Finite Group Databasebeta

← #22622012

Subgroups — #22622012

Order 9344.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989294C211yesmaximal, characteristic, complemented
2#17988946C211yesmaximal, characteristic, complemented
3#17988920C211yesmaximal, characteristic, complemented
4#17988898C211yesmaximal, characteristic, complemented
5#17988867C211yesmaximal, characteristic, complemented
6#17988831C211yesmaximal, characteristic, complemented
7#17988826C211yesmaximal, characteristic, complemented
8#17988806C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988738C211yesmaximal, characteristic, complemented
11#17988687C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988588C211yesmaximal, characteristic, complemented
14C2×#14556512C211yesmaximal, characteristic, complemented
15#546×C73C211yesmaximal, characteristic
16C2×#11924018C2211yescharacteristic, complemented
17C2×#11924016C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924012C2211yescharacteristic, complemented
20C22×#10596831C2211yescharacteristic
21#14556591C2211yescharacteristic, complemented
22#14556582—21no—
23#14556570C2211yescharacteristic
24#14556570C2211yescharacteristic, complemented
25#14556568—21no—
26#14556568—21no—
27C4×Dic146C2211yescharacteristic, complemented
28D4×Dic73—21no—
29C2×C4⋊Dic73C2211yescharacteristic
30C2×C4⋊Dic73C2211yescharacteristic, complemented
31#14556524C2211yescharacteristic, complemented
32#14556524C2211yescharacteristic, complemented
33#14556524C2211yescharacteristic, complemented
34C4⋊#10596831C2211yescharacteristic, complemented
35#14556515C2211yescharacteristic, complemented
36#14556515C2211yescharacteristic, complemented
37#14556515C2211yescharacteristic, complemented
38#14556514C2211yescharacteristic, complemented
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556512C2211yescharacteristic
43#14556512C2211yescharacteristic
44#14556512C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic, complemented
47#14556502C2211yescharacteristic, complemented
48C2×#41×C73C2211yescharacteristic
49C22×D4×C73C2211yescharacteristic
50#124×C73C2211yescharacteristic
51#123×C73—21no—
52C22⋊Q8×C73C2211yescharacteristic
53#121×C73—21no—
54#121×C73C2211yescharacteristic
55#120×C73—21no—
56C4×D4×C73C2211yescharacteristic
57C4×D4×C73C2211yescharacteristic
58C2×C22⋊C4×C73—21no—
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C22×Dic73—21no—
62C22×Dic73—21no—
63#11924018—41no—
64#11924016—22no—
65#11924016—41no—
66#11924012—41no—
67C2×#10596831—41no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C4×Dic73—21no—
84C24×C73—21no—
85#41×C73—22no—
86#41×C73—41no—
87C2×Q8×C73C2311yescharacteristic
88C2×D4×C73—22no—
89C2×D4×C73—21no—
90C2×D4×C73—21no—
91C2×D4×C73—21no—
92C2×D4×C73—41no—
93C2×D4×C73D411yescharacteristic
94C2×D4×C73C2311yescharacteristic
95C2×D4×C73C2311yescharacteristic
96C22×C4×C73—21no—
97C22×C4×C73—21no—
98C22×C4×C73C2311yescharacteristic
99C22×C4×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73D411yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C22⋊C4×C73—21no—
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C22⋊C4×C73D411yescharacteristic
109C22⋊C4×C73D411yescharacteristic
110C42×C73C2311yescharacteristic
111C23×C73—21no—
112C23×C73—21no—
113C23×C73—42no—
114C23×C73—42no—
115C23×C73—81no—
116C23×C73C2×D411yescharacteristic
117C23×C73C2×D411yescharacteristic
118Q8×C73—21no—
119Q8×C73—21no—
120D4×C73—22no—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—21no—
124D4×C73—42no—
125D4×C73—42no—
126D4×C73—81no—
127D4×C73#4112yes—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—42no—
135C2×C4×C73—81no—
136C2×C4×C73C2×D411yescharacteristic
137C2×C4×C73C2×D411yescharacteristic
138C2×C4×C73C2×D411yescharacteristic
139C2×C4×C73C2×D411yescharacteristic
140C2×C4×C73C2411yescharacteristic
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—81no—
146C2×Dic73—81no—
147Dic146—21no—
148Dic146—21no—
149Dic146—81no—
150#10596831—21no—
151#10596831—21no—
152#10596831—21no—
153#10596831—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—22no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—84no—
166C22×C73#13712yes—
167C22×C73C22×D411yescharacteristic
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—41no—
173C4×C73—41no—
174C4×C73C2×#4111yescharacteristic
175C4×C73H(5,𝔽2)11yescharacteristic
176Dic73—41no—
177Dic73—41no—
178Dic73—41no—
179Dic73—41no—
180C2×C73—22no—
181C2×C73—41no—
182C2×C73—42no—
183C2×C73—81no—
184C2×C73#54611yescharacteristic
185C2×C73C2×#13711yescharacteristic
186C2×C73#57611yescharacteristic
187#3314—731nomaximal, Sylow
188C73#331411yescharacteristic, complemented, Sylow
189#554—731no—
190#546D7311yescharacteristic
191#489—731no—
192#484—731no—
193#480—731no—
194#474—731no—
195#468—731no—
196#467—731no—
197#464—731no—
198#452—731no—
199#450—731no—
200#440—731no—
201#435—731no—
202#417—731no—
203C2×#102—731no—
204C2×#41C2×D7311yescharacteristic
205C22×D4C2×D7311yescharacteristic
206C2×Q16—731no—
207C2×SD16—731no—
208C2×SD16—731no—
209C2×M16—731no—
210C22×C8—731no—
211C4⋊Q8—731no—
212#125—1461no—
213#124C2×D7311yescharacteristic
214#123—21no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8—1461no—
218C22⋊Q8—1461no—
219C22⋊Q8C2×D7311yescharacteristic
220#121—21no—
221#121C2×D7311yescharacteristic
222#120—21no—
223C4×Q8—731no—
224C4×D4—1461no—
225C4×D4C2×D7311yescharacteristic
226C4×D4C2×D7311yescharacteristic
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229C2×C22⋊C4—21no—
230#107—731no—
231#107—731no—
232#107—731no—
233C4⋊C8—731no—
234#103—731no—
235#103—731no—
236#103—731no—
237#103—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244C22⋊C8—731no—
245C22⋊C8—731no—
246#97—731no—
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—731no—
251C2×Q8—1461no—
252C2×Q8C22×D7311yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D7311yescharacteristic
259C2×D4C22×D7311yescharacteristic
260C2×D4C22×D7311yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4C22×D7311yescharacteristic
266C22×C4C22×D7311yescharacteristic
267Q16—2921no—
268SD16—2921no—
269SD16—1462no—
270M16—2921no—
271C2×C8—2921no—
272C2×C8—731no—
273C2×C8—731no—
274C2×C8—731no—
275C2×C8—731no—
276C4⋊C4—21no—
277C4⋊C4—731no—
278C4⋊C4—731no—
279C4⋊C4—731no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4—1461no—
283C4⋊C4—1461no—
284C4⋊C4—1461no—
285C4⋊C4—1461no—
286C4⋊C4C22⋊D7311yescharacteristic
287C4⋊C4C22×D7311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4C22⋊D7311yescharacteristic
296C22⋊C4C22⋊D7311yescharacteristic
297C42—1461no—
298C42C22×D7311yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D7311yescharacteristic
305C23C2×C22⋊D7311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—5841no—
309Q8—1461no—
310Q8—1461no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#1192402712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—5841no—
328C2×C4—5841no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4—1461no—
333C2×C4C2×C22⋊D7311yescharacteristic
334C2×C4C2×C22⋊D7311yescharacteristic
335C2×C4C2×C22⋊D7311yescharacteristic
336C2×C4C2×C22⋊D7311yescharacteristic
337C2×C4C23×D7311yescharacteristic
338C8—1461no—
339C8—1461no—
340C8—1461no—
341C8—1461no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1455662112yes—
355C22C22×C22⋊D7311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—2921no—
363C4—2921no—
364C4—2921no—
365C4—2921no—
366C4C2×#1192402711yescharacteristic
367C4#1455663611yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1798923111yescharacteristic
373C2C2×#1455662111yescharacteristic
374C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#546×C73C2
socleC22×C73C22×D4
hypercenter#546D73
hypocenterC73#3314
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #17989294C2semidirect
2. #17988946C2semidirect
3. #17988920C2semidirect
4. #17988898C2semidirect
5. #17988867C2semidirect
6. #17988831C2semidirect
7. #17988826C2semidirect
8. #17988806C2semidirect
9. #17988749C2semidirect
10. #17988738C2semidirect
11. #17988687C2semidirect
12. #17988659C2semidirect
13. #17988588C2semidirect
14. C2×#14556512C2semidirect
16. C2×#11924018C22semidirect
19. C2×#11924012C22semidirect
21. #14556591C22semidirect
24. #14556570C22semidirect
27. C4×Dic146C22semidirect
30. C2×C4⋊Dic73C22semidirect
31. #14556524C22semidirect
32. #14556524C22semidirect
33. #14556524C22semidirect
34. C4⋊#10596831C22semidirect
35. #14556515C22semidirect
36. #14556515C22semidirect
37. #14556515C22semidirect
38. #14556514C22semidirect
46. C22⋊#10596831C22semidirect
47. #14556502C22semidirect
188. C73#3314semidirect