Finite Group Databasebeta

← #22622147

Subgroups — #22622147

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989277C211yesmaximal, characteristic, complemented
2#17988941C211yesmaximal, characteristic, complemented
3#17988925C211yesmaximal, characteristic, complemented
4#17988903C211yesmaximal, characteristic, complemented
5#17988887C211yesmaximal, characteristic, complemented
6#17988843C211yesmaximal, characteristic, complemented
7#17988831C211yesmaximal, characteristic, complemented
8#17988806C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988738C211yesmaximal, characteristic, complemented
11C4×#11924016C211yesmaximal, characteristic, complemented
12#17988665C211yesmaximal, characteristic, complemented
13#17988592C211yesmaximal, characteristic, complemented
14#17988588C211yesmaximal, characteristic, complemented
15#546×C73C211yesmaximal, characteristic
16C2×#11924018C2211yescharacteristic, complemented
17C2×#11924016C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×#11924012C2211yescharacteristic
20C2×#11924012C2211yescharacteristic, complemented
21#14556584—21no—
22#14556583C2211yescharacteristic, complemented
23#14556581—21no—
24#14556572—21no—
25#14556570C2211yescharacteristic
26#14556570C2211yescharacteristic, complemented
27C4×Dic146C2211yescharacteristic, complemented
28#14556550C2211yescharacteristic
29#14556547—21no—
30C2×C4⋊Dic73C2211yescharacteristic, complemented
31#14556524C2211yescharacteristic, complemented
32#14556522C2211yescharacteristic, complemented
33#14556522C2211yescharacteristic, 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
47C4×#10596831C2211yescharacteristic, 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×Dic146C2311yescharacteristic
60C22×Dic73—21no—
61#11924018—41no—
62#11924016—22no—
63#11924016—41no—
64#11924012—41no—
65#11924012—41no—
66C2×#10596831C2311yescharacteristic
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C4⋊Dic73—21no—
71C4⋊Dic73C2311yescharacteristic
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74#11924007—21no—
75#11924007—21no—
76#11924007—21no—
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80C22⋊Dic73—21no—
81C22⋊Dic73—21no—
82C4×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—21no—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—41no—
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—42no—
146Dic146—21no—
147Dic146—21no—
148#10596831—21no—
149#10596831—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—22no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—84no—
165C22×C73C22×D411yescharacteristic
166C4×C73—21no—
167C4×C73—21no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73C2×#4111yescharacteristic
173C4×C73H(5,𝔽2)11yescharacteristic
174Dic73—41no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—41no—
179C2×C73—41no—
180C2×C73—42no—
181C2×C73—81no—
182C2×C73#54611yescharacteristic
183C2×C73#57511yescharacteristic
184C2×C73#57711yescharacteristic
185#3323—731nomaximal, Sylow
186C73#332311yescharacteristic, complemented, Sylow
187#552—731no—
188#546D7311yescharacteristic
189#488—731no—
190#485—731no—
191#481—731no—
192#478—731no—
193#470—731no—
194#468—731no—
195#464—731no—
196#452—731no—
197#450—731no—
198C4×SD16—731no—
199#436—731no—
200#418—731no—
201#417—731no—
202C2×#41C2×D7311yescharacteristic
203C22×D4C2×D7311yescharacteristic
204C2×Q16—731no—
205C2×SD16—731no—
206C2×SD16—731no—
207C2×M16—731no—
208C2×M16—731no—
209#126—1461no—
210#125—731no—
211#125—1461no—
212#124C2×D7311yescharacteristic
213#123—21no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8C2×D7311yescharacteristic
218#121—21no—
219#121C2×D7311yescharacteristic
220#120—21no—
221C4×Q8—731no—
222C4×D4C2×D7311yescharacteristic
223C4×D4C2×D7311yescharacteristic
224#117—731no—
225#117—1461no—
226C2×C4⋊C4—731no—
227C2×C22⋊C4—21no—
228#107—731no—
229#106—731no—
230#106—731no—
231C4⋊C8—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103—731no—
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102—731no—
242C22⋊C8—731no—
243C22⋊C8—731no—
244C4×C8—731no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—731no—
249C2×Q8C22×D7311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D7311yescharacteristic
256C2×D4C22×D7311yescharacteristic
257C2×D4C22×D7311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—1461no—
261C22×C4C22×D7311yescharacteristic
262C22×C4C22×D7311yescharacteristic
263Q16—2921no—
264SD16—2921no—
265SD16—1462no—
266M16—2921no—
267M16—2921no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8—731no—
271C2×C8—731no—
272C4⋊C4—21no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4—1461no—
282C4⋊C4C22⋊D7311yescharacteristic
283C4⋊C4C22×D7311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4C22⋊D7311yescharacteristic
293C22⋊C4C22⋊D7311yescharacteristic
294C42—1461no—
295C42—1461no—
296C42C22×D7311yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D7311yescharacteristic
303C23C2×C22⋊D7311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1461no—
307Q8—1461no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1192402712yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—2922no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4C2×C22⋊D7311yescharacteristic
330C2×C4C2×C22⋊D7311yescharacteristic
331C2×C4C2×C22⋊D7311yescharacteristic
332C2×C4C2×C22⋊D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—1461no—
335C8—1461no—
336C8—1461no—
337C8—1461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×C22⋊D7311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—2921no—
359C4—2921no—
360C4—2921no—
361C4—2921no—
362C4C2×#1192402711yescharacteristic
363C4#1455663611yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1798923111yescharacteristic
369C2#1798938511yescharacteristic
370C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#546×C73C2
socleC22×C73C22×D4
hypercenter#546D73
hypocenterC73#3323
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. #17989277C2semidirect
2. #17988941C2semidirect
3. #17988925C2semidirect
4. #17988903C2semidirect
5. #17988887C2semidirect
6. #17988843C2semidirect
7. #17988831C2semidirect
8. #17988806C2semidirect
9. #17988749C2semidirect
10. #17988738C2semidirect
11. C4×#11924016C2semidirect
12. #17988665C2semidirect
13. #17988592C2semidirect
14. #17988588C2semidirect
16. C2×#11924018C22semidirect
20. C2×#11924012C22semidirect
22. #14556583C22semidirect
26. #14556570C22semidirect
27. C4×Dic146C22semidirect
30. C2×C4⋊Dic73C22semidirect
31. #14556524C22semidirect
32. #14556522C22semidirect
33. #14556522C22semidirect
34. C4⋊#10596831C22semidirect
35. #14556515C22semidirect
36. #14556515C22semidirect
37. #14556515C22semidirect
38. #14556514C22semidirect
46. C22⋊#10596831C22semidirect
47. C4×#10596831C22semidirect
186. C73#3323semidirect