Finite Group Databasebeta

← #485×D79 #23773288

Subgroups — #485×D79 #23773288

Order 10112.

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×D79C211yesmaximal, characteristic
2#117×D79C211yesmaximal, characteristic
3#19098907C211yesmaximal, characteristic, complemented
4#19098906C211yesmaximal, characteristic, complemented
5#19098905C211yesmaximal, characteristic, complemented
6#19098904C211yesmaximal, characteristic, complemented
7#19098903C211yesmaximal, characteristic, complemented
8#19098902C211yesmaximal, characteristic, complemented
9#19098901C211yesmaximal, characteristic, complemented
10#107×D79C211yesmaximal, characteristic, complemented
11#106×D79C211yesmaximal, characteristic, complemented
12#103×D79C211yesmaximal, characteristic, complemented
13#103×D79C211yesmaximal, characteristic, complemented
14C22⋊C8×D79C211yesmaximal, characteristic
15#485×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C2×C8×D79C2211yescharacteristic
19C2×C8×D79C2211yescharacteristic
20#14579141C2211yescharacteristic
21#14579140C2211yescharacteristic
22#14579139—21no—
23#14579138—21no—
24#14579137C2211yescharacteristic
25#14579120C2211yescharacteristic
26#14579119C2211yescharacteristic
27#14579119C2211yescharacteristic
28#14579118—21no—
29#14579117—21no—
30C4⋊C4×D79—21no—
31C4⋊C4×D79C2211yescharacteristic
32C4⋊C4×D79C2211yescharacteristic
33C4⋊C4×D79C2211yescharacteristic
34C22⋊C4×D79—21no—
35C22⋊C4×D79—21no—
36C42×D79—21no—
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579085C2211yescharacteristic, complemented
46#14579085C2211yescharacteristic, complemented
47#14579084C2211yescharacteristic, complemented
48#14579084C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C22⋊Q8×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79D411yescharacteristic
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62Q8×D79—22no—
63Q8×D79—22no—
64C22×Dic79D411yescharacteristic
65C2×C4×D79—22no—
66C2×C4×D79—22no—
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79D411yescharacteristic
72C2×C4×D79D411yescharacteristic
73C2×C4×D79C2311yescharacteristic
74C2×C4×D79C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C8×D79—22no—
78C8×D79—22no—
79C4⋊Dic79—21no—
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C2×Q8×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C4⋊C4×C79—21no—
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79—21no—
108C23×C79C2×D411yescharacteristic
109C22×D79—22no—
110C22×D79—22no—
111C22×D79—22no—
112C22×D79C2×D411yescharacteristic
113C22×D79C2×D411yescharacteristic
114Q8×C79—21no—
115Q8×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2411yescharacteristic
124C2×Dic79—22no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131C4×D79—22no—
132C4×D79—21no—
133C4×D79—21no—
134C4×D79—22no—
135C4×D79—42no—
136C4×D79—42no—
137C4×D79—42no—
138C4×D79—42no—
139C4×D79#4112yes—
140C4×D79#4112yes—
141Dic158—21no—
142Dic158—21no—
143Dic158—42no—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79C22×D411yescharacteristic
152C2×D79—21no—
153C2×D79—21no—
154C2×D79—21no—
155C2×D79—44no—
156C2×D79#12312yes—
157C2×D79#13512yes—
158C2×D79#13712yes—
159C4×C79—21no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79C2×#4111yescharacteristic
165C4×C79C2×#4111yescharacteristic
166Dic79—21no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171Dic79#12312yes—
172C2×C79—41no—
173C2×C79C2×#12311yescharacteristic
174C2×C79C2×#13511yescharacteristic
175C2×C79C2×#13711yescharacteristic
176D79—41no—
177D79#48514yesdirect product factor
178C2×#485—791nomaximal, Sylow
179C79C2×#48511yescharacteristic, complemented, Sylow
180C2×C22⋊Q8—791no—
181C2×#117—791no—
182#485—791no—
183#485—791no—
184#485—791no—
185#485—791no—
186#485—791no—
187#485—791no—
188#485—791no—
189#485D7911yescharacteristic, direct product factor
190C2×#107—791no—
191C2×#106—791no—
192C2×#103—791no—
193C2×#103—791no—
194C2×C22⋊C8—791no—
195C22×Q8—791no—
196C23×C4—791no—
197C22×C8—791no—
198C22×C8—791no—
199C22⋊Q8—791no—
200C22⋊Q8—791no—
201C22⋊Q8—791no—
202C22⋊Q8—1581no—
203C22⋊Q8—1581no—
204C22⋊Q8C2×D7911yescharacteristic
205#117—791no—
206#117—791no—
207#117—791no—
208#117—1581no—
209#117—1581no—
210#117C2×D7911yescharacteristic
211C2×C4⋊C4—791no—
212C2×C4⋊C4—791no—
213C2×C4⋊C4—791no—
214C2×C4⋊C4—1581no—
215C2×C22⋊C4—1581no—
216C2×C22⋊C4—1581no—
217C2×C42—1581no—
218#107—791no—
219#107—791no—
220#107—791no—
221#107C2×D7911yescharacteristic, complemented
222#106—791no—
223#106—791no—
224#106—791no—
225#106C2×D7911yescharacteristic, complemented
226#103—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103—791no—
232#103C2×D7911yescharacteristic, complemented
233#103C2×D7911yescharacteristic, complemented
234C22⋊C8—791no—
235C22⋊C8—791no—
236C22⋊C8—791no—
237C22⋊C8C2×D7911yescharacteristic
238C24—791no—
239C2×Q8—791no—
240C2×Q8—1581no—
241C2×Q8—1582no—
242C2×Q8—1582no—
243C2×Q8C22×D7911yescharacteristic
244C22×C4—791no—
245C22×C4—791no—
246C22×C4—791no—
247C22×C4—791no—
248C22×C4—791no—
249C22×C4—1581no—
250C22×C4—1581no—
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4—1582no—
254C22×C4—1582no—
255C22×C4C22×D7911yescharacteristic
256C2×C8—791no—
257C2×C8—791no—
258C2×C8—1582no—
259C2×C8—1582no—
260C2×C8C22×D7911yescharacteristic
261C2×C8C22×D7911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—791no—
264C4⋊C4—791no—
265C4⋊C4—791no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4C22×D7911yescharacteristic
273C4⋊C4C22×D7911yescharacteristic
274C4⋊C4C22×D7911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C42—21no—
284C42—1581no—
285C42—1581no—
286C42—1581no—
287C23—791no—
288C23—791no—
289C23—1582no—
290C23—1582no—
291C23—1582no—
292C23D4×D7911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—3162no—
296Q8—1581no—
297Q8—1581no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—3162no—
305C2×C4—3162no—
306C2×C4—3162no—
307C2×C4—3162no—
308C2×C4—791no—
309C2×C4—792no—
310C2×C4—792no—
311C2×C4—791no—
312C2×C4—1582no—
313C2×C4—1582no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1582no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4D4×D7911yescharacteristic
322C2×C4C23×D7911yescharacteristic
323C8—21no—
324C8—21no—
325C8—1581no—
326C8—1581no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—3164no—
331C22—792no—
332C22—792no—
333C22—792no—
334C22—1581no—
335C22—1581no—
336C22—1581no—
337C22C2×D4×D7911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3161no—
344C4—3161no—
345C4—3161no—
346C4—3161no—
347C4—792no—
348C4—1581no—
349C4#41×D7911yescharacteristic
350C4#41×D7911yescharacteristic
351C2—41no—
352C2—3161no—
353C2—794no—
354C2#123×D7911yescharacteristic
355C2#135×D7911yescharacteristic
356C2#137×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#485×C79C2
socleC22×C79C22×D4
prime radicalC23×D79D4
hypercenter#485D79
hypocenterC79C2×#485
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #19098907C2semidirect
4. #19098906C2semidirect
5. #19098905C2semidirect
6. #19098904C2semidirect
7. #19098903C2semidirect
8. #19098902C2semidirect
9. #19098901C2semidirect
10. #107×D79C2semidirect
11. #106×D79C2semidirect
12. #103×D79C2semidirect
13. #103×D79C2semidirect
15. #485×C79C2semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. #14579092C22semidirect
42. #14579092C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
45. #14579085C22semidirect
46. #14579085C22semidirect
47. #14579084C22semidirect
48. #14579084C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. #103×C79C22semidirect
57. #103×C79C22semidirect
177. D79#485direct (N × H)
179. C79C2×#485semidirect
189. #485D79direct (N × H)
221. #107C2×D79semidirect
225. #106C2×D79semidirect
232. #103C2×D79semidirect
233. #103C2×D79semidirect