Finite Group Databasebeta

← #34001341

Subgroups — #34001341

Order 18688.

516 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C4×#14556658C212yesmaximal
2#22624752C212yesmaximal
3#22624751C212yesmaximal
4C4×#14556589C211yesmaximal, characteristic
5C2×#14556658—22no—
6C2×C4×#10596833—22no—
7#17989453C2214yes—
8C2×#14556589C411yescharacteristic
9C2×C4×Dic146C411yescharacteristic
10#17988494C2211yescharacteristic
11#17988492C2211yescharacteristic
12#17988482—22no—
13#17988456C411yescharacteristic
14C4×#11924007—22no—
15C42×Dic73C2211yescharacteristic
16C2×C4×Q8×C73C411yescharacteristic
17C22×#10596833—24no—
18#14556658—28no—
19C4×#10596833—44no—
20C22×Dic146C2×C411yescharacteristic
21#14556589—22no—
22#14556589C814yescomplemented
23C4×Dic146—42no—
24C2×C4⋊Dic73C2×C411yescharacteristic
25C2×#11924007—22no—
26C2×#11924007—22no—
27C2×#11924007—21no—
28C2×C4×Dic73—21no—
29C2×C4×Dic73C2×C411yescharacteristic
30C2×C4×Dic73D412yes—
31C2×C4×Dic73D412yes—
32C2×C4×Dic73C2311yescharacteristic
33#14556498—22no—
34#14556498—22no—
35C22×Q8×C73C2×C411yescharacteristic
36C4×Q8×C73—42no—
37C2×C4⋊C4×C73—21no—
38C2×C4⋊C4×C73C2×C411yescharacteristic
39C2×C42×C73—21no—
40C2×C42×C73C2×C411yescharacteristic
41C2×#10596833—28no—
42C2×#10596833—44no—
43C2×#10596833—44no—
44C2×Dic146—21no—
45C2×Dic146—41no—
46C2×Dic146—41no—
47C2×Dic146C2×C812yes—
48C22×Dic73—21no—
49C22×Dic73—21no—
50C22×Dic73C22⋊C412yes—
51C22×Dic73C2×D412yes—
52C4⋊Dic73—41no—
53#11924007—28no—
54#11924007—42no—
55#11924007—44no—
56C4×Dic73—24no—
57C4×Dic73—41no—
58C4×Dic73—42no—
59C4×Dic73C2×C812yes—
60C4×Dic73M1612yes—
61C4×Dic73SD1614yes—
62C4×Dic73Q1614yes—
63C2×Q8×C73—21no—
64C2×Q8×C73—41no—
65C2×Q8×C73—41no—
66C2×Q8×C73C2×C812yes—
67C22×C4×C73—21no—
68C22×C4×C73—21no—
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C22⋊C411yescharacteristic
71C22×C4×C73C22×C411yescharacteristic
72C4⋊C4×C73—41no—
73C4⋊C4×C73—42no—
74C42×C73—22no—
75C42×C73—42no—
76C23×C73C2×C22⋊C411yescharacteristic
77Q8×C73—42no—
78Q8×C73—42no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—41no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73—42no—
88C2×C4×C73#10012yes—
89C2×C4×C73#10314yes—
90C2×C4×C73C22×C811yescharacteristic
91C2×C4×C73C2×M1611yescharacteristic
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—41no—
96C2×Dic73—41no—
97C2×Dic73—41no—
98C2×Dic73—42no—
99C2×Dic73C22⋊C814yes—
100C2×Dic73#10314yes—
101C2×Dic73#10414yes—
102C2×Dic73C2×SD1612yes—
103C2×Dic73C2×Q1612yes—
104Dic146—42no—
105Dic146—42no—
106#10596833—48no—
107C22×C73C2×C22⋊C811yescharacteristic
108C22×C73#41011yescharacteristic
109C22×C73C2×#10011yescharacteristic
110C22×C73C2×#10312yes—
111C22×C73C2×#10412yes—
112C4×C73—21no—
113C4×C73—21no—
114C4×C73—42no—
115C4×C73—41no—
116C4×C73—81no—
117C4×C73#33314yes—
118Dic73—22no—
119Dic73—22no—
120Dic73—42no—
121Dic73—81no—
122Dic73Q8⋊C818yes—
123#7571—731nomaximal, Sylow
124C2×C73#146011yescharacteristic
125C2×C73C2×Q8⋊C812yes—
126C2×C73#150312yes—
127C2×C73#152511yescharacteristic
128C2×C73C2×#33311yescharacteristic
129C4×C4⋊Q8—731no—
130C4×C4⋊C8—732no—
131#1272—732no—
132#1272—732no—
133C73#757111yescharacteristic, complemented, Sylow
134C2×C4⋊Q8—731no—
135C2×C4×Q8—731no—
136C2×C4×Q8#6440811yescharacteristic
137C2×C4⋊C8—1462no—
138C2×C4×C8—1462no—
139#391—731no—
140#391—731no—
141#389—1462no—
142#384—731no—
143C4×C4⋊C4—1462no—
144C43—731no—
145#336—734no—
146C22×Q8—731no—
147C22×Q8C2×#6440811yescharacteristic
148C22×C8—1464no—
149C4⋊Q8—734no—
150C4⋊Q8—1462no—
151C4×Q8—42no—
152C4×Q8—2922no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—731no—
155C2×C4⋊C4—1462no—
156C2×C4⋊C4—1461no—
157C2×C4⋊C4—1462no—
158C2×C4⋊C4C2×#6440811yescharacteristic
159C2×C42—21no—
160C2×C42—731no—
161C2×C42—732no—
162C2×C42—731no—
163C2×C42—732no—
164C2×C42—1461no—
165C2×C42C2×#6440811yescharacteristic
166C4⋊C8—1468no—
167C4×C8—2924no—
168#95—1462no—
169#95—1462no—
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—2921no—
174C2×Q8—2921no—
175C2×Q8—732no—
176C2×Q8—1461no—
177C2×Q8#1192403612yes—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—732no—
181C22×C4—732no—
182C22×C4—1461no—
183C22×C4—1461no—
184C22×C4C22⋊#6440811yescharacteristic
185C22×C4C22⋊#6440811yescharacteristic
186C22×C4C22×#6440811yescharacteristic
187C2×C8—2924no—
188C2×C8—2924no—
189C2×C8—1468no—
190C4⋊C4—41no—
191C4⋊C4—42no—
192C4⋊C4—2921no—
193C4⋊C4—2922no—
194C4⋊C4—2924no—
195C4⋊C4—1468no—
196C42—22no—
197C42—42no—
198C42—2921no—
199C42—2922no—
200C42—732no—
201C42—732no—
202C42—734no—
203C42—734no—
204C42—1464no—
205C23C2×C22⋊#6440811yescharacteristic
206Q8—42no—
207Q8—42no—
208Q8—2922no—
209Q8—2922no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—2921no—
220C2×C4—2921no—
221C2×C4—2921no—
222C2×C4—2922no—
223C2×C4—734no—
224C2×C4—734no—
225C2×C4—734no—
226C2×C4—732no—
227C2×C4—732no—
228C2×C4—1462no—
229C2×C4—1462no—
230C2×C4—1462no—
231C2×C4#1455665112yes—
232C2×C4#1455665414yes—
233C2×C4C2×#1192403611yescharacteristic
234C2×C4D73⋊M1611yescharacteristic
235C8—2928no—
236C22#1798955511yescharacteristic
237C22#1798956611yescharacteristic
238C22C2×#1455665111yescharacteristic
239C22C2×#1455665412yes—
240C22D73⋊#10412yes—
241C4—21no—
242C4—21no—
243C4—41no—
244C4—42no—
245C4—81no—
246C4—2922no—
247C4—5841no—
248C4—738no—
249C4—1462no—
250C4—1462no—
251C4#1798944714yes—
252C2#2262517011yescharacteristic
253C2#2262522012yes—
254C2#2262531312yes—
255C2#2262538511yescharacteristic
256C2C2×#1798944711yescharacteristic
subgroupG/H
centerC22×C4C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×C4×Q8×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC2×C4×Q8#64408
hypocenterC73#7571
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
22. #14556589C8semidirect
133. C73#7571semidirect

Maximal subgroups

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

subgroupindex
C4×#145566582
#226247522
#226247512
C4×#145565892
#757173