Finite Group Databasebeta

← #22621537

Subgroups — #22621537

Order 9344.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556618C211yesmaximal, characteristic, complemented
2C2×#14556615C211yesmaximal, characteristic, complemented
3#17989232C211yesmaximal, characteristic, complemented
4#17989230C211yesmaximal, characteristic, complemented
5#17988969C211yesmaximal, characteristic, complemented
6#17988836C211yesmaximal, characteristic, complemented
7#17988832C211yesmaximal, characteristic, complemented
8#17988803C211yesmaximal, characteristic, complemented
9#17988752C211yesmaximal, characteristic, complemented
10#17988746C211yesmaximal, characteristic, complemented
11#17988722C211yesmaximal, characteristic, complemented
12#17988719C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988664C211yesmaximal, characteristic, complemented
15#463×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18C2×D4×D73C2211yescharacteristic, complemented
19C2×D4×D73C2211yescharacteristic, complemented
20#14556618—24no—
21#14556615—24no—
22C2×#11924018C2211yescharacteristic, complemented
23C2×#11924017C2211yescharacteristic, complemented
24C2×#11924016C2211yescharacteristic, complemented
25C2×#11924015C2211yescharacteristic, complemented
26C2×D584C2211yescharacteristic
27C2×#11924013C2211yescharacteristic
28C2×#11924013C2211yescharacteristic
29C2×#11924011C2211yescharacteristic, complemented
30C2×#11924011C2211yescharacteristic, complemented
31#14556579C2211yescharacteristic, complemented
32#14556575—21no—
33#14556573—21no—
34#14556571C2211yescharacteristic, complemented
35#14556567C2211yescharacteristic, complemented
36#14556566C2211yescharacteristic
37#14556565—21no—
38#14556564—21no—
39#14556562C2211yescharacteristic
40#14556561—21no—
41#14556561—21no—
42C4×D292C2211yescharacteristic
43C4×D292C2211yescharacteristic, complemented
44C2×#11924005—21no—
45C22⋊C4×D73—21no—
46#14556524C2211yescharacteristic, complemented
47#14556516C2211yescharacteristic, complemented
48#14556513C2211yescharacteristic, complemented
49#14556512C2211yescharacteristic, complemented
50#14556511C2211yescharacteristic, complemented
51#14556503C2211yescharacteristic, complemented
52#14556503C2211yescharacteristic, complemented
53C4×#10596831C2211yescharacteristic, complemented
54C2×SD16×C73C2211yescharacteristic, complemented
55C2×D8×C73C2211yescharacteristic
56#124×C73C2211yescharacteristic, complemented
57C4×D4×C73C2211yescharacteristic, complemented
58C4⋊C8×C73C2211yescharacteristic, complemented
59#103×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62C23×D73—21no—
63#11924029—22no—
64#11924029—41no—
65#11924027—22no—
66#11924027—41no—
67C2×Dic146C2311yescharacteristic
68C2×D292—21no—
69C2×D292—21no—
70C2×D292D411yescharacteristic
71C2×D292C2311yescharacteristic
72C2×D292C2311yescharacteristic
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C2×C22⋊D73—21no—
76C2×C22⋊D73—21no—
77D4×D73—22no—
78D4×D73—22no—
79D4×D73—41no—
80D4×D73—41no—
81C22×Dic73—21no—
82C2×C4×D73—21no—
83C2×C4×D73—21no—
84C2×C4×D73C2311yescharacteristic
85C2×C4×D73C2311yescharacteristic
86#11924018—41no—
87#11924017—22no—
88#11924016—22no—
89#11924015—22no—
90D584—22no—
91#11924013—41no—
92#11924013D414yescomplemented
93#11924011—22no—
94#11924011—22no—
95C2×#10596831C2311yescharacteristic
96C2×#10596831C2311yescharacteristic
97C4⋊Dic73—21no—
98C4⋊Dic73D411yescharacteristic
99C4⋊Dic73C2311yescharacteristic
100#11924007—21no—
101C22⋊Dic73—21no—
102#11924005—21no—
103#11924005—21no—
104#11924005—21no—
105#11924005—21no—
106#11924005—21no—
107#11924005—21no—
108#11924005D411yescharacteristic
109#11924005D411yescharacteristic
110C2×Q8×C73C2311yescharacteristic
111C2×D4×C73C2311yescharacteristic
112C2×D4×C73C2311yescharacteristic
113C22×C4×C73—21no—
114SD16×C73—22no—
115D8×C73—22no—
116C2×C8×C73C2311yescharacteristic
117C2×C8×C73C2311yescharacteristic
118C4⋊C4×C73C2311yescharacteristic
119C22⋊C4×C73—21no—
120C22⋊C4×C73—21no—
121C22⋊C4×C73—21no—
122C42×C73C2311yescharacteristic
123C23×C73—21no—
124C23×C73—21no—
125C22×D73—21no—
126C22×D73—21no—
127C22×D73—42no—
128C22×D73—42no—
129C22×D73—42no—
130C22×D73—42no—
131C22×D73—81no—
132C22×D73—81no—
133C22×D73C2×D411yescharacteristic
134C22×D73C2×D411yescharacteristic
135Q8×C73—21no—
136Q8×C73—21no—
137D4×C73—21no—
138D4×C73—21no—
139D4×C73—21no—
140D4×C73C2×D412yes—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—81no—
144C2×C4×C73C2×D411yescharacteristic
145C2×C4×C73C2×D411yescharacteristic
146C2×C4×C73C2411yescharacteristic
147C22⋊D73—42no—
148C22⋊D73—42no—
149C22⋊D73—42no—
150C22⋊D73—81no—
151C2×Dic73—21no—
152C2×Dic73—21no—
153C2×Dic73—42no—
154C2×Dic73C2×D411yescharacteristic
155C2×Dic73C2×D411yescharacteristic
156D292—21no—
157D292—21no—
158D292—21no—
159D292—41no—
160D292—42no—
161D292—81no—
162D292C2×D412yes—
163C4×D73—21no—
164C4×D73—21no—
165C4×D73—21no—
166C4×D73—21no—
167C4×D73—42no—
168C4×D73—81no—
169Dic146—21no—
170Dic146—21no—
171C8×C73—21no—
172C8×C73—21no—
173#10596831—21no—
174#10596831C2×D412yes—
175C22×C73—22no—
176C22×C73—41no—
177C22×C73—41no—
178C22×C73—41no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73C22×D411yescharacteristic
182C2×D73—21no—
183C2×D73—21no—
184C2×D73—22no—
185C2×D73—21no—
186C2×D73—21no—
187C2×D73—21no—
188C2×D73—21no—
189C2×D73—41no—
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—84no—
195C2×D73—84no—
196C4×C73—21no—
197C4×C73—21no—
198C4×C73—41no—
199C4×C73—41no—
200C4×C73C22×D411yescharacteristic
201C4×C73H(5,𝔽2)11yescharacteristic
202Dic73—21no—
203Dic73—21no—
204Dic73—41no—
205Dic73—41no—
206C2×C73—42no—
207C2×C73—81no—
208C2×C73D4211yescharacteristic
209C2×C73#57511yescharacteristic
210C2×C73#57611yescharacteristic
211D73—41no—
212D73—41no—
213D73—42no—
214D73—81no—
215#3273—731nomaximal, Sylow
216C73#327311yescharacteristic, complemented, Sylow
217C2×AGL(1,ℤ/8)—731no—
218C2×AGL(1,ℤ/8)—731no—
219#546—731no—
220#546—731no—
221#495—731no—
222#468—731no—
223#468—731no—
224#463—731no—
225#463D7311yescharacteristic, complemented
226#452—731no—
227#452—731no—
228#447—731no—
229#447—731no—
230C4×D8—731no—
231#436—731no—
232C2×#41—731no—
233C2×#41—731no—
234C22×D4—731no—
235C22×D4—731no—
236AGL(1,ℤ/8)—1464no—
237AGL(1,ℤ/8)—1464no—
238C2×Q16—731no—
239C2×SD16—731no—
240C2×SD16—731no—
241C2×SD16—731no—
242C2×SD16C2×D7311yescharacteristic, complemented
243C2×D8—731no—
244C2×D8—731no—
245C2×D8—731no—
246C2×D8C2×D7311yescharacteristic
247C2×M16—731no—
248C2×M16—731no—
249#124—731no—
250#124C2×D7311yescharacteristic, complemented
251#123—1461no—
252#123—1461no—
253C22⋊Q8—731no—
254C22⋊Q8—731no—
255#121—731no—
256#121—731no—
257#121—1461no—
258#121—1461no—
259#120—1461no—
260#120—1461no—
261C4×D4—731no—
262C4×D4—731no—
263C4×D4C2×D7311yescharacteristic, complemented
264C2×C22⋊C4—1461no—
265C2×C22⋊C4—1461no—
266#107—731no—
267C4⋊C8C2×D7311yescharacteristic, complemented
268#103—731no—
269#103C2×D7311yescharacteristic, complemented
270#102—731no—
271#102—731no—
272#102—731no—
273#102C2×D7311yescharacteristic, complemented
274C22⋊C8—731no—
275C22⋊C8—731no—
276C4×C8—731no—
277C24—1461no—
278C24—1461no—
279#41—2921no—
280#41—2921no—
281#41—1462no—
282#41—1462no—
283C2×Q8—731no—
284C2×Q8C22×D7311yescharacteristic
285C2×D4—2921no—
286C2×D4—2921no—
287C2×D4—731no—
288C2×D4—731no—
289C2×D4—731no—
290C2×D4—1461no—
291C2×D4—1461no—
292C2×D4—1461no—
293C2×D4—1461no—
294C2×D4—1462no—
295C2×D4—1461no—
296C2×D4—1462no—
297C2×D4—1461no—
298C2×D4C22×D7311yescharacteristic
299C2×D4C22×D7311yescharacteristic
300C22×C4—21no—
301C22×C4—731no—
302C22×C4—731no—
303C22×C4—1461no—
304C22×C4—1461no—
305C22×C4—1461no—
306Q16—2921no—
307SD16—22no—
308SD16—1462no—
309SD16—1462no—
310SD16—1462no—
311D8—22no—
312D8—2921no—
313D8—734no—
314D8—1462no—
315M16—1462no—
316M16—1462no—
317C2×C8—731no—
318C2×C8—731no—
319C2×C8C22×D7311yescharacteristic
320C2×C8C22×D7311yescharacteristic
321C4⋊C4—731no—
322C4⋊C4—731no—
323C4⋊C4—1461no—
324C4⋊C4—1461no—
325C4⋊C4C22×D7311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—731no—
330C22⋊C4—731no—
331C22⋊C4—1461no—
332C22⋊C4—1461no—
333C22⋊C4—1461no—
334C22⋊C4—1461no—
335C22⋊C4—1461no—
336C22⋊C4—1461no—
337C22⋊C4—1461no—
338C42C22×D7311yescharacteristic
339C23—21no—
340C23—21no—
341C23—2922no—
342C23—2922no—
343C23—2922no—
344C23—2922no—
345C23—5841no—
346C23—5841no—
347C23—731no—
348C23—731no—
349C23—1461no—
350C23—1461no—
351Q8—21no—
352Q8—21no—
353Q8—1461no—
354Q8—1461no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—2921no—
359D4—2922no—
360D4—2922no—
361D4—2922no—
362D4—2922no—
363D4—5841no—
364D4—5841no—
365D4—732no—
366D4—1461no—
367D4—1461no—
368D4—1461no—
369D4D4×D7312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—2922no—
374C2×C4—2922no—
375C2×C4—5841no—
376C2×C4—731no—
377C2×C4—731no—
378C2×C4—1461no—
379C2×C4—1461no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4D4×D7311yescharacteristic
385C2×C4D4×D7311yescharacteristic
386C2×C4C23×D7311yescharacteristic
387C8—21no—
388C8—21no—
389C8—732no—
390C8—1461no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—2921no—
398C22—2921no—
399C22—2921no—
400C22—2921no—
401C22—2921no—
402C22—5844no—
403C22—5844no—
404C22—1461no—
405C22—1461no—
406C22—1461no—
407C22—1461no—
408C22—1462no—
409C22—1461no—
410C22—1461no—
411C22C2×D4×D7311yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—2921no—
417C4—2921no—
418C4—1461no—
419C4—1461no—
420C4C2×D4×D7311yescharacteristic
421C4#1455663711yescharacteristic
422C2—42no—
423C2—81no—
424C2—2922no—
425C2—2921no—
426C2—2921no—
427C2—5841no—
428C2#1798922111yescharacteristic
429C2#1798938411yescharacteristic
430C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#463×C73C2
socleC22×C73C22×D4
hypercenter#463D73
hypocenterC73#3273
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×#14556618C2semidirect
2. C2×#14556615C2semidirect
3. #17989232C2semidirect
4. #17989230C2semidirect
5. #17988969C2semidirect
6. #17988836C2semidirect
7. #17988832C2semidirect
8. #17988803C2semidirect
9. #17988752C2semidirect
10. #17988746C2semidirect
11. #17988722C2semidirect
12. #17988719C2semidirect
13. C4×#11924013C2semidirect
14. #17988664C2semidirect
15. #463×C73C2semidirect
18. C2×D4×D73C22semidirect
19. C2×D4×D73C22semidirect
22. C2×#11924018C22semidirect
23. C2×#11924017C22semidirect
24. C2×#11924016C22semidirect
25. C2×#11924015C22semidirect
29. C2×#11924011C22semidirect
30. C2×#11924011C22semidirect
31. #14556579C22semidirect
34. #14556571C22semidirect
35. #14556567C22semidirect
43. C4×D292C22semidirect
46. #14556524C22semidirect
47. #14556516C22semidirect
48. #14556513C22semidirect
49. #14556512C22semidirect
50. #14556511C22semidirect
51. #14556503C22semidirect
52. #14556503C22semidirect
53. C4×#10596831C22semidirect
54. C2×SD16×C73C22semidirect
56. #124×C73C22semidirect
57. C4×D4×C73C22semidirect
58. C4⋊C8×C73C22semidirect
59. #103×C73C22semidirect
60. #102×C73C22semidirect
92. #11924013D4semidirect
216. C73#3273semidirect
225. #463D73semidirect
242. C2×SD16C2×D73semidirect
250. #124C2×D73semidirect
263. C4×D4C2×D73semidirect
267. C4⋊C8C2×D73semidirect
269. #103C2×D73semidirect
273. #102C2×D73semidirect