Finite Group Databasebeta

← #22621535

Subgroups — #22621535

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×#14556616C211yesmaximal, characteristic, complemented
3#17989228C211yesmaximal, characteristic, complemented
4#17989225C211yesmaximal, characteristic, complemented
5#17988972C211yesmaximal, characteristic, complemented
6#17988836C211yesmaximal, characteristic, complemented
7#17988835C211yesmaximal, characteristic, complemented
8#17988805C211yesmaximal, characteristic, complemented
9#17988804C211yesmaximal, characteristic, complemented
10#17988748C211yesmaximal, characteristic, complemented
11#17988723C211yesmaximal, characteristic, complemented
12#17988722C211yesmaximal, characteristic, complemented
13#17988667C211yesmaximal, characteristic, complemented
14#17988662C211yesmaximal, characteristic, complemented
15#452×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C22×D292C2211yescharacteristic, complemented
18C2×D4×D73C2211yescharacteristic, complemented
19#14556618—24no—
20#14556616—24no—
21C2×#11924015C2211yescharacteristic, complemented
22C2×#11924015C2211yescharacteristic, complemented
23C2×#11924015C2211yescharacteristic, complemented
24C2×D584C2211yescharacteristic
25C2×D584C2211yescharacteristic
26C2×#11924013C2211yescharacteristic
27C2×#11924013C2211yescharacteristic
28C2×#11924012C2211yescharacteristic, complemented
29C2×#11924011C2211yescharacteristic, complemented
30#14556580C2211yescharacteristic, complemented
31#14556580C2211yescharacteristic, complemented
32#14556576—21no—
33#14556574—21no—
34#14556567C2211yescharacteristic, complemented
35#14556566—21no—
36#14556566C2211yescharacteristic
37#14556565C2211yescharacteristic
38#14556563—21no—
39#14556561—21no—
40#14556559—21no—
41D4×Dic73C2211yescharacteristic, complemented
42#14556553C2211yescharacteristic, complemented
43C4×C22⋊D73C2211yescharacteristic
44C2×#11924005—21no—
45C22⋊C4×D73—21no—
46#14556524C2211yescharacteristic, complemented
47#14556520C2211yescharacteristic, complemented
48#14556515C2211yescharacteristic, complemented
49#14556513C2211yescharacteristic, complemented
50#14556513C2211yescharacteristic, complemented
51#14556511C2211yescharacteristic, complemented
52#14556503C2211yescharacteristic, complemented
53C8×Dic73C2211yescharacteristic, complemented
54C2×#41×C73C2211yescharacteristic
55C2×Q16×C73C2211yescharacteristic, complemented
56C2×SD16×C73C2211yescharacteristic, complemented
57C22⋊Q8×C73C2211yescharacteristic, complemented
58#103×C73C2211yescharacteristic, complemented
59#102×C73C2211yescharacteristic, complemented
60C22⋊C8×C73C2211yescharacteristic, complemented
61C23×D73—21no—
62C23×D73—21no—
63#11924029—22no—
64#11924029—41no—
65C2×D292—22no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292—21no—
69C2×D292—41no—
70C2×D292C2311yescharacteristic
71C2×D292C2311yescharacteristic
72C2×D292C2311yescharacteristic
73C2×C22⋊D73—21no—
74C2×C22⋊D73—21no—
75C2×C22⋊D73D411yescharacteristic
76D4×D73—22no—
77D4×D73—41no—
78C22×Dic73—21no—
79C2×C4×D73—21no—
80C2×C4×D73—21no—
81C2×C4×D73C2311yescharacteristic
82#11924015—22no—
83#11924015—22no—
84#11924015—22no—
85D584—22no—
86D584—41no—
87#11924013—22no—
88#11924013D414yescomplemented
89#11924012—22no—
90#11924011—22no—
91C2×#10596831C2311yescharacteristic
92C2×#10596831C2311yescharacteristic
93C4⋊Dic73C2311yescharacteristic
94#11924007—21no—
95#11924007D411yescharacteristic
96C22⋊Dic73—21no—
97C22⋊Dic73D411yescharacteristic
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102#11924005—21no—
103#11924005—21no—
104#11924005—21no—
105#11924005—21no—
106#11924005D411yescharacteristic
107C4×Dic73C2311yescharacteristic
108#41×C73—22no—
109#41×C73—41no—
110C2×Q8×C73C2311yescharacteristic
111C2×Q8×C73C2311yescharacteristic
112C2×D4×C73—21no—
113C2×D4×C73C2311yescharacteristic
114C22×C4×C73—21no—
115C22×C4×C73C2311yescharacteristic
116Q16×C73—41no—
117SD16×C73—22no—
118C2×C8×C73C2311yescharacteristic
119C2×C8×C73C2311yescharacteristic
120C4⋊C4×C73—21no—
121C4⋊C4×C73C2311yescharacteristic
122C22⋊C4×C73—21no—
123C23×C73—21no—
124C23×C73C2×D411yescharacteristic
125C22×D73—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
135Q8×C73—21no—
136Q8×C73—21no—
137Q8×C73—21no—
138Q8×C73—21no—
139D4×C73—21no—
140D4×C73—42no—
141D4×C73C2×D412yes—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—42no—
148C2×C4×C73C2×D411yescharacteristic
149C2×C4×C73C2411yescharacteristic
150C22⋊D73—41no—
151C22⋊D73—42no—
152C22⋊D73—81no—
153C2×Dic73—21no—
154C2×Dic73—81no—
155C2×Dic73C2×D411yescharacteristic
156C2×Dic73C2×D411yescharacteristic
157C2×Dic73C2×D411yescharacteristic
158D292—21no—
159D292—21no—
160D292—21no—
161D292—21no—
162D292—21no—
163D292—42no—
164D292—42no—
165D292—81no—
166D292C2×D412yes—
167C4×D73—21no—
168C4×D73—21no—
169C4×D73—42no—
170C4×D73—81no—
171C8×C73—21no—
172C8×C73—21no—
173#10596831—21no—
174#10596831C2×D412yes—
175C22×C73—22no—
176C22×C73—21no—
177C22×C73—21no—
178C22×C73—21no—
179C22×C73—41no—
180C22×C73—41no—
181C22×C73C22×D411yescharacteristic
182C2×D73—21no—
183C2×D73—22no—
184C2×D73—21no—
185C2×D73—21no—
186C2×D73—41no—
187C2×D73—41no—
188C2×D73—41no—
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—41no—
198C4×C73—41no—
199C4×C73—41no—
200C4×C73C22×D411yescharacteristic
201C4×C73H(5,𝔽2)11yescharacteristic
202Dic73—21no—
203Dic73—21no—
204Dic73—21no—
205Dic73—41no—
206C2×C73—41no—
207C2×C73—42no—
208C2×C73D4211yescharacteristic
209C2×C73#57511yescharacteristic
210C2×C73#57611yescharacteristic
211D73—41no—
212D73—42no—
213D73—81no—
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#463—731no—
226#452—731no—
227#452D7311yescharacteristic, complemented
228#447—731no—
229#447—731no—
230C4×D8—731no—
231#436—731no—
232C2×#41—731no—
233C2×#41C2×D7311yescharacteristic
234C22×D4—731no—
235C22×D4—731no—
236AGL(1,ℤ/8)—1464no—
237AGL(1,ℤ/8)—1464no—
238C2×Q16C2×D7311yescharacteristic, complemented
239C2×SD16—731no—
240C2×SD16—731no—
241C2×SD16—731no—
242C2×SD16C2×D7311yescharacteristic, complemented
243C2×D8—731no—
244C2×D8—731no—
245C2×D8—731no—
246C2×D8—731no—
247C2×M16—731no—
248C2×M16—731no—
249#124—731no—
250#124—731no—
251#123—1461no—
252#123—1461no—
253C22⋊Q8—731no—
254C22⋊Q8C2×D7311yescharacteristic, complemented
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×D4—731no—
264C2×C22⋊C4—1461no—
265C2×C22⋊C4—1461no—
266#107—731no—
267C4⋊C8—731no—
268#103—731no—
269#103C2×D7311yescharacteristic, complemented
270#102—731no—
271#102—731no—
272#102—731no—
273#102C2×D7311yescharacteristic, complemented
274C22⋊C8—731no—
275C22⋊C8C2×D7311yescharacteristic, complemented
276C4×C8—731no—
277C24—1461no—
278C24—1461no—
279#41—22no—
280#41—41no—
281#41—2921no—
282#41—1462no—
283C2×Q8C22×D7311yescharacteristic
284C2×Q8C22×D7311yescharacteristic
285C2×D4—21no—
286C2×D4—2921no—
287C2×D4—2921no—
288C2×D4—731no—
289C2×D4—731no—
290C2×D4—731no—
291C2×D4—731no—
292C2×D4—1461no—
293C2×D4—1462no—
294C2×D4—1461no—
295C2×D4—1461no—
296C2×D4—1462no—
297C2×D4—1461no—
298C2×D4—1461no—
299C2×D4C22×D7311yescharacteristic
300C22×C4—21no—
301C22×C4—731no—
302C22×C4—1461no—
303C22×C4—1461no—
304C22×C4—1461no—
305C22×C4C22×D7311yescharacteristic
306Q16—41no—
307SD16—22no—
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×C8C22×D7311yescharacteristic
320C2×C8C22×D7311yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—731no—
323C4⋊C4—731no—
324C4⋊C4—1461no—
325C4⋊C4C22×D7311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—731no—
328C22⋊C4—731no—
329C22⋊C4—1461no—
330C22⋊C4—1461no—
331C22⋊C4—1461no—
332C22⋊C4—1461no—
333C22⋊C4—1461no—
334C22⋊C4—1461no—
335C22⋊C4—1461no—
336C22⋊C4—1461no—
337C22⋊C4—1461no—
338C42—731no—
339C23—21no—
340C23—2922no—
341C23—2922no—
342C23—2922no—
343C23—2922no—
344C23—5841no—
345C23—5841no—
346C23—731no—
347C23—1461no—
348C23—1461no—
349C23—1461no—
350C23D4×D7311yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—21no—
354Q8—21no—
355D4—21no—
356D4—42no—
357D4—2922no—
358D4—2922no—
359D4—2922no—
360D4—2921no—
361D4—5841no—
362D4—5841no—
363D4—732no—
364D4—1461no—
365D4—1461no—
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—42no—
376C2×C4—2922no—
377C2×C4—5841no—
378C2×C4—5841no—
379C2×C4—731no—
380C2×C4—731no—
381C2×C4—731no—
382C2×C4—1461no—
383C2×C4—1461no—
384C2×C4—1461no—
385C2×C4D4×D7311yescharacteristic
386C2×C4C23×D7311yescharacteristic
387C8—21no—
388C8—21no—
389C8—732no—
390C8—1461no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—2921no—
398C22—2921no—
399C22—2921no—
400C22—2921no—
401C22—2921no—
402C22—2921no—
403C22—2921no—
404C22—2921no—
405C22—5844no—
406C22—5844no—
407C22—1461no—
408C22—1461no—
409C22—1462no—
410C22—1461no—
411C22C2×D4×D7311yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—2921no—
417C4—1461no—
418C4—1461no—
419C4—1461no—
420C4C2×D4×D7311yescharacteristic
421C4#1455663611yescharacteristic
422C2—41no—
423C2—42no—
424C2—2922no—
425C2—2921no—
426C2—5841no—
427C2—5841no—
428C2#1798921911yescharacteristic
429C2#1798938611yescharacteristic
430C2#1798938911yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#452×C73C2
socleC22×C73C22×D4
hypercenter#452D73
hypocenterC73#3273
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#14556618C2semidirect
2. C2×#14556616C2semidirect
3. #17989228C2semidirect
4. #17989225C2semidirect
5. #17988972C2semidirect
6. #17988836C2semidirect
7. #17988835C2semidirect
8. #17988805C2semidirect
9. #17988804C2semidirect
10. #17988748C2semidirect
11. #17988723C2semidirect
12. #17988722C2semidirect
13. #17988667C2semidirect
14. #17988662C2semidirect
15. #452×C73C2semidirect
17. C22×D292C22semidirect
18. C2×D4×D73C22semidirect
21. C2×#11924015C22semidirect
22. C2×#11924015C22semidirect
23. C2×#11924015C22semidirect
28. C2×#11924012C22semidirect
29. C2×#11924011C22semidirect
30. #14556580C22semidirect
31. #14556580C22semidirect
34. #14556567C22semidirect
41. D4×Dic73C22semidirect
42. #14556553C22semidirect
46. #14556524C22semidirect
47. #14556520C22semidirect
48. #14556515C22semidirect
49. #14556513C22semidirect
50. #14556513C22semidirect
51. #14556511C22semidirect
52. #14556503C22semidirect
53. C8×Dic73C22semidirect
55. C2×Q16×C73C22semidirect
56. C2×SD16×C73C22semidirect
57. C22⋊Q8×C73C22semidirect
58. #103×C73C22semidirect
59. #102×C73C22semidirect
60. C22⋊C8×C73C22semidirect
88. #11924013D4semidirect
216. C73#3273semidirect
227. #452D73semidirect
238. C2×Q16C2×D73semidirect
242. C2×SD16C2×D73semidirect
254. C22⋊Q8C2×D73semidirect
269. #103C2×D73semidirect
273. #102C2×D73semidirect
275. C22⋊C8C2×D73semidirect