Finite Group Databasebeta

← #22622006

Subgroups — #22622006

Order 9344.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989233C211yesmaximal, characteristic
2#17988949C211yesmaximal, characteristic, complemented
3#17988922C211yesmaximal, characteristic, complemented
4#17988900C211yesmaximal, characteristic, complemented
5#17988864C211yesmaximal, characteristic, complemented
6#17988835C211yesmaximal, characteristic, complemented
7#17988826C211yesmaximal, characteristic, complemented
8#17988809C211yesmaximal, characteristic, complemented
9#17988747C211yesmaximal, characteristic, complemented
10#17988737C211yesmaximal, characteristic, complemented
11#17988685C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988586C211yesmaximal, characteristic, complemented
14C2×#14556511C211yesmaximal, characteristic, complemented
15#554×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic, complemented
19C2×#11924015C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21C2×#11924012C2211yescharacteristic, complemented
22C22×#10596831C2211yescharacteristic
23#14556579C2211yescharacteristic
24#14556576—21no—
25#14556570C2211yescharacteristic
26#14556565C2211yescharacteristic
27#14556564—21no—
28#14556559—21no—
29C4×D292C2211yescharacteristic
30C22⋊C4×D73—21no—
31#14556524C2211yescharacteristic, complemented
32#14556524C2211yescharacteristic, complemented
33#14556524C2211yescharacteristic, complemented
34C4⋊#10596831C2211yescharacteristic, complemented
35#14556515C2211yescharacteristic, complemented
36#14556514C2211yescharacteristic, complemented
37#14556514C2211yescharacteristic, complemented
38#14556514C2211yescharacteristic, complemented
39#14556511C2211yescharacteristic
40#14556511C2211yescharacteristic
41#14556511C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556511C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic, complemented
47#14556502C2211yescharacteristic, complemented
48C4⋊Q8×C73C2211yescharacteristic, complemented
49#125×C73—21no—
50C22⋊Q8×C73—21no—
51C22⋊Q8×C73—21no—
52C22⋊Q8×C73C2211yescharacteristic
53C22⋊Q8×C73C2211yescharacteristic, complemented
54C4×Q8×C73C2211yescharacteristic, complemented
55C4×D4×C73—21no—
56C4×D4×C73C2211yescharacteristic
57C2×C4⋊C4×C73C2211yescharacteristic
58C2×C4⋊C4×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—22no—
61#11924028—41no—
62C2×Dic146C2311yescharacteristic
63C2×D292—22no—
64C2×D292—21no—
65C2×D292—41no—
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72#11924018—41no—
73#11924015—22no—
74#11924015—41no—
75#11924012—41no—
76C2×#10596831—41no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83C22⋊Dic73—21no—
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88C2×Q8×C73—21no—
89C2×Q8×C73C2311yescharacteristic
90C2×D4×C73D411yescharacteristic
91C22×C4×C73—21no—
92C22×C4×C73—21no—
93C22×C4×C73C2311yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C4⋊C4×C73—21no—
96C4⋊C4×C73—21no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73D411yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C42×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73C2×D411yescharacteristic
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—42no—
116C22×D73—42no—
117C22×D73—81no—
118Q8×C73—21no—
119Q8×C73—21no—
120Q8×C73—81no—
121D4×C73—22no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—81no—
131C2×C4×C73—81no—
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2×D411yescharacteristic
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2411yescharacteristic
137C22⋊D73—42no—
138C22⋊D73—81no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—42no—
145D292#4112yes—
146C4×D73—42no—
147C4×D73—81no—
148Dic146—21no—
149Dic146—21no—
150#10596831—21no—
151#10596831—21no—
152#10596831—21no—
153#10596831—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73#13712yes—
160C22×C73C22×D411yescharacteristic
161C2×D73—22no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—84no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—41no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73C2×#4111yescharacteristic
177C4×C73H(5,𝔽2)11yescharacteristic
178Dic73—41no—
179Dic73—41no—
180C2×C73—22no—
181C2×C73—41no—
182C2×C73#54611yescharacteristic
183C2×C73C2×#13711yescharacteristic
184C2×C73#57611yescharacteristic
185D73—42no—
186D73—81no—
187#3314—731nomaximal, Sylow
188C73#331411yescharacteristic, complemented, Sylow
189#554D7311yescharacteristic, complemented
190#546—731no—
191#489—731no—
192#484—731no—
193#480—731no—
194#474—731no—
195#468—731no—
196#467—731no—
197#464—731no—
198#452—731no—
199#450—731no—
200#440—731no—
201#435—731no—
202#417—731no—
203C2×#102—731no—
204C2×#41—731no—
205C22×D4—731no—
206C2×Q16—731no—
207C2×SD16—731no—
208C2×SD16—731no—
209C2×M16—731no—
210C22×C8—731no—
211C4⋊Q8C2×D7311yescharacteristic, complemented
212#125—21no—
213#124—731no—
214#123—1461no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—731no—
218C22⋊Q8C2×D7311yescharacteristic
219C22⋊Q8C2×D7311yescharacteristic, complemented
220#121—731no—
221#121—1461no—
222#120—1461no—
223C4×Q8C2×D7311yescharacteristic, complemented
224C4×D4—21no—
225C4×D4—731no—
226C4×D4C2×D7311yescharacteristic
227C2×C4⋊C4C2×D7311yescharacteristic
228C2×C4⋊C4C2×D7311yescharacteristic, complemented
229C2×C22⋊C4—1461no—
230#107—731no—
231#107—731no—
232#107—731no—
233C4⋊C8—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#103—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244C22⋊C8—731no—
245C22⋊C8—731no—
246#97—731no—
247C24—1461no—
248#41—2921no—
249#41—1462no—
250C2×Q8—21no—
251C2×Q8—731no—
252C2×Q8C22×D7311yescharacteristic
253C2×D4—2921no—
254C2×D4—731no—
255C2×D4—731no—
256C2×D4—1462no—
257C2×D4—1461no—
258C2×D4—1461no—
259C2×D4—1461no—
260C2×D4C22⋊D7311yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4C22×D7311yescharacteristic
266C22×C4C22×D7311yescharacteristic
267Q16—2921no—
268SD16—2921no—
269SD16—1462no—
270M16—2921no—
271C2×C8—2921no—
272C2×C8—731no—
273C2×C8—731no—
274C2×C8—731no—
275C2×C8—731no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—731no—
283C4⋊C4—1461no—
284C4⋊C4C22⋊D7311yescharacteristic
285C4⋊C4C22×D7311yescharacteristic
286C4⋊C4C22×D7311yescharacteristic
287C4⋊C4C22×D7311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4C22⋊D7311yescharacteristic
296C22⋊C4C22⋊D7311yescharacteristic
297C42—21no—
298C42C22×D7311yescharacteristic
299C23—2922no—
300C23—2922no—
301C23—5841no—
302C23—1461no—
303C23—1461no—
304C23C2×C22⋊D7311yescharacteristic
305C23C2×C22⋊D7311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—81no—
309Q8—1461no—
310Q8—1461no—
311D4—22no—
312D4—2922no—
313D4—2922no—
314D4—5841no—
315D4—732no—
316D4—1461no—
317D4—1461no—
318D4—1461no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—2922no—
330C2×C4—5841no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4C2×C22⋊D7311yescharacteristic
334C2×C4C2×C22⋊D7311yescharacteristic
335C2×C4C2×C22⋊D7311yescharacteristic
336C2×C4C2×C22⋊D7311yescharacteristic
337C2×C4C23×D7311yescharacteristic
338C8—1461no—
339C8—1461no—
340C8—1461no—
341C8—1461no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—2921no—
348C22—2921no—
349C22—2921no—
350C22—2921no—
351C22—2921no—
352C22—5844no—
353C22—1462no—
354C22#1455662212yes—
355C22C22×C22⋊D7311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—2921no—
365C4—2921no—
366C4#41×D7311yescharacteristic
367C4#1455663711yescharacteristic
368C2—22no—
369C2—41no—
370C2—2922no—
371C2—5841no—
372C2#1798922511yescharacteristic
373C2C2×#1455662211yescharacteristic
374C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#554×C73C2
socleC22×C73C22×D4
hypercenter#554D73
hypocenterC73#3314
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #17988949C2semidirect
3. #17988922C2semidirect
4. #17988900C2semidirect
5. #17988864C2semidirect
6. #17988835C2semidirect
7. #17988826C2semidirect
8. #17988809C2semidirect
9. #17988747C2semidirect
10. #17988737C2semidirect
11. #17988685C2semidirect
12. #17988659C2semidirect
13. #17988586C2semidirect
14. C2×#14556511C2semidirect
15. #554×C73C2semidirect
18. C2×#11924018C22semidirect
21. C2×#11924012C22semidirect
31. #14556524C22semidirect
32. #14556524C22semidirect
33. #14556524C22semidirect
34. C4⋊#10596831C22semidirect
35. #14556515C22semidirect
36. #14556514C22semidirect
37. #14556514C22semidirect
38. #14556514C22semidirect
46. C22⋊#10596831C22semidirect
47. #14556502C22semidirect
48. C4⋊Q8×C73C22semidirect
53. C22⋊Q8×C73C22semidirect
54. C4×Q8×C73C22semidirect
58. C2×C4⋊C4×C73C22semidirect
188. C73#3314semidirect
189. #554D73semidirect
211. C4⋊Q8C2×D73semidirect
219. C22⋊Q8C2×D73semidirect
223. C4×Q8C2×D73semidirect
228. C2×C4⋊C4C2×D73semidirect