Finite Group Databasebeta

← #35301180

Subgroups — #35301180

Order 21248.

490 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916935C211yesmaximal, characteristic
2#24907478C211yesmaximal, characteristic, complemented
3#24906024C211yesmaximal, characteristic
4#24905863C211yesmaximal, characteristic
5#24905359C211yesmaximal, characteristic, complemented
6#24905322C211yesmaximal, characteristic, complemented
7C83×#2982C211yesmaximal, characteristic, complemented
8C2×#14581823—21no—
9#19128251C2211yescharacteristic
10#19127923—22no—
11#19127911C412yescomplemented
12#19127901C412yescomplemented
13#19127725C2211yescharacteristic
14C2×C4⋊(C83⋊C8)C2211yescharacteristic
15#19127700—21no—
16C2×#14581716—21no—
17#19127567C2211yescharacteristic
18#19127463—21no—
19#19127436—22no—
20#19127430—22no—
21C2×C4×Q8×C83C2211yescharacteristic
22C8×Q8×C83—22no—
23C8×Q8×C83—22no—
24#431×C83—22no—
25#431×C83C2211yescharacteristic
26#431×C83C2211yescharacteristic
27C2×#13050590—21no—
28#14581823—42no—
29#14581823—42no—
30C2×#13050580—22no—
31C2×#13050577—22no—
32C2×#13050574—21no—
33C22×C83⋊C8—21no—
34#14581792C2×C411yescharacteristic
35#14581789C2×C411yescharacteristic
36#14581780—21no—
37#14581766—21no—
38#14581766—21no—
39C4×D332—21no—
40C4×D332—21no—
41C2×C4⋊Dic83—21no—
42C4⋊(C83⋊C8)—21no—
43C4⋊(C83⋊C8)—21no—
44C4⋊(C83⋊C8)—21no—
45C4⋊(C83⋊C8)C2×C412yes—
46#14581716—42no—
47#14581715—22no—
48#14581712—22no—
49C83⋊#95—21no—
50C83⋊#95—21no—
51C22×Q8×C83D411yescharacteristic
52C4×Q8×C83—21no—
53C4×Q8×C83—21no—
54C4×Q8×C83C2×C412yes—
55C4×Q8×C83D412yes—
56C2×C4⋊C4×C83—21no—
57C2×C4⋊C4×C83D411yescharacteristic
58C2×C42×C83—21no—
59C2×C42×C83C2311yescharacteristic
60C4⋊C8×C83—24no—
61C4⋊C8×C83—21no—
62C4⋊C8×C83—21no—
63C22⋊C8×C83—21no—
64C22⋊C8×C83D412yes—
65C4×C8×C83—24no—
66C4×C8×C83—21no—
67C4×C8×C83D412yes—
68#13050590—41no—
69#13050590—41no—
70#13050590—41no—
71#13050590—41no—
72C2×Dic166—21no—
73C2×D332—21no—
74C2×D332—21no—
75C2×D332—21no—
76C2×C22⋊D83—41no—
77C22×Dic83—41no—
78C2×C4×D83—41no—
79#13050580—44no—
80#13050577—44no—
81#13050574—41no—
82#13050574—41no—
83C2×C83⋊C8—22no—
84C2×C83⋊C8—41no—
85C2×C83⋊C8—41no—
86C2×C83⋊C8—41no—
87C4⋊Dic83—21no—
88C4⋊Dic83—21no—
89C4⋊Dic83—41no—
90C4⋊Dic83—41no—
91(C2×D83)⋊C4—41no—
92(C2×D83)⋊C4—41no—
93C2×Q8×C83—21no—
94C2×Q8×C83—21no—
95C2×Q8×C83—21no—
96C2×Q8×C83C22⋊C412yes—
97C2×Q8×C83D812yes—
98C2×Q8×C83SD1612yes—
99C22×C4×C83—21no—
100C22×C4×C83—21no—
101C22×C4×C83C2×D411yescharacteristic
102C22×C4×C83C2×D411yescharacteristic
103C22×C4×C83#4111yescharacteristic
104C2×C8×C83—22no—
105C2×C8×C83—22no—
106C4⋊C4×C83—22no—
107C4⋊C4×C83—21no—
108C4⋊C4×C83—22no—
109C4⋊C4×C83C22⋊C412yes—
110C42×C83—22no—
111C42×C83—22no—
112C42×C83C22×C411yescharacteristic
113C42×C83C2×D411yescharacteristic
114C42×C83C2×D411yescharacteristic
115C42×C83#4111yescharacteristic
116C23×C83#12111yescharacteristic
117C22×D83—41no—
118Q8×C83—22no—
119Q8×C83—22no—
120Q8×C83—22no—
121Q8×C83#10214yes—
122C2×C4×C83—22no—
123C2×C4×C83—22no—
124C2×C4×C83—22no—
125C2×C4×C83—22no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—81no—
129C2×C4×C83C2×C22⋊C411yescharacteristic
130C2×C4×C83C4×D411yescharacteristic
131C2×C4×C83C4×D411yescharacteristic
132C2×C4×C83#12011yescharacteristic
133C2×C4×C83#12111yescharacteristic
134C2×C4×C83#12311yescharacteristic
135C2×C4×C83C2×D811yescharacteristic
136C2×C4×C83C2×SD1611yescharacteristic
137C2×C4×C83#13511yescharacteristic
138C2×C4×C83#13511yescharacteristic
139C22⋊D83—81no—
140C22⋊D83—81no—
141C2×Dic83—41no—
142C2×Dic83—81no—
143C2×Dic83—81no—
144C2×Dic83—81no—
145D332—42no—
146D332—41no—
147D332—41no—
148D332—81no—
149C4×D83—81no—
150C4×D83—81no—
151Dic166—41no—
152Dic166—41no—
153C8×C83—42no—
154C8×C83—42no—
155C83⋊C8—42no—
156C83⋊C8—81no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83#38611yescharacteristic
160C22×C83#46511yescharacteristic
161C22×C83#46611yescharacteristic
162C2×D83—81no—
163C2×D83—81no—
164C2×D83—81no—
165C4×C83—21no—
166C4×C83—21no—
167C4×C83—24no—
168C4×C83—21no—
169C4×C83—21no—
170C4×C83—42no—
171C4×C83C2×#10211yescharacteristic
172C4×C83#41611yescharacteristic
173C4×C83#46511yescharacteristic
174C4×C83#46611yescharacteristic
175Dic83—81no—
176Dic83—161no—
177#9306—831nomaximal, Sylow
178C2×C83—21no—
179C2×C83—21no—
180C2×C83#188111yescharacteristic
181C2×C83#189311yescharacteristic
182C2×C83#190511yescharacteristic
183D83—161no—
184#3037—831no—
185#2982D8311yescharacteristic, complemented
186#1805—831no—
187#1517—831no—
188#1480—831no—
189#1301—831no—
190#1286—831no—
191C83#930611yescharacteristic, complemented, Sylow
192C2×#137—1661no—
193#532—831no—
194C2×C4×Q8C2×D8311yescharacteristic
195#464—1662no—
196#462—832no—
197#460—832no—
198C8×Q8—22no—
199C8×Q8—22no—
200#431—22no—
201#431C2×D8311yescharacteristic
202#431C2×D8311yescharacteristic
203#423—831no—
204C2×C4⋊C8—831no—
205#417—1661no—
206C2×#103—1661no—
207#382—831no—
208#340—1661no—
209#327—1662no—
210D4⋊C8—1662no—
211C2×#41—1661no—
212C22×Q8D33211yescharacteristic
213#137—3322no—
214#137—3322no—
215C2×Q16—1662no—
216C2×SD16—1662no—
217C2×M16—1661no—
218C22×C8—1661no—
219C4⋊Q8—831no—
220#127—831no—
221#124—1661no—
222#121—1661no—
223#121—1661no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8C4×D8312yes—
227C4×Q8C22⋊D8312yes—
228C4×D4—1661no—
229C4×D4—1661no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—1661no—
232C2×C4⋊C4D33211yescharacteristic
233C2×C42—21no—
234C2×C42C22×D8311yescharacteristic
235C4⋊C8—24no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—832no—
239C4⋊C8—1661no—
240C4⋊C8—1661no—
241C4⋊C8—1661no—
242#103—3322no—
243#103—1662no—
244#102—1662no—
245C22⋊C8—21no—
246C22⋊C8C22⋊D8312yes—
247C4×C8—24no—
248C4×C8—21no—
249C4×C8C22⋊D8312yes—
250#95—1661no—
251#95—1661no—
252#41—3321no—
253#41—3321no—
254#41—3321no—
255#41—3321no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—1661no—
260C2×Q8(C2×D83)⋊C412yes—
261C2×Q8D66412yes—
262C2×Q8#1305057912yes—
263C2×D4—3321no—
264C2×D4—1661no—
265C2×D4—1661no—
266C2×D4—1661no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3321no—
270C22×C4—3321no—
271C22×C4C2×C22⋊D8311yescharacteristic
272C22×C4C2×D33211yescharacteristic
273C22×C4#1305059011yescharacteristic
274Q16—3324no—
275SD16—3324no—
276M16—3321no—
277M16—3321no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—3321no—
281C2×C8—3321no—
282C2×C8—3321no—
283C2×C8—1662no—
284C4⋊C4—21no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—3321no—
288C4⋊C4—3321no—
289C4⋊C4—1661no—
290C4⋊C4—1661no—
291C4⋊C4(C2×D83)⋊C412yes—
292C22⋊C4—3321no—
293C22⋊C4—3321no—
294C42—22no—
295C42—22no—
296C42C2×C4×D8311yescharacteristic
297C42C2×C22⋊D8311yescharacteristic
298C42C2×C22⋊D8311yescharacteristic
299C42#1305059011yescharacteristic
300C23—3321no—
301C23#1458176611yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—22no—
305Q8—3321no—
306Q8—3321no—
307Q8#1458171414yes—
308D4—3322no—
309D4—3321no—
310D4—3321no—
311D4—6641no—
312D4—6641no—
313D4—6641no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—3321no—
322C2×C4—6641no—
323C2×C4—6641no—
324C2×C4—6641no—
325C2×C4—6641no—
326C2×C4—6641no—
327C2×C4C2×(C2×D83)⋊C411yescharacteristic
328C2×C4C4×C22⋊D8311yescharacteristic
329C2×C4C4×C22⋊D8311yescharacteristic
330C2×C4#1458176111yescharacteristic
331C2×C4#1458176611yescharacteristic
332C2×C4#1458177511yescharacteristic
333C2×C4C2×D66411yescharacteristic
334C2×C4C2×#1305057911yescharacteristic
335C2×C4#1458181411yescharacteristic
336C2×C4#1458181411yescharacteristic
337C8—42no—
338C8—42no—
339C8—3322no—
340C8—6641no—
341C22—21no—
342C22—21no—
343C22—6641no—
344C22—6641no—
345C22—6641no—
346C22#1912758011yescharacteristic
347C22#1912793011yescharacteristic
348C22#1912793711yescharacteristic
349C4—21no—
350C4—21no—
351C4—24no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—13281no—
356C4—6641no—
357C4C2×#1458171411yescharacteristic
358C4#1912769811yescharacteristic
359C4#1912793011yescharacteristic
360C4#1912793711yescharacteristic
361C2—21no—
362C2—21no—
363C2—13281no—
364C2#2490782511yescharacteristic
365C2#2490789111yescharacteristic
366C2#2490795711yescharacteristic
subgroupG/H
centerC22#19127580
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2982C2
socleC22×C83#386
prime radical#19128251C22
cosocleC2×C42×C83C23
hypercenter#2982D83
hypocenterC83#9306
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #24907478C2semidirect
5. #24905359C2semidirect
6. #24905322C2semidirect
7. C83×#2982C2semidirect
11. #19127911C4semidirect
12. #19127901C4semidirect
185. #2982D83semidirect
191. C83#9306semidirect

Maximal subgroups

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

subgroupindex
#249169352
#249074782
#249060242
#249058632
#249053592
#249053222
C83×#29822
#930683