Finite Group Databasebeta

← #35307845

Subgroups — #35307845

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#24912417C211yesmaximal, characteristic
2#24908425C211yesmaximal, characteristic, complemented
3#24908227C211yesmaximal, characteristic, complemented
4#24907464C211yesmaximal, characteristic
5C2×#19127428C211yesmaximal, characteristic
6#24905302C211yesmaximal, characteristic, complemented
7C2×#332×C83C211yesmaximal, characteristic, complemented
8C2×#14581768—21no—
9C2×#14581768—21no—
10C2×C4×D332C2211yescharacteristic
11C2×#14581724—21no—
12C2×#14581714—21no—
13C2×C4×C83⋊C8C2211yescharacteristic
14#19127636—22no—
15#19127602—21no—
16#19127571C2211yescharacteristic
17#19127570—21no—
18C4×C4⋊Dic83C2211yescharacteristic
19#19127464—21no—
20#19127464—21no—
21#19127463—22no—
22#19127428—22no—
23C2×C4⋊Q8×C83C2211yescharacteristic
24C2×C4⋊C8×C83C2211yescharacteristic
25C2×C4⋊C8×C83C2211yescharacteristic
26#332×C83—22no—
27C22×D332D411yescharacteristic
28C22×C4×D83—21no—
29C22×C83⋊C8—21no—
30#14581768—42no—
31#14581768—42no—
32#14581768—42no—
33#14581768—42no—
34C4×D332—21no—
35C4×D332—21no—
36C4×D332—21no—
37C4×D332—21no—
38C2×C4⋊Dic83—21no—
39C2×C4⋊Dic83—21no—
40C2×C4⋊Dic83—21no—
41C2×C4⋊Dic83D411yescharacteristic
42C2×C4⋊Dic83D411yescharacteristic
43C2×C4⋊Dic83D411yescharacteristic
44C2×Dic83⋊C4—22no—
45C2×Dic83⋊C4—22no—
46C2×(C2×D83)⋊C4—22no—
47C2×(C2×D83)⋊C4—22no—
48C2×(C2×D83)⋊C4—21no—
49C2×C4×Dic83—21no—
50#14581724—42no—
51#14581714—42no—
52C4×C83⋊C8—21no—
53C4×C83⋊C8—21no—
54C83⋊#95—21no—
55C22×Q8×C83—21no—
56C22×C8×C83—21no—
57C22×C8×C83—21no—
58C4⋊Q8×C83—21no—
59C4⋊Q8×C83—21no—
60C4⋊Q8×C83—21no—
61C4⋊Q8×C83—21no—
62C2×C4⋊C4×C83—21no—
63C2×C4⋊C4×C83D412yes—
64C2×C42×C83C2311yescharacteristic
65C4⋊C8×C83—21no—
66C4⋊C8×C83—21no—
67C4⋊C8×C83—21no—
68C4⋊C8×C83D412yes—
69C23×D83—21no—
70C2×D332—21no—
71C2×D332—21no—
72C2×D332—21no—
73C2×D332—21no—
74C2×D332—21no—
75C2×D332SD1612yes—
76C22×Dic83—21no—
77C22×Dic83—21no—
78C22×Dic83—21no—
79C22×Dic83—41no—
80C2×C4×D83—41no—
81C2×C4×D83—41no—
82C2×C4×D83—41no—
83C2×C4×D83—41no—
84C2×C4×D83—41no—
85C2×C4×D83—41no—
86C2×C83⋊C8—22no—
87C2×C83⋊C8—41no—
88C2×C83⋊C8—41no—
89C4⋊Dic83—21no—
90C4⋊Dic83—21no—
91C4⋊Dic83—21no—
92C4⋊Dic83—21no—
93C4⋊Dic83—42no—
94C4⋊Dic83—41no—
95C4⋊Dic83—41no—
96C4⋊Dic83—41no—
97C4⋊Dic83—41no—
98C4⋊Dic83D812yes—
99C4⋊Dic83SD1612yes—
100Dic83⋊C4—44no—
101Dic83⋊C4—44no—
102(C2×D83)⋊C4—44no—
103(C2×D83)⋊C4—44no—
104(C2×D83)⋊C4—41no—
105(C2×D83)⋊C4—41no—
106C4×Dic83—41no—
107C4×Dic83—41no—
108C2×Q8×C83—41no—
109C2×Q8×C83—41no—
110C2×Q8×C83—41no—
111C2×Q8×C83—41no—
112C2×Q8×C83—41no—
113C2×Q8×C83—41no—
114C22×C4×C83—22no—
115C22×C4×C83C2×D411yescharacteristic
116C22×C4×C83C2×D411yescharacteristic
117C22×C4×C83C2×D411yescharacteristic
118C2×C8×C83—22no—
119C2×C8×C83—41no—
120C2×C8×C83—41no—
121C2×C8×C83—41no—
122C2×C8×C83—41no—
123C2×C8×C83—41no—
124C4⋊C4×C83—22no—
125C4⋊C4×C83—22no—
126C4⋊C4×C83—41no—
127C4⋊C4×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—
140Q8×C83—81no—
141Q8×C83—81no—
142Q8×C83—81no—
143Q8×C83—81no—
144C2×C4×C83—21no—
145C2×C4×C83—21no—
146C2×C4×C83—42no—
147C2×C4×C83—42no—
148C2×C4×C83—42no—
149C2×C4×C83#12111yescharacteristic
150C2×C4×C83#12111yescharacteristic
151C2×C4×C83#12111yescharacteristic
152C2×C4×C83#12311yescharacteristic
153C2×C4×C83#12311yescharacteristic
154C2×C4×C83#12411yescharacteristic
155C2×C4×C83C2×D811yescharacteristic
156C2×C4×C83C2×SD1611yescharacteristic
157C2×C4×C83C2×SD1611yescharacteristic
158C2×C4×C83#13511yescharacteristic
159C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C83#13711yescharacteristic
162C2×C4×C83#13711yescharacteristic
163C2×Dic83—22no—
164C2×Dic83—22no—
165C2×Dic83—41no—
166C2×Dic83—41no—
167C2×Dic83—41no—
168C2×Dic83—41no—
169C2×Dic83—41no—
170C2×Dic83—41no—
171C2×Dic83—41no—
172C2×Dic83—81no—
173C2×Dic83—81no—
174C2×Dic83—81no—
175D332—22no—
176D332—22no—
177D332—41no—
178D332—41no—
179C4×D83—81no—
180C4×D83—81no—
181C4×D83—81no—
182C4×D83—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—82no—
203C4×C83#45911yescharacteristic
204C4×C83#46011yescharacteristic
205C4×C83#46511yescharacteristic
206C4×C83#47011yescharacteristic
207C4×C83#48311yescharacteristic
208C4×C83#48511yescharacteristic
209C4×C83#48611yescharacteristic
210C4×C83#49011yescharacteristic
211Dic83—42no—
212Dic83—42no—
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×#332D8311yescharacteristic, complemented
229C2×D4⋊C8—831no—
230#1279—831no—
231C83#1042011yescharacteristic, complemented, Sylow
232C2×C4⋊Q8C2×D8311yescharacteristic
233C2×C22⋊Q8—1661no—
234C2×C22⋊Q8—1661no—
235C2×C4×D4—831no—
236C2×#106—1661no—
237C2×C4⋊C8C2×D8311yescharacteristic
238C2×C4⋊C8C2×D8311yescharacteristic
239C2×#102—1661no—
240C2×C4×C8—831no—
241#399—1662no—
242#390—1661no—
243#384—831no—
244#384—1661no—
245C4×C4⋊C4—831no—
246#340—1661no—
247#340—1661no—
248#340—1662no—
249#332—22no—
250D4⋊C8—1662no—
251C22×Q8—21no—
252C22×D4—831no—
253C23×C4—1661no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—1661no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
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—21no—
270C2×C4⋊C4—831no—
271C2×C4⋊C4—831no—
272C2×C4⋊C4—831no—
273C2×C4⋊C4—1662no—
274C2×C4⋊C4—1662no—
275C2×C4⋊C4—1661no—
276C2×C4⋊C4—1661no—
277C2×C4⋊C4—1661no—
278C2×C4⋊C4D33212yes—
279C2×C22⋊C4—1662no—
280C2×C22⋊C4—1662no—
281C2×C22⋊C4—1661no—
282C2×C42—1661no—
283C2×C42C22×D8311yescharacteristic
284#106—3322no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8C22⋊D8312yes—
289#102—3322no—
290C4×C8—1661no—
291C4×C8—1661no—
292#95—1661no—
293C24—1661no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×D4—832no—
301C2×D4—1661no—
302C2×D4—1661no—
303C2×D4—1661no—
304C2×D4—1661no—
305C2×D4—1661no—
306C22×C4—22no—
307C22×C4—3321no—
308C22×C4—3321no—
309C22×C4—3321no—
310C22×C4—3321no—
311C22×C4—3321no—
312C22×C4—3321no—
313C22×C4—3321no—
314C22×C4—1661no—
315C22×C4—1661no—
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—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—3322no—
334C4⋊C4—3324no—
335C4⋊C4—3324no—
336C4⋊C4—3321no—
337C4⋊C4—3321no—
338C4⋊C4—3321no—
339C4⋊C4—3321no—
340C4⋊C4—832no—
341C4⋊C4—832no—
342C4⋊C4—1661no—
343C4⋊C4—1661no—
344C4⋊C4—1661no—
345C4⋊C4—1661no—
346C22⋊C4—3324no—
347C22⋊C4—3324no—
348C22⋊C4—3321no—
349C22⋊C4—3321no—
350C42—3321no—
351C42—3321no—
352C42C2×C22⋊D8311yescharacteristic
353C42#1305058911yescharacteristic
354C42#1305058911yescharacteristic
355C42#1305059011yescharacteristic
356C23—3321no—
357C23—3321no—
358C23—3321no—
359C23—3321no—
360C23—3321no—
361C23—3321no—
362C23—1662no—
363C23#1458176211yescharacteristic
364Q8—81no—
365Q8—81no—
366Q8—81no—
367Q8—81no—
368D4—3321no—
369D4—3321no—
370D4—1662no—
371D4—1662no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—3321no—
378C2×C4—3321no—
379C2×C4—3321no—
380C2×C4—3321no—
381C2×C4—3321no—
382C2×C4—3321no—
383C2×C4—3321no—
384C2×C4—6641no—
385C2×C4—6641no—
386C2×C4—6641no—
387C2×C4—6641no—
388C2×C4—6641no—
389C2×C4—6641no—
390C2×C4—6641no—
391C2×C4—1662no—
392C2×C4—1662no—
393C2×C4#1458176311yescharacteristic
394C2×C4#1458176411yescharacteristic
395C2×C4#1458176611yescharacteristic
396C2×C4#1458177411yescharacteristic
397C2×C4#1458177611yescharacteristic
398C2×C4#1458177811yescharacteristic
399C2×C4D8×D8311yescharacteristic
400C2×C4SD16×D8311yescharacteristic
401C2×C4SD16×D8311yescharacteristic
402C2×C4#1458181311yescharacteristic
403C2×C4#1458181611yescharacteristic
404C2×C4#1458181911yescharacteristic
405C2×C4#1458182411yescharacteristic
406C2×C4#1458182411yescharacteristic
407C8—42no—
408C8—81no—
409C8—3322no—
410C22—3322no—
411C22—3322no—
412C22—3322no—
413C22—6641no—
414C22—6641no—
415C22—6641no—
416C22—6641no—
417C22#1912761711yescharacteristic
418C22#1912783611yescharacteristic
419C22#1912784111yescharacteristic
420C22#1912785311yescharacteristic
421C22#1912786611yescharacteristic
422C22#1912787611yescharacteristic
423C22#1912788611yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—13281no—
428C4—3322no—
429C4—3322no—
430C4—6641no—
431C4#1912789411yescharacteristic
432C4#1912789911yescharacteristic
433C4#1912792711yescharacteristic
434C4#1912795611yescharacteristic
435C4#1912803011yescharacteristic
436C4#1912804011yescharacteristic
437C4#1912804611yescharacteristic
438C4#1912806411yescharacteristic
439C2—6642no—
440C2#2490656711yescharacteristic
441C2#2490661511yescharacteristic
442C2#2490669911yescharacteristic
443C2#2490672711yescharacteristic
444C2#2490865811yescharacteristic
445C2#2490868111yescharacteristic
446C2#2490869611yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC2×#332×C83C2
socleC23×C83#120
prime radicalC22×D332D4
hypercenterC2×#332D83
hypocenterC83#10420
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #24908425C2semidirect
3. #24908227C2semidirect
6. #24905302C2semidirect
7. C2×#332×C83C2semidirect
228. C2×#332D83semidirect
231. C83#10420semidirect

Maximal subgroups

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

subgroupindex
#249124172
#249084252
#249082272
#249074642
C2×#191274282
#249053022
C2×#332×C832
#1042083