Finite Group Databasebeta

← #16818023

Subgroups — #16818023

Order 3712.

274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D29C211yesmaximal, characteristic
2#14271125C211yesmaximal, characteristic
3#14271025C211yesmaximal, characteristic
4#14270901C211yesmaximal, characteristic, complemented
5#14270900C211yesmaximal, characteristic, complemented
6#14270899C211yesmaximal, characteristic, complemented
7C29×#328C211yesmaximal, characteristic, complemented
8C2×Q8×D29C411yescharacteristic, complemented
9C22×C4×D29C2211yescharacteristic
10C29×C22⋊Q8C2211yescharacteristic
11#11745308C411yescharacteristic, complemented
12C2×#90781—21no—
13#11745286C2211yescharacteristic
14C2×#90772—21no—
15#11745259C411yescharacteristic, complemented
16#11745258—21no—
17C4⋊C4×D29—21no—
18C4⋊C4×D29C411yescharacteristic, complemented
19C22⋊C4×D29—21no—
20#11745240—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179—21no—
24#11745179C2211yescharacteristic
25C22⋊#6597C2211yescharacteristic
26#11745168—21no—
27C23×D29D411yescharacteristic
28C2×Q8×C29C2×C411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C22×Dic29—21no—
32C22×Dic29D411yescharacteristic
33Q8×D29—42no—
34C2×C4×D29—21no—
35C2×C4×D29—21no—
36C2×C4×D29—42no—
37C2×C4×D29C2×C411yescharacteristic
38C2×C4×D29C2×C411yescharacteristic
39C2×C4×D29D411yescharacteristic
40C2×C4×D29D411yescharacteristic
41C2×Dic58—21no—
42C2×Dic58C2×C411yescharacteristic
43C2×C8×C29—21no—
44C4⋊C4×C29—21no—
45C4⋊C4×C29C2×C411yescharacteristic
46C22⋊C4×C29—21no—
47C22⋊Dic29—21no—
48#90781—21no—
49#90781—21no—
50#90781—42no—
51C4⋊Dic29—21no—
52C4⋊Dic29C2×C411yescharacteristic
53#90779—21no—
54#90779—21no—
55#90779—21no—
56C2×#6597—21no—
57#90772—42no—
58C23×C29C2×D411yescharacteristic
59C22×D29—21no—
60C22×D29—21no—
61C22×D29—22no—
62C22×D29—41no—
63C22×D29C22⋊C411yescharacteristic
64C22×D29C22⋊C411yescharacteristic
65Q8×C29—41no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—41no—
69C2×C4×C29—41no—
70C2×C4×C29—41no—
71C2×C4×C29—41no—
72C2×C4×C29C22×C411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—41no—
77C2×Dic29—41no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29C22⋊C411yescharacteristic
81C2×Dic29C22⋊C411yescharacteristic
82C4×D29—22no—
83C4×D29—22no—
84C4×D29—41no—
85C4×D29—41no—
86C4×D29—42no—
87C4×D29—42no—
88Dic58—42no—
89Dic58—41no—
90C8×C29—41no—
91#6597—41no—
92#1511—291nomaximal, Sylow
93C22×C29—21no—
94C22×C29—21no—
95C22×C29C2×C22⋊C411yescharacteristic
96C22×C29#13711yescharacteristic
97C22×C29#13711yescharacteristic
98C2×D29—21no—
99C2×D29—21no—
100C2×D29—21no—
101C2×D29—21no—
102C2×D29—21no—
103C2×D29—42no—
104C2×D29—42no—
105C2×D29#9912yes—
106C4×C29—21no—
107C4×C29—21no—
108C4×C29—41no—
109C4×C29—41no—
110C4×C29—81no—
111Dic29—21no—
112Dic29—21no—
113Dic29—41no—
114Dic29—41no—
115Dic29—81no—
116C2×C22⋊Q8—291no—
117#407—291no—
118#381—291no—
119#328—291no—
120#328—291no—
121#328—291no—
122#328D2911yescharacteristic, complemented
123C2×C29—21no—
124C2×C29—21no—
125C2×C29C2×#9911yescharacteristic
126C2×C29#41911yescharacteristic
127C2×C29#42111yescharacteristic
128D29—22no—
129D29—41no—
130C22×Q8—291no—
131C23×C4—291no—
132C2×M16—581no—
133C22⋊Q8—291no—
134C22⋊Q8—291no—
135C22⋊Q8—291no—
136C22⋊Q8—581no—
137C22⋊Q8—581no—
138C22⋊Q8C2×D2911yescharacteristic
139C2×C4⋊C4—291no—
140C2×C4⋊C4—581no—
141C2×C22⋊C4—581no—
142C2×C22⋊C4—581no—
143C22⋊C8—291no—
144C22⋊C8—581no—
145C22⋊C8C2×D2911yescharacteristic
146#95—291no—
147#95—581no—
148#95C2×D2911yescharacteristic
149C29#151111yescharacteristic, complemented, Sylow
150C24—291no—
151C2×Q8—291no—
152C2×Q8—581no—
153C2×Q8—1162no—
154C2×Q8C4×D2911yescharacteristic
155C22×C4—21no—
156C22×C4—291no—
157C22×C4—291no—
158C22×C4—291no—
159C22×C4—291no—
160C22×C4—291no—
161C22×C4—581no—
162C22×C4—581no—
163C22×C4—581no—
164C22×C4—1162no—
165C22×C4C22×D2911yescharacteristic
166M16—1162no—
167C2×C8—21no—
168C2×C8—581no—
169C4⋊C4—21no—
170C4⋊C4—291no—
171C4⋊C4—581no—
172C4⋊C4—581no—
173C4⋊C4—581no—
174C4⋊C4—581no—
175C4⋊C4C4×D2911yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—581no—
178C22⋊C4—581no—
179C22⋊C4—581no—
180C22⋊C4—1162no—
181C23—291no—
182C23—291no—
183C23—582no—
184C23—581no—
185C23—581no—
186C23—1161no—
187C23D4×D2911yescharacteristic
188Q8—41no—
189Q8—1161no—
190Q8—1162no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—291no—
198C2×C4—291no—
199C2×C4—582no—
200C2×C4—582no—
201C2×C4—581no—
202C2×C4—581no—
203C2×C4—1161no—
204C2×C4—1161no—
205C2×C4—1162no—
206C2×C4—1162no—
207C2×C4—1161no—
208C2×C4—1161no—
209C2×C4—1161no—
210C2×C4—1161no—
211C2×C4C2×C4×D2911yescharacteristic
212C2×C4D4×D2911yescharacteristic
213C8—41no—
214C8—1161no—
215C22—21no—
216C22—21no—
217C22—292no—
218C22—581no—
219C22—581no—
220C22—581no—
221C22—581no—
222C22—581no—
223C22—1162no—
224C22—1162no—
225C22C22⋊C4×D2911yescharacteristic
226C22#1174527711yescharacteristic
227C22#1174528011yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—81no—
233C4—581no—
234C4—581no—
235C4—1161no—
236C4—1161no—
237C4—2321no—
238C2—21no—
239C2—21no—
240C2—582no—
241C2—1161no—
242C2#99×D2911yescharacteristic
243C2#1427117011yescharacteristic
244C2#1427117811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29C2×C22⋊C4
prime radicalC23×D29D4
cosocleC22×C4×C29C23
hypercenter#328D29
hypocenterC29#1511
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. #14270901C2semidirect
5. #14270900C2semidirect
6. #14270899C2semidirect
7. C29×#328C2semidirect
8. C2×Q8×D29C4semidirect
11. #11745308C4semidirect
15. #11745259C4semidirect
18. C4⋊C4×D29C4semidirect
122. #328D29semidirect
149. C29#1511semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D292
#142711252
#142710252
#142709012
#142709002
#142708992
C29×#3282
#151129