Finite Group Databasebeta

← C79×#13303 #34124992

Subgroups — C79×#13303 #34124992

Order 20224.

396 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
1C79×#2565C211yesmaximal, characteristic
2C79×#1801C211yesmaximal, characteristic
3C4×#101×C79C211yesmaximal, characteristic
4C79×#1394C212yesmaximal
5C79×#1394C212yesmaximal
6C2×#125×C79C411yescharacteristic
7C2×C4×Q8×C79C2211yescharacteristic
8#423×C79—21no—
9C2×#101×C79C2212yes—
10C2×#101×C79C2212yes—
11C4×M16×C79—21no—
12#398×C79—21no—
13#398×C79—21no—
14#391×C79C2211yescharacteristic
15#391×C79C2211yescharacteristic
16#387×C79—21no—
17#387×C79—21no—
18#384×C79C411yescharacteristic
19#382×C79C411yescharacteristic
20C4×C4⋊C4×C79C411yescharacteristic
21#343×C79—21no—
22#343×C79—21no—
23C22×Q8×C79C2311yescharacteristic
24C2×M16×C79—22no—
25C2×M16×C79—22no—
26#125×C79—41no—
27#125×C79—41no—
28C4×Q8×C79—41no—
29C4×Q8×C79—41no—
30C2×C4⋊C4×C79—21no—
31C2×C4⋊C4×C79—21no—
32C2×C4⋊C4×C79—21no—
33C2×C4⋊C4×C79—21no—
34C2×C4⋊C4×C79—21no—
35C2×C4⋊C4×C79C2×C411yescharacteristic
36C2×C4⋊C4×C79C2×C411yescharacteristic
37C2×C4⋊C4×C79C2×C411yescharacteristic
38C2×C4⋊C4×C79D411yescharacteristic
39C2×C4⋊C4×C79D411yescharacteristic
40C2×C42×C79C2×C411yescharacteristic
41C2×C42×C79C2×C411yescharacteristic
42C2×C42×C79C2×C411yescharacteristic
43C2×C42×C79D411yescharacteristic
44C2×C42×C79D411yescharacteristic
45C4⋊C8×C79—41no—
46C4⋊C8×C79—41no—
47#101×C79—22no—
48#101×C79—24no—
49#101×C79Q814yes—
50#97×C79—41no—
51C4×C8×C79—41no—
52#95×C79—21no—
53#95×C79—21no—
54#95×C79—21no—
55#95×C79—21no—
56#95×C79—21no—
57#95×C79—21no—
58#95×C79—21no—
59C2×Q8×C79—41no—
60C2×Q8×C79—41no—
61C2×Q8×C79C2×Q812yes—
62C2×Q8×C79#4112yes—
63C22×C4×C79—21no—
64C22×C4×C79—21no—
65C22×C4×C79—21no—
66C22×C4×C79—21no—
67C22×C4×C79C22⋊C411yescharacteristic
68C22×C4×C79C22⋊C411yescharacteristic
69C22×C4×C79C22⋊C411yescharacteristic
70C22×C4×C79C22⋊C411yescharacteristic
71C22×C4×C79C22×C411yescharacteristic
72C22×C4×C79C2×D411yescharacteristic
73C22×C4×C79C2×D411yescharacteristic
74M16×C79—24no—
75M16×C79—42no—
76M16×C79—42no—
77M16×C79—42no—
78C2×C8×C79—42no—
79C2×C8×C79—42no—
80C4⋊C4×C79—41no—
81C4⋊C4×C79—41no—
82C4⋊C4×C79—41no—
83C4⋊C4×C79—42no—
84C4⋊C4×C79—42no—
85C4⋊C4×C79—42no—
86C4⋊C4×C79—42no—
87C4⋊C4×C79—41no—
88C4⋊C4×C79—41no—
89C4⋊C4×C79—41no—
90C4⋊C4×C79—41no—
91C42×C79—21no—
92C42×C79—21no—
93C42×C79—21no—
94C42×C79—21no—
95C42×C79—21no—
96C42×C79—21no—
97C42×C79—41no—
98C42×C79—41no—
99C23×C79C2×C22⋊C411yescharacteristic
100Q8×C79—42no—
101Q8×C79—42no—
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—22no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—21no—
112C2×C4×C79—41no—
113C2×C4×C79—41no—
114C2×C4×C79—41no—
115C2×C4×C79—41no—
116C2×C4×C79—41no—
117C2×C4×C79—41no—
118C2×C4×C79—41no—
119C2×C4×C79—41no—
120C2×C4×C79—41no—
121C2×C4×C79—41no—
122C2×C4×C79—42no—
123C2×C4×C79—41no—
124C2×C4×C79—41no—
125C2×C4×C79—41no—
126C2×C4×C79#9911yescharacteristic
127C2×C4×C79#9911yescharacteristic
128C2×C4×C79C4×Q812yes—
129C2×C4×C79C22⋊Q812yes—
130C2×C4×C79#12411yescharacteristic
131C2×C4×C79C4⋊Q811yescharacteristic
132C8×C79—44no—
133C8×C79—82no—
134C22×C79—21no—
135C22×C79—21no—
136C22×C79#39111yescharacteristic
137C22×C79C2×#9911yescharacteristic
138C22×C79#41011yescharacteristic
139C4×C79—21no—
140C4×C79—21no—
141C4×C79—22no—
142C4×C79—22no—
143C4×C79—21no—
144C4×C79—21no—
145C4×C79—42no—
146C4×C79—41no—
147C4×C79—41no—
148C4×C79—41no—
149C4×C79—81no—
150C4×C79—81no—
151C4×C79—81no—
152#13303C7911yesmaximal, characteristic, direct product factor, Sylow
153C2×C79—21no—
154C2×C79—21no—
155C2×C79#199611yescharacteristic
156C2×C79#213211yescharacteristic
157C2×C79#213311yescharacteristic
158#2565C2×C7911yescharacteristic
159#1801C2×C7911yescharacteristic
160C4×#101C2×C7911yescharacteristic
161#1394C2×C7912yes—
162#1394C2×C7912yes—
163C79#1330311yescharacteristic, direct product factor, Sylow
164C2×#125C4×C7911yescharacteristic
165C2×C4×Q8C22×C7911yescharacteristic
166#423—21no—
167C2×#101C22×C7912yes—
168C2×#101C22×C7912yes—
169C4×M16—21no—
170#398—21no—
171#398—21no—
172#391C22×C7911yescharacteristic
173#391C22×C7911yescharacteristic
174#387—21no—
175#387—21no—
176#384C4×C7911yescharacteristic
177#382C4×C7911yescharacteristic
178C4×C4⋊C4C4×C7911yescharacteristic
179#343—21no—
180#343—21no—
181C22×Q8C23×C7911yescharacteristic
182C2×M16—22no—
183C2×M16—22no—
184#125—41no—
185#125—41no—
186C4×Q8—41no—
187C4×Q8—41no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×C4×C7911yescharacteristic
194C2×C4⋊C4C2×C4×C7911yescharacteristic
195C2×C4⋊C4C2×C4×C7911yescharacteristic
196C2×C4⋊C4D4×C7911yescharacteristic
197C2×C4⋊C4D4×C7911yescharacteristic
198C2×C42C2×C4×C7911yescharacteristic
199C2×C42C2×C4×C7911yescharacteristic
200C2×C42C2×C4×C7911yescharacteristic
201C2×C42D4×C7911yescharacteristic
202C2×C42D4×C7911yescharacteristic
203C4⋊C8—41no—
204C4⋊C8—41no—
205#101—22no—
206#101—24no—
207#101Q8×C7914yes—
208#97—41no—
209C4×C8—41no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8C2×Q8×C7912yes—
220C2×Q8#41×C7912yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C22⋊C4×C7911yescharacteristic
226C22×C4C22⋊C4×C7911yescharacteristic
227C22×C4C22⋊C4×C7911yescharacteristic
228C22×C4C22⋊C4×C7911yescharacteristic
229C22×C4C22×C4×C7911yescharacteristic
230C22×C4C2×D4×C7911yescharacteristic
231C22×C4C2×D4×C7911yescharacteristic
232M16—24no—
233M16—42no—
234M16—42no—
235M16—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—41no—
256C42—41no—
257C23C2×C22⋊C4×C7911yescharacteristic
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4#99×C7911yescharacteristic
285C2×C4#99×C7911yescharacteristic
286C2×C4C4×Q8×C7912yes—
287C2×C4C22⋊Q8×C7912yes—
288C2×C4#124×C7911yescharacteristic
289C2×C4C4⋊Q8×C7911yescharacteristic
290C8—44no—
291C8—82no—
292C22—21no—
293C22—21no—
294C22#391×C7911yescharacteristic
295C22C2×#99×C7911yescharacteristic
296C22#410×C7911yescharacteristic
297C4—22no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—81no—
308C4—81no—
309C4—81no—
310C2—21no—
311C2—21no—
312C2C79×#199611yescharacteristic
313C2C79×#213211yescharacteristic
314C2C79×#213311yescharacteristic
subgroupG/H
center, socleC22×C79C2×#99
commutatorC22×C4C22×C4×C79
Frattini, cosocleC22×Q8C23×C79
prime radicalC23×C79C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C79 ◁ C22×C4×C79 ◁ C2×C4×Q8×C79 ◁ G

Complements

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

NH ≅ G/Ntype
152. #13303C79direct (N × H)
163. C79#13303direct (N × H)

Maximal subgroups

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

subgroupindex
C79×#25652
C79×#18012
C4×#101×C792
C79×#13942
#1330379