Finite Group Databasebeta

← #22622014

Subgroups — #22622014

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#17989294C211yesmaximal, characteristic, complemented
2#17989233C211yesmaximal, characteristic
3#17988947C211yesmaximal, characteristic, complemented
4#17988923C211yesmaximal, characteristic, complemented
5#17988901C211yesmaximal, characteristic, complemented
6#17988868C211yesmaximal, characteristic, complemented
7#17988833C211yesmaximal, characteristic, complemented
8#17988828C211yesmaximal, characteristic, complemented
9#17988810C211yesmaximal, characteristic, complemented
10#17988751C211yesmaximal, characteristic, complemented
11#17988740C211yesmaximal, characteristic, complemented
12#17988689C211yesmaximal, characteristic, complemented
13#17988589C211yesmaximal, characteristic, complemented
14C2×#14556513C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×Dic292C2211yescharacteristic, complemented
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21#14556591C2211yescharacteristic, complemented
22#14556582—21no—
23#14556579C2211yescharacteristic
24#14556576—21no—
25#14556570C2211yescharacteristic
26#14556570C2211yescharacteristic
27#14556570C2211yescharacteristic, complemented
28#14556568—21no—
29#14556568—21no—
30#14556565C2211yescharacteristic
31#14556564—21no—
32#14556559—21no—
33C4×Dic146C2211yescharacteristic, complemented
34C4×D292C2211yescharacteristic
35D4×Dic73—21no—
36C2×C4⋊Dic73C2211yescharacteristic
37C2×C4⋊Dic73C2211yescharacteristic, complemented
38C22⋊C4×D73—21no—
39#14556525C2211yescharacteristic, complemented
40#14556525C2211yescharacteristic, complemented
41#14556525C2211yescharacteristic, 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, complemented
53C22×C8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic, complemented
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic, complemented
58#97×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—22no—
61#11924028—41no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64C2×Dic146C2311yescharacteristic
65C2×D292—22no—
66C2×D292—21no—
67C2×D292—41no—
68C2×D292C2311yescharacteristic
69C2×D292C2311yescharacteristic
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C22×Dic73—21no—
73C22×Dic73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76Dic292—41no—
77#11924017—22no—
78#11924017—41no—
79C4⋊Dic73—21no—
80C4⋊Dic73—21no—
81C4⋊Dic73—21no—
82C4⋊Dic73C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97C4×Dic73—21no—
98C2×D4×C73D411yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101M16×C73—41no—
102C2×C8×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—22no—
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—81no—
137C2×Dic73—81no—
138D292—21no—
139D292—21no—
140D292—21no—
141D292—42no—
142D292#4112yes—
143C4×D73—42no—
144C4×D73—81no—
145Dic146—21no—
146Dic146—21no—
147Dic146—21no—
148Dic146—21no—
149Dic146—81no—
150C8×C73—21no—
151C8×C73—21no—
152C8×C73—21no—
153C8×C73—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×C73C2×#4111yescharacteristic
173C4×C73H(5,𝔽2)11yescharacteristic
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
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#554—731no—
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#435D7311yescharacteristic, complemented
202#417—731no—
203C2×#102—731no—
204C2×#41—731no—
205C22×D4—731no—
206C2×Q16—731no—
207C2×SD16—731no—
208C2×SD16—731no—
209C2×M16C2×D7311yescharacteristic, complemented
210C22×C8C2×D7311yescharacteristic
211C4⋊Q8—731no—
212#125—1461no—
213#124—731no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8—731no—
218C22⋊Q8—1461no—
219C22⋊Q8—1461no—
220#121—731no—
221#121—1461no—
222#120—1461no—
223C4×Q8—731no—
224C4×D4—731no—
225C4×D4—1461no—
226C4×D4C2×D7311yescharacteristic
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229C2×C22⋊C4—1461no—
230#107—731no—
231#107—731no—
232#107—731no—
233C4⋊C8C2×D7311yescharacteristic, complemented
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⋊C8C2×D7311yescharacteristic
245C22⋊C8C2×D7311yescharacteristic, complemented
246#97C2×D7311yescharacteristic, complemented
247C24—1461no—
248#41—2921no—
249#41—1462no—
250C2×Q8—731no—
251C2×Q8—731no—
252C2×Q8—1461no—
253C2×D4—2921no—
254C2×D4—731no—
255C2×D4—731no—
256C2×D4—1462no—
257C2×D4—1461no—
258C2×D4—1461no—
259C2×D4—1461no—
260C2×D4D29211yescharacteristic
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4C22×D7311yescharacteristic
266C22×C4C22×D7311yescharacteristic
267Q16—2921no—
268SD16—2921no—
269SD16—1462no—
270M16—41no—
271C2×C8—41no—
272C2×C8C22×D7311yescharacteristic
273C2×C8C22×D7311yescharacteristic
274C2×C8C22×D7311yescharacteristic
275C2×C8C22×D7311yescharacteristic
276C4⋊C4—731no—
277C4⋊C4—731no—
278C4⋊C4—731no—
279C4⋊C4—731no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4D29211yescharacteristic
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4D29211yescharacteristic
296C22⋊C4D29211yescharacteristic
297C42—1461no—
298C42C22×D7311yescharacteristic
299C23—2922no—
300C23—2922no—
301C23—5841no—
302C23—1461no—
303C23—1461no—
304C23C2×D29211yescharacteristic
305C23C2×D29211yescharacteristic
306Q8—5841no—
307Q8—1461no—
308Q8—1461no—
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—2922no—
324C2×C4—5841no—
325C2×C4—5841no—
326C2×C4—5841no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4C2×D29211yescharacteristic
334C2×C4C2×D29211yescharacteristic
335C2×C4C2×D29211yescharacteristic
336C2×C4C2×D29211yescharacteristic
337C2×C4C23×D7311yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
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#1455662412yes—
355C22C22×D29211yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—2921no—
361C4—2921no—
362C4—2921no—
363C4—2921no—
364C4—2921no—
365C4—2921no—
366C4#41×D7311yescharacteristic
367C4#1455663611yescharacteristic
368C2—22no—
369C2—41no—
370C2—2922no—
371C2—5841no—
372C2#1798923211yescharacteristic
373C2C2×#1455662411yescharacteristic
374C2#1798939211yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#435×C73C2
socleC22×C73C22×D4
hypercenter#435D73
hypocenterC73#3314
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #17989294C2semidirect
3. #17988947C2semidirect
4. #17988923C2semidirect
5. #17988901C2semidirect
6. #17988868C2semidirect
7. #17988833C2semidirect
8. #17988828C2semidirect
9. #17988810C2semidirect
10. #17988751C2semidirect
11. #17988740C2semidirect
12. #17988689C2semidirect
13. #17988589C2semidirect
14. C2×#14556513C2semidirect
15. #435×C73C2semidirect
18. C2×Dic292C22semidirect
21. #14556591C22semidirect
27. #14556570C22semidirect
33. C4×Dic146C22semidirect
37. C2×C4⋊Dic73C22semidirect
39. #14556525C22semidirect
40. #14556525C22semidirect
41. #14556525C22semidirect
42. #14556516C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
45. #14556516C22semidirect
52. C2×M16×C73C22semidirect
55. C4⋊C8×C73C22semidirect
57. C22⋊C8×C73C22semidirect
58. #97×C73C22semidirect
188. C73#3314semidirect
201. #435D73semidirect
209. C2×M16C2×D73semidirect
233. C4⋊C8C2×D73semidirect
245. C22⋊C8C2×D73semidirect
246. #97C2×D73semidirect