Finite Group Databasebeta

← #22620722

Subgroups — #22620722

Order 9344.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989099C211yesmaximal, characteristic, complemented
2#17989097C211yesmaximal, characteristic, complemented
3#17988931C211yesmaximal, characteristic, complemented
4#17988928C211yesmaximal, characteristic, complemented
5#17988914C211yesmaximal, characteristic, complemented
6#17988829C211yesmaximal, characteristic, complemented
7#17988822C211yesmaximal, characteristic, complemented
8#17988817C211yesmaximal, characteristic, complemented
9#17988815C211yesmaximal, characteristic, complemented
10#17988751C211yesmaximal, characteristic, complemented
11#17988750C211yesmaximal, characteristic, complemented
12#17988733C211yesmaximal, characteristic, complemented
13#17988730C211yesmaximal, characteristic, complemented
14C22⋊C8×D73C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C2×Dic292C2211yescharacteristic, complemented
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×#11924013C2211yescharacteristic, complemented
23C2×C8×D73C2211yescharacteristic
24C2×C8×D73C2211yescharacteristic
25#14556575—21no—
26#14556573—21no—
27#14556571C2211yescharacteristic
28#14556571C2211yescharacteristic
29#14556571C2211yescharacteristic
30#14556570C2211yescharacteristic
31#14556566C2211yescharacteristic
32#14556566C2211yescharacteristic
33#14556562C2211yescharacteristic
34#14556561—21no—
35#14556559—21no—
36C4×D292—21no—
37C4×D292—21no—
38D4×Dic73—21no—
39#14556551—21no—
40#14556549C2211yescharacteristic
41#14556524C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556514C2211yescharacteristic, complemented
45#14556514C2211yescharacteristic, complemented
46#14556514C2211yescharacteristic, complemented
47#14556513C2211yescharacteristic, complemented
48#14556511C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52#121×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic
59C23×D73D411yescharacteristic
60#11924028—41no—
61#11924028—41no—
62#11924027—41no—
63#11924027—41no—
64C2×Dic146C2311yescharacteristic
65C2×Dic146C2311yescharacteristic
66C2×D292—21no—
67C2×D292—21no—
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C22×Dic73—21no—
73C22×Dic73D411yescharacteristic
74C2×C4×D73—21no—
75C2×C4×D73—41no—
76C2×C4×D73—41no—
77C2×C4×D73D411yescharacteristic
78C2×C4×D73D411yescharacteristic
79C2×C4×D73C2311yescharacteristic
80C2×C4×D73C2311yescharacteristic
81Dic292—41no—
82#11924017—41no—
83#11924016—41no—
84#11924013—41no—
85C2×#10596831C2311yescharacteristic
86C2×#10596831C2311yescharacteristic
87C8×D73—41no—
88C8×D73—41no—
89C4⋊Dic73—21no—
90C4⋊Dic73—21no—
91C4⋊Dic73—21no—
92C4⋊Dic73C2311yescharacteristic
93#11924007—21no—
94C22⋊Dic73—21no—
95C22⋊Dic73—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102C4×Dic73—21no—
103C2×D4×C73—21no—
104C2×D4×C73C2311yescharacteristic
105C22×C4×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C42×C73—21no—
114C23×C73—21no—
115C23×C73C2×D411yescharacteristic
116C22×D73—22no—
117C22×D73—21no—
118C22×D73—41no—
119C22×D73—41no—
120C22×D73C2×D411yescharacteristic
121C22×D73C2×D411yescharacteristic
122D4×C73—21no—
123D4×C73—21no—
124D4×C73—42no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2411yescharacteristic
132C22⋊D73—42no—
133C22⋊D73—42no—
134C22⋊D73—42no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—41no—
139C2×Dic73—42no—
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142D292—21no—
143D292—21no—
144D292—42no—
145D292—42no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—41no—
151C4×D73—41no—
152C4×D73—42no—
153Dic146—21no—
154Dic146—21no—
155Dic146—21no—
156Dic146—21no—
157C8×C73—21no—
158C8×C73—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73C22×D411yescharacteristic
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—44no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—41no—
177C2×D73#13512yes—
178C4×C73—21no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73H(5,𝔽2)11yescharacteristic
183C4×C73H(5,𝔽2)11yescharacteristic
184Dic73—21no—
185Dic73—21no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189C2×C73—41no—
190C2×C73—81no—
191C2×C73#53411yescharacteristic
192C2×C73C2×#13511yescharacteristic
193C2×C73#57511yescharacteristic
194D73—22no—
195D73—41no—
196D73—81no—
197#3191—731nomaximal, Sylow
198C73#319111yescharacteristic, complemented, Sylow
199#525—731no—
200#525—731no—
201#485—731no—
202#485—731no—
203#482—731no—
204#482D7311yescharacteristic, complemented
205#467—731no—
206#466—731no—
207#465—731no—
208#465—731no—
209#452—731no—
210#452—731no—
211#449—731no—
212#449—731no—
213C2×C22⋊C8—731no—
214C2×#41—731no—
215C2×#41—731no—
216C23×C4—731no—
217C2×Q16—731no—
218C2×SD16—731no—
219C2×SD16—731no—
220C2×D8—731no—
221C22×C8—731no—
222C22×C8—731no—
223#123—1461no—
224#123—1461no—
225C22⋊Q8—731no—
226C22⋊Q8—731no—
227C22⋊Q8—731no—
228C22⋊Q8—731no—
229#121—731no—
230#121—731no—
231#121—731no—
232#121C2×D7311yescharacteristic
233#120—1461no—
234#120—1461no—
235C4×D4—1461no—
236C4×D4—1461no—
237C4×D4—1461no—
238C4×D4—1461no—
239#117—731no—
240#117C2×D7311yescharacteristic
241#107—731no—
242#107C2×D7311yescharacteristic, complemented
243#106—731no—
244#106C2×D7311yescharacteristic, complemented
245#103—731no—
246#103—731no—
247#103—731no—
248#103—731no—
249#102—731no—
250#102—731no—
251#102C2×D7311yescharacteristic, complemented
252#102C2×D7311yescharacteristic, complemented
253C22⋊C8—731no—
254C22⋊C8—731no—
255C22⋊C8—731no—
256C22⋊C8C2×D7311yescharacteristic
257C24—731no—
258#41—2921no—
259#41—2921no—
260#41—2921no—
261#41—2921no—
262C2×Q8—731no—
263C2×Q8—731no—
264C2×D4—21no—
265C2×D4—731no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4C22×D7311yescharacteristic
272C22×C4—2921no—
273C22×C4—2921no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—1461no—
280C22×C4—1461no—
281C22×C4C22×D7311yescharacteristic
282Q16—2921no—
283SD16—2921no—
284SD16—2921no—
285D8—2921no—
286C2×C8—2921no—
287C2×C8—2921no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8C22×D7311yescharacteristic
291C2×C8C22×D7311yescharacteristic
292C4⋊C4—731no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4—1461no—
296C4⋊C4—1461no—
297C4⋊C4C22×D7311yescharacteristic
298C4⋊C4C22×D7311yescharacteristic
299C4⋊C4C22×D7311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4—1461no—
305C22⋊C4—1461no—
306C22⋊C4—1461no—
307C22⋊C4—1461no—
308C22⋊C4—1461no—
309C22⋊C4—1461no—
310C42—21no—
311C42—1461no—
312C23—21no—
313C23—2921no—
314C23—2921no—
315C23—731no—
316C23—731no—
317C23—1462no—
318C23—1461no—
319C23D4×D7311yescharacteristic
320Q8—1461no—
321Q8—1461no—
322Q8—1461no—
323Q8—1461no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2922no—
328D4—2922no—
329D4—2922no—
330D4—2922no—
331D4—2922no—
332D4—1461no—
333D4—1461no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—2922no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2922no—
343C2×C4—2921no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4D4×D7311yescharacteristic
354C2×C4C23×D7311yescharacteristic
355C8—21no—
356C8—21no—
357C8—1461no—
358C8—1461no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—2924no—
366C22—2921no—
367C22—2921no—
368C22—2921no—
369C22—732no—
370C22—1461no—
371C22—1461no—
372C22—1461no—
373C22—1461no—
374C22—1461no—
375C22C2×D4×D7311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2921no—
381C4—2921no—
382C4—2921no—
383C4—1461no—
384C4—1461no—
385C4#1455663711yescharacteristic
386C4#1455663711yescharacteristic
387C2—41no—
388C2—81no—
389C2—2921no—
390C2—5841no—
391C2—1462no—
392C2#1798914811yescharacteristic
393C2#135×D7311yescharacteristic
394C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3191
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #17989099C2semidirect
2. #17989097C2semidirect
3. #17988931C2semidirect
4. #17988928C2semidirect
5. #17988914C2semidirect
6. #17988829C2semidirect
7. #17988822C2semidirect
8. #17988817C2semidirect
9. #17988815C2semidirect
10. #17988751C2semidirect
11. #17988750C2semidirect
12. #17988733C2semidirect
13. #17988730C2semidirect
14. C22⋊C8×D73C2semidirect
15. #482×C73C2semidirect
19. C2×Dic292C22semidirect
20. C2×#11924017C22semidirect
21. C2×#11924016C22semidirect
22. C2×#11924013C22semidirect
41. #14556524C22semidirect
42. #14556522C22semidirect
43. #14556516C22semidirect
44. #14556514C22semidirect
45. #14556514C22semidirect
46. #14556514C22semidirect
47. #14556513C22semidirect
48. #14556511C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. #102×C73C22semidirect
57. #102×C73C22semidirect
198. C73#3191semidirect
204. #482D73semidirect
242. #107C2×D73semidirect
244. #106C2×D73semidirect
251. #102C2×D73semidirect
252. #102C2×D73semidirect