Finite Group Databasebeta

← #22620719

Subgroups — #22620719

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#17989098C211yesmaximal, characteristic, complemented
2#17988928C211yesmaximal, characteristic, complemented
3#17988925C211yesmaximal, characteristic, complemented
4#17988911C211yesmaximal, characteristic, complemented
5#17988908C211yesmaximal, characteristic, complemented
6#17988826C211yesmaximal, characteristic, complemented
7#17988821C211yesmaximal, characteristic, complemented
8#17988818C211yesmaximal, characteristic, complemented
9#17988814C211yesmaximal, characteristic, complemented
10#17988749C211yesmaximal, characteristic, complemented
11#17988747C211yesmaximal, characteristic, complemented
12#17988732C211yesmaximal, characteristic, complemented
13#17988730C211yesmaximal, characteristic, complemented
14C2×C22⋊#10596831C211yesmaximal, characteristic, complemented
15#525×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924018C2211yescharacteristic, complemented
18C2×#11924016C2211yescharacteristic, complemented
19C2×#11924015C2211yescharacteristic, complemented
20C2×#11924013C2211yescharacteristic, complemented
21C22×#10596831C2211yescharacteristic
22C22×#10596831C2211yescharacteristic
23#14556574—21no—
24#14556570C2211yescharacteristic
25#14556570C2211yescharacteristic
26#14556565C2211yescharacteristic
27#14556565C2211yescharacteristic
28#14556560—21no—
29C4×C22⋊D73—21no—
30C4×C22⋊D73—21no—
31#14556550C2211yescharacteristic
32#14556524C2211yescharacteristic, complemented
33#14556524C2211yescharacteristic, complemented
34#14556522C2211yescharacteristic, complemented
35#14556522C2211yescharacteristic, complemented
36#14556515C2211yescharacteristic, complemented
37#14556515C2211yescharacteristic, complemented
38#14556514C2211yescharacteristic, complemented
39#14556514C2211yescharacteristic, complemented
40#14556512C2211yescharacteristic, complemented
41#14556512C2211yescharacteristic, complemented
42#14556511C2211yescharacteristic, complemented
43#14556511C2211yescharacteristic, complemented
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47C22⋊#10596831C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C23×C4×C73C2211yescharacteristic
50#123×C73—21no—
51C22⋊Q8×C73C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53#121×C73C2211yescharacteristic
54#121×C73C2211yescharacteristic
55#120×C73—21no—
56C4×D4×C73—21no—
57C4×D4×C73—21no—
58#117×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C4×D73—21no—
67#11924018—41no—
68#11924016—41no—
69#11924015—41no—
70#11924013—41no—
71C2×#10596831—41no—
72C2×#10596831—41no—
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84#11924005—21no—
85#11924005—21no—
86C4×Dic73—21no—
87C24×C73D411yescharacteristic
88#41×C73—41no—
89#41×C73—41no—
90C2×Q8×C73C2311yescharacteristic
91C2×D4×C73—21no—
92C2×D4×C73—21no—
93C2×D4×C73—21no—
94C2×D4×C73C2311yescharacteristic
95C22×C4×C73—21no—
96C22×C4×C73—41no—
97C22×C4×C73—41no—
98C22×C4×C73D411yescharacteristic
99C22×C4×C73D411yescharacteristic
100C22×C4×C73D411yescharacteristic
101C22×C4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73—21no—
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C22⋊C4×C73—21no—
109C22⋊C4×C73—21no—
110C22⋊C4×C73—21no—
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C42×C73—21no—
114C23×C73—22no—
115C23×C73—21no—
116C23×C73—41no—
117C23×C73—41no—
118C23×C73C2×D411yescharacteristic
119C23×C73C2×D411yescharacteristic
120C23×C73C2×D411yescharacteristic
121C22×D73—21no—
122Q8×C73—21no—
123Q8×C73—21no—
124D4×C73—21no—
125D4×C73—21no—
126D4×C73—42no—
127D4×C73—42no—
128D4×C73—42no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73—42no—
142C2×C4×C73C2×D411yescharacteristic
143C2×C4×C73C2×D411yescharacteristic
144C2×C4×C73C2×D411yescharacteristic
145C2×C4×C73C2411yescharacteristic
146C22⋊D73—42no—
147C22⋊D73—42no—
148C22⋊D73—42no—
149C2×Dic73—21no—
150C2×Dic73—21no—
151C2×Dic73—21no—
152D292—21no—
153D292—21no—
154C4×D73—42no—
155Dic146—21no—
156Dic146—21no—
157#10596831—21no—
158#10596831—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—44no—
170C22×C73—41no—
171C22×C73—41no—
172C22×C73—41no—
173C22×C73#13512yes—
174C22×C73C22×D411yescharacteristic
175C2×D73—41no—
176C2×D73—41no—
177C2×D73—41no—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73—21no—
181C4×C73—41no—
182C4×C73—41no—
183C4×C73—41no—
184C4×C73H(5,𝔽2)11yescharacteristic
185C4×C73H(5,𝔽2)11yescharacteristic
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189C2×C73—22no—
190C2×C73—41no—
191C2×C73—41no—
192C2×C73—81no—
193C2×C73#53411yescharacteristic
194C2×C73C2×#13511yescharacteristic
195C2×C73#57511yescharacteristic
196D73—81no—
197#3191—731nomaximal, Sylow
198C73#319111yescharacteristic, complemented, Sylow
199#525—731no—
200#525D7311yescharacteristic, complemented
201#485—731no—
202#485—731no—
203#482—731no—
204#482—731no—
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×#41C2×D7311yescharacteristic
216C23×C4C2×D7311yescharacteristic
217C2×Q16—731no—
218C2×SD16—731no—
219C2×SD16—731no—
220C2×D8—731no—
221C22×C8—731no—
222C22×C8—731no—
223#123—21no—
224#123—1461no—
225C22⋊Q8—731no—
226C22⋊Q8—731no—
227C22⋊Q8C2×D7311yescharacteristic
228C22⋊Q8C2×D7311yescharacteristic
229#121—731no—
230#121—731no—
231#121C2×D7311yescharacteristic
232#121C2×D7311yescharacteristic
233#120—21no—
234#120—1461no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—1461no—
238C4×D4—1461no—
239#117—731no—
240#117C2×D7311yescharacteristic
241#107—731no—
242#107—731no—
243#106—731no—
244#106—731no—
245#103—731no—
246#103—731no—
247#103—731no—
248#103—731no—
249#102—731no—
250#102—731no—
251#102—731no—
252#102—731no—
253C22⋊C8—731no—
254C22⋊C8—731no—
255C22⋊C8—731no—
256C22⋊C8—731no—
257C24C22⋊D7311yescharacteristic
258#41—41no—
259#41—41no—
260#41—2921no—
261#41—2921no—
262C2×Q8—731no—
263C2×Q8C22×D7311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—731no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4C22×D7311yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—1461no—
276C22×C4C22⋊D7311yescharacteristic
277C22×C4C22⋊D7311yescharacteristic
278C22×C4C22⋊D7311yescharacteristic
279C22×C4C22×D7311yescharacteristic
280C22×C4C22×D7311yescharacteristic
281C22×C4C22×D7311yescharacteristic
282Q16—2921no—
283SD16—2921no—
284SD16—2921no—
285D8—2921no—
286C2×C8—2921no—
287C2×C8—2921no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8—731no—
291C2×C8—731no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—731no—
295C4⋊C4—731no—
296C4⋊C4—1461no—
297C4⋊C4—1461no—
298C4⋊C4C22×D7311yescharacteristic
299C4⋊C4C22×D7311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—1461no—
306C22⋊C4—1461no—
307C22⋊C4—1461no—
308C22⋊C4—1461no—
309C22⋊C4—1461no—
310C42—21no—
311C42—1461no—
312C23—22no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—1461no—
317C23C2×C22⋊D7311yescharacteristic
318C23C2×C22⋊D7311yescharacteristic
319C23C2×C22⋊D7311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1461no—
323Q8—1461no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
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—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—2922no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4C2×C22⋊D7311yescharacteristic
352C2×C4C2×C22⋊D7311yescharacteristic
353C2×C4C2×C22⋊D7311yescharacteristic
354C2×C4C23×D7311yescharacteristic
355C8—1461no—
356C8—1461no—
357C8—1461no—
358C8—1461no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—2921no—
372C22—2921no—
373C22—2921no—
374C22#1455661112yes—
375C22C22×C22⋊D7311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—2921no—
383C4—2921no—
384C4—2921no—
385C4#1455663611yescharacteristic
386C4#1455663611yescharacteristic
387C2—22no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—5841no—
392C2#1798914611yescharacteristic
393C2C2×#1455661111yescharacteristic
394C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#525×C73C2
socleC22×C73C22×D4
hypercenter#525D73
hypocenterC73#3191
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #17989098C2semidirect
2. #17988928C2semidirect
3. #17988925C2semidirect
4. #17988911C2semidirect
5. #17988908C2semidirect
6. #17988826C2semidirect
7. #17988821C2semidirect
8. #17988818C2semidirect
9. #17988814C2semidirect
10. #17988749C2semidirect
11. #17988747C2semidirect
12. #17988732C2semidirect
13. #17988730C2semidirect
14. C2×C22⋊#10596831C2semidirect
15. #525×C73C2semidirect
17. C2×#11924018C22semidirect
18. C2×#11924016C22semidirect
19. C2×#11924015C22semidirect
20. C2×#11924013C22semidirect
32. #14556524C22semidirect
33. #14556524C22semidirect
34. #14556522C22semidirect
35. #14556522C22semidirect
36. #14556515C22semidirect
37. #14556515C22semidirect
38. #14556514C22semidirect
39. #14556514C22semidirect
40. #14556512C22semidirect
41. #14556512C22semidirect
42. #14556511C22semidirect
43. #14556511C22semidirect
198. C73#3191semidirect
200. #525D73semidirect