Finite Group Databasebeta

← #23773510

Subgroups — #23773510

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#19099099C211yesmaximal, characteristic, complemented
2#41×Dic79C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098872C211yesmaximal, characteristic, complemented
6#19098865C211yesmaximal, characteristic, complemented
7#19098787C211yesmaximal, characteristic, complemented
8#19098780C211yesmaximal, characteristic, complemented
9#19098708C211yesmaximal, characteristic
10#19098672C211yesmaximal, characteristic, complemented
11#19098670C211yesmaximal, characteristic, complemented
12#19098666C211yesmaximal, characteristic, complemented
13#19098664C211yesmaximal, characteristic, complemented
14#19098617C211yesmaximal, characteristic, complemented
15#452×C79C211yesmaximal, characteristic, complemented
16C2×#11929611C2211yescharacteristic
17C2×#11929609C2211yescharacteristic
18#14579156—21no—
19#14579152C2211yescharacteristic
20#14579150C2211yescharacteristic
21#14579145—21no—
22#14579135C2211yescharacteristic
23Q8×Dic79C2211yescharacteristic
24Q8×Dic79C2211yescharacteristic
25Q8×Dic79C2211yescharacteristic
26D4×Dic79—21no—
27D4×Dic79—21no—
28D4×Dic79C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30#14579123C2211yescharacteristic
31(C22⋊D79)⋊C4—21no—
32#14579120—21no—
33#14579120C2211yescharacteristic
34#14579119—21no—
35C2×C4×Dic79—21no—
36C2×C4×Dic79C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579094C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579085C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic
51#14579071C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×Q16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×D316C2311yescharacteristic
60C2×C22⋊D79—21no—
61C22×Dic79—21no—
62C22×Dic79—21no—
63C22×Dic79D411yescharacteristic
64C22×Dic79D411yescharacteristic
65C2×C4×D79—21no—
66#11929611—22no—
67#11929609—22no—
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C4⋊Dic79—21no—
71C4⋊Dic79—21no—
72C4⋊Dic79—21no—
73C4⋊Dic79—21no—
74C4⋊Dic79C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78C22⋊Dic79—21no—
79C22⋊Dic79—21no—
80C22⋊Dic79—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84(C2×D79)⋊C4—21no—
85C4×Dic79—21no—
86C4×Dic79—21no—
87C4×Dic79—21no—
88C4×Dic79—21no—
89C4×Dic79D411yescharacteristic
90C4×Dic79D411yescharacteristic
91C4×Dic79C2311yescharacteristic
92C4×Dic79C2311yescharacteristic
93#41×C79—22no—
94#41×C79—22no—
95C2×Q8×C79C2311yescharacteristic
96C2×Q8×C79C2311yescharacteristic
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C22×C4×C79—21no—
100C22×C4×C79C2311yescharacteristic
101Q16×C79—22no—
102SD16×C79—22no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79—21no—
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111Q8×C79—21no—
112Q8×C79—21no—
113Q8×C79—21no—
114Q8×C79#4112yes—
115D4×C79—24no—
116D4×C79—21no—
117D4×C79#4112yes—
118C2×C4×C79—24no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C22⋊D79—42no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—41no—
131C2×Dic79—41no—
132C2×Dic79—42no—
133C2×Dic79—42no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—21no—
139D316—21no—
140C4×D79—42no—
141C8×C79—21no—
142C8×C79—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—21no—
146C22×C79—22no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79C22×D411yescharacteristic
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C4×C79—21no—
156C4×C79—22no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79C2×#4111yescharacteristic
160C4×C79C2×#4111yescharacteristic
161Dic79—21no—
162Dic79—21no—
163Dic79—21no—
164Dic79—21no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168C2×C79—41no—
169C2×C79—42no—
170C2×C79#52511yescharacteristic
171C2×C79#57511yescharacteristic
172C2×C79#57511yescharacteristic
173D79—81no—
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#463—791no—
184#452D7911yescharacteristic, complemented
185#449—791no—
186#442—791no—
187#441—791no—
188#440—791no—
189#440—791no—
190#432—791no—
191C2×#41C2×D7911yescharacteristic
192C2×Q16C2×D7911yescharacteristic
193C2×SD16—791no—
194C2×SD16C2×D7911yescharacteristic
195C2×D8—791no—
196#126—1581no—
197#125—791no—
198#124—791no—
199#123—1581no—
200C22⋊Q8C2×D7911yescharacteristic
201#121—791no—
202C4×Q8—791no—
203C4×Q8—791no—
204C4×Q8—791no—
205C4×D4—791no—
206C4×D4—791no—
207C4×D4—791no—
208C4×D4—1581no—
209C4×D4—1581no—
210C4×D4—1581no—
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⋊C8—791no—
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⋊C8C2×D7911yescharacteristic
232#97—791no—
233#97—791no—
234#41—22no—
235#41—22no—
236C2×Q8C22×D7911yescharacteristic
237C2×Q8C22×D7911yescharacteristic
238C2×D4—21no—
239C2×D4—791no—
240C2×D4—1581no—
241C2×D4C22×D7911yescharacteristic
242C22×C4—21no—
243C22×C4—791no—
244C22×C4—791no—
245C22×C4—1581no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4C22×D7911yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—1582no—
252D8—1582no—
253C2×C8—791no—
254C2×C8—791no—
255C2×C8C22×D7911yescharacteristic
256C2×C8C22×D7911yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4C22×D7911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—1581no—
269C22⋊C4—1581no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C42—791no—
276C42—791no—
277C42—791no—
278C42—791no—
279C42—1581no—
280C42—1581no—
281C42—1581no—
282C42—1581no—
283C23—21no—
284C23—1581no—
285C23D4×D7911yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8#1192962312yes—
290D4—24no—
291D4—21no—
292D4—3162no—
293D4—1581no—
294D4—1581no—
295D4#1192962312yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—3162no—
303C2×C4—3162no—
304C2×C4—3162no—
305C2×C4—3161no—
306C2×C4—3161no—
307C2×C4—791no—
308C2×C4—791no—
309C2×C4—791no—
310C2×C4—791no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4D4×D7911yescharacteristic
315C2×C4C23×D7911yescharacteristic
316C8—21no—
317C8—21no—
318C8—1581no—
319C8—1581no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—3161no—
327C22—3161no—
328C22—3161no—
329C22C2×D4×D7911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4—1581no—
338C4—1581no—
339C4—1581no—
340C4—1581no—
341C4C2×#1192962311yescharacteristic
342C4C2×#1192962311yescharacteristic
343C2—41no—
344C2—42no—
345C2—6321no—
346C2#1909906911yescharacteristic
347C2#1909936011yescharacteristic
348C2#1909936211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#452×C79C2
socleC22×C79C22×D4
prime radical#19098708C2
hypercenter#452D79
hypocenterC79#3111
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #19099099C2semidirect
2. #41×Dic79C2semidirect
3. #19098901C2semidirect
4. #19098888C2semidirect
5. #19098872C2semidirect
6. #19098865C2semidirect
7. #19098787C2semidirect
8. #19098780C2semidirect
10. #19098672C2semidirect
11. #19098670C2semidirect
12. #19098666C2semidirect
13. #19098664C2semidirect
14. #19098617C2semidirect
15. #452×C79C2semidirect
175. C79#3111semidirect
184. #452D79semidirect