Finite Group Databasebeta

← #35323759

Subgroups — #35323759

Order 21248.

462 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128079C211yesmaximal, characteristic
2C2×#19127506C211yesmaximal, characteristic
3C2×#19127505C211yesmaximal, characteristic
4C2×#19127504C211yesmaximal, characteristic
5#24908197C211yesmaximal, characteristic
6#24905540C211yesmaximal, characteristic
7C2×#358×C83C211yesmaximal, characteristic
8C22×Dic332C2211yescharacteristic
9C22×#13050580—21no—
10C2×#14581790—21no—
11C22×C83⋊C16C2211yescharacteristic
12#19128079—22no—
13#19128079—22no—
14C2×#14581726C2211yescharacteristic
15C2×C8×Dic83C2211yescharacteristic
16#19127600—21no—
17#19127506—22no—
18#19127505—22no—
19#19127504—22no—
20#19127463—21no—
21C22×Q16×C83C2211yescharacteristic
22C22×C16×C83C2211yescharacteristic
23C2×#107×C83C2211yescharacteristic
24#358×C83—22no—
25C22×Dic166—21no—
26C2×Dic332—21no—
27C2×Dic332—21no—
28C2×Dic332—21no—
29C2×Dic332—21no—
30C2×Dic332—21no—
31C2×Dic332D412yes—
32C2×#13050580—24no—
33C2×#13050580—42no—
34C2×#13050580—42no—
35C22×C83⋊C8D411yescharacteristic
36#14581790—24no—
37#14581790—42no—
38C2×C4⋊Dic83—21no—
39C2×C4⋊Dic83—41no—
40C2×Dic83⋊C4—41no—
41C2×Dic83⋊C4—41no—
42C2×C4×Dic83D411yescharacteristic
43C2×C83⋊C16—21no—
44C2×C83⋊C16—21no—
45C2×C83⋊C16—21no—
46#14581726—21no—
47#14581726—21no—
48C8×Dic83—21no—
49C8×Dic83—21no—
50C83⋊#95—41no—
51C22×Q8×C83—21no—
52C2×Q16×C83—21no—
53C2×Q16×C83—21no—
54C2×Q16×C83—21no—
55C2×Q16×C83—21no—
56C2×Q16×C83—21no—
57C2×Q16×C83D412yes—
58C22×C8×C83C2311yescharacteristic
59C2×C4⋊C4×C83—21no—
60C2×C16×C83—21no—
61C2×C16×C83—21no—
62C2×C16×C83—21no—
63#107×C83—21no—
64#107×C83D412yes—
65C2×Dic166—22no—
66C2×Dic166—41no—
67C2×Dic166—41no—
68C2×Dic166—41no—
69C2×Dic166—41no—
70C2×Dic166—41no—
71C22×Dic83—41no—
72C22×Dic83—41no—
73C22×Dic83D811yescharacteristic
74C22×Dic83D811yescharacteristic
75Dic332—22no—
76Dic332—22no—
77Dic332—41no—
78Dic332—41no—
79#13050580—48no—
80C2×C83⋊C8—21no—
81C2×C83⋊C8—21no—
82C2×C83⋊C8SD1612yes—
83C4⋊Dic83—41no—
84C4⋊Dic83—41no—
85C4⋊Dic83—82no—
86Dic83⋊C4—44no—
87Dic83⋊C4—44no—
88C4×Dic83—21no—
89C4×Dic83—21no—
90C83⋊C16—41no—
91C2×Q8×C83—22no—
92C2×Q8×C83—41no—
93C2×Q8×C83—41no—
94C2×Q8×C83—41no—
95C2×Q8×C83—41no—
96C2×Q8×C83—41no—
97C22×C4×C83—41no—
98C22×C4×C83—41no—
99C22×C4×C83C2×D411yescharacteristic
100Q16×C83—22no—
101Q16×C83—22no—
102Q16×C83—41no—
103Q16×C83—41no—
104C2×C8×C83C2×D411yescharacteristic
105C2×C8×C83C2×D411yescharacteristic
106C2×C8×C83C2×D411yescharacteristic
107C2×C8×C83#4111yescharacteristic
108C2×C8×C83#4111yescharacteristic
109C2×C8×C83#4111yescharacteristic
110C4⋊C4×C83—22no—
111C4⋊C4×C83—41no—
112C16×C83—41no—
113C23×C83C2×D811yescharacteristic
114Q8×C83—42no—
115Q8×C83—42no—
116Q8×C83—81no—
117Q8×C83—81no—
118C2×C4×C83—42no—
119C2×C4×C83—42no—
120C2×C4×C83—81no—
121C2×C4×C83—81no—
122C2×C4×C83—81no—
123C2×C4×C83—81no—
124C2×C4×C83#12011yescharacteristic
125C2×C4×C83#12111yescharacteristic
126C2×C4×C83#12411yescharacteristic
127C2×C4×C83C2×SD1611yescharacteristic
128C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—42no—
135C2×Dic83—81no—
136C2×Dic83—81no—
137C2×Dic83—81no—
138C2×Dic83—81no—
139C2×Dic83—81no—
140C2×Dic83SD3212yes—
141C2×Dic83Q3212yes—
142Dic166—42no—
143Dic166—42no—
144Dic166—81no—
145Dic166—81no—
146C8×C83#12111yescharacteristic
147C8×C83#12111yescharacteristic
148C8×C83#12311yescharacteristic
149C8×C83#12311yescharacteristic
150C83⋊C8—22no—
151C22×C83#44711yescharacteristic
152C22×C83#45911yescharacteristic
153C22×C83#48611yescharacteristic
154C22×C83C2×SD3211yescharacteristic
155C22×C83C2×Q3211yescharacteristic
156C22×C83#51011yescharacteristic
157C22×C83#51011yescharacteristic
158C4×C83—82no—
159C4×C83—82no—
160C4×C83#39411yescharacteristic
161C4×C83#45011yescharacteristic
162C4×C83#46011yescharacteristic
163C4×C83#49011yescharacteristic
164Dic83—22no—
165Dic83—22no—
166Dic83—82no—
167Dic83—161no—
168#13409—831nomaximal, Sylow
169C2×C83#204111yescharacteristic
170C2×C83#218511yescharacteristic
171C2×C83#218811yescharacteristic
172C2×C83#220811yescharacteristic
173C2×C83#220911yescharacteristic
174C2×C83#224111yescharacteristic
175C2×C83#224511yescharacteristic
176C2×#494—831no—
177C2×#358—831no—
178C2×#358—831no—
179C2×#358—831no—
180C2×#358D8311yescharacteristic
181#1942—831no—
182#1374—831no—
183C83#1340911yescharacteristic, complemented, Sylow
184C22×Q16—831no—
185C22×Q16—1661no—
186C22×Q16C2×D8311yescharacteristic
187C2×C4⋊Q8—1661no—
188C22×C16—831no—
189C22×C16C2×D8311yescharacteristic
190#494—1662no—
191#494—1662no—
192C2×#107—831no—
193C2×#107C2×D8311yescharacteristic
194C2×C4×C8—831no—
195#389—1661no—
196#358—22no—
197#358—1662no—
198#358—1662no—
199#358—1662no—
200#340—1661no—
201C22×Q8—21no—
202C22×Q8—1661no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—3322no—
209C2×Q16—3322no—
210C2×Q16—832no—
211C2×Q16—1664no—
212C2×Q16—1661no—
213C2×Q16—1661no—
214C2×Q16—1661no—
215C2×Q16—1661no—
216C2×Q16—1661no—
217C2×Q16D33212yes—
218C22×C8—831no—
219C22×C8C22×D8311yescharacteristic
220C4⋊Q8—3322no—
221C4⋊Q8—1664no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—3321no—
224C2×C4⋊C4—3321no—
225C2×C4⋊C4—3321no—
226C2×C4⋊C4—1661no—
227C2×C42—831no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—1661no—
232C2×C16—1661no—
233C2×C16—1661no—
234#107—21no—
235#107—1661no—
236#107—1661no—
237#107C22⋊D8312yes—
238C4×C8—1661no—
239C4×C8—1661no—
240#95—3321no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—3321no—
248C2×Q8—3321no—
249C2×Q8—3321no—
250C2×Q8—3321no—
251C2×Q8—3321no—
252C2×Q8—1662no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—3321no—
256C22×C4—3321no—
257C22×C4—831no—
258C22×C4—831no—
259C22×C4D4×D8311yescharacteristic
260Q16—22no—
261Q16—22no—
262Q16—41no—
263Q16—41no—
264Q16—3328no—
265Q16—3321no—
266Q16—3321no—
267Q16—1662no—
268Q16—1662no—
269C2×C8—832no—
270C2×C8—1661no—
271C2×C8—1661no—
272C2×C8D4×D8311yescharacteristic
273C2×C8C2×C22⋊D8311yescharacteristic
274C2×C8C2×D33211yescharacteristic
275C2×C8#1305058911yescharacteristic
276C2×C8#1305058911yescharacteristic
277C2×C8#1305059011yescharacteristic
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—3324no—
281C4⋊C4—3324no—
282C4⋊C4—3321no—
283C4⋊C4—3321no—
284C4⋊C4—6642no—
285C42—1661no—
286C42—1661no—
287C16—41no—
288C16—3321no—
289C23D8×D8311yescharacteristic
290Q8—42no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—3322no—
295Q8—3322no—
296Q8—6641no—
297Q8—6641no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—3322no—
305C2×C4—832no—
306C2×C4—832no—
307C2×C4—6641no—
308C2×C4—6641no—
309C2×C4—6641no—
310C2×C4—6641no—
311C2×C4—6641no—
312C2×C4—1661no—
313C2×C4—1661no—
314C2×C4—1661no—
315C2×C4—1661no—
316C2×C4#1458176211yescharacteristic
317C2×C4#1458176411yescharacteristic
318C2×C4#1458177811yescharacteristic
319C2×C4SD16×D8311yescharacteristic
320C2×C4#1458181611yescharacteristic
321C2×C4#1458181911yescharacteristic
322C8—1662no—
323C8#1458176311yescharacteristic
324C8#1458176611yescharacteristic
325C8#1458177411yescharacteristic
326C8#1458177611yescharacteristic
327C22#1912783611yescharacteristic
328C22#1912789411yescharacteristic
329C22#1912804611yescharacteristic
330C22SD32×D8311yescharacteristic
331C22Q32×D8311yescharacteristic
332C22#1912814011yescharacteristic
333C22#1912814311yescharacteristic
334C4—82no—
335C4—82no—
336C4—13281no—
337C4—6642no—
338C4—1662no—
339C4—1662no—
340C4#1912761711yescharacteristic
341C4#1912785311yescharacteristic
342C4#1912789911yescharacteristic
343C4#1912806411yescharacteristic
344C2#2490869611yescharacteristic
345C2#2490938111yescharacteristic
346C2#2490939811yescharacteristic
347C2#2490950611yescharacteristic
348C2#2490951111yescharacteristic
349C2#2490968911yescharacteristic
350C2#2490970711yescharacteristic
subgroupG/H
centerC23D8×D83
commutator, cosocleC22×C8×C83C23
FrattiniC22×C8C22×D83
FittingC2×#358×C83C2
socle, prime radicalC23×C83C2×D8
hypercenterC2×#358D83
hypocenterC83#13409
LCSG ▷ C22×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
183. C83#13409semidirect

Maximal subgroups

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

subgroupindex
C2×#191280792
C2×#191275062
C2×#191275052
C2×#191275042
#249081972
#249055402
C2×#358×C832
#1340983