Finite Group Databasebeta

← #22622157

Subgroups — #22622157

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#17989308C211yesmaximal, characteristic, complemented
2#17989221C211yesmaximal, characteristic
3#17988932C211yesmaximal, characteristic, complemented
4#17988914C211yesmaximal, characteristic, complemented
5#17988908C211yesmaximal, characteristic, complemented
6#17988866C211yesmaximal, characteristic, complemented
7#17988836C211yesmaximal, characteristic, complemented
8#17988785C211yesmaximal, characteristic, complemented
9#17988737C211yesmaximal, characteristic, complemented
10#17988736C211yesmaximal, characteristic, complemented
11#17988672C211yesmaximal, characteristic, complemented
12#17988663C211yesmaximal, characteristic, complemented
13#17988593C211yesmaximal, characteristic, complemented
14#17988590C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C22×D292C2211yescharacteristic
17C2×D4×D73—21no—
18C2×D4×D73C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924015C2211yescharacteristic, complemented
21C2×#11924011C2211yescharacteristic, complemented
22#14556590C2211yescharacteristic, complemented
23#14556587C2211yescharacteristic
24#14556586—21no—
25#14556584—21no—
26#14556577—21no—
27#14556567C2211yescharacteristic, complemented
28#14556566C2211yescharacteristic
29#14556564—21no—
30#14556561—21no—
31#14556559—21no—
32Q8×Dic73C2211yescharacteristic, complemented
33#14556556—21no—
34#14556553C2211yescharacteristic
35C4×C22⋊D73C2211yescharacteristic
36#14556550C2211yescharacteristic, complemented
37#14556549C2211yescharacteristic, complemented
38#14556524C2211yescharacteristic, complemented
39#14556522C2211yescharacteristic, complemented
40#14556520C2211yescharacteristic, complemented
41#14556513C2211yescharacteristic
42#14556513C2211yescharacteristic
43#14556513C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic, complemented
45#14556512C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic, complemented
50#14556503C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C2×SD16×C73C2211yescharacteristic, complemented
53C2×M16×C73C2211yescharacteristic, complemented
54C22⋊Q8×C73C2211yescharacteristic, complemented
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58#102×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C23×D73—21no—
61C2×Dic146—21no—
62C2×D292—22no—
63C2×D292—21no—
64C2×D292—21no—
65C2×D292—41no—
66C2×D292C2311yescharacteristic
67C2×D292C2311yescharacteristic
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73D411yescharacteristic
72D4×D73—22no—
73D4×D73—41no—
74D4×D73—44no—
75C2×C4×D73—21no—
76C2×C4×D73C2311yescharacteristic
77#11924015—22no—
78#11924015—41no—
79#11924011—41no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C4⋊Dic73—21no—
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85#11924007—21no—
86#11924007—21no—
87#11924007D411yescharacteristic
88C22⋊Dic73—21no—
89C22⋊Dic73D411yescharacteristic
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C4×Dic73C2311yescharacteristic
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73C2311yescharacteristic
103SD16×C73—41no—
104M16×C73—41no—
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C22⋊C4×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
123Q8×C73—21no—
124Q8×C73—21no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—42no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73C2×D411yescharacteristic
134C2×C4×C73C2411yescharacteristic
135C22⋊D73—22no—
136C22⋊D73—42no—
137C22⋊D73—42no—
138C22⋊D73—81no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143C2×Dic73C2×D411yescharacteristic
144D292—21no—
145D292—21no—
146D292—21no—
147D292—42no—
148D292—42no—
149D292#4112yes—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—42no—
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#482—731no—
202#474—731no—
203#468—731no—
204#468D7311yescharacteristic, complemented
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×SD16C2×D7311yescharacteristic, complemented
218C2×M16—731no—
219C2×M16C2×D7311yescharacteristic, complemented
220C4⋊Q8—731no—
221#127—731no—
222#126—1461no—
223#126—1461no—
224#124—1461no—
225C22⋊Q8—731no—
226C22⋊Q8C2×D7311yescharacteristic, complemented
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#117—731no—
238#107—731no—
239#107C2×D7311yescharacteristic, complemented
240#106—731no—
241C4⋊C8—731no—
242#103C2×D7311yescharacteristic, complemented
243#102—731no—
244#102—731no—
245#102—731no—
246#102—731no—
247#102—731no—
248#102—731no—
249#102—731no—
250#102—731no—
251#102C2×D7311yescharacteristic, complemented
252C22⋊C8—731no—
253C22⋊C8—731no—
254C4×C8—731no—
255C24—1461no—
256C24—1461no—
257C2×Q8—1461no—
258C2×Q8C22×D7311yescharacteristic
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—41no—
278SD16—2921no—
279SD16—1462no—
280M16—41no—
281M16—2921no—
282C2×C8—731no—
283C2×C8—731no—
284C2×C8C22×D7311yescharacteristic
285C2×C8C22×D7311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—731no—
288C4⋊C4—731no—
289C4⋊C4—731no—
290C4⋊C4—1461no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
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—731no—
305C42—1461no—
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—21no—
320Q8—21no—
321Q8—2922no—
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#1455663611yescharacteristic
383C2—41no—
384C2—81no—
385C2—2922no—
386C2—2921no—
387C2—5841no—
388C2#1798922611yescharacteristic
389C2AGL(1,ℤ/8)×D7311yescharacteristic
390C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3324
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #17989308C2semidirect
3. #17988932C2semidirect
4. #17988914C2semidirect
5. #17988908C2semidirect
6. #17988866C2semidirect
7. #17988836C2semidirect
8. #17988785C2semidirect
9. #17988737C2semidirect
10. #17988736C2semidirect
11. #17988672C2semidirect
12. #17988663C2semidirect
13. #17988593C2semidirect
14. #17988590C2semidirect
15. #468×C73C2semidirect
20. C2×#11924015C22semidirect
21. C2×#11924011C22semidirect
22. #14556590C22semidirect
27. #14556567C22semidirect
32. Q8×Dic73C22semidirect
36. #14556550C22semidirect
37. #14556549C22semidirect
38. #14556524C22semidirect
39. #14556522C22semidirect
40. #14556520C22semidirect
43. #14556513C22semidirect
44. #14556513C22semidirect
45. #14556512C22semidirect
46. #14556512C22semidirect
48. #14556511C22semidirect
49. C22⋊#10596831C22semidirect
50. #14556503C22semidirect
51. C8×Dic73C22semidirect
52. C2×SD16×C73C22semidirect
53. C2×M16×C73C22semidirect
54. C22⋊Q8×C73C22semidirect
56. #107×C73C22semidirect
57. #103×C73C22semidirect
58. #102×C73C22semidirect
196. C73#3324semidirect
204. #468D73semidirect
217. C2×SD16C2×D73semidirect
219. C2×M16C2×D73semidirect
226. C22⋊Q8C2×D73semidirect
239. #107C2×D73semidirect
242. #103C2×D73semidirect
251. #102C2×D73semidirect