Finite Group Databasebeta

← #34011552

Subgroups — #34011552

Order 18688.

306 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 94 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#22626261C211yesmaximal, characteristic
2#22625481C211yesmaximal, characteristic
3#22624948C214yesmaximal, complemented
4#22620442C211yesmaximal, characteristic
5C2×#14556664—21no—
6#17989606—21no—
7#17989508C2212yes—
8C4⋊#11924031—21no—
9#17989450—21no—
10#17989449C2212yes—
11#17989142—21no—
12#17988992C411yescharacteristic
13#17988988—21no—
14#17988988C2212yes—
15#17988983—21no—
16#17988624—21no—
17#17988624C412yes—
18C4×C8×D73C2211yescharacteristic
19#500×C73C411yescharacteristic
20#14556664—42no—
21C2×#11924031—22no—
22C4⋊#10596833—22no—
23#14556648—41no—
24C4×#10596833—41no—
25C2×C8×D73C2×C411yescharacteristic
26C2×C8×D73D411yescharacteristic
27#14556591—21no—
28#14556582—22no—
29#14556571—41no—
30#14556567—41no—
31Q8×Dic73—41no—
32#14556556—41no—
33#14556549—22no—
34C42×D73D411yescharacteristic
35#14556525—21no—
36#14556525C2×C412yes—
37#14556522—22no—
38#14556522—22no—
39C4×#10596831D411yescharacteristic
40C8×Dic73D411yescharacteristic
41C8×Dic73C2311yescharacteristic
42C4⋊Q8×C73—21no—
43#107×C73—21no—
44#107×C73C2×C412yes—
45C4×C8×C73C2×C411yescharacteristic
46C2×#10596833—42no—
47#11924031—42no—
48C2×Dic146—41no—
49C2×C4×D73C22⋊C411yescharacteristic
50C2×C4×D73D811yescharacteristic
51C2×C4×D73SD1611yescharacteristic
52C2×#10596831C22⋊C411yescharacteristic
53C2×#10596831C2×D411yescharacteristic
54C8×D73—22no—
55C8×D73SD1612yes—
56C8×D73Q1612yes—
57C4⋊Dic73—22no—
58C4⋊Dic73—41no—
59C4⋊Dic73—42no—
60#11924007—42no—
61#11924005—42no—
62C4×Dic73—42no—
63C4×Dic73D811yescharacteristic
64C4×Dic73SD1611yescharacteristic
65C4×Dic73C2×D411yescharacteristic
66C2×Q8×C73—41no—
67C2×C8×C73C22⋊C411yescharacteristic
68C2×C8×C73C22×C411yescharacteristic
69C4⋊C4×C73—22no—
70C4⋊C4×C73—41no—
71C42×C73C22⋊C411yescharacteristic
72C22×D73#10211yescharacteristic
73Q8×C73—82no—
74C2×C4×C73—42no—
75C2×C4×C73#10211yescharacteristic
76C2×C4×C73#10211yescharacteristic
77C2×C4×C73C2×C22⋊C411yescharacteristic
78C2×Dic73—42no—
79C2×Dic73#10211yescharacteristic
80C2×Dic73C2×D811yescharacteristic
81C2×Dic73C2×SD1611yescharacteristic
82C4×D73—22no—
83C4×D73—41no—
84C4×D73#10112yes—
85C4×D73#10312yes—
86Dic146—82no—
87#10596833—82no—
88C8×C73—21no—
89C8×C73#10312yes—
90#10596831—21no—
91#10596831C2×SD1611yescharacteristic
92#10596831C2×Q1611yescharacteristic
93C22×C73C2×#10211yescharacteristic
94C2×D73—21no—
95C2×D73—21no—
96C2×D73#33212yes—
97C4×C73—21no—
98C4×C73—82no—
99C4×C73#35912yes—
100C4×C73C2×#10111yescharacteristic
101C4×C73C2×#10311yescharacteristic
102Dic73—21no—
103Dic73—21no—
104Dic73—82no—
105Dic73#33212yes—
106#11934—731nomaximal, Sylow
107C2×C73C2×#33211yescharacteristic
108C2×C73C2×#35911yescharacteristic
109C2×C73#214511yescharacteristic
110D73—22no—
111#3160—731no—
112C2×C4⋊C16—731no—
113#1564—731no—
114#1363—734no—
115C73#1193411yescharacteristic, complemented, Sylow
116#533—1461no—
117C22×C16—1461no—
118#500—731no—
119#500#6440811yescharacteristic
120#499—732no—
121#499—1461no—
122#498—1461no—
123#431—1461no—
124#427—732no—
125#427—1461no—
126C2×C4×C8—731no—
127C4⋊C16—732no—
128C4⋊C16—1461no—
129#335—1461no—
130#334—732no—
131C22×C8—731no—
132C22×C8—731no—
133C4⋊Q8—21no—
134C4⋊Q8—1461no—
135#125—1462no—
136C22⋊Q8—2921no—
137C22⋊Q8—2921no—
138C4×Q8—2921no—
139C4×Q8—2921no—
140#117—1462no—
141C2×C42—731no—
142C2×C16—2922no—
143C2×C16—1462no—
144#107—21no—
145#107—732no—
146#107—1461no—
147#107C2×#6440812yes—
148#106—1462no—
149#106—1462no—
150C4⋊C8—1462no—
151C22⋊C8—2921no—
152C4×C8—2921no—
153C4×C8—731no—
154C4×C8—731no—
155C4×C8—731no—
156C4×C8C2×#6440811yescharacteristic
157C2×Q8—41no—
158C2×Q8—2921no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C2×C8—2922no—
163C2×C8—731no—
164C2×C8—732no—
165C2×C8—732no—
166C2×C8—731no—
167C2×C8—1462no—
168C2×C8C22⋊#6440811yescharacteristic
169C2×C8C22×#6440811yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—2922no—
173C4⋊C4—2922no—
174C4⋊C4—2921no—
175C4⋊C4—1462no—
176C22⋊C4—2922no—
177C42—2922no—
178C42—731no—
179C42—731no—
180C42—731no—
181C42C22⋊#6440811yescharacteristic
182C16—2922no—
183C23—731no—
184Q8—82no—
185Q8—5842no—
186C2×C4—42no—
187C2×C4—2921no—
188C2×C4—2922no—
189C2×C4—731no—
190C2×C4—732no—
191C2×C4—732no—
192C2×C4—731no—
193C2×C4—731no—
194C2×C4—1462no—
195C2×C4#1455665311yescharacteristic
196C2×C4#1455665311yescharacteristic
197C2×C4C2×C22⋊#6440811yescharacteristic
198C8—21no—
199C8—5842no—
200C8—731no—
201C8—731no—
202C8—1461no—
203C8#1455665412yes—
204C22—732no—
205C22—1461no—
206C22—1461no—
207C22C2×#1455665311yescharacteristic
208C4—21no—
209C4—82no—
210C4—5842no—
211C4—732no—
212C4—1461no—
213C4—1461no—
214C4#1798950212yes—
215C4D73⋊#10111yescharacteristic
216C4C2×#1455665411yescharacteristic
217C2—1462no—
218C2D73⋊#33211yescharacteristic
219C2C2×#1798950211yescharacteristic
220C2#2262625211yescharacteristic
subgroupG/H
centerC22C2×#14556653
commutatorC2×C8×C73C22×C4
FrattiniC2×C8C22×#64408
Fitting#500×C73C4
socleC22×C73C2×#102
prime radicalC22×D73#102
cosocleC8×Dic73C23
hypercenter#500#64408
hypocenterC73#11934
LCSG ▷ C2×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #22624948C2semidirect
115. C73#11934semidirect

Maximal subgroups

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

subgroupindex
#226262612
#226254812
#226249482
#226204422
#1193473