Finite Group Databasebeta

← #22615405

Subgroups — #22615405

Order 9344.

596 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14556562C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3#17988527C211yesmaximal, characteristic, complemented
4#17988526C211yesmaximal, characteristic, complemented
5#17988501C211yesmaximal, characteristic, complemented
6#17988480C212yesmaximal, complemented
7#17988475C212yesmaximal, complemented
8#17988463C212yesmaximal, complemented
9#17988463C212yesmaximal, complemented
10#17988434C211yesmaximal, characteristic, complemented
11#394×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2212yes—
13C22×C4×D73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556562—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C4⋊C4×D73—24no—
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×C22⋊Dic73C2212yes—
25C2×#11924005C2212yes—
26C2×C4×Dic73C2212yes—
27#14556498C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2212yes—
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—24no—
39C2×C22⋊D73—24no—
40C2×C22⋊D73—24no—
41C22×Dic73C2312yes—
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2311yescharacteristic
46C2×C4×D73—22no—
47C2×C4×D73—22no—
48C2×C4×D73—22no—
49C2×C4×D73—22no—
50C2×C4×D73—42no—
51C2×C4×D73—42no—
52C2×C4×D73D414yes—
53C4⋊Dic73—22no—
54C4⋊Dic73—22no—
55#11924007—22no—
56#11924007—22no—
57C22⋊Dic73—24no—
58C22⋊Dic73—24no—
59C22⋊Dic73—42no—
60#11924005—24no—
61C4×Dic73—42no—
62C24×C73C2312yes—
63C2×D4×C73—22no—
64C2×D4×C73—42no—
65C22×C4×C73C2312yes—
66C22×C4×C73C2311yescharacteristic
67C22×C4×C73C2311yescharacteristic
68C22×C4×C73C2311yescharacteristic
69C4⋊C4×C73—22no—
70C22⋊C4×C73—24no—
71C22⋊C4×C73—42no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73—22no—
79C23×C73C2411yescharacteristic
80C22×D73—21no—
81C22×D73—21no—
82C22×D73—22no—
83C22×D73C2×D412yes—
84C22×D73#4114yes—
85D4×C73—44no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73C2×D412yes—
95C2×C4×C73#4112yes—
96C22⋊D73—48no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—21no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73C2×D412yes—
109C2×Dic73#4112yes—
110C4×D73—28no—
111C4×D73—44no—
112C4×D73—44no—
113C22×C73—42no—
114C22×C73—42no—
115C22×C73—42no—
116C22×C73—42no—
117C22×C73—42no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73C22×D411yescharacteristic
121C22×C73C2×#4111yescharacteristic
122C22×C73C2×#4112yes—
123C22×C73C2×#4111yescharacteristic
124C22×C73H(5,𝔽2)12yes—
125C2×D73—22no—
126C2×D73—22no—
127C2×D73—24no—
128C2×D73—24no—
129C2×D73#12414yes—
130C4×C73—22no—
131C4×C73—22no—
132C4×C73—41no—
133C4×C73—42no—
134Dic73—22no—
135Dic73—22no—
136Dic73—42no—
137Dic73—41no—
138Dic73—42no—
139C2×C73—82no—
140C2×C73#52511yescharacteristic
141C2×C73C2×#12411yescharacteristic
142C2×C73#53411yescharacteristic
143C2×C73#55312yes—
144C2×C73#55312yes—
145D73—24no—
146#2591—731nomaximal, Sylow
147C73#259111yescharacteristic, complemented, Sylow
148C2×#121—731no—
149C22×C4⋊C4—731no—
150#400—731no—
151#400—731no—
152#394—731no—
153#394D7311yescharacteristic, complemented
154#388—732no—
155#388—732no—
156#386—732no—
157#386—732no—
158C4×C22⋊C4—731no—
159C22×D4—732no—
160C22×D4C2×D7311yescharacteristic
161C23×C4—731no—
162C23×C4—731no—
163C23×C4—731no—
164#121—1464no—
165C2×C4⋊C4—731no—
166C2×C4⋊C4—731no—
167C2×C4⋊C4—731no—
168C2×C4⋊C4—731no—
169C2×C4⋊C4—1464no—
170C2×C4⋊C4C2×D7311yescharacteristic
171C2×C22⋊C4—732no—
172C2×C22⋊C4—732no—
173C2×C22⋊C4—732no—
174C2×C22⋊C4—732no—
175C2×C22⋊C4C2×D7312yes—
176C2×C22⋊C4C2×D7312yes—
177C2×C42—732no—
178#95—731no—
179#95—732no—
180#95—732no—
181#95—732no—
182#95—732no—
183#95C2×D7311yescharacteristic
184C24—731no—
185C24C22×D7312yes—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—1464no—
189C2×D4—1464no—
190C2×D4—1464no—
191C22×C4—2922no—
192C22×C4—2922no—
193C22×C4—734no—
194C22×C4—731no—
195C22×C4—731no—
196C22×C4—732no—
197C22×C4—732no—
198C22×C4—731no—
199C22×C4—1462no—
200C22×C4—1462no—
201C22×C4—1462no—
202C22×C4—1462no—
203C22×C4C22×D7312yes—
204C22×C4C22×D7311yescharacteristic
205C22×C4C22×D7311yescharacteristic
206C22×C4C22×D7311yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—1462no—
209C4⋊C4—1462no—
210C4⋊C4—1462no—
211C4⋊C4—1462no—
212C22⋊C4—24no—
213C22⋊C4—42no—
214C22⋊C4—2922no—
215C22⋊C4—1464no—
216C22⋊C4—1464no—
217C22⋊C4—1464no—
218C42—2922no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—732no—
227C23—734no—
228C23—1461no—
229C23—1461no—
230C23—1462no—
231C23C23×D7311yescharacteristic
232D4—44no—
233D4—2928no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—2924no—
243C2×C4—2924no—
244C2×C4—732no—
245C2×C4—732no—
246C2×C4—1468no—
247C2×C4—1462no—
248C2×C4—1461no—
249C2×C4—1462no—
250C2×C4—1462no—
251C2×C4—1462no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1461no—
256C2×C4—1461no—
257C2×C4—1462no—
258C2×C4D4×D7312yes—
259C2×C4#1192402712yes—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—734no—
268C22—1462no—
269C22—1464no—
270C22—1464no—
271C22—1462no—
272C22C2×D4×D7311yescharacteristic
273C22#41×D7311yescharacteristic
274C22#41×D7312yes—
275C22C2×#1192402711yescharacteristic
276C22#1455663612yes—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—42no—
281C4—2921no—
282C4—2922no—
283C4—2922no—
284C4—1462no—
285C4—1462no—
286C2—82no—
287C2—1464no—
288C2#1798909711yescharacteristic
289C2#124×D7311yescharacteristic
290C2#1798914711yescharacteristic
291C2#1798928212yes—
292C2#1798928412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2591
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D73C2semidirect
3. #17988527C2semidirect
4. #17988526C2semidirect
5. #17988501C2semidirect
6. #17988480C2semidirect
7. #17988475C2semidirect
8. #17988463C2semidirect
9. #17988463C2semidirect
10. #17988434C2semidirect
11. #394×C73C2semidirect
147. C73#2591semidirect
153. #394D73semidirect