Finite Group Databasebeta

← #35307849

Subgroups — #35307849

Order 21248.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912412C211yesmaximal, characteristic
2#24908424C211yesmaximal, characteristic, complemented
3#24908226C211yesmaximal, characteristic, complemented
4#24907464C211yesmaximal, characteristic
5C2×#19127446C211yesmaximal, characteristic, complemented
6C2×#19127430C211yesmaximal, characteristic
7C83×#1279C211yesmaximal, characteristic, complemented
8C2×#14581792C2211yescharacteristic
9C2×#14581772—21no—
10C2×#14581772—21no—
11C2×C4×D332C2211yescharacteristic
12C2×#14581723—21no—
13C2×C4⋊(C83⋊C8)C2211yescharacteristic
14C2×#14581714—21no—
15#19127638—22no—
16#19127603—21no—
17#19127571—21no—
18#19127571C2211yescharacteristic
19#19127464—22no—
20#19127464—21no—
21#19127463—21no—
22#19127446—22no—
23#19127430—22no—
24C2×C4⋊C8×C83C2211yescharacteristic
25C2×C4×C8×C83C2211yescharacteristic
26C4×C4⋊C4×C83C2211yescharacteristic
27C22×Dic166—21no—
28C22×D332D411yescharacteristic
29C22×C4×D83—21no—
30C22×C83⋊C8—21no—
31#14581792—21no—
32#14581792—21no—
33#14581792—21no—
34#14581792—21no—
35#14581772—42no—
36#14581772—42no—
37#14581772—42no—
38#14581772—42no—
39C4×D332—21no—
40C4×D332—21no—
41C4×D332—21no—
42C4×D332—21no—
43C2×C4⋊Dic83—22no—
44C2×C4⋊Dic83—22no—
45C2×C4⋊Dic83—21no—
46C2×C4⋊Dic83—21no—
47C2×C4⋊Dic83—21no—
48C2×C4⋊Dic83—21no—
49C2×C4⋊Dic83D411yescharacteristic
50C2×C4⋊Dic83D412yes—
51C2×(C2×D83)⋊C4—22no—
52C2×(C2×D83)⋊C4—22no—
53C2×(C2×D83)⋊C4—21no—
54#14581723—42no—
55C4⋊(C83⋊C8)—21no—
56C4⋊(C83⋊C8)D412yes—
57#14581714—42no—
58C22×C8×C83—21no—
59C22×C8×C83—21no—
60C2×C4⋊C4×C83D411yescharacteristic
61C2×C4⋊C4×C83D411yescharacteristic
62C2×C42×C83—21no—
63C2×C42×C83C2311yescharacteristic
64C4⋊C8×C83—21no—
65C4⋊C8×C83—21no—
66C4×C8×C83—21no—
67C4×C8×C83—21no—
68#95×C83—21no—
69C23×D83—21no—
70C2×Dic166—41no—
71C2×Dic166—41no—
72C2×Dic166—41no—
73C2×Dic166—41no—
74C2×Dic166—41no—
75C2×Dic166—41no—
76C2×D332—21no—
77C2×D332—21no—
78C2×D332—21no—
79C2×D332—21no—
80C2×D332—21no—
81C2×D332SD1612yes—
82C22×Dic83—21no—
83C22×Dic83—22no—
84C22×Dic83—41no—
85C2×C4×D83—41no—
86C2×C4×D83—41no—
87C2×C4×D83—41no—
88C2×C4×D83—41no—
89C2×C4×D83—41no—
90C2×C4×D83—41no—
91C2×C83⋊C8—22no—
92C2×C83⋊C8—41no—
93C2×C83⋊C8—41no—
94C4⋊Dic83—22no—
95C4⋊Dic83—21no—
96C4⋊Dic83—22no—
97C4⋊Dic83—21no—
98C4⋊Dic83—44no—
99C4⋊Dic83—44no—
100C4⋊Dic83—41no—
101C4⋊Dic83—41no—
102C4⋊Dic83—42no—
103C4⋊Dic83—41no—
104C4⋊Dic83—41no—
105C4⋊Dic83—41no—
106C4⋊Dic83—41no—
107(C2×D83)⋊C4—44no—
108(C2×D83)⋊C4—44no—
109(C2×D83)⋊C4—41no—
110(C2×D83)⋊C4—41no—
111C22×C4×C83—21no—
112C22×C4×C83—21no—
113C22×C4×C83C2×D411yescharacteristic
114C22×C4×C83C2×D411yescharacteristic
115C22×C4×C83C2×D411yescharacteristic
116C2×C8×C83—22no—
117C2×C8×C83—41no—
118C2×C8×C83—41no—
119C2×C8×C83—41no—
120C2×C8×C83—41no—
121C2×C8×C83—41no—
122C4⋊C4×C83—21no—
123C4⋊C4×C83—21no—
124C4⋊C4×C83D812yes—
125C4⋊C4×C83SD1612yes—
126C42×C83—41no—
127C42×C83—41no—
128C42×C83C2×D411yescharacteristic
129C42×C83#4111yescharacteristic
130C42×C83#4111yescharacteristic
131C42×C83#4111yescharacteristic
132C23×C83#12011yescharacteristic
133C22×D83—22no—
134C22×D83—41no—
135C22×D83—41no—
136C22×D83—41no—
137C22×D83—41no—
138C22×D83—41no—
139C22×D83—41no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—22no—
143C2×C4×C83—22no—
144C2×C4×C83—41no—
145C2×C4×C83—41no—
146C2×C4×C83—41no—
147C2×C4×C83—41no—
148C2×C4×C83#12111yescharacteristic
149C2×C4×C83#12111yescharacteristic
150C2×C4×C83#12111yescharacteristic
151C2×C4×C83#12311yescharacteristic
152C2×C4×C83#12311yescharacteristic
153C2×C4×C83#12411yescharacteristic
154C2×C4×C83C2×D811yescharacteristic
155C2×C4×C83C2×SD1611yescharacteristic
156C2×C4×C83C2×SD1611yescharacteristic
157C2×C4×C83#13511yescharacteristic
158C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C83#13711yescharacteristic
161C2×C4×C83#13711yescharacteristic
162C2×Dic83—41no—
163C2×Dic83—42no—
164C2×Dic83—42no—
165C2×Dic83—41no—
166C2×Dic83—42no—
167C2×Dic83—41no—
168C2×Dic83—81no—
169C2×Dic83—81no—
170C2×Dic83—81no—
171D332—22no—
172D332—22no—
173D332—41no—
174D332—41no—
175C4×D83—81no—
176C4×D83—81no—
177C4×D83—81no—
178C4×D83—81no—
179Dic166—81no—
180Dic166—81no—
181Dic166—81no—
182Dic166—81no—
183C8×C83—42no—
184C8×C83—81no—
185C83⋊C8—42no—
186C22×C83#39411yescharacteristic
187C22×C83#44711yescharacteristic
188C22×C83#44811yescharacteristic
189C22×C83#45011yescharacteristic
190C22×C83#45211yescharacteristic
191C22×C83#45411yescharacteristic
192C22×C83#45611yescharacteristic
193C2×D83—42no—
194C2×D83—42no—
195C2×D83—42no—
196C2×D83—81no—
197C2×D83—81no—
198C2×D83—81no—
199C2×D83—81no—
200C4×C83—21no—
201C4×C83—21no—
202C4×C83—42no—
203C4×C83—42no—
204C4×C83#45911yescharacteristic
205C4×C83#46011yescharacteristic
206C4×C83#46511yescharacteristic
207C4×C83#47011yescharacteristic
208C4×C83#48311yescharacteristic
209C4×C83#48511yescharacteristic
210C4×C83#48611yescharacteristic
211C4×C83#49011yescharacteristic
212Dic83—82no—
213Dic83—81no—
214Dic83—161no—
215#10420—831nomaximal, Sylow
216C2×C83#162711yescharacteristic
217C2×C83#163511yescharacteristic
218C2×C83#164711yescharacteristic
219C2×C83#165111yescharacteristic
220C2×C83#203511yescharacteristic
221C2×C83#203811yescharacteristic
222C2×C83#204111yescharacteristic
223D83—82no—
224#2542—831no—
225#1990—831no—
226#1948—831no—
227#1802—831no—
228C2×#332—831no—
229C2×D4⋊C8—831no—
230#1279D8311yescharacteristic, complemented
231C83#1042011yescharacteristic, complemented, Sylow
232C2×C4⋊Q8—831no—
233C2×C22⋊Q8—1661no—
234C2×C22⋊Q8—1661no—
235C2×C4×D4—831no—
236C2×#106—1661no—
237C2×C4⋊C8—831no—
238C2×C4⋊C8C2×D8311yescharacteristic
239C2×#102—1661no—
240C2×C4×C8C2×D8311yescharacteristic
241#399—1662no—
242#390—1661no—
243#384—831no—
244#384—1661no—
245C4×C4⋊C4C2×D8311yescharacteristic
246#340—1661no—
247#340—1662no—
248#340—1661no—
249#332—1662no—
250D4⋊C8—1662no—
251C22×Q8—1661no—
252C22×D4—831no—
253C23×C4—1661no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—1661no—
257C4⋊Q8—1661no—
258C4⋊Q8—1661no—
259C4⋊Q8—1661no—
260C4⋊Q8—1661no—
261C22⋊Q8—3322no—
262C22⋊Q8—3322no—
263C22⋊Q8—3322no—
264C22⋊Q8—3322no—
265C4×D4—1661no—
266C4×D4—1661no—
267C4×D4—1661no—
268C4×D4—1661no—
269C2×C4⋊C4—831no—
270C2×C4⋊C4—832no—
271C2×C4⋊C4—1662no—
272C2×C4⋊C4—1662no—
273C2×C4⋊C4—1661no—
274C2×C4⋊C4—1661no—
275C2×C4⋊C4—1661no—
276C2×C4⋊C4—1661no—
277C2×C4⋊C4D33211yescharacteristic
278C2×C4⋊C4D33211yescharacteristic
279C2×C22⋊C4—1662no—
280C2×C22⋊C4—1662no—
281C2×C22⋊C4—1661no—
282C2×C42—21no—
283C2×C42C22×D8311yescharacteristic
284#106—3322no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—832no—
288C4⋊C8—1661no—
289#102—3322no—
290C4×C8—21no—
291C4×C8—21no—
292#95—21no—
293C24—1661no—
294C2×Q8—3321no—
295C2×Q8—3321no—
296C2×Q8—3321no—
297C2×Q8—3321no—
298C2×Q8—3321no—
299C2×Q8—3321no—
300C2×D4—832no—
301C2×D4—1661no—
302C2×D4—1661no—
303C2×D4—1661no—
304C2×D4—1661no—
305C2×D4—1661no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—3321no—
309C22×C4—3321no—
310C22×C4—3321no—
311C22×C4—3321no—
312C22×C4—3321no—
313C22×C4—3321no—
314C22×C4—3321no—
315C22×C4—1662no—
316C22×C4—1661no—
317C22×C4D4×D8311yescharacteristic
318C22×C4D4×D8311yescharacteristic
319C22×C4C2×D33211yescharacteristic
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—3321no—
327C2×C8—3321no—
328C2×C8—1662no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—3324no—
332C4⋊C4—3324no—
333C4⋊C4—3322no—
334C4⋊C4—3321no—
335C4⋊C4—3321no—
336C4⋊C4—3321no—
337C4⋊C4—3321no—
338C4⋊C4—3321no—
339C4⋊C4—3321no—
340C4⋊C4—1661no—
341C4⋊C4—1662no—
342C4⋊C4—1661no—
343C4⋊C4—1662no—
344C4⋊C4D66412yes—
345C4⋊C4#1305057912yes—
346C22⋊C4—3324no—
347C22⋊C4—3324no—
348C22⋊C4—3321no—
349C22⋊C4—3321no—
350C42—41no—
351C42—41no—
352C42D4×D8311yescharacteristic
353C42#1305059011yescharacteristic
354C42#1305059011yescharacteristic
355C42#1305059111yescharacteristic
356C23—3321no—
357C23—3321no—
358C23—3321no—
359C23—3321no—
360C23—3321no—
361C23—3321no—
362C23—1662no—
363C23#1458176211yescharacteristic
364Q8—6641no—
365Q8—6641no—
366Q8—6641no—
367Q8—6641no—
368D4—3321no—
369D4—3321no—
370D4—1662no—
371D4—1662no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—3322no—
381C2×C4—3321no—
382C2×C4—3322no—
383C2×C4—3321no—
384C2×C4—3321no—
385C2×C4—3322no—
386C2×C4—6641no—
387C2×C4—6641no—
388C2×C4—6641no—
389C2×C4—6641no—
390C2×C4—6641no—
391C2×C4—6641no—
392C2×C4—6641no—
393C2×C4#1458176511yescharacteristic
394C2×C4#1458176511yescharacteristic
395C2×C4#1458176711yescharacteristic
396C2×C4#1458177711yescharacteristic
397C2×C4#1458177711yescharacteristic
398C2×C4#1458178011yescharacteristic
399C2×C4C2×D66411yescharacteristic
400C2×C4SD16×D8311yescharacteristic
401C2×C4C2×#1305057911yescharacteristic
402C2×C4#1458181111yescharacteristic
403C2×C4#1458182011yescharacteristic
404C2×C4#1458182011yescharacteristic
405C2×C4#1458182111yescharacteristic
406C2×C4#1458182411yescharacteristic
407C8—42no—
408C8—81no—
409C8—3322no—
410C22—3322no—
411C22—3322no—
412C22—3322no—
413C22—6641no—
414C22—6641no—
415C22—6641no—
416C22—6641no—
417C22#1912761911yescharacteristic
418C22#1912783711yescharacteristic
419C22#1912784111yescharacteristic
420C22#1912785411yescharacteristic
421C22#1912786411yescharacteristic
422C22#1912787511yescharacteristic
423C22#1912788511yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—13281no—
429C4—6641no—
430C4—6642no—
431C4#1912789711yescharacteristic
432C4#1912790211yescharacteristic
433C4#1912792911yescharacteristic
434C4#1912795811yescharacteristic
435C4#1912803311yescharacteristic
436C4#1912804411yescharacteristic
437C4#1912804811yescharacteristic
438C4#1912806611yescharacteristic
439C2—6642no—
440C2#2490656811yescharacteristic
441C2#2490661611yescharacteristic
442C2#2490670011yescharacteristic
443C2#2490672911yescharacteristic
444C2#2490866211yescharacteristic
445C2#2490868311yescharacteristic
446C2#2490869811yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1279C2
socleC23×C83#120
prime radicalC22×D332D4
hypercenter#1279D83
hypocenterC83#10420
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #24908424C2semidirect
3. #24908226C2semidirect
5. C2×#19127446C2semidirect
7. C83×#1279C2semidirect
230. #1279D83semidirect
231. C83#10420semidirect

Maximal subgroups

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

subgroupindex
#249124122
#249084242
#249082262
#249074642
C2×#191274462
C2×#191274302
C83×#12792
#1042083