Finite Group Databasebeta

← #22615307

Subgroups — #22615307

Order 9344.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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
1C2×#14556567C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic
3#17988519C211yesmaximal, characteristic, complemented
4#17988517C211yesmaximal, characteristic, complemented
5#17988506C211yesmaximal, characteristic, complemented
6#17988484C212yesmaximal, complemented
7#17988483C212yesmaximal, complemented
8#17988461C212yesmaximal
9#17988458C212yesmaximal
10#17988434C211yesmaximal, characteristic
11#395×C73C211yesmaximal, characteristic, complemented
12C22×C4×D73C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15#14556567—24no—
16C2×C4⋊Dic73C2212yes—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2212yes—
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2212yes—
24C4⋊C4×D73—24no—
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×C4×Dic73C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×Q8×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C22×Dic73C2312yes—
39C22×Dic73C2311yescharacteristic
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2312yes—
42C22×Dic73C2311yescharacteristic
43C2×C4×D73—22no—
44C2×C4×D73—22no—
45C2×C4×D73—22no—
46C2×C4×D73—22no—
47C2×C4×D73—42no—
48C2×C4×D73—42no—
49C2×C4×D73D414yes—
50C4⋊Dic73—22no—
51C4⋊Dic73—22no—
52C4⋊Dic73—24no—
53#11924007—22no—
54#11924007—24no—
55#11924007—22no—
56#11924007—24no—
57#11924007—42no—
58#11924005—24no—
59#11924005Q818yescomplemented
60C4×Dic73—42no—
61C2×Q8×C73—22no—
62C2×Q8×C73—42no—
63C22×C4×C73C2312yes—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2312yes—
67C22×C4×C73C2311yescharacteristic
68C4⋊C4×C73—22no—
69C4⋊C4×C73—42no—
70C23×C73C2411yescharacteristic
71C22×D73—21no—
72C22×D73—21no—
73C22×D73—22no—
74C22×D73C2×D412yes—
75C22×D73C2×Q814yes—
76Q8×C73—44no—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73C2×D412yes—
88C2×C4×C73C2×Q814yes—
89C2×C4×C73#4112yes—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—21no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73C2×D412yes—
101C2×Dic73C2×Q814yes—
102C2×Dic73#4112yes—
103C4×D73—28no—
104C4×D73—44no—
105C4×D73—44no—
106C22×C73C22×D411yescharacteristic
107C22×C73C22×Q812yes—
108C22×C73C2×#4111yescharacteristic
109C22×C73C2×#4111yescharacteristic
110C22×C73H(5,𝔽2)12yes—
111C2×D73—22no—
112C2×D73—22no—
113C2×D73—24no—
114C2×D73—24no—
115C2×D73C4⋊Q814yes—
116C4×C73—22no—
117C4×C73—22no—
118C4×C73—24no—
119C4×C73—41no—
120C4×C73—42no—
121Dic73—22no—
122Dic73—22no—
123Dic73—24no—
124Dic73—42no—
125Dic73—41no—
126C2×C73#52511yescharacteristic
127C2×C73C2×C4⋊Q811yescharacteristic
128C2×C73#53411yescharacteristic
129C2×C73#55412yes—
130C2×C73#55412yes—
131D73—24no—
132#2583—731nomaximal, Sylow
133C73#258311yescharacteristic, complemented, Sylow
134C2×C22⋊Q8—731no—
135C22×C4⋊C4—731no—
136#398—731no—
137#398—731no—
138#395—731no—
139#395D7311yescharacteristic, complemented
140#389—732no—
141#389—732no—
142#385—732no—
143#385—732no—
144C4×C22⋊C4—731no—
145C22×Q8C2×D7311yescharacteristic
146C23×C4—731no—
147C23×C4—731no—
148C23×C4—731no—
149C22⋊Q8—1464no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—731no—
152C2×C4⋊C4—731no—
153C2×C4⋊C4—731no—
154C2×C4⋊C4—732no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—732no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4—1464no—
159C2×C4⋊C4C2×D7311yescharacteristic
160C2×C4⋊C4C2×D7312yes—
161C2×C22⋊C4—732no—
162C2×C22⋊C4—732no—
163C2×C42—732no—
164#95—731no—
165#95—732no—
166#95—732no—
167#95—732no—
168#95C2×D7311yescharacteristic
169#95C2×D7312yes—
170C24—731no—
171C2×Q8—22no—
172C2×Q8—42no—
173C22×C4—2922no—
174C22×C4—2922no—
175C22×C4—734no—
176C22×C4—732no—
177C22×C4—731no—
178C22×C4—731no—
179C22×C4—732no—
180C22×C4—731no—
181C22×C4—1462no—
182C22×C4—1462no—
183C22×C4—1462no—
184C22×C4—1462no—
185C22×C4C22×D7311yescharacteristic
186C22×C4C22×D7312yes—
187C22×C4C22×D7311yescharacteristic
188C22×C4C22×D7312yes—
189C22×C4C22×D7311yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—2922no—
193C4⋊C4—1462no—
194C4⋊C4—1464no—
195C4⋊C4—1464no—
196C4⋊C4—1462no—
197C4⋊C4—1462no—
198C4⋊C4—1462no—
199C4⋊C4—1464no—
200C22⋊C4—738no—
201C22⋊C4—1464no—
202C42—2922no—
203C23—732no—
204C23—734no—
205C23—1461no—
206C23—1461no—
207C23—1462no—
208C23C23×D7311yescharacteristic
209Q8—44no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—2924no—
221C2×C4—2924no—
222C2×C4—732no—
223C2×C4—734no—
224C2×C4—732no—
225C2×C4—1468no—
226C2×C4—1462no—
227C2×C4—1461no—
228C2×C4—1462no—
229C2×C4—1462no—
230C2×C4—1462no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1461no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4D4×D7312yes—
237C2×C4Q8×D7314yes—
238C2×C4#1192402912yes—
239C22—734no—
240C22—1462no—
241C22—1464no—
242C22—1464no—
243C22—1462no—
244C22C2×D4×D7311yescharacteristic
245C22C2×Q8×D7312yes—
246C22#41×D7311yescharacteristic
247C22C2×#1192402911yescharacteristic
248C22#1455663612yes—
249C4—22no—
250C4—24no—
251C4—22no—
252C4—41no—
253C4—42no—
254C4—2921no—
255C4—2922no—
256C4—1462no—
257C4—1464no—
258C4—1462no—
259C2—1464no—
260C2#1798910011yescharacteristic
261C2C4⋊Q8×D7311yescharacteristic
262C2#1798914711yescharacteristic
263C2#1798929112yes—
264C2#1798929812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#395×C73C2
hypercenter#395D73
hypocenterC73#2583
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #17988519C2semidirect
4. #17988517C2semidirect
5. #17988506C2semidirect
6. #17988484C2semidirect
7. #17988483C2semidirect
11. #395×C73C2semidirect
59. #11924005Q8semidirect
133. C73#2583semidirect
139. #395D73semidirect