Finite Group Databasebeta

← #23768848

Subgroups — #23768848

Order 10112.

436 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098503C211yesmaximal, characteristic, complemented
2#19098499C211yesmaximal, characteristic
3#19098494C211yesmaximal, characteristic, complemented
4#19098475C211yesmaximal, characteristic
5#19098467C211yesmaximal, characteristic, complemented
6#19098467C211yesmaximal, characteristic, complemented
7#19098458C211yesmaximal, characteristic, complemented
8#19098457C211yesmaximal, characteristic
9#19098457C211yesmaximal, characteristic
10#19098445C211yesmaximal, characteristic, complemented
11#19098444C211yesmaximal, characteristic, complemented
12#19098436C211yesmaximal, characteristic
13C4⋊C4×Dic79C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic79C211yesmaximal, characteristic
15#385×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C2×C4⋊Dic79C2211yescharacteristic
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×C22⋊Dic79C2211yescharacteristic
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C4×Dic79C2211yescharacteristic
29C2×C4×Dic79C2211yescharacteristic
30C2×C4×Dic79C2211yescharacteristic
31C2×C4×Dic79C2211yescharacteristic
32C79⋊#95C2211yescharacteristic
33C79⋊#95C2211yescharacteristic
34C79⋊#95C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C23×C4×C79C2211yescharacteristic
45C2×C4⋊C4×C79C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C2×Dic158—22no—
52C2×Dic158—22no—
53C2×Dic158—41no—
54C22×Dic79C2311yescharacteristic
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C4⋊Dic79—22no—
63Dic79⋊C4—22no—
64Dic79⋊C4—22no—
65Dic79⋊C4—22no—
66Dic79⋊C4—41no—
67Dic79⋊C4—41no—
68Dic79⋊C4—41no—
69C22⋊Dic79—22no—
70C22⋊Dic79—22no—
71C22⋊Dic79—41no—
72C22⋊Dic79Q814yescomplemented
73C4×Dic79—22no—
74C4×Dic79—41no—
75C4×Dic79—41no—
76C4×Dic79—41no—
77C24×C79C2311yescharacteristic
78C22×C4×C79—22no—
79C22×C4×C79—41no—
80C22×C4×C79—41no—
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C4⋊C4×C79—22no—
88C4⋊C4×C79—41no—
89C22⋊C4×C79—22no—
90C22⋊C4×C79—41no—
91C23×C79—21no—
92C23×C79—21no—
93C23×C79—21no—
94C23×C79—21no—
95C23×C79—21no—
96C23×C79—21no—
97C23×C79C2×Q812yes—
98C23×C79C2411yescharacteristic
99C2×C4×C79—21no—
100C2×C4×C79—21no—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—21no—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—44no—
116C2×C4×C79#4112yes—
117C2×C4×C79#4112yes—
118C2×Dic79—21no—
119C2×Dic79—21no—
120C2×Dic79—21no—
121C2×Dic79—21no—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79C2×Q812yes—
139C2×Dic79C2×Q812yes—
140C2×Dic79#4112yes—
141C2×Dic79#4112yes—
142Dic158—44no—
143C22×C79—22no—
144C22×C79—22no—
145C22×C79—22no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79C22×Q811yescharacteristic
151C22×C79C2×#4111yescharacteristic
152C22×C79C2×#4111yescharacteristic
153C22×C79C2×#4111yescharacteristic
154C22×C79C2×#4111yescharacteristic
155C22×C79H(5,𝔽2)11yescharacteristic
156C22×C79H(5,𝔽2)11yescharacteristic
157C4×C79—22no—
158C4×C79—22no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79—41no—
163Dic79—22no—
164Dic79—22no—
165Dic79—22no—
166Dic79—22no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171C2×C79—42no—
172C2×C79#52911yescharacteristic
173C2×C79#53311yescharacteristic
174C2×C79#53811yescharacteristic
175C2×C79#55111yescharacteristic
176C2×C79#55411yescharacteristic
177C2×C79#55411yescharacteristic
178C2×C79#55911yescharacteristic
179#2589—791nomaximal, Sylow
180C79#258911yescharacteristic, complemented, Sylow
181#400—791no—
182#399—791no—
183#398—791no—
184#393—791no—
185#391—791no—
186#391—791no—
187#389—791no—
188#388—791no—
189#388—791no—
190#387—791no—
191#387—791no—
192#385—791no—
193#385D7911yescharacteristic
194C4×C4⋊C4—791no—
195C4×C22⋊C4—791no—
196C22×Q8—791no—
197C23×C4C2×D7911yescharacteristic
198C2×C4⋊C4—791no—
199C2×C4⋊C4—791no—
200C2×C4⋊C4—791no—
201C2×C4⋊C4—791no—
202C2×C4⋊C4—791no—
203C2×C4⋊C4—791no—
204C2×C4⋊C4—791no—
205C2×C4⋊C4C2×D7911yescharacteristic
206C2×C4⋊C4C2×D7911yescharacteristic
207C2×C22⋊C4—791no—
208C2×C22⋊C4—791no—
209C2×C22⋊C4—791no—
210C2×C22⋊C4—791no—
211C2×C22⋊C4C2×D7911yescharacteristic
212C2×C22⋊C4C2×D7911yescharacteristic
213C2×C42—791no—
214C2×C42—791no—
215C2×C42—791no—
216C2×C42—791no—
217#95—791no—
218#95—791no—
219#95—791no—
220#95—791no—
221#95—791no—
222#95—791no—
223#95—791no—
224#95—791no—
225#95—791no—
226#95—791no—
227#95—791no—
228#95—791no—
229#95C2×D7911yescharacteristic
230#95C2×D7911yescharacteristic
231C24C22×D7911yescharacteristic
232C2×Q8—3161no—
233C2×Q8—1582no—
234C2×Q8—1582no—
235C22×C4—22no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—791no—
239C22×C4—791no—
240C22×C4—791no—
241C22×C4—791no—
242C22×C4—791no—
243C22×C4—791no—
244C22×C4—791no—
245C22×C4—791no—
246C22×C4C22×D7911yescharacteristic
247C22×C4C22×D7911yescharacteristic
248C22×C4C22×D7911yescharacteristic
249C22×C4C22×D7911yescharacteristic
250C22×C4C22×D7911yescharacteristic
251C22×C4C22×D7911yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—3161no—
255C4⋊C4—3161no—
256C4⋊C4—3161no—
257C4⋊C4—1582no—
258C4⋊C4—1582no—
259C4⋊C4—1582no—
260C4⋊C4—1582no—
261C22⋊C4—22no—
262C22⋊C4—41no—
263C22⋊C4—3161no—
264C22⋊C4—794no—
265C22⋊C4—1582no—
266C22⋊C4—1582no—
267C42—3161no—
268C42—3161no—
269C42—3161no—
270C42—1582no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23Q8×D7912yes—
278C23C23×D7911yescharacteristic
279Q8—3164no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—44no—
297C2×C4—792no—
298C2×C4—792no—
299C2×C4—792no—
300C2×C4—792no—
301C2×C4—1581no—
302C2×C4—1581no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4#1192962312yes—
322C2×C4#1192962412yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×Q8×D7911yescharacteristic
331C22#41×D7911yescharacteristic
332C22#41×D7911yescharacteristic
333C22C2×#1192962311yescharacteristic
334C22C2×#1192962411yescharacteristic
335C22#1457920611yescharacteristic
336C22#1457920611yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3161no—
344C4—3161no—
345C4—3161no—
346C4—3161no—
347C4—1582no—
348C4—1582no—
349C4—1582no—
350C4—1582no—
351C2—42no—
352C2#1909909311yescharacteristic
353C2#1909911511yescharacteristic
354C2#1909914811yescharacteristic
355C2#1909924111yescharacteristic
356C2#1909926711yescharacteristic
357C2#1909926811yescharacteristic
358C2#1909929611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#385×C79C2
prime radicalC24×C79C23
hypercenter#385D79
hypocenterC79#2589
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #19098503C2semidirect
3. #19098494C2semidirect
5. #19098467C2semidirect
6. #19098467C2semidirect
7. #19098458C2semidirect
10. #19098445C2semidirect
11. #19098444C2semidirect
13. C4⋊C4×Dic79C2semidirect
72. C22⋊Dic79Q8semidirect
180. C79#2589semidirect