Finite Group Databasebeta

← #22620807

Subgroups — #22620807

Order 9344.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989158C211yesmaximal, characteristic, complemented
2#17988925C211yesmaximal, characteristic, complemented
3#17988922C211yesmaximal, characteristic, complemented
4#17988917C211yesmaximal, characteristic, complemented
5#17988908C211yesmaximal, characteristic, complemented
6#17988843C211yesmaximal, characteristic, complemented
7#17988831C211yesmaximal, characteristic, complemented
8#17988826C211yesmaximal, characteristic, complemented
9#17988814C211yesmaximal, characteristic, complemented
10#17988749C211yesmaximal, characteristic, complemented
11#17988749C211yesmaximal, characteristic, complemented
12#17988742C211yesmaximal, characteristic, complemented
13#17988725C211yesmaximal, characteristic, complemented
14#17988554C211yesmaximal, characteristic, complemented
15#537×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C2×#11924018C2211yescharacteristic
18C2×#11924018C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×#11924016C2211yescharacteristic
21C2×#11924012C2211yescharacteristic
22C22×#10596831C2211yescharacteristic
23#14556589—21no—
24#14556578—21no—
25#14556572—21no—
26#14556572—21no—
27#14556570C2211yescharacteristic
28#14556570C2211yescharacteristic
29#14556570C2211yescharacteristic
30#14556570C2211yescharacteristic
31#14556550C2211yescharacteristic
32#14556524C2211yescharacteristic
33#14556524C2211yescharacteristic
34#14556522C2211yescharacteristic
35#14556522C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556514C2211yescharacteristic
39#14556514C2211yescharacteristic
40#14556514C2211yescharacteristic
41#14556514C2211yescharacteristic
42#14556512C2211yescharacteristic
43#14556512C2211yescharacteristic
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47C22⋊#10596831C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C2×#41×C73C2211yescharacteristic
50C22⋊Q8×C73—21no—
51C22⋊Q8×C73C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53#121×C73—21no—
54#121×C73—21no—
55#121×C73—21no—
56#121×C73C2211yescharacteristic
57#121×C73C2211yescharacteristic
58C2×C4⋊C4×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146—41no—
61C2×Dic146—41no—
62C2×Dic146C2311yescharacteristic
63C2×Dic146C2311yescharacteristic
64C22×Dic73—21no—
65#11924018—41no—
66#11924018—41no—
67#11924016—41no—
68#11924016—41no—
69#11924012—41no—
70C2×#10596831—41no—
71C2×#10596831C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C2×#10596831C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81C22⋊Dic73—21no—
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C4×Dic73—21no—
87#41×C73—41no—
88#41×C73—41no—
89#41×C73—41no—
90#41×C73—41no—
91C2×Q8×C73D411yescharacteristic
92C2×Q8×C73C2311yescharacteristic
93C2×D4×C73—21no—
94C2×D4×C73—21no—
95C2×D4×C73—21no—
96C2×D4×C73D411yescharacteristic
97C2×D4×C73D411yescharacteristic
98C2×D4×C73D411yescharacteristic
99C2×D4×C73C2311yescharacteristic
100C22×C4×C73—21no—
101C22×C4×C73—21no—
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C22×C4×C73C2311yescharacteristic
105C4⋊C4×C73—21no—
106C4⋊C4×C73—21no—
107C4⋊C4×C73—21no—
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C22⋊C4×C73—21no—
114C23×C73—21no—
115C23×C73C2×D411yescharacteristic
116C23×C73C2×D411yescharacteristic
117C23×C73C2×D411yescharacteristic
118Q8×C73—21no—
119Q8×C73—21no—
120Q8×C73—41no—
121D4×C73—21no—
122D4×C73—21no—
123D4×C73—41no—
124D4×C73—41no—
125D4×C73—41no—
126D4×C73—42no—
127D4×C73—81no—
128D4×C73—81no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—42no—
139C2×C4×C73—81no—
140C2×C4×C73C2×D411yescharacteristic
141C2×C4×C73C2×D411yescharacteristic
142C2×C4×C73C2×D411yescharacteristic
143C2×C4×C73C2411yescharacteristic
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—21no—
148C2×Dic73—42no—
149Dic146—21no—
150Dic146—21no—
151Dic146—21no—
152Dic146—21no—
153Dic146—42no—
154#10596831—21no—
155#10596831—21no—
156#10596831—21no—
157#10596831—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73C22×D411yescharacteristic
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—21no—
174C4×C73—41no—
175C4×C73—41no—
176C4×C73—41no—
177C4×C73H(5,𝔽2)11yescharacteristic
178C4×C73H(5,𝔽2)11yescharacteristic
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182Dic73—41no—
183C2×C73—41no—
184C2×C73—41no—
185C2×C73—41no—
186C2×C73—81no—
187C2×C73#53411yescharacteristic
188C2×C73#57711yescharacteristic
189C2×C73#57811yescharacteristic
190#3201—731nomaximal, Sylow
191C73#320111yescharacteristic, complemented, Sylow
192#537D7311yescharacteristic
193#536—731no—
194#485—731no—
195#484—731no—
196#483—731no—
197#482—731no—
198#470—731no—
199#468—731no—
200#467—731no—
201#465—731no—
202#452—731no—
203#452—731no—
204#451—731no—
205#448—731no—
206#408—731no—
207C2×#41C2×D7311yescharacteristic
208C2×#41C2×D7311yescharacteristic
209C22×Q8—731no—
210C2×Q16—731no—
211C2×Q16—731no—
212C2×SD16—731no—
213C2×SD16—731no—
214C2×M16—731no—
215C22×C8—731no—
216C4⋊Q8—1461no—
217#124—1461no—
218#123—1461no—
219#123—1461no—
220C22⋊Q8—21no—
221C22⋊Q8—731no—
222C22⋊Q8—731no—
223C22⋊Q8—731no—
224C22⋊Q8—731no—
225C22⋊Q8C2×D7311yescharacteristic
226C22⋊Q8C2×D7311yescharacteristic
227#121—21no—
228#121—21no—
229#121—21no—
230#121C2×D7311yescharacteristic
231#121C2×D7311yescharacteristic
232#117—731no—
233C2×C4⋊C4C2×D7311yescharacteristic
234#107—731no—
235#107—731no—
236#106—731no—
237#106—731no—
238#103—731no—
239#103—731no—
240#103—731no—
241#103—731no—
242#103—731no—
243#103—731no—
244#102—731no—
245#102—731no—
246C22⋊C8—731no—
247C22⋊C8—731no—
248C22⋊C8—731no—
249C22⋊C8—731no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—2921no—
255C2×Q8—2921no—
256C2×Q8—731no—
257C2×Q8—731no—
258C2×Q8—1461no—
259C2×Q8C22⋊D7311yescharacteristic
260C2×Q8C22×D7311yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊D7311yescharacteristic
265C2×D4C22⋊D7311yescharacteristic
266C2×D4C22⋊D7311yescharacteristic
267C2×D4C22×D7311yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—1461no—
271C22×C4C22×D7311yescharacteristic
272C22×C4C22×D7311yescharacteristic
273C22×C4C22×D7311yescharacteristic
274Q16—2921no—
275Q16—2921no—
276SD16—2921no—
277SD16—2921no—
278M16—2921no—
279C2×C8—2921no—
280C2×C8—731no—
281C2×C8—731no—
282C2×C8—731no—
283C2×C8—731no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—731no—
288C4⋊C4—731no—
289C4⋊C4—1461no—
290C4⋊C4—1461no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
293C4⋊C4C22×D7311yescharacteristic
294C4⋊C4C22×D7311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C42—1461no—
305C23—21no—
306C23C2×C22⋊D7311yescharacteristic
307C23C2×C22⋊D7311yescharacteristic
308C23C2×C22⋊D7311yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—41no—
312Q8—2922no—
313Q8—1461no—
314Q8—1461no—
315Q8—1461no—
316Q8—1461no—
317D4—21no—
318D4—21no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—2922no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4C2×C22⋊D7311yescharacteristic
342C2×C4C2×C22⋊D7311yescharacteristic
343C2×C4C2×C22⋊D7311yescharacteristic
344C2×C4C23×D7311yescharacteristic
345C8—1461no—
346C8—1461no—
347C8—1461no—
348C8—1461no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×C22⋊D7311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2921no—
369C4—2921no—
370C4—2921no—
371C4—2921no—
372C4#1455663611yescharacteristic
373C4#1455663611yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2#1798914611yescharacteristic
379C2#1798939811yescharacteristic
380C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#537×C73C2
socleC22×C73C22×D4
hypercenter#537D73
hypocenterC73#3201
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #17989158C2semidirect
2. #17988925C2semidirect
3. #17988922C2semidirect
4. #17988917C2semidirect
5. #17988908C2semidirect
6. #17988843C2semidirect
7. #17988831C2semidirect
8. #17988826C2semidirect
9. #17988814C2semidirect
10. #17988749C2semidirect
11. #17988749C2semidirect
12. #17988742C2semidirect
13. #17988725C2semidirect
14. #17988554C2semidirect
191. C73#3201semidirect