Finite Group Databasebeta

← #485×D73 #22619819

Subgroups — #485×D73 #22619819

Order 9344.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D73C211yesmaximal, characteristic
2#117×D73C211yesmaximal, characteristic
3#17988931C211yesmaximal, characteristic, complemented
4#17988930C211yesmaximal, characteristic, complemented
5#17988929C211yesmaximal, characteristic, complemented
6#17988928C211yesmaximal, characteristic, complemented
7#17988927C211yesmaximal, characteristic, complemented
8#17988926C211yesmaximal, characteristic, complemented
9#17988925C211yesmaximal, characteristic, complemented
10#107×D73C211yesmaximal, characteristic, complemented
11#106×D73C211yesmaximal, characteristic, complemented
12#103×D73C211yesmaximal, characteristic, complemented
13#103×D73C211yesmaximal, characteristic, complemented
14C22⋊C8×D73C211yesmaximal, characteristic
15#485×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C2×C8×D73C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20#14556571C2211yescharacteristic
21#14556570C2211yescharacteristic
22#14556569—21no—
23#14556568—21no—
24#14556567C2211yescharacteristic
25#14556550C2211yescharacteristic
26#14556549C2211yescharacteristic
27#14556549C2211yescharacteristic
28#14556548—21no—
29#14556547—21no—
30C4⋊C4×D73—21no—
31C4⋊C4×D73C2211yescharacteristic
32C4⋊C4×D73C2211yescharacteristic
33C4⋊C4×D73C2211yescharacteristic
34C22⋊C4×D73—21no—
35C22⋊C4×D73—21no—
36C42×D73—21no—
37#14556525C2211yescharacteristic, complemented
38#14556524C2211yescharacteristic, complemented
39#14556524C2211yescharacteristic, complemented
40#14556523C2211yescharacteristic, complemented
41#14556522C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556515C2211yescharacteristic, complemented
46#14556515C2211yescharacteristic, complemented
47#14556514C2211yescharacteristic, complemented
48#14556514C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C22⋊Q8×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56#103×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic
59C23×D73D411yescharacteristic
60C2×Dic146—21no—
61C2×Dic146C2311yescharacteristic
62Q8×D73—22no—
63Q8×D73—22no—
64C22×Dic73D411yescharacteristic
65C2×C4×D73—22no—
66C2×C4×D73—22no—
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73D411yescharacteristic
72C2×C4×D73D411yescharacteristic
73C2×C4×D73C2311yescharacteristic
74C2×C4×D73C2311yescharacteristic
75C2×#10596831C2311yescharacteristic
76C2×#10596831C2311yescharacteristic
77C8×D73—22no—
78C8×D73—22no—
79C4⋊Dic73—21no—
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C2×Q8×C73C2311yescharacteristic
98C22×C4×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C4⋊C4×C73—21no—
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C42×C73—21no—
108C23×C73C2×D411yescharacteristic
109C22×D73—22no—
110C22×D73—22no—
111C22×D73—22no—
112C22×D73C2×D411yescharacteristic
113C22×D73C2×D411yescharacteristic
114Q8×C73—21no—
115Q8×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2411yescharacteristic
124C2×Dic73—22no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C4×D73—22no—
132C4×D73—21no—
133C4×D73—21no—
134C4×D73—22no—
135C4×D73—42no—
136C4×D73—42no—
137C4×D73—42no—
138C4×D73—42no—
139C4×D73#4112yes—
140C4×D73#4112yes—
141Dic146—21no—
142Dic146—21no—
143Dic146—42no—
144C8×C73—21no—
145C8×C73—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73C22×D411yescharacteristic
152C2×D73—21no—
153C2×D73—21no—
154C2×D73—21no—
155C2×D73—44no—
156C2×D73#12312yes—
157C2×D73#13512yes—
158C2×D73#13712yes—
159C4×C73—21no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73C2×#4111yescharacteristic
165C4×C73C2×#4111yescharacteristic
166Dic73—21no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171Dic73#12312yes—
172C2×C73—41no—
173C2×C73C2×#12311yescharacteristic
174C2×C73C2×#13511yescharacteristic
175C2×C73C2×#13711yescharacteristic
176D73—41no—
177D73#48514yesdirect product factor
178C2×#485—731nomaximal, Sylow
179C73C2×#48511yescharacteristic, complemented, Sylow
180C2×C22⋊Q8—731no—
181C2×#117—731no—
182#485—731no—
183#485—731no—
184#485—731no—
185#485—731no—
186#485—731no—
187#485—731no—
188#485—731no—
189#485D7311yescharacteristic, direct product factor
190C2×#107—731no—
191C2×#106—731no—
192C2×#103—731no—
193C2×#103—731no—
194C2×C22⋊C8—731no—
195C22×Q8—731no—
196C23×C4—731no—
197C22×C8—731no—
198C22×C8—731no—
199C22⋊Q8—731no—
200C22⋊Q8—731no—
201C22⋊Q8—731no—
202C22⋊Q8—1461no—
203C22⋊Q8—1461no—
204C22⋊Q8C2×D7311yescharacteristic
205#117—731no—
206#117—731no—
207#117—731no—
208#117—1461no—
209#117—1461no—
210#117C2×D7311yescharacteristic
211C2×C4⋊C4—731no—
212C2×C4⋊C4—731no—
213C2×C4⋊C4—731no—
214C2×C4⋊C4—1461no—
215C2×C22⋊C4—1461no—
216C2×C22⋊C4—1461no—
217C2×C42—1461no—
218#107—731no—
219#107—731no—
220#107—731no—
221#107C2×D7311yescharacteristic, complemented
222#106—731no—
223#106—731no—
224#106—731no—
225#106C2×D7311yescharacteristic, complemented
226#103—731no—
227#103—731no—
228#103—731no—
229#103—731no—
230#103—731no—
231#103—731no—
232#103C2×D7311yescharacteristic, complemented
233#103C2×D7311yescharacteristic, complemented
234C22⋊C8—731no—
235C22⋊C8—731no—
236C22⋊C8—731no—
237C22⋊C8C2×D7311yescharacteristic
238C24—731no—
239C2×Q8—731no—
240C2×Q8—1461no—
241C2×Q8—1462no—
242C2×Q8—1462no—
243C2×Q8C22×D7311yescharacteristic
244C22×C4—731no—
245C22×C4—731no—
246C22×C4—731no—
247C22×C4—731no—
248C22×C4—731no—
249C22×C4—1461no—
250C22×C4—1461no—
251C22×C4—1461no—
252C22×C4—1461no—
253C22×C4—1462no—
254C22×C4—1462no—
255C22×C4C22×D7311yescharacteristic
256C2×C8—731no—
257C2×C8—731no—
258C2×C8—1462no—
259C2×C8—1462no—
260C2×C8C22×D7311yescharacteristic
261C2×C8C22×D7311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—731no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4—1461no—
272C4⋊C4C22×D7311yescharacteristic
273C4⋊C4C22×D7311yescharacteristic
274C4⋊C4C22×D7311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C42—21no—
284C42—1461no—
285C42—1461no—
286C42—1461no—
287C23—731no—
288C23—731no—
289C23—1462no—
290C23—1462no—
291C23—1462no—
292C23D4×D7311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—2922no—
296Q8—1461no—
297Q8—1461no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—2922no—
305C2×C4—2922no—
306C2×C4—2922no—
307C2×C4—2922no—
308C2×C4—731no—
309C2×C4—732no—
310C2×C4—732no—
311C2×C4—731no—
312C2×C4—1462no—
313C2×C4—1462no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1462no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4D4×D7311yescharacteristic
322C2×C4C23×D7311yescharacteristic
323C8—21no—
324C8—21no—
325C8—1461no—
326C8—1461no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—2924no—
331C22—732no—
332C22—732no—
333C22—732no—
334C22—1461no—
335C22—1461no—
336C22—1461no—
337C22C2×D4×D7311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2921no—
344C4—2921no—
345C4—2921no—
346C4—2921no—
347C4—732no—
348C4—1461no—
349C4#41×D7311yescharacteristic
350C4#41×D7311yescharacteristic
351C2—41no—
352C2—2921no—
353C2—734no—
354C2#123×D7311yescharacteristic
355C2#135×D7311yescharacteristic
356C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#485×C73C2
socleC22×C73C22×D4
hypercenter#485D73
hypocenterC73C2×#485
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #17988931C2semidirect
4. #17988930C2semidirect
5. #17988929C2semidirect
6. #17988928C2semidirect
7. #17988927C2semidirect
8. #17988926C2semidirect
9. #17988925C2semidirect
10. #107×D73C2semidirect
11. #106×D73C2semidirect
12. #103×D73C2semidirect
13. #103×D73C2semidirect
15. #485×C73C2semidirect
37. #14556525C22semidirect
38. #14556524C22semidirect
39. #14556524C22semidirect
40. #14556523C22semidirect
41. #14556522C22semidirect
42. #14556522C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
45. #14556515C22semidirect
46. #14556515C22semidirect
47. #14556514C22semidirect
48. #14556514C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. #103×C73C22semidirect
57. #103×C73C22semidirect
177. D73#485direct (N × H)
179. C73C2×#485semidirect
189. #485D73direct (N × H)
221. #107C2×D73semidirect
225. #106C2×D73semidirect
232. #103C2×D73semidirect
233. #103C2×D73semidirect