Finite Group Databasebeta

← #16830056

Subgroups — #16830056

Order 3712.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271697C211yesmaximal, characteristic, complemented
2#14271562C211yesmaximal, characteristic, complemented
3#14271545C211yesmaximal, characteristic, complemented
4#14271520C211yesmaximal, characteristic, complemented
5#14271517C211yesmaximal, characteristic, complemented
6#14271402C211yesmaximal, characteristic, complemented
7#14271397C211yesmaximal, characteristic
8#14271394C211yesmaximal, characteristic, complemented
9#14271390C211yesmaximal, characteristic, complemented
10C4×#90785C211yesmaximal, characteristic, complemented
11C4×#90784C211yesmaximal, characteristic, complemented
12C4×#90783C211yesmaximal, characteristic, complemented
13C4×#90782C211yesmaximal, characteristic, complemented
14C2×C4×#6597C211yesmaximal, characteristic, complemented
15C29×#529C211yesmaximal, characteristic, complemented
16C29×#126—21no—
17C29×#125C2211yescharacteristic
18C29×#124C2211yescharacteristic
19C29×#123—21no—
20C29×C22⋊Q8C2211yescharacteristic
21C29×#121C2211yescharacteristic
22C4×Q8×C29C2211yescharacteristic
23C4×D4×C29—21no—
24C4×D4×C29C2211yescharacteristic
25C29×#117—21no—
26C2×C42×C29C2211yescharacteristic
27C2×#90785C2211yescharacteristic
28C2×#90784C2211yescharacteristic
29C2×#90783C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745291—21no—
33C4×C22⋊D29—21no—
34#11745286C2211yescharacteristic
35C22×#6597C2211yescharacteristic
36C22×#6597C2211yescharacteristic
37#11745238—21no—
38#11745237C2211yescharacteristic
39C4×D116C2211yescharacteristic
40#11745234—21no—
41#11745232C2211yescharacteristic
42C4×Dic58C2211yescharacteristic
43#11745183C2211yescharacteristic
44#11745183C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745158C2211yescharacteristic
48#11745158C2211yescharacteristic
49#11745157C2211yescharacteristic
50#11745157C2211yescharacteristic
51#11745156C2211yescharacteristic
52#11745156C2211yescharacteristic
53#11745155C2211yescharacteristic
54#11745155C2211yescharacteristic
55C4×#6597C2211yescharacteristic
56C4×#6597C2211yescharacteristic
57C4×#6597C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29—21no—
63C22×C4×C29D411yescharacteristic
64C22×C4×C29D411yescharacteristic
65C22×C4×C29C2311yescharacteristic
66C2×C22⋊D29—21no—
67C2×D116C2311yescharacteristic
68C2×C4×D29—21no—
69C2×Dic58C2311yescharacteristic
70C4⋊C4×C29—21no—
71C4⋊C4×C29—21no—
72C4⋊C4×C29—21no—
73C4⋊C4×C29—21no—
74C4⋊C4×C29C2311yescharacteristic
75C4⋊C4×C29C2311yescharacteristic
76C22⋊C4×C29—21no—
77C22⋊C4×C29—21no—
78C22⋊C4×C29—21no—
79C22⋊C4×C29—21no—
80C22⋊C4×C29—21no—
81C42×C29—21no—
82C42×C29D411yescharacteristic
83C42×C29D411yescharacteristic
84C42×C29C2311yescharacteristic
85C42×C29C2311yescharacteristic
86C22⋊Dic29—21no—
87#90785—22no—
88#90784—22no—
89#90783—22no—
90#90782—22no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95C4⋊Dic29C2311yescharacteristic
96C4⋊Dic29C2311yescharacteristic
97#90779—21no—
98#90779—21no—
99#90779—21no—
100#90779—21no—
101C4×Dic29—21no—
102C2×#6597—22no—
103C2×#6597—22no—
104C2×#6597C2311yescharacteristic
105C2×#6597C2311yescharacteristic
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110C22×D29—21no—
111Q8×C29—21no—
112Q8×C29—21no—
113D4×C29—21no—
114D4×C29—21no—
115D4×C29—42no—
116C2×C4×C29—22no—
117C2×C4×C29—22no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—42no—
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2×D411yescharacteristic
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C22⋊D29—42no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134D116—21no—
135D116—21no—
136C4×D29—42no—
137Dic58—21no—
138Dic58—21no—
139#6597—21no—
140#6597—21no—
141#6597#4112yes—
142#6597#4112yes—
143#3168—291nomaximal, Sylow
144C22×C29—21no—
145C22×C29—21no—
146C22×C29—41no—
147C22×C29—41no—
148C22×C29—41no—
149C22×C29#13512yes—
150C22×C29C22×D411yescharacteristic
151C2×D29—41no—
152C2×D29—41no—
153C2×D29—41no—
154C4×C29—21no—
155C4×C29—21no—
156C4×C29—21no—
157C4×C29—21no—
158C4×C29—41no—
159C4×C29—41no—
160C4×C29—41no—
161C4×C29#13512yes—
162C4×C29C2×#4111yescharacteristic
163C4×C29C2×#4111yescharacteristic
164Dic29—41no—
165Dic29—41no—
166Dic29—41no—
167#529—291no—
168#529D2911yescharacteristic, complemented
169#499—291no—
170#495—291no—
171#488—291no—
172#488—291no—
173#467—291no—
174#466—291no—
175#465—291no—
176#465—291no—
177C4×Q16—291no—
178C4×SD16—291no—
179C4×SD16—291no—
180C4×D8—291no—
181C2×C4×C8—291no—
182C2×C29—22no—
183C2×C29—81no—
184C2×C29#53211yescharacteristic
185C2×C29C2×#13511yescharacteristic
186C2×C29C2×#13511yescharacteristic
187D29—81no—
188C2×Q16—291no—
189C2×SD16—291no—
190C2×SD16—291no—
191C2×D8—291no—
192C22×C8—291no—
193C22×C8—291no—
194#126—21no—
195#126—581no—
196#125—291no—
197#125C2×D2911yescharacteristic
198#124—291no—
199#124C2×D2911yescharacteristic
200#123—21no—
201#123—581no—
202C22⋊Q8—291no—
203C22⋊Q8C2×D2911yescharacteristic
204#121—291no—
205#121C2×D2911yescharacteristic
206C4×Q8—291no—
207C4×Q8C2×D2911yescharacteristic
208C4×D4—21no—
209C4×D4—291no—
210C4×D4—581no—
211C4×D4C2×D2911yescharacteristic
212#117—21no—
213#117—581no—
214C2×C42C2×D2911yescharacteristic
215#107—291no—
216#107—291no—
217#106—291no—
218#106—291no—
219#103—291no—
220#103—291no—
221#103—291no—
222#103—291no—
223#102—291no—
224#102—291no—
225#102—291no—
226#102—291no—
227C4×C8—291no—
228C4×C8—291no—
229C4×C8—291no—
230C4×C8—291no—
231C29#316811yescharacteristic, complemented, Sylow
232C2×Q8—291no—
233C2×Q8C22×D2911yescharacteristic
234C2×D4—21no—
235C2×D4—291no—
236C2×D4—581no—
237C2×D4C22×D2911yescharacteristic
238C22×C4—21no—
239C22×C4—581no—
240C22×C4C22⋊D2911yescharacteristic
241C22×C4C22⋊D2911yescharacteristic
242C22×C4C22×D2911yescharacteristic
243Q16—582no—
244SD16—582no—
245SD16—582no—
246D8—582no—
247C2×C8—291no—
248C2×C8—291no—
249C2×C8—291no—
250C2×C8—291no—
251C2×C8—582no—
252C2×C8—582no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—291no—
258C4⋊C4—291no—
259C4⋊C4—581no—
260C4⋊C4—581no—
261C4⋊C4—581no—
262C4⋊C4—581no—
263C4⋊C4C22×D2911yescharacteristic
264C4⋊C4C22×D2911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—581no—
271C22⋊C4—581no—
272C22⋊C4—581no—
273C22⋊C4—581no—
274C22⋊C4—581no—
275C42—21no—
276C42—581no—
277C42C22⋊D2911yescharacteristic
278C42C22⋊D2911yescharacteristic
279C42C22×D2911yescharacteristic
280C42C22×D2911yescharacteristic
281C23—21no—
282C23—581no—
283C23C2×C22⋊D2911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—581no—
287Q8—581no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—581no—
292D4—581no—
293D4—1162no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—581no—
303C2×C4—581no—
304C2×C4—581no—
305C2×C4—1162no—
306C2×C4C2×C22⋊D2911yescharacteristic
307C2×C4C2×C22⋊D2911yescharacteristic
308C2×C4C2×C22⋊D2911yescharacteristic
309C2×C4C2×C22⋊D2911yescharacteristic
310C2×C4C2×C22⋊D2911yescharacteristic
311C2×C4C23×D2911yescharacteristic
312C8—292no—
313C8—292no—
314C8—581no—
315C8—581no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1161no—
322C22—1161no—
323C22—1161no—
324C22#1174531212yes—
325C22C22×C22⋊D2911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1161no—
334C4—1161no—
335C4—1161no—
336C4#1174531212yes—
337C4#41×D2911yescharacteristic
338C4#41×D2911yescharacteristic
339C2—22no—
340C2—81no—
341C2—2321no—
342C2#1427170911yescharacteristic
343C2C2×#1174531211yescharacteristic
344C2C2×#1174531211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#529C2
socleC22×C29C22×D4
prime radical#14271397C2
hypercenter#529D29
hypocenterC29#3168
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #14271697C2semidirect
2. #14271562C2semidirect
3. #14271545C2semidirect
4. #14271520C2semidirect
5. #14271517C2semidirect
6. #14271402C2semidirect
8. #14271394C2semidirect
9. #14271390C2semidirect
10. C4×#90785C2semidirect
11. C4×#90784C2semidirect
12. C4×#90783C2semidirect
13. C4×#90782C2semidirect
14. C2×C4×#6597C2semidirect
15. C29×#529C2semidirect
168. #529D29semidirect
231. C29#3168semidirect

Maximal subgroups

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

subgroupindex
#142716972
#142715622
#142715452
#142715202
#142715172
#142714022
#142713972
#142713942
#142713902
C4×#907852
C4×#907842
C4×#907832
C4×#907822
C2×C4×#65972
C29×#5292
#316829