Finite Group Databasebeta

← #22615413

Subgroups — #22615413

Order 9344.

520 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556577C211yesmaximal, characteristic
2C2×Q8×Dic73C211yesmaximal, characteristic, complemented
3#17988514C211yesmaximal, characteristic, complemented
4#17988512C211yesmaximal, characteristic, complemented
5#17988498C211yesmaximal, characteristic, complemented
6#17988491C212yesmaximal, complemented
7#17988487C212yesmaximal
8#17988480C212yesmaximal, complemented
9#17988479C212yesmaximal, complemented
10#17988438C211yesmaximal, characteristic, complemented
11#393×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14#14556577—24no—
15Q8×Dic73—24no—
16C2×C4⋊Dic73C2212yes—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×C22⋊Dic73C2211yescharacteristic
20C2×C22⋊Dic73C2212yes—
21C2×#11924005C2211yescharacteristic
22C2×#11924005C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2212yes—
25C2×C4×Dic73C2212yes—
26C2×C4×Dic73C2212yes—
27C2×C4×Dic73C2211yescharacteristic
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×Q8×C73C2211yescharacteristic
33C2×C22⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—24no—
40C2×C22⋊D73—22no—
41C2×C22⋊D73—24no—
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2312yes—
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C4⋊Dic73—22no—
48C4⋊Dic73—24no—
49#11924007—24no—
50C22⋊Dic73—22no—
51C22⋊Dic73—42no—
52#11924005—22no—
53#11924005—24no—
54#11924005—22no—
55#11924005—42no—
56C4×Dic73—24no—
57C4×Dic73—42no—
58C4×Dic73D414yes—
59C24×C73C2311yescharacteristic
60C2×Q8×C73—22no—
61C2×Q8×C73—24no—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2312yes—
66C22⋊C4×C73—22no—
67C22⋊C4×C73—24no—
68C23×C73—21no—
69C23×C73—22no—
70C23×C73—22no—
71C23×C73—21no—
72C23×C73—21no—
73C23×C73C2411yescharacteristic
74C22×D73—21no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—21no—
78C22×D73—21no—
79Q8×C73—28no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73C2×D412yes—
89C2×C4×C73#4114yes—
90C22⋊D73—44no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73C2×D412yes—
102C2×Dic73C2×D412yes—
103C2×Dic73#4114yes—
104Dic146—44no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73—41no—
108C22×C73—42no—
109C22×C73—42no—
110C22×C73C22×D411yescharacteristic
111C22×C73C2×#4112yes—
112C22×C73C2×#4112yes—
113C22×C73H(5,𝔽2)11yescharacteristic
114C22×C732−1+411yescharacteristic
115C2×D73—41no—
116C2×D73—41no—
117C2×D73—41no—
118C2×D73—42no—
119C2×D73—42no—
120C4×C73—22no—
121C4×C73—24no—
122C4×C73—41no—
123C4×C73—42no—
124Dic73—22no—
125Dic73—41no—
126Dic73—42no—
127Dic73—42no—
128Dic73#12414yes—
129C2×C73—81no—
130C2×C73#52511yescharacteristic
131C2×C73C2×#12411yescharacteristic
132C2×C73#53711yescharacteristic
133C2×C73#55612yes—
134C2×C73#55912yes—
135D73—81no—
136#2592—731nomaximal, Sylow
137C73#259211yescharacteristic, complemented, Sylow
138C2×#124—731no—
139C2×C4×Q8—731no—
140#397—731no—
141#397—731no—
142#393—731no—
143#393D7311yescharacteristic, complemented
144#391—732no—
145#390—732no—
146#388—732no—
147#388—732no—
148C4×C4⋊C4—731no—
149C22×Q8—731no—
150C22×Q8C2×D7311yescharacteristic
151C22×D4—731no—
152#124—1464no—
153C4×Q8—1464no—
154C2×C4⋊C4—732no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—732no—
157C2×C22⋊C4—732no—
158C2×C22⋊C4—732no—
159C2×C22⋊C4—731no—
160C2×C22⋊C4—731no—
161C2×C22⋊C4—731no—
162C2×C22⋊C4—732no—
163C2×C22⋊C4C2×D7311yescharacteristic
164C2×C22⋊C4C2×D7312yes—
165C2×C42—732no—
166C2×C42—731no—
167C2×C42—732no—
168#95—731no—
169#95—732no—
170#95—732no—
171#95—732no—
172#95C2×D7311yescharacteristic
173#95C2×D7312yes—
174C24—731no—
175C24C22×D7311yescharacteristic
176C2×Q8—22no—
177C2×Q8—24no—
178C2×Q8—1462no—
179C2×Q8—1464no—
180C2×D4—1462no—
181C2×D4—1464no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4—731no—
185C22×C4—732no—
186C22×C4—732no—
187C22×C4C22×D7311yescharacteristic
188C22×C4C22×D7312yes—
189C22×C4C22×D7311yescharacteristic
190C22×C4C22×D7312yes—
191C4⋊C4—1464no—
192C4⋊C4—1464no—
193C4⋊C4—1462no—
194C22⋊C4—22no—
195C22⋊C4—24no—
196C22⋊C4—2922no—
197C22⋊C4—2922no—
198C22⋊C4—1462no—
199C22⋊C4—1462no—
200C22⋊C4—1462no—
201C22⋊C4—1464no—
202C42—2922no—
203C42—734no—
204C42—1464no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—1461no—
211C23—1462no—
212C23—1462no—
213C23—1461no—
214C23—1461no—
215C23C23×D7311yescharacteristic
216Q8—28no—
217Q8—2924no—
218D4—2924no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—732no—
228C2×C4—734no—
229C2×C4—732no—
230C2×C4—1462no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4—1462no—
237C2×C4—1462no—
238C2×C4—1461no—
239C2×C4—1461no—
240C2×C4D4×D7312yes—
241C2×C4#1192402714yes—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—41no—
246C22—41no—
247C22—2921no—
248C22—2922no—
249C22—2922no—
250C22—2921no—
251C22—2921no—
252C22C2×D4×D7311yescharacteristic
253C22#41×D7312yes—
254C22C2×#1192402712yes—
255C22#1455663711yescharacteristic
256C22#1455663911yescharacteristic
257C4—22no—
258C4—24no—
259C4—42no—
260C4—41no—
261C4—2922no—
262C4—2922no—
263C4—2921no—
264C4—734no—
265C4—1462no—
266C2—81no—
267C2—5841no—
268C2#1798909311yescharacteristic
269C2#124×D7311yescharacteristic
270C2#1798916711yescharacteristic
271C2#1798930812yes—
272C2#1798931912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#393×C73C2
hypercenter#393D73
hypocenterC73#2592
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic73C2semidirect
3. #17988514C2semidirect
4. #17988512C2semidirect
5. #17988498C2semidirect
6. #17988491C2semidirect
8. #17988480C2semidirect
9. #17988479C2semidirect
10. #17988438C2semidirect
11. #393×C73C2semidirect
137. C73#2592semidirect
143. #393D73semidirect