Finite Group Databasebeta

← #16819506

Subgroups — #16819506

Order 3712.

292 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11745249C211yesmaximal, characteristic
2C2×#11745162C211yesmaximal, characteristic
3C2×#11745164C211yesmaximal, characteristic
4C2×#11745158C211yesmaximal, characteristic
5#14271028C211yesmaximal, characteristic
6#14270925C211yesmaximal, characteristic
7C29×#340C211yesmaximal, characteristic
8C22×Dic58C2211yescharacteristic
9C22×C8×C29C2211yescharacteristic
10C2×C4⋊C4×C29C2211yescharacteristic
11C2×C4⋊C4×C29C2211yescharacteristic
12C2×C4⋊Dic29C2211yescharacteristic
13C2×#90779—21no—
14C2×C4×Dic29—21no—
15C2×C4×Dic29C2211yescharacteristic
16C22×#6597C2211yescharacteristic
17#11745249—22no—
18#11745249C414yescomplemented
19#11745179—21no—
20#11745179—21no—
21#11745164—22no—
22#11745162—22no—
23#11745158—22no—
24C22×C4×C29—21no—
25C22×C4×C29—21no—
26C22×C4×C29C2311yescharacteristic
27C22×Dic29—21no—
28C22×Dic29—21no—
29C22×Dic29D411yescharacteristic
30C22×Dic29D411yescharacteristic
31C2×Dic58—21no—
32C2×Dic58—21no—
33C2×Dic58—21no—
34C2×Dic58C2×C412yes—
35C2×Dic58D412yes—
36C2×Dic58Q812yes—
37C2×C8×C29—21no—
38C2×C8×C29—21no—
39C2×C8×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29C2×C412yes—
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46#90779—24no—
47C4×Dic29—24no—
48C4×Dic29C2×C412yes—
49C4×Dic29D412yes—
50C2×#6597—21no—
51C2×#6597—21no—
52C2×#6597—21no—
53C23×C29C2×D411yescharacteristic
54C2×C4×C29—22no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29C22×C411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×Q811yescharacteristic
64C2×C4×C29#4111yescharacteristic
65C2×C4×C29#4111yescharacteristic
66C2×Dic29—22no—
67C2×Dic29—22no—
68C2×Dic29—22no—
69C2×Dic29—21no—
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—41no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29C22⋊C412yes—
77C2×Dic29C22⋊C412yes—
78Dic58—22no—
79Dic58—22no—
80Dic58—22no—
81Dic58C4⋊C414yes—
82C8×C29—41no—
83#6597—41no—
84#1805—291nomaximal, Sylow
85C22×C29C2×C22⋊C411yescharacteristic
86C22×C29#12111yescharacteristic
87C22×C29C22⋊Q811yescharacteristic
88C22×C29#13511yescharacteristic
89C22×C29#13511yescharacteristic
90C22×C29#13711yescharacteristic
91C22×C29#13711yescharacteristic
92C4×C29—42no—
93C4×C29—81no—
94C4×C29C2×C4⋊C411yescharacteristic
95C4×C29#11711yescharacteristic
96C4×C29#12111yescharacteristic
97C4×C29C22⋊Q811yescharacteristic
98Dic29—24no—
99Dic29—22no—
100Dic29—22no—
101Dic29—81no—
102C2×C4×Q8—291no—
103C2×C4⋊C8—291no—
104C2×#103—291no—
105C2×#103—291no—
106#382—291no—
107#340—291no—
108#340D2911yescharacteristic
109C2×C29#38011yescharacteristic
110C2×C29#41611yescharacteristic
111C2×C29#41911yescharacteristic
112C2×C29#46411yescharacteristic
113C2×C29#46411yescharacteristic
114C2×C29#47911yescharacteristic
115C2×C29#47911yescharacteristic
116C22×Q8—291no—
117C22×C8—291no—
118C22×C8C2×D2911yescharacteristic
119C4×Q8—294no—
120C4×Q8—582no—
121C2×C4⋊C4—291no—
122C2×C4⋊C4—581no—
123C2×C4⋊C4C2×D2911yescharacteristic
124C2×C4⋊C4C2×D2911yescharacteristic
125C2×C42—291no—
126C2×C42—581no—
127C4⋊C8—582no—
128#103—582no—
129#103—582no—
130#95—581no—
131#95—581no—
132C29#180511yescharacteristic, complemented, Sylow
133C2×Q8—292no—
134C2×Q8—292no—
135C2×Q8—292no—
136C2×Q8—581no—
137C2×Q8—581no—
138C2×Q8—581no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—291no—
142C22×C4—291no—
143C22×C4—581no—
144C22×C4—581no—
145C22×C4C22×D2911yescharacteristic
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—581no—
150C2×C8—581no—
151C2×C8—581no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—584no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4C4×D2912yes—
159C42—292no—
160C42—292no—
161C42—584no—
162C23D4×D2911yescharacteristic
163Q8—294no—
164Q8—582no—
165Q8—582no—
166Q8—582no—
167C2×C4—22no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—292no—
174C2×C4—292no—
175C2×C4—581no—
176C2×C4—582no—
177C2×C4—582no—
178C2×C4—582no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—1161no—
183C2×C4—1161no—
184C2×C4—1161no—
185C2×C4C2×C4×D2911yescharacteristic
186C2×C4#9080511yescharacteristic
187C2×C4#9080511yescharacteristic
188C2×C4D4×D2911yescharacteristic
189C2×C4D4×D2911yescharacteristic
190C2×C4Q8×D2911yescharacteristic
191C8—41no—
192C8—1161no—
193C22C22⋊C4×D2911yescharacteristic
194C22#1174524611yescharacteristic
195C22#1174525811yescharacteristic
196C22#1174527411yescharacteristic
197C22#1174527711yescharacteristic
198C22#1174527811yescharacteristic
199C22#1174528011yescharacteristic
200C4—42no—
201C4—81no—
202C4—584no—
203C4—582no—
204C4—582no—
205C4—2321no—
206C4#1174523411yescharacteristic
207C4#1174524611yescharacteristic
208C4C4⋊C4×D2911yescharacteristic
209C4#1174525811yescharacteristic
210C2#1427102211yescharacteristic
211C2#1427115611yescharacteristic
212C2#1427117011yescharacteristic
213C2#1427138411yescharacteristic
214C2#1427138811yescharacteristic
215C2#1427146911yescharacteristic
216C2#1427147311yescharacteristic
subgroupG/H
centerC23D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#340C2
socle, prime radicalC23×C29C2×D4
cosocleC22×C4×C29C23
hypercenter#340D29
hypocenterC29#1805
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
18. #11745249C4semidirect
132. C29#1805semidirect

Maximal subgroups

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

subgroupindex
C2×#117452492
C2×#117451622
C2×#117451642
C2×#117451582
#142710282
#142709252
C29×#3402
#180529