Finite Group Databasebeta

← #34011071

Subgroups — #34011071

Order 18688.

378 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 74 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×#14556652C211yesmaximal, characteristic
2#22625193C211yesmaximal, characteristic
3#22624930C214yesmaximal
4#22615147C211yesmaximal, characteristic
5#17989608—21no—
6C2×#14556652—21no—
7C4×#11924037—21no—
8#17989467C2212yes—
9#17989433C2212yes—
10#17989432—21no—
11C2×C4×Dic146C2211yescharacteristic
12#17988525C412yes—
13#17988525C2212yes—
14#17988494—21no—
15#17988494—21no—
16#17988492—21no—
17#17988452—21no—
18C4×C4⋊Dic73C411yescharacteristic
19C2×C4⋊Q8×C73C411yescharacteristic
20C2×#11924037—22no—
21C4⋊#10596833—41no—
22#14556652—24no—
23C22⋊#10596833—22no—
24#14556646—41no—
25#14556646—41no—
26C4×#10596833—41no—
27C22×Dic146D411yescharacteristic
28C4×Dic146—41no—
29C4×Dic146—41no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73D411yescharacteristic
32C2×#11924007C2×C411yescharacteristic
33C2×#11924007C2311yescharacteristic
34C2×C4×Dic73—21no—
35C2×C4×Dic73D411yescharacteristic
36C2×C4×Dic73D411yescharacteristic
37#14556498—22no—
38#14556498—22no—
39#14556498—22no—
40#14556498—22no—
41#14556498C2×C412yes—
42C22×Q8×C73—21no—
43C4⋊Q8×C73—41no—
44C4⋊Q8×C73—41no—
45C2×C4⋊C4×C73—21no—
46C2×C4⋊C4×C73C2×C412yes—
47C2×C42×C73C2×C411yescharacteristic
48#11924037—24no—
49#11924037—42no—
50C2×#10596833—42no—
51C2×#10596833—42no—
52C2×Dic146—22no—
53C2×Dic146—22no—
54C2×Dic146—41no—
55C22×Dic73—22no—
56C22×Dic73C22⋊C411yescharacteristic
57C22×Dic73C22⋊C411yescharacteristic
58C22×Dic73C2×D411yescharacteristic
59C22×Dic73C2×D411yescharacteristic
60C4⋊Dic73—41no—
61C4⋊Dic73—42no—
62#11924007—41no—
63#11924007—41no—
64C4×Dic73—21no—
65C4×Dic73—21no—
66C4×Dic73—21no—
67C4×Dic73—21no—
68C4×Dic73—42no—
69C2×Q8×C73—44no—
70C2×Q8×C73—41no—
71C2×Q8×C73—41no—
72C22×C4×C73—22no—
73C22×C4×C73C22⋊C411yescharacteristic
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22×C411yescharacteristic
76C4⋊C4×C73—42no—
77C4⋊C4×C73—42no—
78C42×C73—21no—
79C42×C73—21no—
80C23×C73C2×C22⋊C411yescharacteristic
81Q8×C73—82no—
82Q8×C73—82no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—22no—
86C2×C4×C73—21no—
87C2×C4×C73—41no—
88C2×C4×C73—44no—
89C2×C4×C73—42no—
90C2×C4×C73#9911yescharacteristic
91C2×C4×C73#9911yescharacteristic
92C2×C4×C73#10412yes—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—41no—
101C2×Dic73—41no—
102C2×Dic73—42no—
103C2×Dic73—42no—
104C2×Dic73—42no—
105C2×Dic73#13712yes—
106Dic146—44no—
107#10596833—44no—
108#10596833—82no—
109C22×C73—21no—
110C22×C73—21no—
111C22×C73C2×#9911yescharacteristic
112C22×C73#41911yescharacteristic
113C22×C73C2×#10411yescharacteristic
114C4×C73—21no—
115C4×C73—22no—
116C4×C73—41no—
117C4×C73—82no—
118C4×C73#35512yes—
119Dic73—22no—
120Dic73—41no—
121Dic73—41no—
122Dic73—41no—
123Dic73—82no—
124#11794—731nomaximal, Sylow
125C2×C73—21no—
126C2×C73—21no—
127C2×C73#150811yescharacteristic
128C2×C73#212311yescharacteristic
129C2×C73C2×#35511yescharacteristic
130#2568—731no—
131C4×#101—731no—
132#1467—731no—
133#1353—734no—
134C73#1179411yescharacteristic, complemented, Sylow
135C2×C4⋊Q8#6440811yescharacteristic
136C2×C4×Q8—731no—
137#432—1461no—
138C2×#101—1461no—
139C4×M16—1461no—
140#400—732no—
141#400—732no—
142#391—1461no—
143#391—1461no—
144#391—1461no—
145#382—1461no—
146C4×C4⋊C4—731no—
147#343—732no—
148#324—732no—
149#324—1461no—
150C22×Q8—21no—
151C22×Q8—731no—
152C2×M16—1462no—
153C4⋊Q8—41no—
154C4⋊Q8—41no—
155C4×Q8—2921no—
156C4×Q8—2921no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—731no—
159C2×C4⋊C4—731no—
160C2×C4⋊C4—731no—
161C2×C4⋊C4—1461no—
162C2×C4⋊C4C2×#6440812yes—
163C2×C42—731no—
164C2×C42—731no—
165C2×C42—1461no—
166C2×C42C2×#6440811yescharacteristic
167C4⋊C8—2921no—
168#101—1464no—
169C22⋊C8—1462no—
170#97—2921no—
171#97—2921no—
172C4×C8—2921no—
173#95—732no—
174#95—1462no—
175#95—1462no—
176#95—1462no—
177#95—1462no—
178C2×Q8—44no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—2921no—
182C2×Q8—1462no—
183C2×Q8—1462no—
184C22×C4—22no—
185C22×C4—731no—
186C22×C4—731no—
187C22×C4—731no—
188C22×C4—731no—
189C22×C4—1462no—
190C22×C4C22⋊#6440811yescharacteristic
191C22×C4C22⋊#6440811yescharacteristic
192C22×C4C22×#6440811yescharacteristic
193M16—2922no—
194M16—1464no—
195C2×C8—2922no—
196C2×C8—2922no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—2922no—
200C4⋊C4—2921no—
201C4⋊C4—2921no—
202C4⋊C4—2921no—
203C42—21no—
204C42—21no—
205C42—2922no—
206C42—1461no—
207C42—1461no—
208C42—1461no—
209C42—1461no—
210C23C2×C22⋊#6440811yescharacteristic
211Q8—82no—
212Q8—82no—
213Q8—2924no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—2921no—
222C2×C4—2921no—
223C2×C4—2922no—
224C2×C4—2922no—
225C2×C4—2922no—
226C2×C4—732no—
227C2×C4—1461no—
228C2×C4—1461no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4—1461no—
233C2×C4—1461no—
234C2×C4#1455664911yescharacteristic
235C2×C4#1455664911yescharacteristic
236C2×C4#1455665612yes—
237C8—2924no—
238C8—5842no—
239C22—21no—
240C22—21no—
241C22C2×#1455664911yescharacteristic
242C22#1798958011yescharacteristic
243C22C2×#1455665611yescharacteristic
244C4—22no—
245C4—21no—
246C4—41no—
247C4—82no—
248C4—2921no—
249C4—2921no—
250C4—2921no—
251C4—5842no—
252C4—1462no—
253C4#1798949512yes—
254C2—21no—
255C2—21no—
256C2#2262533111yescharacteristic
257C2#2262619311yescharacteristic
258C2C2×#1798949511yescharacteristic
subgroupG/H
centerC22C2×#14556649
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×C4⋊Q8×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×#11924007C23
hypercenterC2×C4⋊Q8#64408
hypocenterC73#11794
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
134. C73#11794semidirect

Maximal subgroups

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

subgroupindex
C4×#145566522
#226251932
#226249302
#226151472
#1179473