Finite Group Databasebeta

← #35292842

Subgroups — #35292842

Order 21248.

396 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 97 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#24915849C211yesmaximal, characteristic
2#24907311C211yesmaximal, characteristic
3#24907210C211yesmaximal, characteristic
4#24905287C211yesmaximal, characteristic
5#24905286C211yesmaximal, characteristic
6#24905285C211yesmaximal, characteristic
7C83×#1271C211yesmaximal, characteristic
8C2×Dic83⋊C8—21no—
9C2×#14581702—21no—
10C2×C8×Dic83—21no—
11#19127600C411yescharacteristic
12#19127599C2211yescharacteristic
13#19127597C411yescharacteristic
14#19127587—21no—
15#19127586—21no—
16#19127583—21no—
17#19127582—21no—
18#19127566C411yescharacteristic
19#19127566C411yescharacteristic
20C42×Dic83C2211yescharacteristic
21#19127456C2211yescharacteristic
22#19127456C2211yescharacteristic
23#19127455—21no—
24#389×C83C2211yescharacteristic
25#336×C83C2211yescharacteristic
26#336×C83C2211yescharacteristic
27C22×C83⋊C8—21no—
28C22×C83⋊C8—21no—
29C2×C4⋊Dic83—21no—
30C2×C4⋊Dic83C2×C411yescharacteristic
31C2×C4⋊Dic83C2×C411yescharacteristic
32C2×Dic83⋊C4—21no—
33C2×Dic83⋊C4—21no—
34C2×C4×Dic83C2×C411yescharacteristic
35C2×C4×Dic83C2×C411yescharacteristic
36C2×C4×Dic83D411yescharacteristic
37C2×C4×Dic83D411yescharacteristic
38C2×C4×Dic83D411yescharacteristic
39C2×C4×Dic83D411yescharacteristic
40Dic83⋊C8—24no—
41#14581702—24no—
42C8×Dic83—42no—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C83⋊#95—21no—
48C83⋊#95—21no—
49C83⋊#95—21no—
50C22×C8×C83—21no—
51C22×C8×C83—21no—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83C2×C411yescharacteristic
54C2×C4⋊C4×C83C2×C411yescharacteristic
55C2×C42×C83C2311yescharacteristic
56#95×C83—21no—
57C22×Dic83—21no—
58C22×Dic83—21no—
59C22×Dic83C22⋊C411yescharacteristic
60C22×Dic83C22⋊C411yescharacteristic
61C22×Dic83C22⋊C411yescharacteristic
62C22×Dic83C22⋊C411yescharacteristic
63C2×C83⋊C8—22no—
64C2×C83⋊C8—22no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8—41no—
69C4⋊Dic83—21no—
70C4⋊Dic83—21no—
71C4⋊Dic83—42no—
72C4⋊Dic83—41no—
73Dic83⋊C4—41no—
74Dic83⋊C4—41no—
75Dic83⋊C4—42no—
76C4×Dic83—21no—
77C4×Dic83—21no—
78C4×Dic83—21no—
79C4×Dic83—21no—
80C4×Dic83—21no—
81C4×Dic83—21no—
82C4×Dic83—22no—
83C4×Dic83—22no—
84C4×Dic83—22no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83C22×C411yescharacteristic
88C22×C4×C83C2×D411yescharacteristic
89C22×C4×C83C2×D411yescharacteristic
90C2×C8×C83—22no—
91C2×C8×C83—22no—
92C2×C8×C83—41no—
93C2×C8×C83—41no—
94C2×C8×C83—41no—
95C2×C8×C83—41no—
96C4⋊C4×C83—21no—
97C4⋊C4×C83—21no—
98C4⋊C4×C83—41no—
99C4⋊C4×C83—41no—
100C4⋊C4×C83—41no—
101C42×C83—41no—
102C23×C83C2×C22⋊C411yescharacteristic
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83#13111yescharacteristic
116C2×C4×C83#13111yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C83#13711yescharacteristic
121C2×Dic83—21no—
122C2×Dic83—21no—
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—41no—
131C2×Dic83—41no—
132C2×Dic83—41no—
133C2×Dic83—41no—
134C2×Dic83—41no—
135C2×Dic83—41no—
136C2×Dic83#10112yes—
137C2×Dic83#10412yes—
138C2×Dic83#10412yes—
139C8×C83—42no—
140C8×C83—42no—
141C83⋊C8—42no—
142C83⋊C8—42no—
143C22×C83#40811yescharacteristic
144C22×C83#41011yescharacteristic
145C22×C83C2×#10111yescharacteristic
146C22×C83#41611yescharacteristic
147C22×C83#41711yescharacteristic
148C22×C83C2×#10411yescharacteristic
149C22×C83C2×#10411yescharacteristic
150C4×C83—21no—
151C4×C83—21no—
152C4×C83—21no—
153C4×C83—21no—
154C4×C83—21no—
155C4×C83—21no—
156C4×C83—81no—
157C4×C83—81no—
158Dic83—22no—
159Dic83—22no—
160Dic83—22no—
161Dic83—41no—
162Dic83—81no—
163Dic83—81no—
164#7677—831nomaximal, Sylow
165C2×C83#147011yescharacteristic
166C2×C83#148311yescharacteristic
167C2×C83#149411yescharacteristic
168C2×C83#150011yescharacteristic
169C2×C83#150911yescharacteristic
170C2×C83#152611yescharacteristic
171C2×C83#155211yescharacteristic
172#2864—831no—
173C4×C4⋊C8—831no—
174#1745—831no—
175#1271—831no—
176#1271—831no—
177#1271—831no—
178#1271D8311yescharacteristic
179C83#767711yescharacteristic, complemented, Sylow
180C2×C4⋊C8—1661no—
181C2×#97—1661no—
182C2×C4×C8—1661no—
183#389—831no—
184#389—831no—
185#389—831no—
186#389C2×D8311yescharacteristic
187#387—1661no—
188#387—1661no—
189#387—1661no—
190#387—1661no—
191#382—831no—
192#382—831no—
193C43—831no—
194#336—831no—
195#336—831no—
196#336—1661no—
197#336C2×D8311yescharacteristic
198#336C2×D8311yescharacteristic
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1661no—
202C22×C8—1661no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—831no—
205C2×C4⋊C4—831no—
206C2×C4⋊C4—1661no—
207C2×C4⋊C4—1661no—
208C2×C4⋊C4—1661no—
209C2×C4⋊C4C4×D8311yescharacteristic
210C2×C4⋊C4C4×D8311yescharacteristic
211C2×C42—831no—
212C2×C42—831no—
213C2×C42—831no—
214C2×C42—831no—
215C2×C42—831no—
216C2×C42—831no—
217C2×C42C22×D8311yescharacteristic
218C4⋊C8—1664no—
219#97—1664no—
220C4×C8—3322no—
221#95—21no—
222#95—1661no—
223#95—1661no—
224#95—1661no—
225#95—1661no—
226#95—1661no—
227#95—1661no—
228#95—1661no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—831no—
232C22×C4—831no—
233C22×C4—831no—
234C22×C4—831no—
235C22×C4—1661no—
236C22×C4—1661no—
237C22×C4C2×C4×D8311yescharacteristic
238C22×C4D4×D8311yescharacteristic
239C22×C4D4×D8311yescharacteristic
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—3321no—
247C2×C8—3321no—
248C2×C8—3321no—
249C2×C8—3321no—
250C2×C8—1662no—
251C2×C8—1662no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—3321no—
258C4⋊C4—3322no—
259C4⋊C4—3322no—
260C4⋊C4—3321no—
261C4⋊C4—3321no—
262C4⋊C4—1661no—
263C4⋊C4—1661no—
264C42—41no—
265C42—1662no—
266C42—1662no—
267C42—1662no—
268C42—1661no—
269C42—1661no—
270C42—1661no—
271C42—1661no—
272C42—1661no—
273C42—1661no—
274C23C22⋊C4×D8311yescharacteristic
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—3321no—
288C2×C4—3321no—
289C2×C4—3321no—
290C2×C4—3321no—
291C2×C4—3321no—
292C2×C4—3321no—
293C2×C4—832no—
294C2×C4—832no—
295C2×C4—832no—
296C2×C4—1661no—
297C2×C4—1661no—
298C2×C4—1661no—
299C2×C4—1661no—
300C2×C4—1661no—
301C2×C4—1661no—
302C2×C4—1661no—
303C2×C4—1661no—
304C2×C4—1661no—
305C2×C4#1458179811yescharacteristic
306C2×C4#1458180011yescharacteristic
307C2×C4#1458181311yescharacteristic
308C2×C4#1458181511yescharacteristic
309C2×C4#1458181611yescharacteristic
310C2×C4#1458182111yescharacteristic
311C8—42no—
312C8—42no—
313C8—3322no—
314C8—3322no—
315C22#1912766611yescharacteristic
316C22#1912767311yescharacteristic
317C22#101×D8311yescharacteristic
318C22#1912769611yescharacteristic
319C22#1912769911yescharacteristic
320C22#104×D8311yescharacteristic
321C22#104×D8311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—3321no—
331C4—6641no—
332C4—6641no—
333C4—1662no—
334C4—1662no—
335C4—1662no—
336C2#2490581711yescharacteristic
337C2#2490587311yescharacteristic
338C2#2490592211yescharacteristic
339C2#2490594811yescharacteristic
340C2#2490598511yescharacteristic
341C2#2490605611yescharacteristic
342C2#2490616211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D83
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1271C2
socle, prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenter#1271D83
hypocenterC83#7677
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
179. C83#7677semidirect

Maximal subgroups

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

subgroupindex
#249158492
#249073112
#249072102
#249052872
#249052862
#249052852
C83×#12712
#767783