Finite Group Databasebeta

← #35293288

Subgroups — #35293288

Order 21248.

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

normal subgroups only

This group has 436 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#24908796C211yesmaximal, characteristic
2#24908709C211yesmaximal, characteristic
3#24908604C211yesmaximal, characteristic
4#24905289C211yesmaximal, characteristic
5#24905286C211yesmaximal, characteristic
6#24905286C211yesmaximal, characteristic
7C83×#2734C211yesmaximal, 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
18C2×C4⋊Q8×C83—21no—
19#398×C83—21no—
20#395×C83—21no—
21#395×C83—21no—
22#391×C83C2211yescharacteristic
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×C83—21no—
39C22×Q8×C83D411yescharacteristic
40C4⋊Q8×C83—42no—
41C4⋊Q8×C83—42no—
42C2×C4⋊C4×C83—21no—
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C4⋊C4×C83D411yescharacteristic
50C2×C4⋊C4×C83D411yescharacteristic
51C2×C4⋊C4×C83D411yescharacteristic
52C2×C42×C83—21no—
53C2×C42×C83C2311yescharacteristic
54#95×C83—21no—
55#95×C83—21no—
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61C2×Dic166—22no—
62C2×Dic166—41no—
63C2×Dic166—41no—
64C2×Dic166—41no—
65C2×Dic166—41no—
66C2×Dic166—41no—
67C22×Dic83—41no—
68C2×C83⋊C8—22no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8—41no—
72C2×C83⋊C8—41no—
73C2×C83⋊C8—41no—
74C2×C83⋊C8—41no—
75C2×C83⋊C8—41no—
76C2×C83⋊C8—41no—
77C4⋊Dic83—22no—
78C4⋊Dic83—22no—
79C4⋊Dic83—41no—
80C4⋊Dic83—41no—
81C2×Q8×C83—21no—
82C2×Q8×C83—42no—
83C2×Q8×C83—41no—
84C2×Q8×C83—41no—
85C2×Q8×C83—81no—
86C2×Q8×C83—81no—
87C2×Q8×C83SD1612yes—
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—21no—
91C22×C4×C83—21no—
92C22×C4×C83—21no—
93C22×C4×C83—21no—
94C22×C4×C83C2×D411yescharacteristic
95C22×C4×C83C2×D411yescharacteristic
96C22×C4×C83C2×D411yescharacteristic
97C4⋊C4×C83—21no—
98C4⋊C4×C83—21no—
99C4⋊C4×C83—41no—
100C4⋊C4×C83—41no—
101C4⋊C4×C83—41no—
102C4⋊C4×C83—42no—
103C4⋊C4×C83—42no—
104C4⋊C4×C83—41no—
105C4⋊C4×C83—41no—
106C4⋊C4×C83—41no—
107C4⋊C4×C83—41no—
108C4⋊C4×C83—81no—
109C4⋊C4×C83SD1612yes—
110C4⋊C4×C83Q1612yes—
111C42×C83—41no—
112C42×C83—42no—
113C23×C83#12011yescharacteristic
114Q8×C83—42no—
115Q8×C83—81no—
116Q8×C83—84no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—22no—
124C2×C4×C83—22no—
125C2×C4×C83—22no—
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×C83—41no—
135C2×C4×C83—41no—
136C2×C4×C83—41no—
137C2×C4×C83—41no—
138C2×C4×C83—41no—
139C2×C4×C83—41no—
140C2×C4×C83—41no—
141C2×C4×C83C2×SD1611yescharacteristic
142C2×C4×C83C2×SD1611yescharacteristic
143C2×C4×C83C2×Q1611yescharacteristic
144C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C83#13711yescharacteristic
146C2×C4×C83#13711yescharacteristic
147C2×Dic83—42no—
148C2×Dic83—81no—
149C2×Dic83—81no—
150Dic166—42no—
151Dic166—42no—
152Dic166—81no—
153Dic166—81no—
154C83⋊C8—42no—
155C83⋊C8—81no—
156C83⋊C8—81no—
157C22×C83#44811yescharacteristic
158C22×C83#45011yescharacteristic
159C22×C83#45111yescharacteristic
160C22×C83#45411yescharacteristic
161C22×C83#45511yescharacteristic
162C22×C83#45611yescharacteristic
163C22×C83B(4,𝔽2)11yescharacteristic
164C4×C83—21no—
165C4×C83—21no—
166C4×C83—21no—
167C4×C83—21no—
168C4×C83—21no—
169C4×C83—21no—
170C4×C83—42no—
171C4×C83—42no—
172C4×C83—42no—
173C4×C83—81no—
174C4×C83—81no—
175C4×C83—81no—
176Dic83—82no—
177#7766—831nomaximal, Sylow
178C2×C83#159911yescharacteristic
179C2×C83#160111yescharacteristic
180C2×C83#160511yescharacteristic
181C2×C83#163711yescharacteristic
182C2×C83#164511yescharacteristic
183C2×C83#165111yescharacteristic
184C2×C83#166411yescharacteristic
185#2734D8311yescharacteristic
186#2058—831no—
187#2043—831no—
188#2024—831no—
189#1272—831no—
190#1271—831no—
191#1271—831no—
192C83#776611yescharacteristic, complemented, Sylow
193C2×C4⋊Q8—21no—
194C2×C4⋊Q8—831no—
195C2×#106—1661no—
196C2×#103—1661no—
197C2×#103—1661no—
198C2×#103—1661no—
199#398—21no—
200#395—21no—
201#395—21no—
202#391C2×D8311yescharacteristic
203#389C2×D8311yescharacteristic
204#389C2×D8311yescharacteristic
205#387—21no—
206#387—21no—
207#340—1661no—
208#340—1661no—
209#336—831no—
210#336—831no—
211#336—831no—
212C22×Q8—21no—
213C22×Q8—1661no—
214C22×Q8C22⋊D8311yescharacteristic
215C22×C8—1661no—
216C22×C8—1661no—
217C22×C8—1661no—
218C4⋊Q8—42no—
219C4⋊Q8—42no—
220C4⋊Q8—3322no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—1661no—
227C2×C4⋊C4—1661no—
228C2×C4⋊C4C22⋊D8311yescharacteristic
229C2×C4⋊C4C22⋊D8311yescharacteristic
230C2×C4⋊C4C22⋊D8311yescharacteristic
231C2×C4⋊C4C22⋊D8311yescharacteristic
232C2×C4⋊C4C22⋊D8311yescharacteristic
233C2×C42—21no—
234C2×C42C22×D8311yescharacteristic
235#106—3322no—
236#103—3322no—
237#103—3322no—
238#103—3322no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246C2×Q8—21no—
247C2×Q8—42no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—81no—
251C2×Q8—81no—
252C2×Q8—3321no—
253C2×Q8—3321no—
254C2×Q8—3321no—
255C2×Q8—3321no—
256C2×Q8—3321no—
257C2×Q8—1662no—
258C2×Q8#1305057812yes—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—3321no—
266C22×C4C2×C22⋊D8311yescharacteristic
267C22×C4C2×C22⋊D8311yescharacteristic
268C22×C4C2×C22⋊D8311yescharacteristic
269C2×C8—3321no—
270C2×C8—3321no—
271C2×C8—3321no—
272C2×C8—3321no—
273C2×C8—3321no—
274C2×C8—3321no—
275C2×C8—3321no—
276C2×C8—3321no—
277C2×C8—1662no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—81no—
290C4⋊C4—3321no—
291C4⋊C4—3321no—
292C4⋊C4—1662no—
293C4⋊C4—1662no—
294C4⋊C4#1305057712yes—
295C4⋊C4#1305058012yes—
296C42—41no—
297C42—42no—
298C23#1458176111yescharacteristic
299Q8—42no—
300Q8—81no—
301Q8—84no—
302Q8—3322no—
303Q8—3322no—
304Q8—6641no—
305Q8—6641no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—3322no—
331C2×C4—6641no—
332C2×C4—6641no—
333C2×C4C2×#1305057711yescharacteristic
334C2×C4C2×#1305057811yescharacteristic
335C2×C4C2×#1305058011yescharacteristic
336C2×C4#1458181811yescharacteristic
337C2×C4#1458182311yescharacteristic
338C2×C4#1458182311yescharacteristic
339C8—3322no—
340C8—6641no—
341C8—6641no—
342C22#1912784011yescharacteristic
343C22#1912785211yescharacteristic
344C22#1912785711yescharacteristic
345C22#1912787411yescharacteristic
346C22#1912787911yescharacteristic
347C22#1912788411yescharacteristic
348C22#1912788811yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—42no—
357C4—42no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—6642no—
362C2#2490640311yescharacteristic
363C2#2490641511yescharacteristic
364C2#2490643711yescharacteristic
365C2#2490662811yescharacteristic
366C2#2490668411yescharacteristic
367C2#2490672611yescharacteristic
368C2#2490679711yescharacteristic
subgroupG/H
centerC23#14581761
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2734C2
socle, prime radicalC23×C83#120
hypercenter#2734D83
hypocenterC83#7766
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2734

Complements

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

NH ≅ G/Ntype
192. C83#7766semidirect

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×#27342
#776683