Finite Group Databasebeta

← #22624327

Subgroups — #22624327

Order 9344.

1114 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989335C211yesmaximal, characteristic, complemented
2#17989331C212yesmaximal, complemented
3#17989291C214yesmaximal, complemented
4#17989255C214yesmaximal, complemented
5#17989235C214yesmaximal, complemented
6#17989189C214yesmaximal, complemented
7#17989167C214yesmaximal, complemented
8#17989164C214yesmaximal, complemented
9#17989143C211yesmaximal, characteristic, complemented
10#17989136C212yesmaximal, complemented
11#562×C73C211yesmaximal, characteristic, complemented
12C2×#11924029C2212yes—
13C2×#11924028C2214yes—
14C2×#11924027C2212yes—
15C2×#11924027C2214yes—
16#14556590C2212yes—
17#14556589C2212yes—
18#14556587C2212yes—
19#14556587C2214yes—
20#14556583C2211yescharacteristic
21#14556581C2214yes—
22#14556579C2212yes—
23#14556576C2214yes—
24#14556575C2214yes—
25#14556573C2214yes—
26#14556569C2214yes—
27#14556569C2214yes—
28#14556569C2214yes—
29#14556568C2214yes—
30#14556568C2214yes—
31#14556567C2214yes—
32#14556566C2214yes—
33#14556566C2214yes—
34#14556565C2214yes—
35#14556564C2214yes—
36#14556564C2214yes—
37#14556564C2214yes—
38#14556564C2214yes—
39#14556564C2214yes—
40#14556563C2214yes—
41#14556563C2214yes—
42#14556563C2214yes—
43#14556556C2214yes—
44C4×C22⋊D73C2214yes—
45#14556551C2214yes—
46#14556551C2214yes—
47#14556551C2214yes—
48#14556549C2212yes—
49C2×#11924007C2214yes—
50C4⋊C4×D73C2214yes—
51C42×D73C2211yescharacteristic
52#125×C73C2211yescharacteristic
53#124×C73C2212yes—
54#123×C73C2214yes—
55C22⋊Q8×C73C2214yes—
56#121×C73C2214yes—
57#11924029—44no—
58#11924028—48no—
59#11924027—48no—
60#11924027—44no—
61C2×Dic146C2314yes—
62C2×Dic146C2312yes—
63C2×D292C2314yes—
64C2×D292C2312yes—
65C2×D292C2314yes—
66C2×C22⋊D73C2314yes—
67C2×C22⋊D73C2314yes—
68C2×C22⋊D73C2314yes—
69C2×C22⋊D73C2314yes—
70C2×C22⋊D73C2314yes—
71C22×Dic73C2314yes—
72C22×Dic73C2314yes—
73C2×C4×D73C2311yescharacteristic
74C2×C4×D73C2312yes—
75C2×C4×D73C2314yes—
76C2×C4×D73C2314yes—
77C2×C4×D73C2314yes—
78C4⋊Dic73C2314yes—
79C4⋊Dic73C2312yes—
80#11924007C2314yes—
81#11924007C2314yes—
82#11924007C2314yes—
83#11924007C2314yes—
84#11924007C2314yes—
85#11924007C2314yes—
86C22⋊Dic73C2314yes—
87#11924005C2314yes—
88#11924005C2314yes—
89#11924005C2314yes—
90#11924005C2314yes—
91#11924005C2314yes—
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2312yes—
94C4×Dic73C2314yes—
95C2×Q8×C73C2312yes—
96C2×D4×C73C2314yes—
97C2×D4×C73C2312yes—
98C22×C4×C73C2314yes—
99C4⋊C4×C73C2314yes—
100C4⋊C4×C73C2314yes—
101C4⋊C4×C73C2312yes—
102C22⋊C4×C73C2314yes—
103C22⋊C4×C73C2314yes—
104C22⋊C4×C73C2314yes—
105C42×C73C2311yescharacteristic
106C23×C73C2414yes—
107C22×D73C2414yes—
108C22×D73C2411yescharacteristic
109Q8×C73—42no—
110D4×C73—44no—
111D4×C73—42no—
112C2×C4×C73—44no—
113C2×C4×C73C2411yescharacteristic
114C2×C4×C73C2412yes—
115C2×C4×C73C2414yes—
116C2×C4×C73C2414yes—
117C22⋊D73—28no—
118C22⋊D73—28no—
119C22⋊D73—44no—
120C22⋊D73—44no—
121C22⋊D73—44no—
122C2×Dic73—28no—
123C2×Dic73—44no—
124C2×Dic73C2414yes—
125C2×Dic73C2414yes—
126C2×Dic73C2412yes—
127C2×Dic73C2411yescharacteristic
128D292—44no—
129D292—42no—
130D292—44no—
131C4×D73—24no—
132C4×D73—28no—
133C4×D73—22no—
134C4×D73—44no—
135C4×D73—44no—
136Dic146—28no—
137Dic146—42no—
138C22×C73—24no—
139C22×C73—24no—
140C22×C73—24no—
141C22×C73C2511yescharacteristic
142C2×D73—24no—
143C2×D73—22no—
144C2×D73—24no—
145C2×D73—21no—
146C2×D73—24no—
147C4×C73—24no—
148C4×C73—22no—
149C4×C73—24no—
150C4×C73—21no—
151Dic73—24no—
152Dic73—24no—
153Dic73H(5,𝔽2)14yes—
154Dic732−1+412yes—
155C2×C73—44no—
156C2×C73C2×H(5,𝔽2)12yes—
157C2×C73C2×2−1+411yescharacteristic
158D73—44no—
159D73—41no—
160#3548—731nomaximal, Sylow
161C73#354811yescharacteristic, complemented, Sylow
162#562—731no—
163#562—732no—
164#562D7311yescharacteristic, complemented
165#554—734no—
166#550—734no—
167#547—734no—
168#540—734no—
169#537—734no—
170#537—734no—
171#533—731no—
172#532—732no—
173C2×#41—732no—
174C2×#41—732no—
175C2×#41—734no—
176C2×#41—734no—
177C4⋊Q8—732no—
178C4⋊Q8—732no—
179#127—732no—
180#127—734no—
181#125—734no—
182#125—731no—
183#125C2×D7311yescharacteristic
184#124—732no—
185#124C2×D7312yes—
186#123—734no—
187#123—734no—
188#123—734no—
189#123C2×D7314yes—
190C22⋊Q8—734no—
191C22⋊Q8—734no—
192C22⋊Q8—734no—
193C22⋊Q8—734no—
194C22⋊Q8—734no—
195C22⋊Q8—734no—
196C22⋊Q8C2×D7314yes—
197#121—734no—
198#121—734no—
199#121—734no—
200#121—734no—
201#121—734no—
202#121—734no—
203#121—734no—
204#121—734no—
205#121—734no—
206#121—734no—
207#121—734no—
208#121C2×D7314yes—
209C4×Q8—734no—
210C4×D4—734no—
211C4×D4—734no—
212C4×D4—734no—
213C4×D4—734no—
214#117—732no—
215C2×C4⋊C4—734no—
216C2×C4⋊C4—734no—
217C2×C42—731no—
218#41—2928no—
219#41—2928no—
220#41—2924no—
221#41—2924no—
222C2×Q8—732no—
223C2×Q8—734no—
224C2×Q8C22×D7312yes—
225C2×D4—734no—
226C2×D4—734no—
227C2×D4—734no—
228C2×D4—734no—
229C2×D4—734no—
230C2×D4—734no—
231C2×D4—734no—
232C2×D4—732no—
233C2×D4C22×D7314yes—
234C2×D4C22×D7312yes—
235C22×C4—734no—
236C22×C4—734no—
237C22×C4—734no—
238C22×C4—734no—
239C22×C4—731no—
240C22×C4—732no—
241C22×C4—734no—
242C22×C4C22×D7314yes—
243C4⋊C4—734no—
244C4⋊C4—734no—
245C4⋊C4—734no—
246C4⋊C4—734no—
247C4⋊C4—734no—
248C4⋊C4—734no—
249C4⋊C4—734no—
250C4⋊C4—732no—
251C4⋊C4C22×D7314yes—
252C4⋊C4C22×D7312yes—
253C4⋊C4C22×D7314yes—
254C22⋊C4—734no—
255C22⋊C4—734no—
256C22⋊C4—734no—
257C22⋊C4—734no—
258C22⋊C4—734no—
259C22⋊C4—734no—
260C22⋊C4C22×D7314yes—
261C22⋊C4C22×D7314yes—
262C22⋊C4C22×D7314yes—
263C42—731no—
264C42—732no—
265C42—734no—
266C42C22×D7311yescharacteristic
267C23—734no—
268C23—731no—
269C23C23×D7314yes—
270Q8—42no—
271Q8—2922no—
272Q8—1468no—
273D4—44no—
274D4—42no—
275D4—2924no—
276D4—2924no—
277D4—2922no—
278D4—2924no—
279D4—2924no—
280D4—2924no—
281D4—1468no—
282D4—1468no—
283C2×C4—44no—
284C2×C4—2924no—
285C2×C4—2924no—
286C2×C4—2924no—
287C2×C4—731no—
288C2×C4—732no—
289C2×C4—734no—
290C2×C4—734no—
291C2×C4—1468no—
292C2×C4—1464no—
293C2×C4—1462no—
294C2×C4—1468no—
295C2×C4C23×D7311yescharacteristic
296C2×C4C23×D7312yes—
297C2×C4C23×D7314yes—
298C2×C4C23×D7314yes—
299C22—24no—
300C22—24no—
301C22—24no—
302C22—1464no—
303C22—1464no—
304C22—1462no—
305C22—1461no—
306C22—1464no—
307C22C24×D7311yescharacteristic
308C4—24no—
309C4—24no—
310C4—22no—
311C4—21no—
312C4—734no—
313C4—732no—
314C4—1464no—
315C4—1464no—
316C2—44no—
317C2—2924no—
318C2—2921no—
319C2H(5,𝔽2)×D7312yes—
320C22−1+4×D7311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
Fitting#562×C73C2
hypercenter#562D73
hypocenterC73#3548
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #17989335C2semidirect
2. #17989331C2semidirect
3. #17989291C2semidirect
4. #17989255C2semidirect
5. #17989235C2semidirect
6. #17989189C2semidirect
7. #17989167C2semidirect
8. #17989164C2semidirect
9. #17989143C2semidirect
10. #17989136C2semidirect
11. #562×C73C2semidirect
161. C73#3548semidirect
164. #562D73semidirect