Finite Group Databasebeta

← #16835633

Subgroups — #16835633

Order 3712.

408 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×#11745215C212yesmaximal, complemented
2C2×#11745227C212yesmaximal, complemented
3#14272105C211yesmaximal, characteristic, complemented
4C4×C22⋊#1181C211yesmaximal, characteristic, complemented
5C2×#11745246C211yesmaximal, characteristic
6C22×C22⋊D29C411yescharacteristic, complemented
7C22×C22⋊D29C2211yescharacteristic
8C22×D116C2211yescharacteristic
9C22×C4×D29C2211yescharacteristic
10C2×C22⋊#1181C2212yes—
11C2×C22⋊#1181C2212yes—
12C2×C4⋊#1181—21no—
13C2×C4×#1181—21no—
14C2×C22⋊C4×C29C411yescharacteristic, complemented
15C2×#90781C411yescharacteristic, complemented
16C2×#90779C411yescharacteristic, complemented
17#11745246—21no—
18#11745246—21no—
19#11745246—21no—
20#11745246—21no—
21#11745227—24no—
22(C2×#1181)⋊C4—21no—
23(C2×#1181)⋊C4—21no—
24#11745215—24no—
25C24×C29C2×C411yescharacteristic
26C23×D29C2×C411yescharacteristic
27C23×D29C2311yescharacteristic
28C22×#1181—22no—
29C22×#1181—22no—
30C22×C4×C29C2×C411yescharacteristic
31C22×C4×C29C2×C411yescharacteristic
32C2×C22⋊D29—22no—
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C2×C22⋊D29—22no—
36C2×C22⋊D29—21no—
37C2×C22⋊D29—21no—
38C2×C22⋊D29—42no—
39C22×Dic29C2×C411yescharacteristic
40C22×Dic29C2×C411yescharacteristic
41C2×D116—22no—
42C2×D116—21no—
43C2×D116—21no—
44C2×D116—22no—
45C2×C4×D29—42no—
46C2×C4×D29D411yescharacteristic
47C2×C4×D29D411yescharacteristic
48C2×C4×D29D411yescharacteristic
49C2×C4×D29D411yescharacteristic
50C22⋊#1181—22no—
51C22⋊#1181—22no—
52C22⋊#1181—22no—
53C22⋊#1181D414yescomplemented
54C4⋊#1181—42no—
55C4×#1181—42no—
56C22⋊C4×C29—21no—
57C22⋊C4×C29—21no—
58#90781—21no—
59#90781—21no—
60#90779—21no—
61#90779—21no—
62C23×C29—21no—
63C23×C29—22no—
64C23×C29—41no—
65C23×C29—41no—
66C23×C29C22×C411yescharacteristic
67C22×D29—21no—
68C22×D29—22no—
69C22×D29—41no—
70C22×D29—41no—
71C22×D29—41no—
72C22×D29—41no—
73C22×D29C2×D411yescharacteristic
74C22×D29C2×D411yescharacteristic
75C22×D29C2×D412yes—
76C22×D29#4112yes—
77C2×#1181—24no—
78C2×#1181—42no—
79C2×#1181—42no—
80C2×#1181—42no—
81C2×#1181—42no—
82C2×#1181—42no—
83C2×C4×C29—21no—
84C2×C4×C29—22no—
85C2×C4×C29—41no—
86C2×C4×C29C22⋊C411yescharacteristic
87C2×C4×C29C22⋊C411yescharacteristic
88C22⋊D29—42no—
89C22⋊D29—42no—
90C22⋊D29—41no—
91C22⋊D29—41no—
92C22⋊D29—42no—
93C2×Dic29—22no—
94C2×Dic29—21no—
95C2×Dic29—22no—
96C2×Dic29C22⋊C411yescharacteristic
97C2×Dic29C22⋊C411yescharacteristic
98D116—42no—
99D116—41no—
100D116—41no—
101C4×D29—22no—
102C4×D29—22no—
103C4×D29—41no—
104C4×D29—41no—
105#1964—291nomaximal, Sylow
106C22×C29—21no—
107C22×C29—21no—
108C22×C29—41no—
109C22×C29—41no—
110C22×C29—41no—
111C22×C29—82no—
112C22×C29C2×C22⋊C411yescharacteristic
113C22×C29C4×D412yes—
114C2×D29—21no—
115C2×D29—21no—
116C2×D29—21no—
117C2×D29—21no—
118C2×D29—42no—
119C2×D29—42no—
120C2×D29—41no—
121C2×D29—41no—
122C2×D29—41no—
123C2×D29—82no—
124C2×D29#12112yes—
125C2×D29#12411yescharacteristic
126C2×D29#12711yescharacteristic
127#1181—44no—
128#1181—82no—
129C4×C29—21no—
130C4×C29—21no—
131C4×C29—41no—
132Dic29—21no—
133Dic29—41no—
134Dic29#9912yescomplemented
135C2×#121—291no—
136C2×#99—292no—
137C2×#99—292no—
138#380—291no—
139C4×C22⋊C4—291no—
140C2×C29—22no—
141C2×C29—81no—
142C2×C29#39011yescharacteristic
143C2×C29C2×#9911yescharacteristic
144C2×C29#41011yescharacteristic
145D29—22no—
146D29—21no—
147D29—21no—
148D29—81no—
149C22×D4—291no—
150C22×D4—291no—
151C22×D4—291no—
152C23×C4—291no—
153#121—581no—
154#121—581no—
155#121—581no—
156#121—581no—
157C2×C4⋊C4—291no—
158C2×C4⋊C4—581no—
159C2×C22⋊C4—292no—
160C2×C22⋊C4—291no—
161C2×C22⋊C4—292no—
162C2×C22⋊C4#118111yescharacteristic, complemented
163C2×C42—581no—
164#99—584no—
165#99—584no—
166#95—581no—
167#95—581no—
168C29#196411yescharacteristic, complemented, Sylow
169C24—291no—
170C24—291no—
171C24C2×#118111yescharacteristic
172C2×D4—582no—
173C2×D4—581no—
174C2×D4—581no—
175C2×D4—582no—
176C2×D4—581no—
177C2×D4—581no—
178C2×D4—582no—
179C2×D4—581no—
180C2×D4—581no—
181C2×D4—582no—
182C2×D4—1162no—
183C22×C4—291no—
184C22×C4—291no—
185C22×C4—291no—
186C22×C4—291no—
187C22×C4—291no—
188C22×C4—291no—
189C22×C4—582no—
190C22×C4—582no—
191C22×C4—1162no—
192C22×C4C2×#118111yescharacteristic
193C22×C4C2×#118111yescharacteristic
194C4⋊C4—581no—
195C4⋊C4—581no—
196C4⋊C4—1162no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—294no—
200C22⋊C4—582no—
201C22⋊C4—581no—
202C22⋊C4—581no—
203C22⋊C4—582no—
204C22⋊C4—582no—
205C42—1162no—
206C23—21no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—291no—
211C23—291no—
212C23—292no—
213C23—292no—
214C23—581no—
215C23—582no—
216C23—1161no—
217C23—1161no—
218C23—1161no—
219C23—1161no—
220C23C22×#118111yescharacteristic
221D4—1162no—
222D4—1161no—
223D4—1161no—
224D4—1162no—
225D4—1162no—
226D4—1162no—
227D4—1161no—
228D4—1161no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—291no—
233C2×C4—291no—
234C2×C4—582no—
235C2×C4—582no—
236C2×C4—582no—
237C2×C4—584no—
238C2×C4—582no—
239C2×C4—581no—
240C2×C4—1161no—
241C2×C4—1161no—
242C2×C4—1162no—
243C2×C4—1162no—
244C2×C4—1162no—
245C2×C4—1162no—
246C2×C4—1162no—
247C2×C4C22⋊#118111yescharacteristic
248C2×C4C22⋊#118111yescharacteristic
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—82no—
255C22—292no—
256C22—291no—
257C22—291no—
258C22—581no—
259C22—581no—
260C22—581no—
261C22—581no—
262C22—1162no—
263C22—1162no—
264C22—1161no—
265C22—1161no—
266C22—1161no—
267C22—2322no—
268C22D4×#118112yes—
269C22C2×C22⋊#118111yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—292no—
274C4—581no—
275C4—1164no—
276C4—1161no—
277C4—2322no—
278C2—22no—
279C2—81no—
280C2—582no—
281C2—581no—
282C2—581no—
283C2—2321no—
284C2#1427211511yescharacteristic
285C2D29⋊#9911yescharacteristic
286C2#1427214211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#11745246C2
cosocleC23×D29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29#1964
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11745215C2semidirect
2. C2×#11745227C2semidirect
3. #14272105C2semidirect
4. C4×C22⋊#1181C2semidirect
6. C22×C22⋊D29C4semidirect
14. C2×C22⋊C4×C29C4semidirect
15. C2×#90781C4semidirect
16. C2×#90779C4semidirect
53. C22⋊#1181D4semidirect
134. Dic29#99semidirect
162. C2×C22⋊C4#1181semidirect
168. C29#1964semidirect

Maximal subgroups

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

subgroupindex
C2×#117452152
C2×#117452272
#142721052
C4×C22⋊#11812
C2×#117452462
#196429