Finite Group Databasebeta

← #35322807

Subgroups — #35322807

Order 21248.

426 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128131C211yesmaximal, characteristic
2C2×#19127530C211yesmaximal, characteristic, complemented
3C2×#19127508C211yesmaximal, characteristic, complemented
4C2×#19127507C211yesmaximal, characteristic, complemented
5C2×C4×C83⋊C16C211yesmaximal, characteristic, complemented
6#24908351C211yesmaximal, characteristic, complemented
7C83×#1974C211yesmaximal, characteristic, complemented
8C2×#14581814C2211yescharacteristic
9#19128131—22no—
10#19128131—22no—
11C2×#14581738C411yescharacteristic, complemented
12C2×#14581736C411yescharacteristic, complemented
13C2×#14581735C411yescharacteristic, complemented
14C2×#14581733C411yescharacteristic, complemented
15C22×C83⋊C16C2211yescharacteristic
16C22×C83⋊C16C2211yescharacteristic
17C2×#14581728C2211yescharacteristic
18C2×#14581720—21no—
19#19127667—21no—
20#19127530—22no—
21#19127508—22no—
22#19127507—22no—
23C4×C83⋊C16—22no—
24C2×#135×C83C2211yescharacteristic
25C2×#108×C83C2211yescharacteristic
26C2×#104×C83—21no—
27#408×C83—21no—
28C2×C4×C8×C83C2211yescharacteristic
29C2×#13050590—21no—
30#14581814—21no—
31#14581814—21no—
32#14581814—21no—
33#14581814—21no—
34C2×Dic332C2×C411yescharacteristic
35C2×#13050579—21no—
36C2×D664C2×C411yescharacteristic
37C2×#13050574—21no—
38#14581738—22no—
39#14581736—22no—
40#14581735—22no—
41#14581733—22no—
42C2×C83⋊C16—21no—
43C2×C83⋊C16—21no—
44C2×C83⋊C16C2×C411yescharacteristic
45C2×C83⋊C16C2×C411yescharacteristic
46C2×C83⋊C16D412yes—
47C2×C83⋊C16D412yes—
48C2×C83⋊C16D412yes—
49#14581728—21no—
50#14581728—21no—
51#14581720—42no—
52(C2×D83)⋊C8—42no—
53C2×#41×C83—21no—
54#135×C83—21no—
55#135×C83—21no—
56#135×C83—21no—
57#135×C83—21no—
58C2×Q16×C83C2×C411yescharacteristic
59C2×SD16×C83—21no—
60C2×D8×C83C2×C411yescharacteristic
61C2×M16×C83—21no—
62C22×C8×C83D411yescharacteristic
63C22×C8×C83C2311yescharacteristic
64C2×C42×C83D411yescharacteristic
65#108×C83—21no—
66#108×C83—21no—
67#104×C83—42no—
68C22⋊C8×C83—42no—
69C4×C8×C83—21no—
70C4×C8×C83—21no—
71#13050590—41no—
72#13050590—41no—
73#13050590—41no—
74#13050590—41no—
75C2×Dic166—21no—
76C2×D332—21no—
77C2×C22⋊D83—41no—
78C2×C4×D83—41no—
79Dic332—21no—
80Dic332—21no—
81#13050579—41no—
82#13050579—41no—
83D664—21no—
84D664—21no—
85#13050574—41no—
86#13050574—41no—
87C2×C83⋊C8—41no—
88C83⋊C16—22no—
89C83⋊C16C22⋊C412yes—
90C83⋊C16C22⋊C412yes—
91#41×C83—41no—
92#41×C83—41no—
93#41×C83—41no—
94#41×C83—41no—
95C2×Q8×C83—21no—
96C2×D4×C83—21no—
97C2×D4×C83—41no—
98C22×C4×C83—21no—
99C22×C4×C83—41no—
100C22×C4×C83C2×D411yescharacteristic
101Q16×C83—21no—
102Q16×C83—21no—
103SD16×C83—41no—
104SD16×C83—41no—
105D8×C83—21no—
106D8×C83—21no—
107M16×C83—41no—
108M16×C83—41no—
109C2×C8×C83—21no—
110C2×C8×C83—21no—
111C2×C8×C83—41no—
112C2×C8×C83D812yes—
113C2×C8×C83C22×C411yescharacteristic
114C2×C8×C83C2×D411yescharacteristic
115C2×C8×C83C2×D411yescharacteristic
116C2×C8×C83C2×D411yescharacteristic
117C2×C8×C83#4111yescharacteristic
118C2×C8×C83#4111yescharacteristic
119C42×C83—21no—
120C42×C83D812yes—
121C23×C83—41no—
122C23×C83#13511yescharacteristic
123C22×D83—41no—
124Q8×C83—41no—
125Q8×C83—41no—
126D4×C83—41no—
127D4×C83—41no—
128D4×C83—81no—
129D4×C83—81no—
130C2×C4×C83—24no—
131C2×C4×C83—22no—
132C2×C4×C83—41no—
133C2×C4×C83—81no—
134C2×C4×C83—81no—
135C2×C4×C83C4×D411yescharacteristic
136C2×C4×C83#12111yescharacteristic
137C2×C4×C83#12711yescharacteristic
138C2×C4×C83C2×D811yescharacteristic
139C2×C4×C83C2×D811yescharacteristic
140C2×C4×C83#13511yescharacteristic
141C22⋊D83—81no—
142C22⋊D83—81no—
143C2×Dic83—41no—
144D332—41no—
145D332—41no—
146C4×D83—81no—
147C4×D83—81no—
148Dic166—41no—
149Dic166—41no—
150C8×C83—22no—
151C8×C83—81no—
152C8×C83C2×C22⋊C411yescharacteristic
153C8×C83C4×D411yescharacteristic
154C8×C83#12111yescharacteristic
155C8×C83#12411yescharacteristic
156C83⋊C8—81no—
157C22×C83—22no—
158C22×C83—82no—
159C22×C83—81no—
160C22×C83C4×D811yescharacteristic
161C22×C83#46611yescharacteristic
162C22×C83#49511yescharacteristic
163C2×D83—82no—
164C2×D83—81no—
165C4×C83—24no—
166C4×C83—81no—
167C4×C83#39011yescharacteristic
168C4×C83C4×D811yescharacteristic
169C4×C83#46611yescharacteristic
170C4×C83#49311yescharacteristic
171Dic83—81no—
172#13241—831nomaximal, Sylow
173C2×C83—21no—
174C2×C83—21no—
175C2×C83—161no—
176C2×C83#197011yescharacteristic
177C2×C83#217812yes—
178D83—161no—
179C2×#508—831no—
180C2×#368—831no—
181C2×#359—831no—
182C2×#359—831no—
183C2×C4×C16—831no—
184#1974—831no—
185#1974D8311yescharacteristic, complemented
186C83#1324111yescharacteristic, complemented, Sylow
187C2×#135—831no—
188C2×#135C2×D8311yescharacteristic
189#508—1662no—
190#508—1662no—
191C2×Q32—831no—
192C2×SD32—831no—
193C2×SD32—831no—
194C2×D16—831no—
195C22×C16—831no—
196C22×C16—831no—
197C2×#108—831no—
198C2×#108C2×D8311yescharacteristic
199C2×#104—21no—
200C2×#104—1661no—
201#408—21no—
202#408—1661no—
203C2×C4×C8C2×D8311yescharacteristic
204#368—1662no—
205#359—1662no—
206#359—1662no—
207C4×C16—1662no—
208C2×#41—21no—
209C2×#41—1661no—
210#135—21no—
211#135—21no—
212#135—21no—
213#135—21no—
214#135—1661no—
215#135—1661no—
216#135—1661no—
217#135—1661no—
218C2×Q16—831no—
219C2×Q16C4×D8311yescharacteristic
220C2×SD16—21no—
221C2×SD16—1661no—
222C2×D8—831no—
223C2×D8C4×D8311yescharacteristic
224C2×M16—21no—
225C2×M16—1661no—
226C22×C8C22⋊D8311yescharacteristic
227C22×C8C22×D8311yescharacteristic
228C2×C42C22⋊D8311yescharacteristic
229Q32—1662no—
230SD32—1662no—
231SD32—1662no—
232D16—1662no—
233C2×C16—831no—
234C2×C16—831no—
235C2×C16—832no—
236C2×C16—832no—
237C2×C16—832no—
238C2×C16—1661no—
239C2×C16—1661no—
240#108—21no—
241#108—21no—
242#108—1661no—
243#108—1661no—
244#104—42no—
245#104—3322no—
246C22⋊C8—42no—
247C22⋊C8—3322no—
248C4×C8—21no—
249C4×C8—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—3321no—
255#41—3321no—
256#41—3321no—
257#41—3321no—
258C2×Q8—21no—
259C2×Q8—1661no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—3321no—
263C2×D4—1661no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—3321no—
267C22×C4C2×C22⋊D8311yescharacteristic
268Q16—21no—
269Q16—21no—
270Q16—1661no—
271Q16—1661no—
272SD16—41no—
273SD16—41no—
274SD16—3321no—
275SD16—3321no—
276D8—21no—
277D8—21no—
278D8—1661no—
279D8—1661no—
280M16—41no—
281M16—41no—
282M16—3321no—
283M16—3321no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—3321no—
288C2×C8#1305057512yes—
289C2×C8C2×C4×D8311yescharacteristic
290C2×C8D4×D8311yescharacteristic
291C2×C8D4×D8311yescharacteristic
292C2×C8D4×D8311yescharacteristic
293C2×C8#1305058911yescharacteristic
294C2×C8#1305059011yescharacteristic
295C42—21no—
296C42#1305057512yes—
297C16—832no—
298C16—832no—
299C16—1662no—
300C23—41no—
301C23—3321no—
302C23#1458181211yescharacteristic
303Q8—41no—
304Q8—41no—
305Q8—3321no—
306Q8—3321no—
307D4—41no—
308D4—41no—
309D4—81no—
310D4—81no—
311D4—3321no—
312D4—3321no—
313D4—6641no—
314D4—6641no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—3321no—
321C2×C4—6641no—
322C2×C4—6641no—
323C2×C4C4×C22⋊D8311yescharacteristic
324C2×C4#1458176411yescharacteristic
325C2×C4#1458178811yescharacteristic
326C2×C4C2×#1305057511yescharacteristic
327C2×C4C2×#1305057511yescharacteristic
328C2×C4#1458181211yescharacteristic
329C8—22no—
330C8—81no—
331C8—6641no—
332C8C22⋊C4×D8311yescharacteristic
333C8(C22⋊D83)⋊C411yescharacteristic
334C8#1458176511yescharacteristic
335C8#1458177811yescharacteristic
336C22—22no—
337C22—82no—
338C22—81no—
339C22—6642no—
340C22—6641no—
341C22C4×#1305057511yescharacteristic
342C22#1912793511yescharacteristic
343C22#1912808311yescharacteristic
344C4—24no—
345C4—81no—
346C4—6641no—
347C4#1912760111yescharacteristic
348C4C4×#1305057511yescharacteristic
349C4#1912793511yescharacteristic
350C4#1912807711yescharacteristic
351C2—21no—
352C2—21no—
353C2—161no—
354C2—13281no—
355C2#2490832811yescharacteristic
356C2#2490934212yes—
subgroupG/H
centerC2×C4C2×#13050575
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC83×#1974C2
socleC22×C83C4×D8
prime radicalC2×#19128131C2
cosocleC22×C8×C83C23
hypercenter#1974D83
hypocenterC83#13241
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#19127530C2semidirect
3. C2×#19127508C2semidirect
4. C2×#19127507C2semidirect
5. C2×C4×C83⋊C16C2semidirect
6. #24908351C2semidirect
7. C83×#1974C2semidirect
11. C2×#14581738C4semidirect
12. C2×#14581736C4semidirect
13. C2×#14581735C4semidirect
14. C2×#14581733C4semidirect
185. #1974D83semidirect
186. C83#13241semidirect

Maximal subgroups

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

subgroupindex
C2×#191281312
C2×#191275302
C2×#191275082
C2×#191275072
C2×C4×C83⋊C162
#249083512
C83×#19742
#1324183