Finite Group Databasebeta

← #22622160

Subgroups — #22622160

Order 9344.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989305C211yesmaximal, characteristic, complemented
2#17989221C211yesmaximal, characteristic
3#17988932C211yesmaximal, characteristic, complemented
4#17988913C211yesmaximal, characteristic, complemented
5#17988866C211yesmaximal, characteristic, complemented
6#17988834C211yesmaximal, characteristic, complemented
7#17988831C211yesmaximal, characteristic, complemented
8#17988786C211yesmaximal, characteristic, complemented
9#17988740C211yesmaximal, characteristic, complemented
10#17988739C211yesmaximal, characteristic, complemented
11#17988674C211yesmaximal, characteristic, complemented
12#17988662C211yesmaximal, characteristic, complemented
13#17988591C211yesmaximal, characteristic, complemented
14#17988590C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C2×D4×D73—21no—
18C2×D4×D73C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic, complemented
22C2×#11924012C2211yescharacteristic, complemented
23C2×#11924011C2211yescharacteristic, complemented
24#14556590C2211yescharacteristic, complemented
25#14556587C2211yescharacteristic
26#14556585—21no—
27#14556584—21no—
28#14556577—21no—
29#14556571C2211yescharacteristic, complemented
30#14556570C2211yescharacteristic, complemented
31#14556566C2211yescharacteristic
32#14556564—21no—
33#14556561—21no—
34#14556559—21no—
35C4×Dic146—21no—
36#14556556C2211yescharacteristic, complemented
37#14556553C2211yescharacteristic
38C4×C22⋊D73C2211yescharacteristic
39#14556549C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556514C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic, complemented
45#14556512C2211yescharacteristic, complemented
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic, complemented
49#14556511C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52#121×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic, complemented
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73—21no—
61C2×Dic146—21no—
62C2×Dic146C2311yescharacteristic
63C2×D292—22no—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—41no—
67C2×D292C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73D411yescharacteristic
73D4×D73—22no—
74D4×D73—41no—
75D4×D73—44no—
76C2×C4×D73—21no—
77C2×C4×D73C2311yescharacteristic
78#11924017—22no—
79#11924017—41no—
80#11924016—41no—
81#11924012—41no—
82#11924011—41no—
83C2×#10596831C2311yescharacteristic
84C2×#10596831C2311yescharacteristic
85C4⋊Dic73—21no—
86C4⋊Dic73C2311yescharacteristic
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90#11924007D411yescharacteristic
91C22⋊Dic73—21no—
92C22⋊Dic73D411yescharacteristic
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005D411yescharacteristic
98C4×Dic73—21no—
99C4×Dic73—21no—
100C4×Dic73C2311yescharacteristic
101C2×D4×C73—21no—
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C4⋊C4×C73C2311yescharacteristic
107C4⋊C4×C73C2311yescharacteristic
108C4⋊C4×C73C2311yescharacteristic
109C22⋊C4×C73—21no—
110C22⋊C4×C73—21no—
111C42×C73—21no—
112C23×C73—21no—
113C23×C73C2×D411yescharacteristic
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—42no—
117C22×D73—42no—
118C22×D73—42no—
119C22×D73—42no—
120C22×D73—81no—
121C22×D73—81no—
122C22×D73C2×D411yescharacteristic
123D4×C73—21no—
124D4×C73—21no—
125D4×C73—42no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—22no—
134C22⋊D73—42no—
135C22⋊D73—42no—
136C22⋊D73—81no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73C2×D411yescharacteristic
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142D292—21no—
143D292—21no—
144D292—21no—
145D292—42no—
146D292—42no—
147D292#4112yes—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—42no—
151Dic146—21no—
152Dic146—21no—
153Dic146—42no—
154C8×C73—21no—
155C8×C73—21no—
156#10596831—21no—
157#10596831—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73C22×D411yescharacteristic
165C2×D73—21no—
166C2×D73—22no—
167C2×D73—21no—
168C2×D73—21no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—84no—
175C2×D73—84no—
176C4×C73—21no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73—41no—
180C4×C73C2×#4111yescharacteristic
181C4×C73H(5,𝔽2)11yescharacteristic
182Dic73—21no—
183Dic73—21no—
184Dic73—41no—
185Dic73—41no—
186Dic73AGL(1,ℤ/8)12yes—
187C2×C73—41no—
188C2×C73—81no—
189C2×C73#54611yescharacteristic
190C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C73#57711yescharacteristic
192D73—41no—
193D73—42no—
194D73—81no—
195#3324—731nomaximal, Sylow
196C73#332411yescharacteristic, complemented, Sylow
197#556—731no—
198D42—731no—
199#486—731no—
200#482—731no—
201#482D7311yescharacteristic, complemented
202#474—731no—
203#468—731no—
204#468—731no—
205#460—731no—
206#450—731no—
207#450—731no—
208C4×SD16—731no—
209#436—731no—
210#418—731no—
211#418—731no—
212C22×D4—731no—
213C22×D4—731no—
214C22×D4—1461no—
215C2×SD16—731no—
216C2×SD16—731no—
217C2×SD16—731no—
218C2×M16—731no—
219C2×M16—731no—
220C4⋊Q8—731no—
221#127—731no—
222#126—1461no—
223#126—1461no—
224#124—1461no—
225C22⋊Q8—731no—
226C22⋊Q8—731no—
227#121—731no—
228#121—1461no—
229#121C2×D7311yescharacteristic
230#120—1461no—
231#120—1461no—
232C4×Q8—731no—
233C4×Q8—1461no—
234C4×D4—731no—
235C4×D4—731no—
236#117—731no—
237#117C2×D7311yescharacteristic, complemented
238#107—731no—
239#107C2×D7311yescharacteristic, complemented
240#106C2×D7311yescharacteristic, complemented
241C4⋊C8—731no—
242#103—731no—
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248#102—731no—
249#102—731no—
250#102C2×D7311yescharacteristic, complemented
251#102C2×D7311yescharacteristic, complemented
252C22⋊C8—731no—
253C22⋊C8C2×D7311yescharacteristic, complemented
254C4×C8—731no—
255C24—1461no—
256C24—1461no—
257C2×Q8—731no—
258C2×Q8—1461no—
259C2×D4—21no—
260C2×D4—2921no—
261C2×D4—2924no—
262C2×D4—2921no—
263C2×D4—731no—
264C2×D4—731no—
265C2×D4—731no—
266C2×D4—1461no—
267C2×D4—1462no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4—1462no—
272C2×D4—1461no—
273C2×D4C22×D7311yescharacteristic
274C22×C4—731no—
275C22×C4—1461no—
276C22×C4C22×D7311yescharacteristic
277SD16—2921no—
278SD16—2921no—
279SD16—1462no—
280M16—2921no—
281M16—2921no—
282C2×C8—731no—
283C2×C8—731no—
284C2×C8C22×D7311yescharacteristic
285C2×C8C22×D7311yescharacteristic
286C4⋊C4—731no—
287C4⋊C4—731no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C4⋊C4—1461no—
291C4⋊C4—1461no—
292C4⋊C4C22×D7311yescharacteristic
293C4⋊C4C22×D7311yescharacteristic
294C4⋊C4C22×D7311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—731no—
298C22⋊C4—731no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C42—21no—
305C42—731no—
306C42—1461no—
307C42—1461no—
308C23—21no—
309C23—2922no—
310C23—2922no—
311C23—2922no—
312C23—2922no—
313C23—5841no—
314C23—5841no—
315C23—731no—
316C23—1461no—
317C23—1461no—
318C23D4×D7311yescharacteristic
319Q8—2922no—
320Q8—1461no—
321Q8—1461no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—2922no—
326D4—2922no—
327D4—2922no—
328D4—2922no—
329D4—5841no—
330D4—732no—
331D4—1462no—
332D4—1461no—
333D4—1461no—
334D4—1461no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—2922no—
341C2×C4—731no—
342C2×C4—731no—
343C2×C4—731no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4D4×D7311yescharacteristic
349C2×C4C23×D7311yescharacteristic
350C8—21no—
351C8—21no—
352C8—1461no—
353C8—1461no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—2921no—
365C22—5844no—
366C22—5844no—
367C22—1461no—
368C22—1461no—
369C22—1462no—
370C22—1461no—
371C22C2×D4×D7311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—2921no—
377C4—2921no—
378C4—732no—
379C4—1461no—
380C4—1461no—
381C4#41×D7311yescharacteristic
382C4#1455663711yescharacteristic
383C2—41no—
384C2—81no—
385C2—2922no—
386C2—2921no—
387C2—5841no—
388C2#1798922911yescharacteristic
389C2AGL(1,ℤ/8)×D7311yescharacteristic
390C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3324
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #17989305C2semidirect
3. #17988932C2semidirect
4. #17988913C2semidirect
5. #17988866C2semidirect
6. #17988834C2semidirect
7. #17988831C2semidirect
8. #17988786C2semidirect
9. #17988740C2semidirect
10. #17988739C2semidirect
11. #17988674C2semidirect
12. #17988662C2semidirect
13. #17988591C2semidirect
14. #17988590C2semidirect
15. #482×C73C2semidirect
20. C2×#11924017C22semidirect
21. C2×#11924016C22semidirect
22. C2×#11924012C22semidirect
23. C2×#11924011C22semidirect
24. #14556590C22semidirect
29. #14556571C22semidirect
30. #14556570C22semidirect
36. #14556556C22semidirect
39. #14556549C22semidirect
40. #14556524C22semidirect
41. #14556520C22semidirect
42. #14556514C22semidirect
44. #14556513C22semidirect
45. #14556512C22semidirect
48. #14556511C22semidirect
49. #14556511C22semidirect
50. #14556503C22semidirect
51. C8×Dic73C22semidirect
53. #117×C73C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. #102×C73C22semidirect
57. #102×C73C22semidirect
58. C22⋊C8×C73C22semidirect
196. C73#3324semidirect
201. #482D73semidirect
237. #117C2×D73semidirect
239. #107C2×D73semidirect
240. #106C2×D73semidirect
250. #102C2×D73semidirect
251. #102C2×D73semidirect
253. C22⋊C8C2×D73semidirect