Finite Group Databasebeta

← #16831379

Subgroups — #16831379

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#14271517C211yesmaximal, characteristic, complemented
3#14271501C211yesmaximal, characteristic, complemented
4#14271474C211yesmaximal, characteristic, complemented
5#14271470C211yesmaximal, characteristic, complemented
6#14271402C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271382C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271319C211yesmaximal, characteristic, complemented
11C4×#90785C211yesmaximal, characteristic, complemented
12D4×#6597C211yesmaximal, characteristic, complemented
13#14271159C211yesmaximal, characteristic, complemented
14C2×#11745183C211yesmaximal, characteristic, complemented
15C29×#548C211yesmaximal, characteristic
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C29×#124—21no—
19C29×#124C2211yescharacteristic
20C29×C22⋊Q8—21no—
21C29×C22⋊Q8C2211yescharacteristic
22C29×#121—21no—
23C29×#121C2211yescharacteristic
24C4×Q8×C29C2211yescharacteristic
25C4×D4×C29—21no—
26C4×D4×C29C2211yescharacteristic
27C2×#90785C2211yescharacteristic
28C2×#90785C2211yescharacteristic
29#11745297—21no—
30C2×#90783C2211yescharacteristic
31#11745288C2211yescharacteristic
32C2×C4⋊Dic29C2211yescharacteristic
33#11745286C2211yescharacteristic
34#11745286C2211yescharacteristic
35C22×#6597C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745251—21no—
38#11745241—21no—
39#11745239—21no—
40#11745232C2211yescharacteristic
41C4×Dic58C2211yescharacteristic
42#11745183C2211yescharacteristic
43#11745183C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745183C2211yescharacteristic
47#11745183C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745180C2211yescharacteristic
51C22⋊#6597C2211yescharacteristic
52C22⋊#6597C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745156C2211yescharacteristic
55#11745155C2211yescharacteristic
56#11745155C2211yescharacteristic
57C4⋊#6597C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59#41×C29—22no—
60#41×C29—41no—
61C2×Q8×C29—21no—
62C2×Q8×C29—22no—
63C2×Q8×C29—41no—
64C2×Q8×C29C2311yescharacteristic
65C2×Q8×C29C2311yescharacteristic
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29D411yescharacteristic
69C2×D4×C29C2311yescharacteristic
70C22×C4×C29—21no—
71C22×C4×C29—21no—
72C22×C4×C29C2311yescharacteristic
73C22×C4×C29C2311yescharacteristic
74C22×Dic29—21no—
75C2×Dic58C2311yescharacteristic
76C4⋊C4×C29—21no—
77C4⋊C4×C29—21no—
78C4⋊C4×C29D411yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C22⋊C4×C29—21no—
81C22⋊C4×C29—21no—
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C22⋊C4×C29D411yescharacteristic
85C22⋊C4×C29D411yescharacteristic
86C42×C29—21no—
87C42×C29C2311yescharacteristic
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91#90785—22no—
92#90785—41no—
93#90783—41no—
94C4⋊Dic29—21no—
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779—21no—
103C4×Dic29—21no—
104C4×Dic29—21no—
105C2×#6597—41no—
106C2×#6597—41no—
107C2×#6597C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C23×C29C2×D411yescharacteristic
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—21no—
117Q8×C29—42no—
118Q8×C29#4112yes—
119D4×C29—22no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—42no—
123D4×C29—42no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—42no—
132C2×C4×C29—42no—
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29C2×D411yescharacteristic
136C2×C4×C29C2×D411yescharacteristic
137C2×C4×C29C2411yescharacteristic
138C2×Dic29—21no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29—21no—
142C2×Dic29—42no—
143Dic58—21no—
144Dic58—21no—
145#6597—21no—
146#6597—21no—
147#6597—21no—
148#6597—21no—
149#3300—291nomaximal, Sylow
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—41no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29#13512yes—
159C22×C29C22×D411yescharacteristic
160C4×C29—21no—
161C4×C29—21no—
162C4×C29—22no—
163C4×C29—21no—
164C4×C29—21no—
165C4×C29—41no—
166C4×C29—41no—
167C4×C29C2×#4111yescharacteristic
168C4×C29H(5,𝔽2)11yescharacteristic
169Dic29—41no—
170Dic29—41no—
171Dic29—41no—
172Dic29—41no—
173#552—291no—
174#548D2911yescharacteristic
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×D4—291no—
186#416—291no—
187C2×#103—291no—
188C2×C29—22no—
189C2×C29—41no—
190C2×C29—81no—
191C2×C29#54611yescharacteristic
192C2×C29C2×#13511yescharacteristic
193C2×C29#57811yescharacteristic
194C2×#41C2×D2911yescharacteristic
195C22×Q8C2×D2911yescharacteristic
196C2×Q16—291no—
197C2×Q16—291no—
198C2×SD16—291no—
199C22×C8—291no—
200C22×C8—291no—
201#126—581no—
202#125—291no—
203#125—581no—
204#124—21no—
205#124C2×D2911yescharacteristic
206#123—581no—
207C22⋊Q8—21no—
208C22⋊Q8—291no—
209C22⋊Q8—291no—
210C22⋊Q8C2×D2911yescharacteristic
211#121—21no—
212#121C2×D2911yescharacteristic
213C4×Q8—291no—
214C4×Q8C2×D2911yescharacteristic
215C4×D4—21no—
216C4×D4C2×D2911yescharacteristic
217#117—291no—
218#117—581no—
219C2×C4⋊C4—291no—
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#103—291no—
230#103—291no—
231#102—291no—
232#102—291no—
233#102—291no—
234C22⋊C8—291no—
235C22⋊C8—291no—
236C4×C8—291no—
237C29#330011yescharacteristic, complemented, Sylow
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—291no—
244C2×Q8C22×D2911yescharacteristic
245C2×Q8C22×D2911yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22⋊D2911yescharacteristic
249C2×D4C22×D2911yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—581no—
253C22×C4C22×D2911yescharacteristic
254C22×C4C22×D2911yescharacteristic
255Q16—582no—
256Q16—1161no—
257SD16—1161no—
258C2×C8—291no—
259C2×C8—291no—
260C2×C8—291no—
261C2×C8—291no—
262C2×C8—1161no—
263C2×C8—1161no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—291no—
267C4⋊C4—291no—
268C4⋊C4—291no—
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—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—581no—
282C22⋊C4—581no—
283C22⋊C4—581no—
284C22⋊C4C22⋊D2911yescharacteristic
285C22⋊C4C22⋊D2911yescharacteristic
286C42—21no—
287C42—581no—
288C42—581no—
289C42C22×D2911yescharacteristic
290C23—21no—
291C23C2×C22⋊D2911yescharacteristic
292C23C2×C22⋊D2911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—581no—
298Q8—581no—
299Q8#9080712yes—
300D4—22no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—581no—
315C2×C4—581no—
316C2×C4—581no—
317C2×C4—581no—
318C2×C4—1162no—
319C2×C4C2×C22⋊D2911yescharacteristic
320C2×C4C2×C22⋊D2911yescharacteristic
321C2×C4C2×C22⋊D2911yescharacteristic
322C2×C4C2×C22⋊D2911yescharacteristic
323C2×C4C23×D2911yescharacteristic
324C8—581no—
325C8—581no—
326C8—581no—
327C8—581no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22#1174531212yes—
337C22C22×C22⋊D2911yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—1161no—
346C4—1161no—
347C4—1161no—
348C4—1161no—
349C4C2×#9080711yescharacteristic
350C4#1174535911yescharacteristic
351C2—22no—
352C2—41no—
353C2—81no—
354C2#1427180711yescharacteristic
355C2C2×#1174531211yescharacteristic
356C2#1427197811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC29×#548C2
socleC22×C29C22×D4
hypercenter#548D29
hypocenterC29#3300
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14271853C2semidirect
2. #14271517C2semidirect
3. #14271501C2semidirect
4. #14271474C2semidirect
5. #14271470C2semidirect
6. #14271402C2semidirect
7. #14271390C2semidirect
8. #14271382C2semidirect
9. #14271325C2semidirect
10. #14271319C2semidirect
11. C4×#90785C2semidirect
12. D4×#6597C2semidirect
13. #14271159C2semidirect
14. C2×#11745183C2semidirect
237. C29#3300semidirect

Maximal subgroups

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

subgroupindex
#142718532
#142715172
#142715012
#142714742
#142714702
#142714022
#142713902
#142713822
#142713252
#142713192
C4×#907852
D4×#65972
#142711592
C2×#117451832
C29×#5482
#330029