Finite Group Databasebeta

← #22621538

Subgroups — #22621538

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×#14556617C211yesmaximal, characteristic, complemented
2C2×#14556616C211yesmaximal, characteristic, complemented
3#17989233C211yesmaximal, characteristic, complemented
4#17988969C211yesmaximal, characteristic, complemented
5#17988835C211yesmaximal, characteristic, complemented
6#17988831C211yesmaximal, characteristic, complemented
7#17988802C211yesmaximal, characteristic, complemented
8#17988799C211yesmaximal, characteristic, complemented
9#17988749C211yesmaximal, characteristic, complemented
10#17988747C211yesmaximal, characteristic, complemented
11#17988721C211yesmaximal, characteristic, complemented
12#17988720C211yesmaximal, characteristic, complemented
13C4×#11924013C211yesmaximal, characteristic, complemented
14#17988665C211yesmaximal, characteristic, complemented
15#546×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic, complemented
18#14556617—24no—
19#14556616—24no—
20C2×#11924018C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×#11924016C2211yescharacteristic, complemented
23C2×#11924015C2211yescharacteristic, complemented
24C2×#11924015C2211yescharacteristic, complemented
25C2×#11924013C2211yescharacteristic
26C2×#11924013C2211yescharacteristic
27C2×#11924013C2211yescharacteristic
28C2×#11924013C2211yescharacteristic
29C2×#11924012C2211yescharacteristic, complemented
30C2×#11924012C2211yescharacteristic, complemented
31#14556579C2211yescharacteristic, complemented
32#14556576—21no—
33#14556570C2211yescharacteristic, complemented
34#14556565C2211yescharacteristic
35#14556564—21no—
36#14556559—21no—
37C4×D292C2211yescharacteristic, complemented
38C22⋊C4×D73—21no—
39#14556524C2211yescharacteristic, complemented
40C4⋊#10596831C2211yescharacteristic, complemented
41#14556515C2211yescharacteristic, complemented
42#14556514C2211yescharacteristic, complemented
43#14556512C2211yescharacteristic, complemented
44#14556512C2211yescharacteristic, complemented
45#14556511C2211yescharacteristic, complemented
46#14556511C2211yescharacteristic, complemented
47C22⋊#10596831C2211yescharacteristic, complemented
48C22⋊#10596831C2211yescharacteristic, complemented
49C4×#10596831C2211yescharacteristic, complemented
50C2×#41×C73C2211yescharacteristic
51C22×D4×C73C2211yescharacteristic, complemented
52#124×C73C2211yescharacteristic, complemented
53#123×C73—21no—
54C22⋊Q8×C73C2211yescharacteristic, complemented
55#121×C73—21no—
56#121×C73C2211yescharacteristic
57#120×C73—21no—
58C4×D4×C73C2211yescharacteristic
59C4×D4×C73C2211yescharacteristic, complemented
60C2×C22⋊C4×C73—21no—
61C23×D73—21no—
62#11924028—22no—
63#11924028—41no—
64C2×Dic146C2311yescharacteristic
65C2×D292—22no—
66C2×D292—21no—
67C2×D292—41no—
68C2×D292C2311yescharacteristic
69C2×D292C2311yescharacteristic
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74#11924018—41no—
75#11924016—22no—
76#11924016—22no—
77#11924015—22no—
78#11924015—22no—
79#11924013—22no—
80#11924013—22no—
81#11924013—41no—
82#11924013D414yescomplemented
83#11924012—22no—
84#11924012—22no—
85C2×#10596831C2311yescharacteristic
86C2×#10596831C2311yescharacteristic
87C2×#10596831C2311yescharacteristic
88C2×#10596831C2311yescharacteristic
89C4⋊Dic73C2311yescharacteristic
90#11924007—21no—
91C22⋊Dic73—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96C24×C73—21no—
97#41×C73—22no—
98#41×C73—41no—
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—22no—
101C2×D4×C73—21no—
102C2×D4×C73—21no—
103C2×D4×C73—21no—
104C2×D4×C73—41no—
105C2×D4×C73D411yescharacteristic
106C2×D4×C73C2311yescharacteristic
107C2×D4×C73C2311yescharacteristic
108C22×C4×C73—21no—
109C22×C4×C73—21no—
110C22×C4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C4⋊C4×C73—21no—
113C4⋊C4×C73D411yescharacteristic
114C4⋊C4×C73C2311yescharacteristic
115C22⋊C4×C73—21no—
116C22⋊C4×C73—21no—
117C22⋊C4×C73—21no—
118C22⋊C4×C73—21no—
119C22⋊C4×C73—21no—
120C22⋊C4×C73D411yescharacteristic
121C22⋊C4×C73D411yescharacteristic
122C42×C73C2311yescharacteristic
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—42no—
126C23×C73—42no—
127C23×C73—81no—
128C23×C73C2×D411yescharacteristic
129C23×C73C2×D411yescharacteristic
130C22×D73—21no—
131C22×D73—21no—
132C22×D73—42no—
133C22×D73—42no—
134C22×D73—81no—
135Q8×C73—21no—
136Q8×C73—21no—
137D4×C73—21no—
138D4×C73—21no—
139D4×C73—21no—
140D4×C73—41no—
141D4×C73—42no—
142D4×C73—42no—
143D4×C73—81no—
144D4×C73C2×D412yes—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—42no—
152C2×C4×C73—81no—
153C2×C4×C73C2×D411yescharacteristic
154C2×C4×C73C2×D411yescharacteristic
155C2×C4×C73C2×D411yescharacteristic
156C2×C4×C73C2×D411yescharacteristic
157C2×C4×C73C2411yescharacteristic
158C22⋊D73—42no—
159C22⋊D73—81no—
160C2×Dic73—21no—
161C2×Dic73—21no—
162D292—21no—
163D292—21no—
164D292—21no—
165D292—42no—
166D292C2×D412yes—
167C4×D73—42no—
168C4×D73—81no—
169Dic146—21no—
170Dic146—21no—
171#10596831—21no—
172#10596831—21no—
173#10596831—21no—
174#10596831C2×D412yes—
175C22×C73—21no—
176C22×C73—21no—
177C22×C73—22no—
178C22×C73—21no—
179C22×C73—21no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73—41no—
185C22×C73—41no—
186C22×C73—41no—
187C22×C73—84no—
188C22×C73C22×D411yescharacteristic
189C2×D73—22no—
190C2×D73—41no—
191C2×D73—41no—
192C2×D73—41no—
193C2×D73—41no—
194C2×D73—41no—
195C2×D73—84no—
196C4×C73—21no—
197C4×C73—21no—
198C4×C73—21no—
199C4×C73—21no—
200C4×C73—41no—
201C4×C73—41no—
202C4×C73C22×D411yescharacteristic
203C4×C73H(5,𝔽2)11yescharacteristic
204Dic73—41no—
205Dic73—41no—
206C2×C73—41no—
207C2×C73—41no—
208C2×C73—42no—
209C2×C73—81no—
210C2×C73D4211yescharacteristic
211C2×C73#57511yescharacteristic
212C2×C73#57611yescharacteristic
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#546D7311yescharacteristic, complemented
221#495—731no—
222#468—731no—
223#468—731no—
224#463—731no—
225#463—731no—
226#452—731no—
227#452—731no—
228#447—731no—
229#447—731no—
230C4×D8—731no—
231#436—731no—
232C2×#41—731no—
233C2×#41C2×D7311yescharacteristic
234C22×D4—731no—
235C22×D4C2×D7311yescharacteristic, complemented
236AGL(1,ℤ/8)—1464no—
237AGL(1,ℤ/8)—1464no—
238C2×Q16—731no—
239C2×SD16—731no—
240C2×SD16—731no—
241C2×SD16—731no—
242C2×SD16—731no—
243C2×D8—731no—
244C2×D8—731no—
245C2×D8—731no—
246C2×D8—731no—
247C2×M16—731no—
248C2×M16—731no—
249#124—731no—
250#124C2×D7311yescharacteristic, complemented
251#123—21no—
252#123—1461no—
253C22⋊Q8—731no—
254C22⋊Q8C2×D7311yescharacteristic, complemented
255#121—21no—
256#121—731no—
257#121—1461no—
258#121C2×D7311yescharacteristic
259#120—21no—
260#120—1461no—
261C4×D4—731no—
262C4×D4C2×D7311yescharacteristic
263C4×D4C2×D7311yescharacteristic, complemented
264C2×C22⋊C4—21no—
265C2×C22⋊C4—1461no—
266#107—731no—
267C4⋊C8—731no—
268#103—731no—
269#103—731no—
270#102—731no—
271#102—731no—
272#102—731no—
273#102—731no—
274C22⋊C8—731no—
275C22⋊C8—731no—
276C4×C8—731no—
277C24—21no—
278C24—1461no—
279#41—22no—
280#41—41no—
281#41—2921no—
282#41—1462no—
283C2×Q8—731no—
284C2×Q8C22×D7311yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—2921no—
291C2×D4—731no—
292C2×D4—731no—
293C2×D4—1462no—
294C2×D4—1461no—
295C2×D4—1461no—
296C2×D4—1461no—
297C2×D4C22⋊D7311yescharacteristic
298C2×D4C22×D7311yescharacteristic
299C2×D4C22×D7311yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—1461no—
303C22×C4—1461no—
304C22×C4C22×D7311yescharacteristic
305C22×C4C22×D7311yescharacteristic
306Q16—2921no—
307SD16—1462no—
308SD16—1462no—
309SD16—1462no—
310SD16—1462no—
311D8—2921no—
312D8—734no—
313D8—1462no—
314D8—1462no—
315M16—1462no—
316M16—1462no—
317C2×C8—731no—
318C2×C8—731no—
319C2×C8—731no—
320C2×C8—731no—
321C4⋊C4—21no—
322C4⋊C4—731no—
323C4⋊C4—1461no—
324C4⋊C4C22⋊D7311yescharacteristic
325C4⋊C4C22×D7311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—1461no—
332C22⋊C4—1461no—
333C22⋊C4—1461no—
334C22⋊C4—1461no—
335C22⋊C4—1461no—
336C22⋊C4C22⋊D7311yescharacteristic
337C22⋊C4C22⋊D7311yescharacteristic
338C42C22×D7311yescharacteristic
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—2922no—
345C23—2922no—
346C23—5841no—
347C23—1461no—
348C23—1461no—
349C23C2×C22⋊D7311yescharacteristic
350C23C2×C22⋊D7311yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—1461no—
354Q8—1461no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—41no—
359D4—42no—
360D4—42no—
361D4—81no—
362D4—2922no—
363D4—2922no—
364D4—5841no—
365D4—732no—
366D4—1461no—
367D4—1461no—
368D4—1461no—
369D4D4×D7312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—2922no—
379C2×C4—5841no—
380C2×C4—1461no—
381C2×C4—1461no—
382C2×C4C2×C22⋊D7311yescharacteristic
383C2×C4C2×C22⋊D7311yescharacteristic
384C2×C4C2×C22⋊D7311yescharacteristic
385C2×C4C2×C22⋊D7311yescharacteristic
386C2×C4C23×D7311yescharacteristic
387C8—732no—
388C8—1461no—
389C8—1461no—
390C8—1461no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—2921no—
405C22—2921no—
406C22—2921no—
407C22—2921no—
408C22—2921no—
409C22—5844no—
410C22—1462no—
411C22C22×C22⋊D7311yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—2921no—
419C4—2921no—
420C4C2×D4×D7311yescharacteristic
421C4#1455663611yescharacteristic
422C2—41no—
423C2—41no—
424C2—42no—
425C2—81no—
426C2—2922no—
427C2—5841no—
428C2D4×C22⋊D7311yescharacteristic
429C2#1798938511yescharacteristic
430C2#1798939011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#546×C73C2
socleC22×C73C22×D4
hypercenter#546D73
hypocenterC73#3273
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14556617C2semidirect
2. C2×#14556616C2semidirect
3. #17989233C2semidirect
4. #17988969C2semidirect
5. #17988835C2semidirect
6. #17988831C2semidirect
7. #17988802C2semidirect
8. #17988799C2semidirect
9. #17988749C2semidirect
10. #17988747C2semidirect
11. #17988721C2semidirect
12. #17988720C2semidirect
13. C4×#11924013C2semidirect
14. #17988665C2semidirect
15. #546×C73C2semidirect
17. C22×D292C22semidirect
20. C2×#11924018C22semidirect
21. C2×#11924016C22semidirect
22. C2×#11924016C22semidirect
23. C2×#11924015C22semidirect
24. C2×#11924015C22semidirect
29. C2×#11924012C22semidirect
30. C2×#11924012C22semidirect
31. #14556579C22semidirect
33. #14556570C22semidirect
37. C4×D292C22semidirect
39. #14556524C22semidirect
40. C4⋊#10596831C22semidirect
41. #14556515C22semidirect
42. #14556514C22semidirect
43. #14556512C22semidirect
44. #14556512C22semidirect
45. #14556511C22semidirect
46. #14556511C22semidirect
47. C22⋊#10596831C22semidirect
48. C22⋊#10596831C22semidirect
49. C4×#10596831C22semidirect
51. C22×D4×C73C22semidirect
52. #124×C73C22semidirect
54. C22⋊Q8×C73C22semidirect
59. C4×D4×C73C22semidirect
82. #11924013D4semidirect
216. C73#3273semidirect
220. #546D73semidirect
235. C22×D4C2×D73semidirect
250. #124C2×D73semidirect
254. C22⋊Q8C2×D73semidirect
263. C4×D4C2×D73semidirect