Finite Group Databasebeta

← #22615716

Subgroups — #22615716

Order 9344.

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

normal subgroups only

This group has 526 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×#14556573C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3#17988527C211yesmaximal, characteristic, complemented
4#17988525C211yesmaximal, characteristic, complemented
5#17988523C211yesmaximal, characteristic, complemented
6#17988520C212yesmaximal, complemented
7#17988515C212yesmaximal, complemented
8#17988463C212yesmaximal
9#17988458C212yesmaximal, complemented
10#17988449C211yesmaximal, characteristic, complemented
11#399×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14C22×C4×D73C2212yes—
15#14556573—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2212yes—
21C4⋊C4×D73—24no—
22C2×C22⋊Dic73C2211yescharacteristic
23C2×C22⋊Dic73C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—24no—
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2312yes—
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2312yes—
44C22×Dic73C2311yescharacteristic
45C2×C4×D73—24no—
46C2×C4×D73—24no—
47C2×C4×D73—42no—
48C2×C4×D73—42no—
49C2×C4×D73D414yes—
50C4⋊Dic73—22no—
51C4⋊Dic73—22no—
52#11924007—22no—
53#11924007—24no—
54#11924007—42no—
55C22⋊Dic73—22no—
56C22⋊Dic73—42no—
57#11924005—22no—
58#11924005—24no—
59C24×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C22×C4×C73C2312yes—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2311yescharacteristic
64C4⋊C4×C73—22no—
65C4⋊C4×C73—42no—
66C22⋊C4×C73—22no—
67C22⋊C4×C73—42no—
68C23×C73—21no—
69C23×C73—22no—
70C23×C73—22no—
71C23×C73—21no—
72C23×C73—21no—
73C23×C73C2411yescharacteristic
74C22×D73—22no—
75C22×D73—21no—
76C22×D73—21no—
77C22×D73C2×D412yes—
78C22×D73#4114yes—
79C2×C4×C73—22no—
80C2×C4×C73—21no—
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×C73C2×D412yes—
89C22⋊D73—44no—
90C2×Dic73—22no—
91C2×Dic73—21no—
92C2×Dic73—22no—
93C2×Dic73—21no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—21no—
100C2×Dic73—21no—
101C2×Dic73—22no—
102C2×Dic73C2×D412yes—
103C4×D73—28no—
104C4×D73—48no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73—41no—
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—22no—
116C2×D73—22no—
117C2×D73—24no—
118C2×D73—24no—
119C2×D73#12314yes—
120C4×C73—22no—
121C4×C73—42no—
122C4×C73—41no—
123C4×C73—42no—
124Dic73—22no—
125Dic73—41no—
126Dic73—42no—
127Dic73—41no—
128Dic73—42no—
129C2×C73—81no—
130C2×C73C2×#12311yescharacteristic
131C2×C73#53511yescharacteristic
132C2×C73#53611yescharacteristic
133C2×C73#53912yes—
134C2×C73#53912yes—
135D73—24no—
136#2623—731nomaximal, Sylow
137C73#262311yescharacteristic, complemented, Sylow
138C2×#123—731no—
139C22×C4⋊C4—731no—
140#400—731no—
141#400—731no—
142#399—731no—
143#399D7311yescharacteristic, complemented
144#398—732no—
145#397—732no—
146#386—732no—
147#385—732no—
148#381—731no—
149C22×D4—731no—
150C23×C4—732no—
151C23×C4—731no—
152#123—1464no—
153C2×C4⋊C4—732no—
154C2×C4⋊C4—732no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—731no—
157C2×C4⋊C4—731no—
158C2×C4⋊C4—1464no—
159C2×C4⋊C4C2×D7311yescharacteristic
160C2×C4⋊C4C2×D7312yes—
161C2×C22⋊C4—732no—
162C2×C22⋊C4—731no—
163C2×C22⋊C4—731no—
164C2×C22⋊C4—732no—
165C2×C22⋊C4C2×D7311yescharacteristic
166C2×C22⋊C4C2×D7312yes—
167#95—732no—
168#95—731no—
169#95—732no—
170#95—732no—
171#95—732no—
172#95—732no—
173#95C2×D7311yescharacteristic
174C24—731no—
175C24C22×D7311yescharacteristic
176C2×D4—1462no—
177C2×D4—1464no—
178C22×C4—2922no—
179C22×C4—2922no—
180C22×C4—731no—
181C22×C4—734no—
182C22×C4—731no—
183C22×C4—732no—
184C22×C4—731no—
185C22×C4—732no—
186C22×C4—1464no—
187C22×C4—1464no—
188C22×C4C22×D7312yes—
189C22×C4C22×D7312yes—
190C22×C4C22×D7311yescharacteristic
191C22×C4C22×D7311yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—2922no—
195C4⋊C4—1464no—
196C4⋊C4—1462no—
197C4⋊C4—1462no—
198C4⋊C4—1462no—
199C22⋊C4—22no—
200C22⋊C4—42no—
201C22⋊C4—2922no—
202C22⋊C4—1464no—
203C22⋊C4—1462no—
204C22⋊C4—1462no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—732no—
211C23—734no—
212C23—1462no—
213C23—1461no—
214C23—1461no—
215C23C23×D7311yescharacteristic
216D4—2924no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—2928no—
227C2×C4—732no—
228C2×C4—1468no—
229C2×C4—1461no—
230C2×C4—1462no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4—1462no—
237C2×C4—1461no—
238C2×C4—1461no—
239C2×C4—1462no—
240C2×C4—1462no—
241C2×C4D4×D7312yes—
242C22—41no—
243C22—41no—
244C22—42no—
245C22—42no—
246C22—41no—
247C22—734no—
248C22—1462no—
249C22—1462no—
250C22—1464no—
251C22—1464no—
252C22C2×D4×D7311yescharacteristic
253C22#41×D7312yes—
254C22#1455663612yes—
255C22#1455663811yescharacteristic
256C22#1455663911yescharacteristic
257C4—22no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—2922no—
262C4—2921no—
263C4—2922no—
264C4—2921no—
265C4—1462no—
266C2—81no—
267C2—1464no—
268C2#123×D7311yescharacteristic
269C2#1798915011yescharacteristic
270C2#1798916011yescharacteristic
271C2#1798918012yes—
272C2#1798918312yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2623
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D73C2semidirect
3. #17988527C2semidirect
4. #17988525C2semidirect
5. #17988523C2semidirect
6. #17988520C2semidirect
7. #17988515C2semidirect
9. #17988458C2semidirect
10. #17988449C2semidirect
11. #399×C73C2semidirect
137. C73#2623semidirect
143. #399D73semidirect