Finite Group Databasebeta

← #23768655

Subgroups — #23768655

Order 10112.

412 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#19098504C211yesmaximal, characteristic, complemented
2#19098504C211yesmaximal, characteristic, complemented
3#19098491C211yesmaximal, characteristic
4#19098486C211yesmaximal, characteristic
5#19098460C211yesmaximal, characteristic, complemented
6#19098456C211yesmaximal, characteristic
7#19098451C211yesmaximal, characteristic
8#19098450C211yesmaximal, characteristic, complemented
9#19098448C211yesmaximal, characteristic, complemented
10#19098446C211yesmaximal, characteristic, complemented
11#19098436C211yesmaximal, characteristic
12#19098430C211yesmaximal, characteristic, complemented
13#19098414C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic79C211yesmaximal, characteristic
15#381×C79C211yesmaximal, characteristic
16C2×C4⋊Dic79C2211yescharacteristic
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×C22⋊C4×C79C2211yescharacteristic
46C2×C22⋊C4×C79C2211yescharacteristic
47#95×C79C2211yescharacteristic
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C22×Dic79C2311yescharacteristic
52C22×Dic79C2311yescharacteristic
53C22×Dic79C2311yescharacteristic
54C22×Dic79C2311yescharacteristic
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C4⋊Dic79—22no—
60C4⋊Dic79—22no—
61Dic79⋊C4—22no—
62Dic79⋊C4—22no—
63Dic79⋊C4—22no—
64Dic79⋊C4—22no—
65Dic79⋊C4—41no—
66Dic79⋊C4—41no—
67C22⋊Dic79—22no—
68C22⋊Dic79—22no—
69C22⋊Dic79—22no—
70C22⋊Dic79—22no—
71C4×Dic79—22no—
72C4×Dic79—22no—
73C4×Dic79—41no—
74C4×Dic79—41no—
75C24×C79C2311yescharacteristic
76C22×C4×C79—22no—
77C22×C4×C79—22no—
78C22×C4×C79—41no—
79C22×C4×C79C2311yescharacteristic
80C22×C4×C79C2311yescharacteristic
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22⋊C4×C79—22no—
86C22⋊C4×C79—41no—
87C23×C79—21no—
88C23×C79—21no—
89C23×C79—21no—
90C23×C79—21no—
91C23×C79—21no—
92C23×C79—21no—
93C23×C79#4112yes—
94C23×C79C2411yescharacteristic
95C2×C4×C79—21no—
96C2×C4×C79—21no—
97C2×C4×C79—21no—
98C2×C4×C79—21no—
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—44no—
113C2×C4×C79#4112yes—
114C2×Dic79—21no—
115C2×Dic79—21no—
116C2×Dic79—21no—
117C2×Dic79—21no—
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#4112yes—
136C2×Dic79#4112yes—
137C2×Dic79#4112yes—
138C22×C79—22no—
139C22×C79—22no—
140C22×C79—22no—
141C22×C79—41no—
142C22×C79—41no—
143C22×C79—41no—
144C22×C79—41no—
145C22×C79C2×#4111yescharacteristic
146C22×C79C2×#4111yescharacteristic
147C22×C79C2×#4111yescharacteristic
148C22×C79C2×#4111yescharacteristic
149C22×C79C2×#4111yescharacteristic
150C22×C79H(5,𝔽2)11yescharacteristic
151C22×C792−1+411yescharacteristic
152C4×C79—22no—
153C4×C79—41no—
154C4×C79—41no—
155C4×C79—41no—
156C4×C79—41no—
157C4×C79—41no—
158Dic79—22no—
159Dic79—22no—
160Dic79—22no—
161Dic79—41no—
162Dic79—41no—
163Dic79—41no—
164Dic79—41no—
165Dic79—41no—
166C2×C79—42no—
167C2×C79#52911yescharacteristic
168C2×C79#52911yescharacteristic
169C2×C79#53911yescharacteristic
170C2×C79#55111yescharacteristic
171C2×C79#55211yescharacteristic
172C2×C79#55311yescharacteristic
173C2×C79#55611yescharacteristic
174#2573—791nomaximal, Sylow
175C79#257311yescharacteristic, complemented, Sylow
176#400—791no—
177#400—791no—
178#397—791no—
179#396—791no—
180#389—791no—
181#388—791no—
182#388—791no—
183#387—791no—
184#387—791no—
185#387—791no—
186#385—791no—
187#383—791no—
188#381D7911yescharacteristic
189C4×C4⋊C4—791no—
190C4×C22⋊C4—791no—
191C23×C4C2×D7911yescharacteristic
192C2×C4⋊C4—791no—
193C2×C4⋊C4—791no—
194C2×C4⋊C4—791no—
195C2×C4⋊C4—791no—
196C2×C4⋊C4—791no—
197C2×C4⋊C4—791no—
198C2×C4⋊C4—791no—
199C2×C4⋊C4—791no—
200C2×C22⋊C4—791no—
201C2×C22⋊C4—791no—
202C2×C22⋊C4—791no—
203C2×C22⋊C4—791no—
204C2×C22⋊C4C2×D7911yescharacteristic
205C2×C22⋊C4C2×D7911yescharacteristic
206C2×C42—791no—
207C2×C42—791no—
208C2×C42—791no—
209C2×C42—791no—
210#95—791no—
211#95—791no—
212#95—791no—
213#95—791no—
214#95—791no—
215#95—791no—
216#95—791no—
217#95—791no—
218#95—791no—
219#95—791no—
220#95—791no—
221#95—791no—
222#95C2×D7911yescharacteristic
223#95C2×D7911yescharacteristic
224#95C2×D7911yescharacteristic
225#95C2×D7911yescharacteristic
226C24C22×D7911yescharacteristic
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—41no—
230C22×C4—791no—
231C22×C4—791no—
232C22×C4—791no—
233C22×C4—791no—
234C22×C4—791no—
235C22×C4—791no—
236C22×C4—791no—
237C22×C4—791no—
238C22×C4C22×D7911yescharacteristic
239C22×C4C22×D7911yescharacteristic
240C22×C4C22×D7911yescharacteristic
241C22×C4C22×D7911yescharacteristic
242C22×C4C22×D7911yescharacteristic
243C22×C4C22×D7911yescharacteristic
244C4⋊C4—3161no—
245C4⋊C4—3161no—
246C4⋊C4—1582no—
247C4⋊C4—1582no—
248C4⋊C4—1582no—
249C4⋊C4—1582no—
250C4⋊C4—1582no—
251C4⋊C4—1582no—
252C22⋊C4—22no—
253C22⋊C4—41no—
254C22⋊C4—1582no—
255C22⋊C4—1582no—
256C22⋊C4—1582no—
257C22⋊C4—1582no—
258C42—3161no—
259C42—3161no—
260C42—1582no—
261C42—1582no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#1192962312yes—
269C23C23×D7911yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—44no—
288C2×C4—792no—
289C2×C4—792no—
290C2×C4—792no—
291C2×C4—1581no—
292C2×C4—1581no—
293C2×C4—1581no—
294C2×C4—1581no—
295C2×C4—1581no—
296C2×C4—1581no—
297C2×C4—1581no—
298C2×C4—1581no—
299C2×C4—1581no—
300C2×C4—1581no—
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#1192962412yes—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#41×D7911yescharacteristic
321C22#41×D7911yescharacteristic
322C22#41×D7911yescharacteristic
323C22C2×#1192962311yescharacteristic
324C22C2×#1192962411yescharacteristic
325C22#1457920611yescharacteristic
326C22#1457920811yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—3161no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4—3161no—
338C4—1582no—
339C4—1582no—
340C4—1582no—
341C2—42no—
342C2#1909909011yescharacteristic
343C2#1909909111yescharacteristic
344C2#1909915611yescharacteristic
345C2#1909923911yescharacteristic
346C2#1909925011yescharacteristic
347C2#1909925811yescharacteristic
348C2#1909928111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#381×C79C2
prime radicalC24×C79C23
hypercenter#381D79
hypocenterC79#2573
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #19098504C2semidirect
2. #19098504C2semidirect
5. #19098460C2semidirect
8. #19098450C2semidirect
9. #19098448C2semidirect
10. #19098446C2semidirect
12. #19098430C2semidirect
13. #19098414C2semidirect
175. C79#2573semidirect