Finite Group Databasebeta

← #22615726

Subgroups — #22615726

Order 9344.

548 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556564C211yesmaximal, characteristic
2C2×#14556549C211yesmaximal, characteristic, complemented
3#17988524C211yesmaximal, characteristic, complemented
4#17988523C211yesmaximal, characteristic, complemented
5#17988513C211yesmaximal, characteristic, complemented
6#17988505C212yesmaximal, complemented
7#17988503C212yesmaximal, complemented
8#17988487C212yesmaximal, complemented
9#17988484C212yesmaximal, complemented
10#17988446C211yesmaximal, characteristic, complemented
11#397×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14C22×C22⋊D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556564—24no—
17#14556549—24no—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2212yes—
20C2×#11924007C2212yes—
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×#11924005C2212yes—
29C2×C4×Dic73C2212yes—
30#14556498C2211yescharacteristic
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C22⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C23×D73C2311yescharacteristic
39C2×D292—22no—
40C2×D292—42no—
41C2×C22⋊D73—22no—
42C2×C22⋊D73—22no—
43C2×C22⋊D73—24no—
44C2×C22⋊D73—42no—
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2312yes—
48C22×Dic73C2311yescharacteristic
49C2×C4×D73—24no—
50C2×C4×D73D414yes—
51C4⋊Dic73—22no—
52C4⋊Dic73—42no—
53#11924007—22no—
54#11924007—24no—
55#11924007—42no—
56C22⋊Dic73—42no—
57#11924005—24no—
58#11924005—22no—
59#11924005—42no—
60#11924005—42no—
61#11924005—42no—
62C4×Dic73—24no—
63C24×C73C2311yescharacteristic
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2312yes—
67C22×C4×C73C2311yescharacteristic
68C4⋊C4×C73—22no—
69C22⋊C4×C73—22no—
70C22⋊C4×C73—42no—
71C23×C73—21no—
72C23×C73—22no—
73C23×C73—21no—
74C23×C73—22no—
75C23×C73—21no—
76C23×C73C2411yescharacteristic
77C22×D73—22no—
78C22×D73—21no—
79C22×D73—22no—
80C22×D73—21no—
81C22×D73—21no—
82C22×D73—22no—
83C22×D73—21no—
84C22×D73—22no—
85C22×D73—21no—
86C22×D73C2×D412yes—
87C2×C4×C73—22no—
88C2×C4×C73—21no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73C2×D412yes—
97C22⋊D73—44no—
98C22⋊D73—44no—
99C2×Dic73—22no—
100C2×Dic73—21no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73C2×D412yes—
108C2×Dic73#4114yes—
109D292—44no—
110C4×D73—28no—
111C22×C73—41no—
112C22×C73—41no—
113C22×C73—41no—
114C22×C73—42no—
115C22×C73—42no—
116C22×C73C22×D411yescharacteristic
117C22×C73C2×#4112yes—
118C22×C73H(5,𝔽2)11yescharacteristic
119C22×C73H(5,𝔽2)12yes—
120C22×C732−1+411yescharacteristic
121C2×D73—22no—
122C2×D73—22no—
123C2×D73—22no—
124C2×D73—42no—
125C2×D73—42no—
126C2×D73—41no—
127C2×D73—41no—
128C2×D73—41no—
129C2×D73—42no—
130C2×D73—42no—
131C4×C73—22no—
132C4×C73—41no—
133C4×C73—42no—
134C4×C73—42no—
135Dic73—42no—
136Dic73—41no—
137Dic73—42no—
138Dic73#12314yes—
139C2×C73—81no—
140C2×C73C2×#12311yescharacteristic
141C2×C73#53511yescharacteristic
142C2×C73#53711yescharacteristic
143C2×C73#54012yes—
144C2×C73#54212yes—
145D73—42no—
146D73—81no—
147#2624—731nomaximal, Sylow
148C73#262411yescharacteristic, complemented, Sylow
149C2×#121—731no—
150C2×#117—731no—
151#399—731no—
152#399—731no—
153#397—731no—
154#397D7311yescharacteristic, complemented
155#394—732no—
156#394—732no—
157#390—732no—
158#389—732no—
159#380—731no—
160C22×D4—731no—
161C22×D4—731no—
162C22×D4—731no—
163C23×C4—731no—
164#121—1464no—
165#117—1464no—
166C2×C4⋊C4—732no—
167C2×C4⋊C4—732no—
168C2×C4⋊C4—731no—
169C2×C4⋊C4—731no—
170C2×C4⋊C4—732no—
171C2×C4⋊C4C2×D7311yescharacteristic
172C2×C22⋊C4—732no—
173C2×C22⋊C4—732no—
174C2×C22⋊C4—732no—
175C2×C22⋊C4—732no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4—731no—
178C2×C22⋊C4C2×D7311yescharacteristic
179C2×C22⋊C4C2×D7312yes—
180C2×C42—732no—
181#95—731no—
182#95—732no—
183#95C2×D7311yescharacteristic
184#95C2×D7312yes—
185C24—731no—
186C24—731no—
187C24C22×D7311yescharacteristic
188C2×D4—2922no—
189C2×D4—2922no—
190C2×D4—1462no—
191C2×D4—1462no—
192C2×D4—1464no—
193C2×D4—1462no—
194C22×C4—731no—
195C22×C4—734no—
196C22×C4—732no—
197C22×C4—731no—
198C22×C4—732no—
199C22×C4—1464no—
200C22×C4C22×D7312yes—
201C22×C4C22×D7312yes—
202C22×C4C22×D7311yescharacteristic
203C22×C4C22×D7311yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—2922no—
206C4⋊C4—2922no—
207C4⋊C4—1464no—
208C4⋊C4—1462no—
209C4⋊C4—1462no—
210C22⋊C4—22no—
211C22⋊C4—42no—
212C22⋊C4—2922no—
213C22⋊C4—2922no—
214C22⋊C4—2922no—
215C22⋊C4—2922no—
216C22⋊C4—1464no—
217C22⋊C4—1462no—
218C42—1464no—
219C23—21no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—732no—
225C23—1461no—
226C23—1462no—
227C23—1461no—
228C23—1462no—
229C23—1461no—
230C23—1462no—
231C23—1461no—
232C23—1462no—
233C23—1461no—
234C23C23×D7311yescharacteristic
235D4—2924no—
236D4—2924no—
237D4—2924no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—732no—
248C2×C4—734no—
249C2×C4—1468no—
250C2×C4—1462no—
251C2×C4—1461no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1462no—
257C2×C4—1462no—
258C2×C4D4×D7312yes—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—42no—
263C22—41no—
264C22—2922no—
265C22—2922no—
266C22—2921no—
267C22—2921no—
268C22—2922no—
269C22—2922no—
270C22—2921no—
271C22—1462no—
272C22—1462no—
273C22—1462no—
274C22C2×D4×D7311yescharacteristic
275C22#41×D7312yes—
276C22#1455663611yescharacteristic
277C22#1455663712yes—
278C22#1455663811yescharacteristic
279C4—22no—
280C4—41no—
281C4—42no—
282C4—42no—
283C4—2921no—
284C4—2922no—
285C4—2922no—
286C4—734no—
287C2—81no—
288C2—2922no—
289C2—5841no—
290C2#123×D7311yescharacteristic
291C2#1798915511yescharacteristic
292C2#1798916611yescharacteristic
293C2#1798918912yes—
294C2#1798920312yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2624
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#14556549C2semidirect
3. #17988524C2semidirect
4. #17988523C2semidirect
5. #17988513C2semidirect
6. #17988505C2semidirect
7. #17988503C2semidirect
8. #17988487C2semidirect
9. #17988484C2semidirect
10. #17988446C2semidirect
11. #397×C73C2semidirect
148. C73#2624semidirect
154. #397D73semidirect