Finite Group Databasebeta

← #22620932

Subgroups — #22620932

Order 9344.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989141C211yesmaximal, characteristic, complemented
2#124×D73C211yesmaximal, characteristic
3#17988980C211yesmaximal, characteristic, complemented
4#17988978C211yesmaximal, characteristic, complemented
5#17988948C211yesmaximal, characteristic, complemented
6#17988945C211yesmaximal, characteristic, complemented
7#17988810C211yesmaximal, characteristic, complemented
8#17988809C211yesmaximal, characteristic, complemented
9#17988806C211yesmaximal, characteristic, complemented
10#17988744C211yesmaximal, characteristic, complemented
11#17988741C211yesmaximal, characteristic, complemented
12#17988739C211yesmaximal, characteristic
13#17988736C211yesmaximal, characteristic
14#17988643C211yesmaximal, characteristic, complemented
15#464×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×Dic292C2211yescharacteristic, complemented
19C2×#11924018C2211yescharacteristic, complemented
20C2×#11924018C2211yescharacteristic, complemented
21C2×#11924017C2211yescharacteristic
22C2×#11924016C2211yescharacteristic
23C2×#11924015C2211yescharacteristic
24#14556590C2211yescharacteristic, complemented
25#14556589C2211yescharacteristic, complemented
26#14556581—21no—
27#14556580C2211yescharacteristic
28#14556579C2211yescharacteristic
29#14556578C2211yescharacteristic
30#14556577—21no—
31#14556577—21no—
32#14556571C2211yescharacteristic
33#14556569—21no—
34#14556567C2211yescharacteristic
35C4×Dic146—21no—
36C4×Dic146C2211yescharacteristic, complemented
37#14556548—21no—
38C22⋊C4×D73—21no—
39C22⋊C4×D73—21no—
40C42×D73C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556514C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic, complemented
51#14556501C2211yescharacteristic, complemented
52C2×Q16×C73C2211yescharacteristic, complemented
53C2×SD16×C73C2211yescharacteristic
54#124×C73C2211yescharacteristic
55C4×Q8×C73C2211yescharacteristic, complemented
56C4⋊C8×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58#102×C73C2211yescharacteristic
59C23×D73—21no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64Q8×D73—41no—
65Q8×D73—41no—
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68D4×D73—41no—
69D4×D73—41no—
70C2×C4×D73—21no—
71C2×C4×D73D411yescharacteristic
72C2×C4×D73D411yescharacteristic
73C2×C4×D73C2311yescharacteristic
74Dic292—41no—
75#11924018—41no—
76#11924018—41no—
77#11924017—41no—
78#11924016—41no—
79#11924015—41no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97C4×Dic73—21no—
98C4×Dic73D411yescharacteristic
99C4×Dic73D411yescharacteristic
100C4×Dic73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C2×Q8×C73C2311yescharacteristic
103C2×D4×C73C2311yescharacteristic
104Q16×C73—41no—
105SD16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C22⋊C4×C73—21no—
112C42×C73—21no—
113C42×C73C2311yescharacteristic
114C23×C73—21no—
115C22×D73—21no—
116C22×D73—42no—
117C22×D73—42no—
118C22×D73—42no—
119C22×D73C2×D411yescharacteristic
120Q8×C73—21no—
121Q8×C73—21no—
122Q8×C73—21no—
123Q8×C73—21no—
124D4×C73—21no—
125D4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2411yescharacteristic
132C22⋊D73—42no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139D292—21no—
140D292—21no—
141C4×D73—22no—
142C4×D73—21no—
143C4×D73—21no—
144C4×D73—41no—
145C4×D73—42no—
146Dic146—21no—
147Dic146—21no—
148Dic146—21no—
149Dic146—21no—
150Dic146—42no—
151Dic146—42no—
152C8×C73—21no—
153C8×C73—21no—
154#10596831—21no—
155#10596831—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73C22×D411yescharacteristic
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—84no—
166C2×D73#13712yes—
167C4×C73—21no—
168C4×C73—21no—
169C4×C73—41no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73H(5,𝔽2)11yescharacteristic
173C4×C73H(5,𝔽2)11yescharacteristic
174Dic73—21no—
175Dic73—21no—
176Dic73—21no—
177Dic73—41no—
178Dic73—41no—
179Dic73—41no—
180C2×C73—81no—
181C2×C73#53511yescharacteristic
182C2×C73C2×#13711yescharacteristic
183C2×C73#57511yescharacteristic
184D73—22no—
185D73—81no—
186#3215—731nomaximal, Sylow
187C73#321511yescharacteristic, complemented, Sylow
188#533—731no—
189C2×#124—731no—
190#497—731no—
191#497—731no—
192#489—731no—
193#489—731no—
194#464—731no—
195#464—731no—
196#464—731no—
197#464D7311yescharacteristic, complemented
198#451—731no—
199#451—731no—
200#450—731no—
201#450—731no—
202#432—731no—
203C22×Q8—731no—
204C22×D4—731no—
205C2×Q16—731no—
206C2×Q16—731no—
207C2×Q16—731no—
208C2×Q16C2×D7311yescharacteristic, complemented
209C2×SD16—731no—
210C2×SD16—731no—
211C2×SD16—731no—
212C2×SD16C2×D7311yescharacteristic
213C4⋊Q8—731no—
214C4⋊Q8—731no—
215#125—1461no—
216#124—731no—
217#124—731no—
218#124—731no—
219#124—1461no—
220#124—1461no—
221#124C2×D7311yescharacteristic
222C22⋊Q8—731no—
223C22⋊Q8—731no—
224C22⋊Q8—1461no—
225C4×Q8—731no—
226C4×Q8—1461no—
227C4×Q8C2×D7311yescharacteristic, complemented
228#117—1461no—
229C2×C22⋊C4—1461no—
230C2×C22⋊C4—1461no—
231C2×C42—731no—
232C4⋊C8—731no—
233C4⋊C8C2×D7311yescharacteristic, complemented
234#103—731no—
235#103—731no—
236#103—731no—
237#103C2×D7311yescharacteristic, complemented
238#102—731no—
239#102—731no—
240#102—731no—
241#102C2×D7311yescharacteristic
242C22⋊C8—731no—
243C22⋊C8—731no—
244#97—731no—
245#97—731no—
246C24—1461no—
247C2×Q8—2921no—
248C2×Q8—2921no—
249C2×Q8—731no—
250C2×Q8—731no—
251C2×Q8—1461no—
252C2×Q8—1461no—
253C2×Q8C22×D7311yescharacteristic
254C2×Q8C22×D7311yescharacteristic
255C2×D4—2921no—
256C2×D4—2921no—
257C2×D4—731no—
258C2×D4—1461no—
259C2×D4C22×D7311yescharacteristic
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—1461no—
264Q16—41no—
265Q16—2921no—
266Q16—2921no—
267Q16—2921no—
268SD16—41no—
269SD16—2921no—
270SD16—2921no—
271SD16—2921no—
272C2×C8—731no—
273C2×C8—731no—
274C2×C8C22×D7311yescharacteristic
275C2×C8C22×D7311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—731no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4C22×D7311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C42—21no—
296C42—731no—
297C42—731no—
298C42—731no—
299C42—1461no—
300C42C22×D7311yescharacteristic
301C23—21no—
302C23—2922no—
303C23—2922no—
304C23—2922no—
305C23—731no—
306C23—1461no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—2922no—
312Q8—2922no—
313Q8—1461no—
314Q8—1461no—
315Q8—1461no—
316Q8—1461no—
317D4—21no—
318D4—21no—
319D4—2922no—
320D4—1461no—
321D4—1461no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—2921no—
326C2×C4—2922no—
327C2×C4—731no—
328C2×C4—731no—
329C2×C4—731no—
330C2×C4—1462no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4—1461no—
335C2×C4—1461no—
336C2×C4D4×D7311yescharacteristic
337C2×C4D4×D7311yescharacteristic
338C2×C4C23×D7311yescharacteristic
339C8—21no—
340C8—21no—
341C8—1461no—
342C8—1461no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—2921no—
347C22—2921no—
348C22—2921no—
349C22—5844no—
350C22—732no—
351C22—1461no—
352C22—1461no—
353C22C2×D4×D7311yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—2921no—
360C4—2921no—
361C4—2921no—
362C4—1461no—
363C4—1461no—
364C4—1461no—
365C4#1455663611yescharacteristic
366C4#1455663711yescharacteristic
367C2—81no—
368C2—5841no—
369C2—1462no—
370C2#1798915311yescharacteristic
371C2#137×D7311yescharacteristic
372C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#464×C73C2
socleC22×C73C22×D4
hypercenter#464D73
hypocenterC73#3215
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #17989141C2semidirect
3. #17988980C2semidirect
4. #17988978C2semidirect
5. #17988948C2semidirect
6. #17988945C2semidirect
7. #17988810C2semidirect
8. #17988809C2semidirect
9. #17988806C2semidirect
10. #17988744C2semidirect
11. #17988741C2semidirect
14. #17988643C2semidirect
15. #464×C73C2semidirect
18. C2×Dic292C22semidirect
19. C2×#11924018C22semidirect
20. C2×#11924018C22semidirect
24. #14556590C22semidirect
25. #14556589C22semidirect
36. C4×Dic146C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556516C22semidirect
43. #14556515C22semidirect
44. #14556514C22semidirect
50. #14556501C22semidirect
51. #14556501C22semidirect
52. C2×Q16×C73C22semidirect
55. C4×Q8×C73C22semidirect
56. C4⋊C8×C73C22semidirect
57. #103×C73C22semidirect
187. C73#3215semidirect
197. #464D73semidirect
208. C2×Q16C2×D73semidirect
227. C4×Q8C2×D73semidirect
233. C4⋊C8C2×D73semidirect
237. #103C2×D73semidirect