Finite Group Databasebeta

← #34033596

Subgroups — #34033596

Order 18688.

364 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 81 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×#17989685C212yesmaximal
2#22626972C214yesmaximal, complemented
3#22626573C211yesmaximal, characteristic
4C2×#14556687—22no—
5#17989685—22no—
6#17989685C2214yes—
7C22×#11924037C411yescharacteristic
8C22×#11924037C2211yescharacteristic
9#17989593—22no—
10#17989593C412yes—
11#17989593C2212yes—
12#17989590—22no—
13C2×#14556547C411yescharacteristic
14#14556687—24no—
15#14556687—42no—
16C2×#11924040—42no—
17C2×#11924037—21no—
18C2×#11924037—21no—
19C2×#11924037—42no—
20C2×#11924037—42no—
21C2×#11924037C2×C411yescharacteristic
22C2×#11924037D412yes—
23C2×#11924037C2311yescharacteristic
24C22×#10596833C2×C412yes—
25C22×#10596833D412yes—
26#14556658—22no—
27#14556658—22no—
28C4⋊#10596833—22no—
29C4⋊#10596833—22no—
30C23×Dic73C2×C411yescharacteristic
31#14556547—21no—
32#14556547—21no—
33#14556547C812yes—
34#14556547C2×C412yes—
35C2×#11924007—21no—
36C2×C22⋊Dic73C811yescharacteristic
37C2×C4×Dic73—21no—
38C2×C22⋊C4×C73C811yescharacteristic
39#11924040—44no—
40#11924037—41no—
41#11924037—42no—
42#11924037—41no—
43#11924037—42no—
44#11924037—42no—
45C2×#10596833—22no—
46C2×#10596833—22no—
47C2×#10596833—22no—
48C2×#10596833—42no—
49C2×#10596833C22⋊C412yes—
50C2×#10596833C2×D412yes—
51C22×Dic73—22no—
52C22×Dic73—22no—
53C22×Dic73—21no—
54C22×Dic73C22⋊C411yescharacteristic
55C22×Dic73C22⋊C411yescharacteristic
56C22×Dic73C2×C811yescharacteristic
57C22×Dic73M1611yescharacteristic
58C22×Dic73M1611yescharacteristic
59C22×Dic73C22×C411yescharacteristic
60#11924007—22no—
61#11924007—22no—
62C22⋊Dic73—21no—
63C22⋊Dic73C2×C812yes—
64C4×Dic73—22no—
65C4×Dic73—22no—
66C24×C73C2×C811yescharacteristic
67C22×C4×C73—21no—
68C22⋊C4×C73—21no—
69C22⋊C4×C73C2×C812yes—
70C23×C73—22no—
71C23×C73—81no—
72C23×C73C22⋊C811yescharacteristic
73C23×C73C22⋊C811yescharacteristic
74C23×C73C22×C811yescharacteristic
75C2×C4×C73—22no—
76C2×C4×C73—81no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—22no—
85C2×Dic73—81no—
86C2×Dic73C22⋊C811yescharacteristic
87C2×Dic73C22⋊C811yescharacteristic
88C2×Dic73#9912yes—
89C2×Dic73#10112yes—
90C2×Dic73C2×C22⋊C411yescharacteristic
91C2×Dic73C2×M1611yescharacteristic
92#10596833—22no—
93#10596833—22no—
94#10596833—42no—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—82no—
101C22×C73#32412yes—
102C22×C73C2×C22⋊C811yescharacteristic
103C4×C73—42no—
104Dic73—21no—
105Dic73—21no—
106Dic73—42no—
107Dic73#32412yes—
108Dic73C2×#9911yescharacteristic
109Dic73C2×#10111yescharacteristic
110#11458—731nomaximal, Sylow
111C2×C73—21no—
112C2×C73—22no—
113C2×C73—41no—
114C2×C73—41no—
115C2×C73C2×#32411yescharacteristic
116#2905—731no—
117C2×#349—732no—
118#1328—734no—
119C73#1145811yescharacteristic, complemented, Sylow
120C22×M16—731no—
121C22×M16—731no—
122C2×#117—731no—
123C2×M32—1462no—
124#424—732no—
125#424—732no—
126#424—1462no—
127#423—1462no—
128#349—734no—
129#349—1462no—
130C23×C4—731no—
131C2×M16—2922no—
132C2×M16—2922no—
133C2×M16—731no—
134C2×M16—732no—
135C2×M16—731no—
136C2×M16—1461no—
137C2×M16—1461no—
138C22×C8—732no—
139C22×C8—732no—
140#117—732no—
141#117—732no—
142#117—1461no—
143#117—1461no—
144C2×C4⋊C4—1461no—
145C2×C22⋊C4—731no—
146C2×C22⋊C4#1059684211yescharacteristic
147C2×C42—1461no—
148M32—2922no—
149M32—1464no—
150C2×C16—2922no—
151C4⋊C8—1462no—
152C4⋊C8—1462no—
153C4⋊C8—1462no—
154C4⋊C8—1462no—
155C24C2×#1059684211yescharacteristic
156C22×C4—21no—
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—731no—
163C22×C4—1461no—
164C22×C4—1462no—
165C22×C4—1462no—
166M16—2922no—
167M16—2922no—
168M16—2921no—
169M16—2922no—
170M16—2921no—
171C2×C8—2922no—
172C2×C8—732no—
173C2×C8—732no—
174C2×C8—1462no—
175C2×C8—1462no—
176C2×C8—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1462no—
179C22⋊C4—21no—
180C22⋊C4—732no—
181C22⋊C4—1461no—
182C22⋊C4C2×#1059684212yes—
183C42—1462no—
184C42—1462no—
185C16—2924no—
186C23—22no—
187C23—81no—
188C23C22⋊#1059684211yescharacteristic
189C23C22⋊#1059684211yescharacteristic
190C23C22×#1059684211yescharacteristic
191C2×C4—22no—
192C2×C4—81no—
193C2×C4—5841no—
194C2×C4—732no—
195C2×C4—732no—
196C2×C4—731no—
197C2×C4—731no—
198C2×C4—731no—
199C2×C4—731no—
200C2×C4—1462no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4—1461no—
206C2×C4—1461no—
207C2×C4—1462no—
208C8—2922no—
209C8—1462no—
210C8—1462no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—82no—
217C22#1798967312yes—
218C22C2×C22⋊#1059684211yescharacteristic
219C4—42no—
220C4—2922no—
221C4—731no—
222C4—732no—
223C4—731no—
224C4—1461no—
225C4—1461no—
226C2—21no—
227C2—22no—
228C2—41no—
229C2—41no—
230C2C2×#1798967311yescharacteristic
subgroupG/H
centerC2C2×#17989673
commutatorC23×C73C22×C8
FrattiniC23C22×#10596842
FittingC2×C22⋊C4×C73C8
socleC2×C73C2×#324
prime radicalC24×C73C2×C8
cosocleC2×#11924037C23
hypercenterC2×C22⋊C4#10596842
hypocenterC73#11458
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #22626972C2semidirect
119. C73#11458semidirect

Maximal subgroups

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

subgroupindex
C2×#179896852
#226269722
#226265732
#1145873