Finite Group Databasebeta

← #35304457

Subgroups — #35304457

Order 21248.

556 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127585C211yesmaximal, characteristic
2#24907443C211yesmaximal, characteristic
3#24905305C212yesmaximal
4#24905305C212yesmaximal
5C83×#1749C211yesmaximal, characteristic
6C22×Dic83⋊C4C411yescharacteristic
7C22×Dic83⋊C4C411yescharacteristic
8C2×C4⋊(C83⋊C8)—21no—
9C2×C22⋊(C83⋊C8)C2212yes—
10#19127585—21no—
11#19127585—21no—
12#19127585—21no—
13#19127585—21no—
14C2×C83⋊#95C411yescharacteristic
15C2×C83⋊#95C411yescharacteristic
16C2×C83⋊#95C2211yescharacteristic
17C2×C83⋊#95C2211yescharacteristic
18#19127456—21no—
19C22×C42×C83C2211yescharacteristic
20C2×C22⋊C8×C83C2212yes—
21C2×#97×C83—21no—
22#336×C83—21no—
23C23×Dic83C2×C411yescharacteristic
24C23×Dic83C2×C411yescharacteristic
25C23×Dic83C2×C411yescharacteristic
26C23×Dic83C2×C411yescharacteristic
27C22×C83⋊C8—22no—
28C2×Dic83⋊C4—22no—
29C2×Dic83⋊C4—22no—
30C2×Dic83⋊C4—21no—
31C2×Dic83⋊C4—21no—
32C2×Dic83⋊C4—21no—
33C2×Dic83⋊C4—21no—
34C2×Dic83⋊C4—42no—
35C4⋊(C83⋊C8)—42no—
36C22⋊(C83⋊C8)—24no—
37C83⋊#95—21no—
38C83⋊#95—21no—
39C83⋊#95—21no—
40C83⋊#95—21no—
41C83⋊#95—21no—
42C83⋊#95—21no—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C23×C4×C83C2×C411yescharacteristic
46C23×C4×C83C2×C411yescharacteristic
47C23×C4×C83C2311yescharacteristic
48C22×C8×C83—22no—
49C2×C42×C83—42no—
50C2×C42×C83D411yescharacteristic
51C2×C42×C83D411yescharacteristic
52C2×C42×C83D411yescharacteristic
53C2×C42×C83D411yescharacteristic
54C22⋊C8×C83—22no—
55C22⋊C8×C83Q814yes—
56#97×C83—42no—
57C22×Dic83—21no—
58C22×Dic83—21no—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—21no—
62C22×Dic83—21no—
63C22×Dic83—22no—
64C22×Dic83—22no—
65C22×Dic83—41no—
66C22×Dic83—41no—
67C22×Dic83—41no—
68C22×Dic83—41no—
69C22×Dic83—41no—
70C22×Dic83—41no—
71C22×Dic83—41no—
72C22×Dic83—41no—
73C22×Dic83M1612yes—
74C22×Dic83M1612yes—
75C2×C83⋊C8—42no—
76C2×C83⋊C8—42no—
77C2×C83⋊C8—42no—
78Dic83⋊C4—24no—
79Dic83⋊C4—24no—
80Dic83⋊C4—42no—
81Dic83⋊C4—42no—
82C24×C83C22×C411yescharacteristic
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—22no—
86C22×C4×C83—22no—
87C22×C4×C83—41no—
88C22×C4×C83—41no—
89C22×C4×C83—41no—
90C22×C4×C83—41no—
91C22×C4×C83—41no—
92C22×C4×C83C22⋊C411yescharacteristic
93C22×C4×C83C22⋊C411yescharacteristic
94C22×C4×C83C22⋊C411yescharacteristic
95C22×C4×C83C22⋊C411yescharacteristic
96C22×C4×C83C2×D411yescharacteristic
97C22×C4×C83C2×D411yescharacteristic
98C22×C4×C83C2×Q812yes—
99C22×C4×C83#4112yes—
100C2×C8×C83—24no—
101C2×C8×C83—42no—
102C2×C8×C83—42no—
103C42×C83—22no—
104C42×C83—22no—
105C42×C83—41no—
106C42×C83—41no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83C2×C22⋊C411yescharacteristic
112C23×C83C4×Q812yes—
113C23×C83C2×M1611yescharacteristic
114C23×C83C2×M1611yescharacteristic
115C23×C83#13112yes—
116C2×C4×C83—21no—
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—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—42no—
132C2×C4×C83—42no—
133C2×C4×C83—44no—
134C2×C4×C83—42no—
135C2×C4×C83—42no—
136C2×C4×C83#9912yes—
137C2×C4×C83C22⋊Q812yes—
138C2×C4×C83#12411yescharacteristic
139C2×C4×C83C4⋊Q811yescharacteristic
140C2×Dic83—22no—
141C2×Dic83—22no—
142C2×Dic83—42no—
143C2×Dic83—42no—
144C2×Dic83—41no—
145C2×Dic83—41no—
146C2×Dic83—41no—
147C2×Dic83—41no—
148C2×Dic83—42no—
149C2×Dic83—42no—
150C2×Dic83—41no—
151C2×Dic83—41no—
152C2×Dic83—41no—
153C2×Dic83—41no—
154C2×Dic83—41no—
155C2×Dic83—41no—
156C2×Dic83—82no—
157C2×Dic83—82no—
158C8×C83—44no—
159C83⋊C8—82no—
160C22×C83—21no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83—21no—
164C22×C83—22no—
165C22×C83—22no—
166C22×C83—22no—
167C22×C83—22no—
168C22×C83#39111yescharacteristic
169C22×C83#40711yescharacteristic
170C22×C83#40811yescharacteristic
171C22×C83C2×#9911yescharacteristic
172C22×C83#41011yescharacteristic
173C22×C83#41311yescharacteristic
174C22×C83#41311yescharacteristic
175C22×C83#44612yes—
176C22×C83#44612yes—
177C4×C83—22no—
178C4×C83—21no—
179C4×C83—22no—
180C4×C83—21no—
181C4×C83—41no—
182C4×C83—41no—
183C4×C83—41no—
184Dic83—42no—
185Dic83—42no—
186Dic83—81no—
187Dic83—81no—
188#9881—831nomaximal, Sylow
189C2×C83—22no—
190C2×C83—22no—
191C2×C83#146411yescharacteristic
192C2×C83#146511yescharacteristic
193C2×C83#146811yescharacteristic
194C2×C83#147311yescharacteristic
195C2×C83#198511yescharacteristic
196C2×C83#199611yescharacteristic
197C2×C83#199811yescharacteristic
198C2×#387—831no—
199#1797—831no—
200#1749D8311yescharacteristic
201#1280—832no—
202#1280—832no—
203C83#988111yescharacteristic, complemented, Sylow
204C22×C4⋊C4—831no—
205C22×C4⋊C4—831no—
206C22×C42C2×D8311yescharacteristic
207C2×C4⋊C8—1661no—
208C2×C22⋊C8—832no—
209C2×C22⋊C8C2×D8312yes—
210C2×#97—21no—
211#387—1661no—
212#387—1661no—
213#387—1661no—
214#387—1661no—
215C2×#95—831no—
216C2×#95—831no—
217C2×#95—831no—
218C2×#95—831no—
219#336—21no—
220#336—1661no—
221C23×C4—831no—
222C23×C4—831no—
223C23×C4—831no—
224C23×C4—831no—
225C23×C4C4×D8311yescharacteristic
226C23×C4C4×D8311yescharacteristic
227C23×C4C22×D8311yescharacteristic
228C22×C8—22no—
229C22×C8—1662no—
230C2×C4⋊C4—3322no—
231C2×C4⋊C4—1661no—
232C2×C4⋊C4—1661no—
233C2×C4⋊C4—1662no—
234C2×C4⋊C4—1662no—
235C2×C4⋊C4—1661no—
236C2×C4⋊C4—1661no—
237C2×C42—42no—
238C2×C42D33211yescharacteristic
239C2×C42D33211yescharacteristic
240C2×C42C22⋊D8311yescharacteristic
241C2×C42C22⋊D8311yescharacteristic
242C4⋊C8—3322no—
243C22⋊C8—22no—
244C22⋊C8—1664no—
245C22⋊C8Dic16614yes—
246#97—42no—
247#95—1661no—
248#95—1661no—
249#95—1661no—
250#95—1661no—
251#95—1661no—
252#95—1661no—
253#95—1661no—
254#95—1661no—
255C24C2×C4×D8311yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—3321no—
266C22×C4—3321no—
267C22×C4—3321no—
268C22×C4—3321no—
269C22×C4—3321no—
270C22×C4—3321no—
271C22×C4—3321no—
272C22×C4—3321no—
273C22×C4—832no—
274C22×C4—832no—
275C22×C4—1661no—
276C22×C4—1661no—
277C22×C4—1661no—
278C22×C4—1661no—
279C22×C4—1661no—
280C22×C4—1661no—
281C22×C4—1662no—
282C22×C4—1662no—
283C22×C4(C2×D83)⋊C411yescharacteristic
284C22×C4(C2×D83)⋊C411yescharacteristic
285C22×C4(C2×D83)⋊C411yescharacteristic
286C22×C4(C2×D83)⋊C411yescharacteristic
287C22×C4C2×C22⋊D8311yescharacteristic
288C22×C4C2×D33211yescharacteristic
289C22×C4C2×Dic16612yes—
290C22×C4#1305059012yes—
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—3322no—
295C2×C8—3322no—
296C2×C8—3322no—
297C4⋊C4—3322no—
298C4⋊C4—3322no—
299C4⋊C4—1664no—
300C4⋊C4—1664no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—41no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×(C2×D83)⋊C411yescharacteristic
310C23C4×Dic16612yes—
311C23M16×D8311yescharacteristic
312C23M16×D8311yescharacteristic
313C23#1458180012yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—3322no—
335C2×C4—3322no—
336C2×C4—3321no—
337C2×C4—3321no—
338C2×C4—3321no—
339C2×C4—3321no—
340C2×C4—3322no—
341C2×C4—3322no—
342C2×C4—3321no—
343C2×C4—3321no—
344C2×C4—3321no—
345C2×C4—3321no—
346C2×C4—3321no—
347C2×C4—3321no—
348C2×C4—6642no—
349C2×C4—6642no—
350C2×C4—1662no—
351C2×C4—1662no—
352C2×C4#1458170612yes—
353C2×C4#1458177112yes—
354C2×C4#1458178011yescharacteristic
355C2×C4#1458179211yescharacteristic
356C8—44no—
357C8—6642no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22#1912760711yescharacteristic
367C22#1912766411yescharacteristic
368C22#1912766911yescharacteristic
369C22C2×#1458170611yescharacteristic
370C22#1912767411yescharacteristic
371C22#1912768311yescharacteristic
372C22#1912768311yescharacteristic
373C22#1912782912yes—
374C22#1912782912yes—
375C4—22no—
376C4—22no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3322no—
383C4—3322no—
384C4—6641no—
385C4—6641no—
386C2—22no—
387C2—22no—
388C2#2490579511yescharacteristic
389C2#2490579911yescharacteristic
390C2#2490581211yescharacteristic
391C2#2490583311yescharacteristic
392C2#2490840311yescharacteristic
393C2#2490844811yescharacteristic
394C2#2490845611yescharacteristic
subgroupG/H
centerC23C2×(C2×D83)⋊C4
commutator, prime radicalC24×C83C22×C4
FrattiniC23×C4C22×D83
FittingC83×#1749C2
socleC23×C83C2×C22⋊C4
cosocleC23×C4×C83C23
hypercenter#1749D83
hypocenterC83#9881
LCSG ▷ C24×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
203. C83#9881semidirect

Maximal subgroups

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

subgroupindex
C2×#191275852
#249074432
#249053052
C83×#17492
#988183