Finite Group Databasebeta

← #22620788

Subgroups — #22620788

Order 9344.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989168C211yesmaximal, characteristic, complemented
2#17989153C211yesmaximal, characteristic, complemented
3#17988931C211yesmaximal, characteristic, complemented
4#17988913C211yesmaximal, characteristic, complemented
5#17988900C211yesmaximal, characteristic, complemented
6#17988841C211yesmaximal, characteristic, complemented
7#17988832C211yesmaximal, characteristic, complemented
8#17988822C211yesmaximal, characteristic, complemented
9#17988817C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988734C211yesmaximal, characteristic, complemented
12#17988730C211yesmaximal, characteristic, complemented
13#17988722C211yesmaximal, characteristic, complemented
14#17988552C211yesmaximal, characteristic, complemented
15#481×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924028C2211yescharacteristic, complemented
18C2×D4×D73C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924016C2211yescharacteristic
21C2×D584C2211yescharacteristic
22C2×#11924013C2211yescharacteristic
23C2×#11924011C2211yescharacteristic, complemented
24C2×C8×D73C2211yescharacteristic, complemented
25#14556587—21no—
26#14556577—21no—
27#14556571—21no—
28#14556571C2211yescharacteristic
29#14556571C2211yescharacteristic, complemented
30#14556566—21no—
31#14556566C2211yescharacteristic
32#14556566C2211yescharacteristic
33#14556566C2211yescharacteristic, complemented
34#14556565—21no—
35#14556565—21no—
36#14556565C2211yescharacteristic
37#14556562C2211yescharacteristic
38#14556561—21no—
39#14556559—21no—
40#14556549C2211yescharacteristic
41#14556524C2211yescharacteristic, complemented
42#14556524C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556514C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic, complemented
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52#121×C73C2211yescharacteristic
53C2×C4⋊C4×C73C2211yescharacteristic, complemented
54#106×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—41no—
61#11924028—41no—
62#11924028—41no—
63#11924028—41no—
64C2×Dic146D411yescharacteristic
65C2×Dic146C2311yescharacteristic
66C2×D292—21no—
67C2×D292—21no—
68C2×D292—21no—
69C2×D292D411yescharacteristic
70C2×D292C2311yescharacteristic
71C2×D292C2311yescharacteristic
72C2×C22⋊D73—21no—
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C2×C22⋊D73—21no—
76C2×C22⋊D73D411yescharacteristic
77C2×C22⋊D73D411yescharacteristic
78D4×D73—41no—
79D4×D73—41no—
80C2×C4×D73—21no—
81C2×C4×D73C2311yescharacteristic
82C2×C4×D73C2311yescharacteristic
83#11924017—41no—
84#11924016—41no—
85D584—41no—
86#11924013—41no—
87#11924011—41no—
88C2×#10596831C2311yescharacteristic
89C2×#10596831C2311yescharacteristic
90C8×D73—41no—
91C4⋊Dic73—21no—
92C4⋊Dic73—21no—
93C4⋊Dic73C2311yescharacteristic
94C22⋊Dic73—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102C4×Dic73—21no—
103C2×D4×C73—21no—
104C2×D4×C73C2311yescharacteristic
105C22×C4×C73—21no—
106C22×C4×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C4⋊C4×C73—21no—
110C4⋊C4×C73C2311yescharacteristic
111C4⋊C4×C73C2311yescharacteristic
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C23×C73—21no—
115C23×C73C2×D411yescharacteristic
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—42no—
119C22×D73—81no—
120C22×D73—81no—
121C22×D73C2×D411yescharacteristic
122C22×D73C2×D411yescharacteristic
123D4×C73—21no—
124D4×C73—21no—
125D4×C73—81no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—81no—
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2411yescharacteristic
134C22⋊D73—41no—
135C22⋊D73—41no—
136C22⋊D73—42no—
137C22⋊D73—42no—
138C22⋊D73—81no—
139C22⋊D73—81no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73C2×D411yescharacteristic
143C2×Dic73C2×D411yescharacteristic
144D292—21no—
145D292—21no—
146D292—21no—
147D292—21no—
148D292—41no—
149D292—81no—
150D292—81no—
151D292—81no—
152C4×D73—21no—
153C4×D73—21no—
154C4×D73—21no—
155C4×D73—21no—
156C4×D73—42no—
157Dic146—21no—
158Dic146—21no—
159Dic146—41no—
160C8×C73—21no—
161C8×C73—21no—
162#10596831—21no—
163#10596831—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73C22×D411yescharacteristic
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—41no—
178C2×D73—41no—
179C2×D73—41no—
180C2×D73—41no—
181C2×D73—41no—
182C2×D73—41no—
183C2×D73—84no—
184C4×C73—21no—
185C4×C73—41no—
186C4×C73—41no—
187C4×C73—41no—
188C4×C73H(5,𝔽2)11yescharacteristic
189C4×C73H(5,𝔽2)11yescharacteristic
190Dic73—21no—
191Dic73—21no—
192Dic73—41no—
193Dic73—41no—
194C2×C73—41no—
195C2×C73—81no—
196C2×C73#53411yescharacteristic
197C2×C73#57611yescharacteristic
198C2×C73#57711yescharacteristic
199D73—41no—
200D73—41no—
201D73—81no—
202D73—81no—
203#3198—731nomaximal, Sylow
204C73#319811yescharacteristic, complemented, Sylow
205#537—731no—
206#535—731no—
207#485—731no—
208#482—731no—
209#481D7311yescharacteristic, complemented
210#480—731no—
211#469—731no—
212#468—731no—
213#466—731no—
214#465—731no—
215#450—731no—
216#449—731no—
217#449—731no—
218#447—731no—
219#408—731no—
220C2×#41—731no—
221C2×#41—731no—
222C22×D4—731no—
223C2×SD16—731no—
224C2×SD16—731no—
225C2×D8—731no—
226C2×D8—731no—
227C2×M16—731no—
228C22×C8—731no—
229#127—1461no—
230#124—1461no—
231C22⋊Q8—731no—
232C22⋊Q8—731no—
233C22⋊Q8—1461no—
234#121—731no—
235#121—731no—
236#121—731no—
237#121—731no—
238#121—731no—
239#121—1461no—
240#121—1461no—
241#121—1461no—
242#121C2×D7311yescharacteristic
243#120—1461no—
244#120—1461no—
245#117—731no—
246C2×C4⋊C4C2×D7311yescharacteristic, complemented
247#107—731no—
248#107—731no—
249#106C2×D7311yescharacteristic, complemented
250#106C2×D7311yescharacteristic, complemented
251#103—731no—
252#103—731no—
253#102—731no—
254#102—731no—
255#102—731no—
256#102—731no—
257#102C2×D7311yescharacteristic
258#102C2×D7311yescharacteristic
259C22⋊C8—731no—
260C22⋊C8—731no—
261C22⋊C8—731no—
262C22⋊C8C2×D7311yescharacteristic, complemented
263C24—1461no—
264#41—2921no—
265#41—2921no—
266#41—2921no—
267#41—2921no—
268C2×Q8—731no—
269C2×Q8—731no—
270C2×D4—21no—
271C2×D4—2921no—
272C2×D4—2921no—
273C2×D4—731no—
274C2×D4—731no—
275C2×D4—731no—
276C2×D4—731no—
277C2×D4—731no—
278C2×D4—1461no—
279C2×D4—1461no—
280C2×D4—1461no—
281C2×D4—1461no—
282C2×D4—1461no—
283C2×D4—1461no—
284C2×D4—1461no—
285C2×D4C22×D7311yescharacteristic
286C22×C4—21no—
287C22×C4—731no—
288C22×C4—731no—
289C22×C4—1461no—
290C22×C4C22×D7311yescharacteristic
291SD16—2921no—
292SD16—2921no—
293D8—2921no—
294D8—2921no—
295M16—2921no—
296C2×C8—2921no—
297C2×C8—731no—
298C2×C8—731no—
299C2×C8C22×D7311yescharacteristic
300C2×C8C22×D7311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—731no—
303C4⋊C4—1461no—
304C4⋊C4—1461no—
305C4⋊C4C22×D7311yescharacteristic
306C4⋊C4C22×D7311yescharacteristic
307C4⋊C4C22×D7311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—1461no—
310C22⋊C4—1461no—
311C22⋊C4—1461no—
312C22⋊C4—1461no—
313C22⋊C4—1461no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C42—1461no—
318C23—21no—
319C23—2922no—
320C23—5841no—
321C23—5841no—
322C23—731no—
323C23—731no—
324C23—1461no—
325C23—1461no—
326C23D4×D7311yescharacteristic
327Q8—2921no—
328Q8—1461no—
329Q8—1461no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—2921no—
334D4—2922no—
335D4—2921no—
336D4—2921no—
337D4—2922no—
338D4—5841no—
339D4—5841no—
340D4—5841no—
341D4—5841no—
342D4—5841no—
343D4—1461no—
344D4—1461no—
345D4—1461no—
346D4—1461no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—81no—
353C2×C4—2922no—
354C2×C4—731no—
355C2×C4—731no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4—1461no—
362C2×C4D4×D7311yescharacteristic
363C2×C4C23×D7311yescharacteristic
364C8—21no—
365C8—21no—
366C8—1461no—
367C8—1461no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—2921no—
375C22—2921no—
376C22—2921no—
377C22—2921no—
378C22—2921no—
379C22—2921no—
380C22—5844no—
381C22—1461no—
382C22—1461no—
383C22—1461no—
384C22—1461no—
385C22—1461no—
386C22—1461no—
387C22C2×D4×D7311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—2921no—
393C4—2921no—
394C4—1461no—
395C4—1461no—
396C4#1455663711yescharacteristic
397C4#1455663711yescharacteristic
398C2—41no—
399C2—81no—
400C2—2921no—
401C2—2921no—
402C2—5841no—
403C2—5841no—
404C2#1798914811yescharacteristic
405C2#1798939111yescharacteristic
406C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#481×C73C2
socleC22×C73C22×D4
hypercenter#481D73
hypocenterC73#3198
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #17989168C2semidirect
2. #17989153C2semidirect
3. #17988931C2semidirect
4. #17988913C2semidirect
5. #17988900C2semidirect
6. #17988841C2semidirect
7. #17988832C2semidirect
8. #17988822C2semidirect
9. #17988817C2semidirect
10. #17988739C2semidirect
11. #17988734C2semidirect
12. #17988730C2semidirect
13. #17988722C2semidirect
14. #17988552C2semidirect
15. #481×C73C2semidirect
17. C2×#11924028C22semidirect
23. C2×#11924011C22semidirect
24. C2×C8×D73C22semidirect
29. #14556571C22semidirect
33. #14556566C22semidirect
41. #14556524C22semidirect
42. #14556524C22semidirect
43. #14556516C22semidirect
44. #14556514C22semidirect
45. #14556513C22semidirect
48. #14556511C22semidirect
49. C22⋊#10596831C22semidirect
53. C2×C4⋊C4×C73C22semidirect
54. #106×C73C22semidirect
55. #106×C73C22semidirect
58. C22⋊C8×C73C22semidirect
204. C73#3198semidirect
209. #481D73semidirect
246. C2×C4⋊C4C2×D73semidirect
249. #106C2×D73semidirect
250. #106C2×D73semidirect
262. C22⋊C8C2×D73semidirect