Finite Group Databasebeta

← #34010318

Subgroups — #34010318

Order 18688.

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

normal subgroups only

This group has 374 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
1#22625193C211yesmaximal, characteristic
2#22625173C211yesmaximal, characteristic
3#22624874C214yesmaximal
4#22615140C211yesmaximal, characteristic
5#17989608—21no—
6#17989604—21no—
7#17989433—21no—
8#17989433—21no—
9#17989432C2212yes—
10#17989432C2212yes—
11C2×C4×Dic146C2211yescharacteristic
12#17988506—21no—
13#17988506—21no—
14#17988492C412yes—
15#17988483—21no—
16#17988483—21no—
17#17988456C2212yes—
18C4×C4⋊Dic73C411yescharacteristic
19C2×C4⋊Q8×C73C411yescharacteristic
20#14556658—41no—
21C4⋊#10596833—41no—
22C22⋊#10596833—22no—
23C22⋊#10596833—22no—
24#14556646—41no—
25C4×#10596833—41no—
26C22×Dic146C2×C411yescharacteristic
27C4×Dic146—41no—
28C4×Dic146—41no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73C2311yescharacteristic
31C2×#11924007—22no—
32C2×#11924007—22no—
33C2×#11924007D411yescharacteristic
34C2×#11924007D411yescharacteristic
35C2×C4×Dic73C2×C412yes—
36C2×C4×Dic73D411yescharacteristic
37C2×C4×Dic73D411yescharacteristic
38#14556498—22no—
39#14556498—22no—
40#14556498—21no—
41C22×Q8×C73—21no—
42C4⋊Q8×C73—41no—
43C4⋊Q8×C73—41no—
44C2×C4⋊C4×C73—21no—
45C2×C4⋊C4×C73C2×C412yes—
46C2×C42×C73C2×C411yescharacteristic
47C2×#10596833—42no—
48C2×#10596833—42no—
49C2×Dic146—22no—
50C2×Dic146—22no—
51C2×Dic146—41no—
52C22×Dic73—22no—
53C22×Dic73C22⋊C411yescharacteristic
54C22×Dic73C22⋊C411yescharacteristic
55C22×Dic73C2×D411yescharacteristic
56C22×Dic73C2×D411yescharacteristic
57C4⋊Dic73—24no—
58C4⋊Dic73—41no—
59#11924007—41no—
60#11924007—41no—
61#11924007—82no—
62#11924007—82no—
63C4×Dic73—21no—
64C4×Dic73—21no—
65C4×Dic73—21no—
66C4×Dic73—21no—
67C4×Dic73—24no—
68C2×Q8×C73—42no—
69C2×Q8×C73—82no—
70C22×C4×C73—22no—
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22⋊C411yescharacteristic
73C22×C4×C73C22×C411yescharacteristic
74C4⋊C4×C73—42no—
75C4⋊C4×C73—41no—
76C4⋊C4×C73—41no—
77C42×C73—21no—
78C42×C73—21no—
79C23×C73C2×C22⋊C411yescharacteristic
80Q8×C73—84no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73—41no—
86C2×C4×C73—42no—
87C2×C4×C73—42no—
88C2×C4×C73—42no—
89C2×C4×C73#9911yescharacteristic
90C2×C4×C73#9911yescharacteristic
91C2×C4×C73#13112yes—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—24no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—42no—
101C2×Dic73—42no—
102C2×Dic73—41no—
103C2×Dic73—41no—
104C2×Dic73#10112yes—
105Dic146—44no—
106#10596833—82no—
107#10596833—82no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73#40811yescharacteristic
111C22×C73C2×#9911yescharacteristic
112C22×C73C2×#10111yescharacteristic
113C4×C73—21no—
114C4×C73—22no—
115C4×C73—41no—
116C4×C73—82no—
117C4×C73#35612yes—
118Dic73—22no—
119Dic73—44no—
120Dic73—41no—
121Dic73—41no—
122Dic73—41no—
123#11574—731nomaximal, Sylow
124C2×C73—21no—
125C2×C73—21no—
126C2×C73#147211yescharacteristic
127C2×C73#212811yescharacteristic
128C2×C73C2×#35611yescharacteristic
129#2567—731no—
130#1467—731no—
131#1461—731no—
132#1325—734no—
133C73#1157411yescharacteristic, complemented, Sylow
134C2×C4⋊Q8#6440811yescharacteristic
135C2×C4×Q8—731no—
136#432—1461no—
137#431—1461no—
138#395—1461no—
139#395—1461no—
140#391—732no—
141#389—1461no—
142#389—1461no—
143#384—732no—
144C4×C4⋊C4—731no—
145#324—732no—
146#324—732no—
147#324—1461no—
148#324—1461no—
149C22×Q8—21no—
150C22×Q8—731no—
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—2921no—
154C4×Q8—2921no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—731no—
157C2×C4⋊C4—731no—
158C2×C4⋊C4—731no—
159C2×C4⋊C4—1462no—
160C2×C4⋊C4—1462no—
161C2×C4⋊C4—1461no—
162C2×C4⋊C4C2×#6440812yes—
163C2×C42—731no—
164C2×C42—731no—
165C2×C42—732no—
166C2×C42C2×#6440811yescharacteristic
167C4⋊C8—2921no—
168C4⋊C8—2921no—
169C22⋊C8—1462no—
170C22⋊C8—1462no—
171#97—2921no—
172C4×C8—2921no—
173#95—1462no—
174#95—1462no—
175#95—1461no—
176C2×Q8—42no—
177C2×Q8—82no—
178C2×Q8—2921no—
179C2×Q8—1462no—
180C2×Q8—1462no—
181C22×C4—22no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4—731no—
185C22×C4—731no—
186C22×C4—1462no—
187C22×C4C22⋊#6440811yescharacteristic
188C22×C4C22⋊#6440811yescharacteristic
189C22×C4C22×#6440811yescharacteristic
190C2×C8—2922no—
191C2×C8—2922no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—2921no—
196C4⋊C4—2921no—
197C4⋊C4—2921no—
198C4⋊C4—5842no—
199C4⋊C4—5842no—
200C4⋊C4—1464no—
201C42—21no—
202C42—21no—
203C42—1464no—
204C42—1461no—
205C42—1461no—
206C42—1461no—
207C42—1461no—
208C23C2×C22⋊#6440811yescharacteristic
209Q8—84no—
210Q8—2924no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—2922no—
220C2×C4—2922no—
221C2×C4—2921no—
222C2×C4—2921no—
223C2×C4—732no—
224C2×C4—1464no—
225C2×C4—1461no—
226C2×C4—1461no—
227C2×C4—1461no—
228C2×C4—1461no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4#1455664911yescharacteristic
233C2×C4#1455664911yescharacteristic
234C2×C4#1455667912yes—
235C8—5842no—
236C8—5842no—
237C22—21no—
238C22—21no—
239C22#1798956211yescharacteristic
240C22C2×#1455664911yescharacteristic
241C22D73⋊#10111yescharacteristic
242C4—21no—
243C4—22no—
244C4—41no—
245C4—82no—
246C4—2924no—
247C4—2921no—
248C4—2921no—
249C4—2921no—
250C4—1462no—
251C4#1798949712yes—
252C2—21no—
253C2—21no—
254C2#2262521111yescharacteristic
255C2#2262621011yescharacteristic
256C2C2×#1798949711yescharacteristic
subgroupG/H
centerC22C2×#14556649
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×C4⋊Q8×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊Dic73C23
hypercenterC2×C4⋊Q8#64408
hypocenterC73#11574
LCSG ▷ C22×C4×C73 ▷ C22×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
133. C73#11574semidirect

Maximal subgroups

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

subgroupindex
#226251932
#226251732
#226248742
#226151402
#1157473