Finite Group Databasebeta

← #34000381

Subgroups — #34000381

Order 18688.

248 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 62 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#22626168C211yesmaximal, characteristic
2#22625686C211yesmaximal, characteristic
3#22611544C211yesmaximal, characteristic
4#17989643—21no—
5#17989573C411yescharacteristic
6#17989566C411yescharacteristic
7#17989550—21no—
8#17989484—21no—
9#17989483C412yescomplemented
10#17989469—21no—
11C2×#14556597C2211yescharacteristic
12C2×#14556531C411yescharacteristic, complemented
13#17988366—21no—
14#17988366—21no—
15C22×C16×C73C411yescharacteristic, complemented
16D73⋊M16—21no—
17#14556670—21no—
18#14556666—41no—
19#14556665—22no—
20#14556664—41no—
21#14556652C812yes—
22#14556651—21no—
23#14556650C812yes—
24#14556649—21no—
25#14556645—41no—
26C8×#64408—41no—
27C2×#11924028C2×C411yescharacteristic
28#14556597—41no—
29#14556597—41no—
30C2×#11924012C2×C411yescharacteristic
31C2×#11924011D411yescharacteristic
32C2×#11924011Q811yescharacteristic
33C2×C8×D73D411yescharacteristic
34C2×C8×D73D411yescharacteristic
35#14556531—41no—
36C2×#11924003—21no—
37C22×C8×C73C2×C411yescharacteristic
38C2×C16×C73—21no—
39C2×C16×C73—41no—
40#11924038—41no—
41#11924037—22no—
42#11924036—41no—
43C4⋊#64408—41no—
44C22⋊#64408—22no—
45C4×#64408—41no—
46#11924031—42no—
47#11924028—41no—
48#11924028—41no—
49C2×Dic146C2×C811yescharacteristic
50C2×D292C2×C811yescharacteristic
51C2×C22⋊D73M1611yescharacteristic
52C2×C22⋊D73M1611yescharacteristic
53C2×C4×D73C22⋊C411yescharacteristic
54C2×C4×D73C4⋊C411yescharacteristic
55#11924012—41no—
56#11924011—41no—
57#11924011—41no—
58C2×#10596831C22⋊C411yescharacteristic
59C2×#10596831C4⋊C411yescharacteristic
60C8×D73—21no—
61C8×D73—21no—
62C8×D73—21no—
63C8×D73—21no—
64#11924003—41no—
65C22×C4×C73C4211yescharacteristic
66C2×C8×C73—21no—
67C2×C8×C73—21no—
68C2×C8×C73C22⋊C411yescharacteristic
69C2×C8×C73C4⋊C411yescharacteristic
70C16×C73—41no—
71C23×C73#9711yescharacteristic
72C22×D73C22⋊C811yescharacteristic
73C22×D73C4⋊C811yescharacteristic
74C2×#64408—42no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73#9511yescharacteristic
78C2×C4×C73C4×C811yescharacteristic
79C22⋊D73—41no—
80C22⋊D73—41no—
81C2×Dic73C22⋊C811yescharacteristic
82C2×Dic73C4⋊C811yescharacteristic
83D292—41no—
84C4×D73—21no—
85C4×D73—21no—
86C4×D73—21no—
87C4×D73—21no—
88Dic146—41no—
89#10596833—42no—
90C8×C73—21no—
91C8×C73#9911yescharacteristic
92C8×C73#9911yescharacteristic
93#10596831—21no—
94#10596831—21no—
95C22×C73—21no—
96C22×C73—41no—
97C22×C73#33611yescharacteristic
98C2×D73—21no—
99C2×D73—21no—
100C2×D73—41no—
101C2×D73—41no—
102#64408—82no—
103C4×C73—21no—
104C4×C73#34211yescharacteristic
105C4×C73#34411yescharacteristic
106Dic73—21no—
107Dic73—21no—
108#7208—731nomaximal, Sylow
109C2×C73—21no—
110C2×C73—41no—
111C2×C73#128211yescharacteristic
112D73—41no—
113D73—41no—
114#2115—731no—
115#2113—731no—
116#1757—731no—
117C73#720811yescharacteristic, complemented, Sylow
118C2×#131—731no—
119C2×M32—731no—
120C2×M32—1461no—
121C22×C16#6440811yescharacteristic, complemented
122#413—731no—
123#410—731no—
124#405—1461no—
125#349—732no—
126#349—1461no—
127C22⋊C16—1461no—
128C22⋊C16—1461no—
129#344—1461no—
130C2×#41—731no—
131#131—2921no—
132#131—2921no—
133C2×M16—731no—
134C2×M16—731no—
135C2×M16—731no—
136C2×M16—1461no—
137C22×C8—731no—
138C22×C8—731no—
139C22×C8C2×#6440811yescharacteristic
140#117—1461no—
141M32—2921no—
142M32—2921no—
143M32—1462no—
144C2×C16—21no—
145C2×C16—41no—
146C2×C16—2921no—
147C2×C16—1461no—
148#101—732no—
149#100—1461no—
150#99—732no—
151#99—1461no—
152#97—2921no—
153C4×C8—2921no—
154#41—2921no—
155#41—2921no—
156C2×Q8—731no—
157C2×D4—731no—
158C2×D4—731no—
159C2×D4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4C4×#6440811yescharacteristic
163M16—2921no—
164M16—2921no—
165M16—2921no—
166M16—2921no—
167M16—1462no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—2921no—
171C2×C8—731no—
172C2×C8—731no—
173C2×C8—1461no—
174C2×C8—1461no—
175C2×C8—1461no—
176C2×C8—1461no—
177C2×C8C22⋊#6440811yescharacteristic
178C2×C8C4⋊#6440811yescharacteristic
179C4⋊C4—2921no—
180C22⋊C4—1462no—
181C42—2921no—
182C16—41no—
183C16—2922no—
184C16—2921no—
185C23—731no—
186C23—731no—
187C23#1455664511yescharacteristic
188Q8—2921no—
189D4—2921no—
190D4—2921no—
191D4—2921no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—2922no—
195C2×C4—731no—
196C2×C4—731no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4(C2×#64408)⋊C411yescharacteristic
202C2×C4C8×#6440811yescharacteristic
203C8—21no—
204C8—2922no—
205C8—1461no—
206C8—1461no—
207C8#1455664911yescharacteristic
208C8#1455665011yescharacteristic
209C22—21no—
210C22—41no—
211C22—2921no—
212C22—2921no—
213C22—1461no—
214C22—1461no—
215C22#1798945211yescharacteristic
216C4—21no—
217C4—5842no—
218C4—1461no—
219C4—1461no—
220C4#1798946511yescharacteristic
221C4#1798946911yescharacteristic
222C2—21no—
223C2—41no—
224C2—2921no—
225C2—2921no—
226C2#2262477311yescharacteristic
subgroupG/H
centerC8#14556650
commutatorC2×C4×C73C4×C8
FrattiniC22×C8C2×#64408
FittingC22×C16×C73C4
socleC2×C73#1282
prime radicalC2×#11924028C2×C4
cosocleC2×#14556597C22
hypercenterC22×C16#64408
hypocenterC73#7208
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
9. #17989483C4semidirect
12. C2×#14556531C4semidirect
15. C22×C16×C73C4semidirect
117. C73#7208semidirect
121. C22×C16#64408semidirect

Maximal subgroups

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

subgroupindex
#226261682
#226256862
#226115442
#720873