Finite Group Databasebeta

← #49159935

Subgroups — #49159935

Order 37504.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22627615C211yesmaximal, characteristic
2C2×#22627549C211yesmaximal, characteristic
3C2×#22627547C211yesmaximal, characteristic
4#34036034C211yesmaximal, characteristic
5#34035891C211yesmaximal, characteristic
6#34035883C211yesmaximal, characteristic
7#340×C293C211yesmaximal, characteristic
8C22×Dic586C2211yescharacteristic
9C22×#14556873C2211yescharacteristic
10#22627615—22no—
11#22627615—22no—
12C2×C4⋊Dic293—21no—
13C2×C4⋊Dic293C2211yescharacteristic
14C2×#17989781—21no—
15C2×C4×Dic293C2211yescharacteristic
16#22627549—22no—
17#22627547—22no—
18#22627531—21no—
19#22627531—21no—
20C22×C8×C293C2211yescharacteristic
21C2×C4⋊C4×C293C2211yescharacteristic
22C2×C4⋊C4×C293C2211yescharacteristic
23C2×Dic586—21no—
24C2×Dic586—21no—
25C2×Dic586—21no—
26C2×Dic586—21no—
27C2×Dic586—21no—
28C2×Dic586Q812yes—
29C22×Dic293—21no—
30C22×Dic293—21no—
31C22×Dic293D411yescharacteristic
32C22×Dic293D411yescharacteristic
33C2×#14556873—21no—
34C2×#14556873—21no—
35C2×#14556873—21no—
36C4⋊Dic293—24no—
37C4⋊Dic293—21no—
38C4⋊Dic293D412yes—
39#17989781—24no—
40C4×Dic293—21no—
41C4×Dic293—21no—
42C22×C4×C293—21no—
43C22×C4×C293—21no—
44C22×C4×C293C2311yescharacteristic
45C2×C8×C293—21no—
46C2×C8×C293—21no—
47C2×C8×C293—21no—
48C4⋊C4×C293—21no—
49C4⋊C4×C293—21no—
50C4⋊C4×C293—21no—
51C4⋊C4×C293D412yes—
52Dic586—22no—
53Dic586—22no—
54Dic586—41no—
55Dic586—41no—
56C2×Dic293—21no—
57C2×Dic293—21no—
58C2×Dic293—22no—
59C2×Dic293—22no—
60C2×Dic293—21no—
61C2×Dic293—21no—
62C2×Dic293—21no—
63C2×Dic293—21no—
64C2×Dic293—41no—
65C2×Dic293—41no—
66C2×Dic293—41no—
67C2×Dic293—41no—
68#14556873—41no—
69C23×C293C2×D411yescharacteristic
70C2×C4×C293—22no—
71C2×C4×C293—41no—
72C2×C4×C293—41no—
73C2×C4×C293—41no—
74C2×C4×C293—41no—
75C2×C4×C293—41no—
76C2×C4×C293C2×D411yescharacteristic
77C2×C4×C293C2×D411yescharacteristic
78C2×C4×C293C2×Q811yescharacteristic
79C2×C4×C293#4111yescharacteristic
80C2×C4×C293#4111yescharacteristic
81C2×C4×C293#4111yescharacteristic
82C8×C293—41no—
83C22×C293#12011yescharacteristic
84C22×C293C22⋊Q811yescharacteristic
85C22×C293#12411yescharacteristic
86C22×C293#13511yescharacteristic
87C22×C293#13511yescharacteristic
88C22×C293#13711yescharacteristic
89C22×C293#13711yescharacteristic
90C4×C293—42no—
91C4×C293—81no—
92C4×C293C22⋊Q811yescharacteristic
93C4×C293C22⋊Q811yescharacteristic
94C4×C293#12411yescharacteristic
95C4×C293#12411yescharacteristic
96Dic293—42no—
97Dic293—41no—
98Dic293—41no—
99Dic293—42no—
100C2×C293#39311yescharacteristic
101C2×C293#45211yescharacteristic
102C2×C293#45211yescharacteristic
103C2×C293#47911yescharacteristic
104C2×C293#47911yescharacteristic
105C2×C293#48811yescharacteristic
106C2×C293#49111yescharacteristic
107C293#202611yescharacteristic, complemented, Sylow
108#2026—2931nomaximal, Sylow
109C2×#125—2931no—
110C2×#103—2931no—
111C2×#103—2931no—
112#391—2931no—
113#340—2931no—
114#340D29311yescharacteristic
115#336—2931no—
116C22×Q8—2931no—
117C22×C8—2931no—
118C22×C8C2×D29311yescharacteristic
119#125—5862no—
120#125—5862no—
121C2×C4⋊C4—2931no—
122C2×C4⋊C4—5861no—
123C2×C4⋊C4—5861no—
124C2×C4⋊C4C2×D29311yescharacteristic
125C2×C4⋊C4C2×D29311yescharacteristic
126C2×C42—2931no—
127#103—5862no—
128#103—5862no—
129#95—5861no—
130#95—5861no—
131C2×Q8—2932no—
132C2×Q8—5861no—
133C2×Q8—5861no—
134C2×Q8—5861no—
135C2×Q8—5861no—
136C2×Q8—5861no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—2931no—
140C22×C4—2931no—
141C22×C4—5861no—
142C22×C4—5861no—
143C22×C4C22×D29311yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—5861no—
148C2×C8—5861no—
149C2×C8—5861no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—2932no—
154C4⋊C4—5864no—
155C4⋊C4—5864no—
156C4⋊C4—5861no—
157C4⋊C4D117212yes—
158C42—5861no—
159C42—5861no—
160C23D4×D29311yescharacteristic
161Q8—5862no—
162Q8—5862no—
163Q8—11721no—
164Q8—11721no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5861no—
172C2×C4—5861no—
173C2×C4—5862no—
174C2×C4—5862no—
175C2×C4—5861no—
176C2×C4—5861no—
177C2×C4—5861no—
178C2×C4—5861no—
179C2×C4—11721no—
180C2×C4—11721no—
181C2×C4—11721no—
182C2×C4—11721no—
183C2×C4D4×D29311yescharacteristic
184C2×C4C2×D117211yescharacteristic
185C2×C4Q8×D29311yescharacteristic
186C2×C4#1798980111yescharacteristic
187C2×C4#1798980211yescharacteristic
188C2×C4#1798980211yescharacteristic
189C8—41no—
190C8—11721no—
191C22#2262759411yescharacteristic
192C22#2262760211yescharacteristic
193C22#2262761011yescharacteristic
194C22#2262764311yescharacteristic
195C22#2262764511yescharacteristic
196C22#2262765311yescharacteristic
197C22#2262765611yescharacteristic
198C4—42no—
199C4—81no—
200C4—11721no—
201C4—11721no—
202C4—11722no—
203C4—11722no—
204C4#2262760211yescharacteristic
205C4#2262760411yescharacteristic
206C4#2262761011yescharacteristic
207C4#2262761211yescharacteristic
208C2#3403604211yescharacteristic
209C2#3403629211yescharacteristic
210C2#3403629411yescharacteristic
211C2#3403643511yescharacteristic
212C2#3403643911yescharacteristic
213C2#3403648211yescharacteristic
214C2#3403649611yescharacteristic
subgroupG/H
centerC23D4×D293
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
Fitting#340×C293C2
socle, prime radicalC23×C293C2×D4
hypercenter#340D293
hypocenterC293#2026
LCSG ▷ C22×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
107. C293#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#226276152
C2×#226275492
C2×#226275472
#340360342
#340358912
#340358832
#340×C2932
#2026293