Finite Group Databasebeta

← #34186424

Subgroups — #34186424

Order 20224.

356 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23764119C211yesmaximal, characteristic
2C4×#14579092C211yesmaximal, characteristic
3#23763270C211yesmaximal, characteristic
4#23761240C211yesmaximal, characteristic
5#23761234C211yesmaximal, characteristic
6C79⋊#1273C211yesmaximal, characteristic
7C79×#1279C211yesmaximal, characteristic
8C2×#14579092C411yescharacteristic
9C2×#14579092C411yescharacteristic
10C2×C4⋊(C79⋊C8)—21no—
11C2×C4⋊(C79⋊C8)C2211yescharacteristic
12C2×#14579071—21no—
13C2×C4×C79⋊C8C2211yescharacteristic
14C2×C4×C79⋊C8C2211yescharacteristic
15C4×C4⋊Dic79C2211yescharacteristic
16#19098325C411yescharacteristic
17#19098325C411yescharacteristic
18#19098318—21no—
19#19098317—21no—
20C2×C4⋊C8×C79C2211yescharacteristic
21C2×C4×C8×C79C2211yescharacteristic
22C4×C4⋊C4×C79C2211yescharacteristic
23C22×C79⋊C8—21no—
24C22×C79⋊C8C2×C411yescharacteristic
25C22×C79⋊C8C2×C411yescharacteristic
26C22×C79⋊C8D411yescharacteristic
27C22×C79⋊C8D411yescharacteristic
28C2×C4⋊Dic79C2×C411yescharacteristic
29C2×C4⋊Dic79C2×C411yescharacteristic
30C2×C4×Dic79—21no—
31#14579092—22no—
32#14579092—22no—
33C4⋊(C79⋊C8)—21no—
34C4⋊(C79⋊C8)—21no—
35C4⋊(C79⋊C8)—42no—
36#14579071—42no—
37C4×C79⋊C8—21no—
38C4×C79⋊C8—21no—
39C4×C79⋊C8—21no—
40C4×C79⋊C8—21no—
41C79⋊#95—21no—
42C22×C8×C79—21no—
43C22×C8×C79—21no—
44C2×C4⋊C4×C79C2×C411yescharacteristic
45C2×C4⋊C4×C79C2×C411yescharacteristic
46C2×C42×C79—21no—
47C2×C42×C79C2311yescharacteristic
48C4⋊C8×C79—21no—
49C4⋊C8×C79Q812yes—
50C4×C8×C79—21no—
51C4×C8×C79—21no—
52#95×C79—21no—
53C22×Dic79—21no—
54C22×Dic79—21no—
55C2×C79⋊C8—21no—
56C2×C79⋊C8—21no—
57C2×C79⋊C8—21no—
58C2×C79⋊C8—21no—
59C2×C79⋊C8—21no—
60C2×C79⋊C8—21no—
61C2×C79⋊C8—21no—
62C2×C79⋊C8—21no—
63C2×C79⋊C8—21no—
64C2×C79⋊C8—21no—
65C2×C79⋊C8—41no—
66C2×C79⋊C8—41no—
67C2×C79⋊C8—41no—
68C2×C79⋊C8M1612yes—
69C2×C79⋊C8SD1612yes—
70C4⋊Dic79—21no—
71C4⋊Dic79—21no—
72C4⋊Dic79—21no—
73C4⋊Dic79—21no—
74C4×Dic79—41no—
75C4×Dic79—41no—
76C22×C4×C79—21no—
77C22×C4×C79—21no—
78C22×C4×C79C22×C411yescharacteristic
79C22×C4×C79C2×D411yescharacteristic
80C22×C4×C79#4111yescharacteristic
81C2×C8×C79—22no—
82C2×C8×C79—22no—
83C2×C8×C79—41no—
84C2×C8×C79—41no—
85C2×C8×C79—41no—
86C2×C8×C79—41no—
87C4⋊C4×C79—21no—
88C4⋊C4×C79—21no—
89C4⋊C4×C79—21no—
90C4⋊C4×C79M1612yes—
91C42×C79—41no—
92C42×C79—41no—
93C42×C79C2×Q811yescharacteristic
94C42×C79#4111yescharacteristic
95C42×C79#4111yescharacteristic
96C42×C79#4111yescharacteristic
97C23×C79C4×D411yescharacteristic
98C2×C4×C79—21no—
99C2×C4×C79—21no—
100C2×C4×C79—22no—
101C2×C4×C79—41no—
102C2×C4×C79—41no—
103C2×C4×C79—41no—
104C2×C4×C79—41no—
105C2×C4×C79—41no—
106C2×C4×C79#11711yescharacteristic
107C2×C4×C79C4×Q811yescharacteristic
108C2×C4×C79C22⋊Q811yescharacteristic
109C2×C4×C79#12311yescharacteristic
110C2×C4×C79#12511yescharacteristic
111C2×C4×C79#12611yescharacteristic
112C2×C4×C79C2×M1611yescharacteristic
113C2×C4×C79C2×M1611yescharacteristic
114C2×C4×C79#13111yescharacteristic
115C2×C4×C79#13111yescharacteristic
116C2×C4×C79C2×SD1611yescharacteristic
117C2×C4×C79#13511yescharacteristic
118C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C79#13711yescharacteristic
120C2×Dic79—41no—
121C2×Dic79—41no—
122C2×Dic79—41no—
123C2×Dic79—41no—
124C2×Dic79—41no—
125C2×Dic79—41no—
126C8×C79—42no—
127C8×C79—42no—
128C79⋊C8—22no—
129C79⋊C8—22no—
130C79⋊C8—41no—
131C79⋊C8—41no—
132C79⋊C8—81no—
133C22×C79#38711yescharacteristic
134C22×C79#43511yescharacteristic
135C22×C79#43611yescharacteristic
136C22×C79C4×SD1611yescharacteristic
137C22×C79#44011yescharacteristic
138C22×C79#44311yescharacteristic
139C22×C79#44411yescharacteristic
140C4×C79—21no—
141C4×C79—21no—
142C4×C79—42no—
143C4×C79—81no—
144C4×C79#43211yescharacteristic
145C4×C79#43311yescharacteristic
146C4×C79#44611yescharacteristic
147C4×C79#44611yescharacteristic
148C4×C79#47511yescharacteristic
149C4×C79#47811yescharacteristic
150C4×C79#48111yescharacteristic
151C4×C79#48511yescharacteristic
152Dic79—81no—
153Dic79—81no—
154#9538—791nomaximal, Sylow
155C2×C79#158211yescharacteristic
156C2×C79#158811yescharacteristic
157C2×C79#159011yescharacteristic
158C2×C79#159211yescharacteristic
159C2×C79#191711yescharacteristic
160C2×C79#191911yescharacteristic
161C2×C79#192211yescharacteristic
162#1939—791no—
163C4×#106—791no—
164#1770—791no—
165#1279—791no—
166#1279D7911yescharacteristic
167#1277—791no—
168#1273—791no—
169C79#953811yescharacteristic, complemented, Sylow
170C2×#106—791no—
171C2×#106—791no—
172C2×C4⋊C8—791no—
173C2×C4⋊C8—1581no—
174C2×C4⋊C8C2×D7911yescharacteristic
175C2×#97—1581no—
176C2×C4×C8—791no—
177C2×C4×C8—791no—
178C2×C4×C8C2×D7911yescharacteristic
179C4×C4⋊C4—791no—
180C4×C4⋊C4C2×D7911yescharacteristic
181#340—791no—
182#340—791no—
183#336—1581no—
184#336—1581no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—791no—
188C22×C8—791no—
189C22×C8—791no—
190C22×C8—791no—
191C22×C8—1581no—
192C2×C4⋊C4—791no—
193C2×C4⋊C4—791no—
194C2×C4⋊C4C4×D7911yescharacteristic
195C2×C4⋊C4C4×D7911yescharacteristic
196C2×C42—21no—
197C2×C42—1581no—
198C2×C42C22×D7911yescharacteristic
199#106—1582no—
200#106—1582no—
201C4⋊C8—21no—
202C4⋊C8—3162no—
203C4⋊C8—1581no—
204C4⋊C8—1581no—
205C4⋊C8Dic15812yes—
206#97—3162no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8—1581no—
210C4×C8—1581no—
211C4×C8—1581no—
212C4×C8—1581no—
213#95—21no—
214#95—1581no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—1581no—
218C22×C4—1581no—
219C22×C4C2×C4×D7911yescharacteristic
220C22×C4D4×D7911yescharacteristic
221C22×C4#1192962311yescharacteristic
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—3161no—
229C2×C8—3161no—
230C2×C8—3161no—
231C2×C8—792no—
232C2×C8—792no—
233C2×C8—1581no—
234C2×C8—1581no—
235C2×C8—1581no—
236C2×C8—1581no—
237C2×C8—1581no—
238C2×C8—1581no—
239C2×C8—1581no—
240C2×C8—1581no—
241C2×C8—1581no—
242C2×C8—1581no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—1581no—
247C4⋊C4—1581no—
248C4⋊C4—1581no—
249C4⋊C4—1581no—
250C4⋊C4#1192960712yes—
251C42—41no—
252C42—41no—
253C42—3161no—
254C42—3161no—
255C42C2×Dic15811yescharacteristic
256C42#1192962311yescharacteristic
257C42#1192962411yescharacteristic
258C42#1192962511yescharacteristic
259C23(C22⋊D79)⋊C411yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—3161no—
269C2×C4—3161no—
270C2×C4—3161no—
271C2×C4—3161no—
272C2×C4—3161no—
273C2×C4—3161no—
274C2×C4#1457911911yescharacteristic
275C2×C4C4×Dic15811yescharacteristic
276C2×C4#1457913811yescharacteristic
277C2×C4#1457914611yescharacteristic
278C2×C4#1457915211yescharacteristic
279C2×C4#1457915411yescharacteristic
280C2×C4M16×D7911yescharacteristic
281C2×C4C2×#1192960711yescharacteristic
282C2×C4#1457916711yescharacteristic
283C2×C4#1457916911yescharacteristic
284C2×C4SD16×D7911yescharacteristic
285C2×C4#1457918011yescharacteristic
286C2×C4#1457918811yescharacteristic
287C2×C4#1457919311yescharacteristic
288C8—42no—
289C8—42no—
290C8—3161no—
291C8—3161no—
292C8—6321no—
293C8—1582no—
294C8—1582no—
295C22#1909845011yescharacteristic
296C22#1909863111yescharacteristic
297C22#1909863811yescharacteristic
298C22#1909865411yescharacteristic
299C22#1909866611yescharacteristic
300C22#1909867711yescharacteristic
301C22#1909868211yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—81no—
306C4—6321no—
307C4—6321no—
308C4#1909861911yescharacteristic
309C4#1909862311yescharacteristic
310C4#1909869111yescharacteristic
311C4#1909869311yescharacteristic
312C4#1909884611yescharacteristic
313C4#1909886111yescharacteristic
314C4#1909888311yescharacteristic
315C4#1909890611yescharacteristic
316C2#2376223311yescharacteristic
317C2#2376227511yescharacteristic
318C2#2376229311yescharacteristic
319C2#2376230511yescharacteristic
320C2#2376396711yescharacteristic
321C2#2376398111yescharacteristic
322C2#2376400211yescharacteristic
subgroupG/H
centerC22×C4D4×D79
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1279C2
socle, prime radicalC23×C79C4×D4
cosocleC2×C42×C79C23
hypercenter#1279D79
hypocenterC79#9538
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
169. C79#9538semidirect

Maximal subgroups

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

subgroupindex
#237641192
C4×#145790922
#237632702
#237612402
#237612342
C79⋊#12732
C79×#12792
#953879