Finite Group Databasebeta

← #35307228

Subgroups — #35307228

Order 21248.

554 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128106C211yesmaximal, characteristic
2C2×#19128052C211yesmaximal, characteristic
3C2×#19128052C211yesmaximal, characteristic
4#24908424C211yesmaximal, characteristic
5#24908424C211yesmaximal, characteristic
6#24908265C211yesmaximal, characteristic
7C83×#1273C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×#14581792C2211yescharacteristic
10C2×#14581792C2211yescharacteristic
11#19128106—22no—
12#19128106—22no—
13#19128052—22no—
14#19128052—22no—
15#19128052—22no—
16#19128052—22no—
17C2×#14581726—22no—
18C2×#14581717—22no—
19C2×#14581717—22no—
20C2×#14581717—22no—
21#19127571C2211yescharacteristic
22#19127464—22no—
23#19127464—22no—
24C2×C4×C8×C83C2211yescharacteristic
25C2×C4×C8×C83C2211yescharacteristic
26C2×C4×C8×C83C2211yescharacteristic
27C22×Dic166—21no—
28C22×Dic166—21no—
29C22×Dic166—21no—
30#14581792—21no—
31#14581792—21no—
32#14581792—21no—
33#14581792—21no—
34#14581792—21no—
35#14581792—21no—
36#14581792—21no—
37#14581792—21no—
38#14581792—21no—
39#14581792D412yes—
40#14581792D412yes—
41#14581792D412yes—
42C2×C4⋊Dic83—21no—
43C2×C4⋊Dic83—21no—
44C2×C4⋊Dic83—21no—
45C2×C4⋊Dic83—21no—
46C2×C4⋊Dic83—21no—
47C2×C4⋊Dic83—21no—
48C2×C4⋊Dic83—21no—
49C2×C4⋊Dic83—21no—
50C2×C4⋊Dic83—21no—
51#14581726—28no—
52#14581717—28no—
53#14581717—28no—
54#14581717—44no—
55C22×C8×C83D412yes—
56C22×C8×C83D412yes—
57C22×C8×C83D412yes—
58C2×C42×C83C2311yescharacteristic
59C4×C8×C83—21no—
60C4×C8×C83—21no—
61C4×C8×C83—21no—
62C4×C8×C83—21no—
63C4×C8×C83—21no—
64C4×C8×C83—21no—
65C2×Dic166—22no—
66C2×Dic166—22no—
67C2×Dic166—22no—
68C2×Dic166—42no—
69C2×Dic166—42no—
70C2×Dic166—42no—
71C2×Dic166—42no—
72C2×Dic166—42no—
73C2×Dic166—42no—
74C2×Dic166—41no—
75C2×Dic166—41no—
76C2×Dic166—41no—
77C22×Dic83—41no—
78C22×Dic83—41no—
79C22×Dic83—41no—
80C22×Dic83—41no—
81C4⋊Dic83—22no—
82C4⋊Dic83—22no—
83C4⋊Dic83—22no—
84C4⋊Dic83—22no—
85C4⋊Dic83—22no—
86C4⋊Dic83—22no—
87C4⋊Dic83—41no—
88C4⋊Dic83—41no—
89C4⋊Dic83—41no—
90C4⋊Dic83—41no—
91C4⋊Dic83—41no—
92C4⋊Dic83—41no—
93C4⋊Dic83—42no—
94C4⋊Dic83—42no—
95C4⋊Dic83—42no—
96C22×C4×C83C2×D411yescharacteristic
97C22×C4×C83C2×D411yescharacteristic
98C22×C4×C83C2×D411yescharacteristic
99C2×C8×C83—22no—
100C2×C8×C83—22no—
101C2×C8×C83—22no—
102C2×C8×C83—22no—
103C2×C8×C83—22no—
104C2×C8×C83—22no—
105C2×C8×C83—22no—
106C2×C8×C83—22no—
107C2×C8×C83Q1614yes—
108C42×C83C2×D411yescharacteristic
109C42×C83C2×D411yescharacteristic
110C42×C83C2×D411yescharacteristic
111C42×C83#4111yescharacteristic
112C23×C83#12711yescharacteristic
113C2×C4×C83#12011yescharacteristic
114C2×C4×C83#12011yescharacteristic
115C2×C4×C83#12011yescharacteristic
116C2×C4×C83#12111yescharacteristic
117C2×C4×C83#12111yescharacteristic
118C2×C4×C83#12111yescharacteristic
119C2×C4×C83C2×Q1612yes—
120C2×C4×C83#13512yes—
121C2×C4×C83#13512yes—
122C2×C4×C83AGL(1,ℤ/8)12yes—
123C2×C4×C83#13712yes—
124C2×C4×C83#13712yes—
125C2×Dic83—42no—
126C2×Dic83—42no—
127C2×Dic83—42no—
128C2×Dic83—81no—
129C2×Dic83—81no—
130C2×Dic83—81no—
131C2×Dic83—81no—
132C2×Dic83—81no—
133C2×Dic83—81no—
134C2×Dic83—81no—
135C2×Dic83—81no—
136C2×Dic83—81no—
137Dic166—44no—
138Dic166—44no—
139Dic166—44no—
140Dic166—82no—
141Dic166—82no—
142Dic166—82no—
143C8×C83—24no—
144C8×C83—42no—
145C8×C83—42no—
146C22×C83#39211yescharacteristic
147C22×C83#49411yescharacteristic
148C22×C83#49511yescharacteristic
149C22×C83#49511yescharacteristic
150C22×C83#49611yescharacteristic
151C22×C83#49711yescharacteristic
152C22×C83#49711yescharacteristic
153C4×C83#44912yes—
154C4×C83#45112yes—
155C4×C83#45212yes—
156C4×C83#46212yes—
157C4×C83#46312yes—
158C4×C83#46412yes—
159Dic83—82no—
160Dic83—82no—
161Dic83—82no—
162Dic83—161no—
163#10313—831nomaximal, Sylow
164C2×C83#171011yescharacteristic
165C2×C83#171811yescharacteristic
166C2×C83#171911yescharacteristic
167C2×C83#172311yescharacteristic
168C2×C83#201211yescharacteristic
169C2×C83#201511yescharacteristic
170C2×C83#201611yescharacteristic
171C2×#500—831no—
172C2×#487—831no—
173C2×#487—831no—
174#1990—831no—
175#1990—831no—
176#1956—831no—
177#1273D8311yescharacteristic
178C83#1031311yescharacteristic, complemented, Sylow
179C2×C4⋊Q8—831no—
180C2×C4⋊Q8—831no—
181C2×C4⋊Q8—831no—
182#500—1662no—
183#500—1662no—
184#487—1662no—
185#487—1662no—
186#487—1662no—
187#487—1662no—
188C2×#107—1662no—
189C2×#103—1662no—
190C2×#103—1662no—
191C2×#103—1662no—
192C2×C4×C8C2×D8311yescharacteristic
193C2×C4×C8C2×D8311yescharacteristic
194C2×C4×C8C2×D8311yescharacteristic
195#384—831no—
196#340—1662no—
197#340—1662no—
198C22×Q8—1661no—
199C22×Q8—1661no—
200C22×Q8—1661no—
201C22×C8D33212yes—
202C22×C8D33212yes—
203C22×C8D33212yes—
204C4⋊Q8—832no—
205C4⋊Q8—832no—
206C4⋊Q8—832no—
207C4⋊Q8—1661no—
208C4⋊Q8—1661no—
209C4⋊Q8—1661no—
210C4⋊Q8—1661no—
211C4⋊Q8—1661no—
212C4⋊Q8—1661no—
213C4⋊Q8—1661no—
214C4⋊Q8—1661no—
215C4⋊Q8—1661no—
216C2×C4⋊C4—1661no—
217C2×C4⋊C4—1661no—
218C2×C4⋊C4—1661no—
219C2×C4⋊C4—1661no—
220C2×C4⋊C4—1661no—
221C2×C4⋊C4—1661no—
222C2×C4⋊C4—1661no—
223C2×C4⋊C4—1661no—
224C2×C4⋊C4—1661no—
225C2×C42C22×D8311yescharacteristic
226#107—1668no—
227#103—3324no—
228#103—1668no—
229#103—1668no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8—21no—
236C2×Q8—3321no—
237C2×Q8—3321no—
238C2×Q8—3321no—
239C2×Q8—3322no—
240C2×Q8—3322no—
241C2×Q8—3322no—
242C2×Q8—3322no—
243C2×Q8—3322no—
244C2×Q8—3322no—
245C2×Q8—1662no—
246C2×Q8—1662no—
247C2×Q8—1662no—
248C22×C4—3321no—
249C22×C4—3321no—
250C22×C4—3321no—
251C22×C4—3321no—
252C22×C4C2×D33211yescharacteristic
253C22×C4C2×D33211yescharacteristic
254C22×C4C2×D33211yescharacteristic
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8Dic33214yes—
264C4⋊C4—3321no—
265C4⋊C4—3321no—
266C4⋊C4—3321no—
267C4⋊C4—3321no—
268C4⋊C4—3321no—
269C4⋊C4—3321no—
270C4⋊C4—3322no—
271C4⋊C4—3322no—
272C4⋊C4—3322no—
273C4⋊C4—1662no—
274C4⋊C4—1662no—
275C4⋊C4—1662no—
276C4⋊C4—1662no—
277C4⋊C4—1662no—
278C4⋊C4—1662no—
279C42D4×D8311yescharacteristic
280C42D4×D8311yescharacteristic
281C42D4×D8311yescharacteristic
282C42#1305059111yescharacteristic
283C23#1458178911yescharacteristic
284Q8—3324no—
285Q8—3324no—
286Q8—3324no—
287Q8—6642no—
288Q8—6642no—
289Q8—6642no—
290C2×C4—3322no—
291C2×C4—3322no—
292C2×C4—3322no—
293C2×C4—6641no—
294C2×C4—6641no—
295C2×C4—6641no—
296C2×C4—6641no—
297C2×C4—6641no—
298C2×C4—6641no—
299C2×C4—6641no—
300C2×C4—6641no—
301C2×C4—6641no—
302C2×C4#1458176211yescharacteristic
303C2×C4#1458176211yescharacteristic
304C2×C4#1458176211yescharacteristic
305C2×C4#1458176711yescharacteristic
306C2×C4#1458176711yescharacteristic
307C2×C4#1458176711yescharacteristic
308C2×C4C2×Dic33212yes—
309C2×C4#1458181412yes—
310C2×C4#1458181412yes—
311C2×C4#1458182012yes—
312C2×C4#1458182512yes—
313C2×C4#1458182512yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22#1912761111yescharacteristic
318C22#1912808111yescharacteristic
319C22#1912808511yescharacteristic
320C22#1912808511yescharacteristic
321C22#1912809011yescharacteristic
322C22#1912809511yescharacteristic
323C22#1912809511yescharacteristic
324C4—13281no—
325C4—6642no—
326C4—6642no—
327C4—6642no—
328C4#1912784812yes—
329C4#1912785912yes—
330C4#1912786512yes—
331C4#1912791212yes—
332C4#1912791712yes—
333C4#1912792412yes—
334C2#2490707311yescharacteristic
335C2#2490710911yescharacteristic
336C2#2490711611yescharacteristic
337C2#2490714011yescharacteristic
338C2#2490854311yescharacteristic
339C2#2490856011yescharacteristic
340C2#2490856511yescharacteristic
subgroupG/H
centerC23#14581789
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1273C2
socle, prime radicalC23×C83#127
hypercenter#1273D83
hypocenterC83#10313
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1273

Complements

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

NH ≅ G/Ntype
178. C83#10313semidirect

Maximal subgroups

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

subgroupindex
C2×#191281062
C2×#191280522
#249084242
#249082652
C83×#12732
#1031383