Finite Group Databasebeta

← #34198497

Subgroups — #34198497

Order 20224.

466 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊(C79⋊C16)C211yesmaximal, characteristic, complemented
2#23763117C211yesmaximal, characteristic, complemented
3#23761412C212yesmaximal, complemented
4#23761409C212yesmaximal, complemented
5C79×#3050C211yesmaximal, characteristic
6C2×#14579120—21no—
7C22×C79⋊C16—21no—
8C22⋊(C79⋊C16)—21no—
9C22⋊(C79⋊C16)C2212yes—
10#19098326—21no—
11#19098326C2212yes—
12C2×#135×C79C411yescharacteristic, complemented
13C23×C8×C79C2211yescharacteristic
14#525×C79—21no—
15#467×C79C411yescharacteristic, complemented
16#467×C79C2211yescharacteristic
17#466×C79C411yescharacteristic, complemented
18#466×C79C2211yescharacteristic
19#465×C79—21no—
20#465×C79—21no—
21#427×C79C411yescharacteristic, complemented
22#416×C79—21no—
23#14579120—24no—
24#14579120—42no—
25C2×C4⋊Dic79—22no—
26C2×C22⋊Dic79—41no—
27C2×C4×Dic79—41no—
28C2×C79⋊C16—22no—
29C2×C79⋊C16—42no—
30C2×#41×C79—21no—
31C23×C4×C79D411yescharacteristic
32#135×C79—42no—
33C2×Q16×C79C2×C411yescharacteristic
34C2×SD16×C79—21no—
35C2×D8×C79C2×C411yescharacteristic
36C22×C8×C79—42no—
37C22×C8×C79C2×C411yescharacteristic
38C22×C8×C79C2×C411yescharacteristic
39C22×C8×C79D411yescharacteristic
40C22×C8×C79D411yescharacteristic
41C22×C8×C79D411yescharacteristic
42C22×C8×C79C2311yescharacteristic
43#123×C79—41no—
44C22⋊Q8×C79—21no—
45C22⋊Q8×C79—21no—
46#121×C79—21no—
47#121×C79—21no—
48#120×C79—41no—
49C4×D4×C79—41no—
50C4×D4×C79—41no—
51#117×C79—21no—
52#107×C79C2×C411yescharacteristic
53#107×C79C2×C411yescharacteristic
54#106×C79—21no—
55#103×C79—21no—
56#103×C79—21no—
57#102×C79—21no—
58#102×C79—21no—
59C22×Dic79—42no—
60C4⋊Dic79—24no—
61C4⋊Dic79—42no—
62C22⋊Dic79—44no—
63C4×Dic79—44no—
64C79⋊C16—42no—
65C24×C79D811yescharacteristic
66#41×C79—42no—
67#41×C79—42no—
68C2×Q8×C79—21no—
69C2×D4×C79—21no—
70C2×D4×C79—41no—
71C2×D4×C79—41no—
72C2×D4×C79—41no—
73C22×C4×C79—22no—
74C22×C4×C79—22no—
75C22×C4×C79—41no—
76C22×C4×C79C22⋊C411yescharacteristic
77C22×C4×C79C22⋊C411yescharacteristic
78C22×C4×C79D811yescharacteristic
79C22×C4×C79SD1611yescharacteristic
80C22×C4×C79SD1611yescharacteristic
81C22×C4×C79C2×D411yescharacteristic
82Q16×C79—41no—
83SD16×C79—42no—
84D8×C79—41no—
85C2×C8×C79—22no—
86C2×C8×C79—22no—
87C2×C8×C79—41no—
88C2×C8×C79—41no—
89C2×C8×C79—41no—
90C2×C8×C79—41no—
91C2×C8×C79C22⋊C411yescharacteristic
92C2×C8×C79C22⋊C411yescharacteristic
93C2×C8×C79C22×C411yescharacteristic
94C2×C8×C79C2×D411yescharacteristic
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—41no—
98C4⋊C4×C79—41no—
99C22⋊C4×C79—41no—
100C22⋊C4×C79—41no—
101C22⋊C4×C79—41no—
102C22⋊C4×C79—41no—
103C22⋊C4×C79—41no—
104C42×C79—41no—
105C23×C79—22no—
106C23×C79—22no—
107C23×C79—41no—
108C23×C79—41no—
109C23×C79#10211yescharacteristic
110C23×C79#10211yescharacteristic
111C23×C79C2×D811yescharacteristic
112Q8×C79—41no—
113Q8×C79—41no—
114D4×C79—41no—
115D4×C79—41no—
116D4×C79—82no—
117D4×C79—82no—
118D4×C79—82no—
119C2×C4×C79—22no—
120C2×C4×C79—22no—
121C2×C4×C79—22no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—41no—
127C2×C4×C79—41no—
128C2×C4×C79—41no—
129C2×C4×C79—82no—
130C2×C4×C79#9912yes—
131C2×C4×C79#10211yescharacteristic
132C2×C4×C79#10211yescharacteristic
133C2×C4×C79#10412yes—
134C2×C4×C79C2×C22⋊C411yescharacteristic
135C2×C4×C79C2×SD1611yescharacteristic
136C2×Dic79—44no—
137C2×Dic79—82no—
138C2×Dic79—82no—
139C8×C79—21no—
140C8×C79—21no—
141C8×C79—21no—
142C8×C79—21no—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79—21no—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—44no—
151C22×C79—81no—
152C22×C79—81no—
153C22×C79—81no—
154C22×C79#32712yes—
155C22×C79C2×#10211yescharacteristic
156C22×C79#50812yes—
157C4×C79—21no—
158C4×C79—21no—
159C4×C79—81no—
160C4×C79—81no—
161C4×C79—81no—
162C4×C79#32712yes—
163C4×C79C2×#9911yescharacteristic
164C4×C79C2×#10411yescharacteristic
165Dic79—84no—
166#11703—791nomaximal, Sylow
167C2×C79—22no—
168C2×C79—22no—
169C2×C79—41no—
170C2×C79—161no—
171C2×C79C2×#32711yescharacteristic
172C2×C79#213811yescharacteristic
173C2×C79#214511yescharacteristic
174#3050D7911yescharacteristic
175C2×C22⋊C16—791no—
176#1735—791no—
177#1348—792no—
178#1347—792no—
179C79#1170311yescharacteristic, complemented, Sylow
180C2×#135Dic7911yescharacteristic, complemented
181C23×C8C2×D7911yescharacteristic
182#525—21no—
183C2×#117—1581no—
184C22×C16—1581no—
185#467Dic7911yescharacteristic, complemented
186#467C2×D7911yescharacteristic
187#466Dic7911yescharacteristic, complemented
188#466C2×D7911yescharacteristic
189#465—21no—
190#465—21no—
191#427Dic7911yescharacteristic, complemented
192#416—21no—
193C22⋊C16—792no—
194C22⋊C16—1581no—
195#340—792no—
196#340—1581no—
197C2×#41—21no—
198C23×C4C22⋊D7911yescharacteristic
199#135—42no—
200C2×Q16C2×Dic7911yescharacteristic
201C2×SD16—21no—
202C2×D8C2×Dic7911yescharacteristic
203C22×C8—42no—
204C22×C8C2×Dic7911yescharacteristic
205C22×C8C2×Dic7911yescharacteristic
206C22×C8C22⋊D7911yescharacteristic
207C22×C8C22⋊D7911yescharacteristic
208C22×C8C22⋊D7911yescharacteristic
209C22×C8C22×D7911yescharacteristic
210#123—41no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213#121—21no—
214#121—21no—
215#120—41no—
216C4×D4—41no—
217C4×D4—41no—
218#117—21no—
219#117—3162no—
220#117—1584no—
221C2×C4⋊C4—1582no—
222C2×C22⋊C4—3161no—
223C2×C42—3161no—
224C2×C16—3162no—
225C2×C16—1582no—
226#107C2×Dic7911yescharacteristic
227#107C2×Dic7911yescharacteristic
228#106—21no—
229#103—21no—
230#103—21no—
231#102—21no—
232#102—21no—
233C24#1192960911yescharacteristic
234#41—42no—
235#41—42no—
236C2×Q8—21no—
237C2×D4—21no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—3162no—
245C22×C4C22⋊Dic7911yescharacteristic
246C22×C4C22⋊Dic7911yescharacteristic
247C22×C4#1192960911yescharacteristic
248C22×C4#1192961211yescharacteristic
249C22×C4#1192961211yescharacteristic
250C22×C4C2×C22⋊D7911yescharacteristic
251Q16—41no—
252SD16—42no—
253D8—41no—
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22⋊Dic7911yescharacteristic
261C2×C8C22⋊Dic7911yescharacteristic
262C2×C8C22×Dic7911yescharacteristic
263C2×C8C2×C22⋊D7911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—3162no—
269C4⋊C4—1584no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—3164no—
276C42—41no—
277C42—3164no—
278C16—3162no—
279C23—22no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23#1457908211yescharacteristic
284C23#1457908211yescharacteristic
285C23C2×#1192960911yescharacteristic
286Q8—41no—
287Q8—41no—
288D4—41no—
289D4—41no—
290D4—82no—
291D4—82no—
292D4—82no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—82no—
304C2×C4—3164no—
305C2×C4—6322no—
306C2×C4—6322no—
307C2×C4#1457907612yes—
308C2×C4#1457908211yescharacteristic
309C2×C4#1457908211yescharacteristic
310C2×C4#1457908812yes—
311C2×C4C2×C22⋊Dic7911yescharacteristic
312C2×C4C2×#1192961211yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—44no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22#1909829712yes—
329C22C2×#1457908211yescharacteristic
330C22#1909899312yes—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—6324no—
337C4#1909829712yes—
338C4C2×#1457907611yescharacteristic
339C4C2×#1457908811yescharacteristic
340C2—22no—
341C2—22no—
342C2—41no—
343C2—161no—
344C2C2×#1909829711yescharacteristic
345C2#2376510711yescharacteristic
346C2#2376513611yescharacteristic
subgroupG/H
centerC2×C4#14579082
commutatorC2×C8×C79C22×C4
FrattiniC22×C8C22×D79
Fitting, prime radicalC79×#3050C2
socleC22×C79C2×#102
cosocleC22×C8×C79C23
hypercenter#3050D79
hypocenterC79#11703
LCSG ▷ C2×C8×C79 ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊(C79⋊C16)C2semidirect
2. #23763117C2semidirect
3. #23761412C2semidirect
4. #23761409C2semidirect
12. C2×#135×C79C4semidirect
15. #467×C79C4semidirect
17. #466×C79C4semidirect
21. #427×C79C4semidirect
179. C79#11703semidirect
180. C2×#135Dic79semidirect
185. #467Dic79semidirect
187. #466Dic79semidirect
191. #427Dic79semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊(C79⋊C16)2
#237631172
#237614122
#237614092
C79×#30502
#1170379