Finite Group Databasebeta

← #35298727

Subgroups — #35298727

Order 21248.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916129C211yesmaximal, characteristic
2#24907483C211yesmaximal, characteristic
3#24906238C211yesmaximal, characteristic, complemented
4#24906219C211yesmaximal, characteristic, complemented
5#24905365C211yesmaximal, characteristic, complemented
6#24905303C211yesmaximal, characteristic, complemented
7C83×#1476C211yesmaximal, characteristic
8#19127762—22no—
9#19127758—21no—
10#19127754—21no—
11#19127725C2211yescharacteristic
12#19127725C2211yescharacteristic
13C2×C4⋊(C83⋊C8)C2211yescharacteristic
14C2×#14581719—21no—
15#19127668—21no—
16#19127657—21no—
17C4×C4⋊Dic83C2211yescharacteristic
18#19127460—21no—
19#19127454—21no—
20#19127454—21no—
21#19127452—22no—
22C4×#41×C83C2211yescharacteristic
23#431×C83C2211yescharacteristic
24C2×C4×C8×C83C2211yescharacteristic
25Q8⋊C8×C83C411yescharacteristic, complemented
26Q8⋊C8×C83C411yescharacteristic, complemented
27D4⋊C8×C83C411yescharacteristic, complemented
28D4⋊C8×C83C411yescharacteristic, complemented
29C2×#13050574—21no—
30C2×#13050574—21no—
31C22×C83⋊C8—21no—
32C2×C4⋊Dic83—21no—
33C2×C4×Dic83—21no—
34C4⋊(C83⋊C8)—21no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)D412yes—
39C4⋊(C83⋊C8)D411yescharacteristic
40C4⋊(C83⋊C8)D411yescharacteristic
41#14581719—42no—
42C22⋊(C83⋊C8)—22no—
43C22⋊(C83⋊C8)—22no—
44#14581703—22no—
45C4×C83⋊C8—22no—
46C83⋊#95—21no—
47C2×#41×C83D411yescharacteristic
48C22×C8×C83—21no—
49C4×Q8×C83C2×C411yescharacteristic
50C4×Q8×C83Q811yescharacteristic
51C4×D4×C83—21no—
52C4×D4×C83—21no—
53C4×D4×C83C2×C411yescharacteristic
54C4×D4×C83Q811yescharacteristic
55#117×C83—21no—
56#117×C83D411yescharacteristic
57C2×C42×C83—21no—
58C2×C42×C83C2311yescharacteristic
59C4⋊C8×C83C2×C411yescharacteristic
60C4⋊C8×C83C2×C411yescharacteristic
61C22⋊C8×C83—21no—
62C4×C8×C83—21no—
63C4×C8×C83—21no—
64C4×C8×C83C2×C411yescharacteristic
65C4×C8×C83C2×C411yescharacteristic
66C22×Dic83—41no—
67#13050574—41no—
68#13050574—41no—
69#13050574—41no—
70#13050574—41no—
71C2×C83⋊C8—21no—
72C2×C83⋊C8—21no—
73C2×C83⋊C8—22no—
74C2×C83⋊C8—41no—
75C2×C83⋊C8—41no—
76C2×C83⋊C8—41no—
77C4⋊Dic83—22no—
78C4⋊Dic83—41no—
79C4×Dic83—41no—
80C4×Dic83—41no—
81#41×C83—21no—
82#41×C83—21no—
83#41×C83—21no—
84#41×C83—21no—
85C2×Q8×C83C4⋊C411yescharacteristic
86C2×D4×C83—21no—
87C2×D4×C83C4⋊C411yescharacteristic
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—21no—
91C22×C4×C83C2×D411yescharacteristic
92C22×C4×C83#4111yescharacteristic
93C22×C4×C83#4111yescharacteristic
94C2×C8×C83—21no—
95C2×C8×C83—21no—
96C2×C8×C83—21no—
97C2×C8×C83—21no—
98C2×C8×C83—42no—
99C4⋊C4×C83—21no—
100C4⋊C4×C83—21no—
101C4⋊C4×C83C4⋊C411yescharacteristic
102C4⋊C4×C83C4⋊C411yescharacteristic
103C22⋊C4×C83—21no—
104C22⋊C4×C83—21no—
105C22⋊C4×C83—21no—
106C42×C83—21no—
107C42×C83—21no—
108C42×C83—21no—
109C42×C83C22×C411yescharacteristic
110C42×C83C2×D411yescharacteristic
111C42×C83C2×D411yescharacteristic
112C42×C83C2×Q811yescharacteristic
113C23×C83—21no—
114C23×C83#12311yescharacteristic
115Q8×C83—21no—
116Q8×C83—21no—
117D4×C83—21no—
118D4×C83—21no—
119D4×C83—41no—
120D4×C83—41no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83—81no—
132C2×C4×C83C2×C4⋊C411yescharacteristic
133C2×C4×C83C4×D411yescharacteristic
134C2×C4×C83C4×D411yescharacteristic
135C2×C4×C83#12011yescharacteristic
136C2×C4×C83C22⋊Q811yescharacteristic
137C2×C4×C83C22⋊Q811yescharacteristic
138C2×C4×C83#13511yescharacteristic
139C2×C4×C83#13511yescharacteristic
140C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C83#13711yescharacteristic
142C2×Dic83—42no—
143C2×Dic83—81no—
144C2×Dic83—81no—
145C8×C83—22no—
146C8×C83—41no—
147C8×C83—41no—
148C8×C83—41no—
149C83⋊C8—41no—
150C83⋊C8—41no—
151C83⋊C8—42no—
152C83⋊C8—81no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83—41no—
156C22×C83—41no—
157C22×C83—41no—
158C22×C83#38511yescharacteristic
159C22×C83#48211yescharacteristic
160C22×C83#48511yescharacteristic
161C4×C83—21no—
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—41no—
165C4×C83—41no—
166C4×C83—41no—
167C4×C83#42711yescharacteristic
168C4×C83#42811yescharacteristic
169C4×C83#44311yescharacteristic
170C4×C83#44411yescharacteristic
171C4×C83#44911yescharacteristic
172C4×C83#45211yescharacteristic
173Dic83—82no—
174#8905—831nomaximal, Sylow
175C2×C83—21no—
176C2×C83—21no—
177C2×C83—81no—
178C2×C83#185411yescharacteristic
179C2×C83#186111yescharacteristic
180C2×C83#186611yescharacteristic
181#2925—831no—
182#1806—831no—
183#1571—831no—
184#1566—831no—
185#1476D8311yescharacteristic
186#1303—831no—
187#1279—831no—
188C83#890511yescharacteristic, complemented, Sylow
189C4×#41C2×D8311yescharacteristic
190#433—1662no—
191#432—1661no—
192#431—1661no—
193#431C2×D8311yescharacteristic
194#423—831no—
195#423—831no—
196C2×C4⋊C8—831no—
197C2×#104—1661no—
198#408—1661no—
199#405—1661no—
200C2×C4×C8C2×D8311yescharacteristic
201C4×C4⋊C4—831no—
202#339—1661no—
203#335—1661no—
204#335—1661no—
205#334—1662no—
206Q8⋊C8Dic8311yescharacteristic, complemented
207Q8⋊C8Dic8311yescharacteristic, complemented
208D4⋊C8Dic8311yescharacteristic, complemented
209D4⋊C8Dic8311yescharacteristic, complemented
210C2×#41D33211yescharacteristic
211C2×M16—1661no—
212C2×M16—1661no—
213C22×C8—21no—
214C22×C8—1661no—
215C4×Q8Dic16611yescharacteristic
216C4×Q8C2×Dic8311yescharacteristic
217C4×D4—21no—
218C4×D4—21no—
219C4×D4Dic16611yescharacteristic
220C4×D4C2×Dic8311yescharacteristic
221#117—21no—
222#117D33211yescharacteristic
223C2×C4⋊C4—1661no—
224C2×C42—21no—
225C2×C42—1661no—
226C2×C42C22×D8311yescharacteristic
227C4⋊C8—832no—
228C4⋊C8—831no—
229C4⋊C8—831no—
230C4⋊C8—1661no—
231C4⋊C8—1661no—
232C4⋊C8—1661no—
233C4⋊C8—1661no—
234C4⋊C8C2×Dic8311yescharacteristic
235C4⋊C8C2×Dic8311yescharacteristic
236#104—3322no—
237C22⋊C8—21no—
238C22⋊C8—1662no—
239C22⋊C8—1662no—
240#97—1662no—
241C4×C8—21no—
242C4×C8—21no—
243C4×C8—1662no—
244C4×C8C2×Dic8311yescharacteristic
245C4×C8C2×Dic8311yescharacteristic
246#95—1661no—
247#41—21no—
248#41—21no—
249#41—21no—
250#41—21no—
251C2×Q8C4⋊Dic8311yescharacteristic
252C2×D4—21no—
253C2×D4C4⋊Dic8311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—3321no—
258C22×C4C2×D33211yescharacteristic
259C22×C4#1305058911yescharacteristic
260C22×C4#1305058911yescharacteristic
261M16—3321no—
262M16—3321no—
263M16—3321no—
264M16—3321no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—42no—
270C2×C8—3321no—
271C2×C8—3321no—
272C2×C8—3321no—
273C2×C8—1661no—
274C2×C8—1662no—
275C2×C8—1661no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—3321no—
279C4⋊C4—1662no—
280C4⋊C4C4⋊Dic8311yescharacteristic
281C4⋊C4C4⋊Dic8311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C42—21no—
286C42—21no—
287C42—21no—
288C42—3321no—
289C42—3321no—
290C42C22×Dic8311yescharacteristic
291C42D4×D8311yescharacteristic
292C42D4×D8311yescharacteristic
293C42C2×Dic16611yescharacteristic
294C23—21no—
295C23#1458177611yescharacteristic
296Q8—21no—
297Q8—21no—
298D4—21no—
299D4—21no—
300D4—41no—
301D4—41no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—3322no—
314C2×C4—6641no—
315C2×C4—6641no—
316C2×C4C2×C4⋊Dic8311yescharacteristic
317C2×C4D4×Dic8311yescharacteristic
318C2×C4D4×Dic8311yescharacteristic
319C2×C4#1458176211yescharacteristic
320C2×C4#1458176911yescharacteristic
321C2×C4#1458176911yescharacteristic
322C2×C4#1458181411yescharacteristic
323C2×C4#1458181411yescharacteristic
324C2×C4#1458182011yescharacteristic
325C2×C4#1458182511yescharacteristic
326C8—22no—
327C8—41no—
328C8—41no—
329C8—41no—
330C8—3321no—
331C8—3321no—
332C8—3322no—
333C8—6641no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22#1912757611yescharacteristic
340C22#1912802611yescharacteristic
341C22#1912804311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—6642no—
349C4#1912773911yescharacteristic
350C4#1912774311yescharacteristic
351C4#1912781811yescharacteristic
352C4#1912782311yescharacteristic
353C4#1912784811yescharacteristic
354C4#1912786511yescharacteristic
355C2—21no—
356C2—21no—
357C2—81no—
358C2#2490766411yescharacteristic
359C2#2490770511yescharacteristic
360C2#2490774011yescharacteristic
subgroupG/H
centerC2×C4#14581762
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1476C2
socleC22×C83#385
prime radicalC2×#41×C83D4
cosocleC2×C42×C83C23
hypercenter#1476D83
hypocenterC83#8905
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
3. #24906238C2semidirect
4. #24906219C2semidirect
5. #24905365C2semidirect
6. #24905303C2semidirect
25. Q8⋊C8×C83C4semidirect
26. Q8⋊C8×C83C4semidirect
27. D4⋊C8×C83C4semidirect
28. D4⋊C8×C83C4semidirect
188. C83#8905semidirect
206. Q8⋊C8Dic83semidirect
207. Q8⋊C8Dic83semidirect
208. D4⋊C8Dic83semidirect
209. D4⋊C8Dic83semidirect

Maximal subgroups

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

subgroupindex
#249161292
#249074832
#249062382
#249062192
#249053652
#249053032
C83×#14762
#890583