Finite Group Databasebeta

← #22620854

Subgroups — #22620854

Order 9344.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#17989132C211yesmaximal, characteristic
2C2×#14556589C211yesmaximal, characteristic, complemented
3#17988958C212yesmaximal, complemented
4#17988936C212yesmaximal, complemented
5#17988791C212yesmaximal, complemented
6#17988790C212yesmaximal, complemented
7#17988728C211yesmaximal, characteristic, complemented
8#17988726C211yesmaximal, characteristic, complemented
9#17988725C211yesmaximal, characteristic, complemented
10#17988637C211yesmaximal, characteristic, complemented
11#448×C73C211yesmaximal, characteristic, complemented
12C2×#11924027—21no—
13C22×Dic146C2211yescharacteristic
14C2×#11924017C2212yes—
15C2×#11924016C2212yes—
16C2×#11924015C2212yes—
17#14556590C2211yescharacteristic
18#14556589—21no—
19#14556589—21no—
20#14556589C2212yes—
21#14556589C2212yes—
22#14556587C2211yescharacteristic
23#14556577—21no—
24#14556565C2211yescharacteristic
25#14556563—21no—
26D4×Dic73C2211yescharacteristic
27#14556553C2211yescharacteristic
28#14556551—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×C4×Dic73C2211yescharacteristic
32#14556520C2212yes—
33#14556516C2212yes—
34#14556515C2212yes—
35#14556514C2212yes—
36C22⋊#10596831C2211yescharacteristic
37C8×Dic73C2212yes—
38C22×Q8×C73C2211yescharacteristic
39C2×SD16×C73C2212yes—
40#121×C73C2211yescharacteristic
41#103×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43#11924027—44no—
44C2×Dic146—21no—
45C2×Dic146—21no—
46C2×Dic146—42no—
47C2×Dic146C2312yes—
48C2×D292C2311yescharacteristic
49C2×C22⋊D73—21no—
50C2×C22⋊D73—21no—
51C2×C22⋊D73—21no—
52C22×Dic73—21no—
53C22×Dic73—21no—
54C22×Dic73D411yescharacteristic
55C22×Dic73D411yescharacteristic
56C2×C4×D73—21no—
57#11924017—42no—
58#11924016—42no—
59#11924015—42no—
60C2×#10596831C2312yes—
61C4⋊Dic73C2311yescharacteristic
62#11924007—22no—
63#11924007—22no—
64#11924007—22no—
65#11924007—22no—
66#11924007—21no—
67C22⋊Dic73—21no—
68#11924005—21no—
69#11924005—21no—
70C4×Dic73D411yescharacteristic
71C4×Dic73D411yescharacteristic
72C4×Dic73C2311yescharacteristic
73C4×Dic73C2311yescharacteristic
74C2×Q8×C73—21no—
75C2×Q8×C73—42no—
76C2×Q8×C73C2312yes—
77C2×D4×C73—21no—
78C2×D4×C73C2311yescharacteristic
79C22×C4×C73—21no—
80C22×C4×C73C2311yescharacteristic
81SD16×C73—42no—
82C2×C8×C73C2312yes—
83C4⋊C4×C73C2311yescharacteristic
84C22⋊C4×C73—21no—
85C23×C73—21no—
86C23×C73C2×D411yescharacteristic
87C22×D73—21no—
88Q8×C73—22no—
89Q8×C73—22no—
90Q8×C73—42no—
91D4×C73—22no—
92D4×C73—42no—
93C2×C4×C73—22no—
94C2×C4×C73—21no—
95C2×C4×C73—22no—
96C2×C4×C73—42no—
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2411yescharacteristic
99C22⋊D73—42no—
100C22⋊D73—42no—
101C22⋊D73—42no—
102C2×Dic73—22no—
103C2×Dic73—21no—
104C2×Dic73—22no—
105C2×Dic73—42no—
106C2×Dic73—42no—
107C2×Dic73SD1614yescomplemented
108C2×Dic73C2×D411yescharacteristic
109C2×Dic73C2×D411yescharacteristic
110C2×Dic73C2×D411yescharacteristic
111C2×Dic73C2×D411yescharacteristic
112D292—22no—
113C4×D73—42no—
114Dic146—22no—
115Dic146—22no—
116Dic146—42no—
117Dic146—42no—
118C8×C73—22no—
119#10596831—22no—
120C22×C73—21no—
121C22×C73—21no—
122C22×C73—41no—
123C22×C73—41no—
124C22×C73—41no—
125C22×C73C2×SD1612yes—
126C22×C73C22×D411yescharacteristic
127C2×D73—41no—
128C2×D73—41no—
129C2×D73—41no—
130C4×C73—21no—
131C4×C73—42no—
132C4×C73—41no—
133C4×C73H(5,𝔽2)12yes—
134Dic73—21no—
135Dic73—42no—
136Dic73—41no—
137Dic73C2×SD1612yes—
138Dic73C2×SD1612yes—
139Dic73#13712yes—
140C2×C73—22no—
141C2×C73—81no—
142C2×C73#53511yescharacteristic
143C2×C73C22×SD1611yescharacteristic
144C2×C73C2×#13711yescharacteristic
145D73—81no—
146#3206—731nomaximal, Sylow
147C73#320611yescharacteristic, complemented, Sylow
148#532—731no—
149C2×C4⋊Q8—731no—
150#492—732no—
151#487—732no—
152#461—732no—
153#461—732no—
154#448—731no—
155#448—731no—
156#448—731no—
157#448D7311yescharacteristic, complemented
158#431—731no—
159C2×#41—1461no—
160C22×Q8—731no—
161C22×Q8C2×D7311yescharacteristic
162C2×SD16—732no—
163C2×SD16—732no—
164C2×SD16—732no—
165C2×SD16C2×D7312yes—
166C4⋊Q8—731no—
167C4⋊Q8—732no—
168C4⋊Q8—732no—
169C4⋊Q8—1461no—
170C4⋊Q8—1461no—
171#127—731no—
172#124—1461no—
173#121—731no—
174#121—1461no—
175#121C2×D7311yescharacteristic
176C4×D4—731no—
177C4×D4—731no—
178C4×D4—1461no—
179C2×C4⋊C4—1461no—
180C2×C4⋊C4—1461no—
181C2×C42—731no—
182C4⋊C8—732no—
183#103—732no—
184#103—732no—
185#103—732no—
186#103C2×D7312yes—
187C22⋊C8—731no—
188C22⋊C8C2×D7311yescharacteristic
189C4×C8—732no—
190#41—2924no—
191C2×Q8—21no—
192C2×Q8—42no—
193C2×Q8—2922no—
194C2×Q8—732no—
195C2×Q8—1461no—
196C2×Q8—1461no—
197C2×Q8C22×D7312yes—
198C2×D4—21no—
199C2×D4—731no—
200C2×D4—1461no—
201C2×D4—1461no—
202C2×D4—1461no—
203C2×D4C22×D7311yescharacteristic
204C22×C4—21no—
205C22×C4—731no—
206C22×C4—731no—
207C22×C4—1461no—
208C22×C4—1461no—
209C22×C4—1461no—
210C22×C4C22×D7311yescharacteristic
211SD16—42no—
212SD16—2922no—
213SD16—2922no—
214SD16—2922no—
215C2×C8—732no—
216C2×C8C22×D7312yes—
217C4⋊C4—731no—
218C4⋊C4—1462no—
219C4⋊C4—1462no—
220C4⋊C4—1462no—
221C4⋊C4—1462no—
222C4⋊C4—1461no—
223C4⋊C4C22×D7311yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—1461no—
226C22⋊C4—1461no—
227C22⋊C4—1461no—
228C42—731no—
229C42—731no—
230C42—731no—
231C42—731no—
232C23—21no—
233C23—1461no—
234C23D4×D7311yescharacteristic
235Q8—22no—
236Q8—22no—
237Q8—42no—
238Q8—2922no—
239Q8—2922no—
240Q8—1462no—
241Q8—1462no—
242D4—22no—
243D4—42no—
244D4—2922no—
245D4—2922no—
246D4—2922no—
247D4—1462no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—2922no—
253C2×C4—2922no—
254C2×C4—2922no—
255C2×C4—734no—
256C2×C4—731no—
257C2×C4—731no—
258C2×C4—731no—
259C2×C4—731no—
260C2×C4—1461no—
261C2×C4—1462no—
262C2×C4—1462no—
263C2×C4D4×D7311yescharacteristic
264C2×C4C23×D7311yescharacteristic
265C8—22no—
266C8—1462no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—2921no—
273C22—2921no—
274C22—2921no—
275C22SD16×D7312yes—
276C22C2×D4×D7311yescharacteristic
277C4—21no—
278C4—42no—
279C4—41no—
280C4—2922no—
281C4—2921no—
282C4—732no—
283C4—732no—
284C4—732no—
285C4—1461no—
286C4#1455663612yes—
287C2—22no—
288C2—81no—
289C2—5841no—
290C2#1798915211yescharacteristic
291C2C2×SD16×D7311yescharacteristic
292C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#448×C73C2
socleC22×C73C22×D4
hypercenter#448D73
hypocenterC73#3206
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. C2×#14556589C2semidirect
3. #17988958C2semidirect
4. #17988936C2semidirect
5. #17988791C2semidirect
6. #17988790C2semidirect
7. #17988728C2semidirect
8. #17988726C2semidirect
9. #17988725C2semidirect
10. #17988637C2semidirect
11. #448×C73C2semidirect
107. C2×Dic73SD16semidirect
147. C73#3206semidirect
157. #448D73semidirect