Finite Group Databasebeta

← #35321339

Subgroups — #35321339

Order 21248.

626 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127934C211yesmaximal, characteristic
2C2×#107×D83C211yesmaximal, characteristic, complemented
3C2×#19127502C211yesmaximal, characteristic, complemented
4C2×(C2×D83)⋊C16C211yesmaximal, characteristic, complemented
5#24905555C211yesmaximal, characteristic, complemented
6#24905554C211yesmaximal, characteristic, complemented
7C2×#357×C83C211yesmaximal, characteristic, complemented
8C22×C8×D83C2211yescharacteristic
9C2×#14581763—21no—
10C2×C4⋊C4×D83—21no—
11C22×C83⋊C16C2211yescharacteristic
12#19127934—22no—
13#19127934C414yescomplemented
14C2×#14581726C2211yescharacteristic
15C2×#14581726C2211yescharacteristic
16C2×#14581725—21no—
17#107×D83—22no—
18#107×D83—22no—
19C2×#14581713—21no—
20#19127502—22no—
21(C2×D83)⋊C16—22no—
22C22×D8×C83C2211yescharacteristic
23C22×C16×C83C2211yescharacteristic
24C2×#107×C83C2211yescharacteristic
25#357×C83—22no—
26C22×C22⋊D83—41no—
27C22×C4×D83—41no—
28C22×C4×D83D411yescharacteristic
29C22×C83⋊C8D411yescharacteristic
30C2×C8×D83—21no—
31C2×C8×D83—21no—
32C2×C8×D83—21no—
33C2×C8×D83—21no—
34C2×C8×D83C2×C412yes—
35C2×C8×D83D412yes—
36#14581763—24no—
37#14581763—42no—
38C2×C4⋊Dic83—21no—
39C2×C4⋊Dic83—21no—
40C2×Dic83⋊C4—41no—
41C4⋊C4×D83—24no—
42C4⋊C4×D83—42no—
43C2×C22⋊Dic83—41no—
44C2×C83⋊C16—21no—
45C2×C83⋊C16—21no—
46C2×C83⋊C16—21no—
47#14581726—21no—
48#14581726—21no—
49#14581726C2×C412yescomplemented
50#14581726D412yescomplemented
51#14581725—24no—
52#14581713—24no—
53C22×D4×C83—21no—
54C2×D8×C83—21no—
55C2×D8×C83—21no—
56C2×D8×C83—21no—
57C2×D8×C83—21no—
58C2×D8×C83—21no—
59C2×D8×C83C2×C412yescomplemented
60C22×C8×C83C2311yescharacteristic
61C2×C4⋊C4×C83—21no—
62C2×C16×C83—21no—
63C2×C16×C83—21no—
64C2×C16×C83—21no—
65#107×C83—21no—
66#107×C83D412yescomplemented
67C23×D83D811yescharacteristic
68C2×C22⋊D83—44no—
69C2×C22⋊D83—82no—
70C2×C22⋊D83—82no—
71C22×Dic83—41no—
72C22×Dic83—41no—
73C22×Dic83D811yescharacteristic
74C2×C4×D83—21no—
75C2×C4×D83—21no—
76C2×C4×D83—21no—
77C2×C4×D83—21no—
78C2×C4×D83—44no—
79C2×C4×D83—82no—
80C2×C4×D83—82no—
81C2×C4×D83C22⋊C412yes—
82C2×C4×D83SD1612yes—
83C2×C83⋊C8—21no—
84C2×C83⋊C8—21no—
85C2×C83⋊C8C22⋊C412yes—
86C8×D83—22no—
87C8×D83—22no—
88C8×D83—22no—
89C8×D83—22no—
90C4⋊Dic83—22no—
91C4⋊Dic83—22no—
92C4⋊Dic83—41no—
93C4⋊Dic83—41no—
94Dic83⋊C4—44no—
95C22⋊Dic83—44no—
96C83⋊C16—41no—
97C24×C83—41no—
98C2×D4×C83—22no—
99C2×D4×C83—41no—
100C2×D4×C83—41no—
101C2×D4×C83—41no—
102C2×D4×C83—41no—
103C2×D4×C83—41no—
104C22×C4×C83—41no—
105C22×C4×C83C2×D411yescharacteristic
106D8×C83—22no—
107D8×C83—22no—
108D8×C83—41no—
109D8×C83—41no—
110C2×C8×C83C22×C411yescharacteristic
111C2×C8×C83C2×D411yescharacteristic
112C2×C8×C83C2×D411yescharacteristic
113C2×C8×C83C2×D411yescharacteristic
114C2×C8×C83#4111yescharacteristic
115C2×C8×C83#4111yescharacteristic
116C4⋊C4×C83—22no—
117C4⋊C4×C83—41no—
118C16×C83—41no—
119C23×C83—42no—
120C23×C83—81no—
121C23×C83—81no—
122C23×C83—81no—
123C23×C83—81no—
124C23×C83—81no—
125C23×C83—81no—
126C23×C83C2×D811yescharacteristic
127C22×D83—21no—
128C22×D83—21no—
129C22×D83—21no—
130C22×D83—21no—
131C22×D83#10212yes—
132C22×D83D1612yes—
133C22×D83SD3212yes—
134D4×C83—42no—
135D4×C83—42no—
136D4×C83—81no—
137D4×C83—81no—
138C2×C4×C83—42no—
139C2×C4×C83—81no—
140C2×C4×C83—81no—
141C2×C4×C83C2×C22⋊C411yescharacteristic
142C2×C4×C83#12011yescharacteristic
143C2×C4×C83#12311yescharacteristic
144C2×C4×C83C2×SD1611yescharacteristic
145C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C83#13711yescharacteristic
147C22⋊D83—88no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150C2×Dic83—42no—
151C2×Dic83—42no—
152C2×Dic83—81no—
153C2×Dic83—81no—
154C2×Dic83—81no—
155C2×Dic83—81no—
156C2×Dic83#10212yes—
157C4×D83—22no—
158C4×D83—22no—
159C4×D83—22no—
160C4×D83—22no—
161C4×D83—88no—
162C8×C83C4×D411yescharacteristic
163C8×C83C4×D411yescharacteristic
164C8×C83#12111yescharacteristic
165C8×C83#12111yescharacteristic
166C83⋊C8—22no—
167C22×C83—82no—
168C22×C83—82no—
169C22×C83—82no—
170C22×C83—161no—
171C22×C83—161no—
172C22×C83—161no—
173C22×C83—161no—
174C22×C83C2×#10211yescharacteristic
175C22×C83#44711yescharacteristic
176C22×C83#48011yescharacteristic
177C22×C83C2×D1611yescharacteristic
178C22×C83C2×SD3211yescharacteristic
179C22×C83#50911yescharacteristic
180C22×C83#51011yescharacteristic
181C2×D83—22no—
182C2×D83—22no—
183C2×D83—22no—
184C2×D83—22no—
185C2×D83—22no—
186C2×D83—22no—
187C2×D83#35714yescomplemented
188C4×C83—82no—
189C4×C83#38611yescharacteristic
190C4×C83#41711yescharacteristic
191C4×C83#44811yescharacteristic
192C4×C83#48111yescharacteristic
193Dic83—22no—
194Dic83—82no—
195Dic83—82no—
196#12991—831nomaximal, Sylow
197C2×C83—162no—
198C2×C83#187411yescharacteristic
199C2×C83C2×#35711yescharacteristic
200C2×C83#213911yescharacteristic
201C2×C83#218411yescharacteristic
202C2×C83#218511yescharacteristic
203C2×C83#223211yescharacteristic
204C2×C83#223311yescharacteristic
205D83—24no—
206C2×#466—831no—
207C22×#107—831no—
208C2×#357—831no—
209C2×#357D8311yescharacteristic, complemented
210C2×C22⋊C16—831no—
211#1380—831no—
212#1380—831no—
213C83#1299111yescharacteristic, complemented, Sylow
214C22×D8C2×D8311yescharacteristic
215C23×C8—831no—
216C2×#121—1661no—
217C22×C4⋊C4—1661no—
218C22×C16—831no—
219C22×C16C2×D8311yescharacteristic
220#466—834no—
221#466—1662no—
222C2×#107—831no—
223C2×#107—831no—
224C2×#107—1662no—
225C2×#107—1661no—
226C2×#107—1662no—
227C2×#107C2×D8311yescharacteristic
228C2×#102—1661no—
229#357—22no—
230#357—1662no—
231C22⋊C16—1662no—
232C22×D4—21no—
233C22×D4—3321no—
234C23×C4—3321no—
235C23×C4—831no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8—21no—
240C2×D8—21no—
241C2×D8C4×D8312yescomplemented
242C22×C8—831no—
243C22×C8—832no—
244C22×C8—832no—
245C22×C8—1661no—
246C22×C8—1661no—
247C22×C8—1661no—
248C22×C8—1661no—
249C22×C8C22×D8311yescharacteristic
250#121—3322no—
251#121—1664no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—3322no—
254C2×C4⋊C4—3321no—
255C2×C4⋊C4—1664no—
256C2×C4⋊C4—1661no—
257C2×C4⋊C4—1661no—
258C2×C22⋊C4—3321no—
259C2×C16—21no—
260C2×C16—21no—
261C2×C16—21no—
262C2×C16—1661no—
263C2×C16—1661no—
264C2×C16—1661no—
265#107—21no—
266#107—832no—
267#107—832no—
268#107—1664no—
269#107—1661no—
270#107—1661no—
271#107C22⋊D8312yescomplemented
272#102—1664no—
273C24—41no—
274C24—831no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—3324no—
282C2×D4—6642no—
283C2×D4—6642no—
284C22×C4—41no—
285C22×C4—3324no—
286C22×C4—3321no—
287C22×C4—3321no—
288C22×C4—831no—
289C22×C4—832no—
290C22×C4—832no—
291C22×C4—6642no—
292C22×C4—6642no—
293C22×C4—1661no—
294C22×C4—1661no—
295C22×C4—1661no—
296C22×C4—1661no—
297C22×C4D4×D8311yescharacteristic
298D8—22no—
299D8—22no—
300D8—41no—
301D8—41no—
302C2×C8—832no—
303C2×C8—1661no—
304C2×C8—1661no—
305C2×C8—1662no—
306C2×C8—1662no—
307C2×C8—1662no—
308C2×C8—1662no—
309C2×C8C2×C4×D8311yescharacteristic
310C2×C8D4×D8311yescharacteristic
311C2×C8D4×D8311yescharacteristic
312C2×C8C2×C22⋊D8311yescharacteristic
313C2×C8#1305058911yescharacteristic
314C2×C8#1305059011yescharacteristic
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—3324no—
318C4⋊C4—3321no—
319C4⋊C4—3321no—
320C4⋊C4—1662no—
321C4⋊C4—1662no—
322C22⋊C4—3324no—
323C16—41no—
324C16—3321no—
325C23—42no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—832no—
333C23—832no—
334C23—832no—
335C23—1661no—
336C23—1661no—
337C23—1661no—
338C23—1661no—
339C23D8×D8311yescharacteristic
340D4—42no—
341D4—42no—
342D4—81no—
343D4—81no—
344D4—6648no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—3322no—
349C2×C4—3322no—
350C2×C4—832no—
351C2×C4—6648no—
352C2×C4—6641no—
353C2×C4—6641no—
354C2×C4—6641no—
355C2×C4—6641no—
356C2×C4—1661no—
357C2×C4—1661no—
358C2×C4—1662no—
359C2×C4—1662no—
360C2×C4—1662no—
361C2×C4—1662no—
362C2×C4C22⋊C4×D8311yescharacteristic
363C2×C4#1458176011yescharacteristic
364C2×C4#1458177411yescharacteristic
365C2×C4SD16×D8311yescharacteristic
366C2×C4#1458181611yescharacteristic
367C2×C4#1458182111yescharacteristic
368C8—1662no—
369C8(C22⋊D83)⋊C411yescharacteristic
370C8C4×C22⋊D8311yescharacteristic
371C8#1458176311yescharacteristic
372C8#1458176511yescharacteristic
373C22—82no—
374C22—82no—
375C22—82no—
376C22—161no—
377C22—161no—
378C22—161no—
379C22—161no—
380C22—834no—
381C22—1662no—
382C22—1662no—
383C22—1662no—
384C22—1662no—
385C22—1662no—
386C22—1662no—
387C22#102×D8311yescharacteristic
388C22#1912783311yescharacteristic
389C22#1912801311yescharacteristic
390C22D16×D8311yescharacteristic
391C22SD32×D8311yescharacteristic
392C22#1912813511yescharacteristic
393C22#1912814011yescharacteristic
394C4—82no—
395C4—6642no—
396C4—6642no—
397C4—1662no—
398C4#1912757711yescharacteristic
399C4#1912769911yescharacteristic
400C4#1912783811yescharacteristic
401C4#1912801811yescharacteristic
402C2—162no—
403C2—1664no—
404C2#2490777711yescharacteristic
405C2#357×D8311yescharacteristic
406C2#2490917211yescharacteristic
407C2#2490937311yescharacteristic
408C2#2490937811yescharacteristic
409C2#2490964211yescharacteristic
410C2#2490964711yescharacteristic
subgroupG/H
centerC23D8×D83
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC2×#357×C83C2
socleC23×C83C2×D8
prime radicalC2×#19127934C2
cosocleC22×C8×C83C23
hypercenterC2×#357D83
hypocenterC83#12991
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#107×D83C2semidirect
3. C2×#19127502C2semidirect
4. C2×(C2×D83)⋊C16C2semidirect
5. #24905555C2semidirect
6. #24905554C2semidirect
7. C2×#357×C83C2semidirect
13. #19127934C4semidirect
49. #14581726C2×C4semidirect
50. #14581726D4semidirect
59. C2×D8×C83C2×C4semidirect
66. #107×C83D4semidirect
187. C2×D83#357semidirect
209. C2×#357D83semidirect
213. C83#12991semidirect
241. C2×D8C4×D83semidirect
271. #107C22⋊D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191279342
C2×#107×D832
C2×#191275022
C2×(C2×D83)⋊C162
#249055552
#249055542
C2×#357×C832
#1299183