Finite Group Databasebeta

← #22621877

Subgroups — #22621877

Order 9344.

408 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#17989300C211yesmaximal, characteristic, complemented
2#17989256C211yesmaximal, characteristic, complemented
3#17988932C211yesmaximal, characteristic, complemented
4#17988911C211yesmaximal, characteristic, complemented
5#17988909C211yesmaximal, characteristic, complemented
6#17988880C211yesmaximal, characteristic, complemented
7#17988823C211yesmaximal, characteristic, complemented
8#17988822C211yesmaximal, characteristic, complemented
9#17988781C211yesmaximal, characteristic, complemented
10#17988735C211yesmaximal, characteristic, complemented
11#17988732C211yesmaximal, characteristic, complemented
12#17988672C211yesmaximal, characteristic, complemented
13C8×C22⋊D73C211yesmaximal, characteristic, complemented
14#17988582C211yesmaximal, characteristic, complemented
15#416×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18C2×D584C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×C8×D73C2211yescharacteristic
21#14556590C2211yescharacteristic
22#14556587—21no—
23#14556587C2211yescharacteristic
24#14556579—21no—
25#14556577—21no—
26#14556566C2211yescharacteristic
27#14556565—21no—
28#14556565C2211yescharacteristic
29#14556565C2211yescharacteristic
30#14556564—21no—
31#14556562—21no—
32#14556562C2211yescharacteristic
33Q8×Dic73C2211yescharacteristic
34#14556553C2211yescharacteristic
35C4×C22⋊D73—21no—
36C4×C22⋊D73C2211yescharacteristic
37#14556549C2211yescharacteristic
38#14556548—21no—
39#14556525C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556515C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556512C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54#117×C73C2211yescharacteristic
55#103×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924029—22no—
60#11924029—41no—
61C2×Dic146—21no—
62C2×D292—21no—
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73D411yescharacteristic
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73C2311yescharacteristic
75#11924015—22no—
76D584—41no—
77#11924013—41no—
78C2×#10596831C2311yescharacteristic
79C2×#10596831C2311yescharacteristic
80C8×D73—41no—
81C4⋊Dic73—21no—
82C4⋊Dic73C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007D411yescharacteristic
86C22⋊Dic73—21no—
87C22⋊Dic73D411yescharacteristic
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005D411yescharacteristic
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97#41×C73—22no—
98#41×C73—41no—
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73C2311yescharacteristic
104C2×C8×C73—41no—
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C42×C73—21no—
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73—21no—
115C22×D73C2×D411yescharacteristic
116Q8×C73—21no—
117Q8×C73#4112yes—
118D4×C73—21no—
119D4×C73—21no—
120D4×C73—42no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—42no—
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C22⋊D73—22no—
130C22⋊D73—42no—
131C22⋊D73—81no—
132C22⋊D73—81no—
133C22⋊D73—81no—
134C22⋊D73—81no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73C2×D411yescharacteristic
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140D292—21no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—42no—
145D292—81no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—42no—
149C4×D73—42no—
150Dic146—81no—
151C8×C73—21no—
152C8×C73—21no—
153#10596831—21no—
154#10596831—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73C22×D411yescharacteristic
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—21no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C4×C73—22no—
172C4×C73—21no—
173C4×C73—41no—
174C4×C73—41no—
175C4×C73C2×#4111yescharacteristic
176C4×C73H(5,𝔽2)11yescharacteristic
177Dic73—21no—
178Dic73—21no—
179Dic73—41no—
180Dic73—41no—
181Dic73#13512yes—
182C2×C73—41no—
183C2×C73—81no—
184C2×C73#54611yescharacteristic
185C2×C73C2×#13511yescharacteristic
186C2×C73#57611yescharacteristic
187D73—41no—
188D73—81no—
189D73—81no—
190#3305—731nomaximal, Sylow
191C73#330511yescharacteristic, complemented, Sylow
192#555—731no—
193#550—731no—
194#486—731no—
195#482—731no—
196#482—731no—
197#477—731no—
198#466—731no—
199#466—731no—
200#459—731no—
201#449—731no—
202#449—731no—
203C4×SD16—731no—
204C8×D4—731no—
205#416—731no—
206#416D7311yescharacteristic, complemented
207C2×#41—731no—
208C2×#41C2×D7311yescharacteristic
209C2×SD16—731no—
210C2×D8—731no—
211C2×D8—731no—
212C22×C8—731no—
213C22×C8C2×D7311yescharacteristic
214C4⋊Q8—731no—
215#127—731no—
216#127—1461no—
217#124—1461no—
218#124—1461no—
219#121—731no—
220#121—731no—
221#121—731no—
222#121—731no—
223#121—1461no—
224#121—1461no—
225#121—1461no—
226C4×Q8—731no—
227C4×D4—731no—
228C4×D4—731no—
229C4×D4—1461no—
230#117—731no—
231#117—1461no—
232#117C2×D7311yescharacteristic
233#107—731no—
234#107—731no—
235#106—731no—
236C4⋊C8—731no—
237#103—731no—
238#103C2×D7311yescharacteristic
239#103C2×D7311yescharacteristic
240#102—731no—
241#102—731no—
242#102—731no—
243#102—731no—
244#102—731no—
245#102C2×D7311yescharacteristic
246#102C2×D7311yescharacteristic
247C22⋊C8—731no—
248C22⋊C8—731no—
249C4×C8—731no—
250#41—22no—
251#41—41no—
252#41—2921no—
253#41—1462no—
254C2×Q8—1461no—
255C2×Q8C22×D7311yescharacteristic
256C2×D4—21no—
257C2×D4—731no—
258C2×D4—731no—
259C2×D4—731no—
260C2×D4—1461no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4—1461no—
266C2×D4—1461no—
267C2×D4C22×D7311yescharacteristic
268C22×C4—21no—
269C22×C4—731no—
270C22×C4—1461no—
271C22×C4—1461no—
272C22×C4C22×D7311yescharacteristic
273SD16—1462no—
274D8—2921no—
275D8—2921no—
276C2×C8—41no—
277C2×C8—2921no—
278C2×C8—731no—
279C2×C8—731no—
280C2×C8C22×D7311yescharacteristic
281C2×C8C22×D7311yescharacteristic
282C4⋊C4—731no—
283C4⋊C4—731no—
284C4⋊C4—731no—
285C4⋊C4—1461no—
286C4⋊C4—1461no—
287C4⋊C4C22×D7311yescharacteristic
288C4⋊C4C22×D7311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—731no—
291C22⋊C4—731no—
292C22⋊C4—1461no—
293C22⋊C4—1461no—
294C22⋊C4—1461no—
295C22⋊C4—1461no—
296C22⋊C4—1461no—
297C22⋊C4—1461no—
298C42—21no—
299C42—731no—
300C42—1461no—
301C42—1461no—
302C23—21no—
303C23—731no—
304C23—1461no—
305C23—1461no—
306C23D4×D7311yescharacteristic
307Q8—21no—
308Q8—5841no—
309Q8#1192402812yes—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—2922no—
314D4—2922no—
315D4—5841no—
316D4—5841no—
317D4—5841no—
318D4—5841no—
319D4—5841no—
320D4—1462no—
321D4—1461no—
322D4—1461no—
323D4—1461no—
324D4—1461no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—2922no—
332C2×C4—2922no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—1461no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4D4×D7311yescharacteristic
341C2×C4C23×D7311yescharacteristic
342C8—21no—
343C8—21no—
344C8—1461no—
345C8—1461no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—2921no—
353C22—2921no—
354C22—2921no—
355C22—2921no—
356C22—2921no—
357C22—2921no—
358C22—1461no—
359C22—1461no—
360C22—1461no—
361C22C2×D4×D7311yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—2921no—
367C4—2921no—
368C4—732no—
369C4—1461no—
370C4—1461no—
371C4C2×#1192402811yescharacteristic
372C4#1455663611yescharacteristic
373C2—41no—
374C2—81no—
375C2—2921no—
376C2—5841no—
377C2—5841no—
378C2#1798922711yescharacteristic
379C2#135×D7311yescharacteristic
380C2#1798938911yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#416×C73C2
socleC22×C73C22×D4
hypercenter#416D73
hypocenterC73#3305
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #17989300C2semidirect
2. #17989256C2semidirect
3. #17988932C2semidirect
4. #17988911C2semidirect
5. #17988909C2semidirect
6. #17988880C2semidirect
7. #17988823C2semidirect
8. #17988822C2semidirect
9. #17988781C2semidirect
10. #17988735C2semidirect
11. #17988732C2semidirect
12. #17988672C2semidirect
13. C8×C22⋊D73C2semidirect
14. #17988582C2semidirect
15. #416×C73C2semidirect
191. C73#3305semidirect
206. #416D73semidirect