Finite Group Databasebeta

← #34000382

Subgroups — #34000382

Order 18688.

248 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 70 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#22626167C211yesmaximal, characteristic
2#22626161C211yesmaximal, characteristic
3#22609733C211yesmaximal, characteristic
4C2×#14556665—21no—
5C2×#14556665C411yescharacteristic, complemented
6C22×#11924031C411yescharacteristic, complemented
7#17989483—21no—
8#17989483C412yescomplemented
9C22⋊#11924031—21no—
10C22⋊#11924031—21no—
11C2×#14556598C2211yescharacteristic
12#17988571C411yescharacteristic
13#17988543—21no—
14#17988357—21no—
15#410×C73C411yescharacteristic
16#14556665—22no—
17#14556665—41no—
18#14556665—41no—
19C2×#11924031—21no—
20C2×#11924031—21no—
21C2×#11924031—41no—
22C2×#11924031—41no—
23#14556598—41no—
24#14556598—41no—
25C2×#11924012—21no—
26C2×#11924012C2×C411yescharacteristic
27C2×#11924012D411yescharacteristic
28C2×#11924012Q811yescharacteristic
29C22×#10596831C2×C411yescharacteristic
30C22×#10596831D411yescharacteristic
31C22×#10596831D411yescharacteristic
32#14556510C812yes—
33#14556508—21no—
34#14556502—41no—
35C4×#10596831—41no—
36C2×#41×C73C2×C411yescharacteristic
37#117×C73—21no—
38#99×C73—21no—
39#99×C73C812yes—
40#11924031—42no—
41#11924031—41no—
42#11924031—41no—
43#11924012—22no—
44#11924012—41no—
45#11924012—41no—
46#11924012—41no—
47#11924012—41no—
48C2×#10596831—21no—
49C2×#10596831—21no—
50C2×#10596831—21no—
51C2×#10596831—21no—
52C2×#10596831—21no—
53C2×#10596831—21no—
54C2×#10596831—41no—
55C2×#10596831C22⋊C411yescharacteristic
56C2×#10596831C22⋊C411yescharacteristic
57C2×#10596831C4⋊C411yescharacteristic
58C2×#10596831C4⋊C411yescharacteristic
59#41×C73—41no—
60#41×C73—41no—
61C2×Q8×C73C2×C811yescharacteristic
62C2×D4×C73C2×C811yescharacteristic
63C2×D4×C73M1611yescharacteristic
64C2×D4×C73M1611yescharacteristic
65C22×C4×C73C4211yescharacteristic
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C4⋊C411yescharacteristic
68C4⋊C4×C73—41no—
69C22⋊C4×C73—22no—
70C42×C73—41no—
71C23×C73#9711yescharacteristic
72C23×C73C22⋊C811yescharacteristic
73C23×C73C4⋊C811yescharacteristic
74Q8×C73—41no—
75D4×C73—41no—
76D4×C73—41no—
77D4×C73—41no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—42no—
85C2×C4×C73#9511yescharacteristic
86C2×C4×C73C4×C811yescharacteristic
87C2×C4×C73C22⋊C811yescharacteristic
88C2×C4×C73C4⋊C811yescharacteristic
89#10596831—21no—
90#10596831—21no—
91#10596831—21no—
92#10596831—42no—
93#10596831#9911yescharacteristic
94#10596831#9911yescharacteristic
95C22×C73—21no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—41no—
101C22×C73#33611yescharacteristic
102C4×C73—21no—
103C4×C73—21no—
104C4×C73—21no—
105C4×C73—82no—
106C4×C73#34211yescharacteristic
107C4×C73#34411yescharacteristic
108#7208—731nomaximal, Sylow
109C2×C73—21no—
110C2×C73—41no—
111C2×C73—41no—
112C2×C73—41no—
113C2×C73#128211yescharacteristic
114#2115—731no—
115#2113—731no—
116#1757—731no—
117C73#720811yescharacteristic, complemented, Sylow
118C2×#131—731no—
119C2×M32—731no—
120C2×M32—1461no—
121C22×C16—731no—
122#413—731no—
123#410#6440811yescharacteristic
124#405—1461no—
125#349—732no—
126#349—1461no—
127C22⋊C16—1461no—
128C22⋊C16—1461no—
129#344—1461no—
130C2×#41C2×#6440811yescharacteristic
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×C8—731no—
140#117—21no—
141M32—2921no—
142M32—2921no—
143M32—1462no—
144C2×C16—2921no—
145C2×C16—2921no—
146C2×C16—1461no—
147C2×C16—1461no—
148#101—732no—
149#100—1461no—
150#99—21no—
151#99#1059683312yes—
152#97—2921no—
153C4×C8—2921no—
154#41—41no—
155#41—41no—
156C2×Q8#1192403611yescharacteristic
157C2×D4C2×#1059683311yescharacteristic
158C2×D4#1192403711yescharacteristic
159C2×D4#1192403811yescharacteristic
160C22×C4C4×#6440811yescharacteristic
161C22×C4C22⋊#6440811yescharacteristic
162C22×C4C4⋊#6440811yescharacteristic
163M16—2921no—
164M16—2921no—
165M16—2921no—
166M16—2921no—
167M16—1462no—
168C2×C8—2921no—
169C2×C8—731no—
170C2×C8—731no—
171C2×C8—731no—
172C2×C8—731no—
173C2×C8—1461no—
174C2×C8—1461no—
175C2×C8—1461no—
176C2×C8—1461no—
177C2×C8—1461no—
178C2×C8—1461no—
179C4⋊C4—41no—
180C22⋊C4—22no—
181C42—41no—
182C16—2921no—
183C16—2921no—
184C16—2922no—
185C23#1455664611yescharacteristic
186C23C22⋊#1059683311yescharacteristic
187C23C4⋊#1059683311yescharacteristic
188Q8—41no—
189D4—41no—
190D4—41no—
191D4—41no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4(C2×#64408)⋊C411yescharacteristic
200C2×C4C4×#1059683311yescharacteristic
201C2×C4#1455664811yescharacteristic
202C2×C4#1455665811yescharacteristic
203C8—2922no—
204C8—731no—
205C8—731no—
206C8—1461no—
207C8—1461no—
208C8—1461no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22#1798945311yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—82no—
220C4#1798946411yescharacteristic
221C4#1798946811yescharacteristic
222C2—21no—
223C2—41no—
224C2—41no—
225C2—41no—
226C2#2262477411yescharacteristic
subgroupG/H
centerC4#17989464
commutatorC2×C4×C73C4×C8
FrattiniC2×#41C2×#64408
Fitting#410×C73C4
socleC2×C73#1282
prime radicalC2×#41×C73C2×C4
cosocleC2×#14556598C22
hypercenter#410#64408
hypocenterC73#7208
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
5. C2×#14556665C4semidirect
6. C22×#11924031C4semidirect
8. #17989483C4semidirect
117. C73#7208semidirect

Maximal subgroups

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

subgroupindex
#226261672
#226261612
#226097332
#720873