Finite Group Databasebeta

← #22622776

Subgroups — #22622776

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#17989314C211yesmaximal, characteristic, complemented
2#17989307C211yesmaximal, characteristic
3#17988957C211yesmaximal, characteristic, complemented
4#17988945C211yesmaximal, characteristic
5#17988940C211yesmaximal, characteristic
6#17988897C211yesmaximal, characteristic, complemented
7#17988881C211yesmaximal, characteristic, complemented
8#17988808C211yesmaximal, characteristic
9#17988808C211yesmaximal, characteristic
10#17988798C211yesmaximal, characteristic, complemented
11#17988716C211yesmaximal, characteristic, complemented
12#17988693C211yesmaximal, characteristic, complemented
13#17988687C211yesmaximal, characteristic
14#17988681C211yesmaximal, characteristic, complemented
15#478×C73C211yesmaximal, characteristic
16C2×Dic292C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19#14556591C2211yescharacteristic
20#14556590—21no—
21#14556590C2211yescharacteristic
22#14556584—21no—
23#14556584—21no—
24#14556582C2211yescharacteristic
25#14556581—21no—
26#14556581—21no—
27#14556578C2211yescharacteristic
28#14556578C2211yescharacteristic
29#14556570—21no—
30C4×Dic146C2211yescharacteristic
31C4×Dic146C2211yescharacteristic
32#14556556—21no—
33#14556556C2211yescharacteristic
34#14556556C2211yescharacteristic
35#14556556C2211yescharacteristic
36#14556556C2211yescharacteristic
37#14556550—21no—
38#14556524C2211yescharacteristic
39#14556520C2211yescharacteristic
40#14556520C2211yescharacteristic
41#14556516C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556502C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52#125×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146D411yescharacteristic
61C2×Dic146C2311yescharacteristic
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64Dic292—22no—
65Dic292—22no—
66#11924016—22no—
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C4⋊Dic73—21no—
70C4⋊Dic73—21no—
71C4⋊Dic73—21no—
72C4⋊Dic73D411yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007D411yescharacteristic
82#11924007D411yescharacteristic
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2311yescharacteristic
94C2×D4×C73C2311yescharacteristic
95C22×C4×C73—21no—
96C2×C8×C73C2311yescharacteristic
97C2×C8×C73C2311yescharacteristic
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73C2311yescharacteristic
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C42×C73C2311yescharacteristic
105C23×C73—21no—
106D4×C73—21no—
107D4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—42no—
112C2×C4×C73C2×D411yescharacteristic
113C2×C4×C73C2×D411yescharacteristic
114C2×C4×C73C2411yescharacteristic
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73C2×D411yescharacteristic
120C2×Dic73C2×D411yescharacteristic
121C2×Dic73C2×D411yescharacteristic
122C2×Dic73C2×D411yescharacteristic
123Dic146—21no—
124Dic146—21no—
125Dic146—21no—
126Dic146—21no—
127Dic146—21no—
128Dic146—41no—
129Dic146—42no—
130Dic146#4112yes—
131C8×C73—21no—
132C8×C73—21no—
133#10596831—21no—
134#10596831—21no—
135C22×C73—41no—
136C22×C73—41no—
137C22×C73—41no—
138C22×C73C22×D411yescharacteristic
139C4×C73—21no—
140C4×C73—21no—
141C4×C73—41no—
142C4×C73—41no—
143C4×C73—41no—
144C4×C73C2×#4111yescharacteristic
145C4×C732−1+411yescharacteristic
146Dic73—22no—
147Dic73—21no—
148Dic73—21no—
149Dic73—21no—
150Dic73—21no—
151Dic73—41no—
152Dic73—41no—
153Dic73—41no—
154C2×C73—81no—
155C2×C73#54811yescharacteristic
156C2×C73#57511yescharacteristic
157C2×C73#57811yescharacteristic
158#3377—731nomaximal, Sylow
159C73#337711yescharacteristic, complemented, Sylow
160#557—731no—
161#556—731no—
162#491—731no—
163#489—731no—
164#488—731no—
165#479—731no—
166#478D7311yescharacteristic
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—731no—
179C4⋊Q8—731no—
180C4⋊Q8—1461no—
181#126—1461no—
182#126—1461no—
183#125—731no—
184#125—1461no—
185#125—1461no—
186#125C2×D7311yescharacteristic
187#124—731no—
188#124—731no—
189C22⋊Q8—1461no—
190C4×Q8—731no—
191C4×Q8—731no—
192C4×Q8—731no—
193C4×Q8—731no—
194C4×Q8—731no—
195C4×Q8—731no—
196C4×Q8—1461no—
197C4×D4C2×D7311yescharacteristic
198#117—1461no—
199#107—731no—
200#107C2×D7311yescharacteristic
201#106C2×D7311yescharacteristic
202C4⋊C8—731no—
203C4⋊C8—731no—
204C4⋊C8C2×D7311yescharacteristic
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#102C2×D7311yescharacteristic
214#102C2×D7311yescharacteristic
215#97—731no—
216#97—731no—
217C4×C8—731no—
218C2×Q8—731no—
219C2×Q8—731no—
220C2×Q8—731no—
221C2×Q8—731no—
222C2×Q8—1461no—
223C2×D4C22×D7311yescharacteristic
224C22×C4—21no—
225Q16—1462no—
226Q16—1462no—
227SD16—1462no—
228C2×C8—731no—
229C2×C8—731no—
230C2×C8C22×D7311yescharacteristic
231C2×C8C22×D7311yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—731no—
235C4⋊C4—731no—
236C4⋊C4—731no—
237C4⋊C4—731no—
238C4⋊C4—1461no—
239C4⋊C4—1461no—
240C4⋊C4—1461no—
241C4⋊C4—1461no—
242C4⋊C4—1461no—
243C4⋊C4—1461no—
244C4⋊C4—1461no—
245C4⋊C4—1461no—
246C4⋊C4—1461no—
247C4⋊C4—1461no—
248C4⋊C4C22×D7311yescharacteristic
249C4⋊C4C22×D7311yescharacteristic
250C4⋊C4C22×D7311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—1461no—
253C22⋊C4—1461no—
254C22⋊C4—1461no—
255C22⋊C4—1461no—
256C42—731no—
257C42—731no—
258C42—1461no—
259C42—1461no—
260C42—1461no—
261C42—1461no—
262C42—1461no—
263C42C22×D7311yescharacteristic
264C23—21no—
265Q8—2921no—
266Q8—2922no—
267Q8—732no—
268Q8—1461no—
269Q8—1461no—
270Q8—1461no—
271Q8—1461no—
272Q8—1461no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—731no—
280C2×C4—731no—
281C2×C4—731no—
282C2×C4—731no—
283C2×C4—1461no—
284C2×C4—1461no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4D4×D7311yescharacteristic
288C2×C4D4×D7311yescharacteristic
289C2×C4C23×D7311yescharacteristic
290C8—21no—
291C8—21no—
292C8—1461no—
293C8—1461no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C2×D4×D7311yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—2921no—
304C4—2921no—
305C4—2921no—
306C4—1461no—
307C4—1461no—
308C4—1461no—
309C4—1461no—
310C4—1462no—
311C4#41×D7311yescharacteristic
312C4#1455663911yescharacteristic
313C2—81no—
314C2#1798924711yescharacteristic
315C2#1798938311yescharacteristic
316C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#478×C73C2
socleC22×C73C22×D4
hypercenter#478D73
hypocenterC73#3377
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #17989314C2semidirect
3. #17988957C2semidirect
6. #17988897C2semidirect
7. #17988881C2semidirect
10. #17988798C2semidirect
11. #17988716C2semidirect
12. #17988693C2semidirect
14. #17988681C2semidirect
159. C73#3377semidirect