Finite Group Databasebeta

← #16832180

Subgroups — #16832180

Order 3712.

336 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271890C211yesmaximal, characteristic, complemented
2#14271885C211yesmaximal, characteristic
3#14271520C211yesmaximal, characteristic
4#14271519C211yesmaximal, characteristic
5#14271512C211yesmaximal, characteristic, complemented
6#14271473C211yesmaximal, characteristic, complemented
7#14271442C211yesmaximal, characteristic
8#14271388C211yesmaximal, characteristic
9#14271386C211yesmaximal, characteristic
10#14271372C211yesmaximal, characteristic, complemented
11#14271287C211yesmaximal, characteristic, complemented
12#14271257C211yesmaximal, characteristic, complemented
13C4×#90785C211yesmaximal, characteristic, complemented
14#14271250C211yesmaximal, characteristic
15C29×#479C211yesmaximal, characteristic, complemented
16C29×#125C2211yescharacteristic
17C4×Q8×C29C2211yescharacteristic
18#11745309C2211yescharacteristic
19#11745306C2211yescharacteristic
20C2×#90785C2211yescharacteristic
21C2×Dic116C2211yescharacteristic
22C2×#90773C2211yescharacteristic
23#11745260—21no—
24#11745258—21no—
25#11745255C2211yescharacteristic
26#11745252C2211yescharacteristic
27#11745251—21no—
28#11745251—21no—
29#11745250—21no—
30#11745250C2211yescharacteristic
31#11745249—21no—
32#11745249C2211yescharacteristic
33#11745249C2211yescharacteristic
34#11745249C2211yescharacteristic
35#11745238—21no—
36#11745237C2211yescharacteristic
37#11745234—21no—
38C4×Dic58C2211yescharacteristic
39C4×Dic58C2211yescharacteristic
40C29×#107C2211yescharacteristic
41C29×#106C2211yescharacteristic
42C29×C4⋊C8C2211yescharacteristic
43C29×#103C2211yescharacteristic
44C29×#103C2211yescharacteristic
45#11745183C2211yescharacteristic
46#11745169C2211yescharacteristic
47#11745164C2211yescharacteristic
48#11745162C2211yescharacteristic
49#11745162C2211yescharacteristic
50C8×Dic29C2211yescharacteristic
51C8×Dic29C2211yescharacteristic
52#11745158C2211yescharacteristic
53#11745158C2211yescharacteristic
54#11745158C2211yescharacteristic
55#11745157C2211yescharacteristic
56#11745157C2211yescharacteristic
57#11745155C2211yescharacteristic
58C4×#6597C2211yescharacteristic
59C2×Q8×C29C2311yescharacteristic
60C2×D116C2311yescharacteristic
61C2×C4×D29—21no—
62C2×Dic58—21no—
63C2×Dic58D411yescharacteristic
64C2×Dic58C2311yescharacteristic
65C2×Dic58C2311yescharacteristic
66C2×C8×C29C2311yescharacteristic
67C2×C8×C29C2311yescharacteristic
68C4⋊C4×C29—21no—
69C4⋊C4×C29—21no—
70C4⋊C4×C29—21no—
71C4⋊C4×C29C2311yescharacteristic
72C4⋊C4×C29C2311yescharacteristic
73C4⋊C4×C29C2311yescharacteristic
74C42×C29—21no—
75C42×C29C2311yescharacteristic
76#90785—22no—
77#90781—21no—
78#90781—21no—
79#90781—21no—
80#90781—21no—
81#90781—21no—
82C4⋊Dic29—21no—
83C4⋊Dic29D411yescharacteristic
84C4⋊Dic29C2311yescharacteristic
85#90779—21no—
86#90779—21no—
87#90779—21no—
88#90779—21no—
89#90779—21no—
90#90779—21no—
91#90779—21no—
92#90779—21no—
93#90779D411yescharacteristic
94#90779D411yescharacteristic
95C4×Dic29—21no—
96C4×Dic29—21no—
97C4×Dic29—21no—
98C4×Dic29—21no—
99C4×Dic29C2311yescharacteristic
100C4×Dic29C2311yescharacteristic
101C2×#6597C2311yescharacteristic
102C2×#6597C2311yescharacteristic
103Dic116—22no—
104#90773—22no—
105C22×D29—21no—
106Q8×C29—21no—
107Q8×C29—21no—
108C2×C4×C29—21no—
109C2×C4×C29—21no—
110C2×C4×C29—21no—
111C2×C4×C29—21no—
112C2×C4×C29C2×D411yescharacteristic
113C2×C4×C29C2×D411yescharacteristic
114C2×C4×C29C2411yescharacteristic
115C2×Dic29—21no—
116C2×Dic29—21no—
117C2×Dic29—21no—
118C2×Dic29C2×D411yescharacteristic
119C2×Dic29C2×D411yescharacteristic
120C2×Dic29C2×D411yescharacteristic
121C2×Dic29C2×D411yescharacteristic
122D116—21no—
123D116—21no—
124C4×D29—42no—
125Dic58—21no—
126Dic58—22no—
127Dic58—21no—
128Dic58—21no—
129Dic58—42no—
130Dic58#4112yes—
131C8×C29—21no—
132C8×C29—21no—
133#6597—21no—
134#6597—21no—
135#3364—291nomaximal, Sylow
136C22×C29C22×D411yescharacteristic
137C2×D29—41no—
138C2×D29—41no—
139C2×D29—41no—
140C4×C29—21no—
141C4×C29—21no—
142C4×C29—41no—
143C4×C29—41no—
144C4×C29—41no—
145C4×C29—41no—
146C4×C29C2×#4111yescharacteristic
147C4×C292−1+411yescharacteristic
148Dic29—22no—
149Dic29—21no—
150Dic29—21no—
151Dic29—21no—
152Dic29—41no—
153Dic29—41no—
154Dic29#13512yes—
155#557—291no—
156#556—291no—
157#488—291no—
158#488—291no—
159#487—291no—
160#479—291no—
161#479D2911yescharacteristic, complemented
162#474—291no—
163#464—291no—
164#464—291no—
165#462—291no—
166C8×Q8—291no—
167C4×Q16—291no—
168C4×Q16—291no—
169C4×SD16—291no—
170C2×C29#54811yescharacteristic
171C2×C29C2×#13511yescharacteristic
172C2×C29#57811yescharacteristic
173D29—81no—
174C2×Q16—291no—
175C2×Q16—291no—
176C2×SD16—291no—
177C4⋊Q8—291no—
178C4⋊Q8—291no—
179C4⋊Q8—581no—
180#126—581no—
181#126—581no—
182#125—291no—
183#125—581no—
184#125—581no—
185#125C2×D2911yescharacteristic
186#124—291no—
187#124—291no—
188C22⋊Q8—581no—
189C4×Q8—291no—
190C4×Q8—291no—
191C4×Q8—291no—
192C4×Q8—291no—
193C4×Q8—291no—
194C4×Q8—581no—
195C4×Q8C2×D2911yescharacteristic
196C4×D4—291no—
197#117—581no—
198#107—291no—
199#107C2×D2911yescharacteristic
200#106C2×D2911yescharacteristic
201C4⋊C8—291no—
202C4⋊C8—291no—
203C4⋊C8C2×D2911yescharacteristic
204#103—291no—
205#103—291no—
206#103—291no—
207#103—291no—
208#103—291no—
209#103C2×D2911yescharacteristic
210#103C2×D2911yescharacteristic
211#102—291no—
212#102—291no—
213#102—291no—
214C4×C8—291no—
215C4×C8—291no—
216C4×C8—291no—
217C29#336411yescharacteristic, complemented, Sylow
218C2×Q8—291no—
219C2×Q8—291no—
220C2×Q8—291no—
221C2×Q8—581no—
222C2×Q8C22×D2911yescharacteristic
223C2×D4—291no—
224C22×C4—581no—
225Q16—582no—
226Q16—582no—
227SD16—582no—
228C2×C8—291no—
229C2×C8—291no—
230C2×C8C22×D2911yescharacteristic
231C2×C8C22×D2911yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—291no—
236C4⋊C4—291no—
237C4⋊C4—291no—
238C4⋊C4—291no—
239C4⋊C4—581no—
240C4⋊C4—581no—
241C4⋊C4—581no—
242C4⋊C4—581no—
243C4⋊C4—581no—
244C4⋊C4—581no—
245C4⋊C4—581no—
246C4⋊C4—581no—
247C4⋊C4—581no—
248C4⋊C4C22×D2911yescharacteristic
249C4⋊C4C22×D2911yescharacteristic
250C4⋊C4C22×D2911yescharacteristic
251C22⋊C4—581no—
252C22⋊C4—581no—
253C22⋊C4—581no—
254C22⋊C4—581no—
255C22⋊C4—581no—
256C42—21no—
257C42—291no—
258C42—291no—
259C42—581no—
260C42—581no—
261C42—581no—
262C42—581no—
263C42C22×D2911yescharacteristic
264C23—581no—
265Q8—21no—
266Q8—21no—
267Q8—292no—
268Q8—582no—
269Q8—581no—
270Q8—581no—
271Q8—581no—
272Q8—1162no—
273D4—581no—
274D4—581no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—291no—
280C2×C4—291no—
281C2×C4—291no—
282C2×C4—291no—
283C2×C4—581no—
284C2×C4—581no—
285C2×C4—581no—
286C2×C4—1162no—
287C2×C4D4×D2911yescharacteristic
288C2×C4D4×D2911yescharacteristic
289C2×C4C23×D2911yescharacteristic
290C8—21no—
291C8—21no—
292C8—581no—
293C8—581no—
294C22—1161no—
295C22—1161no—
296C22—1161no—
297C22C2×D4×D2911yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—292no—
305C4—582no—
306C4—581no—
307C4—581no—
308C4—581no—
309C4—1161no—
310C4—1161no—
311C4#1174536211yescharacteristic
312C4#41×D2911yescharacteristic
313C2—2321no—
314C2#1427182311yescharacteristic
315C2#135×D2911yescharacteristic
316C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#479C2
socleC22×C29C22×D4
prime radicalC2×D116C23
hypercenter#479D29
hypocenterC29#3364
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14271890C2semidirect
5. #14271512C2semidirect
6. #14271473C2semidirect
10. #14271372C2semidirect
11. #14271287C2semidirect
12. #14271257C2semidirect
13. C4×#90785C2semidirect
15. C29×#479C2semidirect
161. #479D29semidirect
217. C29#3364semidirect

Maximal subgroups

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

subgroupindex
#142718902
#142718852
#142715202
#142715192
#142715122
#142714732
#142714422
#142713882
#142713862
#142713722
#142712872
#142712572
C4×#907852
#142712502
C29×#4792
#336429