Finite Group Databasebeta

← #16830867

Subgroups — #16830867

Order 3712.

348 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#14271718C211yesmaximal, characteristic, complemented
2#14271695C211yesmaximal, characteristic
3#14271473C212yesmaximal, complemented
4#14271455C211yesmaximal, characteristic, complemented
5#14271422C212yesmaximal, complemented
6#14271408C212yesmaximal
7#14271384C212yesmaximal, complemented
8#14271374C211yesmaximal, characteristic, complemented
9#14271368C211yesmaximal, characteristic, complemented
10#14271185C211yesmaximal, characteristic, complemented
11C29×#476C211yesmaximal, characteristic, complemented
12C29×C4⋊Q8C2211yescharacteristic
13C4×D4×C29C2211yescharacteristic
14#11745308—21no—
15Q8×Dic29—21no—
16#11745300C2211yescharacteristic
17#11745298C2211yescharacteristic
18C2×#90783C2212yes—
19C4×C22⋊D29—21no—
20#11745288—21no—
21C2×Dic116C2212yes—
22C2×#90772C2212yes—
23#11745259C2212yes—
24#11745259C2211yescharacteristic
25#11745254—21no—
26#11745252—21no—
27#11745252C2211yescharacteristic
28#11745249C2212yes—
29#11745245—21no—
30#11745241—21no—
31C42×D29C2211yescharacteristic
32#11745231C2211yescharacteristic
33C4×Dic58C2211yescharacteristic
34C29×#106C2212yes—
35C29×C4⋊C8C2211yescharacteristic
36C29×#102C2212yes—
37#11745164C2212yes—
38#11745162C2212yes—
39#11745158C2212yes—
40#11745158C2212yes—
41#11745155C2212yes—
42C4⋊#6597C2211yescharacteristic
43C2×Q8×C29—21no—
44C2×D4×C29C2311yescharacteristic
45C22×C4×C29—21no—
46C2×C22⋊D29—21no—
47C2×C4×D29D411yescharacteristic
48C2×C4×D29D411yescharacteristic
49C2×C4×D29C2311yescharacteristic
50C2×Dic58C2312yes—
51C2×Dic58C2311yescharacteristic
52C2×C8×C29C2312yes—
53C4⋊C4×C29—21no—
54C4⋊C4×C29C2311yescharacteristic
55C4⋊C4×C29C2312yes—
56C22⋊C4×C29—21no—
57C42×C29C2311yescharacteristic
58C22⋊Dic29—21no—
59C22⋊Dic29—21no—
60C22⋊Dic29—21no—
61#90783—42no—
62#90781—21no—
63#90781—22no—
64C4⋊Dic29—21no—
65C4⋊Dic29—21no—
66C4⋊Dic29—21no—
67C4⋊Dic29—21no—
68C4⋊Dic29—22no—
69C4⋊Dic29C2311yescharacteristic
70#90779—21no—
71#90779—21no—
72#90779—22no—
73C4×Dic29—21no—
74C4×Dic29—22no—
75C4×Dic29D411yescharacteristic
76C4×Dic29D411yescharacteristic
77C4×Dic29C2311yescharacteristic
78C2×#6597C2312yes—
79Dic116—42no—
80#90772—42no—
81C23×C29—21no—
82C22×D29C2×D411yescharacteristic
83Q8×C29—42no—
84D4×C29—21no—
85D4×C29—21no—
86C2×C4×C29—22no—
87C2×C4×C29—21no—
88C2×C4×C29—42no—
89C2×C4×C29C2×D411yescharacteristic
90C2×C4×C29C2×D411yescharacteristic
91C2×C4×C29C2411yescharacteristic
92C22⋊D29—42no—
93C2×Dic29—21no—
94C2×Dic29—22no—
95C2×Dic29—21no—
96C2×Dic29C2×D411yescharacteristic
97C2×Dic29C2×D411yescharacteristic
98C2×Dic29C2×D411yescharacteristic
99C4×D29—22no—
100C4×D29—21no—
101C4×D29—21no—
102C4×D29—41no—
103Dic58—21no—
104Dic58—22no—
105Dic58—22no—
106Dic58—21no—
107C8×C29—22no—
108#6597—22no—
109#3252—291nomaximal, Sylow
110C22×C29—41no—
111C22×C29—41no—
112C22×C29—41no—
113C22×C29C22×D411yescharacteristic
114C2×D29—21no—
115C2×D29—21no—
116C2×D29—21no—
117C4×C29—21no—
118C4×C29—41no—
119C4×C29—42no—
120C4×C29#13712yes—
121C4×C29H(5,𝔽2)11yescharacteristic
122C4×C292−1+411yescharacteristic
123Dic29—21no—
124Dic29—21no—
125Dic29—21no—
126Dic29—41no—
127Dic29—42no—
128Dic29—41no—
129#533—291no—
130#529—291no—
131#479—292no—
132#477—291no—
133#476D2911yescharacteristic, complemented
134#470—292no—
135#468—292no—
136#464—292no—
137#462—291no—
138#461—291no—
139#423—291no—
140C2×C29—81no—
141C2×C29#53711yescharacteristic
142C2×C29C2×#13711yescharacteristic
143C2×C29#57511yescharacteristic
144D29—41no—
145C2×Q16—292no—
146C2×SD16—292no—
147C2×M16—292no—
148C4⋊Q8—291no—
149C4⋊Q8C2×D2911yescharacteristic
150#126—581no—
151#125—291no—
152#125—581no—
153#124—291no—
154#123—581no—
155C22⋊Q8—291no—
156C22⋊Q8—292no—
157C22⋊Q8—581no—
158#121—291no—
159C4×Q8—292no—
160C4×Q8—291no—
161C4×Q8—581no—
162C4×D4—581no—
163C4×D4C2×D2911yescharacteristic
164#117—581no—
165#117—581no—
166C2×C42—291no—
167#107—292no—
168#106C2×D2912yes—
169C4⋊C8—292no—
170C4⋊C8—291no—
171C4⋊C8C2×D2911yescharacteristic
172#103—292no—
173#103—292no—
174#103—292no—
175#102C2×D2912yes—
176C29#325211yescharacteristic, complemented, Sylow
177C2×Q8—21no—
178C2×Q8—291no—
179C2×Q8—292no—
180C2×D4—581no—
181C2×D4C22×D2911yescharacteristic
182C22×C4—21no—
183C22×C4—291no—
184C22×C4—291no—
185C22×C4—291no—
186Q16—1162no—
187SD16—1162no—
188M16—1162no—
189C2×C8—292no—
190C2×C8C22×D2912yes—
191C4⋊C4—21no—
192C4⋊C4—291no—
193C4⋊C4—581no—
194C4⋊C4—581no—
195C4⋊C4—581no—
196C4⋊C4—582no—
197C4⋊C4—582no—
198C4⋊C4—581no—
199C4⋊C4—581no—
200C4⋊C4—581no—
201C4⋊C4C22×D2912yes—
202C4⋊C4C22×D2911yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—582no—
205C22⋊C4—581no—
206C22⋊C4—581no—
207C22⋊C4—581no—
208C22⋊C4—581no—
209C42—291no—
210C42—291no—
211C42—291no—
212C42—582no—
213C42—581no—
214C42C22×D2911yescharacteristic
215C23—21no—
216C23—291no—
217Q8—42no—
218Q8—581no—
219Q8—582no—
220Q8—582no—
221Q8—581no—
222D4—21no—
223D4—21no—
224D4—1162no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—291no—
229C2×C4—291no—
230C2×C4—291no—
231C2×C4—581no—
232C2×C4—581no—
233C2×C4—582no—
234C2×C4—581no—
235C2×C4—581no—
236C2×C4—582no—
237C2×C4—1161no—
238C2×C4D4×D2911yescharacteristic
239C2×C4D4×D2911yescharacteristic
240C2×C4C23×D2911yescharacteristic
241C8—22no—
242C8—582no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—581no—
247C22—581no—
248C22—581no—
249C22C2×D4×D2911yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—581no—
254C4—581no—
255C4—581no—
256C4—1161no—
257C4—1161no—
258C4—1162no—
259C4#1174527712yes—
260C4#1174536211yescharacteristic
261C4#1174536411yescharacteristic
262C2—81no—
263C2—1161no—
264C2#1427174311yescharacteristic
265C2C2×#1174527711yescharacteristic
266C2#1427195911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#476C2
socleC22×C29C22×D4
prime radical#11745300C22
hypercenter#476D29
hypocenterC29#3252
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #14271718C2semidirect
3. #14271473C2semidirect
4. #14271455C2semidirect
5. #14271422C2semidirect
7. #14271384C2semidirect
8. #14271374C2semidirect
9. #14271368C2semidirect
10. #14271185C2semidirect
11. C29×#476C2semidirect
133. #476D29semidirect
176. C29#3252semidirect

Maximal subgroups

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

subgroupindex
#142717182
#142716952
#142714732
#142714552
#142714222
#142714082
#142713842
#142713742
#142713682
#142711852
C29×#4762
#325229