Finite Group Databasebeta

← #22626754

Subgroups — #22626754

Order 9344.

362 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#17989639C211yesmaximal, characteristic, complemented
2#17989637C211yesmaximal, characteristic, complemented
3#17989621C211yesmaximal, characteristic, complemented
4#17989620C211yesmaximal, characteristic, complemented
5#17989619C211yesmaximal, characteristic, complemented
6#17989617C211yesmaximal, characteristic, complemented
7#17989616C211yesmaximal, characteristic, complemented
8#17989616C211yesmaximal, characteristic, complemented
9#17989612C211yesmaximal, characteristic, complemented
10#17989611C211yesmaximal, characteristic, complemented
11#17989609C211yesmaximal, characteristic, complemented
12#17989552C211yesmaximal, characteristic, complemented
13#17989551C211yesmaximal, characteristic, complemented
14C4×#11924038C211yesmaximal, characteristic, complemented
15#17989120C211yesmaximal, characteristic
16C2×#11924038C2211yescharacteristic
17C2×#11924038C2211yescharacteristic
18C2×#11924038C2211yescharacteristic
19C2×#11924037C2211yescharacteristic
20C2×#11924036C2211yescharacteristic
21C22×#10596833C2211yescharacteristic
22#14556658C2211yescharacteristic
23#14556658C2211yescharacteristic
24C4⋊#10596833C2211yescharacteristic
25C4⋊#10596833C2211yescharacteristic
26C4⋊#10596833C2211yescharacteristic
27C4⋊#10596833C2211yescharacteristic
28#14556648C2211yescharacteristic
29#14556648C2211yescharacteristic
30#14556648C2211yescharacteristic
31#14556648C2211yescharacteristic
32C22⋊#10596833C2211yescharacteristic
33C22⋊#10596833C2211yescharacteristic
34#14556646C2211yescharacteristic
35#14556646C2211yescharacteristic
36#14556646C2211yescharacteristic
37#14556646C2211yescharacteristic
38#14556646C2211yescharacteristic
39#14556646C2211yescharacteristic
40C4×#10596833C2211yescharacteristic
41C4×#10596833C2211yescharacteristic
42C4×#10596833C2211yescharacteristic
43C4×#10596833C2211yescharacteristic
44#14556585C411yescharacteristic
45#14556581C411yescharacteristic
46#14556577C411yescharacteristic
47#14556576C411yescharacteristic
48#14556573C411yescharacteristic
49#14556569C411yescharacteristic
50#14556564C411yescharacteristic
51#14556556C2211yescharacteristic
52#14556553C2211yescharacteristic
53#14556551C2211yescharacteristic
54#14556551C2211yescharacteristic
55#14556549C2211yescharacteristic
56#14556547C2211yescharacteristic
57C42×D73C2211yescharacteristic
58#126×C73C411yescharacteristic
59#11924038—22no—
60#11924038—22no—
61#11924038—22no—
62#11924037—22no—
63#11924036—22no—
64C2×#10596833—22no—
65C2×#10596833C2311yescharacteristic
66C2×#10596833C2311yescharacteristic
67C2×#10596833C2311yescharacteristic
68C2×#10596833C2311yescharacteristic
69C2×#10596833C2311yescharacteristic
70C2×#10596833C2311yescharacteristic
71C2×#10596833C2311yescharacteristic
72C2×#10596833C2311yescharacteristic
73C2×Dic146C2×C411yescharacteristic
74C2×D292C2×C411yescharacteristic
75C2×C22⋊D73C2×C411yescharacteristic
76C2×C22⋊D73C2×C411yescharacteristic
77C22×Dic73C2311yescharacteristic
78C2×C4×D73C2×C411yescharacteristic
79C2×C4×D73C2×C411yescharacteristic
80C2×C4×D73C2311yescharacteristic
81C2×C4×D73C2311yescharacteristic
82C4⋊Dic73C2×C411yescharacteristic
83#11924007C2×C411yescharacteristic
84#11924007C2×C411yescharacteristic
85#11924007C2×C411yescharacteristic
86#11924007C2×C411yescharacteristic
87#11924007C2×C411yescharacteristic
88#11924007C2×C411yescharacteristic
89C22⋊Dic73C2×C411yescharacteristic
90#11924005C2×C411yescharacteristic
91#11924005C2×C411yescharacteristic
92#11924005C2×C411yescharacteristic
93#11924005C2×C411yescharacteristic
94#11924005C2×C411yescharacteristic
95#11924005C2×C411yescharacteristic
96C4×Dic73C2×C411yescharacteristic
97C4×Dic73C2311yescharacteristic
98C4×Dic73C2311yescharacteristic
99C4×Dic73C2311yescharacteristic
100C4×Dic73C2311yescharacteristic
101C4⋊C4×C73C2×C411yescharacteristic
102C4⋊C4×C73C2×C411yescharacteristic
103C4⋊C4×C73C2×C411yescharacteristic
104C22⋊C4×C73C2×C411yescharacteristic
105C22⋊C4×C73C2×C411yescharacteristic
106C22⋊C4×C73C2×C411yescharacteristic
107C42×C73C2×C411yescharacteristic
108C23×C73C22×C411yescharacteristic
109C22×D73C22×C411yescharacteristic
110C22×D73C22×C411yescharacteristic
111C2×C4×C73C22×C411yescharacteristic
112C2×C4×C73C22×C411yescharacteristic
113C2×C4×C73C22×C411yescharacteristic
114C2×C4×C73C22×C411yescharacteristic
115C2×C4×C73C22×C411yescharacteristic
116C2×C4×C73C22×C411yescharacteristic
117C22⋊D73—41no—
118C22⋊D73—41no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73C22×C411yescharacteristic
122C2×Dic73C22×C411yescharacteristic
123C2×Dic73C22×C411yescharacteristic
124C2×Dic73C22×C411yescharacteristic
125C2×Dic73C22×C411yescharacteristic
126C2×Dic73C2411yescharacteristic
127D292—41no—
128C4×D73—21no—
129C4×D73—21no—
130C4×D73—21no—
131C4×D73—21no—
132C4×D73—41no—
133C4×D73—41no—
134Dic146—41no—
135#10596833—21no—
136#10596833—21no—
137#10596833—21no—
138#10596833—21no—
139#10596833—21no—
140#10596833—21no—
141#10596833#4112yes—
142#10596833#4112yes—
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—21no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—21no—
159Dic73—21no—
160Dic73—21no—
161Dic73—21no—
162Dic73—21no—
163Dic73—21no—
164Dic73C2×#4111yescharacteristic
165Dic73C2×#4111yescharacteristic
166C2×C73—41no—
167C2×C73C4×#4111yescharacteristic
168C2×C73#56811yescharacteristic
169C2×C73#56811yescharacteristic
170D73—41no—
171D73—41no—
172#2967—731nomaximal, Sylow
173C73#296711yescharacteristic, complemented, Sylow
174#529—731no—
175#446—731no—
176#446—731no—
177#436—731no—
178#436—731no—
179#435—731no—
180#435—731no—
181#435—731no—
182#435—731no—
183#433—731no—
184#433—731no—
185#432—731no—
186#405—731no—
187#405—731no—
188C4×M16—731no—
189C2×M16—731no—
190C2×M16—731no—
191C2×M16—731no—
192C2×M16—731no—
193C22×C8—731no—
194C22×C8—731no—
195#126—731no—
196#126#6440811yescharacteristic
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#117—731no—
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#97—731no—
227#97—731no—
228C4×C8—731no—
229C4×C8—731no—
230C4×C8—731no—
231C4×C8—731no—
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×C4—731no—
241M16—1462no—
242M16—1462no—
243M16—1462no—
244M16—1462no—
245C2×C8—731no—
246C2×C8—731no—
247C2×C8—731no—
248C2×C8—731no—
249C2×C8—731no—
250C2×C8—731no—
251C2×C8—731no—
252C2×C8—731no—
253C2×C8—1462no—
254C2×C8—1462no—
255C4⋊C4—731no—
256C4⋊C4—731no—
257C4⋊C4—731no—
258C4⋊C4—731no—
259C4⋊C4—731no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4C2×#6440811yescharacteristic
263C4⋊C4C2×#6440811yescharacteristic
264C4⋊C4C2×#6440811yescharacteristic
265C22⋊C4—731no—
266C22⋊C4—731no—
267C22⋊C4—731no—
268C22⋊C4—731no—
269C22⋊C4—731no—
270C22⋊C4—731no—
271C22⋊C4—731no—
272C22⋊C4C2×#6440811yescharacteristic
273C22⋊C4C2×#6440811yescharacteristic
274C22⋊C4C2×#6440811yescharacteristic
275C42—731no—
276C42—731no—
277C42—731no—
278C42—731no—
279C42—731no—
280C42C2×#6440811yescharacteristic
281C23—731no—
282C23—731no—
283C23C22×#6440811yescharacteristic
284Q8—2921no—
285D4—2921no—
286D4—2921no—
287D4—2921no—
288C2×C4—2921no—
289C2×C4—2921no—
290C2×C4—731no—
291C2×C4—731no—
292C2×C4—731no—
293C2×C4—731no—
294C2×C4—731no—
295C2×C4—731no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4C22×#6440811yescharacteristic
303C2×C4C22×#6440811yescharacteristic
304C2×C4C22×#6440811yescharacteristic
305C2×C4C22×#6440811yescharacteristic
306C2×C4C22×#6440811yescharacteristic
307C2×C4C22×#6440811yescharacteristic
308C8—732no—
309C8—732no—
310C8—1461no—
311C8—1461no—
312C8—1461no—
313C8—1461no—
314C8—1461no—
315C8—1461no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—1461no—
320C22—1461no—
321C22—1461no—
322C22—1461no—
323C22—1461no—
324C22—1461no—
325C22C23×#6440811yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—731no—
333C4—731no—
334C4—1461no—
335C4—1461no—
336C4—1461no—
337C4—1461no—
338C4—1461no—
339C2—41no—
340C2—2921no—
341C2—2921no—
342C2#41×#6440811yescharacteristic
343C2#1798966611yescharacteristic
344C2#1798966611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#64408
commutator, socleC22×C73C23×C4
Fitting#126×C73C4
hypercenter#126#64408
hypocenterC73#2967
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #17989639C2semidirect
2. #17989637C2semidirect
3. #17989621C2semidirect
4. #17989620C2semidirect
5. #17989619C2semidirect
6. #17989617C2semidirect
7. #17989616C2semidirect
8. #17989616C2semidirect
9. #17989612C2semidirect
10. #17989611C2semidirect
11. #17989609C2semidirect
12. #17989552C2semidirect
13. #17989551C2semidirect
14. C4×#11924038C2semidirect
173. C73#2967semidirect