Finite Group Databasebeta

← #34199337

Subgroups — #34199337

Order 20224.

422 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊(C79⋊C16)C211yesmaximal, characteristic, complemented
2#23763425C211yesmaximal, characteristic, complemented
3#23761412C212yesmaximal, complemented
4#23761409C212yesmaximal, complemented
5C79×#3050C211yesmaximal, characteristic
6C22×C79⋊C16—21no—
7C2×#14579093—21no—
8#19098423—21no—
9C22⋊(C79⋊C16)—21no—
10C22⋊(C79⋊C16)C2212yes—
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—
23C2×C4⋊Dic79—22no—
24C2×C22⋊Dic79—41no—
25C2×C79⋊C16—22no—
26C2×C79⋊C16—42no—
27#14579093—42no—
28C79⋊#95—41no—
29C2×#41×C79—21no—
30C23×C4×C79D411yescharacteristic
31#135×C79—42no—
32C2×Q16×C79C2×C411yescharacteristic
33C2×SD16×C79—21no—
34C2×D8×C79C2×C411yescharacteristic
35C22×C8×C79—42no—
36C22×C8×C79C2×C411yescharacteristic
37C22×C8×C79C2×C411yescharacteristic
38C22×C8×C79D411yescharacteristic
39C22×C8×C79D411yescharacteristic
40C22×C8×C79D411yescharacteristic
41C22×C8×C79C2311yescharacteristic
42#123×C79—41no—
43C22⋊Q8×C79—21no—
44C22⋊Q8×C79—21no—
45#121×C79—21no—
46#121×C79—21no—
47#120×C79—41no—
48C4×D4×C79—41no—
49C4×D4×C79—41no—
50#117×C79—21no—
51#107×C79C2×C411yescharacteristic
52#107×C79C2×C411yescharacteristic
53#106×C79—21no—
54#103×C79—21no—
55#103×C79—21no—
56#102×C79—21no—
57#102×C79—21no—
58C22×Dic79—42no—
59C4⋊Dic79—42no—
60C4⋊Dic79—42no—
61C22⋊Dic79—82no—
62C79⋊C16—42no—
63C24×C79D811yescharacteristic
64#41×C79—42no—
65#41×C79—42no—
66C2×Q8×C79—21no—
67C2×D4×C79—21no—
68C2×D4×C79—41no—
69C2×D4×C79—41no—
70C2×D4×C79—41no—
71C22×C4×C79—41no—
72C22×C4×C79—41no—
73C22×C4×C79—41no—
74C22×C4×C79C22⋊C411yescharacteristic
75C22×C4×C79C22⋊C411yescharacteristic
76C22×C4×C79D811yescharacteristic
77C22×C4×C79SD1611yescharacteristic
78C22×C4×C79SD1611yescharacteristic
79C22×C4×C79C2×D411yescharacteristic
80Q16×C79—41no—
81SD16×C79—42no—
82D8×C79—41no—
83C2×C8×C79—22no—
84C2×C8×C79—22no—
85C2×C8×C79—22no—
86C2×C8×C79—41no—
87C2×C8×C79—41no—
88C2×C8×C79—41no—
89C2×C8×C79C22⋊C411yescharacteristic
90C2×C8×C79C22⋊C411yescharacteristic
91C2×C8×C79C22×C411yescharacteristic
92C2×C8×C79C2×D411yescharacteristic
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—41no—
96C4⋊C4×C79—41no—
97C22⋊C4×C79—41no—
98C22⋊C4×C79—41no—
99C22⋊C4×C79—41no—
100C22⋊C4×C79—41no—
101C22⋊C4×C79—41no—
102C42×C79—41no—
103C23×C79—22no—
104C23×C79—22no—
105C23×C79—41no—
106C23×C79—41no—
107C23×C79#10211yescharacteristic
108C23×C79#10211yescharacteristic
109C23×C79C2×D811yescharacteristic
110Q8×C79—41no—
111Q8×C79—41no—
112D4×C79—41no—
113D4×C79—41no—
114D4×C79—82no—
115D4×C79—82no—
116D4×C79—82no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—41no—
124C2×C4×C79—41no—
125C2×C4×C79—41no—
126C2×C4×C79—41no—
127C2×C4×C79—41no—
128C2×C4×C79—41no—
129C2×C4×C79—82no—
130C2×C4×C79#10211yescharacteristic
131C2×C4×C79#10211yescharacteristic
132C2×C4×C79C2×C22⋊C411yescharacteristic
133C2×C4×C79C2×SD1611yescharacteristic
134C2×Dic79—82no—
135C2×Dic79—82no—
136C2×Dic79—82no—
137C8×C79—21no—
138C8×C79—21no—
139C8×C79—21no—
140C8×C79#9912yes—
141C22×C79—21no—
142C22×C79—21no—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79—21no—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79—44no—
149C22×C79—81no—
150C22×C79—81no—
151C22×C79—81no—
152C22×C79#36012yes—
153C22×C79C2×#10211yescharacteristic
154C22×C79#50812yes—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—81no—
159C4×C79—81no—
160C4×C79—81no—
161C4×C79C2×#9911yescharacteristic
162C4×C79#42111yescharacteristic
163Dic79—162no—
164#11885—791nomaximal, Sylow
165C2×C79—22no—
166C2×C79—22no—
167C2×C79—41no—
168C2×C79—161no—
169C2×C79#151911yescharacteristic
170C2×C79#213811yescharacteristic
171C2×C79C2×#36011yescharacteristic
172#3050D7911yescharacteristic
173C2×C22⋊C16—791no—
174#1807—791no—
175#1348—792no—
176#1347—792no—
177C79#1188511yescharacteristic, complemented, Sylow
178C2×#135Dic7911yescharacteristic, complemented
179C23×C8C2×D7911yescharacteristic
180#525—21no—
181C22×C16—1581no—
182#467Dic7911yescharacteristic, complemented
183#467C2×D7911yescharacteristic
184#466Dic7911yescharacteristic, complemented
185#466C2×D7911yescharacteristic
186#465—21no—
187#465—21no—
188#427Dic7911yescharacteristic, complemented
189C2×#106—1581no—
190#416—21no—
191#380—1581no—
192C22⋊C16—792no—
193C22⋊C16—1581no—
194#340—792no—
195C2×#41—21no—
196C23×C4C22⋊D7911yescharacteristic
197#135—42no—
198C2×Q16C2×Dic7911yescharacteristic
199C2×SD16—21no—
200C2×D8C2×Dic7911yescharacteristic
201C22×C8—42no—
202C22×C8C2×Dic7911yescharacteristic
203C22×C8C2×Dic7911yescharacteristic
204C22×C8C22⋊D7911yescharacteristic
205C22×C8C22⋊D7911yescharacteristic
206C22×C8C22⋊D7911yescharacteristic
207C22×C8C22×D7911yescharacteristic
208#123—41no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#121—21no—
212#121—21no—
213#120—41no—
214C4×D4—41no—
215C4×D4—41no—
216#117—21no—
217C2×C4⋊C4—1582no—
218C2×C22⋊C4—3161no—
219C2×C16—3162no—
220C2×C16—1582no—
221#107C2×Dic7911yescharacteristic
222#107C2×Dic7911yescharacteristic
223#106—21no—
224#106—3162no—
225#103—21no—
226#103—21no—
227#102—21no—
228#102—21no—
229#95—3161no—
230C24#1192960911yescharacteristic
231#41—42no—
232#41—42no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—3162no—
242C22×C4C22⋊Dic7911yescharacteristic
243C22×C4C22⋊Dic7911yescharacteristic
244C22×C4#1192960911yescharacteristic
245C22×C4#1192961211yescharacteristic
246C22×C4#1192961211yescharacteristic
247C22×C4C2×C22⋊D7911yescharacteristic
248Q16—41no—
249SD16—42no—
250D8—41no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8C22⋊Dic7911yescharacteristic
258C2×C8C22⋊Dic7911yescharacteristic
259C2×C8C22×Dic7911yescharacteristic
260C2×C8C2×C22⋊D7911yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—3162no—
266C4⋊C4—3162no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—6322no—
273C42—41no—
274C16—3162no—
275C23—22no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23#1457908211yescharacteristic
280C23#1457908211yescharacteristic
281C23C2×#1192960911yescharacteristic
282Q8—41no—
283Q8—41no—
284D4—41no—
285D4—41no—
286D4—82no—
287D4—82no—
288D4—82no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—6322no—
303C2×C4—6322no—
304C2×C4—6322no—
305C2×C4#1457908211yescharacteristic
306C2×C4#1457908211yescharacteristic
307C2×C4C2×C22⋊Dic7911yescharacteristic
308C2×C4C2×#1192961211yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8#1457907612yes—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—44no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#1909837312yes—
325C22C2×#1457908211yescharacteristic
326C22#1909899312yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—12642no—
334C4C2×#1457907611yescharacteristic
335C4#1909858011yescharacteristic
336C2—22no—
337C2—22no—
338C2—41no—
339C2—161no—
340C2#2376196811yescharacteristic
341C2#2376510711yescharacteristic
342C2C2×#1909837311yescharacteristic
subgroupG/H
centerC22C2×#14579082
commutatorC2×C8×C79C22×C4
FrattiniC22×C8C22×D79
Fitting, prime radicalC79×#3050C2
socleC22×C79C2×#102
cosocleC22×C8×C79C23
hypercenter#3050D79
hypocenterC79#11885
LCSG ▷ C2×C8×C79 ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ 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. #23763425C2semidirect
3. #23761412C2semidirect
4. #23761409C2semidirect
12. C2×#135×C79C4semidirect
15. #467×C79C4semidirect
17. #466×C79C4semidirect
21. #427×C79C4semidirect
177. C79#11885semidirect
178. C2×#135Dic79semidirect
182. #467Dic79semidirect
184. #466Dic79semidirect
188. #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
#237634252
#237614122
#237614092
C79×#30502
#1188579