Finite Group Databasebeta

← #22622400

Subgroups — #22622400

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989290C211yesmaximal, characteristic, complemented
2#17989240C211yesmaximal, characteristic, complemented
3#17988914C211yesmaximal, characteristic, complemented
4#17988907C211yesmaximal, characteristic, complemented
5#17988907C211yesmaximal, characteristic, complemented
6#17988902C211yesmaximal, characteristic, complemented
7#17988884C211yesmaximal, characteristic, complemented
8#17988874C211yesmaximal, characteristic, complemented
9#17988841C211yesmaximal, characteristic, complemented
10#17988824C211yesmaximal, characteristic, complemented
11#17988700C211yesmaximal, characteristic, complemented
12#17988660C211yesmaximal, characteristic, complemented
13#17988628C211yesmaximal, characteristic, complemented
14#106×D73C211yesmaximal, characteristic, complemented
15#501×C73C211yesmaximal, characteristic, complemented
16C2×#11924029—21no—
17C2×D584C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556586—21no—
21#14556576—21no—
22#14556576—21no—
23#14556576—21no—
24#14556567—21no—
25#14556566—21no—
26#14556566C2211yescharacteristic
27#14556566C2211yescharacteristic
28#14556566C2211yescharacteristic
29#14556566C2211yescharacteristic
30C4×D292C2211yescharacteristic
31C4×D292C2211yescharacteristic
32C4×D292C2211yescharacteristic
33#14556553—21no—
34#14556549C2211yescharacteristic
35C4⋊C4×D73C2211yescharacteristic
36C4⋊C4×D73C2211yescharacteristic
37C4⋊C4×D73C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556523C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556522C2211yescharacteristic
43C4⋊#10596831C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C4⋊Q8×C73C2211yescharacteristic
53#125×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#107×C73C2211yescharacteristic
56#106×C73C2211yescharacteristic
57#106×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924029—44no—
60C2×D292—21no—
61C2×D292—21no—
62C2×D292—21no—
63C2×D292—21no—
64C2×D292D411yescharacteristic
65C2×D292C2311yescharacteristic
66C2×D292C2311yescharacteristic
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73C2311yescharacteristic
73C2×C4×D73C2311yescharacteristic
74D584—22no—
75#11924011—22no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C8×D73—22no—
79C4⋊Dic73D411yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005D411yescharacteristic
93#11924005D411yescharacteristic
94C4×Dic73—21no—
95C2×Q8×C73—21no—
96C2×C8×C73C2311yescharacteristic
97C2×C8×C73C2311yescharacteristic
98C4⋊C4×C73—21no—
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C42×C73C2311yescharacteristic
106C22×D73—21no—
107C22×D73—21no—
108C22×D73C2×D411yescharacteristic
109C22×D73C2×D411yescharacteristic
110Q8×C73—42no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2411yescharacteristic
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73C2×D411yescharacteristic
121C2×Dic73C2×D411yescharacteristic
122D292—22no—
123D292—21no—
124D292—21no—
125D292—21no—
126D292—21no—
127D292—42no—
128D292—42no—
129D292—42no—
130D292—81no—
131C4×D73—21no—
132C4×D73—21no—
133C4×D73—21no—
134C4×D73—21no—
135C4×D73—42no—
136C4×D73—42no—
137C4×D73—42no—
138C4×D73—81no—
139C4×D73—81no—
140C8×C73—21no—
141C8×C73#4112yescomplemented
142#10596831—21no—
143#10596831—21no—
144C22×C73C22×D411yescharacteristic
145C2×D73—21no—
146C2×D73—21no—
147C2×D73—21no—
148C2×D73—21no—
149C2×D73—21no—
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C2×D73—41no—
156C2×D73AGL(1,ℤ/8)12yes—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C732−1+411yescharacteristic
165Dic73—21no—
166Dic73—21no—
167Dic73—41no—
168Dic73—41no—
169C2×C73#54711yescharacteristic
170C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C73#57711yescharacteristic
172D73—22no—
173D73—41no—
174D73—81no—
175D73—81no—
176#3345—731nomaximal, Sylow
177C73#334511yescharacteristic, complemented, Sylow
178#553—731no—
179#547—731no—
180#501D7311yescharacteristic, complemented
181#482—731no—
182#481—731no—
183#481—731no—
184#480—731no—
185#478—731no—
186#476—731no—
187#469—731no—
188#466—731no—
189#442—731no—
190#435—731no—
191#428—731no—
192C2×#106—731no—
193C2×#41—1461no—
194C2×D8—731no—
195C2×M16—731no—
196C22×C8—731no—
197C4⋊Q8C2×D7311yescharacteristic
198#126—1461no—
199#125C2×D7311yescharacteristic
200#123—1461no—
201#123—1461no—
202#123—1461no—
203C22⋊Q8—1461no—
204#121—731no—
205#121—731no—
206#121—731no—
207#121—731no—
208#121—1461no—
209C4×D4—731no—
210C4×D4—731no—
211C4×D4—731no—
212C4×D4—1461no—
213#117—731no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217#107—731no—
218#107C2×D7311yescharacteristic
219#107C2×D7311yescharacteristic
220#106—731no—
221#106—731no—
222#106—731no—
223#106—731no—
224#106C2×D7311yescharacteristic
225#106C2×D7311yescharacteristic
226C4⋊C8—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233C22⋊C8—731no—
234C22⋊C8—731no—
235#97C2×D7311yescharacteristic
236#41—2924no—
237C2×Q8—21no—
238C2×D4—731no—
239C2×D4—731no—
240C2×D4—731no—
241C2×D4—1461no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4—1461no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—1461no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4—1461no—
252D8—1462no—
253M16—1462no—
254C2×C8—731no—
255C2×C8—731no—
256C2×C8—1462no—
257C2×C8C22×D7311yescharacteristic
258C2×C8C22×D7311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4C22×D7311yescharacteristic
269C4⋊C4C22×D7311yescharacteristic
270C4⋊C4C22×D7311yescharacteristic
271C4⋊C4C22×D7311yescharacteristic
272C22⋊C4—731no—
273C22⋊C4—731no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C42—1461no—
282C42C22×D7311yescharacteristic
283C23—731no—
284C23—731no—
285C23—1461no—
286C23—1461no—
287Q8—42no—
288D4—2922no—
289D4—2922no—
290D4—2922no—
291D4—5841no—
292D4—1462no—
293D4—1461no—
294D4—1461no—
295D4—1461no—
296D4—1461no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2922no—
302C2×C4—2922no—
303C2×C4—2922no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—731no—
307C2×C4—731no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4D4×D7311yescharacteristic
315C2×C4D4×D7311yescharacteristic
316C2×C4C23×D7311yescharacteristic
317C8—21no—
318C8—1461no—
319C8—1461no—
320C8#1192402912yescomplemented
321C22—2921no—
322C22—2921no—
323C22—2921no—
324C22—2921no—
325C22—2921no—
326C22—2921no—
327C22—732no—
328C22—1461no—
329C22—1461no—
330C22—1461no—
331C22—1461no—
332C22—1461no—
333C22C2×D4×D7311yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2921no—
341C4—2921no—
342C4—1461no—
343C4—1461no—
344C4C2×#1192402911yescharacteristic
345C4#1455663911yescharacteristic
346C2—2921no—
347C2—5841no—
348C2—5841no—
349C2—1462no—
350C2#1798924011yescharacteristic
351C2AGL(1,ℤ/8)×D7311yescharacteristic
352C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#501×C73C2
socleC22×C73C22×D4
hypercenter#501D73
hypocenterC73#3345
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #17989290C2semidirect
2. #17989240C2semidirect
3. #17988914C2semidirect
4. #17988907C2semidirect
5. #17988907C2semidirect
6. #17988902C2semidirect
7. #17988884C2semidirect
8. #17988874C2semidirect
9. #17988841C2semidirect
10. #17988824C2semidirect
11. #17988700C2semidirect
12. #17988660C2semidirect
13. #17988628C2semidirect
14. #106×D73C2semidirect
15. #501×C73C2semidirect
141. C8×C73#41semidirect
177. C73#3345semidirect
180. #501D73semidirect
320. C8#11924029semidirect