Finite Group Databasebeta

← #16820593

Subgroups — #16820593

Order 3712.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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×Dic116C211yesmaximal, characteristic
2C22×#90785C211yesmaximal, characteristic
3C2×#11745306C211yesmaximal, characteristic
4C2×#11745158C211yesmaximal, characteristic
5#14271068C211yesmaximal, characteristic
6#14270917C211yesmaximal, characteristic
7C2×C29×#103C211yesmaximal, characteristic
8C22×Q8×C29C2211yescharacteristic
9C22×Dic58C2211yescharacteristic
10C22×Dic58C2211yescharacteristic
11C22×C8×C29C2211yescharacteristic
12C2×C4⋊C4×C29C2211yescharacteristic
13#11745306—22no—
14#11745306—22no—
15C2×#90785—22no—
16C2×#90785—22no—
17C2×#90785—22no—
18C2×#90779—22no—
19C2×C4×Dic29C2211yescharacteristic
20C22×#6597C2211yescharacteristic
21C2×Dic116—22no—
22C2×Dic116—22no—
23C2×Dic116—22no—
24C29×#103—22no—
25#11745179—22no—
26#11745158—22no—
27C2×Q8×C29—21no—
28C2×Q8×C29—21no—
29C2×Q8×C29—21no—
30C2×Q8×C29—21no—
31C2×Q8×C29—21no—
32C2×Q8×C29D412yes—
33C22×C4×C29—21no—
34C22×C4×C29—21no—
35C22×C4×C29C2311yescharacteristic
36C22×Dic29—21no—
37C22×Dic29—21no—
38C22×Dic29D412yes—
39C2×Dic58—21no—
40C2×Dic58—21no—
41C2×Dic58—21no—
42C2×Dic58—21no—
43C2×Dic58—21no—
44C2×Dic58—21no—
45C2×Dic58—21no—
46C2×Dic58—21no—
47C2×Dic58—21no—
48C2×Dic58—21no—
49C2×Dic58D412yes—
50C2×Dic58D412yes—
51C2×C8×C29—21no—
52C2×C8×C29—21no—
53C2×C8×C29D412yes—
54C4⋊C4×C29—21no—
55C4⋊C4×C29—21no—
56#90785—28no—
57#90779—28no—
58C4×Dic29—21no—
59C4×Dic29—21no—
60C2×#6597—21no—
61C2×#6597—21no—
62C2×#6597D412yes—
63Dic116—28no—
64C23×C29C2×D411yescharacteristic
65Q8×C29—22no—
66Q8×C29—22no—
67Q8×C29—41no—
68Q8×C29—41no—
69C2×C4×C29—22no—
70C2×C4×C29—41no—
71C2×C4×C29—41no—
72C2×C4×C29—41no—
73C2×C4×C29—42no—
74C2×C4×C29C2×D411yescharacteristic
75C2×C4×C29C2×D411yescharacteristic
76C2×C4×C29C2×D411yescharacteristic
77C2×C4×C29C2×D411yescharacteristic
78C2×C4×C29C2×D411yescharacteristic
79C2×C4×C29#4111yescharacteristic
80C2×Dic29—22no—
81C2×Dic29—22no—
82C2×Dic29—22no—
83C2×Dic29—22no—
84C2×Dic29—41no—
85C2×Dic29—41no—
86C2×Dic29—41no—
87C2×Dic29—41no—
88C2×Dic29Q1614yescomplemented
89Dic58—22no—
90Dic58—22no—
91Dic58—22no—
92Dic58—22no—
93Dic58—41no—
94Dic58—41no—
95Dic58—41no—
96Dic58—41no—
97C8×C29—22no—
98#6597—22no—
99#2016—291nomaximal, Sylow
100C22×C29#12011yescharacteristic
101C22×C29#12111yescharacteristic
102C22×C29#12711yescharacteristic
103C22×C29C2×Q1612yes—
104C22×C29#13712yes—
105C4×C29—42no—
106C4×C29—81no—
107C4×C29#12011yescharacteristic
108C4×C29#12011yescharacteristic
109C4×C29#12111yescharacteristic
110C4×C29#12111yescharacteristic
111Dic29—24no—
112Dic29—42no—
113Dic29—42no—
114C22×Q16—291no—
115C22×Q16—291no—
116C2×C4⋊Q8—291no—
117C2×#103—291no—
118C2×#103D2911yescharacteristic
119#391—291no—
120#336—291no—
121C2×C29#39211yescharacteristic
122C2×C29#45112yes—
123C2×C29#46212yes—
124C2×C29#49411yescharacteristic
125C2×C29#49711yescharacteristic
126C22×Q8—291no—
127C22×Q8—291no—
128C22×Q8C2×D2911yescharacteristic
129C2×Q16—582no—
130C2×Q16—582no—
131C2×Q16—582no—
132C2×Q16—582no—
133C2×Q16—582no—
134C2×Q16—582no—
135C22×C8—291no—
136C22×C8C2×D2911yescharacteristic
137C4⋊Q8—582no—
138C4⋊Q8—582no—
139C2×C4⋊C4—582no—
140C2×C4⋊C4C2×D2911yescharacteristic
141C2×C42—291no—
142#103—22no—
143#103—582no—
144#95—582no—
145C29#201611yescharacteristic, complemented, Sylow
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—292no—
152C2×Q8—292no—
153C2×Q8—581no—
154C2×Q8—581no—
155C2×Q8—581no—
156C2×Q8—581no—
157C2×Q8—581no—
158C2×Q8—581no—
159C2×Q8—581no—
160C2×Q8—581no—
161C2×Q8—581no—
162C2×Q8—581no—
163C2×Q8D11612yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—292no—
167C22×C4—581no—
168C22×C4—581no—
169C22×C4C22×D2911yescharacteristic
170Q16—588no—
171Q16—588no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—292no—
175C2×C8—581no—
176C2×C8—581no—
177C2×C8C22⋊D2912yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—588no—
181C42—581no—
182C42—581no—
183C23D4×D2911yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—582no—
189Q8—582no—
190Q8—582no—
191Q8—582no—
192Q8—1161no—
193Q8—1161no—
194Q8—1161no—
195Q8—1161no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—294no—
202C2×C4—582no—
203C2×C4—582no—
204C2×C4—582no—
205C2×C4—582no—
206C2×C4—1161no—
207C2×C4—1161no—
208C2×C4—1161no—
209C2×C4—1161no—
210C2×C4C2×D11611yescharacteristic
211C2×C4#9080511yescharacteristic
212C2×C4D4×D2911yescharacteristic
213C2×C4D4×D2911yescharacteristic
214C2×C4D4×D2911yescharacteristic
215C2×C4C2×C22⋊D2911yescharacteristic
216C8—22no—
217C8—582no—
218C22#1174524411yescharacteristic
219C22#1174524611yescharacteristic
220C22#1174527712yes—
221C22Q16×D2912yes—
222C22#1174530211yescharacteristic
223C4—42no—
224C4—81no—
225C4—584no—
226C4—1162no—
227C4—1162no—
228C4#1174524411yescharacteristic
229C4#1174524611yescharacteristic
230C4#1174529211yescharacteristic
231C4#1174529911yescharacteristic
232C2#1427107211yescharacteristic
233C2#1427132012yes—
234C2#1427137212yes—
235C2#1427154111yescharacteristic
236C2#1427155411yescharacteristic
subgroupG/H
centerC23D4×D29
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC2×C29×#103C2
socle, prime radicalC23×C29C2×D4
hypercenterC2×#103D29
hypocenterC29#2016
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
88. C2×Dic29Q16semidirect
145. C29#2016semidirect

Maximal subgroups

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

subgroupindex
C22×Dic1162
C22×#907852
C2×#117453062
C2×#117451582
#142710682
#142709172
C2×C29×#1032
#201629