Finite Group Databasebeta

← #16818469

Subgroups — #16818469

Order 3712.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271750C211yesmaximal, characteristic
2#14271319C211yesmaximal, characteristic, complemented
3#14271074C211yesmaximal, characteristic, complemented
4#14270901C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic, complemented
7C29×#448C211yesmaximal, characteristic, complemented
8C22×Q8×C29C2211yescharacteristic
9C2×SD16×C29—21no—
10C29×#121C2211yescharacteristic
11C2×#90785—21no—
12#11745301—21no—
13#11745299—21no—
14D4×Dic29—21no—
15C2×#90781—21no—
16C2×#90781C2211yescharacteristic
17#11745286C2211yescharacteristic
18#11745260—21no—
19#11745248—21no—
20#11745247—21no—
21C29×#103—21no—
22C29×C22⋊C8C2211yescharacteristic
23#11745183—21no—
24#11745179—21no—
25#11745179C2211yescharacteristic
26C22⋊#6597C2211yescharacteristic
27C23×D29D411yescharacteristic
28C2×Q8×C29—21no—
29C2×Q8×C29—21no—
30C2×Q8×C29—42no—
31C2×D4×C29—21no—
32C2×D4×C29D411yescharacteristic
33C22×C4×C29—21no—
34C22×C4×C29C2311yescharacteristic
35C2×C22⋊D29—21no—
36C2×C22⋊D29—21no—
37C22×Dic29—21no—
38C22×Dic29—21no—
39C22×Dic29D411yescharacteristic
40C2×Dic58D411yescharacteristic
41SD16×C29—42no—
42C2×C8×C29—21no—
43C4⋊C4×C29D411yescharacteristic
44C22⋊C4×C29—21no—
45C22⋊Dic29—21no—
46C22⋊Dic29—21no—
47#90785—42no—
48#90781—21no—
49#90781—21no—
50#90781—21no—
51#90781—21no—
52#90781—42no—
53C4⋊Dic29—21no—
54C4⋊Dic29D411yescharacteristic
55#90779—21no—
56C4×Dic29—21no—
57C2×#6597—21no—
58C23×C29—21no—
59C23×C29C2×D411yescharacteristic
60C22×D29—21no—
61C22×D29—21no—
62C22×D29—21no—
63C22×D29—41no—
64C22×D29—41no—
65Q8×C29—22no—
66Q8×C29—22no—
67Q8×C29—41no—
68Q8×C29—41no—
69D4×C29—41no—
70D4×C29—41no—
71D4×C29—41no—
72C2×C4×C29—22no—
73C2×C4×C29—21no—
74C2×C4×C29—41no—
75C2×C4×C29—41no—
76C2×C4×C29—41no—
77C2×C4×C29C2×D411yescharacteristic
78C2×C4×C29C2×D411yescharacteristic
79C22⋊D29—81no—
80C22⋊D29—81no—
81C2×Dic29—21no—
82C2×Dic29—21no—
83C2×Dic29—21no—
84C2×Dic29—41no—
85C2×Dic29—41no—
86C2×Dic29—41no—
87C2×Dic29—41no—
88C2×Dic29—81no—
89Dic58—41no—
90C8×C29—41no—
91#6597—41no—
92#1606—291nomaximal, Sylow
93C22×C29—21no—
94C22×C29—21no—
95C22×C29—41no—
96C22×C29—41no—
97C22×C29—41no—
98C22×C29#12011yescharacteristic
99C22×C29#13511yescharacteristic
100C22×C29#13711yescharacteristic
101C2×D29—42no—
102C2×D29—41no—
103C2×D29—41no—
104C2×D29—41no—
105C2×D29—81no—
106C4×C29—21no—
107C4×C29—21no—
108C4×C29—41no—
109C4×C29—42no—
110Dic29—41no—
111Dic29—41no—
112Dic29—41no—
113Dic29—81no—
114#538—291no—
115#451—291no—
116#448D2911yescharacteristic, complemented
117#393—291no—
118#328—291no—
119#327—291no—
120#323—291no—
121C2×C29—21no—
122C2×C29—21no—
123C2×C29—81no—
124C2×C29#45211yescharacteristic
125C2×C29#45511yescharacteristic
126C2×C29B(4,𝔽2)11yescharacteristic
127D29—81no—
128C22×Q8C2×D2911yescharacteristic
129C2×Q16—581no—
130C2×SD16—21no—
131#126—581no—
132#124—581no—
133#123—581no—
134C22⋊Q8—291no—
135#121—581no—
136#121C2×D2911yescharacteristic
137#120—581no—
138C4×D4—581no—
139C2×C22⋊C4—291no—
140C2×C22⋊C4—581no—
141#103—21no—
142#103—581no—
143C22⋊C8—291no—
144C22⋊C8C2×D2911yescharacteristic
145#95—291no—
146#95—581no—
147C29#160611yescharacteristic, complemented, Sylow
148C24—291no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8—291no—
153C2×D4—21no—
154C2×D4—581no—
155C2×D4—581no—
156C2×D4C22⋊D2911yescharacteristic
157C22×C4—21no—
158C22×C4—291no—
159C22×C4—581no—
160C22×C4—581no—
161C22×C4C22×D2911yescharacteristic
162Q16—1162no—
163SD16—42no—
164C2×C8—21no—
165C2×C8—581no—
166C4⋊C4—291no—
167C4⋊C4—581no—
168C4⋊C4—581no—
169C4⋊C4C22⋊D2911yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—581no—
172C22⋊C4—581no—
173C22⋊C4—581no—
174C22⋊C4—581no—
175C22⋊C4—581no—
176C22⋊C4—581no—
177C22⋊C4—1162no—
178C42—581no—
179C23—21no—
180C23—581no—
181C23—581no—
182C23—581no—
183C23—1161no—
184C23—1161no—
185C23D4×D2911yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—1161no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—2321no—
195D4—2321no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—581no—
202C2×C4—581no—
203C2×C4—581no—
204C2×C4—1161no—
205C2×C4—1161no—
206C2×C4—1161no—
207C2×C4—1161no—
208C2×C4—2321no—
209C2×C4D4×D2911yescharacteristic
210C2×C4C2×C22⋊D2911yescharacteristic
211C8—41no—
212C8—1161no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—1162no—
219C22—1161no—
220C22—1161no—
221C22—1161no—
222C22—2321no—
223C22#1174527711yescharacteristic
224C22#1174527811yescharacteristic
225C22#1174529911yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—1161no—
231C4—1161no—
232C4—1161no—
233C4—2321no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—2321no—
238C2#1427132211yescharacteristic
239C2#1427133911yescharacteristic
240C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#448C2
socleC22×C29#120
prime radical#14271750C2
hypercenter#448D29
hypocenterC29#1606
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #14271319C2semidirect
3. #14271074C2semidirect
4. #14270901C2semidirect
5. #14270897C2semidirect
6. #14270886C2semidirect
7. C29×#448C2semidirect
116. #448D29semidirect
147. C29#1606semidirect

Maximal subgroups

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

subgroupindex
#142717502
#142713192
#142710742
#142709012
#142708972
#142708862
C29×#4482
#160629