Finite Group Databasebeta

← #22620825

Subgroups — #22620825

Order 9344.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989163C211yesmaximal, characteristic
2#17989160C211yesmaximal, characteristic
3#17988931C211yesmaximal, characteristic, complemented
4#17988930C211yesmaximal, characteristic, complemented
5#17988928C211yesmaximal, characteristic, complemented
6#17988846C211yesmaximal, characteristic, complemented
7#17988844C211yesmaximal, characteristic, complemented
8#17988829C211yesmaximal, characteristic, complemented
9#17988827C211yesmaximal, characteristic, complemented
10#17988745C211yesmaximal, characteristic, complemented
11#17988744C211yesmaximal, characteristic, complemented
12#17988744C211yesmaximal, characteristic, complemented
13#17988742C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic
15#485×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C2×Q8×D73C2211yescharacteristic
19C2×Dic292C2211yescharacteristic
20C2×Dic292C2211yescharacteristic
21C2×#11924018C2211yescharacteristic
22C2×#11924018C2211yescharacteristic
23C2×#11924011C2211yescharacteristic
24C2×C8×D73C2211yescharacteristic
25#14556591—21no—
26#14556590—21no—
27#14556579—21no—
28#14556577—21no—
29#14556576—21no—
30#14556575—21no—
31#14556575—21no—
32#14556573—21no—
33#14556571C2211yescharacteristic
34#14556571C2211yescharacteristic
35#14556571C2211yescharacteristic
36#14556571C2211yescharacteristic
37#14556571C2211yescharacteristic
38#14556570C2211yescharacteristic
39#14556567C2211yescharacteristic
40#14556549C2211yescharacteristic
41#14556524C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556514C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—41no—
60#11924028—41no—
61C2×Dic146—21no—
62C2×Dic146—21no—
63C2×Dic146—41no—
64C2×Dic146—41no—
65C2×Dic146D411yescharacteristic
66C2×Dic146C2311yescharacteristic
67C2×Dic146C2311yescharacteristic
68C2×Dic146C2311yescharacteristic
69Q8×D73—41no—
70Q8×D73—41no—
71C2×D292D411yescharacteristic
72C2×C22⋊D73D411yescharacteristic
73C2×C22⋊D73D411yescharacteristic
74C22×Dic73—21no—
75C2×C4×D73—21no—
76C2×C4×D73C2311yescharacteristic
77C2×C4×D73C2311yescharacteristic
78Dic292—41no—
79Dic292—41no—
80#11924018—41no—
81#11924018—41no—
82#11924011—41no—
83C2×#10596831C2311yescharacteristic
84C2×#10596831C2311yescharacteristic
85C8×D73—41no—
86C4⋊Dic73—21no—
87C4⋊Dic73—21no—
88C4⋊Dic73—21no—
89C4⋊Dic73—21no—
90C4⋊Dic73—21no—
91C4⋊Dic73C2311yescharacteristic
92#11924007—21no—
93#11924007—21no—
94C22⋊Dic73—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102C4×Dic73—21no—
103C2×Q8×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C4⋊C4×C73C2311yescharacteristic
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C42×C73—21no—
114C23×C73C2×D411yescharacteristic
115C22×D73C2×D411yescharacteristic
116C22×D73C2×D411yescharacteristic
117Q8×C73—21no—
118Q8×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—41no—
128C22⋊D73—41no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—42no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136D292—41no—
137C4×D73—21no—
138C4×D73—21no—
139C4×D73—21no—
140C4×D73—21no—
141C4×D73—42no—
142Dic146—21no—
143Dic146—21no—
144Dic146—21no—
145Dic146—21no—
146Dic146—21no—
147Dic146—21no—
148Dic146—41no—
149Dic146—42no—
150Dic146—42no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73C22×D411yescharacteristic
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—21no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73H(5,𝔽2)11yescharacteristic
171C4×C73H(5,𝔽2)11yescharacteristic
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—41no—
179C2×C73#53411yescharacteristic
180C2×C73#57811yescharacteristic
181C2×C73#57811yescharacteristic
182D73—41no—
183D73—41no—
184#3202—731nomaximal, Sylow
185C73#320211yescharacteristic, complemented, Sylow
186#536—731no—
187#536—731no—
188#485—731no—
189#485—731no—
190#485—731no—
191#485D7311yescharacteristic, complemented
192#470—731no—
193#470—731no—
194#467—731no—
195#467—731no—
196#451—731no—
197#451—731no—
198#451—731no—
199#451—731no—
200#408—731no—
201C2×#41—731no—
202C22×Q8—731no—
203C22×Q8—731no—
204C2×Q16—731no—
205C2×Q16—731no—
206C2×Q16—731no—
207C2×Q16—731no—
208C2×M16—731no—
209C22×C8—731no—
210C4⋊Q8—1461no—
211C4⋊Q8—1461no—
212#124—1461no—
213#124—1461no—
214#123—1461no—
215#123—1461no—
216#123—1461no—
217#123—1461no—
218C22⋊Q8—731no—
219C22⋊Q8—731no—
220C22⋊Q8—731no—
221C22⋊Q8—731no—
222C22⋊Q8—731no—
223C22⋊Q8—731no—
224C22⋊Q8—731no—
225C22⋊Q8C2×D7311yescharacteristic
226#117—731no—
227#117C2×D7311yescharacteristic
228#107—731no—
229#107C2×D7311yescharacteristic
230#106—731no—
231#106C2×D7311yescharacteristic
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#103—731no—
238#103C2×D7311yescharacteristic
239#103C2×D7311yescharacteristic
240C22⋊C8—731no—
241C22⋊C8—731no—
242C22⋊C8—731no—
243C22⋊C8C2×D7311yescharacteristic
244#41—2921no—
245#41—2921no—
246C2×Q8—2921no—
247C2×Q8—2921no—
248C2×Q8—2921no—
249C2×Q8—2921no—
250C2×Q8—731no—
251C2×Q8—731no—
252C2×Q8—731no—
253C2×Q8—731no—
254C2×Q8—1461no—
255C2×Q8—1461no—
256C2×Q8C22×D7311yescharacteristic
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4C22×D7311yescharacteristic
265Q16—2921no—
266Q16—2921no—
267Q16—2921no—
268Q16—2921no—
269M16—2921no—
270C2×C8—2921no—
271C2×C8—731no—
272C2×C8—731no—
273C2×C8C22×D7311yescharacteristic
274C2×C8C22×D7311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—731no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4C22×D7311yescharacteristic
285C4⋊C4C22×D7311yescharacteristic
286C4⋊C4C22×D7311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C42—21no—
298C42—1461no—
299C23—731no—
300C23—731no—
301C23D4×D7311yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—2922no—
305Q8—2921no—
306Q8—2922no—
307Q8—1461no—
308Q8—1461no—
309Q8—1461no—
310Q8—1461no—
311Q8—1461no—
312Q8—1461no—
313D4—2921no—
314D4—2921no—
315D4—2921no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—2922no—
323C2×C4—2922no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4—1461no—
334C2×C4D4×D7311yescharacteristic
335C2×C4C23×D7311yescharacteristic
336C8—21no—
337C8—21no—
338C8—1461no—
339C8—1461no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—1461no—
344C22—1461no—
345C22—1461no—
346C22—1461no—
347C22—1461no—
348C22—1461no—
349C22C2×D4×D7311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2921no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—1461no—
360C4—1461no—
361C4#1455663711yescharacteristic
362C4#1455663711yescharacteristic
363C2—41no—
364C2—2921no—
365C2—2921no—
366C2#1798914811yescharacteristic
367C2#1798940111yescharacteristic
368C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#485×C73C2
socleC22×C73C22×D4
hypercenter#485D73
hypocenterC73#3202
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #17988931C2semidirect
4. #17988930C2semidirect
5. #17988928C2semidirect
6. #17988846C2semidirect
7. #17988844C2semidirect
8. #17988829C2semidirect
9. #17988827C2semidirect
10. #17988745C2semidirect
11. #17988744C2semidirect
12. #17988744C2semidirect
13. #17988742C2semidirect
15. #485×C73C2semidirect
185. C73#3202semidirect
191. #485D73semidirect