Finite Group Databasebeta

← #35297279

Subgroups — #35297279

Order 21248.

462 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14581798C211yesmaximal, characteristic
2#24906211C211yesmaximal, characteristic, complemented
3#24905848C212yesmaximal
4#24905313C212yesmaximal, complemented
5C2×#334×C83C211yesmaximal, characteristic, complemented
6C2×#14581798C411yescharacteristic
7C2×#14581798C411yescharacteristic
8C4×#13050590C2211yescharacteristic
9#19127754C2212yes—
10#19127656C411yescharacteristic
11#19127656C411yescharacteristic
12#19127655—21no—
13#19127655—21no—
14C4×#13050574C2211yescharacteristic
15C4×#13050573—21no—
16C4×C8×D83—21no—
17#19127454—21no—
18#19127452—21no—
19#19127431—22no—
20#19127428—22no—
21C2×C4⋊C8×C83C2212yes—
22C2×C4×C8×C83C2211yescharacteristic
23#334×C83—21no—
24#334×C83—21no—
25C2×#13050590C2×C411yescharacteristic
26#14581798—22no—
27#14581798—22no—
28#14581798—22no—
29#14581798C814yescomplemented
30C2×#13050574C2×C411yescharacteristic
31C2×#13050574C2×C411yescharacteristic
32C2×#13050573—21no—
33C2×#13050573—21no—
34C2×C8×D83—21no—
35C2×C8×D83—21no—
36C4×Dic166D411yescharacteristic
37C4×Dic166Q811yescharacteristic
38C4×D332D411yescharacteristic
39C4×D332Q811yescharacteristic
40C4×C22⋊D83—21no—
41C4×C22⋊D83—21no—
42#14581751C2×C411yescharacteristic
43#14581749—21no—
44C42×D83—21no—
45C4⋊(C83⋊C8)—22no—
46C22⋊(C83⋊C8)—22no—
47#14581703—21no—
48#14581702—21no—
49#14581702—21no—
50C4×C83⋊C8—21no—
51C4×C83⋊C8—22no—
52C8×Dic83—21no—
53C8×Dic83—21no—
54C22×C8×C83—22no—
55C22×C8×C83C2×C411yescharacteristic
56C22×C8×C83C2×C411yescharacteristic
57C2×C42×C83C2311yescharacteristic
58C4⋊C8×C83—22no—
59C4⋊C8×C83—22no—
60C4×C8×C83D411yescharacteristic
61C4×C8×C83D411yescharacteristic
62C4×C8×C83D411yescharacteristic
63C4×C8×C83D411yescharacteristic
64#13050590—21no—
65#13050590—21no—
66#13050590C2×C812yes—
67#13050590M1612yes—
68C2×Dic166C4⋊C411yescharacteristic
69C2×D332C4⋊C411yescharacteristic
70C2×C22⋊D83—21no—
71C2×C4×D83—21no—
72C2×C4×D83—21no—
73C2×C4×D83—21no—
74#13050574—21no—
75#13050574—21no—
76#13050574C2×C812yes—
77#13050574M1612yes—
78#13050573—24no—
79#13050573—24no—
80C2×C83⋊C8—21no—
81C2×C83⋊C8—21no—
82C2×C83⋊C8—42no—
83C8×D83—24no—
84C8×D83—24no—
85C4⋊Dic83C4⋊C411yescharacteristic
86C4⋊Dic83C4⋊C411yescharacteristic
87Dic83⋊C4—21no—
88Dic83⋊C4—21no—
89C22⋊Dic83—21no—
90(C2×D83)⋊C4—21no—
91(C2×D83)⋊C4—21no—
92C4×Dic83—21no—
93C4×Dic83—21no—
94C4×Dic83—21no—
95C22×C4×C83C22×C411yescharacteristic
96C22×C4×C83#4111yescharacteristic
97C22×C4×C83#4111yescharacteristic
98C2×C8×C83—21no—
99C2×C8×C83—21no—
100C2×C8×C83—42no—
101C2×C8×C83—82no—
102C2×C8×C83C22⋊C411yescharacteristic
103C2×C8×C83C22⋊C411yescharacteristic
104C2×C8×C83C22⋊C411yescharacteristic
105C2×C8×C83C22⋊C411yescharacteristic
106C2×C8×C83C2×C812yes—
107C2×C8×C83M1612yes—
108C42×C83C2×D411yescharacteristic
109C42×C83C2×D411yescharacteristic
110C42×C83C2×D411yescharacteristic
111C42×C83C2×Q811yescharacteristic
112C23×C83#11711yescharacteristic
113C22×D83—21no—
114C2×C4×C83—22no—
115C2×C4×C83—41no—
116C2×C4×C83C2×C22⋊C411yescharacteristic
117C2×C4×C83C2×C4⋊C411yescharacteristic
118C2×C4×C83#12111yescharacteristic
119C2×C4×C83#12111yescharacteristic
120C2×C4×C83C22⋊Q811yescharacteristic
121C2×C4×C83C22⋊Q811yescharacteristic
122C2×C4×C83C22×C811yescharacteristic
123C2×C4×C83C2×M1611yescharacteristic
124C2×C4×C83C2×M1611yescharacteristic
125C2×C4×C83C2×M1611yescharacteristic
126C22⋊D83—22no—
127C22⋊D83—22no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131D332—21no—
132D332C4⋊C812yes—
133C4×D83—22no—
134C4×D83—22no—
135C4×D83—42no—
136C4×D83—42no—
137Dic166—21no—
138Dic166C4⋊C812yes—
139C8×C83—21no—
140C8×C83—21no—
141C8×C83—82no—
142C8×C83C22⋊C812yes—
143C8×C83C22⋊C812yes—
144C83⋊C8—22no—
145C83⋊C8—22no—
146C83⋊C8—82no—
147C22×C83—21no—
148C22×C83—21no—
149C22×C83#38011yescharacteristic
150C22×C83#43111yescharacteristic
151C22×C83#43211yescharacteristic
152C2×D83—22no—
153C2×D83—41no—
154C2×D83—41no—
155C4×C83—21no—
156C4×C83—21no—
157C4×C83—21no—
158C4×C83C2×C22⋊C811yescharacteristic
159C4×C83#40711yescharacteristic
160C4×C83C2×C4⋊C811yescharacteristic
161C4×C83#42311yescharacteristic
162C4×C83#47112yes—
163Dic83—22no—
164Dic83—41no—
165Dic83—41no—
166#8604—831nomaximal, Sylow
167C2×C83—21no—
168C2×C83—21no—
169C2×C83#179711yescharacteristic
170C2×C83#181411yescharacteristic
171C2×C83#181511yescharacteristic
172D83—42no—
173C4×#131—831no—
174#1564—831no—
175C2×#334D8311yescharacteristic, complemented
176#1477—832no—
177#1283—832no—
178C83#860411yescharacteristic, complemented, Sylow
179C2×#131—831no—
180C2×#131—831no—
181C4×#41—831no—
182#431—832no—
183C2×C4⋊C8C2×D8312yes—
184#405—831no—
185#405—831no—
186#405—1661no—
187#405—1661no—
188C4×M16—831no—
189C4×M16—1661no—
190C2×C4×C8—1661no—
191C2×C4×C8C2×D8311yescharacteristic
192#335—1661no—
193#334—21no—
194#334—21no—
195#334—1661no—
196Q8⋊C8—1662no—
197D4⋊C8—1662no—
198C2×#41—831no—
199#131—834no—
200#131—1662no—
201#131—1662no—
202#131—1662no—
203C2×M16—831no—
204C2×M16—831no—
205C2×M16—1661no—
206C2×M16—1661no—
207C22×C8—22no—
208C22×C8—1661no—
209C22×C8—1661no—
210C22×C8C4×D8311yescharacteristic
211C22×C8C4×D8311yescharacteristic
212C4×Q8—831no—
213C4×Q8—831no—
214C4×D4—831no—
215C4×D4—831no—
216C4×D4—1661no—
217C4×D4—1661no—
218#117—831no—
219#117—1661no—
220C2×C42—1661no—
221C2×C42C22×D8311yescharacteristic
222C4⋊C8—22no—
223C4⋊C8—22no—
224C4⋊C8—1662no—
225C22⋊C8—1662no—
226#97—1661no—
227#97—1661no—
228#97—1661no—
229C4×C8—1661no—
230C4×C8—1661no—
231C4×C8—1662no—
232C4×C8—1661no—
233C4×C8D33211yescharacteristic
234C4×C8D33211yescharacteristic
235C4×C8C22⋊D8311yescharacteristic
236C4×C8C22⋊D8311yescharacteristic
237#41—832no—
238#41—832no—
239#41—1661no—
240#41—1661no—
241C2×Q8—831no—
242C2×D4—831no—
243C2×D4—1661no—
244C22×C4—1661no—
245C22×C4—1661no—
246C22×C4—1661no—
247C22×C4C2×C4×D8311yescharacteristic
248C22×C4#1305058911yescharacteristic
249C22×C4#1305059111yescharacteristic
250M16—832no—
251M16—832no—
252M16—1664no—
253M16—1661no—
254M16—1661no—
255M16—1664no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—42no—
259C2×C8—82no—
260C2×C8—3322no—
261C2×C8—1664no—
262C2×C8—1661no—
263C2×C8—1661no—
264C2×C8—1664no—
265C2×C8(C2×D83)⋊C411yescharacteristic
266C2×C8(C2×D83)⋊C411yescharacteristic
267C2×C8(C2×D83)⋊C411yescharacteristic
268C2×C8(C2×D83)⋊C411yescharacteristic
269C2×C8C8×D8312yes—
270C2×C8#1305057312yes—
271C4⋊C4—831no—
272C4⋊C4—831no—
273C4⋊C4—1661no—
274C4⋊C4—1661no—
275C22⋊C4—1661no—
276C22⋊C4—1661no—
277C22⋊C4—1661no—
278C42—1661no—
279C42—1661no—
280C42—1661no—
281C42D4×D8311yescharacteristic
282C42C2×C22⋊D8311yescharacteristic
283C42C2×D33211yescharacteristic
284C42Q8×D8311yescharacteristic
285C23—1661no—
286C23#1458175011yescharacteristic
287Q8—832no—
288Q8—1661no—
289D4—832no—
290D4—1662no—
291D4—1662no—
292D4—1661no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—3322no—
296C2×C4—3322no—
297C2×C4—1661no—
298C2×C4—1661no—
299C2×C4—1661no—
300C2×C4—1662no—
301C2×C4—1662no—
302C2×C4C2×(C2×D83)⋊C411yescharacteristic
303C2×C4C4⋊C4×D8311yescharacteristic
304C2×C4#1458176311yescharacteristic
305C2×C4#1458176711yescharacteristic
306C2×C4#1458176811yescharacteristic
307C2×C4#1458177211yescharacteristic
308C2×C4C2×C8×D8311yescharacteristic
309C2×C4M16×D8311yescharacteristic
310C2×C4M16×D8311yescharacteristic
311C2×C4C2×#1305057311yescharacteristic
312C8—21no—
313C8—21no—
314C8—82no—
315C8—6642no—
316C8—1662no—
317C8—1662no—
318C8(C2×D83)⋊C812yes—
319C8(C2×D83)⋊C812yes—
320C22—21no—
321C22—21no—
322C22—3321no—
323C22—3321no—
324C22—1662no—
325C22#1912755811yescharacteristic
326C22#1912775311yescharacteristic
327C22#1912775711yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—3321no—
332C4—3321no—
333C4—1662no—
334C4C2×(C2×D83)⋊C811yescharacteristic
335C4#1912766411yescharacteristic
336C4C4⋊C8×D8311yescharacteristic
337C4#1912772311yescharacteristic
338C4#1912796112yes—
339C2—21no—
340C2—21no—
341C2—3322no—
342C2#2490744011yescharacteristic
343C2#2490751811yescharacteristic
344C2#2490752311yescharacteristic
subgroupG/H
centerC2×C4#14581763
commutatorC2×C4×C83C22×C8
FrattiniC2×C42C22×D83
FittingC2×#334×C83C2
socleC22×C83#380
prime radicalC2×#13050590C2×C4
cosocleC2×C42×C83C23
hypercenterC2×#334D83
hypocenterC83#8604
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #24906211C2semidirect
4. #24905313C2semidirect
5. C2×#334×C83C2semidirect
29. #14581798C8semidirect
175. C2×#334D83semidirect
178. C83#8604semidirect

Maximal subgroups

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

subgroupindex
C4×#145817982
#249062112
#249058482
#249053132
C2×#334×C832
#860483