Finite Group Databasebeta

← C79×#9270 #34120959

Subgroups — C79×#9270 #34120959

Order 20224.

412 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3230C211yesmaximal, characteristic
2C79×#2962C211yesmaximal, characteristic
3C79×#1997C211yesmaximal, characteristic
4C79×#1550C211yesmaximal, characteristic
5C2×#332×C79C211yesmaximal, characteristic
6C79×#1301C211yesmaximal, characteristic
7C79×#1283C211yesmaximal, characteristic
8#533×C79C2211yescharacteristic
9C2×C4⋊Q8×C79C2211yescharacteristic
10#500×C79—21no—
11#487×C79—21no—
12#484×C79C414yes—
13#477×C79—22no—
14#446×C79—22no—
15#446×C79—21no—
16C8×Q8×C79—21no—
17#431×C79C2211yescharacteristic
18#424×C79—21no—
19#423×C79C2211yescharacteristic
20C2×C4⋊C8×C79C2211yescharacteristic
21C2×C4⋊C8×C79C2211yescharacteristic
22#405×C79—21no—
23C4×M16×C79C2211yescharacteristic
24#343×C79—21no—
25#343×C79—21no—
26#333×C79—21no—
27#332×C79—21no—
28#332×C79—21no—
29#332×C79—21no—
30C22×Q8×C79—21no—
31C2×M16×C79—21no—
32C2×M16×C79D411yescharacteristic
33C2×M16×C79D411yescharacteristic
34C22×C8×C79—21no—
35C22×C8×C79—21no—
36C4⋊Q8×C79—21no—
37C4⋊Q8×C79—21no—
38C4⋊Q8×C79—21no—
39C4⋊Q8×C79—21no—
40C4⋊Q8×C79D411yescharacteristic
41C4⋊Q8×C79D411yescharacteristic
42#125×C79—21no—
43C22⋊Q8×C79—21no—
44C22⋊Q8×C79C2×C412yes—
45C4×Q8×C79—21no—
46C4×Q8×C79D412yes—
47#117×C79—21no—
48C2×C4⋊C4×C79—21no—
49C2×C4⋊C4×C79C2×C412yes—
50C2×C42×C79C2311yescharacteristic
51#107×C79—24no—
52C4⋊C8×C79—22no—
53C4⋊C8×C79—22no—
54C4⋊C8×C79—21no—
55C4⋊C8×C79—21no—
56C4⋊C8×C79—21no—
57C4⋊C8×C79—21no—
58C4⋊C8×C79—21no—
59C4⋊C8×C79—21no—
60C4⋊C8×C79D411yescharacteristic
61C4⋊C8×C79D411yescharacteristic
62#103×C79—24no—
63C22⋊C8×C79C2×C412yes—
64#97×C79—22no—
65#97×C79—21no—
66C4×C8×C79—22no—
67C4×C8×C79—21no—
68C4×C8×C79—21no—
69C2×Q8×C79—21no—
70C2×Q8×C79—41no—
71C2×Q8×C79—41no—
72C2×Q8×C79—81no—
73C2×Q8×C79—81no—
74C2×Q8×C79C22⋊C412yes—
75C22×C4×C79—22no—
76C22×C4×C79C22×C411yescharacteristic
77C22×C4×C79C2×D411yescharacteristic
78C22×C4×C79#4111yescharacteristic
79M16×C79—21no—
80M16×C79—21no—
81M16×C79—21no—
82M16×C79—41no—
83M16×C79—41no—
84M16×C79Q1612yes—
85C2×C8×C79—22no—
86C2×C8×C79—21no—
87C2×C8×C79—21no—
88C2×C8×C79—21no—
89C2×C8×C79—21no—
90C2×C8×C79—41no—
91C2×C8×C79—41no—
92C2×C8×C79—41no—
93C2×C8×C79—41no—
94C2×C8×C79—81no—
95C4⋊C4×C79—22no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79—22no—
100C4⋊C4×C79—22no—
101C4⋊C4×C79—22no—
102C4⋊C4×C79—41no—
103C4⋊C4×C79—41no—
104C4⋊C4×C79C22⋊C412yes—
105C22⋊C4×C79—22no—
106C42×C79—22no—
107C42×C79C2×D411yescharacteristic
108C42×C79C2×D411yescharacteristic
109C42×C79C2×D411yescharacteristic
110C42×C79#4111yescharacteristic
111C23×C79C4×D411yescharacteristic
112Q8×C79—42no—
113Q8×C79—41no—
114Q8×C79—41no—
115Q8×C79—82no—
116Q8×C79—81no—
117Q8×C79—81no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—22no—
121C2×C4×C79—22no—
122C2×C4×C79—41no—
123C2×C4×C79—42no—
124C2×C4×C79—82no—
125C2×C4×C79C2×C22⋊C411yescharacteristic
126C2×C4×C79C4×D411yescharacteristic
127C2×C4×C79#12011yescharacteristic
128C2×C4×C79#12111yescharacteristic
129C2×C4×C79#12111yescharacteristic
130C2×C4×C79#12311yescharacteristic
131C2×C4×C79C2×Q1611yescharacteristic
132C2×C4×C79#13511yescharacteristic
133C2×C4×C79#13711yescharacteristic
134C2×C4×C79#13711yescharacteristic
135C8×C79—22no—
136C8×C79—42no—
137C8×C79—41no—
138C8×C79—41no—
139C8×C79—41no—
140C8×C79—81no—
141C8×C79—81no—
142C22×C79—21no—
143C22×C79—21no—
144C22×C79#38611yescharacteristic
145C22×C79C4×Q1611yescharacteristic
146C22×C79#44111yescharacteristic
147C4×C79—21no—
148C4×C79—21no—
149C4×C79—21no—
150C4×C79—42no—
151C4×C79—42no—
152C4×C79—82no—
153C4×C79#45111yescharacteristic
154C4×C79#45211yescharacteristic
155C4×C79#46211yescharacteristic
156C4×C79#46411yescharacteristic
157C4×C79#47111yescharacteristic
158C4×C79#47211yescharacteristic
159#9270C7911yesmaximal, characteristic, direct product factor, Sylow
160C2×C79—21no—
161C2×C79—21no—
162C2×C79#187811yescharacteristic
163C2×C79#190711yescharacteristic
164C2×C79#191511yescharacteristic
165#3230C2×C7911yescharacteristic
166#2962C2×C7911yescharacteristic
167#1997C2×C7911yescharacteristic
168#1550C2×C7911yescharacteristic
169C2×#332C2×C7911yescharacteristic
170#1301C2×C7911yescharacteristic
171#1283C2×C7911yescharacteristic
172C79#927011yescharacteristic, direct product factor, Sylow
173#533C22×C7911yescharacteristic
174C2×C4⋊Q8C22×C7911yescharacteristic
175#500—21no—
176#487—21no—
177#484C4×C7914yes—
178#477—22no—
179#446—22no—
180#446—21no—
181C8×Q8—21no—
182#431C22×C7911yescharacteristic
183#424—21no—
184#423C22×C7911yescharacteristic
185C2×C4⋊C8C22×C7911yescharacteristic
186C2×C4⋊C8C22×C7911yescharacteristic
187#405—21no—
188C4×M16C22×C7911yescharacteristic
189#343—21no—
190#343—21no—
191#333—21no—
192#332—21no—
193#332—21no—
194#332—21no—
195C22×Q8—21no—
196C2×M16—21no—
197C2×M16D4×C7911yescharacteristic
198C2×M16D4×C7911yescharacteristic
199C22×C8—21no—
200C22×C8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8D4×C7911yescharacteristic
206C4⋊Q8D4×C7911yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8C2×C4×C7912yes—
210C4×Q8—21no—
211C4×Q8D4×C7912yes—
212#117—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C7912yes—
215C2×C42C23×C7911yescharacteristic
216#107—24no—
217C4⋊C8—22no—
218C4⋊C8—22no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8D4×C7911yescharacteristic
226C4⋊C8D4×C7911yescharacteristic
227#103—24no—
228C22⋊C8C2×C4×C7912yes—
229#97—22no—
230#97—21no—
231C4×C8—22no—
232C4×C8—21no—
233C4×C8—21no—
234C2×Q8—21no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—81no—
238C2×Q8—81no—
239C2×Q8C22⋊C4×C7912yes—
240C22×C4—22no—
241C22×C4C22×C4×C7911yescharacteristic
242C22×C4C2×D4×C7911yescharacteristic
243C22×C4#41×C7911yescharacteristic
244M16—21no—
245M16—21no—
246M16—21no—
247M16—41no—
248M16—41no—
249M16Q16×C7912yes—
250C2×C8—21no—
251C2×C8—22no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—81no—
260C4⋊C4—22no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4C22⋊C4×C7912yes—
270C22⋊C4—22no—
271C42—22no—
272C42C2×D4×C7911yescharacteristic
273C42C2×D4×C7911yescharacteristic
274C42C2×D4×C7911yescharacteristic
275C42#41×C7911yescharacteristic
276C23C4×D4×C7911yescharacteristic
277Q8—42no—
278Q8—41no—
279Q8—41no—
280Q8—82no—
281Q8—81no—
282Q8—81no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4C2×C22⋊C4×C7911yescharacteristic
291C2×C4C4×D4×C7911yescharacteristic
292C2×C4#120×C7911yescharacteristic
293C2×C4#121×C7911yescharacteristic
294C2×C4#121×C7911yescharacteristic
295C2×C4#123×C7911yescharacteristic
296C2×C4C2×Q16×C7911yescharacteristic
297C2×C4#135×C7911yescharacteristic
298C2×C4#137×C7911yescharacteristic
299C2×C4#137×C7911yescharacteristic
300C8—22no—
301C8—42no—
302C8—41no—
303C8—41no—
304C8—41no—
305C8—81no—
306C8—81no—
307C22—21no—
308C22—21no—
309C22#386×C7911yescharacteristic
310C22C4×Q16×C7911yescharacteristic
311C22#441×C7911yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—42no—
317C4—82no—
318C4#451×C7911yescharacteristic
319C4#452×C7911yescharacteristic
320C4#462×C7911yescharacteristic
321C4#464×C7911yescharacteristic
322C4#471×C7911yescharacteristic
323C4#472×C7911yescharacteristic
324C2—21no—
325C2—21no—
326C2C79×#187811yescharacteristic
327C2C79×#190711yescharacteristic
328C2C79×#191511yescharacteristic
subgroupG/H
center, socleC22×C79#386
commutatorC22×C4C22×C4×C79
Frattini, cosocleC2×C42C23×C79
prime radicalC23×C79C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G

Complements

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

NH ≅ G/Ntype
159. #9270C79direct (N × H)
172. C79#9270direct (N × H)

Maximal subgroups

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

subgroupindex
C79×#32302
C79×#29622
C79×#19972
C79×#15502
C2×#332×C792
C79×#13012
C79×#12832
#927079