Finite Group Databasebeta

← #34033684

Subgroups — #34033684

Order 18688.

330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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#22627133C212yesmaximal
2#22626965C212yesmaximal
3#22626964C212yesmaximal
4C2×#17989636C211yesmaximal, characteristic
5C4⋊#11924040—22no—
6C22⋊#11924040C2214yes—
7#17989681—22no—
8#17989636—22no—
9#17989636—22no—
10C2×#14556658C411yescharacteristic
11C2×#14556658C2211yescharacteristic
12C2×C4⋊#10596833C2211yescharacteristic
13C2×C4×#10596833C411yescharacteristic
14C2×C4×#10596833C411yescharacteristic
15C2×C4×#10596833C2211yescharacteristic
16C2×#14556556C411yescharacteristic
17C2×#11924040—24no—
18C22×#10596833C2×C411yescharacteristic
19C22×#10596833C2×C411yescharacteristic
20C22×#10596833C2×C411yescharacteristic
21C22×#10596833C2311yescharacteristic
22#14556658—22no—
23#14556658—22no—
24C4⋊#10596833—22no—
25C4×#10596833—21no—
26C4×#10596833—21no—
27C4×#10596833—21no—
28C4×#10596833—21no—
29C4×#10596833D412yes—
30C4×#10596833D412yes—
31C22×Dic146C811yescharacteristic
32#14556556—22no—
33#14556556—22no—
34C2×#11924007C811yescharacteristic
35C2×#11924007C811yescharacteristic
36C2×C4×Dic73C2×C411yescharacteristic
37C2×C4×Dic73C2×C411yescharacteristic
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4⋊C4×C73C811yescharacteristic
40#11924040—44no—
41C2×#10596833—22no—
42C2×#10596833—21no—
43C2×#10596833—21no—
44C2×#10596833—41no—
45C2×#10596833—41no—
46C2×#10596833—41no—
47C2×#10596833C22⋊C411yescharacteristic
48C2×#10596833C22⋊C411yescharacteristic
49C2×#10596833C2×D412yes—
50C2×Dic146—22no—
51C2×Dic146—22no—
52C2×Dic146—22no—
53C22×Dic73C2×C811yescharacteristic
54C22×Dic73C2×C811yescharacteristic
55C22×Dic73C2×C811yescharacteristic
56C22×Dic73C22×C411yescharacteristic
57#11924007—22no—
58#11924007—22no—
59C4×Dic73—21no—
60C4×Dic73—21no—
61C4×Dic73—21no—
62C4×Dic73—21no—
63C4×Dic73C22⋊C412yes—
64C4×Dic73M1612yes—
65C22×C4×C73C2×C811yescharacteristic
66C22×C4×C73C2×C811yescharacteristic
67C22×C4×C73C2×C811yescharacteristic
68C4⋊C4×C73—22no—
69C23×C73C22×C811yescharacteristic
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—41no—
74C2×C4×C73—41no—
75C2×C4×C73C22⋊C812yes—
76C2×C4×C73M3212yes—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—41no—
85C2×Dic73C22⋊C812yes—
86C2×Dic73M3212yes—
87C2×Dic73C2×C22⋊C411yescharacteristic
88C2×Dic73C2×M1611yescharacteristic
89Dic146—28no—
90#10596833—22no—
91#10596833—21no—
92#10596833—41no—
93#10596833—41no—
94#10596833#10112yes—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73C2×C22⋊C811yescharacteristic
98C22×C73C2×M3211yescharacteristic
99C22×C73C2×M3211yescharacteristic
100C4×C73—22no—
101C4×C73—22no—
102C4×C73—41no—
103Dic73—22no—
104Dic73—22no—
105Dic73—21no—
106Dic73—41no—
107Dic73#41011yescharacteristic
108Dic73C2×#10111yescharacteristic
109#11494—731nomaximal, Sylow
110C2×C73—21no—
111C2×C73—21no—
112C2×C73#146111yescharacteristic
113C2×C73#211211yescharacteristic
114C2×C73#211511yescharacteristic
115C2×C8×Q8—731no—
116#2163—732no—
117#1322—732no—
118#1322—732no—
119C73#1149411yescharacteristic, complemented, Sylow
120C2×C4×Q8—731no—
121C8×Q8—1462no—
122C8×Q8—1462no—
123C2×C4⋊C8—731no—
124C2×C4⋊C8—731no—
125C2×C4⋊C8—731no—
126C2×C4×C8—731no—
127C2×C4×C8—731no—
128C2×C4×C8—731no—
129C4⋊C16—1462no—
130C22⋊C16—734no—
131#346—1462no—
132C22×Q8—731no—
133C22×C8—731no—
134C22×C8—731no—
135C22×C8—731no—
136C22×C8—731no—
137C4×Q8—1462no—
138C4×Q8—1462no—
139C2×C4⋊C4—731no—
140C2×C4⋊C4—731no—
141C2×C4⋊C4#1059684211yescharacteristic
142C2×C42—731no—
143C2×C42—731no—
144C2×C42—731no—
145C2×C16—1464no—
146C4⋊C8—1462no—
147C4⋊C8—1462no—
148C4⋊C8—1462no—
149C4×C8—732no—
150C4×C8—732no—
151C4×C8—1461no—
152C4×C8—1461no—
153C4×C8—1461no—
154C4×C8—1461no—
155C2×Q8—1462no—
156C2×Q8—1462no—
157C2×Q8—1462no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4C2×#1059684211yescharacteristic
163C22×C4C2×#1059684211yescharacteristic
164C22×C4C2×#1059684211yescharacteristic
165C2×C8—2921no—
166C2×C8—2921no—
167C2×C8—2921no—
168C2×C8—731no—
169C2×C8—731no—
170C2×C8—732no—
171C2×C8—1461no—
172C2×C8—1461no—
173C2×C8—1462no—
174C4⋊C4—22no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C42—732no—
178C42—732no—
179C42—1461no—
180C42—1461no—
181C42—1461no—
182C42—1461no—
183C16—2924no—
184C23C22×#1059684211yescharacteristic
185Q8—1468no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—2921no—
192C2×C4—731no—
193C2×C4—731no—
194C2×C4—732no—
195C2×C4—732no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4C22⋊#1059684212yes—
204C2×C4#1455668812yes—
205C8—2921no—
206C8—2921no—
207C8—732no—
208C8—1462no—
209C8—1461no—
210C22—21no—
211C22—21no—
212C22C2×C22⋊#1059684211yescharacteristic
213C22#1798970611yescharacteristic
214C22C2×#1455668811yescharacteristic
215C4—22no—
216C4—22no—
217C4—41no—
218C4—2921no—
219C4—731no—
220C4—731no—
221C4—1462no—
222C4—1462no—
223C4—1461no—
224C2—21no—
225C2—21no—
226C2#2262704611yescharacteristic
227C2#2262709911yescharacteristic
228C2#2262710711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10596842
commutator, prime radicalC23×C73C22×C8
FrattiniC23C22×#10596842
FittingC2×C4⋊C4×C73C8
socleC22×C73C2×C22⋊C8
cosocleC22×#10596833C23
hypercenterC2×C4⋊C4#10596842
hypocenterC73#11494
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
119. C73#11494semidirect

Maximal subgroups

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

subgroupindex
#226271332
#226269652
#226269642
C2×#179896362
#1149473