Finite Group Databasebeta

← #22626799

Subgroups — #22626799

Order 9344.

412 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#17989621C211yesmaximal, characteristic, complemented
2#17989620C211yesmaximal, characteristic, complemented
3#17989619C211yesmaximal, characteristic, complemented
4#17989617C211yesmaximal, characteristic, complemented
5#17989617C211yesmaximal, characteristic, complemented
6#17989616C211yesmaximal, characteristic, complemented
7#17989615C211yesmaximal, characteristic, complemented
8#17989614C211yesmaximal, characteristic, complemented
9#17989611C211yesmaximal, characteristic, complemented
10#17989611C211yesmaximal, characteristic, complemented
11#17989561C211yesmaximal, characteristic, complemented
12#17989560C211yesmaximal, characteristic, complemented
13#17989558C211yesmaximal, characteristic, complemented
14#17989555C211yesmaximal, characteristic, complemented
15#17989095C211yesmaximal, characteristic
16C2×#11924038C2211yescharacteristic
17C2×#11924038C2211yescharacteristic
18C2×#11924038C2211yescharacteristic, complemented
19C2×#11924037C2211yescharacteristic, complemented
20C2×#11924036C2211yescharacteristic
21C2×#11924036C2211yescharacteristic
22C2×#11924036C2211yescharacteristic, complemented
23C22×#10596833C2211yescharacteristic, complemented
24#14556658C2211yescharacteristic, complemented
25#14556658C2211yescharacteristic, complemented
26C4⋊#10596833C2211yescharacteristic, complemented
27C4⋊#10596833C2211yescharacteristic, complemented
28#14556648C2211yescharacteristic
29#14556648C2211yescharacteristic
30#14556648C2211yescharacteristic
31#14556648C2211yescharacteristic
32#14556648C2211yescharacteristic, complemented
33#14556648C2211yescharacteristic, complemented
34C22⋊#10596833C2211yescharacteristic
35C22⋊#10596833C2211yescharacteristic
36C22⋊#10596833C2211yescharacteristic
37C22⋊#10596833C2211yescharacteristic
38C22⋊#10596833C2211yescharacteristic, complemented
39C22⋊#10596833C2211yescharacteristic, complemented
40#14556646C2211yescharacteristic, complemented
41#14556646C2211yescharacteristic, complemented
42C4×#10596833C2211yescharacteristic, complemented
43C4×#10596833C2211yescharacteristic, complemented
44C2×#11924027C2211yescharacteristic
45C22×C4×D73C2211yescharacteristic
46#14556574C411yescharacteristic
47#14556569C411yescharacteristic
48#14556569C411yescharacteristic
49#14556564C411yescharacteristic
50#14556564C411yescharacteristic
51#14556561C411yescharacteristic
52#14556559C411yescharacteristic
53#14556553C2211yescharacteristic
54#14556553C2211yescharacteristic
55#14556551C2211yescharacteristic
56#14556551C2211yescharacteristic
57#14556547C2211yescharacteristic
58#123×C73C411yescharacteristic
59#11924038—41no—
60#11924038—41no—
61#11924038—41no—
62#11924037—41no—
63#11924036—41no—
64#11924036—41no—
65#11924036—41no—
66C2×#10596833—41no—
67C2×#10596833C2311yescharacteristic
68C2×#10596833C2311yescharacteristic
69C2×#10596833C2311yescharacteristic
70C2×#10596833C2311yescharacteristic
71C2×#10596833C2311yescharacteristic
72C2×#10596833C2311yescharacteristic
73C2×#10596833C2311yescharacteristic
74C2×#10596833C2311yescharacteristic
75C23×D73C2×C411yescharacteristic
76#11924027—41no—
77#11924027—41no—
78C2×Dic146C2×C411yescharacteristic
79C2×D292C2×C411yescharacteristic
80C2×D292C2×C411yescharacteristic
81C2×C22⋊D73C2×C411yescharacteristic
82C2×C22⋊D73C2×C411yescharacteristic
83C2×C22⋊D73C2×C411yescharacteristic
84C2×C22⋊D73C2×C411yescharacteristic
85C22×Dic73C2311yescharacteristic
86C22×Dic73C2311yescharacteristic
87C2×C4×D73—41no—
88C2×C4×D73—41no—
89C2×C4×D73C2×C411yescharacteristic
90C2×C4×D73C2×C411yescharacteristic
91C2×C4×D73C2311yescharacteristic
92C2×C4×D73C2311yescharacteristic
93C2×C4×D73C2311yescharacteristic
94#11924007C2×C411yescharacteristic
95#11924007C2×C411yescharacteristic
96#11924007C2×C411yescharacteristic
97#11924007C2×C411yescharacteristic
98C22⋊Dic73C2×C411yescharacteristic
99#11924005C2×C411yescharacteristic
100#11924005C2×C411yescharacteristic
101#11924005C2×C411yescharacteristic
102#11924005C2×C411yescharacteristic
103#11924005C2×C411yescharacteristic
104#11924005C2×C411yescharacteristic
105C4×Dic73C2311yescharacteristic
106C4×Dic73C2311yescharacteristic
107C2×D4×C73C2×C411yescharacteristic
108C22×C4×C73C2×C411yescharacteristic
109C4⋊C4×C73C2×C411yescharacteristic
110C4⋊C4×C73C2×C411yescharacteristic
111C22⋊C4×C73C2×C411yescharacteristic
112C22⋊C4×C73C2×C411yescharacteristic
113C22⋊C4×C73C2×C411yescharacteristic
114C23×C73C22×C411yescharacteristic
115C23×C73C22×C411yescharacteristic
116C22×D73—22no—
117C22×D73—41no—
118C22×D73—41no—
119C22×D73C22×C411yescharacteristic
120C22×D73C22×C411yescharacteristic
121C22×D73C22×C411yescharacteristic
122D4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73C22×C411yescharacteristic
125C2×C4×C73C22×C411yescharacteristic
126C2×C4×C73C22×C411yescharacteristic
127C2×C4×C73C22×C411yescharacteristic
128C2×C4×C73C22×C411yescharacteristic
129C22⋊D73—22no—
130C22⋊D73—41no—
131C22⋊D73—41no—
132C22⋊D73—41no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73C22×C411yescharacteristic
138C2×Dic73C22×C411yescharacteristic
139C2×Dic73C22×C411yescharacteristic
140C2×Dic73C22×C411yescharacteristic
141C2×Dic73C2411yescharacteristic
142D292—22no—
143D292—41no—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—41no—
151C4×D73—41no—
152Dic146—41no—
153#10596833—21no—
154#10596833—21no—
155#10596833—21no—
156#10596833—21no—
157#10596833—21no—
158#10596833—21no—
159#10596833—21no—
160#10596833—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73C23×C411yescharacteristic
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—44no—
177C2×D73#13112yes—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73—21no—
181C4×C73—21no—
182C4×C73—21no—
183Dic73—21no—
184Dic73—21no—
185Dic73—21no—
186Dic73—21no—
187Dic73H(5,𝔽2)11yescharacteristic
188Dic73H(5,𝔽2)11yescharacteristic
189C2×C73—41no—
190C2×C73—41no—
191C2×C73#51811yescharacteristic
192C2×C73C2×#13111yescharacteristic
193C2×C73#56811yescharacteristic
194D73—22no—
195D73—41no—
196D73—41no—
197#2976—731nomaximal, Sylow
198C73#297611yescharacteristic, complemented, Sylow
199#525—731no—
200#436—731no—
201#436—731no—
202#435—731no—
203#435—731no—
204#435—731no—
205#435—731no—
206C8×D4—731no—
207C8×D4—731no—
208#433—731no—
209#433—731no—
210#408—731no—
211#408—731no—
212#407—731no—
213C2×C22⋊C8—731no—
214C2×#41—731no—
215C23×C4—731no—
216C2×M16—731no—
217C2×M16—731no—
218C2×M16—731no—
219C2×M16—731no—
220C22×C8—731no—
221C22×C8—731no—
222C22×C8—731no—
223C22×C8—731no—
224#123—731no—
225#123#6440811yescharacteristic
226C22⋊Q8—731no—
227C22⋊Q8—731no—
228#121—731no—
229#121—731no—
230#120—731no—
231#120—731no—
232C4×D4—731no—
233C4×D4—731no—
234C4×D4—731no—
235C4×D4—731no—
236#117—731no—
237C4⋊C8—731no—
238C4⋊C8—731no—
239C4⋊C8—731no—
240C4⋊C8—731no—
241C22⋊C8—731no—
242C22⋊C8—731no—
243C22⋊C8—731no—
244C22⋊C8—731no—
245C22⋊C8—731no—
246C22⋊C8—731no—
247C22⋊C8—731no—
248C22⋊C8—731no—
249C22⋊C8—731no—
250C22⋊C8—731no—
251C22⋊C8—731no—
252C22⋊C8—731no—
253#97—731no—
254#97—731no—
255C4×C8—731no—
256C4×C8—731no—
257C24—731no—
258#41—2921no—
259#41—2921no—
260C2×Q8—731no—
261C2×D4—731no—
262C2×D4—731no—
263C2×D4—731no—
264C2×D4—731no—
265C2×D4—731no—
266C2×D4—731no—
267C2×D4C2×#6440811yescharacteristic
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4C2×#6440811yescharacteristic
278M16—2921no—
279M16—2921no—
280M16—2921no—
281M16—2921no—
282C2×C8—2921no—
283C2×C8—2921no—
284C2×C8—2921no—
285C2×C8—2921no—
286C2×C8—731no—
287C2×C8—731no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8—731no—
291C2×C8—731no—
292C2×C8—731no—
293C2×C8—731no—
294C4⋊C4—731no—
295C4⋊C4—731no—
296C4⋊C4—731no—
297C4⋊C4—731no—
298C4⋊C4C2×#6440811yescharacteristic
299C4⋊C4C2×#6440811yescharacteristic
300C22⋊C4—731no—
301C22⋊C4—731no—
302C22⋊C4—731no—
303C22⋊C4—731no—
304C22⋊C4—731no—
305C22⋊C4—731no—
306C22⋊C4—731no—
307C22⋊C4C2×#6440811yescharacteristic
308C22⋊C4C2×#6440811yescharacteristic
309C22⋊C4C2×#6440811yescharacteristic
310C42—731no—
311C42—731no—
312C23—2921no—
313C23—2921no—
314C23—731no—
315C23—731no—
316C23—731no—
317C23—1462no—
318C23C22×#6440811yescharacteristic
319C23C22×#6440811yescharacteristic
320Q8—2921no—
321D4—41no—
322D4—2921no—
323D4—2921no—
324D4—2921no—
325D4—2921no—
326D4—1462no—
327D4—1462no—
328C2×C4—41no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—731no—
332C2×C4—731no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4C22×#6440811yescharacteristic
347C2×C4C22×#6440811yescharacteristic
348C2×C4C22×#6440811yescharacteristic
349C2×C4C22×#6440811yescharacteristic
350C2×C4C22×#6440811yescharacteristic
351C8—1461no—
352C8—1461no—
353C8—1461no—
354C8—1461no—
355C8—1461no—
356C8—1461no—
357C8—1461no—
358C8—1461no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—2924no—
366C22—732no—
367C22—1461no—
368C22—1461no—
369C22—1461no—
370C22—1461no—
371C22—1461no—
372C22—1461no—
373C22—1461no—
374C22—1461no—
375C22C23×#6440811yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—731no—
382C4—731no—
383C4—1461no—
384C4—1461no—
385C4—1461no—
386C4—1461no—
387C2—41no—
388C2—41no—
389C2—2921no—
390C2—2921no—
391C2—1462no—
392C2#1798965411yescharacteristic
393C2D73⋊#13111yescharacteristic
394C2#1798966611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#64408
commutator, socleC22×C73C23×C4
Fitting#123×C73C4
hypercenter#123#64408
hypocenterC73#2976
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #17989621C2semidirect
2. #17989620C2semidirect
3. #17989619C2semidirect
4. #17989617C2semidirect
5. #17989617C2semidirect
6. #17989616C2semidirect
7. #17989615C2semidirect
8. #17989614C2semidirect
9. #17989611C2semidirect
10. #17989611C2semidirect
11. #17989561C2semidirect
12. #17989560C2semidirect
13. #17989558C2semidirect
14. #17989555C2semidirect
18. C2×#11924038C22semidirect
19. C2×#11924037C22semidirect
22. C2×#11924036C22semidirect
23. C22×#10596833C22semidirect
24. #14556658C22semidirect
25. #14556658C22semidirect
26. C4⋊#10596833C22semidirect
27. C4⋊#10596833C22semidirect
32. #14556648C22semidirect
33. #14556648C22semidirect
38. C22⋊#10596833C22semidirect
39. C22⋊#10596833C22semidirect
40. #14556646C22semidirect
41. #14556646C22semidirect
42. C4×#10596833C22semidirect
43. C4×#10596833C22semidirect
198. C73#2976semidirect