Finite Group Databasebeta

← #35293295

Subgroups — #35293295

Order 21248.

392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 87 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#24908796C211yesmaximal, characteristic
2#24908709C211yesmaximal, characteristic
3#24908604C211yesmaximal, characteristic
4#24905289C211yesmaximal, characteristic
5#24905286C211yesmaximal, characteristic
6#24905286C211yesmaximal, characteristic
7C83×#2805C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×#14581723—21no—
10C2×#14581716—21no—
11C2×#14581715—21no—
12C2×#14581715—21no—
13#19127463—21no—
14#19127463—21no—
15#19127456C2211yescharacteristic
16#19127456C2211yescharacteristic
17#19127456C2211yescharacteristic
18#400×C83—21no—
19#400×C83—21no—
20#395×C83—21no—
21#391×C83C2211yescharacteristic
22#389×C83—21no—
23#389×C83C2211yescharacteristic
24#389×C83C2211yescharacteristic
25#387×C83—21no—
26#387×C83—21no—
27C22×Dic166—21no—
28C22×C83⋊C8—21no—
29C22×C83⋊C8—21no—
30C22×C83⋊C8—21no—
31#14581792—42no—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83—21no—
34#14581723—42no—
35#14581716—42no—
36#14581715—42no—
37#14581715—42no—
38C22×Q8×C83D411yescharacteristic
39C2×C4⋊C4×C83—21no—
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83—21no—
42C2×C4⋊C4×C83—21no—
43C2×C4⋊C4×C83D411yescharacteristic
44C2×C4⋊C4×C83D411yescharacteristic
45C2×C4⋊C4×C83D411yescharacteristic
46C2×C4⋊C4×C83D411yescharacteristic
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C42×C83—21no—
49C2×C42×C83C2311yescharacteristic
50#95×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53#95×C83—21no—
54#95×C83—21no—
55#95×C83—21no—
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59C2×Dic166—22no—
60C2×Dic166—41no—
61C2×Dic166—41no—
62C2×Dic166—41no—
63C2×Dic166—41no—
64C2×Dic166—41no—
65C22×Dic83—41no—
66C2×C83⋊C8—22no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8—41no—
72C2×C83⋊C8—41no—
73C2×C83⋊C8—41no—
74C2×C83⋊C8—41no—
75C4⋊Dic83—22no—
76C4⋊Dic83—22no—
77C4⋊Dic83—41no—
78C4⋊Dic83—41no—
79C2×Q8×C83—21no—
80C2×Q8×C83—21no—
81C2×Q8×C83—41no—
82C2×Q8×C83—41no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83—21no—
88C22×C4×C83—21no—
89C22×C4×C83C2×D411yescharacteristic
90C22×C4×C83C2×D411yescharacteristic
91C22×C4×C83C2×D411yescharacteristic
92C4⋊C4×C83—21no—
93C4⋊C4×C83—21no—
94C4⋊C4×C83—21no—
95C4⋊C4×C83—41no—
96C4⋊C4×C83—41no—
97C4⋊C4×C83—41no—
98C4⋊C4×C83—41no—
99C4⋊C4×C83—41no—
100C4⋊C4×C83—41no—
101C4⋊C4×C83—41no—
102C4⋊C4×C83—81no—
103C4⋊C4×C83—81no—
104C4⋊C4×C83SD1612yes—
105C42×C83—41no—
106C42×C83—81no—
107C23×C83#12011yescharacteristic
108Q8×C83—42no—
109Q8×C83—81no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—22no—
117C2×C4×C83—41no—
118C2×C4×C83—41no—
119C2×C4×C83—41no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83—41no—
125C2×C4×C83—41no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83C2×SD1611yescharacteristic
135C2×C4×C83#13511yescharacteristic
136C2×C4×C83#13511yescharacteristic
137C2×C4×C83#13711yescharacteristic
138C2×C4×C83#13711yescharacteristic
139C2×C4×C83#13711yescharacteristic
140C2×Dic83—42no—
141C2×Dic83—81no—
142C2×Dic83—81no—
143Dic166—42no—
144Dic166—42no—
145Dic166—81no—
146Dic166—81no—
147C83⋊C8—42no—
148C83⋊C8—81no—
149C83⋊C8—81no—
150C22×C83#44811yescharacteristic
151C22×C83#45211yescharacteristic
152C22×C83#45211yescharacteristic
153C22×C83#45411yescharacteristic
154C22×C83#45511yescharacteristic
155C22×C83#45611yescharacteristic
156C22×C83B(4,𝔽2)11yescharacteristic
157C4×C83—21no—
158C4×C83—21no—
159C4×C83—21no—
160C4×C83—21no—
161C4×C83—21no—
162C4×C83—21no—
163C4×C83—42no—
164C4×C83—81no—
165C4×C83—81no—
166C4×C83—81no—
167C4×C83—81no—
168C4×C83—81no—
169Dic83—82no—
170#7767—831nomaximal, Sylow
171C2×C83#159911yescharacteristic
172C2×C83#160311yescharacteristic
173C2×C83#160611yescharacteristic
174C2×C83#163811yescharacteristic
175C2×C83#164311yescharacteristic
176C2×C83#165311yescharacteristic
177C2×C83#166411yescharacteristic
178#2805D8311yescharacteristic
179#2058—831no—
180#2043—831no—
181#2024—831no—
182#1272—831no—
183#1271—831no—
184#1271—831no—
185C83#776711yescharacteristic, complemented, Sylow
186C2×C4⋊Q8—831no—
187C2×#106—1661no—
188C2×#103—1661no—
189C2×#103—1661no—
190C2×#103—1661no—
191#400—21no—
192#400—21no—
193#395—21no—
194#391C2×D8311yescharacteristic
195#389—21no—
196#389C2×D8311yescharacteristic
197#389C2×D8311yescharacteristic
198#387—21no—
199#387—21no—
200#340—1661no—
201#340—1661no—
202#336—831no—
203#336—831no—
204#336—831no—
205C22×Q8—1661no—
206C22×Q8C22⋊D8311yescharacteristic
207C22×C8—1661no—
208C22×C8—1661no—
209C22×C8—1661no—
210C4⋊Q8—3322no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—1661no—
216C2×C4⋊C4—1661no—
217C2×C4⋊C4C22⋊D8311yescharacteristic
218C2×C4⋊C4C22⋊D8311yescharacteristic
219C2×C4⋊C4C22⋊D8311yescharacteristic
220C2×C4⋊C4C22⋊D8311yescharacteristic
221C2×C4⋊C4C22⋊D8311yescharacteristic
222C2×C42—21no—
223C2×C42C22×D8311yescharacteristic
224#106—3322no—
225#103—3322no—
226#103—3322no—
227#103—3322no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—3321no—
242C2×Q8—3321no—
243C2×Q8—3321no—
244C2×Q8—3321no—
245C2×Q8—3321no—
246C2×Q8—1662no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—3321no—
254C22×C4C2×C22⋊D8311yescharacteristic
255C22×C4C2×C22⋊D8311yescharacteristic
256C22×C4C2×C22⋊D8311yescharacteristic
257C2×C8—3321no—
258C2×C8—3321no—
259C2×C8—3321no—
260C2×C8—3321no—
261C2×C8—3321no—
262C2×C8—3321no—
263C2×C8—3321no—
264C2×C8—3321no—
265C2×C8—1662no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—3321no—
279C4⋊C4—3321no—
280C4⋊C4—1662no—
281C4⋊C4—1662no—
282C4⋊C4#1305057712yes—
283C42—41no—
284C42—81no—
285C23#1458176111yescharacteristic
286Q8—42no—
287Q8—81no—
288Q8—3322no—
289Q8—3322no—
290Q8—6641no—
291Q8—6641no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—3322no—
317C2×C4—6641no—
318C2×C4—6641no—
319C2×C4C2×#1305057711yescharacteristic
320C2×C4#1458181211yescharacteristic
321C2×C4#1458181211yescharacteristic
322C2×C4#1458182211yescharacteristic
323C2×C4#1458182211yescharacteristic
324C2×C4#1458182311yescharacteristic
325C8—3322no—
326C8—6641no—
327C8—6641no—
328C22#1912784011yescharacteristic
329C22#1912786311yescharacteristic
330C22#1912786311yescharacteristic
331C22#1912787411yescharacteristic
332C22#1912787911yescharacteristic
333C22#1912788411yescharacteristic
334C22#1912788811yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—6642no—
348C2#2490640311yescharacteristic
349C2#2490642611yescharacteristic
350C2#2490644311yescharacteristic
351C2#2490663511yescharacteristic
352C2#2490667011yescharacteristic
353C2#2490674011yescharacteristic
354C2#2490679711yescharacteristic
subgroupG/H
centerC23#14581761
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2805C2
socle, prime radicalC23×C83#120
hypercenter#2805D83
hypocenterC83#7767
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

Complements

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

NH ≅ G/Ntype
185. C83#7767semidirect

Maximal subgroups

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

subgroupindex
#249087962
#249087092
#249086042
#249052892
#249052862
C83×#28052
#776783