Finite Group Databasebeta

← #22622024

Subgroups — #22622024

Order 9344.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989275C211yesmaximal, characteristic, complemented
2#17989241C211yesmaximal, characteristic
3#17988957C211yesmaximal, characteristic, complemented
4#17988931C211yesmaximal, characteristic, complemented
5#17988924C211yesmaximal, characteristic, complemented
6#17988846C211yesmaximal, characteristic, complemented
7#17988829C211yesmaximal, characteristic, complemented
8#17988798C211yesmaximal, characteristic, complemented
9#17988750C211yesmaximal, characteristic, complemented
10#17988750C211yesmaximal, characteristic, complemented
11#17988687C211yesmaximal, characteristic, complemented
12#17988657C211yesmaximal, characteristic, complemented
13#17988585C211yesmaximal, characteristic, complemented
14#17988580C211yesmaximal, characteristic, complemented
15#478×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18C2×Dic292C2211yescharacteristic
19C2×Dic292C2211yescharacteristic
20C2×#11924016C2211yescharacteristic
21C2×#11924011C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic
23#14556591C2211yescharacteristic
24#14556586—21no—
25#14556582—21no—
26#14556576—21no—
27#14556575—21no—
28#14556575—21no—
29#14556571C2211yescharacteristic
30#14556571C2211yescharacteristic
31#14556571C2211yescharacteristic
32#14556571C2211yescharacteristic
33#14556565—21no—
34C4×Dic146C2211yescharacteristic
35C4×D292C2211yescharacteristic
36#14556549—21no—
37#14556549C2211yescharacteristic
38C2×C4⋊Dic73—21no—
39C4⋊C4×D73C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556516C2211yescharacteristic
42#14556516C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556514C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556514C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556502C2211yescharacteristic
52#125×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—22no—
60#11924027—22no—
61#11924027—41no—
62#11924027—41no—
63C2×Dic146C2311yescharacteristic
64C2×Dic146C2311yescharacteristic
65C2×Dic146C2311yescharacteristic
66C2×D292D411yescharacteristic
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C22×Dic73—21no—
70C22×Dic73—21no—
71C2×C4×D73—21no—
72C2×C4×D73C2311yescharacteristic
73C2×C4×D73C2311yescharacteristic
74Dic292—41no—
75Dic292—41no—
76#11924016—22no—
77#11924011—41no—
78C2×#10596831C2311yescharacteristic
79C2×#10596831C2311yescharacteristic
80C8×D73—41no—
81C4⋊Dic73—21no—
82C4⋊Dic73—21no—
83C4⋊Dic73—21no—
84C4⋊Dic73—21no—
85C4⋊Dic73—21no—
86C4⋊Dic73—21no—
87C4⋊Dic73D411yescharacteristic
88C4⋊Dic73C2311yescharacteristic
89#11924007—21no—
90#11924007—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005D411yescharacteristic
97#11924005D411yescharacteristic
98C4×Dic73—21no—
99C4×Dic73—21no—
100C2×D4×C73C2311yescharacteristic
101C22×C4×C73—21no—
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C4⋊C4×C73—21no—
105C4⋊C4×C73—21no—
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C22×D73C2×D411yescharacteristic
113C22×D73C2×D411yescharacteristic
114D4×C73—21no—
115D4×C73#4112yes—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—42no—
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2×D411yescharacteristic
122C2×C4×C73C2411yescharacteristic
123C22⋊D73—42no—
124C22⋊D73—42no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—42no—
130C2×Dic73—42no—
131C2×Dic73C2×D411yescharacteristic
132C2×Dic73C2×D411yescharacteristic
133D292—41no—
134C4×D73—21no—
135C4×D73—21no—
136C4×D73—21no—
137C4×D73—21no—
138C4×D73—42no—
139Dic146—21no—
140Dic146—21no—
141Dic146—21no—
142Dic146—21no—
143Dic146—21no—
144Dic146—21no—
145C8×C73—21no—
146C8×C73—21no—
147#10596831—21no—
148#10596831—21no—
149C22×C73—22no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73C22×D411yescharacteristic
153C2×D73—21no—
154C2×D73—21no—
155C2×D73—21no—
156C2×D73—21no—
157C2×D73—21no—
158C2×D73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73C2×#4111yescharacteristic
165C4×C73H(5,𝔽2)11yescharacteristic
166Dic73—21no—
167Dic73—21no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73—41no—
172C2×C73—42no—
173C2×C73#54611yescharacteristic
174C2×C73#57511yescharacteristic
175C2×C73#57811yescharacteristic
176D73—41no—
177D73—41no—
178#3315—731nomaximal, Sylow
179C73#331511yescharacteristic, complemented, Sylow
180#552—731no—
181#547—731no—
182#491—731no—
183#485—731no—
184#484—731no—
185#478D7311yescharacteristic, complemented
186#470—731no—
187#467—731no—
188#462—731no—
189#452—731no—
190#452—731no—
191#440—731no—
192#435—731no—
193#417—731no—
194#416—731no—
195C2×#41—731no—
196C2×#41—731no—
197C2×Q16—731no—
198C2×Q16—731no—
199C2×SD16—731no—
200C2×M16—731no—
201C22×C8—731no—
202C4⋊Q8—731no—
203#126—1461no—
204#125—1461no—
205#125C2×D7311yescharacteristic
206#123—1461no—
207#123—1461no—
208#123—1461no—
209C22⋊Q8—731no—
210C22⋊Q8—731no—
211C22⋊Q8—731no—
212C22⋊Q8—731no—
213#121—1461no—
214C4×Q8—731no—
215C4×D4—731no—
216C4×D4C2×D7311yescharacteristic
217#117—731no—
218#117—1461no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—1461no—
221#107—731no—
222#107C2×D7311yescharacteristic
223#106C2×D7311yescharacteristic
224C4⋊C8C2×D7311yescharacteristic
225#103—731no—
226#103—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#102—731no—
233#102C2×D7311yescharacteristic
234#102C2×D7311yescharacteristic
235C22⋊C8—731no—
236C22⋊C8—731no—
237#97—731no—
238#41—2921no—
239#41—2921no—
240#41—1462no—
241#41—1462no—
242C2×Q8—731no—
243C2×Q8—731no—
244C2×Q8—731no—
245C2×D4—731no—
246C2×D4—1461no—
247C2×D4—1461no—
248C2×D4C22×D7311yescharacteristic
249C22×C4—21no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4—1461no—
255Q16—2921no—
256Q16—2921no—
257SD16—1462no—
258M16—2921no—
259C2×C8—2921no—
260C2×C8—731no—
261C2×C8—731no—
262C2×C8C22×D7311yescharacteristic
263C2×C8C22×D7311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4—1461no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4C22×D7311yescharacteristic
277C4⋊C4C22×D7311yescharacteristic
278C4⋊C4C22×D7311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—731no—
281C22⋊C4—731no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C42—1461no—
288C42—1461no—
289C42C22×D7311yescharacteristic
290C23—21no—
291C23—731no—
292C23—731no—
293Q8—1461no—
294Q8—1461no—
295Q8—1461no—
296Q8—1461no—
297Q8—1461no—
298Q8—1461no—
299D4—21no—
300D4—2921no—
301D4—2922no—
302D4—2922no—
303D4#1192402912yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—2922no—
309C2×C4—2922no—
310C2×C4—2922no—
311C2×C4—731no—
312C2×C4—731no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4D4×D7311yescharacteristic
322C2×C4D4×D7311yescharacteristic
323C2×C4C23×D7311yescharacteristic
324C8—21no—
325C8—21no—
326C8—1461no—
327C8—1461no—
328C22—22no—
329C22—41no—
330C22—41no—
331C22—1461no—
332C22—1461no—
333C22—1461no—
334C22—1461no—
335C22—1461no—
336C22—1461no—
337C22C2×D4×D7311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2921no—
344C4—2921no—
345C4—2921no—
346C4—2921no—
347C4—1461no—
348C4—1461no—
349C4C2×#1192402911yescharacteristic
350C4#1455663711yescharacteristic
351C2—42no—
352C2—2921no—
353C2—2921no—
354C2#1798922811yescharacteristic
355C2#1798938311yescharacteristic
356C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#478×C73C2
socleC22×C73C22×D4
hypercenter#478D73
hypocenterC73#3315
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. #17989275C2semidirect
3. #17988957C2semidirect
4. #17988931C2semidirect
5. #17988924C2semidirect
6. #17988846C2semidirect
7. #17988829C2semidirect
8. #17988798C2semidirect
9. #17988750C2semidirect
10. #17988750C2semidirect
11. #17988687C2semidirect
12. #17988657C2semidirect
13. #17988585C2semidirect
14. #17988580C2semidirect
15. #478×C73C2semidirect
179. C73#3315semidirect
185. #478D73semidirect