Finite Group Databasebeta

← #35307752

Subgroups — #35307752

Order 21248.

620 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 115 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#24913577C211yesmaximal, characteristic
2#24907770C212yesmaximal
3C2×#19127437C212yesmaximal
4#24905306C211yesmaximal, characteristic
5C83×#1444C211yesmaximal, characteristic
6C2×#14581771C2212yes—
7C2×#14581715—22no—
8C2×C22⋊(C83⋊C8)C2212yes—
9#19127633—22no—
10#19127622—22no—
11#19127561—21no—
12#19127561—21no—
13#19127463—22no—
14#19127437—24no—
15C22×C4⋊C4×C83—21no—
16C22×C4⋊C4×C83C2211yescharacteristic
17C2×#95×C83—21no—
18C2×#95×C83C2211yescharacteristic
19C2×#95×C83C2211yescharacteristic
20C22×Dic166D412yes—
21C22×C83⋊C8—22no—
22#14581771—22no—
23#14581771—22no—
24#14581771—22no—
25#14581771—22no—
26C2×C4⋊Dic83—21no—
27C2×C4⋊Dic83—21no—
28C2×C4⋊Dic83—21no—
29C2×C4⋊Dic83—21no—
30C2×C4⋊Dic83D412yes—
31C2×Dic83⋊C4—22no—
32C2×C22⋊Dic83—22no—
33#14581715—44no—
34C22⋊(C83⋊C8)—22no—
35C22⋊(C83⋊C8)—22no—
36C83⋊#95—22no—
37C83⋊#95—22no—
38C23×C4×C83—21no—
39C23×C4×C83—21no—
40C23×C4×C83D411yescharacteristic
41C23×C4×C83D411yescharacteristic
42C23×C4×C83C2311yescharacteristic
43C2×C4⋊C4×C83—22no—
44C2×C4⋊C4×C83—42no—
45C2×C4⋊C4×C83—42no—
46C2×C4⋊C4×C83—42no—
47C2×C4⋊C4×C83—42no—
48#95×C83—22no—
49#95×C83—21no—
50#95×C83—42no—
51#95×C83D412yes—
52C2×Dic166—22no—
53C2×Dic166—22no—
54C2×Dic166—42no—
55C2×Dic166—42no—
56C22×Dic83—22no—
57C22×Dic83—22no—
58C2×C83⋊C8—42no—
59C2×C83⋊C8—42no—
60C2×C83⋊C8—42no—
61C4⋊Dic83—22no—
62C4⋊Dic83—22no—
63C4⋊Dic83—81no—
64C4⋊Dic83—81no—
65C4⋊Dic83—81no—
66C4⋊Dic83—81no—
67Dic83⋊C4—42no—
68Dic83⋊C4—42no—
69C22⋊Dic83—42no—
70C22⋊Dic83—42no—
71C24×C83C2×D411yescharacteristic
72C22×C4×C83—22no—
73C22×C4×C83—22no—
74C22×C4×C83—21no—
75C22×C4×C83—21no—
76C22×C4×C83—22no—
77C22×C4×C83—21no—
78C22×C4×C83—21no—
79C22×C4×C83—22no—
80C22×C4×C83—41no—
81C22×C4×C83—41no—
82C22×C4×C83—41no—
83C22×C4×C83—41no—
84C22×C4×C83—41no—
85C22×C4×C83—41no—
86C22×C4×C83—41no—
87C22×C4×C83—41no—
88C22×C4×C83—41no—
89C22×C4×C83—41no—
90C22×C4×C83—41no—
91C22×C4×C83—41no—
92C22×C4×C83—41no—
93C22×C4×C83—41no—
94C22×C4×C83—41no—
95C22×C4×C83—41no—
96C22×C4×C83SD1612yes—
97C22×C4×C83Q1612yes—
98C22×C4×C83C2×D412yes—
99C22×C4×C83C2×D411yescharacteristic
100C22×C4×C83#4111yescharacteristic
101C22×C4×C83#4112yes—
102C4⋊C4×C83—24no—
103C4⋊C4×C83—42no—
104C4⋊C4×C83—48no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83#12011yescharacteristic
110C23×C83#12111yescharacteristic
111C23×C83#12411yescharacteristic
112C23×C83C2×SD1611yescharacteristic
113C23×C83C2×Q1611yescharacteristic
114C23×C83#13711yescharacteristic
115C23×C83#13711yescharacteristic
116C2×C4×C83—22no—
117C2×C4×C83—22no—
118C2×C4×C83—24no—
119C2×C4×C83—22no—
120C2×C4×C83—22no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—42no—
124C2×C4×C83—42no—
125C2×C4×C83—42no—
126C2×C4×C83—42no—
127C2×C4×C83—42no—
128C2×C4×C83—42no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
132C2×C4×C83—41no—
133C2×C4×C83—42no—
134C2×C4×C83—42no—
135C2×C4×C83—42no—
136C2×C4×C83—42no—
137C2×C4×C83—42no—
138C2×C4×C83—42no—
139C2×C4×C83—81no—
140C2×C4×C83—81no—
141C2×C4×C83—81no—
142C2×C4×C83—81no—
143C2×C4×C83—81no—
144C2×C4×C83—81no—
145C2×C4×C83#12112yes—
146C2×C4×C83#12312yes—
147C2×Dic83—42no—
148C2×Dic83—42no—
149C2×Dic83—42no—
150C2×Dic83—42no—
151C2×Dic83—42no—
152C2×Dic83—42no—
153Dic166—44no—
154Dic166—82no—
155C83⋊C8—82no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83—21no—
164C22×C83—21no—
165C22×C83—21no—
166C22×C83—21no—
167C22×C83—21no—
168C22×C83#39411yescharacteristic
169C22×C83#44811yescharacteristic
170C22×C83#45111yescharacteristic
171C22×C83#45311yescharacteristic
172C22×C83#45611yescharacteristic
173C22×C83B(4,𝔽2)11yescharacteristic
174C22×C83#45811yescharacteristic
175C22×C83#46111yescharacteristic
176C22×C83#46211yescharacteristic
177C22×C83#48711yescharacteristic
178C22×C83#49111yescharacteristic
179C4×C83—22no—
180C4×C83—22no—
181C4×C83—44no—
182C4×C83—42no—
183C4×C83—42no—
184C4×C83—82no—
185Dic83—82no—
186Dic83—82no—
187#10406—831nomaximal, Sylow
188C2×C83—21no—
189C2×C83—21no—
190C2×C83—21no—
191C2×C83—21no—
192C2×C83#159611yescharacteristic
193C2×C83#160511yescharacteristic
194C2×C83#161111yescharacteristic
195C2×C83#161411yescharacteristic
196C2×C83#203911yescharacteristic
197C2×C83#204311yescharacteristic
198C2×C83#204411yescharacteristic
199#2659—831no—
200#1872—832no—
201C2×#328—832no—
202#1444D8311yescharacteristic
203#1280—831no—
204C83#1040611yescharacteristic, complemented, Sylow
205C2×C22⋊Q8—832no—
206C22×C4⋊C4—21no—
207C22×C4⋊C4C2×D8311yescharacteristic
208C2×#103—1662no—
209C2×C22⋊C8—832no—
210#398—1662no—
211#395—1662no—
212#380—1661no—
213#380—1661no—
214C2×#95—21no—
215C2×#95C2×D8311yescharacteristic
216C2×#95C2×D8311yescharacteristic
217#340—1662no—
218#328—1664no—
219C22×Q8—832no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4C22⋊D8311yescharacteristic
223C23×C4C22⋊D8311yescharacteristic
224C23×C4C22×D8311yescharacteristic
225C22×C8—1662no—
226C22⋊Q8—1662no—
227C22⋊Q8—1662no—
228C22⋊Q8—1662no—
229C22⋊Q8—1662no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—832no—
236C2×C4⋊C4—1662no—
237C2×C4⋊C4—1661no—
238C2×C4⋊C4—1661no—
239C2×C4⋊C4—1661no—
240C2×C4⋊C4—1661no—
241C2×C22⋊C4—1662no—
242#103—3324no—
243C22⋊C8—1662no—
244C22⋊C8—1662no—
245#95—22no—
246#95—21no—
247#95—42no—
248#95—1662no—
249#95—1662no—
250#95D33212yes—
251C24C2×C22⋊D8311yescharacteristic
252C2×Q8—3322no—
253C2×Q8—3322no—
254C2×Q8—1662no—
255C2×Q8—1662no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—1662no—
281C22×C4—1662no—
282C22×C4#1305057812yes—
283C22×C4#1305058012yes—
284C22×C4D4×D8312yes—
285C22×C4C2×D33211yescharacteristic
286C22×C4#1305059011yescharacteristic
287C22×C4#1305059112yes—
288C2×C8—3322no—
289C2×C8—3322no—
290C2×C8—3322no—
291C4⋊C4—24no—
292C4⋊C4—42no—
293C4⋊C4—48no—
294C4⋊C4—3322no—
295C4⋊C4—3322no—
296C4⋊C4—6641no—
297C4⋊C4—6641no—
298C4⋊C4—6641no—
299C4⋊C4—6641no—
300C4⋊C4—1662no—
301C4⋊C4—1662no—
302C22⋊C4—3322no—
303C22⋊C4—3322no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#1458176011yescharacteristic
309C23#1458176611yescharacteristic
310C23#1458178111yescharacteristic
311C23C2×#1305057811yescharacteristic
312C23C2×#1305058011yescharacteristic
313C23#1458182211yescharacteristic
314C23#1458182211yescharacteristic
315Q8—3324no—
316Q8—6642no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—3322no—
347C2×C4—3322no—
348C2×C4—3322no—
349C2×C4—3322no—
350C2×C4—3322no—
351C2×C4—3322no—
352C2×C4#1458176712yes—
353C2×C4#1458177712yes—
354C8—6642no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1912761811yescharacteristic
368C22#1912783911yescharacteristic
369C22#1912785611yescharacteristic
370C22#1912786811yescharacteristic
371C22#1912788311yescharacteristic
372C22#1912788711yescharacteristic
373C22#1912789011yescharacteristic
374C22#1912790611yescharacteristic
375C22#1912791111yescharacteristic
376C22#1912805311yescharacteristic
377C22#1912807111yescharacteristic
378C4—22no—
379C4—22no—
380C4—44no—
381C4—42no—
382C4—42no—
383C4—82no—
384C4—6642no—
385C4—6642no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#2490638511yescharacteristic
391C2#2490643611yescharacteristic
392C2#2490647011yescharacteristic
393C2#2490648711yescharacteristic
394C2#2490868711yescharacteristic
395C2#2490870911yescharacteristic
396C2#2490871411yescharacteristic
subgroupG/H
centerC23#14581760
commutator, cosocleC23×C4×C83C23
FrattiniC23×C4C22×D83
FittingC83×#1444C2
socleC23×C83#120
prime radicalC24×C83C2×D4
hypercenter#1444D83
hypocenterC83#10406
LCSG ▷ C23×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1444

Complements

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

NH ≅ G/Ntype
204. C83#10406semidirect

Maximal subgroups

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

subgroupindex
#249135772
#249077702
C2×#191274372
#249053062
C83×#14442
#1040683