Finite Group Databasebeta

← #23773506

Subgroups — #23773506

Order 10112.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099092C211yesmaximal, characteristic, complemented
2C4×#11929623C211yesmaximal, characteristic, complemented
3#19098902C211yesmaximal, characteristic, complemented
4#19098885C211yesmaximal, characteristic, complemented
5#19098871C211yesmaximal, characteristic, complemented
6#19098863C211yesmaximal, characteristic, complemented
7#19098782C211yesmaximal, characteristic, complemented
8#19098722C211yesmaximal, characteristic, complemented
9#19098705C211yesmaximal, characteristic
10#19098675C211yesmaximal, characteristic, complemented
11#19098667C211yesmaximal, characteristic, complemented
12#19098664C211yesmaximal, characteristic, complemented
13#19098660C211yesmaximal, characteristic, complemented
14#19098619C211yesmaximal, characteristic, complemented
15#463×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19#14579154—21no—
20#14579153C2211yescharacteristic
21#14579143—21no—
22#14579137C2211yescharacteristic
23#14579132C2211yescharacteristic
24Q8×Dic79C2211yescharacteristic
25C4×Dic158C2211yescharacteristic
26#14579126C2211yescharacteristic
27D4×Dic79C2211yescharacteristic
28D4×Dic79C2211yescharacteristic
29C4×C22⋊D79—21no—
30(C22⋊D79)⋊C4—21no—
31(C22⋊D79)⋊C4—21no—
32#14579119C2211yescharacteristic
33#14579117—21no—
34#14579117—21no—
35C2×C4×Dic79—21no—
36C42×D79C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579094C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41C4⋊(C79⋊C8)C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic
51#14579071C2211yescharacteristic
52C2×SD16×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic
54#124×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56C4⋊C8×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—22no—
60#11929623—22no—
61C2×Dic158C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C22×Dic79—21no—
67C2×C4×D79D411yescharacteristic
68C2×C4×D79D411yescharacteristic
69C2×C4×D79C2311yescharacteristic
70#11929614—22no—
71#11929612—22no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C4⋊Dic79—21no—
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88C4×Dic79—21no—
89C4×Dic79—21no—
90C4×Dic79—21no—
91C4×Dic79—21no—
92C4×Dic79D411yescharacteristic
93C4×Dic79D411yescharacteristic
94C4×Dic79C2311yescharacteristic
95C2×Q8×C79C2311yescharacteristic
96C2×D4×C79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99SD16×C79—22no—
100D8×C79—22no—
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C22×D79C2×D411yescharacteristic
111Q8×C79—21no—
112Q8×C79—21no—
113D4×C79—21no—
114D4×C79—21no—
115D4×C79—21no—
116D4×C79#4112yes—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—42no—
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2×D411yescharacteristic
122C2×C4×C79C2411yescharacteristic
123C22⋊D79—24no—
124C22⋊D79—42no—
125C2×Dic79—24no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—42no—
131C2×Dic79—42no—
132C2×Dic79C2×D411yescharacteristic
133C2×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135C4×D79—21no—
136C4×D79—21no—
137C4×D79—41no—
138C4×D79—41no—
139Dic158—21no—
140Dic158#4112yes—
141C8×C79—21no—
142C8×C79—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—22no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79C22×D411yescharacteristic
152C2×D79—21no—
153C2×D79—21no—
154C2×D79—21no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79C2×#4111yescharacteristic
160C4×C79C2×#4111yescharacteristic
161Dic79—22no—
162Dic79—21no—
163Dic79—21no—
164Dic79—21no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168C2×C79—42no—
169C2×C79—81no—
170C2×C79#52511yescharacteristic
171C2×C79#57511yescharacteristic
172C2×C79#57511yescharacteristic
173D79—41no—
174#3111—791nomaximal, Sylow
175C79#311111yescharacteristic, complemented, Sylow
176#529—791no—
177C4×#41—791no—
178#485—791no—
179#482—791no—
180#479—791no—
181#478—791no—
182#464—791no—
183#463D7911yescharacteristic, complemented
184#452—791no—
185#449—791no—
186#442—791no—
187#441—791no—
188#440—791no—
189#440—791no—
190#432—791no—
191C2×#41—791no—
192C2×Q16—791no—
193C2×SD16—791no—
194C2×SD16C2×D7911yescharacteristic
195C2×D8C2×D7911yescharacteristic
196#126—1581no—
197#125—791no—
198#124C2×D7911yescharacteristic
199#123—1581no—
200C22⋊Q8—791no—
201#121—791no—
202C4×Q8—791no—
203C4×Q8—791no—
204C4×Q8—791no—
205C4×D4—791no—
206C4×D4—791no—
207C4×D4—1581no—
208C4×D4—1581no—
209C4×D4—1581no—
210C4×D4C2×D7911yescharacteristic
211#117—791no—
212#117—1581no—
213#117—1581no—
214C2×C42—791no—
215C2×C42—1581no—
216#107—791no—
217#107—791no—
218#106—791no—
219#106—791no—
220C4⋊C8—791no—
221C4⋊C8C2×D7911yescharacteristic
222#103—791no—
223#103—791no—
224#103—791no—
225#103C2×D7911yescharacteristic
226#102—791no—
227#102—791no—
228#102—791no—
229#102C2×D7911yescharacteristic
230C22⋊C8—791no—
231C22⋊C8—791no—
232#97—791no—
233#97—791no—
234#41—1582no—
235#41—1582no—
236C2×Q8—791no—
237C2×Q8C22×D7911yescharacteristic
238C2×D4—1581no—
239C2×D4—1581no—
240C2×D4C22×D7911yescharacteristic
241C2×D4C22×D7911yescharacteristic
242C22×C4—21no—
243C22×C4—791no—
244C22×C4—791no—
245C22×C4—791no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4—1581no—
249Q16—1582no—
250SD16—22no—
251SD16—1582no—
252D8—22no—
253C2×C8—791no—
254C2×C8—791no—
255C2×C8C22×D7911yescharacteristic
256C2×C8C22×D7911yescharacteristic
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—1581no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4C22×D7911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C42—791no—
276C42—791no—
277C42—791no—
278C42—1581no—
279C42—1581no—
280C42—1581no—
281C42—1581no—
282C42C22×D7911yescharacteristic
283C23—21no—
284C23—21no—
285C23—791no—
286Q8—21no—
287Q8—21no—
288Q8—792no—
289Q8—1581no—
290D4—21no—
291D4—21no—
292D4—21no—
293D4—3162no—
294D4—1584no—
295D4#1192962312yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—3161no—
300C2×C4—3161no—
301C2×C4—3162no—
302C2×C4—3162no—
303C2×C4—791no—
304C2×C4—791no—
305C2×C4—791no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1584no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4D4×D7911yescharacteristic
314C2×C4D4×D7911yescharacteristic
315C2×C4C23×D7911yescharacteristic
316C8—21no—
317C8—21no—
318C8—1581no—
319C8—1581no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—1581no—
327C22—1581no—
328C22—1581no—
329C22C2×D4×D7911yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4—1581no—
338C4—1582no—
339C4—1581no—
340C4—1581no—
341C4#41×D7911yescharacteristic
342C4C2×#1192962311yescharacteristic
343C2—42no—
344C2—81no—
345C2—3161no—
346C2#1909907311yescharacteristic
347C2#1909935911yescharacteristic
348C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#463×C79C2
socleC22×C79C22×D4
prime radical#19098705C2
hypercenter#463D79
hypocenterC79#3111
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #19099092C2semidirect
2. C4×#11929623C2semidirect
3. #19098902C2semidirect
4. #19098885C2semidirect
5. #19098871C2semidirect
6. #19098863C2semidirect
7. #19098782C2semidirect
8. #19098722C2semidirect
10. #19098675C2semidirect
11. #19098667C2semidirect
12. #19098664C2semidirect
13. #19098660C2semidirect
14. #19098619C2semidirect
15. #463×C79C2semidirect
175. C79#3111semidirect
183. #463D79semidirect