Finite Group Databasebeta

← #22621432

Subgroups — #22621432

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×#14556615C211yesmaximal, characteristic, complemented
2C2×SD16×D73C211yesmaximal, characteristic, complemented
3#17989245C211yesmaximal, characteristic, complemented
4D4×D292C211yesmaximal, characteristic, complemented
5#17988977C211yesmaximal, characteristic, complemented
6#17988836C211yesmaximal, characteristic, complemented
7#17988822C211yesmaximal, characteristic, complemented
8#17988788C211yesmaximal, characteristic, complemented
9#17988736C211yesmaximal, characteristic, complemented
10#17988733C211yesmaximal, characteristic, complemented
11#17988727C211yesmaximal, characteristic, complemented
12#17988719C211yesmaximal, characteristic, complemented
13#17988687C211yesmaximal, characteristic, complemented
14#17988657C211yesmaximal, characteristic, complemented
15#463×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic, complemented
17C2×Q8×D73C2211yescharacteristic, complemented
18C22×D292—21no—
19C2×D4×D73C2211yescharacteristic
20C2×D4×D73C2211yescharacteristic
21#14556615—24no—
22C2×#11924017C2211yescharacteristic, complemented
23C2×#11924017C2211yescharacteristic, complemented
24C2×#11924016C2211yescharacteristic
25C2×#11924015C2211yescharacteristic, complemented
26C2×#11924015C2211yescharacteristic, complemented
27SD16×D73—24no—
28C2×#11924013C2211yescharacteristic, complemented
29C2×#11924013C2211yescharacteristic, complemented
30C2×#11924011C2211yescharacteristic, complemented
31C2×C8×D73C2211yescharacteristic, complemented
32#14556588C2211yescharacteristic
33#14556577—21no—
34#14556568—21no—
35#14556567C2211yescharacteristic, complemented
36#14556566C2211yescharacteristic
37#14556566C2211yescharacteristic
38#14556565—21no—
39#14556564—21no—
40#14556562C2211yescharacteristic, complemented
41#14556561—21no—
42#14556561—21no—
43C4×Dic146C2211yescharacteristic, complemented
44C4×D292C2211yescharacteristic
45#14556551—21no—
46#14556524C2211yescharacteristic, complemented
47#14556514C2211yescharacteristic, complemented
48#14556513C2211yescharacteristic, complemented
49#14556513C2211yescharacteristic, complemented
50#14556512C2211yescharacteristic
51#14556503C2211yescharacteristic, complemented
52#14556503C2211yescharacteristic, complemented
53#14556502C2211yescharacteristic, complemented
54C2×SD16×C73C2211yescharacteristic
55C2×D8×C73C2211yescharacteristic
56#124×C73C2211yescharacteristic, complemented
57C4×D4×C73C2211yescharacteristic
58C4⋊C8×C73C2211yescharacteristic, complemented
59#103×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62C23×D73—21no—
63#11924027—22no—
64#11924027—41no—
65C2×Dic146—21no—
66C2×Dic146C2311yescharacteristic
67Q8×D73—22no—
68Q8×D73—41no—
69C2×D292—21no—
70C2×D292—21no—
71C2×D292—21no—
72C2×D292—21no—
73C2×D292—44no—
74C2×D292D411yescharacteristic
75C2×D292C2311yescharacteristic
76C2×D292C2311yescharacteristic
77C2×C22⋊D73—21no—
78C2×C22⋊D73—21no—
79C2×C22⋊D73—21no—
80C2×C22⋊D73—21no—
81D4×D73—22no—
82D4×D73—22no—
83D4×D73—41no—
84D4×D73—41no—
85C22×Dic73—21no—
86C2×C4×D73—21no—
87C2×C4×D73C2311yescharacteristic
88C2×C4×D73C2311yescharacteristic
89#11924017—22no—
90#11924017—22no—
91#11924016D414yescomplemented
92#11924015—22no—
93#11924015—41no—
94#11924013—22no—
95#11924013—41no—
96#11924011—22no—
97C2×#10596831C2311yescharacteristic
98C2×#10596831C2311yescharacteristic
99C8×D73—22no—
100C4⋊Dic73D411yescharacteristic
101C4⋊Dic73C2311yescharacteristic
102#11924007—21no—
103#11924007—21no—
104C22⋊Dic73—21no—
105#11924005—21no—
106#11924005—21no—
107#11924005—21no—
108#11924005D411yescharacteristic
109#11924005D411yescharacteristic
110C4×Dic73—21no—
111C2×Q8×C73C2311yescharacteristic
112C2×D4×C73C2311yescharacteristic
113C2×D4×C73C2311yescharacteristic
114C22×C4×C73—21no—
115SD16×C73—22no—
116D8×C73—22no—
117C2×C8×C73C2311yescharacteristic
118C2×C8×C73C2311yescharacteristic
119C4⋊C4×C73C2311yescharacteristic
120C22⋊C4×C73—21no—
121C22⋊C4×C73—21no—
122C22⋊C4×C73—21no—
123C42×C73C2311yescharacteristic
124C23×C73—21no—
125C23×C73—21no—
126C22×D73—21no—
127C22×D73—21no—
128C22×D73—42no—
129C22×D73—42no—
130C22×D73—42no—
131C22×D73—42no—
132C22×D73—81no—
133C22×D73—81no—
134C22×D73C2×D411yescharacteristic
135C22×D73C2×D411yescharacteristic
136Q8×C73—21no—
137Q8×C73—21no—
138D4×C73—21no—
139D4×C73—21no—
140D4×C73—21no—
141D4×C73C2×D412yes—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—42no—
145C2×C4×C73C2×D411yescharacteristic
146C2×C4×C73C2×D411yescharacteristic
147C2×C4×C73C2411yescharacteristic
148C22⋊D73—42no—
149C22⋊D73—42no—
150C22⋊D73—42no—
151C22⋊D73—42no—
152C2×Dic73—21no—
153C2×Dic73—21no—
154C2×Dic73—42no—
155C2×Dic73C2×D411yescharacteristic
156C2×Dic73C2×D411yescharacteristic
157D292—22no—
158D292—21no—
159D292—21no—
160D292—21no—
161D292—21no—
162D292—42no—
163D292—42no—
164D292—42no—
165D292—81no—
166C4×D73—21no—
167C4×D73—21no—
168C4×D73—21no—
169C4×D73—21no—
170C4×D73—42no—
171Dic146—21no—
172Dic146—42no—
173Dic146C2×D412yescomplemented
174C8×C73—21no—
175C8×C73—21no—
176#10596831—21no—
177#10596831C2×D412yescomplemented
178C22×C73—22no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73—41no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73C22×D411yescharacteristic
185C2×D73—21no—
186C2×D73—21no—
187C2×D73—21no—
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—84no—
197C2×D73—84no—
198C2×D73AGL(1,ℤ/8)12yescomplemented
199C4×C73—21no—
200C4×C73—21no—
201C4×C73—41no—
202C4×C73—41no—
203C4×C73C22×D411yescharacteristic
204C4×C73H(5,𝔽2)11yescharacteristic
205Dic73—22no—
206Dic73—21no—
207Dic73—21no—
208Dic73—41no—
209C2×C73—42no—
210C2×C73—81no—
211C2×C73D4211yescharacteristic
212C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C73#57711yescharacteristic
214D73—22no—
215D73—41no—
216D73—81no—
217D73—81no—
218#3265—731nomaximal, Sylow
219C73#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—731no—
221C22×SD16—731no—
222#548—731no—
223D42—731no—
224#496—731no—
225#468—731no—
226#466—731no—
227#463D7311yescharacteristic, complemented
228#460—731no—
229#450—731no—
230#449—731no—
231#448—731no—
232#447—731no—
233#440—731no—
234#435—731no—
235C2×#41—731no—
236C22×Q8—731no—
237C22×D4—731no—
238C22×D4—731no—
239C22×D4—1461no—
240AGL(1,ℤ/8)—1464no—
241C2×SD16—731no—
242C2×SD16—731no—
243C2×SD16—731no—
244C2×SD16—731no—
245C2×SD16—731no—
246C2×SD16—1464no—
247C2×SD16C2×D7311yescharacteristic
248C2×D8—731no—
249C2×D8—731no—
250C2×D8C2×D7311yescharacteristic
251C2×M16—731no—
252C22×C8—731no—
253#127—731no—
254#124—1461no—
255#124C2×D7311yescharacteristic, complemented
256C22⋊Q8—731no—
257C22⋊Q8—1461no—
258#121—731no—
259#121—731no—
260#121—731no—
261#121—1461no—
262#121—1461no—
263#120—1461no—
264#120—1461no—
265C4×Q8—731no—
266C4×D4—731no—
267C4×D4—1461no—
268C4×D4C2×D7311yescharacteristic
269#107—731no—
270C4⋊C8C2×D7311yescharacteristic, complemented
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—
279#97—731no—
280C24—1461no—
281C24—1461no—
282#41—2921no—
283#41—1462no—
284C2×Q8—2921no—
285C2×Q8—731no—
286C2×Q8—1461no—
287C2×Q8—1462no—
288C2×Q8C22×D7311yescharacteristic
289C2×D4—2924no—
290C2×D4—2921no—
291C2×D4—2921no—
292C2×D4—731no—
293C2×D4—731no—
294C2×D4—731no—
295C2×D4—1461no—
296C2×D4—1461no—
297C2×D4—1461no—
298C2×D4—1461no—
299C2×D4—1461no—
300C2×D4—1461no—
301C2×D4—1462no—
302C2×D4—1462no—
303C2×D4—1461no—
304C2×D4—1461no—
305C2×D4C22×D7311yescharacteristic
306C2×D4C22×D7311yescharacteristic
307C22×C4—21no—
308C22×C4—731no—
309C22×C4—731no—
310C22×C4—1461no—
311C22×C4—1461no—
312SD16—22no—
313SD16—2921no—
314SD16—734no—
315SD16—1462no—
316SD16—1462no—
317SD16—1462no—
318D8—22no—
319D8—2921no—
320D8—1462no—
321M16—1462no—
322C2×C8—731no—
323C2×C8—731no—
324C2×C8—1462no—
325C2×C8C22×D7311yescharacteristic
326C2×C8C22×D7311yescharacteristic
327C4⋊C4—731no—
328C4⋊C4—731no—
329C4⋊C4—1461no—
330C4⋊C4—1461no—
331C4⋊C4C22×D7311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—731no—
336C22⋊C4—731no—
337C22⋊C4—1461no—
338C22⋊C4—1461no—
339C22⋊C4—1461no—
340C22⋊C4—1461no—
341C42—1461no—
342C42C22×D7311yescharacteristic
343C23—21no—
344C23—21no—
345C23—2922no—
346C23—2922no—
347C23—2922no—
348C23—2922no—
349C23—5841no—
350C23—5841no—
351C23—731no—
352C23—731no—
353C23—1461no—
354C23—1461no—
355Q8—21no—
356Q8—21no—
357Q8—2922no—
358Q8—732no—
359Q8—1461no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—2922no—
364D4—2922no—
365D4—2922no—
366D4—2922no—
367D4—2922no—
368D4—2922no—
369D4—2922no—
370D4—5841no—
371D4—1462no—
372D4—1461no—
373D4—1461no—
374D4—1461no—
375D4—1461no—
376D4D4×D7312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—2922no—
381C2×C4—2922no—
382C2×C4—731no—
383C2×C4—731no—
384C2×C4—1461no—
385C2×C4—1461no—
386C2×C4—1461no—
387C2×C4—1461no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4D4×D7311yescharacteristic
391C2×C4D4×D7311yescharacteristic
392C2×C4C23×D7311yescharacteristic
393C8—21no—
394C8—21no—
395C8—732no—
396C8—1461no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—2921no—
404C22—2921no—
405C22—2921no—
406C22—2921no—
407C22—2921no—
408C22—2921no—
409C22—5844no—
410C22—5844no—
411C22—732no—
412C22—1461no—
413C22—1461no—
414C22—1461no—
415C22—1461no—
416C22—1461no—
417C22C2×D4×D7311yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—2921no—
423C4—1461no—
424C4—1462no—
425C4—1461no—
426C4C2×D4×D7311yescharacteristic
427C4#1455663711yescharacteristic
428C2—42no—
429C2—81no—
430C2—2921no—
431C2—5841no—
432C2—5841no—
433C2—1462no—
434C2#1798922111yescharacteristic
435C2AGL(1,ℤ/8)×D7311yescharacteristic
436C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#463×C73C2
socleC22×C73C22×D4
hypercenter#463D73
hypocenterC73#3265
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14556615C2semidirect
2. C2×SD16×D73C2semidirect
3. #17989245C2semidirect
4. D4×D292C2semidirect
5. #17988977C2semidirect
6. #17988836C2semidirect
7. #17988822C2semidirect
8. #17988788C2semidirect
9. #17988736C2semidirect
10. #17988733C2semidirect
11. #17988727C2semidirect
12. #17988719C2semidirect
13. #17988687C2semidirect
14. #17988657C2semidirect
15. #463×C73C2semidirect
16. C2×#11924027C22semidirect
17. C2×Q8×D73C22semidirect
22. C2×#11924017C22semidirect
23. C2×#11924017C22semidirect
25. C2×#11924015C22semidirect
26. C2×#11924015C22semidirect
28. C2×#11924013C22semidirect
29. C2×#11924013C22semidirect
30. C2×#11924011C22semidirect
31. C2×C8×D73C22semidirect
35. #14556567C22semidirect
40. #14556562C22semidirect
43. C4×Dic146C22semidirect
46. #14556524C22semidirect
47. #14556514C22semidirect
48. #14556513C22semidirect
49. #14556513C22semidirect
51. #14556503C22semidirect
52. #14556503C22semidirect
53. #14556502C22semidirect
56. #124×C73C22semidirect
58. C4⋊C8×C73C22semidirect
59. #103×C73C22semidirect
60. #102×C73C22semidirect
91. #11924016D4semidirect
173. Dic146C2×D4semidirect
177. #10596831C2×D4semidirect
198. C2×D73AGL(1,ℤ/8)semidirect
219. C73#3265semidirect
227. #463D73semidirect
255. #124C2×D73semidirect
270. C4⋊C8C2×D73semidirect
272. #103C2×D73semidirect
276. #102C2×D73semidirect