Finite Group Databasebeta

← #16831405

Subgroups — #16831405

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#14271881C211yesmaximal, characteristic, complemented
2#14271812C211yesmaximal, characteristic
3#14271512C211yesmaximal, characteristic, complemented
4#14271504C211yesmaximal, characteristic, complemented
5#14271503C211yesmaximal, characteristic, complemented
6#14271441C211yesmaximal, characteristic, complemented
7#14271404C211yesmaximal, characteristic, complemented
8#14271403C211yesmaximal, characteristic, complemented
9#14271372C211yesmaximal, characteristic, complemented
10#14271326C211yesmaximal, characteristic, complemented
11#14271325C211yesmaximal, characteristic, complemented
12#14271254C211yesmaximal, characteristic, complemented
13C8×C22⋊D29C211yesmaximal, characteristic, complemented
14#14271156C211yesmaximal, characteristic, complemented
15C29×#416C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90807C2211yescharacteristic
18C22×C8×C29C2211yescharacteristic
19C29×#117C2211yescharacteristic
20#11745308C2211yescharacteristic
21#11745306C2211yescharacteristic
22C2×#90785C2211yescharacteristic
23#11745301—21no—
24#11745297—21no—
25D4×Dic29C2211yescharacteristic
26C2×#90783C2211yescharacteristic
27#11745291—21no—
28C4×C22⋊D29C2211yescharacteristic
29#11745286C2211yescharacteristic
30#11745286C2211yescharacteristic
31C2×#90779—21no—
32C2×Dic116C2211yescharacteristic
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#11745168C2211yescharacteristic
50#11745166C2211yescharacteristic
51#11745164C2211yescharacteristic
52#11745164C2211yescharacteristic
53#11745162C2211yescharacteristic
54C8×Dic29C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745158C2211yescharacteristic
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⋊D29D411yescharacteristic
68C22×Dic29—21no—
69C22×Dic29—21no—
70#90807—22no—
71#90807—41no—
72C2×C4×D29C2311yescharacteristic
73C2×Dic58—21no—
74C2×Dic58C2311yescharacteristic
75C2×Dic58C2311yescharacteristic
76C2×C8×C29—41no—
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C22⋊C4×C29—21no—
82C42×C29—21no—
83C22⋊Dic29—21no—
84C22⋊Dic29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29D411yescharacteristic
87#90785—41no—
88#90783—22no—
89#90781—21no—
90#90781—21no—
91#90781—21no—
92#90781D411yescharacteristic
93C4⋊Dic29—21no—
94C4⋊Dic29C2311yescharacteristic
95C4⋊Dic29C2311yescharacteristic
96#90779—21no—
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779—21no—
103#90779D411yescharacteristic
104C4×Dic29—21no—
105C4×Dic29—21no—
106C4×Dic29C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109Dic116—41no—
110C8×D29—41no—
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C22×D29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116D4×C29—21no—
117D4×C29—42no—
118D4×C29#4112yes—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—42no—
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2411yescharacteristic
127C22⋊D29—22no—
128C22⋊D29—42no—
129C2×Dic29—21no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—42no—
134C2×Dic29—42no—
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138C4×D29—21no—
139C4×D29—21no—
140Dic58—21no—
141Dic58—21no—
142Dic58—21no—
143Dic58—21no—
144Dic58—42no—
145C8×C29—21no—
146C8×C29—21no—
147#6597—21no—
148#6597—21no—
149#3302—291nomaximal, Sylow
150C22×C29—22no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29—21no—
154C22×C29—41no—
155C22×C29—41no—
156C22×C29C22×D411yescharacteristic
157C2×D29—21no—
158C2×D29—21no—
159C2×D29—21no—
160C4×C29—21no—
161C4×C29—41no—
162C4×C29—41no—
163C4×C29—41no—
164C4×C29C2×#4111yescharacteristic
165C4×C29H(5,𝔽2)11yescharacteristic
166Dic29—21no—
167Dic29—21no—
168Dic29—41no—
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172Dic29#13512yes—
173#556—291no—
174#547—291no—
175#487—291no—
176#485—291no—
177#485—291no—
178#474—291no—
179#467—291no—
180#467—291no—
181#462—291no—
182#452—291no—
183#452—291no—
184C4×SD16—291no—
185C8×D4—291no—
186#416—291no—
187#416D2911yescharacteristic, complemented
188C2×C29—41no—
189C2×C29—42no—
190C2×C29#54611yescharacteristic
191C2×C29C2×#13511yescharacteristic
192C2×C29#57811yescharacteristic
193D29—41no—
194C2×#41—291no—
195C2×#41C2×D2911yescharacteristic
196C2×Q16—291no—
197C2×Q16—291no—
198C2×SD16—291no—
199C22×C8—291no—
200C22×C8C2×D2911yescharacteristic
201C4⋊Q8—291no—
202C4⋊Q8—291no—
203#126—581no—
204#126—581no—
205#124—581no—
206#123—581no—
207#123—581no—
208C22⋊Q8—291no—
209C22⋊Q8—291no—
210C22⋊Q8—291no—
211C22⋊Q8—291no—
212#121—581no—
213C4×Q8—291no—
214C4×Q8—581no—
215C4×D4—291no—
216C4×D4—291no—
217#117—291no—
218#117C2×D2911yescharacteristic
219C2×C4⋊C4—581no—
220#107—291no—
221#107—291no—
222#106—291no—
223C4⋊C8—291no—
224#103—291no—
225#103—291no—
226#103—291no—
227#103—291no—
228#103—291no—
229#103C2×D2911yescharacteristic
230#103C2×D2911yescharacteristic
231#102—291no—
232#102C2×D2911yescharacteristic
233#102C2×D2911yescharacteristic
234C22⋊C8—291no—
235C22⋊C8—291no—
236C4×C8—291no—
237C29#330211yescharacteristic, complemented, Sylow
238#41—22no—
239#41—41no—
240#41—582no—
241#41—1161no—
242C2×Q8—291no—
243C2×Q8—291no—
244C2×Q8—581no—
245C2×Q8C22×D2911yescharacteristic
246C2×D4—21no—
247C2×D4—291no—
248C2×D4—581no—
249C2×D4C22×D2911yescharacteristic
250C22×C4—21no—
251C22×C4—291no—
252C22×C4—581no—
253C22×C4—581no—
254C22×C4C22×D2911yescharacteristic
255Q16—1161no—
256Q16—1161no—
257SD16—582no—
258C2×C8—41no—
259C2×C8—291no—
260C2×C8—291no—
261C2×C8—1161no—
262C2×C8C22×D2911yescharacteristic
263C2×C8C22×D2911yescharacteristic
264C4⋊C4—291no—
265C4⋊C4—291no—
266C4⋊C4—291no—
267C4⋊C4—581no—
268C4⋊C4—581no—
269C4⋊C4—581no—
270C4⋊C4—581no—
271C4⋊C4—581no—
272C4⋊C4—581no—
273C4⋊C4—581no—
274C4⋊C4—581no—
275C4⋊C4C22×D2911yescharacteristic
276C4⋊C4C22×D2911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—291no—
279C22⋊C4—291no—
280C22⋊C4—581no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4—581no—
285C22⋊C4—581no—
286C42—21no—
287C42—291no—
288C42—581no—
289C42—581no—
290C23—21no—
291C23—291no—
292C23D4×D2911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—581no—
296Q8—581no—
297Q8—581no—
298Q8—581no—
299Q8—1162no—
300D4—21no—
301D4—42no—
302D4—582no—
303D4—1162no—
304D4#9080512yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—291no—
312C2×C4—291no—
313C2×C4—291no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—581no—
319C2×C4—581no—
320C2×C4—1162no—
321C2×C4—1162no—
322C2×C4D4×D2911yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C8—21no—
325C8—21no—
326C8—581no—
327C8—581no—
328C22—21no—
329C22—22no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—581no—
335C22—581no—
336C22—581no—
337C22C2×D4×D2911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—292no—
343C4—581no—
344C4—581no—
345C4—1161no—
346C4—1161no—
347C4—1161no—
348C4—1161no—
349C4C2×#9080511yescharacteristic
350C4#1174535911yescharacteristic
351C2—41no—
352C2—42no—
353C2—1161no—
354C2#1427180311yescharacteristic
355C2#135×D2911yescharacteristic
356C2#1427197711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#416C2
socleC22×C29C22×D4
prime radical#14271812C2
hypercenter#416D29
hypocenterC29#3302
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. #14271512C2semidirect
4. #14271504C2semidirect
5. #14271503C2semidirect
6. #14271441C2semidirect
7. #14271404C2semidirect
8. #14271403C2semidirect
9. #14271372C2semidirect
10. #14271326C2semidirect
11. #14271325C2semidirect
12. #14271254C2semidirect
13. C8×C22⋊D29C2semidirect
14. #14271156C2semidirect
15. C29×#416C2semidirect
187. #416D29semidirect
237. C29#3302semidirect

Maximal subgroups

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

subgroupindex
#142718812
#142718122
#142715122
#142715042
#142715032
#142714412
#142714042
#142714032
#142713722
#142713262
#142713252
#142712542
C8×C22⋊D292
#142711562
C29×#4162
#330229