Finite Group Databasebeta

← #22621528

Subgroups — #22621528

Order 9344.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556619C211yesmaximal, characteristic, complemented
2C2×#14556618C211yesmaximal, characteristic, complemented
3#17989239C211yesmaximal, characteristic, complemented
4#17989221C211yesmaximal, characteristic, complemented
5#17988958C211yesmaximal, characteristic, complemented
6#17988834C211yesmaximal, characteristic, complemented
7#17988791C211yesmaximal, characteristic, complemented
8#17988781C211yesmaximal, characteristic, complemented
9#17988739C211yesmaximal, characteristic, complemented
10#17988737C211yesmaximal, characteristic, complemented
11#17988735C211yesmaximal, characteristic, complemented
12#17988730C211yesmaximal, characteristic, complemented
13#17988669C211yesmaximal, characteristic, complemented
14#17988663C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic, complemented
17C2×#11924028C2211yescharacteristic, complemented
18C22×D292C2211yescharacteristic
19C2×D4×D73—21no—
20C2×D4×D73C2211yescharacteristic
21#14556619—24no—
22#14556618—24no—
23C2×#11924017C2211yescharacteristic
24C2×#11924017C2211yescharacteristic, complemented
25C2×#11924016C2211yescharacteristic, complemented
26C2×#11924015C2211yescharacteristic
27C2×#11924015C2211yescharacteristic, complemented
28C2×D584C2211yescharacteristic
29C2×D584C2211yescharacteristic, complemented
30C2×#11924013C2211yescharacteristic, complemented
31C2×#11924011C2211yescharacteristic, complemented
32#14556589C2211yescharacteristic, complemented
33#14556587C2211yescharacteristic
34#14556576—21no—
35#14556573—21no—
36#14556571C2211yescharacteristic, complemented
37#14556566C2211yescharacteristic
38#14556564—21no—
39#14556564—21no—
40#14556561—21no—
41#14556559—21no—
42#14556553C2211yescharacteristic
43#14556553C2211yescharacteristic, complemented
44C4×C22⋊D73C2211yescharacteristic
45C4⋊C4×D73—21no—
46#14556520C2211yescharacteristic, complemented
47#14556514C2211yescharacteristic, complemented
48#14556511C2211yescharacteristic
49#14556511C2211yescharacteristic, complemented
50#14556511C2211yescharacteristic, complemented
51C22⋊#10596831C2211yescharacteristic, complemented
52#14556503C2211yescharacteristic, complemented
53C8×Dic73C2211yescharacteristic, complemented
54C2×SD16×C73C2211yescharacteristic, complemented
55C2×M16×C73C2211yescharacteristic, complemented
56C22⋊Q8×C73C2211yescharacteristic, complemented
57#121×C73C2211yescharacteristic
58#107×C73C2211yescharacteristic, complemented
59#103×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62C23×D73—21no—
63#11924029—22no—
64#11924029—41no—
65#11924028—22no—
66#11924028—41no—
67C2×Dic146C2311yescharacteristic
68C2×D292—22no—
69C2×D292—21no—
70C2×D292—21no—
71C2×D292—21no—
72C2×D292—41no—
73C2×D292C2311yescharacteristic
74C2×D292C2311yescharacteristic
75C2×D292C2311yescharacteristic
76C2×C22⋊D73—21no—
77C2×C22⋊D73—21no—
78C2×C22⋊D73—21no—
79C2×C22⋊D73—21no—
80C2×C22⋊D73D411yescharacteristic
81D4×D73—22no—
82D4×D73—41no—
83D4×D73—44no—
84C2×C4×D73—21no—
85C2×C4×D73—21no—
86C2×C4×D73—21no—
87C2×C4×D73—21no—
88C2×C4×D73C2311yescharacteristic
89#11924017—22no—
90#11924017—22no—
91#11924016—41no—
92#11924015—22no—
93#11924015—41no—
94D584—22no—
95D584D414yescomplemented
96#11924013—22no—
97#11924011—22no—
98C2×#10596831C2311yescharacteristic
99C2×#10596831C2311yescharacteristic
100C4⋊Dic73—21no—
101#11924007—21no—
102#11924007—21no—
103#11924007D411yescharacteristic
104C22⋊Dic73D411yescharacteristic
105#11924005—21no—
106#11924005—21no—
107#11924005—21no—
108#11924005—21no—
109#11924005D411yescharacteristic
110C4×Dic73C2311yescharacteristic
111C2×Q8×C73C2311yescharacteristic
112C2×D4×C73—21no—
113C2×D4×C73C2311yescharacteristic
114C22×C4×C73C2311yescharacteristic
115SD16×C73—22no—
116M16×C73—22no—
117C2×C8×C73C2311yescharacteristic
118C2×C8×C73C2311yescharacteristic
119C4⋊C4×C73—21no—
120C4⋊C4×C73C2311yescharacteristic
121C4⋊C4×C73C2311yescharacteristic
122C22⋊C4×C73—21no—
123C22⋊C4×C73—21no—
124C23×C73—21no—
125C23×C73C2×D411yescharacteristic
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—21no—
129C22×D73—42no—
130C22×D73—42no—
131C22×D73—42no—
132C22×D73—42no—
133C22×D73—81no—
134C22×D73—81no—
135C22×D73C2×D411yescharacteristic
136Q8×C73—21no—
137Q8×C73—21no—
138D4×C73—21no—
139D4×C73—21no—
140D4×C73—42no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73C2×D411yescharacteristic
147C2×C4×C73C2411yescharacteristic
148C22⋊D73—22no—
149C22⋊D73—42no—
150C22⋊D73—42no—
151C22⋊D73—42no—
152C22⋊D73—81no—
153C2×Dic73—21no—
154C2×Dic73C2×D411yescharacteristic
155C2×Dic73C2×D411yescharacteristic
156C2×Dic73C2×D411yescharacteristic
157D292—21no—
158D292—21no—
159D292—21no—
160D292—21no—
161D292—42no—
162D292—42no—
163D292—42no—
164D292C2×D412yes—
165D292C2×D412yescomplemented
166C4×D73—21no—
167C4×D73—21no—
168C4×D73—42no—
169C4×D73—42no—
170C4×D73—42no—
171C4×D73—42no—
172Dic146—21no—
173Dic146—21no—
174C8×C73—21no—
175C8×C73C2×D412yescomplemented
176#10596831—21no—
177#10596831—21no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—41no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73C22×D411yescharacteristic
185C2×D73—21no—
186C2×D73—22no—
187C2×D73—22no—
188C2×D73—21no—
189C2×D73—21no—
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C2×D73—41no—
196C2×D73—41no—
197C2×D73—84no—
198C2×D73—84no—
199C4×C73—21no—
200C4×C73—41no—
201C4×C73—41no—
202C4×C73—41no—
203C4×C73C22×D411yescharacteristic
204C4×C73H(5,𝔽2)11yescharacteristic
205Dic73—21no—
206Dic73—21no—
207Dic73—41no—
208Dic73AGL(1,ℤ/8)12yescomplemented
209C2×C73—41no—
210C2×C73—81no—
211C2×C73D4211yescharacteristic
212C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C73#57711yescharacteristic
214D73—41no—
215D73—42no—
216D73—42no—
217D73—81no—
218#3272—731nomaximal, Sylow
219C73#327211yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—731no—
221C2×AGL(1,ℤ/8)—731no—
222#547—731no—
223D42—731no—
224#492—731no—
225#468—731no—
226#468D7311yescharacteristic, complemented
227#461—731no—
228#459—731no—
229#450—731no—
230#450—731no—
231#449—731no—
232#449—731no—
233C4×D8—731no—
234#436—731no—
235C2×#41—731no—
236C2×#41—731no—
237C22×D4—731no—
238C22×D4—731no—
239C22×D4—1461no—
240AGL(1,ℤ/8)—1464no—
241AGL(1,ℤ/8)—1464no—
242C2×SD16—731no—
243C2×SD16—731no—
244C2×SD16—731no—
245C2×SD16—731no—
246C2×SD16—731no—
247C2×SD16C2×D7311yescharacteristic, complemented
248C2×D8—731no—
249C2×D8—731no—
250C2×D8—731no—
251C2×M16—731no—
252C2×M16C2×D7311yescharacteristic, complemented
253C4⋊Q8—731no—
254#127—731no—
255#123—1461no—
256#123—1461no—
257C22⋊Q8—731no—
258C22⋊Q8C2×D7311yescharacteristic, complemented
259#121—731no—
260#121—1461no—
261#121—1461no—
262#121C2×D7311yescharacteristic
263#120—1461no—
264#120—1461no—
265C4×D4—731no—
266C4×D4—731no—
267C4×D4—731no—
268C2×C4⋊C4—1461no—
269#107C2×D7311yescharacteristic, complemented
270C4⋊C8—731no—
271#103—731no—
272#103C2×D7311yescharacteristic, complemented
273#102—731no—
274#102—731no—
275#102—731no—
276#102C2×D7311yescharacteristic, complemented
277C22⋊C8—731no—
278C22⋊C8—731no—
279C4×C8—731no—
280C24—1461no—
281C24—1461no—
282#41—2921no—
283#41—2921no—
284#41—1462no—
285#41—1462no—
286C2×Q8—731no—
287C2×Q8C22×D7311yescharacteristic
288C2×D4—21no—
289C2×D4—2921no—
290C2×D4—2924no—
291C2×D4—2921no—
292C2×D4—731no—
293C2×D4—731no—
294C2×D4—731no—
295C2×D4—731no—
296C2×D4—1461no—
297C2×D4—1461no—
298C2×D4—1462no—
299C2×D4—1461no—
300C2×D4—1461no—
301C2×D4—1461no—
302C2×D4—1462no—
303C2×D4—1461no—
304C2×D4—1461no—
305C2×D4C22×D7311yescharacteristic
306C22×C4—731no—
307C22×C4—1461no—
308C22×C4—1461no—
309C22×C4—1461no—
310C22×C4—1461no—
311C22×C4C22×D7311yescharacteristic
312SD16—22no—
313SD16—2921no—
314SD16—2921no—
315SD16—1462no—
316SD16—1462no—
317SD16—1462no—
318D8—734no—
319D8—1462no—
320D8—1462no—
321M16—22no—
322M16—1462no—
323C2×C8—731no—
324C2×C8—731no—
325C2×C8C22×D7311yescharacteristic
326C2×C8C22×D7311yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—731no—
329C4⋊C4—1461no—
330C4⋊C4—1461no—
331C4⋊C4—1461no—
332C4⋊C4C22×D7311yescharacteristic
333C4⋊C4C22×D7311yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—731no—
337C22⋊C4—731no—
338C22⋊C4—1461no—
339C22⋊C4—1461no—
340C22⋊C4—1461no—
341C22⋊C4—1461no—
342C42—731no—
343C23—21no—
344C23—2922no—
345C23—2922no—
346C23—2922no—
347C23—2922no—
348C23—5841no—
349C23—5841no—
350C23—731no—
351C23—1461no—
352C23—1461no—
353C23—1461no—
354C23D4×D7311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—1461no—
358Q8—1461no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—2922no—
363D4—2922no—
364D4—2922no—
365D4—2922no—
366D4—2922no—
367D4—2922no—
368D4—5841no—
369D4—732no—
370D4—732no—
371D4—1462no—
372D4—1461no—
373D4—1461no—
374D4—1461no—
375D4—1461no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—2922no—
382C2×C4—2922no—
383C2×C4—2922no—
384C2×C4—2922no—
385C2×C4—731no—
386C2×C4—731no—
387C2×C4—731no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4D4×D7311yescharacteristic
392C2×C4C23×D7311yescharacteristic
393C8—21no—
394C8—1461no—
395C8—1461no—
396C8D4×D7312yescomplemented
397C22—21no—
398C22—21no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—2921no—
404C22—2921no—
405C22—2921no—
406C22—2921no—
407C22—2921no—
408C22—2921no—
409C22—2921no—
410C22—5844no—
411C22—5844no—
412C22—1461no—
413C22—1462no—
414C22—1461no—
415C22—1462no—
416C22—1461no—
417C22C2×D4×D7311yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—2921no—
423C4—732no—
424C4—1461no—
425C4—1461no—
426C4C2×D4×D7311yescharacteristic
427C4#1455663711yescharacteristic
428C2—41no—
429C2—81no—
430C2—2922no—
431C2—2922no—
432C2—2921no—
433C2—5841no—
434C2#1798922111yescharacteristic
435C2AGL(1,ℤ/8)×D7311yescharacteristic
436C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3272
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14556619C2semidirect
2. C2×#14556618C2semidirect
3. #17989239C2semidirect
4. #17989221C2semidirect
5. #17988958C2semidirect
6. #17988834C2semidirect
7. #17988791C2semidirect
8. #17988781C2semidirect
9. #17988739C2semidirect
10. #17988737C2semidirect
11. #17988735C2semidirect
12. #17988730C2semidirect
13. #17988669C2semidirect
14. #17988663C2semidirect
15. #468×C73C2semidirect
16. C2×#11924029C22semidirect
17. C2×#11924028C22semidirect
24. C2×#11924017C22semidirect
25. C2×#11924016C22semidirect
27. C2×#11924015C22semidirect
29. C2×D584C22semidirect
30. C2×#11924013C22semidirect
31. C2×#11924011C22semidirect
32. #14556589C22semidirect
36. #14556571C22semidirect
43. #14556553C22semidirect
46. #14556520C22semidirect
47. #14556514C22semidirect
49. #14556511C22semidirect
50. #14556511C22semidirect
51. C22⋊#10596831C22semidirect
52. #14556503C22semidirect
53. C8×Dic73C22semidirect
54. C2×SD16×C73C22semidirect
55. C2×M16×C73C22semidirect
56. C22⋊Q8×C73C22semidirect
58. #107×C73C22semidirect
59. #103×C73C22semidirect
60. #102×C73C22semidirect
95. D584D4semidirect
165. D292C2×D4semidirect
175. C8×C73C2×D4semidirect
208. Dic73AGL(1,ℤ/8)semidirect
219. C73#3272semidirect
226. #468D73semidirect
247. C2×SD16C2×D73semidirect
252. C2×M16C2×D73semidirect
258. C22⋊Q8C2×D73semidirect
269. #107C2×D73semidirect
272. #103C2×D73semidirect
276. #102C2×D73semidirect
396. C8D4×D73semidirect