Finite Group Databasebeta

← #35559490

Subgroups — #35559490

Order 21248.

548 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918049C211yesmaximal, characteristic, complemented
2#24909671C212yesmaximal, complemented
3#24909615C211yesmaximal, characteristic, complemented
4#24909610C211yesmaximal, characteristic, complemented
5#24909513C211yesmaximal, characteristic, complemented
6#24909508C211yesmaximal, characteristic, complemented
7#24909403C212yesmaximal
8#24909332C212yesmaximal, complemented
9#24909327C212yesmaximal, complemented
10#24909266C211yesmaximal, characteristic, complemented
11C4×#135×C83C211yesmaximal, characteristic
12#19128258—21no—
13C2×#14581738C2212yes—
14C2×#14581736C2212yes—
15#19128106C2211yescharacteristic
16#19128081C2211yescharacteristic
17#19128052—21no—
18#19127942—21no—
19#19127942C2212yes—
20C4×Dic332—21no—
21C4×Dic332C2212yes—
22#19127528C2212yes—
23#19127526C2212yes—
24C4⋊(C83⋊C16)C2211yescharacteristic
25C4⋊(C83⋊C16)C2211yescharacteristic
26#19127505C2212yes—
27#19127504C2212yes—
28#19127504C2212yes—
29#19127502C2212yes—
30C22⋊(C83⋊C16)C2212yes—
31#19127477C2212yes—
32C2×#135×C83C2211yescharacteristic
33C4×#41×C83—21no—
34C4×Q16×C83C2211yescharacteristic
35C4×Q16×C83C2211yescharacteristic
36C4×SD16×C83—21no—
37C4×SD16×C83—21no—
38C4×D8×C83C2211yescharacteristic
39C4×D8×C83C2211yescharacteristic
40#427×C83C2211yescharacteristic
41#416×C83—21no—
42C2×C4×C8×C83C2211yescharacteristic
43C2×Dic332—21no—
44C2×Dic332C2312yes—
45#14581792—21no—
46#14581792—21no—
47#14581784—41no—
48#14581771—22no—
49#14581771—41no—
50C4×Dic166—22no—
51C4×Dic166—41no—
52#14581751—41no—
53#14581738—24no—
54#14581736—24no—
55C2×C83⋊C16C2312yes—
56C2×C83⋊C16C2312yes—
57#14581726—21no—
58#14581726C2312yes—
59#14581717—22no—
60#14581717—22no—
61C2×#41×C83—21no—
62#135×C83—22no—
63#135×C83—22no—
64C2×Q16×C83C2311yescharacteristic
65C2×SD16×C83—21no—
66C2×D8×C83C2311yescharacteristic
67C22×C8×C83D411yescharacteristic
68C22×C8×C83C2311yescharacteristic
69C4×Q8×C83—21no—
70C4×Q8×C83—21no—
71C4×D4×C83—21no—
72C4×D4×C83—21no—
73C4×D4×C83—41no—
74C4×D4×C83—41no—
75#117×C83—21no—
76#117×C83—41no—
77C2×C42×C83—41no—
78C2×C42×C83D411yescharacteristic
79#107×C83C2311yescharacteristic
80#107×C83C2311yescharacteristic
81#106×C83—21no—
82#103×C83—21no—
83#103×C83—21no—
84#102×C83—21no—
85#102×C83—21no—
86C4×C8×C83D411yescharacteristic
87C4×C8×C83D411yescharacteristic
88C4×C8×C83C2311yescharacteristic
89C4×C8×C83C2311yescharacteristic
90C2×Dic166—22no—
91C2×Dic166—41no—
92Dic332—22no—
93Dic332—22no—
94Dic332—42no—
95C4⋊Dic83—22no—
96C4⋊Dic83—41no—
97C4⋊Dic83—41no—
98C4⋊Dic83—41no—
99Dic83⋊C4—42no—
100Dic83⋊C4—42no—
101C22⋊Dic83—42no—
102C4×Dic83—42no—
103C83⋊C16—22no—
104C83⋊C16—22no—
105#41×C83—24no—
106#41×C83—42no—
107C2×Q8×C83—21no—
108C2×D4×C83—21no—
109C2×D4×C83—41no—
110C22×C4×C83—41no—
111C22×C4×C83—41no—
112C22×C4×C83—41no—
113C22×C4×C83D811yescharacteristic
114C22×C4×C83D811yescharacteristic
115C22×C4×C83C2×D411yescharacteristic
116Q16×C83—21no—
117Q16×C83#4112yes—
118SD16×C83—24no—
119D8×C83—21no—
120D8×C83#4112yes—
121C2×C8×C83—21no—
122C2×C8×C83—21no—
123C2×C8×C83—41no—
124C2×C8×C83C2×D411yescharacteristic
125C2×C8×C83C2×D411yescharacteristic
126C2×C8×C83C2×D411yescharacteristic
127C2×C8×C83C2411yescharacteristic
128C4⋊C4×C83—21no—
129C4⋊C4×C83—21no—
130C4⋊C4×C83—41no—
131C4⋊C4×C83—41no—
132C22⋊C4×C83—41no—
133C22⋊C4×C83—41no—
134C22⋊C4×C83—41no—
135C42×C83—41no—
136C42×C83—41no—
137C42×C83—41no—
138C42×C83D811yescharacteristic
139C42×C83D811yescharacteristic
140C42×C83C2×D411yescharacteristic
141C42×C83C2×D411yescharacteristic
142C23×C83—41no—
143C23×C83C2×D811yescharacteristic
144Q8×C83—22no—
145Q8×C83—41no—
146D4×C83—22no—
147D4×C83—44no—
148D4×C83—41no—
149C2×C4×C83—21no—
150C2×C4×C83—21no—
151C2×C4×C83—22no—
152C2×C4×C83—41no—
153C2×C4×C83—44no—
154C2×C4×C83—41no—
155C2×C4×C83—41no—
156C2×C4×C83—41no—
157C2×C4×C83—82no—
158C2×C4×C83—82no—
159C2×C4×C83C2×D811yescharacteristic
160C2×C4×C83C2×D811yescharacteristic
161C2×C4×C83C2×D811yescharacteristic
162C2×C4×C83C2×D811yescharacteristic
163C2×C4×C83C2×D811yescharacteristic
164C2×C4×C83C22×D411yescharacteristic
165C2×Dic83—42no—
166C2×Dic83—42no—
167Dic166—42no—
168Dic166—42no—
169Dic166—82no—
170C8×C83—21no—
171C8×C83—21no—
172C8×C83—21no—
173C8×C83C2×#4111yescharacteristic
174C8×C83C2×#4111yescharacteristic
175C22×C83—21no—
176C22×C83—21no—
177C22×C83—21no—
178C22×C83—42no—
179C22×C83—81no—
180C22×C83—81no—
181C22×C83C22×D811yescharacteristic
182C4×C83—21no—
183C4×C83—21no—
184C4×C83—21no—
185C4×C83—21no—
186C4×C83—42no—
187C4×C83—81no—
188C4×C83—81no—
189C4×C83#51012yes—
190C4×C83#52511yescharacteristic
191C4×C83#57511yescharacteristic
192Dic83—82no—
193Dic83—82no—
194#33676—831nomaximal, Sylow
195C2×C83—41no—
196C2×C83—82no—
197C2×C83#310011yescharacteristic
198C2×C83C2×#51011yescharacteristic
199C2×C83#341411yescharacteristic
200#3170—831no—
201C4×#135D8311yescharacteristic
202#2237—832no—
203#2227—831no—
204#2226—831no—
205#2209—831no—
206#2208—831no—
207#2189—832no—
208#2176—832no—
209#2175—832no—
210#2163—831no—
211C83#3367611yescharacteristic, complemented, Sylow
212C2×#135C2×D8311yescharacteristic
213#533—1661no—
214C4×#41—21no—
215C2×Q32—832no—
216C2×SD32—832no—
217#500—831no—
218#494—831no—
219#487—1661no—
220#467—832no—
221#467—1661no—
222C4×Q16—832no—
223C4×Q16—1661no—
224C4×Q16C2×D8311yescharacteristic
225C4×Q16C2×D8311yescharacteristic
226C4×SD16—21no—
227C4×SD16—21no—
228C4×D8C2×D8311yescharacteristic
229C4×D8C2×D8311yescharacteristic
230#427C2×D8311yescharacteristic
231#416—21no—
232C2×C4×C8C2×D8311yescharacteristic
233#367—832no—
234#366—832no—
235C4⋊C16—831no—
236C4⋊C16—831no—
237#358—832no—
238#358—832no—
239#358—832no—
240#357—832no—
241C22⋊C16—832no—
242#346—832no—
243C2×#41—21no—
244#135—22no—
245#135—22no—
246C2×Q16—832no—
247C2×Q16—1661no—
248C2×Q16C22×D8311yescharacteristic
249C2×SD16—21no—
250C2×D8C22×D8311yescharacteristic
251C22×C8C22⋊D8311yescharacteristic
252C22×C8C22×D8311yescharacteristic
253C4⋊Q8—1661no—
254C4⋊Q8—1661no—
255#125—3321no—
256C22⋊Q8—3321no—
257C22⋊Q8—1662no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—3321no—
261C4×Q8—1662no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—41no—
265C4×D4—41no—
266#117—21no—
267#117—41no—
268#117—3321no—
269C2×C42—41no—
270C2×C42C22⋊D8311yescharacteristic
271Q32—1664no—
272SD32—1664no—
273C2×C16—832no—
274C2×C16—832no—
275#107—832no—
276#107—1661no—
277#107C22×D8311yescharacteristic
278#107C22×D8311yescharacteristic
279#106—21no—
280#103—21no—
281#103—21no—
282#103—1662no—
283#103—1662no—
284#102—21no—
285#102—21no—
286C4×C8C22⋊D8311yescharacteristic
287C4×C8C22⋊D8311yescharacteristic
288C4×C8C22×D8311yescharacteristic
289C4×C8C22×D8311yescharacteristic
290#41—24no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—3321no—
294C2×Q8—1662no—
295C2×D4—21no—
296C2×D4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4#1305057511yescharacteristic
301C22×C4#1305057511yescharacteristic
302C22×C4C2×C22⋊D8311yescharacteristic
303Q16—21no—
304Q16—3322no—
305Q16—1662no—
306Q16—1662no—
307Q16#1305059012yes—
308SD16—24no—
309D8—21no—
310D8#1305059012yes—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8C2×C22⋊D8311yescharacteristic
315C2×C8C2×C22⋊D8311yescharacteristic
316C2×C8C2×C22⋊D8311yescharacteristic
317C2×C8C23×D8311yescharacteristic
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—3321no—
323C4⋊C4—3321no—
324C4⋊C4—3321no—
325C4⋊C4—3322no—
326C4⋊C4—3322no—
327C4⋊C4—1662no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—3322no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—3322no—
336C42#1305057511yescharacteristic
337C42#1305057511yescharacteristic
338C42C2×C22⋊D8311yescharacteristic
339C42C2×C22⋊D8311yescharacteristic
340C16—1662no—
341C16—1662no—
342C23—41no—
343C23C2×#1305057511yescharacteristic
344Q8—22no—
345Q8—41no—
346Q8—3322no—
347Q8—3322no—
348Q8—6642no—
349D4—22no—
350D4—44no—
351D4—41no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—44no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—3322no—
363C2×C4—3322no—
364C2×C4C2×#1305057511yescharacteristic
365C2×C4C2×#1305057511yescharacteristic
366C2×C4C2×#1305057511yescharacteristic
367C2×C4C2×#1305057511yescharacteristic
368C2×C4C2×#1305057511yescharacteristic
369C2×C4C22×C22⋊D8311yescharacteristic
370C8—21no—
371C8—21no—
372C8—21no—
373C8C2×#1305059011yescharacteristic
374C8C2×#1305059011yescharacteristic
375C22—21no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22C22×#1305057511yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—81no—
389C4—6642no—
390C4—6642no—
391C4#1912814112yes—
392C4#1912821211yescharacteristic
393C4#1912849911yescharacteristic
394C2—41no—
395C2—82no—
396C2#2491746311yescharacteristic
397C2C2×#1912814111yescharacteristic
398C2#2492059711yescharacteristic
subgroupG/H
centerC22C22×#13050575
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC4×#135×C83C2
socleC22×C83C22×D8
prime radicalC2×#135×C83C22
hypercenterC4×#135D83
hypocenterC83#33676
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #24918049C2semidirect
2. #24909671C2semidirect
3. #24909615C2semidirect
4. #24909610C2semidirect
5. #24909513C2semidirect
6. #24909508C2semidirect
8. #24909332C2semidirect
9. #24909327C2semidirect
10. #24909266C2semidirect
211. C83#33676semidirect

Maximal subgroups

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

subgroupindex
#249180492
#249096712
#249096152
#249096102
#249095132
#249095082
#249094032
#249093322
#249093272
#249092662
C4×#135×C832
#3367683