Finite Group Databasebeta

← #485×D293 #49168673

Subgroups — #485×D293 #49168673

Order 37504.

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×D293C211yesmaximal, characteristic
2#117×D293C211yesmaximal, characteristic
3#34036473C211yesmaximal, characteristic, complemented
4#34036472C211yesmaximal, characteristic, complemented
5#34036471C211yesmaximal, characteristic, complemented
6#34036470C211yesmaximal, characteristic, complemented
7#34036469C211yesmaximal, characteristic, complemented
8#34036468C211yesmaximal, characteristic, complemented
9#34036467C211yesmaximal, characteristic, complemented
10#107×D293C211yesmaximal, characteristic, complemented
11#106×D293C211yesmaximal, characteristic, complemented
12#103×D293C211yesmaximal, characteristic, complemented
13#103×D293C211yesmaximal, characteristic, complemented
14C22⋊C8×D293C211yesmaximal, characteristic
15#485×C293C211yesmaximal, characteristic, complemented
16C2×Q8×D293C2211yescharacteristic
17C22×C4×D293C2211yescharacteristic
18C2×C8×D293C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20#22627604C2211yescharacteristic
21#22627603C2211yescharacteristic
22#22627602—21no—
23#22627601—21no—
24#22627600C2211yescharacteristic
25#22627583C2211yescharacteristic
26#22627582C2211yescharacteristic
27#22627582C2211yescharacteristic
28#22627581—21no—
29#22627580—21no—
30C4⋊C4×D293—21no—
31C4⋊C4×D293C2211yescharacteristic
32C4⋊C4×D293C2211yescharacteristic
33C4⋊C4×D293C2211yescharacteristic
34C22⋊C4×D293—21no—
35C22⋊C4×D293—21no—
36C42×D293—21no—
37#22627558C2211yescharacteristic, complemented
38#22627557C2211yescharacteristic, complemented
39#22627557C2211yescharacteristic, complemented
40#22627556C2211yescharacteristic, complemented
41#22627555C2211yescharacteristic, complemented
42#22627555C2211yescharacteristic, complemented
43#22627549C2211yescharacteristic, complemented
44#22627549C2211yescharacteristic, complemented
45#22627548C2211yescharacteristic, complemented
46#22627548C2211yescharacteristic, complemented
47#22627547C2211yescharacteristic, complemented
48#22627547C2211yescharacteristic, complemented
49C22⋊#14556873C2211yescharacteristic
50#22627536C2211yescharacteristic
51#22627536C2211yescharacteristic
52C22⋊Q8×C293C2211yescharacteristic
53#117×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic, complemented
55#106×C293C2211yescharacteristic, complemented
56#103×C293C2211yescharacteristic, complemented
57#103×C293C2211yescharacteristic, complemented
58C22⋊C8×C293C2211yescharacteristic
59C23×D293D411yescharacteristic
60C2×Dic586—21no—
61C2×Dic586C2311yescharacteristic
62Q8×D293—22no—
63Q8×D293—22no—
64C22×Dic293D411yescharacteristic
65C2×C4×D293—22no—
66C2×C4×D293—22no—
67C2×C4×D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293D411yescharacteristic
72C2×C4×D293D411yescharacteristic
73C2×C4×D293C2311yescharacteristic
74C2×C4×D293C2311yescharacteristic
75C2×#14556873C2311yescharacteristic
76C2×#14556873C2311yescharacteristic
77C8×D293—22no—
78C8×D293—22no—
79C4⋊Dic293—21no—
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88C22⋊Dic293—21no—
89C22⋊Dic293—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94C4×Dic293—21no—
95C4×Dic293—21no—
96C4×Dic293—21no—
97C2×Q8×C293C2311yescharacteristic
98C22×C4×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C4⋊C4×C293—21no—
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C42×C293—21no—
108C22×D293—22no—
109C22×D293—22no—
110C22×D293—22no—
111C22×D293C2×D411yescharacteristic
112C22×D293C2×D411yescharacteristic
113Dic586—21no—
114Dic586—21no—
115Dic586—42no—
116C2×Dic293—22no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293C2×D411yescharacteristic
122C2×Dic293C2×D411yescharacteristic
123C4×D293—22no—
124C4×D293—21no—
125C4×D293—21no—
126C4×D293—22no—
127C4×D293—42no—
128C4×D293—42no—
129C4×D293—42no—
130C4×D293—42no—
131C4×D293#4112yes—
132C4×D293#4112yes—
133#14556873—21no—
134#14556873—21no—
135C23×C293C2×D411yescharacteristic
136Q8×C293—21no—
137Q8×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2411yescharacteristic
146C8×C293—21no—
147C8×C293—21no—
148C22×C293—21no—
149C22×C293—21no—
150C22×C293—21no—
151C22×C293C22×D411yescharacteristic
152C2×D293—21no—
153C2×D293—21no—
154C2×D293—21no—
155C2×D293—44no—
156C2×D293#12312yes—
157C2×D293#13512yes—
158C2×D293#13712yes—
159C4×C293—21no—
160C4×C293—41no—
161C4×C293—41no—
162C4×C293—41no—
163C4×C293—41no—
164C4×C293C2×#4111yescharacteristic
165C4×C293C2×#4111yescharacteristic
166Dic293—21no—
167Dic293—41no—
168Dic293—41no—
169Dic293—41no—
170Dic293—41no—
171Dic293#12312yes—
172C2×C293—41no—
173C2×C293C2×#12311yescharacteristic
174C2×C293C2×#13511yescharacteristic
175C2×C293C2×#13711yescharacteristic
176D293—41no—
177D293#48514yesdirect product factor
178C293C2×#48511yescharacteristic, complemented, Sylow
179C2×#485—2931nomaximal, Sylow
180C2×C22⋊Q8—2931no—
181C2×#117—2931no—
182#485—2931no—
183#485—2931no—
184#485—2931no—
185#485—2931no—
186#485—2931no—
187#485—2931no—
188#485—2931no—
189#485D29311yescharacteristic, direct product factor
190C2×#107—2931no—
191C2×#106—2931no—
192C2×#103—2931no—
193C2×#103—2931no—
194C2×C22⋊C8—2931no—
195C22×Q8—2931no—
196C23×C4—2931no—
197C22×C8—2931no—
198C22×C8—2931no—
199C22⋊Q8—2931no—
200C22⋊Q8—2931no—
201C22⋊Q8—2931no—
202C22⋊Q8—5861no—
203C22⋊Q8—5861no—
204C22⋊Q8C2×D29311yescharacteristic
205#117—2931no—
206#117—2931no—
207#117—2931no—
208#117—5861no—
209#117—5861no—
210#117C2×D29311yescharacteristic
211C2×C4⋊C4—2931no—
212C2×C4⋊C4—2931no—
213C2×C4⋊C4—2931no—
214C2×C4⋊C4—5861no—
215C2×C22⋊C4—5861no—
216C2×C22⋊C4—5861no—
217C2×C42—5861no—
218#107—2931no—
219#107—2931no—
220#107—2931no—
221#107C2×D29311yescharacteristic, complemented
222#106—2931no—
223#106—2931no—
224#106—2931no—
225#106C2×D29311yescharacteristic, complemented
226#103—2931no—
227#103—2931no—
228#103—2931no—
229#103—2931no—
230#103—2931no—
231#103—2931no—
232#103C2×D29311yescharacteristic, complemented
233#103C2×D29311yescharacteristic, complemented
234C22⋊C8—2931no—
235C22⋊C8—2931no—
236C22⋊C8—2931no—
237C22⋊C8C2×D29311yescharacteristic
238C24—2931no—
239C2×Q8—2931no—
240C2×Q8—5861no—
241C2×Q8—5862no—
242C2×Q8—5862no—
243C2×Q8C22×D29311yescharacteristic
244C22×C4—2931no—
245C22×C4—2931no—
246C22×C4—2931no—
247C22×C4—2931no—
248C22×C4—2931no—
249C22×C4—5862no—
250C22×C4—5862no—
251C22×C4—5861no—
252C22×C4—5861no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4C22×D29311yescharacteristic
256C2×C8—2931no—
257C2×C8—2931no—
258C2×C8—5862no—
259C2×C8—5862no—
260C2×C8C22×D29311yescharacteristic
261C2×C8C22×D29311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—2931no—
264C4⋊C4—2931no—
265C4⋊C4—2931no—
266C4⋊C4—5861no—
267C4⋊C4—5861no—
268C4⋊C4—5861no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4C22×D29311yescharacteristic
273C4⋊C4C22×D29311yescharacteristic
274C4⋊C4C22×D29311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—5861no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C42—21no—
284C42—5861no—
285C42—5861no—
286C42—5861no—
287C23—2931no—
288C23—2931no—
289C23—5862no—
290C23—5862no—
291C23—5862no—
292C23D4×D29311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—5861no—
296Q8—5861no—
297Q8—11722no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—2931no—
305C2×C4—2932no—
306C2×C4—2932no—
307C2×C4—2931no—
308C2×C4—5862no—
309C2×C4—5862no—
310C2×C4—5862no—
311C2×C4—5861no—
312C2×C4—5861no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—11722no—
318C2×C4—11722no—
319C2×C4—11722no—
320C2×C4—11722no—
321C2×C4D4×D29311yescharacteristic
322C2×C4C23×D29311yescharacteristic
323C8—21no—
324C8—21no—
325C8—5861no—
326C8—5861no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—2932no—
331C22—2932no—
332C22—2932no—
333C22—5861no—
334C22—5861no—
335C22—5861no—
336C22—11724no—
337C22C2×D4×D29311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2932no—
344C4—5861no—
345C4—11721no—
346C4—11721no—
347C4—11721no—
348C4—11721no—
349C4#41×D29311yescharacteristic
350C4#41×D29311yescharacteristic
351C2—41no—
352C2—2934no—
353C2—11721no—
354C2#123×D29311yescharacteristic
355C2#135×D29311yescharacteristic
356C2#137×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#485×C293C2
socleC22×C293C22×D4
prime radicalC23×D293D4
hypercenter#485D293
hypocenterC293C2×#485
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #34036473C2semidirect
4. #34036472C2semidirect
5. #34036471C2semidirect
6. #34036470C2semidirect
7. #34036469C2semidirect
8. #34036468C2semidirect
9. #34036467C2semidirect
10. #107×D293C2semidirect
11. #106×D293C2semidirect
12. #103×D293C2semidirect
13. #103×D293C2semidirect
15. #485×C293C2semidirect
37. #22627558C22semidirect
38. #22627557C22semidirect
39. #22627557C22semidirect
40. #22627556C22semidirect
41. #22627555C22semidirect
42. #22627555C22semidirect
43. #22627549C22semidirect
44. #22627549C22semidirect
45. #22627548C22semidirect
46. #22627548C22semidirect
47. #22627547C22semidirect
48. #22627547C22semidirect
54. #107×C293C22semidirect
55. #106×C293C22semidirect
56. #103×C293C22semidirect
57. #103×C293C22semidirect
177. D293#485direct (N × H)
178. C293C2×#485semidirect
189. #485D293direct (N × H)
221. #107C2×D293semidirect
225. #106C2×D293semidirect
232. #103C2×D293semidirect
233. #103C2×D293semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22⋊Q8×D2932
#117×D2932
#340364732
#340364722
#340364712
#340364702
#340364692
#340364682
#340364672
#107×D2932
#106×D2932
#103×D2932
C22⋊C8×D2932
#485×C2932
C2×#485293