Finite Group Databasebeta

← #16835362

Subgroups — #16835362

Order 3712.

356 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D29⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C2×#11745223C212yesmaximal
3#14272107C211yesmaximal, characteristic, complemented
4#14272036C212yesmaximal, complemented
5C4×D4×D29C211yesmaximal, characteristic
6C2×D4×D29C2211yescharacteristic
7C22×C4×D29—21no—
8C2×C4⋊#1181C2212yes—
9C2×D29⋊C8C2212yes—
10C4×D4×C29C411yescharacteristic, complemented
11D4×Dic29C411yescharacteristic, complemented
12C4×C22⋊D29—21no—
13#11745255C411yescharacteristic, complemented
14C4⋊C4×D29C2211yescharacteristic
15#11745243—21no—
16C22⋊C4×D29—21no—
17C4×D116C411yescharacteristic, complemented
18C42×D29C2211yescharacteristic
19#11745223—24no—
20(C2×#1181)⋊C4—21no—
21(C2×#1181)⋊C4—21no—
22#11745220—21no—
23C4⋊#6599—21no—
24C23×D29—21no—
25C22×#1181—22no—
26C2×D4×C29C2×C411yescharacteristic
27C22×C4×C29—21no—
28C2×C22⋊D29—21no—
29C22×Dic29—21no—
30D4×D29—21no—
31D4×D29—21no—
32D4×D29D412yes—
33D4×D29Q812yes—
34C2×D116C2×C411yescharacteristic
35C2×C4×D29—21no—
36C2×C4×D29—21no—
37C2×C4×D29—21no—
38C2×C4×D29—44no—
39C2×C4×D29D411yescharacteristic
40C2×C4×D29D411yescharacteristic
41C2×C4×D29C2311yescharacteristic
42C2×#6599—22no—
43C4⋊#1181—22no—
44C4⋊#1181—22no—
45D29⋊C8—22no—
46D29⋊C8—22no—
47C4⋊C4×C29C2×C411yescharacteristic
48C22⋊C4×C29—21no—
49C42×C29C2×C411yescharacteristic
50C22⋊Dic29—21no—
51#90781—21no—
52#90781—21no—
53C4⋊Dic29C2×C411yescharacteristic
54#90779—21no—
55C4×Dic29C2×C411yescharacteristic
56C4×Dic29D411yescharacteristic
57C4×Dic29D411yescharacteristic
58C23×C29—21no—
59C22×D29—21no—
60C22×D29—22no—
61C22×D29—22no—
62C22×D29—42no—
63C22×D29—42no—
64C22×D29C2×D411yescharacteristic
65C2×#1181—42no—
66C2×#1181—42no—
67C2×#1181—42no—
68D4×C29—21no—
69D4×C29C4⋊C412yes—
70C2×C4×C29—21no—
71C2×C4×C29—42no—
72C2×C4×C29C22⋊C411yescharacteristic
73C2×C4×C29C22⋊C411yescharacteristic
74C2×C4×C29C22×C411yescharacteristic
75C22⋊D29—22no—
76C22⋊D29—22no—
77C2×Dic29—21no—
78C2×Dic29—42no—
79C2×Dic29C22⋊C411yescharacteristic
80C2×Dic29C22⋊C411yescharacteristic
81C2×Dic29C2×D411yescharacteristic
82D116—21no—
83D116C4⋊C412yes—
84C4×D29—22no—
85C4×D29—22no—
86C4×D29—42no—
87C4×D29—42no—
88C4×D29—42no—
89C4×D29C2×D411yescharacteristic
90C4×D29C2×Q811yescharacteristic
91C4×D29#4111yescharacteristic
92C4×D29#4111yescharacteristic
93#6599—42no—
94#1804—291nomaximal, Sylow
95C22×C29—22no—
96C22×C29—41no—
97C22×C29—41no—
98C22×C29C2×C22⋊C411yescharacteristic
99C2×D29—22no—
100C2×D29—41no—
101C2×D29—41no—
102C2×D29—44no—
103C2×D29—44no—
104C2×D29#12111yescharacteristic
105C2×D29C22⋊Q811yescharacteristic
106C2×D29#13512yes—
107C2×D29AGL(1,ℤ/8)12yes—
108#1181—82no—
109C4×C29—21no—
110C4×C29—21no—
111C4×C29—41no—
112C4×C29C2×C4⋊C411yescharacteristic
113C4×C29#11711yescharacteristic
114Dic29—21no—
115Dic29—21no—
116Dic29—41no—
117Dic29#12111yescharacteristic
118Dic29C22⋊Q811yescharacteristic
119C2×C4×D4—291no—
120C2×C4⋊C8—291no—
121C2×#102—292no—
122#382—291no—
123#340—292no—
124C2×C29—42no—
125C2×C29#38011yescharacteristic
126C2×C29#41611yescharacteristic
127C2×C29#41811yescharacteristic
128D29—42no—
129D29#46312yes—
130D29#47812yes—
131C22×D4—291no—
132C23×C4—581no—
133C22×C8—292no—
134C4×D4—291no—
135C4×D4—291no—
136C4×D4—291no—
137C4×D4—581no—
138C4×D4—581no—
139C4×D4#118111yescharacteristic, complemented
140C2×C4⋊C4—291no—
141C2×C4⋊C4—292no—
142C2×C22⋊C4—581no—
143C2×C42—291no—
144C4⋊C8—581no—
145C4⋊C8—581no—
146#102—584no—
147#95—581no—
148#95—581no—
149C29#180411yescharacteristic, complemented, Sylow
150C24—581no—
151C2×D4—292no—
152C2×D4—292no—
153C2×D4—291no—
154C2×D4—581no—
155C2×D4—581no—
156C2×D4—581no—
157C2×D4C2×#118111yescharacteristic
158C22×C4—21no—
159C22×C4—291no—
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—581no—
163C22×C4—581no—
164C22×C4—581no—
165C22×C4—581no—
166C22×C4—582no—
167C22×C4—1164no—
168C2×C8—582no—
169C2×C8—582no—
170C2×C8—582no—
171C4⋊C4—291no—
172C4⋊C4—581no—
173C4⋊C4—582no—
174C4⋊C4—582no—
175C4⋊C4C2×#118111yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—581no—
178C22⋊C4—581no—
179C22⋊C4—581no—
180C42—291no—
181C42—291no—
182C42—291no—
183C42C2×#118111yescharacteristic
184C23—21no—
185C23—291no—
186C23—582no—
187C23—582no—
188C23—581no—
189C23—1162no—
190C23—1162no—
191D4—21no—
192D4—292no—
193D4—582no—
194D4—582no—
195D4—581no—
196D4C4⋊#118112yes—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—291no—
200C2×C4—291no—
201C2×C4—291no—
202C2×C4—291no—
203C2×C4—291no—
204C2×C4—291no—
205C2×C4—291no—
206C2×C4—582no—
207C2×C4—582no—
208C2×C4—581no—
209C2×C4—1162no—
210C2×C4—1162no—
211C2×C4—1162no—
212C2×C4—1162no—
213C2×C4—1162no—
214C2×C4—1162no—
215C2×C4—1162no—
216C2×C4C22⋊#118111yescharacteristic
217C2×C4C22⋊#118111yescharacteristic
218C2×C4C22×#118111yescharacteristic
219C8—1162no—
220C22—22no—
221C22—41no—
222C22—41no—
223C22—291no—
224C22—291no—
225C22—292no—
226C22—292no—
227C22—582no—
228C22—1164no—
229C22—1164no—
230C22—1161no—
231C22—1161no—
232C22C2×C22⋊#118111yescharacteristic
233C4—21no—
234C4—21no—
235C4—41no—
236C4—291no—
237C4—291no—
238C4—581no—
239C4—581no—
240C4—1161no—
241C4—2322no—
242C4C2×C4⋊#118111yescharacteristic
243C4#1174534511yescharacteristic
244C2—42no—
245C2—292no—
246C2—292no—
247C2—1162no—
248C2#1427210511yescharacteristic
249C2#1427215311yescharacteristic
250C2#1427215511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×D4×D29C22
cosocleC2×C4×D29C23
hypercenterC4×D4#1181
hypocenterC29#1804
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D29⋊(C4⋊C8)C2semidirect
3. #14272107C2semidirect
4. #14272036C2semidirect
10. C4×D4×C29C4semidirect
11. D4×Dic29C4semidirect
13. #11745255C4semidirect
17. C4×D116C4semidirect
139. C4×D4#1181semidirect
149. C29#1804semidirect

Maximal subgroups

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

subgroupindex
D29⋊(C4⋊C8)2
C2×#117452232
#142721072
#142720362
C4×D4×D292
#180429