Finite Group Databasebeta

← #23773650

Subgroups — #23773650

Order 10112.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099174C211yesmaximal, characteristic, complemented
2#19099035C211yesmaximal, characteristic
3#19098903C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098864C211yesmaximal, characteristic, complemented
6#19098863C211yesmaximal, characteristic, complemented
7#19098765C211yesmaximal, characteristic, complemented
8#19098712C211yesmaximal, characteristic
9#19098712C211yesmaximal, characteristic
10#19098666C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12SD16×Dic79C211yesmaximal, characteristic, complemented
13#19098648C211yesmaximal, characteristic, complemented
14#19098623C211yesmaximal, characteristic, complemented
15#461×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929611C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19#14579156—21no—
20#14579156—21no—
21#14579153C2211yescharacteristic, complemented
22#14579151—21no—
23#14579151—21no—
24#14579137C2211yescharacteristic
25#14579137C2211yescharacteristic
26Q8×Dic79C2211yescharacteristic, complemented
27Q8×Dic79C2211yescharacteristic, complemented
28C4×D316C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30#14579123C2211yescharacteristic
31C4×C22⋊D79—21no—
32(C22⋊D79)⋊C4—21no—
33#14579119C2211yescharacteristic
34#14579118C2211yescharacteristic
35C2×(C2×D79)⋊C4—21no—
36C22⋊C4×D79—21no—
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C4⋊Q8×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56C4⋊C8×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#103×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×D316C2311yescharacteristic
61C2×C22⋊D79—21no—
62D4×D79—22no—
63D4×D79—22no—
64C22×Dic79—21no—
65C2×C4×D79—21no—
66C2×C4×D79—21no—
67C2×C4×D79C2311yescharacteristic
68#11929611—22no—
69#11929611—22no—
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C4⋊Dic79—21no—
73C4⋊Dic79—21no—
74C4⋊Dic79C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4D411yescharacteristic
82Dic79⋊C4D411yescharacteristic
83C22⋊Dic79—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4D411yescharacteristic
90(C2×D79)⋊C4D411yescharacteristic
91C4×Dic79—21no—
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79C2311yescharacteristic
95C2×Q8×C79C2311yescharacteristic
96C2×Q8×C79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99SD16×C79—22no—
100SD16×C79—22no—
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79—21no—
104C4⋊C4×C79—21no—
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C22×D79—21no—
110C22×D79—24no—
111C22×D79—81no—
112C22×D79—81no—
113C22×D79C2×D411yescharacteristic
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—21no—
118D4×C79—21no—
119D4×C79#4112yes—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—81no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—24no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—81no—
132C2×Dic79C2×D411yescharacteristic
133C2×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135D316—21no—
136D316#4112yes—
137C4×D79—21no—
138C4×D79—21no—
139C4×D79—81no—
140C4×D79—81no—
141C8×C79—21no—
142C8×C79—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—22no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79C22×D411yescharacteristic
149C2×D79—22no—
150C2×D79—21no—
151C2×D79—21no—
152C2×D79—21no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—84no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79C2×#4111yescharacteristic
162C4×C79C2×#4111yescharacteristic
163Dic79—21no—
164Dic79—21no—
165Dic79—21no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—42no—
170C2×C79#52511yescharacteristic
171C2×C79#57711yescharacteristic
172C2×C79#57711yescharacteristic
173D79—41no—
174D79—42no—
175#3123—791nomaximal, Sylow
176C79#312311yescharacteristic, complemented, Sylow
177#541—791no—
178#518—791no—
179#485—791no—
180#485—791no—
181#478—791no—
182#478—791no—
183#461—791no—
184#461D7911yescharacteristic, complemented
185#450—791no—
186#450—791no—
187#440—791no—
188#440—791no—
189C4×SD16—791no—
190C4×SD16—791no—
191#433—791no—
192C22×D4—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×SD16C2×D7911yescharacteristic
196C2×SD16C2×D7911yescharacteristic
197C4⋊Q8C2×D7911yescharacteristic, complemented
198#126—1581no—
199#126—1581no—
200#125—791no—
201#125—1581no—
202#125—1581no—
203C22⋊Q8—791no—
204C22⋊Q8—791no—
205C4×Q8—791no—
206C4×Q8—791no—
207C4×D4—791no—
208C4×D4—791no—
209C4×D4—791no—
210C4×D4—1581no—
211C4×D4—1581no—
212C4×D4C2×D7911yescharacteristic
213#117—791no—
214#117—791no—
215C2×C22⋊C4—1581no—
216C2×C22⋊C4—1581no—
217#107—791no—
218#107—791no—
219#106—791no—
220#106—791no—
221C4⋊C8—791no—
222C4⋊C8C2×D7911yescharacteristic, complemented
223#103—791no—
224#103—791no—
225#103C2×D7911yescharacteristic, complemented
226#103C2×D7911yescharacteristic, complemented
227#102—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231C22⋊C8—791no—
232C22⋊C8—791no—
233#97—791no—
234C4×C8—791no—
235C24—1581no—
236C2×Q8C22×D7911yescharacteristic
237C2×Q8C22×D7911yescharacteristic
238C2×D4—791no—
239C2×D4—1581no—
240C2×D4—1582no—
241C2×D4—1582no—
242C2×D4C22×D7911yescharacteristic
243C22×C4—21no—
244C22×C4—791no—
245C22×C4—1581no—
246C22×C4—1581no—
247C22×C4—1581no—
248SD16—22no—
249SD16—22no—
250SD16—1582no—
251SD16—1582no—
252C2×C8—791no—
253C2×C8—791no—
254C2×C8C22×D7911yescharacteristic
255C2×C8C22×D7911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—791no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4C22×D7911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—791no—
272C22⋊C4—791no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C42—791no—
280C42—1581no—
281C42—1581no—
282C42—1581no—
283C42C22×D7911yescharacteristic
284C23—21no—
285C23—791no—
286C23—6321no—
287C23—6321no—
288C23—1584no—
289C23—1581no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—792no—
296D4—1584no—
297D4—1581no—
298D4#1192962312yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—791no—
304C2×C4—791no—
305C2×C4—791no—
306C2×C4—6321no—
307C2×C4—6321no—
308C2×C4—6321no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4D4×D7911yescharacteristic
315C2×C4D4×D7911yescharacteristic
316C2×C4C23×D7911yescharacteristic
317C8—21no—
318C8—21no—
319C8—1581no—
320C8—1581no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—3161no—
325C22—3161no—
326C22—6324no—
327C22—1581no—
328C22—1582no—
329C22—1581no—
330C22—1581no—
331C22C2×D4×D7911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3161no—
338C4—3161no—
339C4—3161no—
340C4—1581no—
341C4—1581no—
342C4—1581no—
343C4#41×D7911yescharacteristic
344C4C2×#1192962311yescharacteristic
345C2—42no—
346C2—3162no—
347C2—3161no—
348C2#1909907311yescharacteristic
349C2#1909936911yescharacteristic
350C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#461×C79C2
socleC22×C79C22×D4
prime radicalC2×D4×D79C22
hypercenter#461D79
hypocenterC79#3123
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #19099174C2semidirect
3. #19098903C2semidirect
4. #19098902C2semidirect
5. #19098864C2semidirect
6. #19098863C2semidirect
7. #19098765C2semidirect
10. #19098666C2semidirect
11. #19098664C2semidirect
12. SD16×Dic79C2semidirect
13. #19098648C2semidirect
14. #19098623C2semidirect
15. #461×C79C2semidirect
21. #14579153C22semidirect
26. Q8×Dic79C22semidirect
27. Q8×Dic79C22semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579085C22semidirect
43. #14579085C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
54. C4⋊Q8×C79C22semidirect
56. C4⋊C8×C79C22semidirect
57. #103×C79C22semidirect
58. #103×C79C22semidirect
176. C79#3123semidirect
184. #461D79semidirect
197. C4⋊Q8C2×D79semidirect
222. C4⋊C8C2×D79semidirect
225. #103C2×D79semidirect
226. #103C2×D79semidirect