Finite Group Databasebeta

← #35299972

Subgroups — #35299972

Order 21248.

694 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127754C211yesmaximal, characteristic, complemented
2#24915794C211yesmaximal, characteristic
3C2×#19127434C212yesmaximal
4#24905342C212yesmaximal, complemented
5C83×#1434C211yesmaximal, characteristic, complemented
6C2×#14581775—21no—
7C2×#14581766C2211yescharacteristic
8#19127754—24no—
9C2×C4⋊(C83⋊C8)—21no—
10C2×C22⋊(C83⋊C8)C2212yes—
11C2×C4×C83⋊C8—21no—
12#19127603C411yescharacteristic, complemented
13#19127603C411yescharacteristic, complemented
14#19127599C411yescharacteristic, complemented
15#19127599C411yescharacteristic, complemented
16#19127592—21no—
17#19127592—21no—
18#19127580—21no—
19#19127561C2211yescharacteristic
20#19127434—24no—
21C22×C42×C83C2211yescharacteristic
22C2×#95×C83—21no—
23C2×#95×C83—21no—
24C2×#95×C83C2212yes—
25C22×D332C2×C411yescharacteristic
26C22×C22⋊D83—21no—
27C22×C83⋊C8—22no—
28#14581775—42no—
29#14581775—42no—
30#14581766—22no—
31#14581766—22no—
32C2×C4⋊Dic83C2×C411yescharacteristic
33C2×C4⋊Dic83C2×C411yescharacteristic
34C2×C4⋊Dic83C2×C411yescharacteristic
35C2×Dic83⋊C4—21no—
36C2×Dic83⋊C4—21no—
37C2×C22⋊Dic83—21no—
38C2×(C2×D83)⋊C4—21no—
39C2×(C2×D83)⋊C4—21no—
40C2×(C2×D83)⋊C4—21no—
41C2×(C2×D83)⋊C4—21no—
42C2×(C2×D83)⋊C4—21no—
43C4⋊(C83⋊C8)—24no—
44C22⋊(C83⋊C8)—22no—
45C22⋊(C83⋊C8)D414yes—
46C4×C83⋊C8—24no—
47C83⋊#95—21no—
48C83⋊#95—21no—
49C83⋊#95—21no—
50C23×C4×C83—22no—
51C23×C4×C83D411yescharacteristic
52C23×C4×C83D411yescharacteristic
53C23×C4×C83C2311yescharacteristic
54C2×C42×C83—22no—
55C2×C42×C83—22no—
56C2×C42×C83C2×C411yescharacteristic
57C2×C42×C83C2×C411yescharacteristic
58C2×C42×C83D411yescharacteristic
59C2×C42×C83D411yescharacteristic
60#95×C83—24no—
61#95×C83—22no—
62#95×C83—22no—
63#95×C83—42no—
64C23×D83—21no—
65C2×D332—22no—
66C2×D332—41no—
67C2×D332—41no—
68C2×C22⋊D83—42no—
69C2×C22⋊D83—41no—
70C2×C22⋊D83—41no—
71C2×C22⋊D83—42no—
72C22×Dic83—21no—
73C22×Dic83—21no—
74C22×Dic83—21no—
75C2×C83⋊C8—24no—
76C2×C83⋊C8—42no—
77C2×C83⋊C8—42no—
78C4⋊Dic83—22no—
79C4⋊Dic83—41no—
80C4⋊Dic83—41no—
81Dic83⋊C4—42no—
82Dic83⋊C4—42no—
83C22⋊Dic83—41no—
84C22⋊Dic83—41no—
85(C2×D83)⋊C4—42no—
86(C2×D83)⋊C4—42no—
87(C2×D83)⋊C4—42no—
88(C2×D83)⋊C4—42no—
89(C2×D83)⋊C4—41no—
90(C2×D83)⋊C4—41no—
91C24×C83C2×D411yescharacteristic
92C22×C4×C83—22no—
93C22×C4×C83—22no—
94C22×C4×C83—22no—
95C22×C4×C83—22no—
96C22×C4×C83—24no—
97C22×C4×C83—41no—
98C22×C4×C83—41no—
99C22×C4×C83—41no—
100C22×C4×C83—42no—
101C22×C4×C83—42no—
102C22×C4×C83—42no—
103C22×C4×C83—42no—
104C22×C4×C83—42no—
105C22×C4×C83—42no—
106C22×C4×C83C22⋊C411yescharacteristic
107C22×C4×C83C22⋊C411yescharacteristic
108C22×C4×C83C22⋊C411yescharacteristic
109C22×C4×C83C22⋊C411yescharacteristic
110C22×C4×C83D812yes—
111C22×C4×C83SD1612yes—
112C22×C4×C83C22×C411yescharacteristic
113C22×C4×C83C2×D412yes—
114C22×C4×C83C2×D411yescharacteristic
115C22×C4×C83#4112yes—
116C42×C83—22no—
117C42×C83—22no—
118C42×C83—21no—
119C42×C83—21no—
120C42×C83—21no—
121C42×C83—21no—
122C23×C83—21no—
123C23×C83—21no—
124C23×C83—21no—
125C23×C83—21no—
126C23×C83C2×C22⋊C411yescharacteristic
127C23×C83#12112yes—
128C23×C83C2×D811yescharacteristic
129C23×C83C2×SD1611yescharacteristic
130C23×C83#13512yes—
131C22×D83—41no—
132C22×D83—41no—
133C22×D83—41no—
134C22×D83—41no—
135C22×D83—41no—
136C22×D83—41no—
137C22×D83—41no—
138C2×C4×C83—21no—
139C2×C4×C83—21no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83—21no—
144C2×C4×C83—21no—
145C2×C4×C83—21no—
146C2×C4×C83—21no—
147C2×C4×C83—21no—
148C2×C4×C83—24no—
149C2×C4×C83—24no—
150C2×C4×C83—21no—
151C2×C4×C83—21no—
152C2×C4×C83—21no—
153C2×C4×C83—42no—
154C2×C4×C83—42no—
155C2×C4×C83—44no—
156C2×C4×C83—44no—
157C2×C4×C83—44no—
158C2×C4×C83—44no—
159C2×C4×C83—82no—
160C2×C4×C83—82no—
161C2×C4×C83—82no—
162C2×C4×C83—82no—
163C2×C4×C83#10212yes—
164C2×C4×C83#10212yes—
165C2×C4×C83#10412yes—
166C2×C4×C83C4×D412yes—
167C2×C4×C83#12011yescharacteristic
168C2×C4×C83#12311yescharacteristic
169C22⋊D83—82no—
170C22⋊D83—82no—
171C2×Dic83—41no—
172C2×Dic83—41no—
173C2×Dic83—41no—
174C2×Dic83—41no—
175C2×Dic83—41no—
176C2×Dic83—41no—
177C2×Dic83—41no—
178C2×Dic83—41no—
179C2×Dic83—41no—
180D332—82no—
181C83⋊C8—44no—
182C22×C83—22no—
183C22×C83—22no—
184C22×C83—22no—
185C22×C83—21no—
186C22×C83—21no—
187C22×C83—21no—
188C22×C83—21no—
189C22×C83—22no—
190C22×C83#38611yescharacteristic
191C22×C83#41011yescharacteristic
192C22×C83#41011yescharacteristic
193C22×C83C2×#10211yescharacteristic
194C22×C83#41611yescharacteristic
195C22×C83C2×#10411yescharacteristic
196C22×C83#42111yescharacteristic
197C22×C83#46512yes—
198C22×C83#46612yes—
199C2×D83—81no—
200C2×D83—81no—
201C2×D83—81no—
202C2×D83—81no—
203C2×D83—81no—
204C2×D83—81no—
205C2×D83—81no—
206C4×C83—22no—
207C4×C83—22no—
208C4×C83—22no—
209C4×C83—21no—
210C4×C83—22no—
211C4×C83—21no—
212C4×C83—41no—
213C4×C83—84no—
214Dic83—81no—
215Dic83—81no—
216Dic83—81no—
217#9114—831nomaximal, Sylow
218C2×C83—22no—
219C2×C83—22no—
220C2×C83#150011yescharacteristic
221C2×C83#150211yescharacteristic
222C2×C83#151711yescharacteristic
223C2×C83#152111yescharacteristic
224C2×C83#187111yescharacteristic
225C2×C83#189311yescharacteristic
226C2×C83#189911yescharacteristic
227D83—161no—
228C2×#431—831no—
229#2854—831no—
230C2×#327—832no—
231#1434D8311yescharacteristic, complemented
232#1294—832no—
233C83#911411yescharacteristic, complemented, Sylow
234C2×#123—1661no—
235C2×#121—831no—
236C22×C42C2×D8311yescharacteristic
237#431—1664no—
238C2×C4⋊C8—1661no—
239C2×C22⋊C8—832no—
240C2×C4×C8—1661no—
241#390—831no—
242#390—831no—
243#389—831no—
244#389—831no—
245#388—1661no—
246#388—1661no—
247#386—1661no—
248#380—831no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95C2×D8312yes—
252#327—1664no—
253C22×D4—831no—
254C22×D4—1661no—
255C23×C4—22no—
256C23×C4C22⋊D8311yescharacteristic
257C23×C4C22⋊D8311yescharacteristic
258C23×C4C22×D8311yescharacteristic
259C22×C8—1662no—
260#123—3322no—
261#123—3322no—
262#121—1662no—
263#121—1662no—
264C2×C4⋊C4—831no—
265C2×C4⋊C4—831no—
266C2×C4⋊C4—831no—
267C2×C4⋊C4—1661no—
268C2×C4⋊C4—1661no—
269C2×C22⋊C4—1661no—
270C2×C22⋊C4—1661no—
271C2×C22⋊C4—1661no—
272C2×C22⋊C4—1661no—
273C2×C22⋊C4—1661no—
274C2×C22⋊C4—1661no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42C4×D8311yescharacteristic
278C2×C42C4×D8311yescharacteristic
279C2×C42D33211yescharacteristic
280C2×C42D33211yescharacteristic
281C4⋊C8—1664no—
282C22⋊C8—834no—
283C22⋊C8—1662no—
284C4×C8—1664no—
285#95—24no—
286#95—22no—
287#95—22no—
288#95—42no—
289#95—1661no—
290#95—1661no—
291#95—1661no—
292C24—1661no—
293C24C2×C22⋊D8311yescharacteristic
294C2×D4—3321no—
295C2×D4—3321no—
296C2×D4—3322no—
297C2×D4—3321no—
298C2×D4—3321no—
299C2×D4—3322no—
300C2×D4—1662no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—1661no—
316C22×C4—1661no—
317C22×C4—1661no—
318C22×C4(C2×D83)⋊C411yescharacteristic
319C22×C4(C2×D83)⋊C411yescharacteristic
320C22×C4(C2×D83)⋊C411yescharacteristic
321C22×C4(C2×D83)⋊C411yescharacteristic
322C22×C4#1305057512yes—
323C22×C4#1305057712yes—
324C22×C4C2×C4×D8311yescharacteristic
325C22×C4D4×D8312yes—
326C22×C4C2×D33211yescharacteristic
327C22×C4#1305058912yes—
328C2×C8—3322no—
329C2×C8—3322no—
330C2×C8—1664no—
331C4⋊C4—3321no—
332C4⋊C4—3321no—
333C4⋊C4—3322no—
334C4⋊C4—3322no—
335C4⋊C4—1662no—
336C22⋊C4—3322no—
337C22⋊C4—3321no—
338C22⋊C4—3321no—
339C22⋊C4—3321no—
340C22⋊C4—3321no—
341C22⋊C4—3322no—
342C22⋊C4—3322no—
343C22⋊C4—3322no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—22no—
349C42—22no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—3321no—
355C23—3321no—
356C23—3321no—
357C23—3321no—
358C23—3321no—
359C23—3321no—
360C23—3321no—
361C23C2×(C2×D83)⋊C411yescharacteristic
362C23#1458176412yes—
363C23C2×#1305057511yescharacteristic
364C23C2×#1305057711yescharacteristic
365C23#1458181212yes—
366D4—6642no—
367D4—6642no—
368D4—6642no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—3321no—
395C2×C4—3321no—
396C2×C4—3321no—
397C2×C4—3321no—
398C2×C4—3321no—
399C2×C4—3321no—
400C2×C4—3321no—
401C2×C4—3321no—
402C2×C4—3321no—
403C2×C4#1458171212yes—
404C2×C4#1458171212yes—
405C2×C4#1458172012yes—
406C2×C4(C22⋊D83)⋊C412yes—
407C2×C4#1458176211yescharacteristic
408C2×C4#1458177611yescharacteristic
409C8—3324no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—6641no—
419C22—6641no—
420C22—6641no—
421C22—6641no—
422C22—6641no—
423C22—6641no—
424C22—6641no—
425C22#1912757811yescharacteristic
426C22#1912767411yescharacteristic
427C22#1912767411yescharacteristic
428C22C2×#1458171211yescharacteristic
429C22#1912769511yescharacteristic
430C22C2×#1458172011yescharacteristic
431C22#1912771911yescharacteristic
432C22#1912793212yes—
433C22#1912793512yes—
434C4—22no—
435C4—22no—
436C4—21no—
437C4—21no—
438C4—22no—
439C4—22no—
440C4—41no—
441C4—84no—
442C4—6641no—
443C4—6641no—
444C4—6641no—
445C2—22no—
446C2—22no—
447C2—13281no—
448C2#2490594711yescharacteristic
449C2#2490595711yescharacteristic
450C2#2490602211yescharacteristic
451C2#2490603811yescharacteristic
452C2#2490776311yescharacteristic
453C2#2490788911yescharacteristic
454C2#2490791911yescharacteristic
subgroupG/H
centerC23C2×(C2×D83)⋊C4
commutatorC22×C4×C83C22×C4
FrattiniC23×C4C22×D83
FittingC83×#1434C2
socleC23×C83C2×C22⋊C4
prime radicalC2×#14581766C22
cosocleC23×C4×C83C23
hypercenter#1434D83
hypocenterC83#9114
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#19127754C2semidirect
4. #24905342C2semidirect
5. C83×#1434C2semidirect
12. #19127603C4semidirect
13. #19127603C4semidirect
14. #19127599C4semidirect
15. #19127599C4semidirect
231. #1434D83semidirect
233. C83#9114semidirect

Maximal subgroups

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

subgroupindex
C2×#191277542
#249157942
C2×#191274342
#249053422
C83×#14342
#911483