Finite Group Databasebeta

← #35307234

Subgroups — #35307234

Order 21248.

570 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128104C211yesmaximal, characteristic
2C2×#19128097C211yesmaximal, characteristic
3C2×#19128052C211yesmaximal, characteristic
4#24908423C211yesmaximal, characteristic
5#24908264C211yesmaximal, characteristic
6C83⋊#1273C211yesmaximal, characteristic
7C83×#1956C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×#14581792C2211yescharacteristic
10#19128104—22no—
11#19128104—22no—
12#19128097—22no—
13#19128097—22no—
14#19128052—22no—
15#19128052—22no—
16C2×#14581725—22no—
17C2×#14581723—22no—
18C2×#14581717—22no—
19C2×#14581715—22no—
20C2×C4×C83⋊C8C2211yescharacteristic
21C2×C4×C83⋊C8C2211yescharacteristic
22#19127463—22no—
23C2×C4⋊Q8×C83C2211yescharacteristic
24C2×#103×C83—22no—
25C2×C4×C8×C83C2211yescharacteristic
26#384×C83C2211yescharacteristic
27C22×Dic166—21no—
28C22×Dic166—21no—
29C22×C83⋊C8D412yes—
30C22×C83⋊C8D412yes—
31#14581792—21no—
32#14581792—21no—
33#14581792—21no—
34#14581792—21no—
35#14581792—21no—
36#14581792—21no—
37#14581792D412yes—
38#14581792D412yes—
39C2×C4⋊Dic83—21no—
40C2×C4⋊Dic83—21no—
41C2×C4⋊Dic83—21no—
42C2×C4⋊Dic83—21no—
43#14581725—28no—
44#14581723—28no—
45#14581717—28no—
46#14581715—44no—
47C4×C83⋊C8—21no—
48C4×C83⋊C8—21no—
49C4×C83⋊C8—21no—
50C4×C83⋊C8—21no—
51C22×Q8×C83—21no—
52C22×C8×C83D412yes—
53C4⋊Q8×C83—21no—
54C4⋊Q8×C83—21no—
55C4⋊Q8×C83—21no—
56C4⋊Q8×C83D412yes—
57C2×C4⋊C4×C83—21no—
58C2×C4⋊C4×C83—21no—
59C2×C4⋊C4×C83—21no—
60C2×C4⋊C4×C83—21no—
61C2×C4⋊C4×C83—21no—
62C2×C42×C83C2311yescharacteristic
63#103×C83—44no—
64C4×C8×C83—21no—
65C4×C8×C83—21no—
66C2×Dic166—22no—
67C2×Dic166—22no—
68C2×Dic166—42no—
69C2×Dic166—42no—
70C2×Dic166—42no—
71C2×Dic166—42no—
72C2×Dic166—41no—
73C2×Dic166—41no—
74C22×Dic83—41no—
75C22×Dic83—41no—
76C2×C83⋊C8—22no—
77C2×C83⋊C8—22no—
78C2×C83⋊C8—22no—
79C2×C83⋊C8—22no—
80C2×C83⋊C8SD1614yes—
81C2×C83⋊C8Q1614yes—
82C4⋊Dic83—22no—
83C4⋊Dic83—22no—
84C4⋊Dic83—22no—
85C4⋊Dic83—22no—
86C4⋊Dic83—41no—
87C4⋊Dic83—41no—
88C4⋊Dic83—41no—
89C4⋊Dic83—41no—
90C2×Q8×C83—22no—
91C2×Q8×C83—41no—
92C2×Q8×C83—42no—
93C2×Q8×C83—42no—
94C22×C4×C83—41no—
95C22×C4×C83—41no—
96C22×C4×C83C2×D411yescharacteristic
97C22×C4×C83C2×D411yescharacteristic
98C22×C4×C83C2×D411yescharacteristic
99C2×C8×C83—22no—
100C2×C8×C83—22no—
101C2×C8×C83—22no—
102C4⋊C4×C83—22no—
103C4⋊C4×C83—22no—
104C4⋊C4×C83—41no—
105C4⋊C4×C83—41no—
106C4⋊C4×C83—42no—
107C4⋊C4×C83—42no—
108C4⋊C4×C83—42no—
109C42×C83C2×D411yescharacteristic
110C42×C83C2×D411yescharacteristic
111C42×C83C2×D411yescharacteristic
112C42×C83#4111yescharacteristic
113C23×C83#12711yescharacteristic
114Q8×C83—44no—
115Q8×C83—82no—
116C2×C4×C83—42no—
117C2×C4×C83—81no—
118C2×C4×C83—81no—
119C2×C4×C83—81no—
120C2×C4×C83—81no—
121C2×C4×C83—81no—
122C2×C4×C83#12011yescharacteristic
123C2×C4×C83#12011yescharacteristic
124C2×C4×C83#12011yescharacteristic
125C2×C4×C83#12111yescharacteristic
126C2×C4×C83#12111yescharacteristic
127C2×C4×C83#12111yescharacteristic
128C2×C4×C83C2×SD1612yes—
129C2×C4×C83C2×Q1612yes—
130C2×C4×C83#13512yes—
131C2×C4×C83AGL(1,ℤ/8)12yes—
132C2×C4×C83#13712yes—
133C2×C4×C83#13712yes—
134C2×Dic83—42no—
135C2×Dic83—42no—
136C2×Dic83—81no—
137C2×Dic83—81no—
138C2×Dic83—81no—
139C2×Dic83—81no—
140Dic166—44no—
141Dic166—44no—
142Dic166—82no—
143Dic166—82no—
144C8×C83—42no—
145C83⋊C8—24no—
146C83⋊C8—24no—
147C22×C83#39211yescharacteristic
148C22×C83#49211yescharacteristic
149C22×C83#49411yescharacteristic
150C22×C83#49511yescharacteristic
151C22×C83#49611yescharacteristic
152C22×C83#49711yescharacteristic
153C22×C83#49711yescharacteristic
154C4×C83—82no—
155C4×C83—161no—
156C4×C83#44812yes—
157C4×C83#44912yes—
158C4×C83#45112yes—
159C4×C83#46112yes—
160C4×C83#46212yes—
161C4×C83#46312yes—
162Dic83—82no—
163Dic83—82no—
164#10314—831nomaximal, Sylow
165C2×C83#170711yescharacteristic
166C2×C83#171411yescharacteristic
167C2×C83#171811yescharacteristic
168C2×C83#172311yescharacteristic
169C2×C83#201211yescharacteristic
170C2×C83#201311yescharacteristic
171C2×C83#201611yescharacteristic
172C2×#500—831no—
173C2×#498—831no—
174C2×#487—831no—
175#1990—831no—
176#1956—831no—
177#1956D8311yescharacteristic
178#1273—831no—
179C83#1031411yescharacteristic, complemented, Sylow
180C2×C4⋊Q8—831no—
181C2×C4⋊Q8—831no—
182C2×C4⋊Q8C2×D8311yescharacteristic
183#500—1662no—
184#500—1662no—
185#498—1662no—
186#498—1662no—
187#487—1662no—
188#487—1662no—
189C2×#107—1662no—
190C2×#106—1662no—
191C2×#103—22no—
192C2×#103—1662no—
193C2×#103—1662no—
194C2×C4×C8—831no—
195C2×C4×C8—831no—
196C2×C4×C8C2×D8311yescharacteristic
197#384C2×D8311yescharacteristic
198#340—1662no—
199C22×Q8—21no—
200C22×Q8—1661no—
201C22×Q8—1661no—
202C22×C8—832no—
203C22×C8—832no—
204C22×C8C22⋊D8312yes—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—832no—
209C4⋊Q8—832no—
210C4⋊Q8—1661no—
211C4⋊Q8—1661no—
212C4⋊Q8—1661no—
213C4⋊Q8—1661no—
214C4⋊Q8—1661no—
215C4⋊Q8—1661no—
216C4⋊Q8D33212yes—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—1661no—
223C2×C4⋊C4—1661no—
224C2×C4⋊C4—1661no—
225C2×C4⋊C4—1661no—
226C2×C42C22×D8311yescharacteristic
227#107—1668no—
228#106—1668no—
229#103—44no—
230#103—3324no—
231#103—1668no—
232C4×C8—21no—
233C4×C8—21no—
234C4×C8—1661no—
235C4×C8—1661no—
236C4×C8—1661no—
237C4×C8—1661no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—3321no—
243C2×Q8—3321no—
244C2×Q8—3322no—
245C2×Q8—3322no—
246C2×Q8—3322no—
247C2×Q8—3322no—
248C2×Q8—1662no—
249C2×Q8—1662no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—3321no—
253C22×C4—3321no—
254C22×C4D4×D8311yescharacteristic
255C22×C4D4×D8311yescharacteristic
256C22×C4C2×C22⋊D8311yescharacteristic
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—834no—
261C2×C8—834no—
262C2×C8—1662no—
263C2×C8—1662no—
264C2×C8—1662no—
265C2×C8—1662no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—3321no—
274C4⋊C4—3321no—
275C4⋊C4—3321no—
276C4⋊C4—3321no—
277C4⋊C4—1662no—
278C4⋊C4—1662no—
279C4⋊C4—1662no—
280C4⋊C4—1662no—
281C42D4×D8311yescharacteristic
282C42D4×D8311yescharacteristic
283C42C2×D33211yescharacteristic
284C42#1305059011yescharacteristic
285C23#1458178811yescharacteristic
286Q8—44no—
287Q8—82no—
288Q8—3324no—
289Q8—3324no—
290Q8—6642no—
291Q8—6642no—
292C2×C4—42no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—3322no—
299C2×C4—3322no—
300C2×C4—6641no—
301C2×C4—6641no—
302C2×C4—6641no—
303C2×C4—6641no—
304C2×C4#1458176011yescharacteristic
305C2×C4#1458176211yescharacteristic
306C2×C4#1458176211yescharacteristic
307C2×C4#1458176511yescharacteristic
308C2×C4#1458176511yescharacteristic
309C2×C4#1458176611yescharacteristic
310C2×C4SD16×D8312yes—
311C2×C4Q16×D8312yes—
312C2×C4#1458181212yes—
313C2×C4#1458181812yes—
314C2×C4#1458182112yes—
315C2×C4#1458182412yes—
316C8—42no—
317C8—1664no—
318C8—1664no—
319C22#1912761011yescharacteristic
320C22#1912807211yescharacteristic
321C22#1912807911yescharacteristic
322C22#1912808311yescharacteristic
323C22#1912808811yescharacteristic
324C22#1912809211yescharacteristic
325C22#1912809411yescharacteristic
326C4—82no—
327C4—161no—
328C4—6642no—
329C4—6642no—
330C4#1912784112yes—
331C4#1912784412yes—
332C4#1912785812yes—
333C4#1912790512yes—
334C4#1912791012yes—
335C4#1912791612yes—
336C2#2490705911yescharacteristic
337C2#2490708311yescharacteristic
338C2#2490710611yescharacteristic
339C2#2490713811yescharacteristic
340C2#2490853911yescharacteristic
341C2#2490854711yescharacteristic
342C2#2490856411yescharacteristic
subgroupG/H
centerC23#14581788
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1956C2
socle, prime radicalC23×C83#127
hypercenter#1956D83
hypocenterC83#10314
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
179. C83#10314semidirect

Maximal subgroups

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

subgroupindex
C2×#191281042
C2×#191280972
C2×#191280522
#249084232
#249082642
C83⋊#12732
C83×#19562
#1031483