Finite Group Databasebeta

← #35323755

Subgroups — #35323755

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×#19127504C211yesmaximal, characteristic, complemented
3C2×#19127504C211yesmaximal, characteristic, complemented
4C2×#19127501C211yesmaximal, characteristic
5C2×#19127501C211yesmaximal, characteristic
6#24905541C211yesmaximal, characteristic, complemented
7C83×#1942C211yesmaximal, characteristic, complemented
8C22×Dic332C2211yescharacteristic
9C22×#13050579—21no—
10C22×D664C2211yescharacteristic
11C2×#14581780—21no—
12C22×C83⋊C16C2211yescharacteristic
13C22×C83⋊C16C2211yescharacteristic
14#19128085—22no—
15#19128085—22no—
16#19127504—22no—
17#19127504—22no—
18#19127501—22no—
19#19127501—22no—
20C2×#107×C83C2211yescharacteristic
21C2×#107×C83C2211yescharacteristic
22C2×C4×C8×C83C2211yescharacteristic
23#389×C83—21no—
24#340×C83—21no—
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×(C2×D83)⋊C4—41no—
45C2×(C2×D83)⋊C4—41no—
46C2×C83⋊C16—21no—
47C2×C83⋊C16—21no—
48C2×C83⋊C16—21no—
49C2×C83⋊C16—21no—
50C2×C83⋊C16—21no—
51C2×C83⋊C16—21no—
52C22×C8×C83D411yescharacteristic
53C22×C8×C83C2311yescharacteristic
54C2×C4⋊C4×C83—21no—
55C2×C4⋊C4×C83—21no—
56C2×C4⋊C4×C83—41no—
57C2×C42×C83D411yescharacteristic
58#107×C83—21no—
59#107×C83—21no—
60#107×C83—21no—
61#107×C83D412yes—
62C4×C8×C83—21no—
63C4×C8×C83—21no—
64#95×C83—41no—
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—
79Dic332—22no—
80Dic332—22no—
81Dic332—41no—
82Dic332—41no—
83#13050579—48no—
84D664—22no—
85D664—22no—
86D664—41no—
87D664—41no—
88(C2×D83)⋊C4—44no—
89(C2×D83)⋊C4—44no—
90C83⋊C16—41no—
91C83⋊C16—41no—
92C22×C4×C83—41no—
93C22×C4×C83—41no—
94C22×C4×C83D811yescharacteristic
95C22×C4×C83D811yescharacteristic
96C22×C4×C83C2×D411yescharacteristic
97C2×C8×C83—21no—
98C2×C8×C83—21no—
99C2×C8×C83SD1612yes—
100C2×C8×C83C2×D411yescharacteristic
101C2×C8×C83C2×D411yescharacteristic
102C2×C8×C83C2×D411yescharacteristic
103C2×C8×C83#4111yescharacteristic
104C2×C8×C83#4111yescharacteristic
105C2×C8×C83#4111yescharacteristic
106C4⋊C4×C83—22no—
107C4⋊C4×C83—41no—
108C4⋊C4×C83—41no—
109C4⋊C4×C83—41no—
110C4⋊C4×C83—82no—
111C42×C83—21no—
112C42×C83—21no—
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—42no—
128C2×C4×C83—81no—
129C2×C4×C83—81no—
130C2×C4×C83—81no—
131C2×C4×C83—81no—
132C2×C4×C83—81no—
133C2×C4×C83#12011yescharacteristic
134C2×C4×C83#12111yescharacteristic
135C2×C4×C83#12411yescharacteristic
136C2×C4×C83C2×SD1611yescharacteristic
137C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
139C2×Dic83—42no—
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—82no—
172C4×C83—161no—
173C4×C83#39411yescharacteristic
174C4×C83#45011yescharacteristic
175C4×C83#46011yescharacteristic
176C4×C83#49011yescharacteristic
177Dic83—82no—
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#1942D8311yescharacteristic, complemented
193#1374—831no—
194C83#1340811yescharacteristic, complemented, Sylow
195C22×Q16—831no—
196C22×SD16—1661no—
197C22×D8—831no—
198C2×#124—1661no—
199C22×C16—831no—
200C22×C16—831no—
201#495—1662no—
202#495—1662no—
203C2×#107C2×D8311yescharacteristic
204C2×#107C2×D8311yescharacteristic
205C2×C4×C8C2×D8311yescharacteristic
206#389—21no—
207#358—1662no—
208#358—1662no—
209#357—1662no—
210#357—1662no—
211#340—21no—
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×C8C22⋊D8311yescharacteristic
230C22×C8C22×D8311yescharacteristic
231#124—3322no—
232#124—1664no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C22⋊C4—3321no—
237C2×C22⋊C4—3321no—
238C2×C42C22⋊D8311yescharacteristic
239C2×C16—1661no—
240C2×C16—1661no—
241C2×C16—1661no—
242C2×C16—1661no—
243C2×C16—1661no—
244C2×C16—1661no—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D33212yes—
249C4×C8—21no—
250C4×C8—21no—
251#95—41no—
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—41no—
266C22×C4—41no—
267C22×C4—3321no—
268C22×C4#1305057511yescharacteristic
269C22×C4#1305057511yescharacteristic
270C22×C4C2×C22⋊D8311yescharacteristic
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#1305057712yes—
283C2×C8D4×D8311yescharacteristic
284C2×C8D4×D8311yescharacteristic
285C2×C8C2×D33211yescharacteristic
286C2×C8#1305059011yescharacteristic
287C2×C8#1305059111yescharacteristic
288C2×C8#1305059111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C22⋊C4—3324no—
295C22⋊C4—3324no—
296C42—21no—
297C42—21no—
298C16—3321no—
299C16—3321no—
300C23—3322no—
301C23—6641no—
302C23—6641no—
303C23—6641no—
304C23—6641no—
305C23—6641no—
306C23—6641no—
307C23C2×#1305057511yescharacteristic
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—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—3322no—
329C2×C4—6641no—
330C2×C4—6641no—
331C2×C4#1458176011yescharacteristic
332C2×C4#1458176611yescharacteristic
333C2×C4#1458178111yescharacteristic
334C2×C4C2×#1305057711yescharacteristic
335C2×C4#1458181711yescharacteristic
336C2×C4#1458181711yescharacteristic
337C8—22no—
338C8#1458176711yescharacteristic
339C8#1458176711yescharacteristic
340C8#1458177711yescharacteristic
341C8#1458177711yescharacteristic
342C22—13281no—
343C22—13281no—
344C22—13281no—
345C22—13281no—
346C22—6642no—
347C22—6642no—
348C22—6642no—
349C22#1912783411yescharacteristic
350C22#1912789611yescharacteristic
351C22#1912804911yescharacteristic
352C22#1912813111yescharacteristic
353C22#1912813111yescharacteristic
354C22#1912813711yescharacteristic
355C22#1912814211yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—161no—
360C4—6642no—
361C4#1912761811yescharacteristic
362C4#1912785111yescharacteristic
363C4#1912790111yescharacteristic
364C4#1912806711yescharacteristic
365C2—13282no—
366C2#2490869711yescharacteristic
367C2#2490938411yescharacteristic
368C2#2490940111yescharacteristic
369C2#2490951811yescharacteristic
370C2#2490952511yescharacteristic
371C2#2490969711yescharacteristic
372C2#2490970211yescharacteristic
subgroupG/H
centerC23C2×#13050575
commutator, cosocleC22×C8×C83C23
FrattiniC22×C8C22×D83
FittingC83×#1942C2
socleC23×C83C2×D8
prime radicalC22×D664C22
hypercenter#1942D83
hypocenterC83#13408
LCSG ▷ C22×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C2×#19127504C2semidirect
3. C2×#19127504C2semidirect
6. #24905541C2semidirect
7. C83×#1942C2semidirect
192. #1942D83semidirect
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×#191275042
C2×#191275012
#249055412
C83×#19422
#1340883