Finite Group Databasebeta

← #34186873

Subgroups — #34186873

Order 20224.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23763517C211yesmaximal, characteristic
2C4×C4⋊(C79⋊C8)C211yesmaximal, characteristic
3C2×#19098315C211yesmaximal, characteristic
4C2×#19098313C211yesmaximal, characteristic
5#23761234C211yesmaximal, characteristic
6#23761234C211yesmaximal, characteristic
7C79×#1767C211yesmaximal, characteristic
8C2×C4⋊(C79⋊C8)C411yescharacteristic
9C2×C4⋊(C79⋊C8)C411yescharacteristic
10C2×C4⋊(C79⋊C8)C2211yescharacteristic
11C2×C4⋊(C79⋊C8)C2211yescharacteristic
12C2×C4×C79⋊C8C2211yescharacteristic
13C2×C4×C79⋊C8C2211yescharacteristic
14#19098318—21no—
15#19098318—21no—
16#19098318C411yescharacteristic
17#19098318C411yescharacteristic
18#19098315—22no—
19#19098313—22no—
20C2×C4⋊C8×C79C2211yescharacteristic
21C2×C4⋊C8×C79C2211yescharacteristic
22C2×#97×C79—21no—
23C43×C79C2211yescharacteristic
24#336×C79—21no—
25C22×C79⋊C8—21no—
26C22×C79⋊C8—21no—
27C22×C79⋊C8C2×C411yescharacteristic
28C22×C79⋊C8C2×C411yescharacteristic
29C22×C79⋊C8C2×C411yescharacteristic
30C22×C79⋊C8C2×C411yescharacteristic
31C4⋊(C79⋊C8)—22no—
32C4⋊(C79⋊C8)—22no—
33C4⋊(C79⋊C8)—21no—
34C4⋊(C79⋊C8)—21no—
35C4⋊(C79⋊C8)—21no—
36C4⋊(C79⋊C8)—21no—
37C4×C79⋊C8—21no—
38C4×C79⋊C8—21no—
39C4×C79⋊C8—21no—
40C4×C79⋊C8—21no—
41C22×C8×C79—21no—
42C22×C8×C79—21no—
43C2×C42×C79C2×C411yescharacteristic
44C2×C42×C79C2×C411yescharacteristic
45C2×C42×C79D411yescharacteristic
46C2×C42×C79D411yescharacteristic
47C2×C42×C79Q811yescharacteristic
48C2×C42×C79Q811yescharacteristic
49C2×C42×C79C2311yescharacteristic
50C4⋊C8×C79—21no—
51C4⋊C8×C79—21no—
52C4⋊C8×C79D412yes—
53C4⋊C8×C79Q812yes—
54#97×C79—42no—
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⋊C8—41no—
69C2×C79⋊C8—41no—
70C2×C79⋊C8—41no—
71C2×C79⋊C8M1612yes—
72C2×C79⋊C8M1612yes—
73C22×C4×C79C4⋊C411yescharacteristic
74C22×C4×C79C4⋊C411yescharacteristic
75C22×C4×C79C4⋊C411yescharacteristic
76C22×C4×C79C4⋊C411yescharacteristic
77C22×C4×C79C22×C411yescharacteristic
78C22×C4×C79C2×D411yescharacteristic
79C22×C4×C79C2×Q811yescharacteristic
80C2×C8×C79—22no—
81C2×C8×C79—22no—
82C2×C8×C79—41no—
83C2×C8×C79—41no—
84C2×C8×C79—41no—
85C2×C8×C79—41no—
86C42×C79—22no—
87C42×C79—21no—
88C42×C79—21no—
89C42×C79—21no—
90C42×C79—21no—
91C42×C79—21no—
92C42×C79—21no—
93C42×C79—21no—
94C42×C79—21no—
95C42×C79—41no—
96C42×C79C2×D411yescharacteristic
97C42×C79C2×Q811yescharacteristic
98C42×C79#4111yescharacteristic
99C42×C79#4111yescharacteristic
100C23×C79C2×C4⋊C411yescharacteristic
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#10812yes—
115C2×C4×C79C4×D411yescharacteristic
116C2×C4×C79C4×Q811yescharacteristic
117C2×C4×C79#12111yescharacteristic
118C2×C4×C79C22⋊Q811yescharacteristic
119C2×C4×C79#12511yescharacteristic
120C2×C4×C79C4⋊Q811yescharacteristic
121C2×C4×C79C2×M1611yescharacteristic
122C2×C4×C79C2×M1611yescharacteristic
123C2×C4×C79#13111yescharacteristic
124C2×C4×C79#13111yescharacteristic
125C2×C4×C79#13511yescharacteristic
126C2×C4×C79#13511yescharacteristic
127C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C79#13711yescharacteristic
129C8×C79—42no—
130C8×C79—42no—
131C79⋊C8—22no—
132C79⋊C8—22no—
133C79⋊C8—41no—
134C79⋊C8—41no—
135C79⋊C8—81no—
136C79⋊C8—81no—
137C22×C79#38911yescharacteristic
138C22×C79#42311yescharacteristic
139C22×C79#42411yescharacteristic
140C22×C79#42711yescharacteristic
141C22×C79#42811yescharacteristic
142C22×C79C2×#10811yescharacteristic
143C22×C79#43011yescharacteristic
144C4×C79—22no—
145C4×C79—21no—
146C4×C79—21no—
147C4×C79—41no—
148C4×C79—41no—
149C4×C79—41no—
150C4×C79#43511yescharacteristic
151C4×C79#43511yescharacteristic
152C4×C79#44611yescharacteristic
153C4×C79#44611yescharacteristic
154C4×C79#46311yescharacteristic
155C4×C79#46411yescharacteristic
156C4×C79#47811yescharacteristic
157C4×C79#47911yescharacteristic
158#9606—791nomaximal, Sylow
159C2×C79#156811yescharacteristic
160C2×C79#156911yescharacteristic
161C2×C79#157211yescharacteristic
162C2×C79#157411yescharacteristic
163C2×C79#194011yescharacteristic
164C2×C79#194911yescharacteristic
165C2×C79#195011yescharacteristic
166#1831—791no—
167#1767D7911yescharacteristic
168C4×C4⋊C8—791no—
169C2×#335—791no—
170C2×#334—791no—
171#1277—791no—
172#1277—791no—
173C79#960611yescharacteristic, complemented, Sylow
174C2×C4⋊C8—791no—
175C2×C4⋊C8—791no—
176C2×C4⋊C8—791no—
177C2×C4⋊C8—791no—
178C2×C4⋊C8C2×D7911yescharacteristic
179C2×C4⋊C8C2×D7911yescharacteristic
180C2×#97—21no—
181C2×C4×C8—791no—
182C2×C4×C8—791no—
183C43C2×D7911yescharacteristic
184#336—21no—
185#336—791no—
186#336—791no—
187#336—1581no—
188#336—1581no—
189#335—1582no—
190#334—1582no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—791no—
194C22×C8—791no—
195C22×C8—791no—
196C22×C8—791no—
197C22×C8—1581no—
198C22×C8—1581no—
199C2×C42Dic15811yescharacteristic
200C2×C42Dic15811yescharacteristic
201C2×C42C4×D7911yescharacteristic
202C2×C42C4×D7911yescharacteristic
203C2×C42C22⋊D7911yescharacteristic
204C2×C42C22⋊D7911yescharacteristic
205C2×C42C22×D7911yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—1582no—
209C4⋊C8—1582no—
210C4⋊C8—1581no—
211C4⋊C8—1581no—
212C4⋊C8—1581no—
213C4⋊C8—1581no—
214C4⋊C8Dic15812yes—
215C4⋊C8D31612yes—
216#97—42no—
217C4×C8—1581no—
218C4×C8—1581no—
219C4×C8—1581no—
220C4×C8—1581no—
221C22×C4Dic79⋊C411yescharacteristic
222C22×C4Dic79⋊C411yescharacteristic
223C22×C4Dic79⋊C411yescharacteristic
224C22×C4Dic79⋊C411yescharacteristic
225C22×C4C2×C4×D7911yescharacteristic
226C22×C4C2×C22⋊D7911yescharacteristic
227C22×C4C2×Dic15811yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—3161no—
235C2×C8—3161no—
236C2×C8—3161no—
237C2×C8—3161no—
238C2×C8—3161no—
239C2×C8—3161no—
240C2×C8—792no—
241C2×C8—792no—
242C2×C8—1581no—
243C2×C8—1581no—
244C2×C8—1581no—
245C2×C8—1581no—
246C2×C8—1581no—
247C2×C8—1581no—
248C2×C8—1581no—
249C2×C8—1581no—
250C2×C8—1581no—
251C2×C8—1581no—
252C42—22no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—41no—
262C42C2×D31611yescharacteristic
263C42C2×Dic15811yescharacteristic
264C42#1192962411yescharacteristic
265C42#1192962411yescharacteristic
266C23C2×Dic79⋊C411yescharacteristic
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#1457909612yes—
281C2×C4C4×D31611yescharacteristic
282C2×C4C4×Dic15811yescharacteristic
283C2×C4#1457913511yescharacteristic
284C2×C4#1457914011yescharacteristic
285C2×C4#1457915311yescharacteristic
286C2×C4#1457916111yescharacteristic
287C2×C4M16×D7911yescharacteristic
288C2×C4M16×D7911yescharacteristic
289C2×C4#1457916911yescharacteristic
290C2×C4#1457916911yescharacteristic
291C2×C4#1457918111yescharacteristic
292C2×C4#1457918111yescharacteristic
293C2×C4#1457918711yescharacteristic
294C2×C4#1457919211yescharacteristic
295C8—42no—
296C8—42no—
297C8—3161no—
298C8—3161no—
299C8—6321no—
300C8—6321no—
301C8—1582no—
302C8—1582no—
303C22#1909846111yescharacteristic
304C22#1909858611yescharacteristic
305C22#1909859111yescharacteristic
306C22#1909859911yescharacteristic
307C22#1909860311yescharacteristic
308C22C2×#1457909611yescharacteristic
309C22#1909861111yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4#1909863611yescharacteristic
317C4#1909863611yescharacteristic
318C4#1909869111yescharacteristic
319C4#1909869111yescharacteristic
320C4#1909877811yescharacteristic
321C4#1909878511yescharacteristic
322C4#1909886311yescharacteristic
323C4#1909887011yescharacteristic
324C2#2376216111yescharacteristic
325C2#2376216511yescharacteristic
326C2#2376218111yescharacteristic
327C2#2376219111yescharacteristic
328C2#2376412311yescharacteristic
329C2#2376416811yescharacteristic
330C2#2376417511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D79
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1767C2
socle, prime radicalC23×C79C2×C4⋊C4
cosocleC2×C42×C79C23
hypercenter#1767D79
hypocenterC79#9606
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
173. C79#9606semidirect

Maximal subgroups

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

subgroupindex
#237635172
C4×C4⋊(C79⋊C8)2
C2×#190983152
C2×#190983132
#237612342
C79×#17672
#960679