Finite Group Databasebeta

← #22619759

Subgroups — #22619759

Order 9344.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989217C211yesmaximal, characteristic, complemented
2#17989059C211yesmaximal, characteristic
3#17988890C211yesmaximal, characteristic, complemented
4#17988885C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988877C211yesmaximal, characteristic, complemented
7#17988876C211yesmaximal, characteristic, complemented
8#17988868C211yesmaximal, characteristic, complemented
9#17988865C211yesmaximal, characteristic, complemented
10#17988626C211yesmaximal, characteristic, complemented
11#17988624C211yesmaximal, characteristic, complemented
12#17988612C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic
14#102×D73C211yesmaximal, characteristic
15#478×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C2×#11924011C2211yescharacteristic
18C2×C8×D73C2211yescharacteristic
19#14556591C2211yescharacteristic, complemented
20#14556590—21no—
21#14556590C2211yescharacteristic, complemented
22#14556582C2211yescharacteristic, complemented
23#14556581—21no—
24#14556571—21no—
25#14556569—21no—
26C4×D292C2211yescharacteristic
27D4×Dic73C2211yescharacteristic
28#14556553C2211yescharacteristic
29C4×C22⋊D73—21no—
30#14556551—21no—
31#14556549C2211yescharacteristic
32#14556549C2211yescharacteristic
33#14556548C2211yescharacteristic
34C4⋊C4×D73C2211yescharacteristic
35C2×#11924005—21no—
36C22⋊C4×D73—21no—
37#14556525C2211yescharacteristic, complemented
38#14556525C2211yescharacteristic, complemented
39#14556524C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41#14556522C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43C4⋊#10596831C2211yescharacteristic, complemented
44#14556520C2211yescharacteristic, complemented
45#14556520C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556512C2211yescharacteristic
50#14556511C2211yescharacteristic
51#14556511C2211yescharacteristic
52#125×C73C2211yescharacteristic, complemented
53C4×D4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56C4⋊C8×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C23×D73—21no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64D4×D73—22no—
65D4×D73Q814yescomplemented
66C22×Dic73—21no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73C2311yescharacteristic
71#11924011—22no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C8×D73—22no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84#11924007D411yescharacteristic
85C22⋊Dic73—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005D411yescharacteristic
91#11924005D411yescharacteristic
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73C2311yescharacteristic
95C2×D4×C73C2311yescharacteristic
96C22×C4×C73—21no—
97C2×C8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C22⋊C4×C73—21no—
105C42×C73C2311yescharacteristic
106C23×C73—21no—
107C22×D73—21no—
108C22×D73—24no—
109C22×D73—81no—
110C22×D73—81no—
111C22×D73C2×D411yescharacteristic
112D4×C73—21no—
113D4×C73C2×Q812yes—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—81no—
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C22⋊D73—24no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—81no—
126C2×Dic73C2×D411yescharacteristic
127C2×Dic73C2×D411yescharacteristic
128C2×Dic73C2×D411yescharacteristic
129D292—21no—
130D292C2×Q812yes—
131C4×D73—81no—
132C4×D73—81no—
133C4×D73—81no—
134C4×D73C2×Q812yes—
135C4×D73#4112yes—
136Dic146—81no—
137Dic146—81no—
138C8×C73—21no—
139C8×C73—21no—
140#10596831—21no—
141#10596831—21no—
142C22×C73—22no—
143C22×C73—41no—
144C22×C73—41no—
145C22×C73C22×D411yescharacteristic
146C2×D73—21no—
147C2×D73—21no—
148C2×D73—22no—
149C2×D73—41no—
150C2×D73—41no—
151C2×D73—84no—
152C2×D73C22⋊Q812yes—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—41no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73C22×Q811yescharacteristic
159C4×C73C2×#4111yescharacteristic
160Dic73—21no—
161Dic73—21no—
162Dic73—41no—
163Dic73—41no—
164Dic73—41no—
165Dic73C22⋊Q812yes—
166C2×C73—42no—
167C2×C73C2×C22⋊Q811yescharacteristic
168C2×C73#57611yescharacteristic
169C2×C73#57711yescharacteristic
170D73—22no—
171D73—42no—
172#3081—731nomaximal, Sylow
173C73#308111yescharacteristic, complemented, Sylow
174#544—731no—
175#518—731no—
176#478—731no—
177#478—731no—
178#478—731no—
179#478D7311yescharacteristic, complemented
180#476—731no—
181#476—731no—
182#474—731no—
183#474—731no—
184#428—731no—
185#427—731no—
186#424—731no—
187#418—731no—
188C2×#102—731no—
189C22×D4—731no—
190C2×M16—731no—
191C22×C8—731no—
192C4⋊Q8—731no—
193C4⋊Q8—731no—
194C4⋊Q8—1461no—
195#125—731no—
196#125—1461no—
197#125C2×D7311yescharacteristic, complemented
198C22⋊Q8—1461no—
199C22⋊Q8—1461no—
200C4×D4—731no—
201C4×D4—731no—
202C4×D4—731no—
203C4×D4—1461no—
204C4×D4—1461no—
205C4×D4C2×D7311yescharacteristic
206#117—731no—
207#117—731no—
208#117—731no—
209C2×C4⋊C4—731no—
210C2×C22⋊C4—1461no—
211C2×C22⋊C4—1461no—
212#107—731no—
213#107—731no—
214#107—731no—
215#107C2×D7311yescharacteristic, complemented
216#106—731no—
217#106—731no—
218#106—731no—
219#106C2×D7311yescharacteristic, complemented
220C4⋊C8—731no—
221C4⋊C8—731no—
222C4⋊C8—731no—
223C4⋊C8C2×D7311yescharacteristic, complemented
224#102—731no—
225#102—731no—
226#102—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230#102C2×D7311yescharacteristic
231#102C2×D7311yescharacteristic
232C24—1461no—
233C2×Q8—1461no—
234C2×Q8—1461no—
235C2×D4—734no—
236C2×D4—731no—
237C2×D4—1462no—
238C2×D4—1461no—
239C2×D4C22×D7311yescharacteristic
240C22×C4—21no—
241C22×C4—731no—
242C22×C4—1461no—
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4—1461no—
246M16—1462no—
247C2×C8—731no—
248C2×C8—731no—
249C2×C8—1462no—
250C2×C8C22×D7311yescharacteristic
251C2×C8C22×D7311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—731no—
255C4⋊C4—731no—
256C4⋊C4—731no—
257C4⋊C4—731no—
258C4⋊C4—731no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4C22×D7311yescharacteristic
265C4⋊C4C22×D7311yescharacteristic
266C4⋊C4C22×D7311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—731no—
269C22⋊C4—731no—
270C22⋊C4—1461no—
271C22⋊C4—1461no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C42—731no—
276C42—1461no—
277C42—1461no—
278C42C22×D7311yescharacteristic
279C23—21no—
280C23—5841no—
281C23—5841no—
282C23—731no—
283C23—1464no—
284C23—1461no—
285Q8—5841no—
286Q8—5841no—
287D4—21no—
288D4—732no—
289D4—1464no—
290D4—1461no—
291D4Q8×D7312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—5841no—
297C2×C4—5841no—
298C2×C4—5841no—
299C2×C4—5841no—
300C2×C4—731no—
301C2×C4—732no—
302C2×C4—732no—
303C2×C4—731no—
304C2×C4—731no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4D4×D7311yescharacteristic
309C2×C4D4×D7311yescharacteristic
310C2×C4C23×D7311yescharacteristic
311C8—21no—
312C8—21no—
313C8—1461no—
314C8—1461no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—2921no—
319C22—2921no—
320C22—5844no—
321C22—732no—
322C22—1462no—
323C22—1461no—
324C22—1461no—
325C22C2×D4×D7311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2921no—
332C4—2921no—
333C4—2921no—
334C4—732no—
335C4—1461no—
336C4—1461no—
337C4C2×Q8×D7311yescharacteristic
338C4#41×D7311yescharacteristic
339C2—42no—
340C2—2922no—
341C2—1462no—
342C2C22⋊Q8×D7311yescharacteristic
343C2#1798938911yescharacteristic
344C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#478×C73C2
socleC22×C73C22×D4
hypercenter#478D73
hypocenterC73#3081
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #17989217C2semidirect
3. #17988890C2semidirect
4. #17988885C2semidirect
5. #17988884C2semidirect
6. #17988877C2semidirect
7. #17988876C2semidirect
8. #17988868C2semidirect
9. #17988865C2semidirect
10. #17988626C2semidirect
11. #17988624C2semidirect
12. #17988612C2semidirect
15. #478×C73C2semidirect
19. #14556591C22semidirect
21. #14556590C22semidirect
22. #14556582C22semidirect
37. #14556525C22semidirect
38. #14556525C22semidirect
39. #14556524C22semidirect
40. #14556522C22semidirect
41. #14556522C22semidirect
42. #14556522C22semidirect
43. C4⋊#10596831C22semidirect
44. #14556520C22semidirect
45. #14556520C22semidirect
52. #125×C73C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. C4⋊C8×C73C22semidirect
65. D4×D73Q8semidirect
173. C73#3081semidirect
179. #478D73semidirect
197. #125C2×D73semidirect
215. #107C2×D73semidirect
219. #106C2×D73semidirect
223. C4⋊C8C2×D73semidirect