Finite Group Databasebeta

← #35314039

Subgroups — #35314039

Order 21248.

494 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 91 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#24905801C211yesmaximal, characteristic, complemented
2#24905781C211yesmaximal, characteristic, complemented
3#24905397C212yesmaximal, complemented
4#24905395C212yesmaximal, complemented
5C83×#2544C211yesmaximal, characteristic
6#19127665—21no—
7C2×C22⋊(C83⋊C8)—21no—
8#19127427C2212yes—
9#19127427C2212yes—
10#19127425—21no—
11#19127425—21no—
12C2×#127×C83C411yescharacteristic
13C2×#124×C83C411yescharacteristic
14C2×#124×C83C411yescharacteristic
15C2×C4×D4×C83C2211yescharacteristic
16#394×C83—21no—
17#394×C83—21no—
18#391×C83C2211yescharacteristic
19#390×C83C2211yescharacteristic
20#386×C83—21no—
21#386×C83—21no—
22C4×C4⋊C4×C83C411yescharacteristic
23C2×#13050574—41no—
24C22×C83⋊C8—41no—
25C22⋊(C83⋊C8)—22no—
26C22⋊(C83⋊C8)—22no—
27C22⋊(C83⋊C8)—41no—
28C22⋊(C83⋊C8)—41no—
29C22×Q8×C83C2×C411yescharacteristic
30C22×D4×C83—21no—
31C22×D4×C83—21no—
32C22×D4×C83C2×C411yescharacteristic
33C22×D4×C83C2×C411yescharacteristic
34C23×C4×C83D411yescharacteristic
35C23×C4×C83D411yescharacteristic
36#127×C83—42no—
37#124×C83—41no—
38#124×C83—41no—
39#124×C83—42no—
40C4×D4×C83—41no—
41C4×D4×C83—41no—
42C2×C4⋊C4×C83—21no—
43C2×C4⋊C4×C83C2311yescharacteristic
44C2×C22⋊C4×C83—21no—
45C2×C22⋊C4×C83—21no—
46C2×C22⋊C4×C83—21no—
47C2×C22⋊C4×C83—21no—
48C2×C22⋊C4×C83—21no—
49C2×C22⋊C4×C83—21no—
50C2×C22⋊C4×C83D411yescharacteristic
51C2×C22⋊C4×C83D411yescharacteristic
52C2×C42×C83C2×C411yescharacteristic
53C2×C42×C83C2×C411yescharacteristic
54C2×C42×C83C2×C411yescharacteristic
55#95×C83—21no—
56#95×C83—21no—
57#95×C83—21no—
58#13050574—82no—
59C2×C83⋊C8—42no—
60C2×C83⋊C8—42no—
61C2×C83⋊C8—82no—
62C24×C83—21no—
63C24×C83C22⋊C411yescharacteristic
64C24×C83C22⋊C411yescharacteristic
65C2×Q8×C83—22no—
66C2×Q8×C83—41no—
67C2×Q8×C83—41no—
68C2×D4×C83—22no—
69C2×D4×C83—22no—
70C2×D4×C83—22no—
71C2×D4×C83—41no—
72C2×D4×C83—41no—
73C2×D4×C83—41no—
74C2×D4×C83—42no—
75C2×D4×C83—42no—
76C2×D4×C83—42no—
77C2×D4×C83—42no—
78C2×D4×C83—81no—
79C2×D4×C83—81no—
80C22×C4×C83—21no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83—81no—
88C22×C4×C83—81no—
89C22×C4×C83C22⋊C411yescharacteristic
90C22×C4×C83C22⋊C411yescharacteristic
91C22×C4×C83C22×C411yescharacteristic
92C22×C4×C83C2×D411yescharacteristic
93C22×C4×C83C2×D411yescharacteristic
94C4⋊C4×C83—41no—
95C4⋊C4×C83—42no—
96C22⋊C4×C83—41no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—42no—
99C22⋊C4×C83—42no—
100C22⋊C4×C83—42no—
101C22⋊C4×C83—41no—
102C22⋊C4×C83—41no—
103C22⋊C4×C83—81no—
104C22⋊C4×C83—81no—
105C42×C83—21no—
106C42×C83—21no—
107C42×C83—41no—
108C42×C83—41no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83—21no—
112C23×C83—21no—
113C23×C83—21no—
114C23×C83—41no—
115C23×C83—41no—
116C23×C83—41no—
117C23×C83—41no—
118C23×C83—41no—
119C23×C83—41no—
120C23×C83—41no—
121C23×C83—41no—
122C23×C83—41no—
123C23×C83—41no—
124C23×C83—41no—
125C23×C83#10012yes—
126C23×C83C2×C22⋊C411yescharacteristic
127Q8×C83—82no—
128D4×C83—44no—
129D4×C83—82no—
130D4×C83—84no—
131D4×C83—84no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—22no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—41no—
139C2×C4×C83—42no—
140C2×C4×C83—42no—
141C2×C4×C83—41no—
142C2×C4×C83—41no—
143C2×C4×C83—41no—
144C2×C4×C83—41no—
145C2×C4×C83—41no—
146C2×C4×C83—41no—
147C2×C4×C83—41no—
148C2×C4×C83—41no—
149C2×C4×C83—41no—
150C2×C4×C83—41no—
151C2×C4×C83—41no—
152C2×C4×C83—81no—
153C2×C4×C83—81no—
154C2×C4×C83#9911yescharacteristic
155C2×C4×C83#9911yescharacteristic
156C2×C4×C83#13112yes—
157C83⋊C8—82no—
158C83⋊C8—82no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83—22no—
162C22×C83—42no—
163C22×C83—42no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—41no—
167C22×C83—41no—
168C22×C83—41no—
169C22×C83—81no—
170C22×C83—81no—
171C22×C83—81no—
172C22×C83—81no—
173C22×C83—81no—
174C22×C83—81no—
175C22×C83—81no—
176C22×C83—81no—
177C22×C83—81no—
178C22×C83#40811yescharacteristic
179C22×C83C2×#9911yescharacteristic
180C22×C83C2×#10011yescharacteristic
181C4×C83—21no—
182C4×C83—21no—
183C4×C83—22no—
184C4×C83—42no—
185C4×C83—41no—
186C4×C83—41no—
187C4×C83—41no—
188C4×C83—81no—
189C4×C83—81no—
190#11566—831nomaximal, Sylow
191C2×C83—21no—
192C2×C83—21no—
193C2×C83—42no—
194C2×C83—81no—
195C2×C83—161no—
196C2×C83#147111yescharacteristic
197C2×C83#212711yescharacteristic
198C2×C83#213211yescharacteristic
199#2544D8311yescharacteristic
200#1465—831no—
201#1459—831no—
202#1319—832no—
203#1318—832no—
204C83#1156611yescharacteristic, complemented, Sylow
205C2×#127Dic8311yescharacteristic
206C2×#124Dic8311yescharacteristic
207C2×#124Dic8311yescharacteristic
208C2×C4×D4C2×D8311yescharacteristic
209#407—1661no—
210C2×C22⋊C8—1661no—
211#394—21no—
212#394—21no—
213#391C2×D8311yescharacteristic
214#390C2×D8311yescharacteristic
215#386—21no—
216#386—21no—
217C4×C4⋊C4Dic8311yescharacteristic
218#324—832no—
219#324—832no—
220#323—1661no—
221#323—1661no—
222C22×Q8C2×Dic8311yescharacteristic
223C22×D4—21no—
224C22×D4—21no—
225C22×D4C2×Dic8311yescharacteristic
226C22×D4C2×Dic8311yescharacteristic
227C23×C4C22⋊D8311yescharacteristic
228C23×C4C22⋊D8311yescharacteristic
229C2×M16—3321no—
230C22×C8—3321no—
231#127—42no—
232#124—41no—
233#124—41no—
234#124—42no—
235C4×D4—41no—
236C4×D4—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C22×D8311yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4C22⋊D8311yescharacteristic
246C2×C22⋊C4C22⋊D8311yescharacteristic
247C2×C42C2×Dic8311yescharacteristic
248C2×C42C2×Dic8311yescharacteristic
249C2×C42C2×Dic8311yescharacteristic
250C22⋊C8—3321no—
251C22⋊C8—3321no—
252C22⋊C8—1662no—
253C22⋊C8—1662no—
254#95—21no—
255#95—21no—
256#95—21no—
257C24—21no—
258C24C22⋊Dic8311yescharacteristic
259C24C22⋊Dic8311yescharacteristic
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—81no—
274C2×D4—81no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4C22⋊Dic8311yescharacteristic
285C22×C4C22⋊Dic8311yescharacteristic
286C22×C4C22×Dic8311yescharacteristic
287C22×C4C2×C22⋊D8311yescharacteristic
288C22×C4C2×C22⋊D8311yescharacteristic
289M16—6642no—
290C2×C8—3322no—
291C2×C8—3322no—
292C2×C8—6642no—
293C4⋊C4—41no—
294C4⋊C4—42no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C42—21no—
305C42—21no—
306C42—41no—
307C42—41no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23#1458170912yes—
325C23C2×C22⋊Dic8311yescharacteristic
326Q8—82no—
327D4—44no—
328D4—82no—
329D4—84no—
330D4—84no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4#1458170711yescharacteristic
354C2×C4#1458170711yescharacteristic
355C2×C4#1458179912yes—
356C8—6642no—
357C8—6642no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22#1912766811yescharacteristic
378C22C2×#1458170711yescharacteristic
379C22C2×#1458170911yescharacteristic
380C4—21no—
381C4—21no—
382C4—22no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—81no—
389C2—21no—
390C2—21no—
391C2—42no—
392C2—81no—
393C2—161no—
394C2#2490582311yescharacteristic
395C2#2490913211yescharacteristic
396C2#2490914811yescharacteristic
subgroupG/H
centerC22C2×#14581707
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#2544C2
socleC22×C83C2×#99
prime radicalC2×#127×C83C4
cosocleC2×C4⋊C4×C83C23
hypercenter#2544D83
hypocenterC83#11566
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2544

Complements

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

NH ≅ G/Ntype
1. #24905801C2semidirect
2. #24905781C2semidirect
3. #24905397C2semidirect
4. #24905395C2semidirect
204. C83#11566semidirect

Maximal subgroups

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

subgroupindex
#249058012
#249057812
#249053972
#249053952
C83×#25442
#1156683