Finite Group Databasebeta

← #22622150

Subgroups — #22622150

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989272C211yesmaximal, characteristic, complemented
2#17989234C211yesmaximal, characteristic
3#17988940C211yesmaximal, characteristic, complemented
4#17988931C211yesmaximal, characteristic, complemented
5#17988886C211yesmaximal, characteristic, complemented
6#17988846C211yesmaximal, characteristic, complemented
7#17988831C211yesmaximal, characteristic, complemented
8#17988808C211yesmaximal, characteristic, complemented
9#17988751C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988674C211yesmaximal, characteristic, complemented
12#17988662C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#17988586C211yesmaximal, characteristic, complemented
15#481×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×Dic292C2211yescharacteristic, complemented
19C2×#11924017C2211yescharacteristic
20C2×#11924016C2211yescharacteristic
21C2×#11924012C2211yescharacteristic, complemented
22C2×#11924011C2211yescharacteristic
23#14556586—21no—
24#14556582C2211yescharacteristic, complemented
25#14556581—21no—
26#14556578C2211yescharacteristic
27#14556574—21no—
28#14556573—21no—
29#14556571C2211yescharacteristic
30#14556571C2211yescharacteristic
31#14556570C2211yescharacteristic, complemented
32#14556562—21no—
33#14556559—21no—
34#14556556C2211yescharacteristic, complemented
35#14556553C2211yescharacteristic
36C4×C22⋊D73C2211yescharacteristic
37#14556550—21no—
38#14556549C2211yescharacteristic
39C22⋊C4×D73—21no—
40#14556524C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556514C2211yescharacteristic, complemented
44#14556514C2211yescharacteristic, complemented
45#14556514C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic, complemented
52#121×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic, complemented
54#106×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—22no—
61#11924028—41no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73D411yescharacteristic
68D4×D73—22no—
69D4×D73—41no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73C2311yescharacteristic
73Dic292—41no—
74#11924017—22no—
75#11924016—41no—
76#11924012—41no—
77#11924011—41no—
78C2×#10596831C2311yescharacteristic
79C2×#10596831C2311yescharacteristic
80C4⋊Dic73—21no—
81C4⋊Dic73—21no—
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007D411yescharacteristic
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73D411yescharacteristic
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005D411yescharacteristic
97C4×Dic73—21no—
98C4×Dic73—21no—
99C4×Dic73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C4⋊C4×C73—21no—
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73—42no—
115C22×D73—42no—
116C22×D73—81no—
117C22×D73C2×D411yescharacteristic
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—81no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—42no—
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C22⋊D73—41no—
130C22⋊D73—42no—
131C22⋊D73—42no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137C2×Dic73C2×D411yescharacteristic
138D292—21no—
139D292#4112yes—
140C4×D73—21no—
141C4×D73—21no—
142C4×D73—42no—
143C4×D73—81no—
144Dic146—21no—
145Dic146—21no—
146Dic146—21no—
147Dic146—21no—
148C8×C73—21no—
149C8×C73—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73C22×D411yescharacteristic
159C2×D73—21no—
160C2×D73—22no—
161C2×D73—21no—
162C2×D73—21no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—84no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73C2×#4111yescharacteristic
171C4×C73H(5,𝔽2)11yescharacteristic
172Dic73—21no—
173Dic73—21no—
174Dic73—21no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—41no—
179C2×C73—81no—
180C2×C73#54611yescharacteristic
181C2×C73#57511yescharacteristic
182C2×C73#57711yescharacteristic
183D73—41no—
184D73—42no—
185#3323—731nomaximal, Sylow
186C73#332311yescharacteristic, complemented, Sylow
187#552—731no—
188#546—731no—
189#488—731no—
190#485—731no—
191#481D7311yescharacteristic, complemented
192#478—731no—
193#470—731no—
194#468—731no—
195#464—731no—
196#452—731no—
197#450—731no—
198C4×SD16—731no—
199#436—731no—
200#418—731no—
201#417—731no—
202C2×#41—731no—
203C22×D4—731no—
204C2×Q16—731no—
205C2×SD16—731no—
206C2×SD16—731no—
207C2×M16—731no—
208C2×M16—731no—
209#126—1461no—
210#125—731no—
211#125—1461no—
212#124—731no—
213#123—1461no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8—731no—
218#121—1461no—
219#121C2×D7311yescharacteristic
220#120—1461no—
221C4×Q8—731no—
222C4×D4—731no—
223C4×D4—731no—
224#117—731no—
225#117—1461no—
226C2×C4⋊C4C2×D7311yescharacteristic, complemented
227C2×C22⋊C4—1461no—
228#107—731no—
229#106C2×D7311yescharacteristic, complemented
230#106C2×D7311yescharacteristic, complemented
231C4⋊C8—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102C2×D7311yescharacteristic
241#102C2×D7311yescharacteristic
242C22⋊C8—731no—
243C22⋊C8C2×D7311yescharacteristic, complemented
244C4×C8—731no—
245C24—1461no—
246#41—2921no—
247#41—1462no—
248C2×Q8—731no—
249C2×Q8—731no—
250C2×D4—21no—
251C2×D4—2921no—
252C2×D4—731no—
253C2×D4—731no—
254C2×D4—1461no—
255C2×D4—1462no—
256C2×D4—1461no—
257C2×D4C22×D7311yescharacteristic
258C22×C4—21no—
259C22×C4—731no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4C22×D7311yescharacteristic
263Q16—2921no—
264SD16—2921no—
265SD16—1462no—
266M16—2921no—
267M16—2921no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8C22×D7311yescharacteristic
271C2×C8C22×D7311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4C22×D7311yescharacteristic
282C4⋊C4C22×D7311yescharacteristic
283C4⋊C4C22×D7311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—731no—
286C22⋊C4—731no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C42—731no—
295C42—1461no—
296C42—1461no—
297C23—21no—
298C23—2922no—
299C23—2922no—
300C23—5841no—
301C23—731no—
302C23—1461no—
303C23D4×D7311yescharacteristic
304Q8—1461no—
305Q8—1461no—
306Q8—1461no—
307Q8—1461no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—2922no—
312D4—2921no—
313D4—2922no—
314D4—732no—
315D4—1461no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—2922no—
323C2×C4—5841no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—731no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4D4×D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1461no—
337C8—1461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—2921no—
345C22—2921no—
346C22—5844no—
347C22—1461no—
348C22—1461no—
349C22—1462no—
350C22—1461no—
351C22C2×D4×D7311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—1461no—
360C4—1461no—
361C4—1461no—
362C4#41×D7311yescharacteristic
363C4#1455663711yescharacteristic
364C2—41no—
365C2—81no—
366C2—2922no—
367C2—2921no—
368C2#1798922911yescharacteristic
369C2#1798938311yescharacteristic
370C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#481×C73C2
socleC22×C73C22×D4
hypercenter#481D73
hypocenterC73#3323
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #17989272C2semidirect
3. #17988940C2semidirect
4. #17988931C2semidirect
5. #17988886C2semidirect
6. #17988846C2semidirect
7. #17988831C2semidirect
8. #17988808C2semidirect
9. #17988751C2semidirect
10. #17988739C2semidirect
11. #17988674C2semidirect
12. #17988662C2semidirect
13. #17988590C2semidirect
14. #17988586C2semidirect
15. #481×C73C2semidirect
18. C2×Dic292C22semidirect
21. C2×#11924012C22semidirect
24. #14556582C22semidirect
31. #14556570C22semidirect
34. #14556556C22semidirect
40. #14556524C22semidirect
41. #14556520C22semidirect
42. #14556516C22semidirect
43. #14556514C22semidirect
44. #14556514C22semidirect
45. #14556514C22semidirect
51. C8×Dic73C22semidirect
53. C2×C4⋊C4×C73C22semidirect
54. #106×C73C22semidirect
55. #106×C73C22semidirect
58. C22⋊C8×C73C22semidirect
186. C73#3323semidirect
191. #481D73semidirect
226. C2×C4⋊C4C2×D73semidirect
229. #106C2×D73semidirect
230. #106C2×D73semidirect
243. C22⋊C8C2×D73semidirect