Finite Group Databasebeta

← #35560682

Subgroups — #35560682

Order 21248.

454 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#24918102C211yesmaximal, characteristic
2#24918002C211yesmaximal, characteristic, complemented
3#24909749C211yesmaximal, characteristic, complemented
4#24909745C211yesmaximal, characteristic, complemented
5#24909700C211yesmaximal, characteristic, complemented
6#24909695C211yesmaximal, characteristic, complemented
7#24909672C211yesmaximal, characteristic, complemented
8#24909661C211yesmaximal, characteristic, complemented
9#24909655C211yesmaximal, characteristic
10#24909649C211yesmaximal, characteristic
11#24909628C211yesmaximal, characteristic, complemented
12#24909621C211yesmaximal, characteristic, complemented
13#24909611C211yesmaximal, characteristic, complemented
14#24909606C211yesmaximal, characteristic, complemented
15C83×#2164C211yesmaximal, characteristic, complemented
16#19128329—21no—
17#19128322—21no—
18#19128110—21no—
19#19128110—21no—
20#19128106C2211yescharacteristic
21#19128106C2211yescharacteristic
22#19128106C2211yescharacteristic
23#19128103C2211yescharacteristic
24#19128103C2211yescharacteristic
25#19128085C2211yescharacteristic
26#19128061—21no—
27#19127947—21no—
28#19127942C2211yescharacteristic
29#19127937C2211yescharacteristic
30#19127803—21no—
31C4×Dic332C2211yescharacteristic
32C4×D664C2211yescharacteristic
33#19127743—21no—
34#19127739C2211yescharacteristic
35C2×#14581726C2211yescharacteristic
36#19127529C2211yescharacteristic
37#19127529C2211yescharacteristic
38#19127529C2211yescharacteristic
39#19127529C2211yescharacteristic
40#19127529C2211yescharacteristic
41#19127529C2211yescharacteristic
42#19127527C2211yescharacteristic
43#19127527C2211yescharacteristic
44#19127506C2211yescharacteristic
45#19127506C2211yescharacteristic
46#19127506C2211yescharacteristic
47#19127506C2211yescharacteristic
48#19127503C2211yescharacteristic
49#19127503C2211yescharacteristic
50#19127503C2211yescharacteristic
51#19127503C2211yescharacteristic
52#405×C83C2211yescharacteristic
53C4⋊C16×C83C2211yescharacteristic
54C4⋊C16×C83C2211yescharacteristic
55C22⋊C16×C83C2211yescharacteristic
56C22⋊C16×C83C2211yescharacteristic
57#346×C83C2211yescharacteristic
58C4×C16×C83C2211yescharacteristic
59C2×Dic332C2311yescharacteristic
60C2×#13050579—21no—
61C2×D664C2311yescharacteristic
62#14581792—21no—
63#14581792—21no—
64#14581792—21no—
65#14581791—41no—
66#14581787—41no—
67#14581784—21no—
68#14581784—21no—
69#14581783—41no—
70#14581780—21no—
71#14581778—41no—
72#14581774—41no—
73#14581771—21no—
74#14581770—41no—
75#14581769—41no—
76#14581769—41no—
77#14581766—21no—
78C4×Dic166—21no—
79C4×D332—21no—
80#14581751—21no—
81C2×C4⋊Dic83—21no—
82#14581726—21no—
83#14581726—21no—
84#14581726—21no—
85#14581726—21no—
86#14581726C2311yescharacteristic
87#14581726C2311yescharacteristic
88#14581726C2311yescharacteristic
89#14581726C2311yescharacteristic
90#14581726C2311yescharacteristic
91#14581726C2311yescharacteristic
92#14581724—21no—
93#14581724—21no—
94#14581724—21no—
95#14581717—21no—
96#14581717—21no—
97#14581714—21no—
98#14581714—21no—
99C2×M16×C83D411yescharacteristic
100C22×C8×C83C2311yescharacteristic
101#117×C83D411yescharacteristic
102C2×C16×C83C2311yescharacteristic
103C2×C16×C83C2311yescharacteristic
104C2×C16×C83C2311yescharacteristic
105C2×C16×C83C2311yescharacteristic
106#97×C83D411yescharacteristic
107#97×C83D411yescharacteristic
108C4×C8×C83C2311yescharacteristic
109C4×C8×C83C2311yescharacteristic
110C2×Dic166—21no—
111C2×Dic166—41no—
112C2×Dic166—41no—
113C2×Dic166—41no—
114C2×D332—21no—
115C2×C22⋊D83—41no—
116C22×Dic83—41no—
117C2×C4×D83—41no—
118Dic332—21no—
119Dic332—21no—
120#13050579—42no—
121D664—21no—
122D664—21no—
123C4⋊Dic83—21no—
124C4⋊Dic83—21no—
125C4⋊Dic83—21no—
126C4⋊Dic83—21no—
127C4⋊Dic83—21no—
128C4⋊Dic83—21no—
129C4⋊Dic83—41no—
130C4⋊Dic83—41no—
131C4⋊Dic83—41no—
132C4⋊Dic83—41no—
133Dic83⋊C4—41no—
134Dic83⋊C4—41no—
135Dic83⋊C4—41no—
136Dic83⋊C4—41no—
137Dic83⋊C4—41no—
138Dic83⋊C4—41no—
139C22⋊Dic83—41no—
140C22⋊Dic83—41no—
141(C2×D83)⋊C4—41no—
142(C2×D83)⋊C4—41no—
143(C2×D83)⋊C4—41no—
144(C2×D83)⋊C4—41no—
145C4×Dic83—41no—
146C4×Dic83—41no—
147C22×C4×C83C2×D411yescharacteristic
148M16×C83—22no—
149C2×C8×C83—21no—
150C2×C8×C83—21no—
151C2×C8×C83C2×D411yescharacteristic
152C2×C8×C83C2×D411yescharacteristic
153C2×C8×C83C2×D411yescharacteristic
154C2×C8×C83C2411yescharacteristic
155C4⋊C4×C83D811yescharacteristic
156C4⋊C4×C83D811yescharacteristic
157C22⋊C4×C83D811yescharacteristic
158C22⋊C4×C83D811yescharacteristic
159C42×C83C2×D411yescharacteristic
160C42×C83C2×D411yescharacteristic
161C16×C83—21no—
162C16×C83—21no—
163C16×C83—21no—
164C16×C83—21no—
165C23×C83C2×D811yescharacteristic
166C22×D83—41no—
167C2×C4×C83—21no—
168C2×C4×C83—21no—
169C2×C4×C83C2×D811yescharacteristic
170C2×C4×C83C2×D811yescharacteristic
171C2×C4×C83C2×D811yescharacteristic
172C2×C4×C83C2×D811yescharacteristic
173C2×C4×C83C2×D811yescharacteristic
174C2×C4×C83C22×D411yescharacteristic
175C22⋊D83—161no—
176C2×Dic83—41no—
177C2×Dic83—41no—
178C2×Dic83—41no—
179C2×Dic83—41no—
180C2×Dic83—41no—
181C2×Dic83—41no—
182C2×Dic83—41no—
183C2×Dic83—161no—
184D332—41no—
185D332—41no—
186C4×D83—161no—
187Dic166—41no—
188Dic166—41no—
189Dic166—161no—
190Dic166—161no—
191Dic166—161no—
192C8×C83—21no—
193C8×C83—21no—
194C8×C83#13712yes—
195C8×C832−1+411yescharacteristic
196C8×C832−1+411yescharacteristic
197C22×C83—21no—
198C22×C83—21no—
199C22×C83—21no—
200C22×C83C22×D811yescharacteristic
201C2×D83—81no—
202C2×D83—81no—
203C2×D83—81no—
204C4×C83—21no—
205C4×C83—21no—
206C4×C83—21no—
207C4×C83—21no—
208C4×C83—21no—
209C4×C83#53611yescharacteristic
210C4×C83C2×#13711yescharacteristic
211Dic83—81no—
212Dic83—81no—
213Dic83—81no—
214Dic83—81no—
215Dic83—81no—
216Dic83—81no—
217Dic83—81no—
218#33810—831nomaximal, Sylow
219C2×C83—41no—
220C2×C83#322611yescharacteristic
221C2×C83#341611yescharacteristic
222C2×C83#341611yescharacteristic
223D83—161no—
224#3175—831no—
225#3164—831no—
226#2255—831no—
227#2254—831no—
228#2243—831no—
229#2242—831no—
230#2237—831no—
231#2235—831no—
232#2234—831no—
233#2233—831no—
234#2229—831no—
235#2228—831no—
236#2226—831no—
237#2225—831no—
238#2164D8311yescharacteristic, complemented
239C83#3381011yescharacteristic, complemented, Sylow
240#544—1661no—
241#542—1661no—
242#501—1661no—
243#501—1661no—
244#500—831no—
245#500—831no—
246#500—831no—
247#499—831no—
248#499—831no—
249#495—831no—
250#489—1661no—
251#468—1661no—
252#467—831no—
253#466—831no—
254#440—1661no—
255C4×Q16—831no—
256C4×D8—831no—
257#428—1661no—
258#427—831no—
259C2×#107—831no—
260#405C2×D8311yescharacteristic
261#367—831no—
262#367—831no—
263#367—831no—
264#367—831no—
265#367—831no—
266#367—831no—
267#366—831no—
268#366—831no—
269C4⋊C16C2×D8311yescharacteristic
270C4⋊C16C2×D8311yescharacteristic
271#358—831no—
272#358—831no—
273#358—831no—
274#358—831no—
275#357—831no—
276#357—831no—
277#357—831no—
278#357—831no—
279C22⋊C16C2×D8311yescharacteristic
280C22⋊C16C2×D8311yescharacteristic
281#346C2×D8311yescharacteristic
282C4×C16C2×D8311yescharacteristic
283C2×Q16—831no—
284C2×SD16—1661no—
285C2×D8—831no—
286C2×M16D33211yescharacteristic
287C22×C8C22×D8311yescharacteristic
288C4⋊Q8—3321no—
289C4⋊Q8—1661no—
290C4⋊Q8—1661no—
291C4⋊Q8—1661no—
292#126—3321no—
293#125—3321no—
294#125—1661no—
295#125—1661no—
296#124—3321no—
297#124—1661no—
298#123—3321no—
299C22⋊Q8—3321no—
300C22⋊Q8—3321no—
301C22⋊Q8—3321no—
302C22⋊Q8—1661no—
303#121—1661no—
304C4×Q8—1661no—
305C4×D4—1661no—
306#117—1661no—
307#117D33211yescharacteristic
308C2×C4⋊C4—1661no—
309C2×C16C22×D8311yescharacteristic
310C2×C16C22×D8311yescharacteristic
311C2×C16C22×D8311yescharacteristic
312C2×C16C22×D8311yescharacteristic
313#107—831no—
314#107—831no—
315#107—831no—
316#107—831no—
317#107—831no—
318#107—831no—
319#107—1661no—
320#107—1661no—
321#107—1661no—
322#107—1661no—
323#106—1661no—
324#106—1661no—
325#106—1661no—
326#103—1661no—
327#103—1661no—
328#102—1661no—
329#102—1661no—
330#97D33211yescharacteristic
331#97D33211yescharacteristic
332C4×C8C22×D8311yescharacteristic
333C4×C8C22×D8311yescharacteristic
334C2×Q8—3321no—
335C2×Q8—3321no—
336C2×Q8—3321no—
337C2×Q8—1661no—
338C2×D4—3321no—
339C2×D4—1661no—
340C22×C4—3321no—
341C22×C4—3321no—
342C22×C4C2×D33211yescharacteristic
343Q16—1661no—
344Q16—1661no—
345SD16—3322no—
346D8—1661no—
347D8—1661no—
348M16—22no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8C2×D33211yescharacteristic
352C2×C8C2×D33211yescharacteristic
353C2×C8C2×D33211yescharacteristic
354C2×C8C23×D8311yescharacteristic
355C4⋊C4—3321no—
356C4⋊C4—3321no—
357C4⋊C4—3321no—
358C4⋊C4—3321no—
359C4⋊C4—3321no—
360C4⋊C4—3321no—
361C4⋊C4—3321no—
362C4⋊C4—3321no—
363C4⋊C4—3321no—
364C4⋊C4—3321no—
365C4⋊C4—1661no—
366C4⋊C4—1661no—
367C4⋊C4—1661no—
368C4⋊C4—1661no—
369C4⋊C4—1661no—
370C4⋊C4—1661no—
371C4⋊C4D66411yescharacteristic
372C4⋊C4D66411yescharacteristic
373C22⋊C4—3321no—
374C22⋊C4—3321no—
375C22⋊C4—3321no—
376C22⋊C4—3321no—
377C22⋊C4—3321no—
378C22⋊C4—3321no—
379C22⋊C4D66411yescharacteristic
380C22⋊C4D66411yescharacteristic
381C42—3321no—
382C42—3321no—
383C42C2×D33211yescharacteristic
384C42C2×D33211yescharacteristic
385C16—21no—
386C16—21no—
387C16—21no—
388C16—21no—
389C23—3321no—
390C23C2×D66411yescharacteristic
391Q8—13281no—
392Q8—13281no—
393Q8—13281no—
394Q8—3321no—
395Q8—3321no—
396D4—13281no—
397D4—3321no—
398D4—3321no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—13281no—
402C2×C4—13281no—
403C2×C4—3321no—
404C2×C4—3321no—
405C2×C4—3321no—
406C2×C4—3321no—
407C2×C4—3321no—
408C2×C4—3321no—
409C2×C4—3321no—
410C2×C4C2×D66411yescharacteristic
411C2×C4C2×D66411yescharacteristic
412C2×C4C2×D66411yescharacteristic
413C2×C4C2×D66411yescharacteristic
414C2×C4C2×D66411yescharacteristic
415C2×C4C22×D33211yescharacteristic
416C8—21no—
417C8—21no—
418C8#1458182512yes—
419C8#1458183911yescharacteristic
420C8#1458183911yescharacteristic
421C22—21no—
422C22—21no—
423C22—21no—
424C22—6641no—
425C22—6641no—
426C22—6641no—
427C22C22×D66411yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—6641no—
434C4—6641no—
435C4—6641no—
436C4—6641no—
437C4—6641no—
438C4—6641no—
439C4—6641no—
440C4#1912827711yescharacteristic
441C4C2×#1458182511yescharacteristic
442C2—41no—
443C2—13281no—
444C2#2491858611yescharacteristic
445C2#2492061111yescharacteristic
446C2#2492061111yescharacteristic
subgroupG/H
centerC22C22×D664
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC83×#2164C2
socleC22×C83C22×D8
prime radical#19127937C22
hypercenter#2164D83
hypocenterC83#33810
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2164

Complements

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

NH ≅ G/Ntype
2. #24918002C2semidirect
3. #24909749C2semidirect
4. #24909745C2semidirect
5. #24909700C2semidirect
6. #24909695C2semidirect
7. #24909672C2semidirect
8. #24909661C2semidirect
11. #24909628C2semidirect
12. #24909621C2semidirect
13. #24909611C2semidirect
14. #24909606C2semidirect
15. C83×#2164C2semidirect
238. #2164D83semidirect
239. C83#33810semidirect

Maximal subgroups

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

subgroupindex
#249181022
#249180022
#249097492
#249097452
#249097002
#249096952
#249096722
#249096612
#249096552
#249096492
#249096282
#249096212
#249096112
#249096062
C83×#21642
#3381083