Finite Group Databasebeta

← #22620877

Subgroups — #22620877

Order 9344.

384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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#17989139C211yesmaximal, characteristic
2C2×#14556589C211yesmaximal, characteristic
3#17988965C212yesmaximal, complemented
4#17988936C212yesmaximal, complemented
5#17988796C212yesmaximal, complemented
6#17988795C212yesmaximal, complemented
7#17988745C211yesmaximal, characteristic
8#17988743C211yesmaximal, characteristic
9#17988742C211yesmaximal, characteristic
10#17988637C211yesmaximal, characteristic
11#451×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C2×Dic292C2212yes—
14C2×#11924018C2212yes—
15C2×#11924018C2212yes—
16#14556590C2211yescharacteristic
17#14556589—21no—
18#14556589—21no—
19#14556589C2212yes—
20#14556589C2212yes—
21#14556589C2211yescharacteristic
22#14556581—21no—
23#14556570C2211yescharacteristic
24#14556568—21no—
25Q8×Dic73C2211yescharacteristic
26#14556556—21no—
27#14556556C2211yescharacteristic
28#14556547—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×C4×Dic73C2211yescharacteristic
32#14556520C2212yes—
33#14556516C2212yes—
34#14556515C2212yes—
35#14556514C2212yes—
36C22⋊#10596831C2211yescharacteristic
37C8×Dic73C2212yes—
38C22×Q8×C73C2211yescharacteristic
39C2×Q16×C73C2212yes—
40C22⋊Q8×C73C2211yescharacteristic
41#103×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146—21no—
45C2×Dic146—42no—
46C2×Dic146C2312yes—
47C2×Dic146C2311yescharacteristic
48C22×Dic73—21no—
49C22×Dic73D411yescharacteristic
50C22×Dic73D411yescharacteristic
51Dic292—42no—
52#11924018—42no—
53#11924018—42no—
54C2×#10596831C2312yes—
55C4⋊Dic73—21no—
56C4⋊Dic73C2311yescharacteristic
57#11924007—21no—
58#11924007—22no—
59#11924007—22no—
60#11924007—22no—
61#11924007—22no—
62#11924007—21no—
63#11924007—21no—
64#11924007—21no—
65#11924007—21no—
66C22⋊Dic73—21no—
67C4×Dic73—21no—
68C4×Dic73—21no—
69C4×Dic73D411yescharacteristic
70C4×Dic73D411yescharacteristic
71C4×Dic73C2311yescharacteristic
72C4×Dic73C2311yescharacteristic
73C2×Q8×C73—21no—
74C2×Q8×C73—42no—
75C2×Q8×C73C2312yes—
76C2×Q8×C73C2311yescharacteristic
77C22×C4×C73—21no—
78C22×C4×C73C2311yescharacteristic
79Q16×C73—42no—
80C2×C8×C73C2312yes—
81C4⋊C4×C73—21no—
82C4⋊C4×C73C2311yescharacteristic
83C22⋊C4×C73—21no—
84C23×C73C2×D411yescharacteristic
85Q8×C73—22no—
86Q8×C73—22no—
87Q8×C73—22no—
88Q8×C73—42no—
89C2×C4×C73—22no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—42no—
94C2×C4×C73C2×D411yescharacteristic
95C2×C4×C73C2411yescharacteristic
96C2×Dic73—22no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—22no—
100C2×Dic73—42no—
101C2×Dic73Q1614yescomplemented
102C2×Dic73C2×D411yescharacteristic
103C2×Dic73C2×D411yescharacteristic
104C2×Dic73C2×D411yescharacteristic
105C2×Dic73C2×D411yescharacteristic
106Dic146—22no—
107Dic146—22no—
108Dic146—22no—
109Dic146—42no—
110Dic146—42no—
111C8×C73—22no—
112#10596831—22no—
113C22×C73—21no—
114C22×C73—21no—
115C22×C73C2×Q1612yes—
116C22×C73C22×D411yescharacteristic
117C4×C73—21no—
118C4×C73—42no—
119C4×C73—41no—
120C4×C73—41no—
121C4×C73H(5,𝔽2)12yes—
122Dic73—21no—
123Dic73—42no—
124Dic73—41no—
125Dic73—41no—
126Dic73C2×Q1612yes—
127Dic73C2×Q1612yes—
128Dic73#13712yes—
129C2×C73—22no—
130C2×C73#53511yescharacteristic
131C2×C73C22×Q1611yescharacteristic
132C2×C73C2×#13711yescharacteristic
133#3209—731nomaximal, Sylow
134C73#320911yescharacteristic, complemented, Sylow
135#533—731no—
136C2×C4⋊Q8—731no—
137#494—732no—
138#487—732no—
139#462—732no—
140#462—732no—
141#451—731no—
142#451—731no—
143#451—731no—
144#451D7311yescharacteristic
145#431—731no—
146C22×Q8—731no—
147C22×Q8C2×D7311yescharacteristic
148C2×Q16—732no—
149C2×Q16—732no—
150C2×Q16—732no—
151C2×Q16C2×D7312yes—
152C4⋊Q8—731no—
153C4⋊Q8—732no—
154C4⋊Q8—732no—
155C4⋊Q8—731no—
156C4⋊Q8—1461no—
157C4⋊Q8—1461no—
158#125—1461no—
159C22⋊Q8—731no—
160C22⋊Q8—1461no—
161C22⋊Q8C2×D7311yescharacteristic
162C4×Q8—731no—
163C4×Q8—731no—
164C4×Q8—1461no—
165#117—1461no—
166C2×C4⋊C4—1461no—
167C2×C4⋊C4—1461no—
168C2×C42—731no—
169C4⋊C8—732no—
170#103—732no—
171#103—732no—
172#103—732no—
173#103C2×D7312yes—
174C22⋊C8—731no—
175C22⋊C8C2×D7311yescharacteristic
176C4×C8—732no—
177C2×Q8—21no—
178C2×Q8—42no—
179C2×Q8—2922no—
180C2×Q8—732no—
181C2×Q8—731no—
182C2×Q8—1461no—
183C2×Q8—1461no—
184C2×Q8C22×D7312yes—
185C2×Q8C22×D7311yescharacteristic
186C22×C4—21no—
187C22×C4—731no—
188C22×C4—731no—
189C22×C4—1461no—
190C22×C4C22×D7311yescharacteristic
191Q16—42no—
192Q16—2922no—
193Q16—2922no—
194Q16—2922no—
195C2×C8—732no—
196C2×C8C22×D7312yes—
197C4⋊C4—21no—
198C4⋊C4—731no—
199C4⋊C4—1462no—
200C4⋊C4—1462no—
201C4⋊C4—1462no—
202C4⋊C4—1462no—
203C4⋊C4—1461no—
204C4⋊C4—1461no—
205C4⋊C4—1461no—
206C4⋊C4—1461no—
207C4⋊C4—1461no—
208C4⋊C4—1461no—
209C4⋊C4C22×D7311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—1461no—
212C42—731no—
213C42—731no—
214C42—731no—
215C42—731no—
216C42—1461no—
217C42—1461no—
218C23D4×D7311yescharacteristic
219Q8—22no—
220Q8—22no—
221Q8—22no—
222Q8—42no—
223Q8—2922no—
224Q8—2922no—
225Q8—1462no—
226Q8—1462no—
227Q8—1462no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—2922no—
234C2×C4—734no—
235C2×C4—731no—
236C2×C4—731no—
237C2×C4—731no—
238C2×C4—731no—
239C2×C4—1461no—
240C2×C4—1461no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4D4×D7311yescharacteristic
244C2×C4C23×D7311yescharacteristic
245C8—22no—
246C8—1462no—
247C22—21no—
248C22—21no—
249C22Q16×D7312yes—
250C22C2×D4×D7311yescharacteristic
251C4—21no—
252C4—41no—
253C4—42no—
254C4—41no—
255C4—2921no—
256C4—2922no—
257C4—2921no—
258C4—732no—
259C4—732no—
260C4—732no—
261C4—1461no—
262C4#1455663612yes—
263C2—22no—
264C2#1798915211yescharacteristic
265C2C2×Q16×D7311yescharacteristic
266C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3209
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #17988965C2semidirect
4. #17988936C2semidirect
5. #17988796C2semidirect
6. #17988795C2semidirect
101. C2×Dic73Q16semidirect
134. C73#3209semidirect