Finite Group Databasebeta

← #22622773

Subgroups — #22622773

Order 9344.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989310C211yesmaximal, characteristic
2#17988957C211yesmaximal, characteristic, complemented
3#17988949C211yesmaximal, characteristic
4#17988944C211yesmaximal, characteristic
5#17988891C211yesmaximal, characteristic, complemented
6#17988884C211yesmaximal, characteristic
7#17988879C211yesmaximal, characteristic, complemented
8#17988809C211yesmaximal, characteristic
9#17988809C211yesmaximal, characteristic
10#17988797C211yesmaximal, characteristic, complemented
11#17988718C211yesmaximal, characteristic, complemented
12#17988692C211yesmaximal, characteristic, complemented
13#17988685C211yesmaximal, characteristic
14C4×#11924018C211yesmaximal, characteristic, complemented
15#557×C73C211yesmaximal, characteristic, complemented
16C2×#11924018C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19#14556591C2211yescharacteristic
20#14556586—21no—
21#14556586—21no—
22#14556579C2211yescharacteristic
23#14556579C2211yescharacteristic
24#14556567—21no—
25C4×Dic146C2211yescharacteristic
26C4×Dic146C2211yescharacteristic
27C4×D292C2211yescharacteristic
28#14556549—21no—
29#14556524C2211yescharacteristic
30#14556524C2211yescharacteristic
31#14556522C2211yescharacteristic
32C4⋊#10596831C2211yescharacteristic
33C4⋊#10596831C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35#14556515C2211yescharacteristic
36#14556514C2211yescharacteristic
37#14556514C2211yescharacteristic
38#14556514C2211yescharacteristic
39#14556514C2211yescharacteristic
40#14556514C2211yescharacteristic
41#14556514C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556511C2211yescharacteristic
45#14556502C2211yescharacteristic
46#14556502C2211yescharacteristic
47C4×#10596831C2211yescharacteristic
48C4⋊Q8×C73—21no—
49C4⋊Q8×C73C2211yescharacteristic
50#125×C73—21no—
51#125×C73—21no—
52#125×C73C2211yescharacteristic
53#125×C73C2211yescharacteristic
54C4×Q8×C73—21no—
55C4×Q8×C73C2211yescharacteristic
56C4×Q8×C73C2211yescharacteristic
57C4×Q8×C73C2211yescharacteristic
58C4×Q8×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C2×Dic146C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C4×D73—21no—
63#11924018—22no—
64#11924018—22no—
65#11924015—22no—
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73C2311yescharacteristic
73#11924007—21no—
74#11924007—21no—
75#11924005—21no—
76#11924005—21no—
77#11924005—21no—
78#11924005—21no—
79#11924005—21no—
80C4×Dic73—21no—
81C4×Dic73—21no—
82C2×Q8×C73—21no—
83C2×Q8×C73D411yescharacteristic
84C2×Q8×C73C2311yescharacteristic
85C4⋊C4×C73—21no—
86C4⋊C4×C73—21no—
87C4⋊C4×C73—21no—
88C4⋊C4×C73—21no—
89C4⋊C4×C73—21no—
90C4⋊C4×C73—21no—
91C4⋊C4×C73—21no—
92C4⋊C4×C73—21no—
93C4⋊C4×C73D411yescharacteristic
94C4⋊C4×C73D411yescharacteristic
95C4⋊C4×C73D411yescharacteristic
96C4⋊C4×C73C2311yescharacteristic
97C4⋊C4×C73C2311yescharacteristic
98C4⋊C4×C73C2311yescharacteristic
99C42×C73—21no—
100C42×C73—21no—
101C42×C73—21no—
102C42×C73C2311yescharacteristic
103C42×C73C2311yescharacteristic
104C42×C73C2311yescharacteristic
105C22×D73—21no—
106Q8×C73—21no—
107Q8×C73—41no—
108Q8×C73—42no—
109Q8×C73#4112yes—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124D292—21no—
125D292—21no—
126C4×D73—42no—
127Dic146—21no—
128Dic146—21no—
129Dic146—21no—
130Dic146—21no—
131#10596831—21no—
132#10596831—21no—
133#10596831—21no—
134#10596831—21no—
135C22×C73C22×D411yescharacteristic
136C2×D73—41no—
137C2×D73—41no—
138C2×D73—41no—
139C4×C73—22no—
140C4×C73—21no—
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—21no—
146C4×C73—41no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73C2×#4111yescharacteristic
150C4×C732−1+411yescharacteristic
151Dic73—41no—
152Dic73—41no—
153Dic73—41no—
154C2×C73#54811yescharacteristic
155C2×C73#57511yescharacteristic
156C2×C73#57811yescharacteristic
157D73—81no—
158#3377—731nomaximal, Sylow
159C73#337711yescharacteristic, complemented, Sylow
160#557D7311yescharacteristic, complemented
161#556—731no—
162#491—731no—
163#489—731no—
164#488—731no—
165#479—731no—
166#478—731no—
167#477—731no—
168#464—731no—
169#464—731no—
170#462—731no—
171#446—731no—
172#441—731no—
173#440—731no—
174C4×Q16—731no—
175C2×Q16—731no—
176C2×Q16—731no—
177C2×SD16—731no—
178C4⋊Q8—21no—
179C4⋊Q8—731no—
180C4⋊Q8C2×D7311yescharacteristic
181#126—1461no—
182#126—1461no—
183#125—21no—
184#125—21no—
185#125C2×D7311yescharacteristic
186#125C2×D7311yescharacteristic
187#124—731no—
188#124—731no—
189C22⋊Q8—1461no—
190C4×Q8—21no—
191C4×Q8—731no—
192C4×Q8—731no—
193C4×Q8C2×D7311yescharacteristic
194C4×Q8C2×D7311yescharacteristic
195C4×Q8C2×D7311yescharacteristic
196C4×Q8C2×D7311yescharacteristic
197C4×D4—731no—
198#117—1461no—
199#107—731no—
200#107—731no—
201#106—731no—
202C4⋊C8—731no—
203C4⋊C8—731no—
204C4⋊C8—731no—
205#103—731no—
206#103—731no—
207#103—731no—
208#103—731no—
209#103—731no—
210#103—731no—
211#103—731no—
212#102—731no—
213#102—731no—
214#102—731no—
215#97—731no—
216#97—731no—
217C4×C8—731no—
218C2×Q8—21no—
219C2×Q8—731no—
220C2×Q8—731no—
221C2×Q8C22⋊D7311yescharacteristic
222C2×Q8C22×D7311yescharacteristic
223C2×D4—731no—
224C22×C4—1461no—
225Q16—1462no—
226Q16—1462no—
227SD16—1462no—
228C2×C8—731no—
229C2×C8—731no—
230C2×C8—731no—
231C2×C8—731no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—731no—
241C4⋊C4—1461no—
242C4⋊C4—1461no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4C22⋊D7311yescharacteristic
246C4⋊C4C22⋊D7311yescharacteristic
247C4⋊C4C22⋊D7311yescharacteristic
248C4⋊C4C22×D7311yescharacteristic
249C4⋊C4C22×D7311yescharacteristic
250C4⋊C4C22×D7311yescharacteristic
251C22⋊C4—1461no—
252C22⋊C4—1461no—
253C22⋊C4—1461no—
254C22⋊C4—1461no—
255C22⋊C4—1461no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—1461no—
260C42—1461no—
261C42C22×D7311yescharacteristic
262C42C22×D7311yescharacteristic
263C42C22×D7311yescharacteristic
264C23—1461no—
265Q8—21no—
266Q8—41no—
267Q8—42no—
268Q8—1461no—
269Q8—1461no—
270Q8—1461no—
271Q8—1461no—
272Q8#1192402912yes—
273D4—1461no—
274D4—1461no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—2922no—
280C2×C4—1461no—
281C2×C4—1461no—
282C2×C4—1461no—
283C2×C4C2×C22⋊D7311yescharacteristic
284C2×C4C2×C22⋊D7311yescharacteristic
285C2×C4C2×C22⋊D7311yescharacteristic
286C2×C4C2×C22⋊D7311yescharacteristic
287C2×C4C2×C22⋊D7311yescharacteristic
288C2×C4C2×C22⋊D7311yescharacteristic
289C2×C4C23×D7311yescharacteristic
290C8—1461no—
291C8—1461no—
292C8—1461no—
293C8—1461no—
294C22—2921no—
295C22—2921no—
296C22—2921no—
297C22C22×C22⋊D7311yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—2921no—
309C4—2921no—
310C4—2921no—
311C4C2×#1192402911yescharacteristic
312C4#1455663911yescharacteristic
313C2—5841no—
314C2#1798924811yescharacteristic
315C2#1798938511yescharacteristic
316C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#557×C73C2
socleC22×C73C22×D4
hypercenter#557D73
hypocenterC73#3377
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
2. #17988957C2semidirect
5. #17988891C2semidirect
7. #17988879C2semidirect
10. #17988797C2semidirect
11. #17988718C2semidirect
12. #17988692C2semidirect
14. C4×#11924018C2semidirect
15. #557×C73C2semidirect
159. C73#3377semidirect
160. #557D73semidirect