Finite Group Databasebeta

← C29×#1996 #16815710

Subgroups — C29×#1996 #16815710

Order 3712.

324 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 116 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×C29×C22⋊Q8C211yesmaximal, characteristic
2C29×#380C211yesmaximal, characteristic
3C4×C22⋊C4×C29C211yesmaximal, characteristic
4C29×#342C214yesmaximal
5C22×Q8×C29C411yescharacteristic, complemented
6C23×C4×C29C2211yescharacteristic
7C29×C22⋊Q8—21no—
8C29×C22⋊Q8—21no—
9C29×C22⋊Q8—21no—
10C29×C22⋊Q8—21no—
11C2×C4⋊C4×C29—21no—
12C2×C4⋊C4×C29C411yescharacteristic, complemented
13C2×C4⋊C4×C29C412yescomplemented
14C2×C22⋊C4×C29C2212yes—
15C2×C22⋊C4×C29C2212yes—
16C2×C22⋊C4×C29C2212yes—
17C2×C42×C29—21no—
18C29×#95—21no—
19C29×#95—21no—
20C24×C29C2311yescharacteristic
21C2×Q8×C29—21no—
22C2×Q8×C29—21no—
23C2×Q8×C29—42no—
24C22×C4×C29—22no—
25C22×C4×C29—22no—
26C22×C4×C29—42no—
27C22×C4×C29C2×C411yescharacteristic
28C22×C4×C29C2×C412yes—
29C22×C4×C29C2×C412yes—
30C22×C4×C29C2×C411yescharacteristic
31C22×C4×C29D411yescharacteristic
32C22×C4×C29D411yescharacteristic
33C22×C4×C29D411yescharacteristic
34C22×C4×C29D411yescharacteristic
35C4⋊C4×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29—22no—
38C4⋊C4×C29—22no—
39C4⋊C4×C29—42no—
40C22⋊C4×C29—22no—
41C22⋊C4×C29—22no—
42C22⋊C4×C29—22no—
43C22⋊C4×C29—24no—
44C22⋊C4×C29Q814yescomplemented
45C42×C29—42no—
46C23×C29—41no—
47C23×C29—41no—
48C23×C29C22×C411yescharacteristic
49C23×C29C2×D411yescharacteristic
50C23×C29C2×D411yescharacteristic
51C23×C29C2×Q812yes—
52C23×C29#4112yes—
53Q8×C29—42no—
54Q8×C29—42no—
55C2×C4×C29—22no—
56C2×C4×C29—22no—
57C2×C4×C29—22no—
58C2×C4×C29—22no—
59C2×C4×C29—22no—
60C2×C4×C29—24no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29—42no—
65C2×C4×C29—42no—
66C2×C4×C29—42no—
67C2×C4×C29—42no—
68C2×C4×C29—42no—
69C2×C4×C29—42no—
70C2×C4×C29—42no—
71C2×C4×C29C22⋊C411yescharacteristic
72C2×C4×C29C22⋊C411yescharacteristic
73C2×C4×C29C22⋊C411yescharacteristic
74C2×C4×C29C22⋊C411yescharacteristic
75#1996C2911yesmaximal, characteristic, direct product factor, Sylow
76C22×C29—21no—
77C22×C29—21no—
78C22×C29—21no—
79C22×C29—21no—
80C22×C29—21no—
81C22×C29—21no—
82C22×C29—42no—
83C22×C29—42no—
84C22×C29C2×C22⋊C411yescharacteristic
85C22×C29C4×Q812yes—
86C22×C29C22⋊Q812yes—
87C22×C29#12411yescharacteristic
88C22×C29C4⋊Q811yescharacteristic
89C4×C29—21no—
90C4×C29—21no—
91C4×C29—21no—
92C4×C29—44no—
93C4×C29—42no—
94C4×C29—42no—
95C4×C29—82no—
96C4×C29#9912yes—
97C2×C22⋊Q8C2×C2911yescharacteristic
98#380C2×C2911yescharacteristic
99C4×C22⋊C4C2×C2911yescharacteristic
100#342C2×C2914yes—
101C2×C29—22no—
102C2×C29—21no—
103C2×C29—22no—
104C2×C29—21no—
105C2×C29#39111yescharacteristic
106C2×C29C2×#9911yescharacteristic
107C2×C29#41011yescharacteristic
108C22×Q8C4×C2911yescharacteristic, complemented
109C23×C4C22×C2911yescharacteristic
110C22⋊Q8—21no—
111C22⋊Q8—21no—
112C22⋊Q8—21no—
113C22⋊Q8—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4C4×C2911yescharacteristic, complemented
116C2×C4⋊C4C4×C2912yescomplemented
117C2×C22⋊C4C22×C2912yes—
118C2×C22⋊C4C22×C2912yes—
119C2×C22⋊C4C22×C2912yes—
120C2×C42—21no—
121#95—21no—
122#95—21no—
123C29#199611yescharacteristic, direct product factor, Sylow
124C24C23×C2911yescharacteristic
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—42no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—42no—
131C22×C4C2×C4×C2911yescharacteristic
132C22×C4C2×C4×C2912yes—
133C22×C4C2×C4×C2912yes—
134C22×C4C2×C4×C2911yescharacteristic
135C22×C4D4×C2911yescharacteristic
136C22×C4D4×C2911yescharacteristic
137C22×C4D4×C2911yescharacteristic
138C22×C4D4×C2911yescharacteristic
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—42no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—22no—
147C22⋊C4—24no—
148C22⋊C4Q8×C2914yescomplemented
149C42—42no—
150C23—41no—
151C23—41no—
152C23C22×C4×C2911yescharacteristic
153C23C2×D4×C2911yescharacteristic
154C23C2×D4×C2911yescharacteristic
155C23C2×Q8×C2912yes—
156C23#41×C2912yes—
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4C22⋊C4×C2911yescharacteristic
176C2×C4C22⋊C4×C2911yescharacteristic
177C2×C4C22⋊C4×C2911yescharacteristic
178C2×C4C22⋊C4×C2911yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×C22⋊C4×C2911yescharacteristic
188C22C4×Q8×C2912yes—
189C22C29×C22⋊Q812yes—
190C22C29×#12411yescharacteristic
191C22C29×C4⋊Q811yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—44no—
196C4—42no—
197C4—42no—
198C4—82no—
199C4C29×#9912yes—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2C29×#39111yescharacteristic
205C2C2×C29×#9911yescharacteristic
206C2C29×#41011yescharacteristic
subgroupG/H
center, socleC22×C29C2×C22⋊C4
commutatorC23C22×C4×C29
Frattini, cosocleC24C23×C29
prime radicalC24×C29C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
5. C22×Q8×C29C4semidirect
12. C2×C4⋊C4×C29C4semidirect
13. C2×C4⋊C4×C29C4semidirect
44. C22⋊C4×C29Q8semidirect
75. #1996C29direct (N × H)
108. C22×Q8C4×C29semidirect
115. C2×C4⋊C4C4×C29semidirect
116. C2×C4⋊C4C4×C29semidirect
123. C29#1996direct (N × H)
148. C22⋊C4Q8×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×C22⋊Q82
C29×#3802
C4×C22⋊C4×C292
C29×#3422
#199629