Finite Group Databasebeta

← #35560674

Subgroups — #35560674

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#24918002C211yesmaximal, characteristic, complemented
2#24909746C211yesmaximal, characteristic, complemented
3#24909743C211yesmaximal, characteristic, complemented
4#24909699C211yesmaximal, characteristic, complemented
5#24909694C211yesmaximal, characteristic, complemented
6#24909668C211yesmaximal, characteristic, complemented
7#24909658C211yesmaximal, characteristic, complemented
8#24909651C211yesmaximal, characteristic
9#24909646C211yesmaximal, characteristic
10#24909627C211yesmaximal, characteristic, complemented
11#24909620C211yesmaximal, characteristic, complemented
12#24909610C211yesmaximal, characteristic, complemented
13#24909605C211yesmaximal, characteristic, complemented
14#24909270C211yesmaximal, characteristic, complemented
15C83×#3175C211yesmaximal, characteristic
16#19128329—21no—
17#19128110—21no—
18#19128110—21no—
19#19128106C2211yescharacteristic
20#19128106C2211yescharacteristic
21#19128103C2211yescharacteristic
22#19128103C2211yescharacteristic
23#19127743—21no—
24#19127739C2211yescharacteristic
25C2×#14581726C2211yescharacteristic
26#19127528C2211yescharacteristic
27#19127528C2211yescharacteristic
28#19127528C2211yescharacteristic
29#19127528C2211yescharacteristic
30#19127528C2211yescharacteristic
31#19127528C2211yescharacteristic
32#19127526C2211yescharacteristic
33#19127526C2211yescharacteristic
34C4⋊(C83⋊C16)C2211yescharacteristic
35C4⋊(C83⋊C16)C2211yescharacteristic
36#19127505C2211yescharacteristic
37#19127505C2211yescharacteristic
38#19127505C2211yescharacteristic
39#19127505C2211yescharacteristic
40#19127502C2211yescharacteristic
41#19127502C2211yescharacteristic
42#19127502C2211yescharacteristic
43#19127502C2211yescharacteristic
44C22⋊(C83⋊C16)C2211yescharacteristic
45C22⋊(C83⋊C16)C2211yescharacteristic
46#19127477C2211yescharacteristic
47C4×C83⋊C16C2211yescharacteristic
48#542×C83—21no—
49#500×C83C2211yescharacteristic
50#495×C83C2211yescharacteristic
51#489×C83—21no—
52#468×C83—21no—
53#467×C83C2211yescharacteristic
54#466×C83C2211yescharacteristic
55#440×C83—21no—
56C4×Q16×C83C2211yescharacteristic
57C4×D8×C83C2211yescharacteristic
58#405×C83C2211yescharacteristic
59#14581792—21no—
60#14581792—21no—
61#14581791—41no—
62#14581784—21no—
63#14581784—21no—
64#14581783—41no—
65#14581769—41no—
66#14581769—41no—
67#14581751—21no—
68C2×C4⋊Dic83—21no—
69C2×C83⋊C16C2311yescharacteristic
70C2×C83⋊C16C2311yescharacteristic
71C2×C83⋊C16C2311yescharacteristic
72C2×C83⋊C16C2311yescharacteristic
73#14581726—21no—
74#14581726—21no—
75#14581726—21no—
76#14581726C2311yescharacteristic
77#14581726C2311yescharacteristic
78#14581726C2311yescharacteristic
79#14581726C2311yescharacteristic
80#14581724—21no—
81#14581724—21no—
82#14581724—21no—
83C2×Q16×C83C2311yescharacteristic
84C2×SD16×C83—21no—
85C2×D8×C83C2311yescharacteristic
86C2×M16×C83D411yescharacteristic
87C22×C8×C83C2311yescharacteristic
88C4⋊Q8×C83—21no—
89#126×C83—41no—
90#124×C83—21no—
91#124×C83—41no—
92#123×C83—41no—
93C22⋊Q8×C83—21no—
94C22⋊Q8×C83—41no—
95#121×C83—21no—
96C4×Q8×C83—21no—
97C4×D4×C83—21no—
98#117×C83D411yescharacteristic
99#107×C83—21no—
100#107×C83C2311yescharacteristic
101#107×C83C2311yescharacteristic
102#103×C83—21no—
103#103×C83—21no—
104#102×C83—21no—
105#102×C83—21no—
106#97×C83D411yescharacteristic
107#97×C83D411yescharacteristic
108C4×C8×C83C2311yescharacteristic
109C4×C8×C83C2311yescharacteristic
110C2×Dic166—41no—
111C2×Dic166—41no—
112C22×Dic83—41no—
113C4⋊Dic83—21no—
114C4⋊Dic83—21no—
115C4⋊Dic83—21no—
116C4⋊Dic83—21no—
117C4⋊Dic83—41no—
118C4⋊Dic83—41no—
119C4⋊Dic83—41no—
120Dic83⋊C4—41no—
121Dic83⋊C4—41no—
122Dic83⋊C4—41no—
123Dic83⋊C4—41no—
124C22⋊Dic83—41no—
125C4×Dic83—41no—
126C83⋊C16—21no—
127C83⋊C16—21no—
128C83⋊C16—21no—
129C83⋊C16—21no—
130C2×Q8×C83—21no—
131C2×Q8×C83—41no—
132C2×D4×C83—21no—
133C2×D4×C83—41no—
134C22×C4×C83—41no—
135C22×C4×C83C2×D411yescharacteristic
136Q16×C83—21no—
137Q16×C83—21no—
138SD16×C83—42no—
139D8×C83—21no—
140D8×C83—21no—
141M16×C83—22no—
142C2×C8×C83—21no—
143C2×C8×C83—21no—
144C2×C8×C83C2×D411yescharacteristic
145C2×C8×C83C2×D411yescharacteristic
146C2×C8×C83C2×D411yescharacteristic
147C2×C8×C83C2411yescharacteristic
148C4⋊C4×C83—21no—
149C4⋊C4×C83—21no—
150C4⋊C4×C83—41no—
151C4⋊C4×C83—41no—
152C4⋊C4×C83—41no—
153C4⋊C4×C83D811yescharacteristic
154C4⋊C4×C83D811yescharacteristic
155C22⋊C4×C83—41no—
156C22⋊C4×C83—41no—
157C22⋊C4×C83—41no—
158C22⋊C4×C83—41no—
159C22⋊C4×C83—41no—
160C22⋊C4×C83D811yescharacteristic
161C22⋊C4×C83D811yescharacteristic
162C42×C83—41no—
163C42×C83C2×D411yescharacteristic
164C42×C83C2×D411yescharacteristic
165C23×C83—41no—
166C23×C83C2×D811yescharacteristic
167Q8×C83—41no—
168Q8×C83—41no—
169Q8×C83—161no—
170D4×C83—41no—
171D4×C83—41no—
172D4×C83—161no—
173C2×C4×C83—21no—
174C2×C4×C83—21no—
175C2×C4×C83—41no—
176C2×C4×C83—41no—
177C2×C4×C83—41no—
178C2×C4×C83—161no—
179C2×C4×C83C2×D811yescharacteristic
180C2×C4×C83C2×D811yescharacteristic
181C2×C4×C83C2×D811yescharacteristic
182C2×C4×C83C2×D811yescharacteristic
183C2×C4×C83C2×D811yescharacteristic
184C2×C4×C83C22×D411yescharacteristic
185C2×Dic83—41no—
186C2×Dic83—41no—
187C2×Dic83—41no—
188C2×Dic83—41no—
189C2×Dic83—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×C83—81no—
201C22×C83—81no—
202C22×C83—81no—
203C22×C83C22×D811yescharacteristic
204C4×C83—21no—
205C4×C83—21no—
206C4×C83—21no—
207C4×C83—21no—
208C4×C83—21no—
209C4×C83—81no—
210C4×C83—81no—
211C4×C83—81no—
212C4×C83#53611yescharacteristic
213C4×C83C2×#13711yescharacteristic
214Dic83—81no—
215Dic83—81no—
216Dic83—81no—
217Dic83—81no—
218#33810—831nomaximal, Sylow
219C2×C83—41no—
220C2×C83—161no—
221C2×C83#322611yescharacteristic
222C2×C83#341611yescharacteristic
223C2×C83#341611yescharacteristic
224#3175D8311yescharacteristic
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#2164—831no—
239C83#3381011yescharacteristic, complemented, Sylow
240#544—1661no—
241#542—21no—
242#501—1661no—
243#501—1661no—
244#500—831no—
245#500—831no—
246#500C2×D8311yescharacteristic
247#499—831no—
248#499—831no—
249#495C2×D8311yescharacteristic
250#489—21no—
251#468—21no—
252#467C2×D8311yescharacteristic
253#466C2×D8311yescharacteristic
254#440—21no—
255C4×Q16C2×D8311yescharacteristic
256C4×D8C2×D8311yescharacteristic
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⋊C16—831no—
270C4⋊C16—831no—
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⋊C16—831no—
280C22⋊C16—831no—
281#346—831no—
282C4×C16—831no—
283C2×Q16C22×D8311yescharacteristic
284C2×SD16—21no—
285C2×D8C22×D8311yescharacteristic
286C2×M16C22⋊D8311yescharacteristic
287C22×C8C22×D8311yescharacteristic
288C4⋊Q8—21no—
289C4⋊Q8—3321no—
290C4⋊Q8—1661no—
291C4⋊Q8—1661no—
292#126—41no—
293#125—3321no—
294#125—1661no—
295#125—1661no—
296#124—21no—
297#124—41no—
298#123—41no—
299C22⋊Q8—21no—
300C22⋊Q8—41no—
301C22⋊Q8—3321no—
302C22⋊Q8—3321no—
303#121—21no—
304C4×Q8—21no—
305C4×D4—21no—
306#117—1661no—
307#117C22⋊D8311yescharacteristic
308C2×C4⋊C4—1661no—
309C2×C16—831no—
310C2×C16—831no—
311C2×C16—831no—
312C2×C16—831no—
313#107—21no—
314#107—831no—
315#107—831no—
316#107—831no—
317#107—831no—
318#107—1661no—
319#107—1661no—
320#107—1661no—
321#107C22×D8311yescharacteristic
322#107C22×D8311yescharacteristic
323#106—1661no—
324#106—1661no—
325#106—1661no—
326#103—21no—
327#103—21no—
328#102—21no—
329#102—21no—
330#97C22⋊D8311yescharacteristic
331#97C22⋊D8311yescharacteristic
332C4×C8C22×D8311yescharacteristic
333C4×C8C22×D8311yescharacteristic
334C2×Q8—21no—
335C2×Q8—41no—
336C2×Q8—3321no—
337C2×Q8—3321no—
338C2×D4—21no—
339C2×D4—41no—
340C22×C4—41no—
341C22×C4—3321no—
342C22×C4C2×C22⋊D8311yescharacteristic
343Q16—21no—
344Q16—21no—
345SD16—42no—
346D8—21no—
347D8—21no—
348M16—22no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8C2×C22⋊D8311yescharacteristic
352C2×C8C2×C22⋊D8311yescharacteristic
353C2×C8C2×C22⋊D8311yescharacteristic
354C2×C8C23×D8311yescharacteristic
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—3321no—
361C4⋊C4—3321no—
362C4⋊C4—3321no—
363C4⋊C4—3321no—
364C4⋊C4—3321no—
365C4⋊C4—3321no—
366C4⋊C4—3321no—
367C4⋊C4—1661no—
368C4⋊C4—1661no—
369C4⋊C4—1661no—
370C4⋊C4—1661no—
371C4⋊C4#1305057511yescharacteristic
372C4⋊C4#1305057511yescharacteristic
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—3321no—
379C22⋊C4#1305057511yescharacteristic
380C22⋊C4#1305057511yescharacteristic
381C42—41no—
382C42—3321no—
383C42C2×C22⋊D8311yescharacteristic
384C42C2×C22⋊D8311yescharacteristic
385C16—1661no—
386C16—1661no—
387C16—1661no—
388C16—1661no—
389C23—41no—
390C23C2×#1305057511yescharacteristic
391Q8—41no—
392Q8—41no—
393Q8—161no—
394Q8—13281no—
395Q8—13281no—
396D4—41no—
397D4—41no—
398D4—161no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—161no—
405C2×C4—13281no—
406C2×C4—3321no—
407C2×C4—3321no—
408C2×C4—3321no—
409C2×C4—3321no—
410C2×C4C2×#1305057511yescharacteristic
411C2×C4C2×#1305057511yescharacteristic
412C2×C4C2×#1305057511yescharacteristic
413C2×C4C2×#1305057511yescharacteristic
414C2×C4C2×#1305057511yescharacteristic
415C2×C4C22×C22⋊D8311yescharacteristic
416C8—21no—
417C8—21no—
418C8#1458182212yes—
419C8#1458183911yescharacteristic
420C8#1458183911yescharacteristic
421C22—21no—
422C22—21no—
423C22—21no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C22×#1305057511yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—6641no—
437C4—6641no—
438C4—6641no—
439C4—6641no—
440C4#1912827211yescharacteristic
441C4C2×#1458182211yescharacteristic
442C2—41no—
443C2—161no—
444C2#2491858111yescharacteristic
445C2#2492060711yescharacteristic
446C2#2492061011yescharacteristic
subgroupG/H
centerC22C22×#13050575
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC83×#3175C2
socleC22×C83C22×D8
prime radical#466×C83C22
hypercenter#3175D83
hypocenterC83#33810
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #24918002C2semidirect
2. #24909746C2semidirect
3. #24909743C2semidirect
4. #24909699C2semidirect
5. #24909694C2semidirect
6. #24909668C2semidirect
7. #24909658C2semidirect
10. #24909627C2semidirect
11. #24909620C2semidirect
12. #24909610C2semidirect
13. #24909605C2semidirect
14. #24909270C2semidirect
239. C83#33810semidirect

Maximal subgroups

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

subgroupindex
#249180022
#249097462
#249097432
#249096992
#249096942
#249096682
#249096582
#249096512
#249096462
#249096272
#249096202
#249096102
#249096052
#249092702
C83×#31752
#3381083