Finite Group Databasebeta

← #22616082

Subgroups — #22616082

Order 9344.

498 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556574C211yesmaximal, characteristic
2#17988525C211yesmaximal, characteristic, complemented
3#17988522C211yesmaximal, characteristic, complemented
4#17988515C212yesmaximal, complemented
5#17988506C211yesmaximal, characteristic, complemented
6#17988502C212yesmaximal
7#17988498C211yesmaximal, characteristic, complemented
8#17988482C212yesmaximal, complemented
9#17988477C212yesmaximal, complemented
10C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
11C2×C22⋊Q8×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13#14556574—24no—
14C2×#11924007C2211yescharacteristic
15C2×#11924007C2212yes—
16C2×#11924007C2211yescharacteristic
17C2×#11924007C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2211yescharacteristic
20C2×#11924005C2211yescharacteristic
21C2×#11924005C2212yes—
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2212yes—
24C2×C4×Dic73C2212yes—
25#14556498C2211yescharacteristic
26#14556498C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31C22×Q8×C73C2211yescharacteristic
32C23×C4×C73C2211yescharacteristic
33C22⋊Q8×C73—24no—
34C2×C4⋊C4×C73C2212yes—
35C2×C4⋊C4×C73C2211yescharacteristic
36C2×C22⋊C4×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—42no—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45#11924007—22no—
46#11924007—22no—
47#11924007—24no—
48#11924007—42no—
49C22⋊Dic73—22no—
50C22⋊Dic73—24no—
51#11924005—22no—
52#11924005—22no—
53#11924005—24no—
54#11924005—42no—
55C4×Dic73—42no—
56C24×C73C2311yescharacteristic
57C2×Q8×C73—22no—
58C2×Q8×C73—42no—
59C22×C4×C73—42no—
60C22×C4×C73D414yes—
61C22×C4×C73C2312yes—
62C22×C4×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C22×C4×C73C2311yescharacteristic
65C4⋊C4×C73—22no—
66C4⋊C4×C73—24no—
67C22⋊C4×C73—24no—
68C23×C73—22no—
69C23×C73—22no—
70C23×C73—21no—
71C23×C73—21no—
72C23×C73C2×D412yes—
73C23×C73C2411yescharacteristic
74C22×D73—21no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—21no—
78C22×D73—21no—
79Q8×C73—44no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—44no—
89C2×C4×C73C2×D412yes—
90C2×C4×C73C2×D412yes—
91C22⋊D73—44no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—22no—
104C2×Dic73#4114yes—
105C22×C73—22no—
106C22×C73—22no—
107C22×C73—22no—
108C22×C73—42no—
109C22×C73—42no—
110C22×C73C22×D411yescharacteristic
111C22×C73C2×#4112yes—
112C22×C73H(5,𝔽2)12yes—
113C22×C732−1+411yescharacteristic
114C22×C732−1+411yescharacteristic
115C2×D73—41no—
116C2×D73—41no—
117C2×D73—41no—
118C2×D73—42no—
119C2×D73—42no—
120C4×C73—22no—
121C4×C73—22no—
122C4×C73—42no—
123C4×C73—42no—
124Dic73—24no—
125Dic73—41no—
126Dic73—41no—
127Dic73—41no—
128Dic73—42no—
129C2×C73—42no—
130C2×C73#53211yescharacteristic
131C2×C73#53411yescharacteristic
132C2×C73#53611yescharacteristic
133C2×C73#53912yes—
134C2×C73#54212yes—
135D73—81no—
136#2663—731nomaximal, Sylow
137C73#266311yescharacteristic, complemented, Sylow
138C2×#123—731no—
139C2×C22⋊Q8D7311yescharacteristic, complemented
140#400—731no—
141#399—731no—
142#397—732no—
143#395—731no—
144#394—732no—
145#393—731no—
146#389—732no—
147#388—732no—
148C4×C22⋊C4—731no—
149C22×Q8C2×D7311yescharacteristic
150C22×D4—731no—
151C23×C4C2×D7311yescharacteristic
152#123—1464no—
153C22⋊Q8—24no—
154C2×C4⋊C4—732no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—731no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4C2×D7312yes—
159C2×C4⋊C4C2×D7311yescharacteristic
160C2×C22⋊C4—732no—
161C2×C22⋊C4—731no—
162C2×C22⋊C4—732no—
163C2×C22⋊C4—731no—
164C2×C22⋊C4—731no—
165C2×C22⋊C4—732no—
166C2×C22⋊C4C2×D7312yes—
167C2×C42—732no—
168#95—731no—
169#95—731no—
170#95—732no—
171#95—732no—
172#95—732no—
173#95—732no—
174C24—731no—
175C24C22×D7311yescharacteristic
176C2×Q8—22no—
177C2×Q8—42no—
178C2×D4—2922no—
179C2×D4—1462no—
180C22×C4—42no—
181C22×C4—732no—
182C22×C4—732no—
183C22×C4—731no—
184C22×C4—731no—
185C22×C4—731no—
186C22×C4C22⋊D7314yes—
187C22×C4C22×D7312yes—
188C22×C4C22×D7312yes—
189C22×C4C22×D7311yescharacteristic
190C22×C4C22×D7311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—24no—
193C4⋊C4—2922no—
194C4⋊C4—1464no—
195C4⋊C4—1462no—
196C4⋊C4—1462no—
197C22⋊C4—24no—
198C22⋊C4—2922no—
199C22⋊C4—1464no—
200C22⋊C4—1464no—
201C22⋊C4—1462no—
202C22⋊C4—1462no—
203C22⋊C4—1462no—
204C42—2922no—
205C23—22no—
206C23—22no—
207C23—21no—
208C23—21no—
209C23—1461no—
210C23—1462no—
211C23—1462no—
212C23—1461no—
213C23—1461no—
214C23C2×C22⋊D7312yes—
215C23C23×D7311yescharacteristic
216Q8—44no—
217D4—2924no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—44no—
227C2×C4—734no—
228C2×C4—1461no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1462no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4—1461no—
236C2×C4—1461no—
237C2×C4—1462no—
238C2×C4—1462no—
239C2×C4—1462no—
240C2×C4C2×C22⋊D7312yes—
241C2×C4C2×C22⋊D7312yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—2921no—
248C22—2921no—
249C22—2921no—
250C22—2922no—
251C22—2922no—
252C22C22×C22⋊D7311yescharacteristic
253C22#41×D7312yes—
254C22#1455663612yes—
255C22#1455663911yescharacteristic
256C22#1455663911yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—2921no—
262C4—2921no—
263C4—2921no—
264C4—2922no—
265C4—1464no—
266C2—42no—
267C2—5841no—
268C2#1798913311yescharacteristic
269C2#1798914611yescharacteristic
270C2#1798916111yescharacteristic
271C2#1798918312yes—
272C2#1798920712yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×C22⋊Q8×C73C2
hypercenterC2×C22⋊Q8D73
hypocenterC73#2663
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988525C2semidirect
3. #17988522C2semidirect
4. #17988515C2semidirect
5. #17988506C2semidirect
7. #17988498C2semidirect
8. #17988482C2semidirect
9. #17988477C2semidirect
10. C4×C22⋊Dic73C2semidirect
11. C2×C22⋊Q8×C73C2semidirect
137. C73#2663semidirect
139. C2×C22⋊Q8D73semidirect