Finite Group Databasebeta

← #34181877

Subgroups — #34181877

Order 20224.

446 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23766340C211yesmaximal, characteristic
2C4×#14579078C211yesmaximal, characteristic
3#23761292C212yesmaximal, complemented
4#23761266C212yesmaximal, complemented
5C79×#1466C211yesmaximal, characteristic
6C2×#14579078—21no—
7C4×#11929608C2212yes—
8#19098456—21no—
9#19098449—21no—
10#19098443—21no—
11#19098431C2211yescharacteristic
12#19098426C411yescharacteristic
13#19098423C411yescharacteristic
14C22⋊C4×Dic79—21no—
15C4×C22⋊Dic79C411yescharacteristic
16#19098409C2211yescharacteristic
17C2×C79⋊#95C411yescharacteristic
18#19098332—21no—
19C2×C4×D4×C79C2211yescharacteristic
20#432×C79C2212yes—
21#323×C79—21no—
22#323×C79—21no—
23C23×Dic79—21no—
24C2×#11929608—22no—
25C2×C4⋊Dic79—21no—
26C2×C22⋊Dic79—21no—
27C2×C22⋊Dic79—21no—
28C2×C22⋊Dic79—21no—
29C2×C4×Dic79—21no—
30C2×C4×Dic79—21no—
31#14579078—24no—
32#14579072—22no—
33C4×C79⋊C8—22no—
34C79⋊#95—21no—
35C79⋊#95—21no—
36C79⋊#95—21no—
37C79⋊#95—21no—
38C79⋊#95—21no—
39C79⋊#95C2×C411yescharacteristic
40C79⋊#95C2×C411yescharacteristic
41C79⋊#95C2×C411yescharacteristic
42C79⋊#95C2×C411yescharacteristic
43C22×D4×C79D411yescharacteristic
44C23×C4×C79C2×C411yescharacteristic
45C23×C4×C79C2×C411yescharacteristic
46C4×D4×C79—22no—
47C4×D4×C79—22no—
48C2×C4⋊C4×C79D411yescharacteristic
49C2×C22⋊C4×C79D411yescharacteristic
50C2×C22⋊C4×C79D411yescharacteristic
51C2×C42×C79C2311yescharacteristic
52C4⋊C8×C79—22no—
53C22⋊C8×C79—22no—
54#97×C79—22no—
55C22×Dic79—21no—
56C22×Dic79—21no—
57C22×Dic79—21no—
58C22×Dic79—21no—
59C22×Dic79—42no—
60C22×Dic79—42no—
61C22×Dic79—81no—
62#11929608—24no—
63#11929608—42no—
64C2×C79⋊C8—42no—
65C4⋊Dic79—81no—
66C22⋊Dic79—42no—
67C22⋊Dic79—42no—
68C22⋊Dic79—81no—
69C4×Dic79—42no—
70C4×Dic79—81no—
71C24×C79C22⋊C411yescharacteristic
72C24×C79C22⋊C411yescharacteristic
73C2×D4×C79—22no—
74C2×D4×C79—22no—
75C2×D4×C79—41no—
76C22×C4×C79—21no—
77C22×C4×C79—21no—
78C22×C4×C79—21no—
79C22×C4×C79—21no—
80C22×C4×C79—81no—
81C22×C4×C79—81no—
82C22×C4×C79C22⋊C411yescharacteristic
83C22×C4×C79C22⋊C411yescharacteristic
84C22×C4×C79C22×C411yescharacteristic
85C22×C4×C79C2×D411yescharacteristic
86C22×C4×C79C2×D411yescharacteristic
87C2×C8×C79—42no—
88C4⋊C4×C79—22no—
89C22⋊C4×C79—22no—
90C22⋊C4×C79—22no—
91C42×C79#4112yes—
92C42×C79#4112yes—
93C23×C79—21no—
94C23×C79—21no—
95C23×C79—21no—
96C23×C79—21no—
97C23×C79—21no—
98C23×C79—41no—
99C23×C79—41no—
100C23×C79—41no—
101C23×C79—41no—
102C23×C79#10412yes—
103C23×C79C2×C22⋊C411yescharacteristic
104D4×C79—44no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—41no—
110C2×C4×C79—41no—
111C2×C4×C79—41no—
112C2×C4×C79—41no—
113C2×C4×C79—81no—
114C2×C4×C79—81no—
115C2×C4×C79—81no—
116C2×C4×C79—81no—
117C2×C4×C79#11711yescharacteristic
118C2×C4×C79#11711yescharacteristic
119C2×C4×C79#12312yes—
120C2×C4×C79#12312yes—
121C2×Dic79—22no—
122C2×Dic79—41no—
123C2×Dic79—41no—
124C2×Dic79—41no—
125C2×Dic79—41no—
126C2×Dic79—41no—
127C2×Dic79—41no—
128C2×Dic79—41no—
129C2×Dic79—41no—
130C2×Dic79—41no—
131C2×Dic79—41no—
132C2×Dic79—41no—
133C2×Dic79—84no—
134C8×C79—82no—
135C79⋊C8—44no—
136C22×C79—21no—
137C22×C79—21no—
138C22×C79—22no—
139C22×C79—42no—
140C22×C79—42no—
141C22×C79—41no—
142C22×C79—41no—
143C22×C79—41no—
144C22×C79—41no—
145C22×C79—41no—
146C22×C79—81no—
147C22×C79—81no—
148C22×C79#38111yescharacteristic
149C22×C79C2×#10411yescharacteristic
150C22×C79#42111yescharacteristic
151C4×C79—22no—
152C4×C79—22no—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—41no—
156C4×C79—41no—
157Dic79—42no—
158Dic79—81no—
159Dic79—81no—
160Dic79—81no—
161#8773—791nomaximal, Sylow
162C2×C79—21no—
163C2×C79—21no—
164C2×C79—42no—
165C2×C79—81no—
166C2×C79#182611yescharacteristic
167C2×C79#182711yescharacteristic
168C2×C79#182911yescharacteristic
169#2353—791no—
170C4×#100—791no—
171#1466D7911yescharacteristic
172#1300—792no—
173#1288—792no—
174C79#877311yescharacteristic, complemented, Sylow
175C2×C4×D4C2×D7911yescharacteristic
176#432C2×D7912yes—
177C2×#100—1581no—
178C4×M16—792no—
179#388—1581no—
180#387—1581no—
181#386—1581no—
182#383—791no—
183#381—791no—
184#380—791no—
185C4×C22⋊C4—791no—
186C4×C22⋊C4—1581no—
187#376—791no—
188C2×#95—791no—
189#343—1581no—
190#323—21no—
191#323—21no—
192C22×D4D31611yescharacteristic
193C23×C4—1581no—
194C23×C4C4×D7911yescharacteristic
195C23×C4C4×D7911yescharacteristic
196C2×M16—1582no—
197C4×D4—22no—
198C4×D4—22no—
199C2×C4⋊C4—1581no—
200C2×C4⋊C4D31611yescharacteristic
201C2×C22⋊C4—1581no—
202C2×C22⋊C4—1581no—
203C2×C22⋊C4—1581no—
204C2×C22⋊C4C22⋊D7911yescharacteristic
205C2×C22⋊C4C22⋊D7911yescharacteristic
206C2×C42—1581no—
207C2×C42—1581no—
208C2×C42C22×D7911yescharacteristic
209C4⋊C8—22no—
210#100—1584no—
211C22⋊C8—22no—
212#97—22no—
213#97—1582no—
214C4×C8—1582no—
215#95—791no—
216#95—791no—
217#95—791no—
218#95—791no—
219#95—1581no—
220#95—1581no—
221#95—1581no—
222#95—1581no—
223#95—1581no—
224C24(C2×D79)⋊C411yescharacteristic
225C24(C2×D79)⋊C411yescharacteristic
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—81no—
234C22×C4—81no—
235C22×C4—3162no—
236C22×C4—3162no—
237C22×C4—6321no—
238C22×C4—1581no—
239C22×C4—1581no—
240C22×C4—1581no—
241C22×C4—1581no—
242C22×C4(C2×D79)⋊C411yescharacteristic
243C22×C4(C2×D79)⋊C411yescharacteristic
244C22×C4C2×C4×D7911yescharacteristic
245C22×C4C2×C22⋊D7911yescharacteristic
246C22×C4C2×D31611yescharacteristic
247M16—3162no—
248M16—1584no—
249C2×C8—42no—
250C2×C8—3162no—
251C4⋊C4—22no—
252C4⋊C4—6321no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—3162no—
256C22⋊C4—3162no—
257C22⋊C4—6321no—
258C42—3162no—
259C42—6321no—
260C42#1192962312yes—
261C42#1192962312yes—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#1457908712yes—
272C23C2×(C2×D79)⋊C411yescharacteristic
273D4—44no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—3161no—
287C2×C4—3161no—
288C2×C4—3161no—
289C2×C4—3161no—
290C2×C4—3161no—
291C2×C4—3161no—
292C2×C4—3161no—
293C2×C4—3161no—
294C2×C4—3161no—
295C2×C4—3161no—
296C2×C4—3161no—
297C2×C4—6324no—
298C2×C4—1582no—
299C2×C4#1457911711yescharacteristic
300C2×C4#1457911711yescharacteristic
301C2×C4#1457914212yes—
302C2×C4#1457914512yes—
303C8—82no—
304C8—3164no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—42no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—81no—
316C22—81no—
317C22#1909842411yescharacteristic
318C22C2×#1457908711yescharacteristic
319C22#1909857911yescharacteristic
320C4—22no—
321C4—22no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—3162no—
327C4—6321no—
328C4—6321no—
329C4—6321no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—81no—
334C2#2376349711yescharacteristic
335C2#2376350111yescharacteristic
336C2#2376350911yescharacteristic
subgroupG/H
centerC22#19098424
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1466C2
socleC22×C79#381
prime radicalC22×D4×C79D4
cosocleC2×C42×C79C23
hypercenter#1466D79
hypocenterC79#8773
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #23761292C2semidirect
4. #23761266C2semidirect
174. C79#8773semidirect

Maximal subgroups

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

subgroupindex
#237663402
C4×#145790782
#237612922
#237612662
C79×#14662
#877379