
262C2×C8C22×D2911yescharacteristic
263C2×C8C22×D2911yescharacteristic
264C4⋊C4—291no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4D11611yescharacteristic
277C22⋊C4—581no—
278C22⋊C4—581no—
279C22⋊C4—581no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4D11611yescharacteristic
285C22⋊C4D11611yescharacteristic
286C42—581no—
287C42—581no—
288C42—581no—
289C42C22×D2911yescharacteristic
290C23—581no—
291C23C2×D11611yescharacteristic
292C23C2×D11611yescharacteristic
293Q8—292no—
294Q8—581no—
295Q8—581no—
296Q8—581no—
297Q8—581no—
298Q8—581no—
299Q8—1162no—
300D4—22no—
301D4—581no—
302D4—581no—
303D4—1162no—
304D4—1162no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—581no—
310C2×C4—581no—
311C2×C4—581no—
312C2×C4—581no—
313C2×C4—581no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—1162no—
317C2×C4—1162no—
318C2×C4—1162no—
319C2×C4C2×D11611yescharacteristic
320C2×C4C2×D11611yescharacteristic
321C2×C4C2×D11611yescharacteristic
322C2×C4C2×D11611yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—1161no—
334C22—1161no—
335C22—1161no—
336C22#1174526612yes—
337C22C22×D11611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—582no—
343C4—1161no—
344C4—1161no—
345C4—1161no—
346C4—1161no—
347C4—1161no—
348C4—1161no—
349C4#1174535911yescharacteristic
350C4#41×D2911yescharacteristic
351C2—22no—
352C2—41no—
353C2—2321no—
354C2#1427180811yescharacteristic
355C2C2×#1174526611yescharacteristic
356C2#1427198011yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC8×D4×C29C2
socleC22×C29C22×D4
prime radical#14271822C2
hypercenterC8×D4D29
hypocenterC29#3300
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14271853C2semidirect
3. #14271518C2semidirect
4. #14271505C2semidirect
5. #14271477C2semidirect
6. #14271471C2semidirect
7. #14271404C2semidirect
8. #14271392C2semidirect
9. #14271386C2semidirect
10. #14271327C2semidirect
11. #14271321C2semidirect
12. C4×Dic116C2semidirect
13. #14271160C2semidirect
14. C2×#11745164C2semidirect
15. C8×D4×C29C2semidirect
185. C8×D4D29semidirect
237. C29#3300semidirect

Maximal subgroups

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

subgroupindex
#142718532
#142718222
#142715182
#142715052
#142714772
#142714712
#142714042
#142713922
#142713862
#142713272
#142713212
C4×Dic1162
#142711602
C2×#117451642
C8×D4×C292
#330029