Finite Group Databasebeta

← C79×#2762 #23760384

Subgroups — C79×#2762 #23760384

Order 10112.

352 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#401×C79C211yesmaximal, characteristic
2#400×C79C211yesmaximal, characteristic
3#400×C79C211yesmaximal, characteristic
4#400×C79C211yesmaximal, characteristic
5#398×C79C211yesmaximal, characteristic
6#395×C79C211yesmaximal, characteristic
7#391×C79C211yesmaximal, characteristic
8#391×C79C211yesmaximal, characteristic
9#387×C79C211yesmaximal, characteristic
10#387×C79C211yesmaximal, characteristic
11#387×C79C211yesmaximal, characteristic
12#387×C79C211yesmaximal, characteristic
13#387×C79C211yesmaximal, characteristic
14#383×C79C211yesmaximal, characteristic
15#382×C79C211yesmaximal, characteristic
16C22×Q8×C79C2211yescharacteristic
17C2×C4⋊C4×C79C2211yescharacteristic
18C2×C4⋊C4×C79C2211yescharacteristic
19C2×C4⋊C4×C79C2211yescharacteristic
20C2×C4⋊C4×C79C2211yescharacteristic
21C2×C4⋊C4×C79C2211yescharacteristic
22C2×C4⋊C4×C79C2211yescharacteristic
23C2×C4⋊C4×C79C2211yescharacteristic
24C2×C4⋊C4×C79C2211yescharacteristic
25C2×C4⋊C4×C79C2211yescharacteristic
26C2×C42×C79C2211yescharacteristic
27C2×C42×C79C2211yescharacteristic
28C2×C42×C79C2211yescharacteristic
29#95×C79C2211yescharacteristic
30#95×C79C2211yescharacteristic
31#95×C79C2211yescharacteristic
32#95×C79C2211yescharacteristic
33#95×C79C2211yescharacteristic
34#95×C79C2211yescharacteristic
35#95×C79C2211yescharacteristic
36#95×C79C2211yescharacteristic
37#95×C79C2211yescharacteristic
38#95×C79C2211yescharacteristic
39#95×C79C2211yescharacteristic
40#95×C79C2211yescharacteristic
41#95×C79C2211yescharacteristic
42#95×C79C2211yescharacteristic
43#95×C79C2211yescharacteristic
44#95×C79C2211yescharacteristic
45#95×C79C2211yescharacteristic
46#95×C79C2211yescharacteristic
47#95×C79C2211yescharacteristic
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C2×Q8×C79—22no—
52C2×Q8×C79—22no—
53C2×Q8×C79—41no—
54C22×C4×C79C2311yescharacteristic
55C22×C4×C79C2311yescharacteristic
56C22×C4×C79C2311yescharacteristic
57C22×C4×C79C2311yescharacteristic
58C22×C4×C79C2311yescharacteristic
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2311yescharacteristic
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2311yescharacteristic
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2311yescharacteristic
67C22×C4×C79C2311yescharacteristic
68C22×C4×C79C2311yescharacteristic
69C4⋊C4×C79—22no—
70C4⋊C4×C79—22no—
71C4⋊C4×C79—22no—
72C4⋊C4×C79—22no—
73C4⋊C4×C79—22no—
74C4⋊C4×C79—41no—
75C4⋊C4×C79—41no—
76C4⋊C4×C79—41no—
77C4⋊C4×C79—41no—
78C42×C79—22no—
79C42×C79—22no—
80C42×C79—41no—
81C23×C79C2411yescharacteristic
82Q8×C79—44no—
83C2×C4×C79—21no—
84C2×C4×C79—21no—
85C2×C4×C79—21no—
86C2×C4×C79—21no—
87C2×C4×C79—21no—
88C2×C4×C79—21no—
89C2×C4×C79—21no—
90C2×C4×C79—21no—
91C2×C4×C79—21no—
92C2×C4×C79—21no—
93C2×C4×C79—21no—
94C2×C4×C79—21no—
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—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79#4112yes—
126C2×C4×C79#4112yes—
127C2×C4×C79#4112yes—
128C22×C79C2×#4111yescharacteristic
129C22×C79C2×#4111yescharacteristic
130C22×C79C2×#4111yescharacteristic
131C22×C79H(5,𝔽2)11yescharacteristic
132C22×C792−1+411yescharacteristic
133C22×C792−1+411yescharacteristic
134C22×C792−1+411yescharacteristic
135C4×C79—22no—
136C4×C79—22no—
137C4×C79—22no—
138C4×C79—41no—
139C4×C79—41no—
140C4×C79—41no—
141C4×C79—41no—
142C4×C79—41no—
143C4×C79—41no—
144C4×C79—41no—
145C4×C79—41no—
146C4×C79—41no—
147C4×C79—41no—
148C4×C79—41no—
149C4×C79—41no—
150C2×C79#54111yescharacteristic
151C2×C79#54111yescharacteristic
152C2×C79#54211yescharacteristic
153C2×C79#55111yescharacteristic
154C2×C79#55211yescharacteristic
155C2×C79#55611yescharacteristic
156C2×C79#56311yescharacteristic
157#2762C7911yesmaximal, characteristic, direct product factor, Sylow
158C79#276211yescharacteristic, direct product factor, Sylow
159#401C2×C7911yescharacteristic
160#400C2×C7911yescharacteristic
161#400C2×C7911yescharacteristic
162#400C2×C7911yescharacteristic
163#398C2×C7911yescharacteristic
164#395C2×C7911yescharacteristic
165#391C2×C7911yescharacteristic
166#391C2×C7911yescharacteristic
167#387C2×C7911yescharacteristic
168#387C2×C7911yescharacteristic
169#387C2×C7911yescharacteristic
170#387C2×C7911yescharacteristic
171#387C2×C7911yescharacteristic
172#383C2×C7911yescharacteristic
173#382C2×C7911yescharacteristic
174C22×Q8C22×C7911yescharacteristic
175C2×C4⋊C4C22×C7911yescharacteristic
176C2×C4⋊C4C22×C7911yescharacteristic
177C2×C4⋊C4C22×C7911yescharacteristic
178C2×C4⋊C4C22×C7911yescharacteristic
179C2×C4⋊C4C22×C7911yescharacteristic
180C2×C4⋊C4C22×C7911yescharacteristic
181C2×C4⋊C4C22×C7911yescharacteristic
182C2×C4⋊C4C22×C7911yescharacteristic
183C2×C4⋊C4C22×C7911yescharacteristic
184C2×C42C22×C7911yescharacteristic
185C2×C42C22×C7911yescharacteristic
186C2×C42C22×C7911yescharacteristic
187#95C22×C7911yescharacteristic
188#95C22×C7911yescharacteristic
189#95C22×C7911yescharacteristic
190#95C22×C7911yescharacteristic
191#95C22×C7911yescharacteristic
192#95C22×C7911yescharacteristic
193#95C22×C7911yescharacteristic
194#95C22×C7911yescharacteristic
195#95C22×C7911yescharacteristic
196#95C22×C7911yescharacteristic
197#95C22×C7911yescharacteristic
198#95C22×C7911yescharacteristic
199#95C22×C7911yescharacteristic
200#95C22×C7911yescharacteristic
201#95C22×C7911yescharacteristic
202#95C22×C7911yescharacteristic
203#95C22×C7911yescharacteristic
204#95C22×C7911yescharacteristic
205#95C22×C7911yescharacteristic
206#95C22×C7911yescharacteristic
207#95C22×C7911yescharacteristic
208#95C22×C7911yescharacteristic
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—41no—
212C22×C4C23×C7911yescharacteristic
213C22×C4C23×C7911yescharacteristic
214C22×C4C23×C7911yescharacteristic
215C22×C4C23×C7911yescharacteristic
216C22×C4C23×C7911yescharacteristic
217C22×C4C23×C7911yescharacteristic
218C22×C4C23×C7911yescharacteristic
219C22×C4C23×C7911yescharacteristic
220C22×C4C23×C7911yescharacteristic
221C22×C4C23×C7911yescharacteristic
222C22×C4C23×C7911yescharacteristic
223C22×C4C23×C7911yescharacteristic
224C22×C4C23×C7911yescharacteristic
225C22×C4C23×C7911yescharacteristic
226C22×C4C23×C7911yescharacteristic
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—22no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C42—22no—
237C42—22no—
238C42—41no—
239C23C24×C7911yescharacteristic
240Q8—44no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
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#41×C7912yes—
284C2×C4#41×C7912yes—
285C2×C4#41×C7912yes—
286C22C2×#41×C7911yescharacteristic
287C22C2×#41×C7911yescharacteristic
288C22C2×#41×C7911yescharacteristic
289C22H(5,𝔽2)×C7911yescharacteristic
290C222−1+4×C7911yescharacteristic
291C222−1+4×C7911yescharacteristic
292C222−1+4×C7911yescharacteristic
293C4—22no—
294C4—22no—
295C4—22no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C2#541×C7911yescharacteristic
309C2#541×C7911yescharacteristic
310C2#542×C7911yescharacteristic
311C2#551×C7911yescharacteristic
312C2#552×C7911yescharacteristic
313C2#556×C7911yescharacteristic
314C2#563×C7911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C79C24
commutator, Frattini, cosocleC23C24×C79
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C79 ◁ G

Complements

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

NH ≅ G/Ntype
157. #2762C79direct (N × H)
158. C79#2762direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#401×C792
#400×C792
#398×C792
#395×C792
#391×C792
#387×C792
#383×C792
#382×C792
#276279