Finite Group Databasebeta

← #22622149

Subgroups — #22622149

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#17989277C211yesmaximal, characteristic, complemented
2#17989233C211yesmaximal, characteristic
3#17988942C211yesmaximal, characteristic, complemented
4#17988929C211yesmaximal, characteristic, complemented
5#17988906C211yesmaximal, characteristic, complemented
6#17988888C211yesmaximal, characteristic, complemented
7#17988845C211yesmaximal, characteristic, complemented
8#17988833C211yesmaximal, characteristic, complemented
9#17988810C211yesmaximal, characteristic, complemented
10#17988751C211yesmaximal, characteristic, complemented
11#17988740C211yesmaximal, characteristic, complemented
12C4×#11924017C211yesmaximal, characteristic, complemented
13#17988593C211yesmaximal, characteristic, complemented
14#17988589C211yesmaximal, characteristic, complemented
15#436×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×Dic292C2211yescharacteristic, complemented
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21#14556584—21no—
22#14556583C2211yescharacteristic, complemented
23#14556581—21no—
24#14556579C2211yescharacteristic
25#14556576—21no—
26#14556572—21no—
27#14556570C2211yescharacteristic
28#14556570C2211yescharacteristic
29#14556570C2211yescharacteristic, complemented
30#14556565C2211yescharacteristic
31#14556564—21no—
32#14556559—21no—
33C4×Dic146C2211yescharacteristic, complemented
34C4×D292C2211yescharacteristic
35#14556550C2211yescharacteristic
36#14556547—21no—
37C2×C4⋊Dic73C2211yescharacteristic, complemented
38C22⋊C4×D73—21no—
39#14556525C2211yescharacteristic, complemented
40#14556523C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556516C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic, complemented
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic, complemented
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic, complemented
58C4×C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—22no—
61#11924028—41no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C2×D292—22no—
65C2×D292—21no—
66C2×D292—41no—
67C2×D292C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C22×Dic73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74Dic292—41no—
75#11924017—22no—
76#11924017—41no—
77C4⋊Dic73—21no—
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C2×D4×C73D411yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101M16×C73—41no—
102M16×C73—41no—
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73D411yescharacteristic
108C22⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C42×C73C2311yescharacteristic
111C23×C73C2×D411yescharacteristic
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73—42no—
116C22×D73—42no—
117C22×D73—81no—
118D4×C73—41no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2411yescharacteristic
128C22⋊D73—42no—
129C22⋊D73—81no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—42no—
137D292—21no—
138D292—21no—
139D292—21no—
140D292—42no—
141D292#4112yes—
142C4×D73—42no—
143C4×D73—81no—
144Dic146—21no—
145Dic146—21no—
146Dic146—21no—
147Dic146—21no—
148C8×C73—21no—
149C8×C73—21no—
150C8×C73—21no—
151C8×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73C22×D411yescharacteristic
159C2×D73—22no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—84no—
166C4×C73—21no—
167C4×C73—21no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73C2×#4111yescharacteristic
171C4×C73H(5,𝔽2)11yescharacteristic
172Dic73—41no—
173Dic73—41no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—41no—
179C2×C73—41no—
180C2×C73#54611yescharacteristic
181C2×C73#57511yescharacteristic
182C2×C73#57711yescharacteristic
183D73—42no—
184D73—81no—
185#3323—731nomaximal, Sylow
186C73#332311yescharacteristic, complemented, Sylow
187#552—731no—
188#546—731no—
189#488—731no—
190#485—731no—
191#481—731no—
192#478—731no—
193#470—731no—
194#468—731no—
195#464—731no—
196#452—731no—
197#450—731no—
198C4×SD16—731no—
199#436D7311yescharacteristic, complemented
200#418—731no—
201#417—731no—
202C2×#41—731no—
203C22×D4—731no—
204C2×Q16—731no—
205C2×SD16—731no—
206C2×SD16—731no—
207C2×M16C2×D7311yescharacteristic
208C2×M16C2×D7311yescharacteristic, complemented
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—731no—
219#121—1461no—
220#120—1461no—
221C4×Q8—731no—
222C4×D4—731no—
223C4×D4C2×D7311yescharacteristic
224#117—731no—
225#117—1461no—
226C2×C4⋊C4—731no—
227C2×C22⋊C4—1461no—
228#107—731no—
229#106—731no—
230#106—731no—
231C4⋊C8C2×D7311yescharacteristic, complemented
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#102—731no—
241#102—731no—
242C22⋊C8C2×D7311yescharacteristic
243C22⋊C8C2×D7311yescharacteristic, complemented
244C4×C8C2×D7311yescharacteristic, complemented
245C24—1461no—
246#41—2921no—
247#41—1462no—
248C2×Q8—731no—
249C2×Q8—731no—
250C2×D4—2921no—
251C2×D4—731no—
252C2×D4—731no—
253C2×D4—1462no—
254C2×D4—1461no—
255C2×D4—1461no—
256C2×D4—1461no—
257C2×D4D29211yescharacteristic
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4C22×D7311yescharacteristic
262C22×C4C22×D7311yescharacteristic
263Q16—2921no—
264SD16—2921no—
265SD16—1462no—
266M16—41no—
267M16—41no—
268C2×C8C22×D7311yescharacteristic
269C2×C8C22×D7311yescharacteristic
270C2×C8C22×D7311yescharacteristic
271C2×C8C22×D7311yescharacteristic
272C4⋊C4—731no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4D29211yescharacteristic
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4D29211yescharacteristic
293C22⋊C4D29211yescharacteristic
294C42—1461no—
295C42—1461no—
296C42C22×D7311yescharacteristic
297C23—2922no—
298C23—2922no—
299C23—5841no—
300C23—1461no—
301C23—1461no—
302C23C2×D29211yescharacteristic
303C23C2×D29211yescharacteristic
304Q8—1461no—
305Q8—1461no—
306Q8—1461no—
307Q8—1461no—
308D4—41no—
309D4—2922no—
310D4—2922no—
311D4—5841no—
312D4—732no—
313D4—1461no—
314D4—1461no—
315D4—1461no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2922no—
321C2×C4—2922no—
322C2×C4—5841no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4C2×D29211yescharacteristic
330C2×C4C2×D29211yescharacteristic
331C2×C4C2×D29211yescharacteristic
332C2×C4C2×D29211yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—2921no—
345C22—2921no—
346C22—2921no—
347C22—2921no—
348C22—2921no—
349C22—5844no—
350C22—1462no—
351C22C22×D29211yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—2921no—
360C4—2921no—
361C4—2921no—
362C4#41×D7311yescharacteristic
363C4#1455663611yescharacteristic
364C2—41no—
365C2—41no—
366C2—2922no—
367C2—5841no—
368C2#1798923211yescharacteristic
369C2#1798938711yescharacteristic
370C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#436×C73C2
socleC22×C73C22×D4
hypercenter#436D73
hypocenterC73#3323
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #17989277C2semidirect
3. #17988942C2semidirect
4. #17988929C2semidirect
5. #17988906C2semidirect
6. #17988888C2semidirect
7. #17988845C2semidirect
8. #17988833C2semidirect
9. #17988810C2semidirect
10. #17988751C2semidirect
11. #17988740C2semidirect
12. C4×#11924017C2semidirect
13. #17988593C2semidirect
14. #17988589C2semidirect
15. #436×C73C2semidirect
18. C2×Dic292C22semidirect
22. #14556583C22semidirect
29. #14556570C22semidirect
33. C4×Dic146C22semidirect
37. C2×C4⋊Dic73C22semidirect
39. #14556525C22semidirect
40. #14556523C22semidirect
41. #14556523C22semidirect
42. #14556516C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
45. #14556516C22semidirect
53. C2×M16×C73C22semidirect
55. C4⋊C8×C73C22semidirect
57. C22⋊C8×C73C22semidirect
58. C4×C8×C73C22semidirect
186. C73#3323semidirect
199. #436D73semidirect
208. C2×M16C2×D73semidirect
231. C4⋊C8C2×D73semidirect
243. C22⋊C8C2×D73semidirect
244. C4×C8C2×D73semidirect