Finite Group Databasebeta

← #16835363

Subgroups — #16835363

Order 3712.

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

normal subgroups only

This group has 292 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
2C2×#11745225C212yesmaximal
3#14272107C211yesmaximal, characteristic
4#14272036C212yesmaximal
5C4×Q8×D29C211yesmaximal, characteristic
6C2×Q8×D29C2211yescharacteristic
7C2×C4⋊#1181C2212yes—
8C2×D29⋊C8C2212yes—
9C4×Q8×C29C411yescharacteristic, complemented
10Q8×Dic29C411yescharacteristic, complemented
11C4⋊C4×D29—21no—
12C4⋊C4×D29C2211yescharacteristic
13#11745249—21no—
14#11745249C411yescharacteristic, complemented
15C42×D29—21no—
16C42×D29C2211yescharacteristic
17C4×Dic58—21no—
18C4×Dic58C411yescharacteristic, complemented
19#11745225—24no—
20(C2×#1181)⋊C4—21no—
21(C2×#1181)⋊C4—21no—
22#11745220—21no—
23C4⋊#6599—21no—
24C22×#1181—22no—
25C2×Q8×C29C2×C411yescharacteristic
26Q8×D29—21no—
27Q8×D29—21no—
28Q8×D29D412yes—
29Q8×D29Q812yes—
30C2×C4×D29—21no—
31C2×C4×D29—21no—
32C2×C4×D29D411yescharacteristic
33C2×C4×D29D411yescharacteristic
34C2×C4×D29C2311yescharacteristic
35C2×Dic58—21no—
36C2×Dic58C2×C411yescharacteristic
37C2×#6599—22no—
38C4⋊#1181—22no—
39C4⋊#1181—22no—
40D29⋊C8—22no—
41D29⋊C8—22no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29C2×C411yescharacteristic
44C42×C29—21no—
45C42×C29C2×C411yescharacteristic
46C4⋊Dic29—21no—
47C4⋊Dic29C2×C411yescharacteristic
48#90779—21no—
49#90779—21no—
50#90779—21no—
51C4×Dic29—21no—
52C4×Dic29—21no—
53C4×Dic29—21no—
54C4×Dic29C2×C411yescharacteristic
55C4×Dic29D411yescharacteristic
56C4×Dic29D411yescharacteristic
57C22×D29C2×D411yescharacteristic
58C2×#1181—42no—
59C2×#1181—42no—
60C2×#1181—42no—
61Q8×C29—21no—
62Q8×C29C4⋊C412yes—
63C2×C4×C29—21no—
64C2×C4×C29—21no—
65C2×C4×C29C22⋊C411yescharacteristic
66C2×C4×C29C22⋊C411yescharacteristic
67C2×C4×C29C22×C411yescharacteristic
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29C22⋊C411yescharacteristic
71C2×Dic29C22⋊C411yescharacteristic
72C2×Dic29C2×D411yescharacteristic
73C4×D29—22no—
74C4×D29—22no—
75C4×D29—22no—
76C4×D29—22no—
77C4×D29—42no—
78C4×D29C2×D411yescharacteristic
79C4×D29C2×Q811yescharacteristic
80C4×D29#4111yescharacteristic
81C4×D29#4111yescharacteristic
82Dic58—21no—
83Dic58—22no—
84Dic58—22no—
85Dic58C4⋊C412yes—
86#6599—42no—
87#1805—291nomaximal, Sylow
88C22×C29C2×C22⋊C411yescharacteristic
89C2×D29#12111yescharacteristic
90C2×D29C22⋊Q811yescharacteristic
91C2×D29#13512yes—
92C2×D29#13712yes—
93#1181—82no—
94C4×C29—22no—
95C4×C29—21no—
96C4×C29—21no—
97C4×C29—41no—
98C4×C29C2×C4⋊C411yescharacteristic
99C4×C29#11711yescharacteristic
100Dic29—22no—
101Dic29—21no—
102Dic29—21no—
103Dic29—41no—
104Dic29#12111yescharacteristic
105Dic29C22⋊Q811yescharacteristic
106C2×C4×Q8—291no—
107C2×C4⋊C8—291no—
108C2×#103—292no—
109#382—291no—
110#340—292no—
111C2×C29#38011yescharacteristic
112C2×C29#41611yescharacteristic
113C2×C29#41911yescharacteristic
114D29#46412yes—
115D29#47912yes—
116C22×Q8—291no—
117C22×C8—292no—
118C4×Q8—291no—
119C4×Q8—291no—
120C4×Q8—291no—
121C4×Q8—581no—
122C4×Q8—581no—
123C4×Q8#118111yescharacteristic, complemented
124C2×C4⋊C4—291no—
125C2×C4⋊C4—292no—
126C2×C4⋊C4—581no—
127C2×C42—291no—
128C2×C42—581no—
129C4⋊C8—581no—
130C4⋊C8—581no—
131#103—584no—
132#95—581no—
133#95—581no—
134C29#180511yescharacteristic, complemented, Sylow
135C2×Q8—292no—
136C2×Q8—292no—
137C2×Q8—291no—
138C2×Q8—581no—
139C2×Q8—581no—
140C2×Q8—581no—
141C2×Q8C2×#118111yescharacteristic
142C22×C4—291no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—581no—
146C22×C4—581no—
147C22×C4—582no—
148C2×C8—582no—
149C2×C8—582no—
150C2×C8—582no—
151C4⋊C4—21no—
152C4⋊C4—291no—
153C4⋊C4—581no—
154C4⋊C4—581no—
155C4⋊C4—581no—
156C4⋊C4—582no—
157C4⋊C4—582no—
158C4⋊C4—581no—
159C4⋊C4C2×#118111yescharacteristic
160C42—21no—
161C42—291no—
162C42—291no—
163C42—291no—
164C42—581no—
165C42—581no—
166C42—581no—
167C42C2×#118111yescharacteristic
168C23—291no—
169Q8—21no—
170Q8—292no—
171Q8—582no—
172Q8—582no—
173Q8—581no—
174Q8C4⋊#118112yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—291no—
178C2×C4—291no—
179C2×C4—291no—
180C2×C4—291no—
181C2×C4—291no—
182C2×C4—291no—
183C2×C4—291no—
184C2×C4—582no—
185C2×C4—582no—
186C2×C4—582no—
187C2×C4—582no—
188C2×C4—581no—
189C2×C4—581no—
190C2×C4—1162no—
191C2×C4—1162no—
192C2×C4—1162no—
193C2×C4—1162no—
194C2×C4C22⋊#118111yescharacteristic
195C2×C4C22⋊#118111yescharacteristic
196C2×C4C22×#118111yescharacteristic
197C8—1162no—
198C22—291no—
199C22—291no—
200C22—292no—
201C22—292no—
202C22C2×C22⋊#118111yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—291no—
208C4—291no—
209C4—582no—
210C4—581no—
211C4—581no—
212C4—1161no—
213C4—2322no—
214C4C2×C4⋊#118111yescharacteristic
215C4#1174534511yescharacteristic
216C2—292no—
217C2—292no—
218C2#1427210511yescharacteristic
219C2#1427215311yescharacteristic
220C2#1427215611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×Q8×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC22×D29C2×D4
cosocleC2×C4×D29C23
hypercenterC4×Q8#1181
hypocenterC29#1805
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
9. C4×Q8×C29C4semidirect
10. Q8×Dic29C4semidirect
14. #11745249C4semidirect
18. C4×Dic58C4semidirect
123. C4×Q8#1181semidirect
134. C29#1805semidirect

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×#117452252
#142721072
#142720362
C4×Q8×D292
#180529