Finite Group Databasebeta

← #35323756

Subgroups — #35323756

Order 21248.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128085C211yesmaximal, characteristic
2C2×#19127506C211yesmaximal, characteristic, complemented
3C2×#19127506C211yesmaximal, characteristic, complemented
4C2×#19127503C211yesmaximal, characteristic
5C2×#19127503C211yesmaximal, characteristic
6#24908196C211yesmaximal, characteristic, complemented
7C83×#1374C211yesmaximal, characteristic, complemented
8C22×Dic332C2211yescharacteristic
9C22×#13050579—21no—
10C22×D664C2211yescharacteristic
11C2×#14581780—21no—
12#19128085—22no—
13#19128085—22no—
14C2×#14581726C2211yescharacteristic
15C2×#14581726C2211yescharacteristic
16#19127599—21no—
17#19127506—22no—
18#19127506—22no—
19#19127503—22no—
20#19127503—22no—
21#19127464—21no—
22C22×C16×C83C2211yescharacteristic
23C22×C16×C83C2211yescharacteristic
24C2×C4×C8×C83C2211yescharacteristic
25C22×Dic166—21no—
26C22×D332—21no—
27C2×Dic332—21no—
28C2×Dic332—21no—
29C2×Dic332—21no—
30C2×Dic332—21no—
31C2×Dic332—21no—
32C2×Dic332D412yes—
33C2×#13050579—24no—
34C2×#13050579—42no—
35C2×#13050579—42no—
36C2×D664—21no—
37C2×D664—21no—
38C2×D664—21no—
39C2×D664—21no—
40C2×D664—21no—
41C2×D664D412yes—
42#14581780—24no—
43#14581780—42no—
44C2×C4⋊Dic83—21no—
45C2×C4⋊Dic83—21no—
46C2×Dic83⋊C4—41no—
47C2×(C2×D83)⋊C4—41no—
48C2×(C2×D83)⋊C4—41no—
49#14581726—21no—
50#14581726—21no—
51#14581726—21no—
52#14581726D412yes—
53C83⋊#95—41no—
54C22×C8×C83D411yescharacteristic
55C22×C8×C83C2311yescharacteristic
56C2×C42×C83D411yescharacteristic
57C2×C16×C83—21no—
58C2×C16×C83—21no—
59C2×C16×C83—21no—
60C2×C16×C83—21no—
61C2×C16×C83—21no—
62C2×C16×C83—21no—
63C4×C8×C83—21no—
64C4×C8×C83—21no—
65C23×D83—41no—
66C2×Dic166—22no—
67C2×Dic166—41no—
68C2×Dic166—41no—
69C2×Dic166—41no—
70C2×Dic166—41no—
71C2×Dic166—41no—
72C2×D332—22no—
73C2×D332—41no—
74C2×D332—41no—
75C2×D332—41no—
76C2×D332—41no—
77C2×D332—41no—
78C22×Dic83—41no—
79C22×Dic83—41no—
80C22×Dic83—41no—
81Dic332—22no—
82Dic332—22no—
83Dic332—41no—
84Dic332—41no—
85#13050579—48no—
86D664—22no—
87D664—22no—
88D664—41no—
89D664—41no—
90C4⋊Dic83—22no—
91C4⋊Dic83—41no—
92C4⋊Dic83—41no—
93C4⋊Dic83—41no—
94Dic83⋊C4—82no—
95(C2×D83)⋊C4—44no—
96(C2×D83)⋊C4—44no—
97C22×C4×C83D811yescharacteristic
98C22×C4×C83D811yescharacteristic
99C22×C4×C83C2×D411yescharacteristic
100C2×C8×C83—21no—
101C2×C8×C83—21no—
102C2×C8×C83SD1612yes—
103C2×C8×C83C2×D411yescharacteristic
104C2×C8×C83C2×D411yescharacteristic
105C2×C8×C83C2×D411yescharacteristic
106C2×C8×C83#4111yescharacteristic
107C2×C8×C83#4111yescharacteristic
108C2×C8×C83#4111yescharacteristic
109C42×C83—21no—
110C42×C83—21no—
111C16×C83—41no—
112C16×C83—41no—
113C23×C83C2×D811yescharacteristic
114C22×D83—42no—
115C22×D83—81no—
116C22×D83—81no—
117C22×D83—81no—
118C22×D83—81no—
119C22×D83—81no—
120C22×D83—81no—
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#12011yescharacteristic
128C2×C4×C83#12111yescharacteristic
129C2×C4×C83#12411yescharacteristic
130C2×C4×C83C2×SD1611yescharacteristic
131C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
133C2×Dic83—42no—
134C2×Dic83—42no—
135C2×Dic83—81no—
136C2×Dic83—81no—
137C2×Dic83—81no—
138C2×Dic83—81no—
139C2×Dic83—81no—
140C2×Dic83—81no—
141C2×Dic83—81no—
142D332—42no—
143D332—42no—
144D332—81no—
145D332—81no—
146Dic166—42no—
147Dic166—42no—
148Dic166—81no—
149Dic166—81no—
150C8×C83—22no—
151C8×C83#12111yescharacteristic
152C8×C83#12111yescharacteristic
153C8×C83#12311yescharacteristic
154C8×C83#12311yescharacteristic
155C22×C83#44711yescharacteristic
156C22×C83#45911yescharacteristic
157C22×C83#48611yescharacteristic
158C22×C83#50811yescharacteristic
159C22×C83#50811yescharacteristic
160C22×C83#50911yescharacteristic
161C22×C83#51011yescharacteristic
162C2×D83—82no—
163C2×D83—82no—
164C2×D83—82no—
165C2×D83—161no—
166C2×D83—161no—
167C2×D83—161no—
168C2×D83—161no—
169C4×C83—41no—
170C4×C83—41no—
171C4×C83#39411yescharacteristic
172C4×C83#45011yescharacteristic
173C4×C83#46011yescharacteristic
174C4×C83#49011yescharacteristic
175Dic83—82no—
176Dic83—82no—
177Dic83—161no—
178#13408—831nomaximal, Sylow
179C2×C83#204111yescharacteristic
180C2×C83#218611yescharacteristic
181C2×C83#218911yescharacteristic
182C2×C83#221011yescharacteristic
183C2×C83#221111yescharacteristic
184C2×C83#224211yescharacteristic
185C2×C83#224311yescharacteristic
186D83—162no—
187C2×#495—831no—
188C2×#358—831no—
189C2×#358—831no—
190C2×#357—831no—
191C2×#357—831no—
192#1942—831no—
193#1374D8311yescharacteristic, complemented
194C83#1340811yescharacteristic, complemented, Sylow
195C22×Q16—831no—
196C22×SD16—1661no—
197C22×D8—831no—
198C2×#124—1661no—
199C22×C16C2×D8311yescharacteristic
200C22×C16C2×D8311yescharacteristic
201#495—1662no—
202#495—1662no—
203C2×#107—831no—
204C2×#107—831no—
205C2×C4×C8C2×D8311yescharacteristic
206#389—1661no—
207#358—1662no—
208#358—1662no—
209#357—1662no—
210#357—1662no—
211#340—1661no—
212C22×Q8—1661no—
213C22×D4—1661no—
214C2×Q16—832no—
215C2×Q16—1661no—
216C2×Q16—1661no—
217C2×Q16—1661no—
218C2×Q16—1661no—
219C2×Q16—1661no—
220C2×SD16—3322no—
221C2×SD16—3322no—
222C2×SD16—1664no—
223C2×D8—832no—
224C2×D8—1661no—
225C2×D8—1661no—
226C2×D8—1661no—
227C2×D8—1661no—
228C2×D8—1661no—
229C22×C8D33211yescharacteristic
230C22×C8C22×D8311yescharacteristic
231#124—3322no—
232#124—1664no—
233C2×C4⋊C4—3321no—
234C2×C4⋊C4—1661no—
235C2×C4⋊C4—1661no—
236C2×C22⋊C4—3321no—
237C2×C22⋊C4—3321no—
238C2×C42D33211yescharacteristic
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245#107—832no—
246#107—1661no—
247#107—1661no—
248#107—1661no—
249C4×C8—21no—
250C4×C8—21no—
251#95—3321no—
252C24—3321no—
253C2×Q8—3321no—
254C2×Q8—3321no—
255C2×Q8—3321no—
256C2×Q8—3321no—
257C2×Q8—3321no—
258C2×Q8—1662no—
259C2×D4—3321no—
260C2×D4—3321no—
261C2×D4—3321no—
262C2×D4—3321no—
263C2×D4—3321no—
264C2×D4—1662no—
265C22×C4—3321no—
266C22×C4—3321no—
267C22×C4—3321no—
268C22×C4D66411yescharacteristic
269C22×C4D66411yescharacteristic
270C22×C4C2×D33211yescharacteristic
271Q16—3321no—
272Q16—3321no—
273Q16—1662no—
274Q16—1662no—
275SD16—3328no—
276D8—3321no—
277D8—3321no—
278D8—1662no—
279D8—1662no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8#1305057912yes—
283C2×C8D4×D8311yescharacteristic
284C2×C8D4×D8311yescharacteristic
285C2×C8D4×D8311yescharacteristic
286C2×C8#1305059011yescharacteristic
287C2×C8#1305059011yescharacteristic
288C2×C8#1305059111yescharacteristic
289C4⋊C4—3321no—
290C4⋊C4—3321no—
291C4⋊C4—3321no—
292C4⋊C4—6642no—
293C4⋊C4—1662no—
294C22⋊C4—3324no—
295C22⋊C4—3324no—
296C42—21no—
297C42—21no—
298C16—41no—
299C16—41no—
300C23—3322no—
301C23—6641no—
302C23—6641no—
303C23—6641no—
304C23—6641no—
305C23—6641no—
306C23—6641no—
307C23C2×D66411yescharacteristic
308Q8—3322no—
309Q8—3322no—
310Q8—6641no—
311Q8—6641no—
312D4—3322no—
313D4—3322no—
314D4—6641no—
315D4—6641no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3322no—
323C2×C4—3322no—
324C2×C4—6641no—
325C2×C4—6641no—
326C2×C4—6641no—
327C2×C4—6641no—
328C2×C4—6641no—
329C2×C4—6641no—
330C2×C4—6641no—
331C2×C4#1458176211yescharacteristic
332C2×C4#1458176711yescharacteristic
333C2×C4#1458178011yescharacteristic
334C2×C4C2×#1305057911yescharacteristic
335C2×C4#1458182011yescharacteristic
336C2×C4#1458182011yescharacteristic
337C8—22no—
338C8#1458176511yescharacteristic
339C8#1458176511yescharacteristic
340C8#1458177711yescharacteristic
341C8#1458177711yescharacteristic
342C22—13281no—
343C22—13281no—
344C22—13281no—
345C22—13281no—
346C22—6642no—
347C22—6642no—
348C22—6642no—
349C22#1912783711yescharacteristic
350C22#1912789711yescharacteristic
351C22#1912804811yescharacteristic
352C22#1912813311yescharacteristic
353C22#1912813311yescharacteristic
354C22#1912813911yescharacteristic
355C22#1912814411yescharacteristic
356C4—41no—
357C4—41no—
358C4—13281no—
359C4—6642no—
360C4—6642no—
361C4#1912761911yescharacteristic
362C4#1912785411yescharacteristic
363C4#1912790211yescharacteristic
364C4#1912806611yescharacteristic
365C2—13282no—
366C2#2490869811yescharacteristic
367C2#2490938811yescharacteristic
368C2#2490940511yescharacteristic
369C2#2490951911yescharacteristic
370C2#2490952611yescharacteristic
371C2#2490969511yescharacteristic
372C2#2490970011yescharacteristic
subgroupG/H
centerC23C2×D664
commutator, cosocleC22×C8×C83C23
FrattiniC22×C8C22×D83
FittingC83×#1374C2
socleC23×C83C2×D8
prime radicalC22×D664C22
hypercenter#1374D83
hypocenterC83#13408
LCSG ▷ C22×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×#19127506C2semidirect
3. C2×#19127506C2semidirect
6. #24908196C2semidirect
7. C83×#1374C2semidirect
193. #1374D83semidirect
194. C83#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#191280852
C2×#191275062
C2×#191275032
#249081962
C83×#13742
#1340883