Finite Group Databasebeta

← #16829144

Subgroups — #16829144

Order 3712.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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×#90785C211yesmaximal, characteristic, complemented
2C2×#11745310C211yesmaximal, characteristic
3#14271734C211yesmaximal, characteristic
4#14271419C214yesmaximal, complemented
5#14271402C214yesmaximal, complemented
6#14271199C211yesmaximal, characteristic, complemented
7#14271172C211yesmaximal, characteristic, complemented
8#14271171C211yesmaximal, characteristic, complemented
9C29×#536C211yesmaximal, characteristic
10C2×#41×C29C2211yescharacteristic
11C22×Q8×C29C2211yescharacteristic
12C22×Dic58C2211yescharacteristic
13C29×C4⋊Q8—21no—
14C29×#124—21no—
15C29×#123—22no—
16C29×C22⋊Q8C2214yes—
17C29×#117C2211yescharacteristic
18#11745310—24no—
19#11745306—21no—
20C2×#90785—24no—
21C2×#90785C2212yes—
22C2×#90785C2212yes—
23#11745298—21no—
24#11745297—22no—
25#11745288C2211yescharacteristic
26#11745286C2214yes—
27C2×#90777C2212yes—
28C2×#90777C2211yescharacteristic
29C22×#6597C2212yes—
30C22×#6597C2211yescharacteristic
31#11745183C2214yes—
32#11745158C2214yes—
33#11745156C2212yes—
34#11745155C2212yes—
35#41×C29—22no—
36#41×C29—22no—
37C2×Q8×C29—21no—
38C2×Q8×C29—22no—
39C2×Q8×C29—22no—
40C2×Q8×C29D411yescharacteristic
41C2×Q8×C29C2312yes—
42C2×D4×C29D412yes—
43C2×D4×C29D411yescharacteristic
44C22×C4×C29—21no—
45C22×C4×C29C2312yes—
46C22×C4×C29C2311yescharacteristic
47C22×Dic29—21no—
48C2×Dic58—22no—
49C2×Dic58—22no—
50C2×Dic58—21no—
51C2×Dic58C2312yes—
52C4⋊C4×C29—24no—
53C4⋊C4×C29C2312yes—
54C22⋊C4×C29—21no—
55C22⋊C4×C29—24no—
56C42×C29—21no—
57C22⋊Dic29—24no—
58C22⋊Dic29—21no—
59#90785—24no—
60#90785—24no—
61C4⋊Dic29C2312yes—
62#90779—24no—
63C4×Dic29—21no—
64#90777—22no—
65#90777—24no—
66C2×#6597—24no—
67C2×#6597D414yes—
68C2×#6597C2312yes—
69C2×#6597C2311yescharacteristic
70C2×#6597C2311yescharacteristic
71C23×C29C2×D412yes—
72C23×C29C2×D411yescharacteristic
73Q8×C29—22no—
74Q8×C29—22no—
75Q8×C29—22no—
76Q8×C29—42no—
77D4×C29—24no—
78D4×C29—22no—
79C2×C4×C29—22no—
80C2×C4×C29—22no—
81C2×C4×C29—22no—
82C2×C4×C29—22no—
83C2×C4×C29—42no—
84C2×C4×C29C2×D412yes—
85C2×C4×C29C2×D412yes—
86C2×C4×C29C2×D411yescharacteristic
87C2×C4×C29#4112yes—
88C2×C4×C29C2411yescharacteristic
89C2×Dic29—22no—
90C2×Dic29—22no—
91C2×Dic29—42no—
92Dic58—22no—
93Dic58—22no—
94Dic58—42no—
95#6597—22no—
96#6597C2×D412yes—
97#6597C2×D412yes—
98#3059—291nomaximal, Sylow
99C22×C29—22no—
100C22×C29—22no—
101C22×C29—24no—
102C22×C29#12112yes—
103C22×C29C22×D411yescharacteristic
104C4×C29—22no—
105C4×C29—42no—
106C4×C29—42no—
107C4×C29#12112yes—
108C4×C29C22×D411yescharacteristic
109C4×C29C2×#4111yescharacteristic
110Dic29—42no—
111Dic29—42no—
112C22×Q16—291no—
113C2×#131—291no—
114#536—291no—
115#536D2911yescharacteristic
116#470—294no—
117#467—294no—
118#427—291no—
119#419—291no—
120#419—291no—
121C2×C29—22no—
122C2×C29—42no—
123C2×C29C2×#12111yescharacteristic
124C2×C29#57812yes—
125C2×#41C2×D2911yescharacteristic
126C22×Q8—291no—
127C22×Q8C2×D2911yescharacteristic
128C2×Q16—292no—
129C2×Q16—292no—
130C2×Q16—584no—
131#131—584no—
132C2×M16—291no—
133C2×M16—292no—
134C22×C8—291no—
135C22×C8—292no—
136C4⋊Q8—21no—
137C4⋊Q8—581no—
138#124—21no—
139#124—581no—
140#123—22no—
141#123—582no—
142C22⋊Q8—294no—
143C22⋊Q8C2×D2914yes—
144#117—291no—
145#117C2×D2911yescharacteristic
146#107—292no—
147#106—292no—
148#103—294no—
149#103—294no—
150C29#305911yescharacteristic, complemented, Sylow
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—292no—
157C2×Q8—581no—
158C2×Q8—582no—
159C2×Q8—582no—
160C2×Q8C22⋊D2911yescharacteristic
161C2×Q8C22×D2912yes—
162C2×D4C22⋊D2912yes—
163C2×D4C22⋊D2911yescharacteristic
164C22×C4—21no—
165C22×C4—581no—
166C22×C4C22×D2912yes—
167C22×C4C22×D2911yescharacteristic
168Q16—584no—
169Q16—584no—
170M16—584no—
171M16—582no—
172C2×C8—294no—
173C2×C8—291no—
174C2×C8—291no—
175C2×C8—292no—
176C2×C8—584no—
177C4⋊C4—24no—
178C4⋊C4—292no—
179C4⋊C4—584no—
180C4⋊C4C22×D2912yes—
181C22⋊C4—21no—
182C22⋊C4—24no—
183C22⋊C4—581no—
184C22⋊C4—584no—
185C42—21no—
186C42—581no—
187C23C2×C22⋊D2912yes—
188C23C2×C22⋊D2911yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—582no—
194Q8—582no—
195Q8—1162no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—582no—
204C2×C4—582no—
205C2×C4—1162no—
206C2×C4D4×D2912yes—
207C2×C4#9080712yes—
208C2×C4C2×C22⋊D2912yes—
209C2×C4C2×C22⋊D2911yescharacteristic
210C2×C4C23×D2911yescharacteristic
211C8—292no—
212C8—292no—
213C8—582no—
214C22—22no—
215C22—22no—
216C22—24no—
217C22#1174530112yes—
218C22C22×C22⋊D2911yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—1162no—
223C4—1162no—
224C4#1174530112yes—
225C4C2×D4×D2911yescharacteristic
226C4C2×#9080711yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#1174530111yescharacteristic
230C2#1427197812yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#536C2
socleC22×C29C22×D4
prime radicalC2×#41×C29C22
hypercenter#536D29
hypocenterC29#3059
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C22×#90785C2semidirect
4. #14271419C2semidirect
5. #14271402C2semidirect
6. #14271199C2semidirect
7. #14271172C2semidirect
8. #14271171C2semidirect
150. C29#3059semidirect

Maximal subgroups

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

subgroupindex
C22×#907852
C2×#117453102
#142717342
#142714192
#142714022
#142711992
#142711722
#142711712
C29×#5362
#305929