Finite Group Databasebeta

← #22618921

Subgroups — #22618921

Order 9344.

372 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989115C211yesmaximal, characteristic
2#17988717C211yesmaximal, characteristic, complemented
3#17988715C211yesmaximal, characteristic, complemented
4#17988660C211yesmaximal, characteristic, complemented
5#17988658C211yesmaximal, characteristic, complemented
6#17988656C211yesmaximal, characteristic, complemented
7#17988656C211yesmaximal, characteristic, complemented
8C8×D292C211yesmaximal, characteristic, complemented
9C8×C22⋊D73C211yesmaximal, characteristic, complemented
10#17988648C211yesmaximal, characteristic, complemented
11#17988646C211yesmaximal, characteristic, complemented
12#17988638C211yesmaximal, characteristic, complemented
13#17988544C211yesmaximal, characteristic, complemented
14#97×D73C211yesmaximal, characteristic, complemented
15#405×C73C211yesmaximal, characteristic, complemented
16C2×#11924011C2211yescharacteristic
17C2×C8×D73C2211yescharacteristic
18C2×C8×D73C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556586C411yescharacteristic
21#14556584C411yescharacteristic
22#14556581C411yescharacteristic
23#14556577C411yescharacteristic
24#14556576C411yescharacteristic
25#14556573C411yescharacteristic
26#14556569C411yescharacteristic
27#14556564C411yescharacteristic
28C4×Dic146C2211yescharacteristic
29C4×D292C2211yescharacteristic
30C4×C22⋊D73C2211yescharacteristic
31C4×C22⋊D73C2211yescharacteristic
32#14556548C2211yescharacteristic
33C42×D73C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35C4⋊#10596831C2211yescharacteristic
36#14556520C2211yescharacteristic
37#14556520C2211yescharacteristic
38#14556520C2211yescharacteristic
39#14556520C2211yescharacteristic
40C22⋊#10596831C2211yescharacteristic
41C22⋊#10596831C2211yescharacteristic
42#14556503C2211yescharacteristic
43#14556503C2211yescharacteristic
44#14556503C2211yescharacteristic
45#14556503C2211yescharacteristic
46#14556502C2211yescharacteristic
47#14556501C2211yescharacteristic
48#14556501C2211yescharacteristic
49#14556501C2211yescharacteristic
50C4×#10596831C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54#117×C73C2211yescharacteristic
55#97×C73C2211yescharacteristic
56#97×C73C2211yescharacteristic
57C4×C8×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59C2×Dic146C2×C411yescharacteristic
60C2×D292C2×C411yescharacteristic
61C2×C22⋊D73C2×C411yescharacteristic
62C2×C22⋊D73C2×C411yescharacteristic
63C2×C4×D73C2×C411yescharacteristic
64C2×C4×D73C2×C411yescharacteristic
65C2×C4×D73C2311yescharacteristic
66C2×C4×D73C2311yescharacteristic
67#11924011—22no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C8×D73—22no—
73C8×D73—22no—
74C8×D73—22no—
75C4⋊Dic73C2×C411yescharacteristic
76C4⋊Dic73C2×C411yescharacteristic
77#11924007C2×C411yescharacteristic
78#11924007C2×C411yescharacteristic
79#11924007C2×C411yescharacteristic
80#11924007C2×C411yescharacteristic
81#11924007C2×C411yescharacteristic
82#11924007C2×C411yescharacteristic
83C22⋊Dic73C2×C411yescharacteristic
84C22⋊Dic73C2×C411yescharacteristic
85#11924005C2×C411yescharacteristic
86#11924005C2×C411yescharacteristic
87#11924005C2×C411yescharacteristic
88#11924005C2×C411yescharacteristic
89#11924005C2×C411yescharacteristic
90#11924005C2×C411yescharacteristic
91C4×Dic73C2×C411yescharacteristic
92C4×Dic73C2×C411yescharacteristic
93C4×Dic73C2311yescharacteristic
94C4×Dic73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96M16×C73—22no—
97C2×C8×C73—22no—
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73C2×C411yescharacteristic
103C4⋊C4×C73C2×C411yescharacteristic
104C22⋊C4×C73C2×C411yescharacteristic
105C22⋊C4×C73C2×C411yescharacteristic
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73C22×C411yescharacteristic
109C22×D73C22×C411yescharacteristic
110C22×D73C22×C411yescharacteristic
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73C22×C411yescharacteristic
114C2×C4×C73C22×C411yescharacteristic
115C2×C4×C73C22×C411yescharacteristic
116C2×C4×C73C22×C411yescharacteristic
117C2×C4×C73C22×C411yescharacteristic
118C2×C4×C73C2411yescharacteristic
119C22⋊D73—22no—
120C22⋊D73—41no—
121C2×Dic73C22×C411yescharacteristic
122C2×Dic73C22×C411yescharacteristic
123C2×Dic73C22×C411yescharacteristic
124C2×Dic73C22×C411yescharacteristic
125C2×Dic73C22×C411yescharacteristic
126C2×Dic73C22×C411yescharacteristic
127D292—22no—
128C4×D73—22no—
129C4×D73—21no—
130C4×D73—21no—
131C4×D73—21no—
132C4×D73—21no—
133C4×D73—41no—
134Dic146—41no—
135C8×C73—21no—
136C8×C73—21no—
137C8×C73#4112yes—
138C8×C73#4112yes—
139#10596831—21no—
140#10596831—21no—
141#10596831—21no—
142#10596831—21no—
143C22×C73—21no—
144C22×C73—21no—
145C22×C73—21no—
146C22×C73C23×C411yescharacteristic
147C2×D73—21no—
148C2×D73—21no—
149C2×D73—21no—
150C2×D73—21no—
151C2×D73—21no—
152C2×D73#13112yes—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73C2×#4111yescharacteristic
159C4×C73C2×#4111yescharacteristic
160Dic73—21no—
161Dic73—21no—
162Dic73—21no—
163Dic73—21no—
164Dic73—21no—
165Dic73—21no—
166C2×C73—41no—
167C2×C73C4×#4111yescharacteristic
168C2×C73C2×#13111yescharacteristic
169C2×C73#56811yescharacteristic
170D73—22no—
171D73—41no—
172#2968—731nomaximal, Sylow
173C73#296811yescharacteristic, complemented, Sylow
174#529—731no—
175#446—731no—
176#446—731no—
177#435—731no—
178#435—731no—
179#435—731no—
180#435—731no—
181C8×D4—731no—
182C8×D4—731no—
183#433—731no—
184#433—731no—
185#431—731no—
186#405—731no—
187#405D7311yescharacteristic, complemented
188C2×#97—731no—
189C2×M16—731no—
190C2×M16C2×D7311yescharacteristic
191C22×C8—731no—
192C22×C8—731no—
193C22×C8—731no—
194C22×C8C2×D7311yescharacteristic
195#126—731no—
196#126—731no—
197#125—731no—
198#124—731no—
199#123—731no—
200#123—731no—
201C22⋊Q8—731no—
202#121—731no—
203C4×Q8—731no—
204C4×D4—731no—
205C4×D4—731no—
206C4×D4—731no—
207#117—731no—
208#117C2×D7311yescharacteristic
209C2×C42—731no—
210C4⋊C8—731no—
211C4⋊C8—731no—
212C4⋊C8—731no—
213C4⋊C8—731no—
214C4⋊C8—731no—
215C4⋊C8—731no—
216C22⋊C8—731no—
217C22⋊C8—731no—
218C22⋊C8—731no—
219C22⋊C8—731no—
220C22⋊C8—731no—
221C22⋊C8—731no—
222#97—731no—
223#97—731no—
224#97—731no—
225#97—731no—
226#97C2×D7311yescharacteristic
227#97C2×D7311yescharacteristic
228C4×C8—731no—
229C4×C8—731no—
230C4×C8C2×D7311yescharacteristic
231C4×C8C2×D7311yescharacteristic
232C2×Q8—731no—
233C2×D4—731no—
234C2×D4—731no—
235C2×D4—731no—
236C22×C4—731no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4C22×D7311yescharacteristic
241M16—22no—
242M16—1462no—
243C2×C8—22no—
244C2×C8—731no—
245C2×C8—731no—
246C2×C8—731no—
247C2×C8—731no—
248C2×C8—1462no—
249C2×C8—1462no—
250C2×C8—1462no—
251C2×C8C22×D7311yescharacteristic
252C2×C8C22×D7311yescharacteristic
253C2×C8C22×D7311yescharacteristic
254C2×C8C22×D7311yescharacteristic
255C4⋊C4—731no—
256C4⋊C4—731no—
257C4⋊C4—731no—
258C4⋊C4—731no—
259C4⋊C4—731no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—731no—
263C4⋊C4C4×D7311yescharacteristic
264C4⋊C4C4×D7311yescharacteristic
265C22⋊C4—731no—
266C22⋊C4—731no—
267C22⋊C4—731no—
268C22⋊C4—731no—
269C22⋊C4—731no—
270C22⋊C4—731no—
271C22⋊C4—731no—
272C22⋊C4—731no—
273C22⋊C4C4×D7311yescharacteristic
274C22⋊C4C4×D7311yescharacteristic
275C42—731no—
276C42—731no—
277C42—731no—
278C42—731no—
279C42C22×D7311yescharacteristic
280C42C22×D7311yescharacteristic
281C23—731no—
282C23—731no—
283C23C2×C4×D7311yescharacteristic
284Q8—2921no—
285D4—2921no—
286D4—1462no—
287D4—1462no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—2921no—
291C2×C4—731no—
292C2×C4—731no—
293C2×C4—731no—
294C2×C4—731no—
295C2×C4—731no—
296C2×C4—731no—
297C2×C4—1462no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4C2×C4×D7311yescharacteristic
303C2×C4C2×C4×D7311yescharacteristic
304C2×C4C2×C4×D7311yescharacteristic
305C2×C4C2×C4×D7311yescharacteristic
306C2×C4C2×C4×D7311yescharacteristic
307C2×C4C23×D7311yescharacteristic
308C8—21no—
309C8—21no—
310C8—1461no—
311C8—1461no—
312C8—1461no—
313C8—1461no—
314C8#1192402812yes—
315C8#1192402812yes—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—732no—
320C22—1461no—
321C22—1461no—
322C22—1461no—
323C22—1461no—
324C22—1461no—
325C22C22×C4×D7311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—1461no—
332C4—1461no—
333C4—1461no—
334C4—1461no—
335C4—1461no—
336C4—1461no—
337C4C2×#1192402811yescharacteristic
338C4C2×#1192402811yescharacteristic
339C2—41no—
340C2—2921no—
341C2—1462no—
342C2C4×#1192402811yescharacteristic
343C2#131×D7311yescharacteristic
344C2#1798935211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D73
commutator, socleC22×C73C23×C4
Fitting#405×C73C2
hypercenter#405D73
hypocenterC73#2968
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #405

Complements

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

NH ≅ G/Ntype
2. #17988717C2semidirect
3. #17988715C2semidirect
4. #17988660C2semidirect
5. #17988658C2semidirect
6. #17988656C2semidirect
7. #17988656C2semidirect
8. C8×D292C2semidirect
9. C8×C22⋊D73C2semidirect
10. #17988648C2semidirect
11. #17988646C2semidirect
12. #17988638C2semidirect
13. #17988544C2semidirect
14. #97×D73C2semidirect
15. #405×C73C2semidirect
173. C73#2968semidirect
187. #405D73semidirect