Finite Group Databasebeta

← #22622706

Subgroups — #22622706

Order 9344.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989320C211yesmaximal, characteristic
2#17989312C211yesmaximal, characteristic, complemented
3#17988950C211yesmaximal, characteristic
4#17988949C211yesmaximal, characteristic, complemented
5#17988940C211yesmaximal, characteristic, complemented
6#17988897C211yesmaximal, characteristic, complemented
7#17988886C211yesmaximal, characteristic, complemented
8#17988810C211yesmaximal, characteristic, complemented
9#17988808C211yesmaximal, characteristic, complemented
10#17988786C211yesmaximal, characteristic
11#17988716C211yesmaximal, characteristic, complemented
12#17988693C211yesmaximal, characteristic, complemented
13#17988687C211yesmaximal, characteristic, complemented
14#17988674C211yesmaximal, characteristic, complemented
15#476×C73C211yesmaximal, characteristic, complemented
16C2×Dic292C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19#14556589—21no—
20#14556587C2211yescharacteristic
21#14556582C2211yescharacteristic
22#14556582C2211yescharacteristic
23#14556581—21no—
24#14556581—21no—
25#14556579C2211yescharacteristic
26#14556578C2211yescharacteristic
27#14556577—21no—
28#14556574—21no—
29#14556573—21no—
30Q8×Dic73—21no—
31C4×Dic146C2211yescharacteristic
32C4×Dic146C2211yescharacteristic
33#14556556C2211yescharacteristic
34#14556556C2211yescharacteristic
35#14556556C2211yescharacteristic
36#14556553C2211yescharacteristic
37C4×C22⋊D73—21no—
38#14556524C2211yescharacteristic
39#14556520C2211yescharacteristic
40#14556520C2211yescharacteristic
41#14556516C2211yescharacteristic
42#14556514C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556502C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C4⋊Q8×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54#106×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C2×Dic146D411yescharacteristic
60C2×Dic146C2311yescharacteristic
61C2×Dic146C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C4×D73—21no—
66Dic292—22no—
67#11924017—22no—
68#11924016—22no—
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73D411yescharacteristic
74C4⋊Dic73C2311yescharacteristic
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—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C4×Dic73C2311yescharacteristic
94C2×Q8×C73—21no—
95C2×D4×C73C2311yescharacteristic
96C22×C4×C73—21no—
97C2×C8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73C2311yescharacteristic
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C42×C73C2311yescharacteristic
105C23×C73—21no—
106C22×D73—21no—
107Q8×C73—42no—
108D4×C73—21no—
109D4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—81no—
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2411yescharacteristic
117C22⋊D73—42no—
118C22⋊D73—81no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124C2×Dic73C2×D411yescharacteristic
125C2×Dic73C2×D411yescharacteristic
126D292—21no—
127D292—21no—
128C4×D73—81no—
129Dic146—21no—
130Dic146—21no—
131Dic146—21no—
132Dic146—41no—
133Dic146#4112yes—
134C8×C73—21no—
135C8×C73—21no—
136#10596831—21no—
137#10596831—21no—
138C22×C73—41no—
139C22×C73—41no—
140C22×C73—41no—
141C22×C73C22×D411yescharacteristic
142C2×D73—41no—
143C2×D73—41no—
144C2×D73—41no—
145C4×C73—21no—
146C4×C73—21no—
147C4×C73—41no—
148C4×C73—41no—
149C4×C73—41no—
150C4×C73C2×#4111yescharacteristic
151C4×C732−1+411yescharacteristic
152Dic73—22no—
153Dic73—21no—
154Dic73—21no—
155Dic73—21no—
156Dic73—21no—
157Dic73—41no—
158Dic73—41no—
159C2×C73—81no—
160C2×C73#54811yescharacteristic
161C2×C73#57511yescharacteristic
162C2×C73#57711yescharacteristic
163D73—81no—
164#3371—731nomaximal, Sylow
165C73#337111yescharacteristic, complemented, Sylow
166#559—731no—
167#557—731no—
168#490—731no—
169#489—731no—
170#488—731no—
171#479—731no—
172#478—731no—
173#476D7311yescharacteristic, complemented
174#464—731no—
175#464—731no—
176#460—731no—
177#446—731no—
178#441—731no—
179#440—731no—
180C4×SD16—731no—
181C2×Q16—731no—
182C2×SD16—731no—
183C2×SD16—731no—
184C4⋊Q8—1461no—
185C4⋊Q8C2×D7311yescharacteristic
186#127—731no—
187#125—731no—
188#125—731no—
189#125—1461no—
190#125—1461no—
191#124—731no—
192#124—731no—
193#124—1461no—
194#123—1461no—
195#123—1461no—
196C4×Q8—731no—
197C4×Q8—731no—
198C4×Q8—731no—
199C4×Q8—731no—
200C4×Q8—731no—
201C4×Q8—1461no—
202C4×D4—731no—
203C4×D4—1461no—
204C4×D4C2×D7311yescharacteristic
205#107—731no—
206#106C2×D7311yescharacteristic
207#106C2×D7311yescharacteristic
208C4⋊C8—731no—
209C4⋊C8—731no—
210C4⋊C8C2×D7311yescharacteristic
211#103—731no—
212#103—731no—
213#103—731no—
214#103—731no—
215#102—731no—
216#102—731no—
217#102—731no—
218#102—731no—
219#102C2×D7311yescharacteristic
220#102C2×D7311yescharacteristic
221#97—731no—
222#97—731no—
223C4×C8—731no—
224C2×Q8—21no—
225C2×Q8—731no—
226C2×Q8—731no—
227C2×Q8—731no—
228C2×D4—731no—
229C2×D4—1461no—
230C2×D4—1461no—
231C2×D4C22×D7311yescharacteristic
232C22×C4—21no—
233C22×C4—1461no—
234Q16—1462no—
235SD16—1462no—
236SD16—1462no—
237C2×C8—731no—
238C2×C8—731no—
239C2×C8C22×D7311yescharacteristic
240C2×C8C22×D7311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—731no—
243C4⋊C4—731no—
244C4⋊C4—731no—
245C4⋊C4—731no—
246C4⋊C4—1461no—
247C4⋊C4—1461no—
248C4⋊C4—1461no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4C22×D7311yescharacteristic
255C4⋊C4C22×D7311yescharacteristic
256C4⋊C4C22×D7311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—1461no—
259C22⋊C4—1461no—
260C22⋊C4—1461no—
261C22⋊C4—1461no—
262C22⋊C4—1461no—
263C42—731no—
264C42—731no—
265C42—1461no—
266C42—1461no—
267C42—1461no—
268C42—1461no—
269C42C22×D7311yescharacteristic
270C23—21no—
271C23—1461no—
272Q8—42no—
273Q8—2921no—
274Q8—732no—
275Q8—1461no—
276Q8—1461no—
277Q8—1461no—
278D4—21no—
279D4—21no—
280D4—2922no—
281D4—5841no—
282D4—1461no—
283D4—1461no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—81no—
288C2×C4—5841no—
289C2×C4—731no—
290C2×C4—731no—
291C2×C4—731no—
292C2×C4—731no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4D4×D7311yescharacteristic
297C2×C4D4×D7311yescharacteristic
298C2×C4C23×D7311yescharacteristic
299C8—21no—
300C8—21no—
301C8—1461no—
302C8—1461no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—2921no—
307C22—2921no—
308C22—2921no—
309C22C2×D4×D7311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—2921no—
316C4—2921no—
317C4—1461no—
318C4—1461no—
319C4—1461no—
320C4—1461no—
321C4—1462no—
322C4#41×D7311yescharacteristic
323C4#1455663911yescharacteristic
324C2—81no—
325C2—5841no—
326C2#1798924711yescharacteristic
327C2#1798938311yescharacteristic
328C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#476×C73C2
socleC22×C73C22×D4
hypercenter#476D73
hypocenterC73#3371
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #17989312C2semidirect
4. #17988949C2semidirect
5. #17988940C2semidirect
6. #17988897C2semidirect
7. #17988886C2semidirect
8. #17988810C2semidirect
9. #17988808C2semidirect
11. #17988716C2semidirect
12. #17988693C2semidirect
13. #17988687C2semidirect
14. #17988674C2semidirect
15. #476×C73C2semidirect
165. C73#3371semidirect
173. #476D73semidirect