Finite Group Databasebeta

← #35321846

Subgroups — #35321846

Order 21248.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127971C211yesmaximal, characteristic
2C2×#19127515C211yesmaximal, characteristic, complemented
3C2×#19127503C211yesmaximal, characteristic, complemented
4#24907527C211yesmaximal, characteristic, complemented
5#24905572C211yesmaximal, characteristic, complemented
6#24905557C211yesmaximal, characteristic, complemented
7C2×#504×C83C211yesmaximal, characteristic, complemented
8C2×#14581817—21no—
9C22×D664C2211yescharacteristic
10#19127971—22no—
11#19127971C414yescomplemented
12C2×#14581728C2211yescharacteristic
13C2×#14581728C2211yescharacteristic
14C2×#14581726C2211yescharacteristic
15#19127702—21no—
16C2×#14581708—21no—
17#19127515—22no—
18#19127503—21no—
19#19127503—21no—
20#19127469—21no—
21C2×#131×C83C2211yescharacteristic
22#504×C83—22no—
23#504×C83—22no—
24C2×M32×C83—21no—
25C2×M32×C83C2211yescharacteristic
26C22×C16×C83—21no—
27C22×C16×C83C2211yescharacteristic
28C22×D332—21no—
29#14581817—24no—
30#14581817—42no—
31C2×#13050577—41no—
32C2×D664—21no—
33C2×D664—21no—
34C2×D664—21no—
35C2×D664—21no—
36C2×D664—21no—
37C2×D664C2×C412yes—
38C2×#13050575—41no—
39C2×#13050574—21no—
40C2×#13050574—21no—
41C2×C4⋊Dic83—21no—
42#14581728—21no—
43#14581728—21no—
44#14581728—21no—
45#14581728C2×C412yes—
46#14581726—21no—
47#14581726—21no—
48#14581716—41no—
49#14581713—41no—
50#14581708—24no—
51C2×#41×C83D411yescharacteristic
52#131×C83—21no—
53#131×C83—21no—
54#131×C83C2×C412yes—
55#131×C83D412yes—
56C2×M16×C83—21no—
57C2×M16×C83D411yescharacteristic
58C22×C8×C83—21no—
59C22×C8×C83C2311yescharacteristic
60M32×C83—24no—
61M32×C83—21no—
62M32×C83D412yes—
63C2×C16×C83—24no—
64C2×C16×C83—21no—
65C2×C16×C83—21no—
66C2×C16×C83—21no—
67C2×C16×C83D411yescharacteristic
68C2×C16×C83D411yescharacteristic
69C23×D83—41no—
70C2×D332—22no—
71C2×D332—41no—
72C2×D332—41no—
73C2×D332—41no—
74C2×D332—41no—
75C2×D332—41no—
76C22×Dic83—41no—
77#13050577—44no—
78D664—22no—
79D664—22no—
80D664—41no—
81D664—41no—
82#13050575—44no—
83#13050574—22no—
84#13050574—41no—
85#13050574—41no—
86#13050574—41no—
87C2×C83⋊C8—41no—
88C2×C83⋊C8—41no—
89C4⋊Dic83—41no—
90C4⋊Dic83—41no—
91#41×C83—21no—
92#41×C83—21no—
93#41×C83C22⋊C412yes—
94#41×C83SD1612yes—
95C2×Q8×C83D811yescharacteristic
96C2×D4×C83—21no—
97C2×D4×C83D811yescharacteristic
98C22×C4×C83—21no—
99C22×C4×C83C2×D411yescharacteristic
100M16×C83—21no—
101M16×C83—22no—
102M16×C83—22no—
103M16×C83C22⋊C412yes—
104C2×C8×C83—21no—
105C2×C8×C83—22no—
106C2×C8×C83—22no—
107C2×C8×C83C22×C411yescharacteristic
108C2×C8×C83C2×D411yescharacteristic
109C2×C8×C83C2×D411yescharacteristic
110C2×C8×C83C2×D411yescharacteristic
111C2×C8×C83#4111yescharacteristic
112C2×C8×C83#4111yescharacteristic
113C16×C83—21no—
114C16×C83—22no—
115C16×C83—21no—
116C23×C83—21no—
117C23×C83#13511yescharacteristic
118C22×D83—42no—
119C22×D83—81no—
120C22×D83—81no—
121C22×D83—161no—
122C22×D83—161no—
123Q8×C83—21no—
124Q8×C83#10212yes—
125D4×C83—22no—
126D4×C83—22no—
127D4×C83—21no—
128D4×C83#10212yes—
129C2×C4×C83—21no—
130C2×C4×C83—22no—
131C2×C4×C83—22no—
132C2×C4×C83C2×C22⋊C411yescharacteristic
133C2×C4×C83#12111yescharacteristic
134C2×C4×C83#12111yescharacteristic
135C2×C4×C83C2×D811yescharacteristic
136C2×C4×C83C2×SD1611yescharacteristic
137C2×C4×C83#13511yescharacteristic
138C2×Dic83—81no—
139C2×Dic83—161no—
140D332—42no—
141D332—42no—
142D332—81no—
143D332—81no—
144C8×C83—22no—
145C8×C83C4×D411yescharacteristic
146C8×C83C4×D411yescharacteristic
147C8×C83#12011yescharacteristic
148C8×C83#12311yescharacteristic
149C83⋊C8—42no—
150C83⋊C8—81no—
151C22×C83—21no—
152C22×C83—21no—
153C22×C83—22no—
154C22×C83—41no—
155C22×C83—41no—
156C22×C83#41611yescharacteristic
157C22×C83#46511yescharacteristic
158C22×C83#46611yescharacteristic
159C2×D83—82no—
160C2×D83—162no—
161C2×D83—161no—
162C2×D83—161no—
163C2×D83—162no—
164C4×C83—22no—
165C4×C83#38611yescharacteristic
166C4×C83C2×#10211yescharacteristic
167C4×C83#46511yescharacteristic
168C4×C83#46611yescharacteristic
169Dic83—161no—
170#13073—831nomaximal, Sylow
171C2×C83—21no—
172C2×C83—21no—
173C2×C83—42no—
174C2×C83#189311yescharacteristic
175C2×C83#222111yescharacteristic
176C2×C83#222311yescharacteristic
177D83—162no—
178C2×#504D8311yescharacteristic, complemented
179C2×#472—831no—
180C2×#361—831no—
181C2×#357—831no—
182#1816—831no—
183#1387—831no—
184#1381—831no—
185C83#1307311yescharacteristic, complemented, Sylow
186C2×AGL(1,ℤ/8)—1661no—
187C22×D8—831no—
188C2×#131C2×D8311yescharacteristic
189#504—22no—
190#504—22no—
191C2×M32—21no—
192C2×M32C2×D8311yescharacteristic
193C22×C16—21no—
194C22×C16C2×D8311yescharacteristic
195#472—834no—
196#472—1662no—
197C2×#108—831no—
198C2×#108—831no—
199C2×#107—831no—
200#417—1661no—
201C2×#100—1661no—
202#361—1662no—
203#357—1661no—
204#357—1661no—
205#343—1661no—
206C2×#41D33211yescharacteristic
207C22×D4—1661no—
208AGL(1,ℤ/8)—3322no—
209AGL(1,ℤ/8)—1664no—
210C2×SD16—3321no—
211C2×D8—3321no—
212C2×D8—832no—
213C2×D8—1661no—
214C2×D8—1661no—
215C2×D8—1661no—
216C2×D8—1661no—
217C2×D8—1661no—
218#131—21no—
219#131—21no—
220#131C4×D8312yes—
221#131C22⋊D8312yes—
222C2×M16—21no—
223C2×M16—1661no—
224C2×M16—1661no—
225C2×M16D33211yescharacteristic
226C22×C8—21no—
227C22×C8C22×D8311yescharacteristic
228C2×C4⋊C4—1661no—
229M32—24no—
230M32—21no—
231M32C22⋊D8312yes—
232C2×C16—24no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16C22⋊D8311yescharacteristic
237C2×C16C22⋊D8311yescharacteristic
238#108—832no—
239#108—1661no—
240#108—1661no—
241#108—1661no—
242#107—1661no—
243#107—1661no—
244#103—3321no—
245#102—3321no—
246#100—1664no—
247C24—3321no—
248#41—21no—
249#41—21no—
250#41(C2×D83)⋊C412yes—
251#41#1305057912yes—
252C2×Q8D66411yescharacteristic
253C2×D4—21no—
254C2×D4—3321no—
255C2×D4—3321no—
256C2×D4—3321no—
257C2×D4—3321no—
258C2×D4—3321no—
259C2×D4—1662no—
260C2×D4D66411yescharacteristic
261C22×C4—21no—
262C22×C4—3321no—
263C22×C4C2×D33211yescharacteristic
264SD16—3324no—
265D8—3324no—
266D8—3321no—
267D8—3321no—
268D8—1662no—
269D8—1662no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—3321no—
274M16—3321no—
275M16—3321no—
276M16—1662no—
277M16(C2×D83)⋊C412yes—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—3321no—
282C2×C8—3321no—
283C2×C8C2×C4×D8311yescharacteristic
284C2×C8C2×C22⋊D8311yescharacteristic
285C2×C8C2×C22⋊D8311yescharacteristic
286C2×C8C2×C22⋊D8311yescharacteristic
287C2×C8#1305059011yescharacteristic
288C2×C8#1305059011yescharacteristic
289C4⋊C4—3321no—
290C4⋊C4—3321no—
291C16—21no—
292C16—22no—
293C16—21no—
294C23—21no—
295C23—13281no—
296C23—13281no—
297C23—3322no—
298C23—6641no—
299C23—6641no—
300C23#1458181411yescharacteristic
301Q8—21no—
302Q8#1458171412yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—3322no—
307D4—3322no—
308D4—6641no—
309D4—6641no—
310D4#1458171412yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—13281no—
315C2×C4—6641no—
316C2×C4C2×(C2×D83)⋊C411yescharacteristic
317C2×C4#1458176611yescharacteristic
318C2×C4#1458176611yescharacteristic
319C2×C4C2×D66411yescharacteristic
320C2×C4C2×#1305057911yescharacteristic
321C2×C4#1458181411yescharacteristic
322C8—22no—
323C8—3322no—
324C8—6641no—
325C8C4×C22⋊D8311yescharacteristic
326C8C4×C22⋊D8311yescharacteristic
327C8#1458176111yescharacteristic
328C8#1458177511yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—13282no—
335C22—13282no—
336C22—13281no—
337C22—13281no—
338C22—6642no—
339C22#1912769811yescharacteristic
340C22#1912793011yescharacteristic
341C22#1912793711yescharacteristic
342C4—22no—
343C4—13281no—
344C4#1912758011yescharacteristic
345C4C2×#1458171411yescharacteristic
346C4#1912793011yescharacteristic
347C4#1912793711yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—13282no—
352C2#2490789111yescharacteristic
353C2#2490958311yescharacteristic
354C2#2490959311yescharacteristic
subgroupG/H
centerC22#19127937
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC2×#504×C83C2
socleC22×C83#466
prime radicalC2×#19127971C2
cosocleC22×C8×C83C23
hypercenterC2×#504D83
hypocenterC83#13073
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
2. C2×#19127515C2semidirect
3. C2×#19127503C2semidirect
4. #24907527C2semidirect
5. #24905572C2semidirect
6. #24905557C2semidirect
7. C2×#504×C83C2semidirect
11. #19127971C4semidirect
178. C2×#504D83semidirect
185. C83#13073semidirect

Maximal subgroups

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

subgroupindex
C2×#191279712
C2×#191275152
C2×#191275032
#249075272
#249055722
#249055572
C2×#504×C832
#1307383