Finite Group Databasebeta

← #22622141

Subgroups — #22622141

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#17989233C211yesmaximal, characteristic
2#17988944C211yesmaximal, characteristic, complemented
3#17988928C211yesmaximal, characteristic, complemented
4#17988905C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988843C211yesmaximal, characteristic, complemented
7#17988835C211yesmaximal, characteristic, complemented
8#17988809C211yesmaximal, characteristic, complemented
9#17988747C211yesmaximal, characteristic, complemented
10#17988737C211yesmaximal, characteristic, complemented
11C4×#11924015C211yesmaximal, characteristic, complemented
12#17988665C211yesmaximal, characteristic, complemented
13#17988591C211yesmaximal, characteristic, complemented
14#17988586C211yesmaximal, characteristic, complemented
15#552×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×#11924018C2211yescharacteristic, complemented
19C2×#11924015C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21C2×#11924012C2211yescharacteristic
22C2×#11924012C2211yescharacteristic, complemented
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#14556522C2211yescharacteristic, complemented
33#14556522C2211yescharacteristic, 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
47C4×#10596831C2211yescharacteristic, complemented
48#126×C73—21no—
49#125×C73—21no—
50#125×C73C2211yescharacteristic, complemented
51#123×C73—21no—
52C22⋊Q8×C73C2211yescharacteristic
53C22⋊Q8×C73C2211yescharacteristic, complemented
54C4×Q8×C73C2211yescharacteristic, complemented
55C4×D4×C73C2211yescharacteristic
56#117×C73—21no—
57#117×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—
76#11924012—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×C73C2311yescharacteristic
89C2×D4×C73D411yescharacteristic
90C22×C4×C73—21no—
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C4⋊C4×C73—21no—
94C4⋊C4×C73—21no—
95C4⋊C4×C73—21no—
96C4⋊C4×C73—21no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73—21no—
99C4⋊C4×C73D411yescharacteristic
100C4⋊C4×C73C2311yescharacteristic
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C22⋊C4×C73D411yescharacteristic
107C22⋊C4×C73D411yescharacteristic
108C42×C73—21no—
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—
120D4×C73—41no—
121C2×C4×C73—21no—
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—42no—
130C2×C4×C73C2×D411yescharacteristic
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2411yescharacteristic
135C22⋊D73—42no—
136C22⋊D73—81no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139D292—21no—
140D292—21no—
141D292—21no—
142D292—42no—
143D292#4112yes—
144C4×D73—42no—
145C4×D73—81no—
146Dic146—21no—
147Dic146—21no—
148#10596831—21no—
149#10596831—21no—
150#10596831—21no—
151#10596831—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×C73—41no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73—41no—
174C4×C73C2×#4111yescharacteristic
175C4×C73H(5,𝔽2)11yescharacteristic
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#552D7311yescharacteristic, complemented
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#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—21no—
210#125—21no—
211#125C2×D7311yescharacteristic, complemented
212#124—731no—
213#123—21no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8C2×D7311yescharacteristic
217C22⋊Q8C2×D7311yescharacteristic, complemented
218#121—731no—
219#121—1461no—
220#120—1461no—
221C4×Q8C2×D7311yescharacteristic, complemented
222C4×D4—731no—
223C4×D4C2×D7311yescharacteristic
224#117—21no—
225#117C2×D7311yescharacteristic
226C2×C4⋊C4C2×D7311yescharacteristic, complemented
227C2×C22⋊C4—1461no—
228#107—731no—
229#106—731no—
230#106—731no—
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#102—731no—
241#102—731no—
242C22⋊C8—731no—
243C22⋊C8—731no—
244C4×C8—731no—
245C24—1461no—
246#41—2921no—
247#41—1462no—
248C2×Q8—731no—
249C2×Q8C22×D7311yescharacteristic
250C2×D4—2921no—
251C2×D4—731no—
252C2×D4—731no—
253C2×D4—1462no—
254C2×D4—1461no—
255C2×D4—1461no—
256C2×D4—1461no—
257C2×D4C22⋊D7311yescharacteristic
258C22×C4—21no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4C22×D7311yescharacteristic
262C22×C4C22×D7311yescharacteristic
263Q16—2921no—
264SD16—2921no—
265SD16—1462no—
266M16—2921no—
267M16—2921no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8—731no—
271C2×C8—731no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—731no—
279C4⋊C4—1461no—
280C4⋊C4C22⋊D7311yescharacteristic
281C4⋊C4C22×D7311yescharacteristic
282C4⋊C4C22×D7311yescharacteristic
283C4⋊C4C22×D7311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4C22⋊D7311yescharacteristic
293C22⋊C4C22⋊D7311yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D7311yescharacteristic
297C23—2922no—
298C23—2922no—
299C23—5841no—
300C23—1461no—
301C23—1461no—
302C23C2×C22⋊D7311yescharacteristic
303C23C2×C22⋊D7311yescharacteristic
304Q8—21no—
305Q8—21no—
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—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—2922no—
326C2×C4—5841no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4C2×C22⋊D7311yescharacteristic
330C2×C4C2×C22⋊D7311yescharacteristic
331C2×C4C2×C22⋊D7311yescharacteristic
332C2×C4C2×C22⋊D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—1461no—
335C8—1461no—
336C8—1461no—
337C8—1461no—
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×C22⋊D7311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—2921no—
361C4—2921no—
362C4#41×D7311yescharacteristic
363C4#1455663711yescharacteristic
364C2—41no—
365C2—41no—
366C2—2922no—
367C2—5841no—
368C2#1798922511yescharacteristic
369C2#1798938511yescharacteristic
370C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#552×C73C2
socleC22×C73C22×D4
hypercenter#552D73
hypocenterC73#3323
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #17988944C2semidirect
3. #17988928C2semidirect
4. #17988905C2semidirect
5. #17988884C2semidirect
6. #17988843C2semidirect
7. #17988835C2semidirect
8. #17988809C2semidirect
9. #17988747C2semidirect
10. #17988737C2semidirect
11. C4×#11924015C2semidirect
12. #17988665C2semidirect
13. #17988591C2semidirect
14. #17988586C2semidirect
15. #552×C73C2semidirect
18. C2×#11924018C22semidirect
22. C2×#11924012C22semidirect
31. #14556524C22semidirect
32. #14556522C22semidirect
33. #14556522C22semidirect
34. C4⋊#10596831C22semidirect
35. #14556515C22semidirect
36. #14556514C22semidirect
37. #14556514C22semidirect
38. #14556514C22semidirect
46. C22⋊#10596831C22semidirect
47. C4×#10596831C22semidirect
50. #125×C73C22semidirect
53. C22⋊Q8×C73C22semidirect
54. C4×Q8×C73C22semidirect
58. C2×C4⋊C4×C73C22semidirect
186. C73#3323semidirect
187. #552D73semidirect
211. #125C2×D73semidirect
217. C22⋊Q8C2×D73semidirect
221. C4×Q8C2×D73semidirect
226. C2×C4⋊C4C2×D73semidirect