Finite Group Databasebeta

← #35299974

Subgroups — #35299974

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
1#24915794C211yesmaximal, characteristic
2C2×#19127436C212yesmaximal
3#24905690C211yesmaximal, characteristic, complemented
4#24905343C212yesmaximal, complemented
5C2×#431×C83C211yesmaximal, characteristic, complemented
6C2×#14581775—21no—
7C2×#14581766C2211yescharacteristic
8#19127603C411yescharacteristic, complemented
9#19127603C411yescharacteristic, complemented
10#19127599C411yescharacteristic, complemented
11#19127599C411yescharacteristic, complemented
12#19127592—21no—
13#19127592—21no—
14#19127580—21no—
15#19127561C2211yescharacteristic
16C2×C83⋊#95—21no—
17C2×C83⋊#95—21no—
18C2×C83⋊#95C2212yes—
19#19127436—24no—
20C22×C42×C83C2211yescharacteristic
21#431×C83—24no—
22C2×C4⋊C8×C83—21no—
23C2×C22⋊C8×C83C2212yes—
24C2×C4×C8×C83—21no—
25C22×D332C2×C411yescharacteristic
26C22×C22⋊D83—21no—
27C23×Dic83—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—
43C83⋊#95—24no—
44C83⋊#95—21no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C83⋊#95—22no—
48C83⋊#95—22no—
49C83⋊#95—42no—
50C23×C4×C83D411yescharacteristic
51C23×C4×C83D411yescharacteristic
52C23×C4×C83C2311yescharacteristic
53C22×C8×C83—22no—
54C2×C42×C83—22no—
55C2×C42×C83—22no—
56C2×C42×C83C2×C411yescharacteristic
57C2×C42×C83C2×C411yescharacteristic
58C2×C42×C83D411yescharacteristic
59C2×C42×C83D411yescharacteristic
60C4⋊C8×C83—24no—
61C22⋊C8×C83—22no—
62C22⋊C8×C83D414yes—
63C4×C8×C83—24no—
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—24no—
73C22×Dic83—21no—
74C22×Dic83—21no—
75C22×Dic83—21no—
76C22×Dic83—42no—
77C22×Dic83—42no—
78C22×Dic83—42no—
79C22×Dic83—42no—
80C22×Dic83—42no—
81C22×Dic83—42no—
82C4⋊Dic83—22no—
83C4⋊Dic83—41no—
84C4⋊Dic83—41no—
85Dic83⋊C4—42no—
86Dic83⋊C4—42no—
87C22⋊Dic83—41no—
88C22⋊Dic83—41no—
89(C2×D83)⋊C4—42no—
90(C2×D83)⋊C4—42no—
91(C2×D83)⋊C4—42no—
92(C2×D83)⋊C4—42no—
93(C2×D83)⋊C4—41no—
94(C2×D83)⋊C4—41no—
95C24×C83C2×D411yescharacteristic
96C22×C4×C83—22no—
97C22×C4×C83—22no—
98C22×C4×C83—22no—
99C22×C4×C83—22no—
100C22×C4×C83—41no—
101C22×C4×C83—41no—
102C22×C4×C83—41no—
103C22×C4×C83C22⋊C411yescharacteristic
104C22×C4×C83C22⋊C411yescharacteristic
105C22×C4×C83C22⋊C411yescharacteristic
106C22×C4×C83C22⋊C411yescharacteristic
107C22×C4×C83D812yes—
108C22×C4×C83SD1612yes—
109C22×C4×C83C22×C411yescharacteristic
110C22×C4×C83C2×D411yescharacteristic
111C22×C4×C83C2×D412yes—
112C22×C4×C83#4112yes—
113C2×C8×C83—24no—
114C2×C8×C83—42no—
115C2×C8×C83—42no—
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#10212yes—
157C2×C4×C83#10212yes—
158C2×C4×C83#10412yes—
159C2×C4×C83C4×D412yes—
160C2×C4×C83#12011yescharacteristic
161C2×C4×C83#12311yescharacteristic
162C22⋊D83—82no—
163C22⋊D83—82no—
164C2×Dic83—44no—
165C2×Dic83—44no—
166C2×Dic83—44no—
167C2×Dic83—41no—
168C2×Dic83—41no—
169C2×Dic83—41no—
170C2×Dic83—41no—
171C2×Dic83—41no—
172C2×Dic83—41no—
173C2×Dic83—41no—
174C2×Dic83—41no—
175C2×Dic83—41no—
176C2×Dic83—82no—
177C2×Dic83—82no—
178C2×Dic83—82no—
179C2×Dic83—82no—
180D332—82no—
181C8×C83—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—
213Dic83—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×#431D8311yescharacteristic, complemented
229#2854—831no—
230C2×#327—832no—
231#1434—831no—
232#1294—832no—
233C83#911411yescharacteristic, complemented, Sylow
234C2×#123—1661no—
235C2×#121—831no—
236C22×C42C2×D8311yescharacteristic
237#431—24no—
238C2×C4⋊C8—21no—
239C2×C22⋊C8C2×D8312yes—
240C2×C4×C8—21no—
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—832no—
250C2×#95—1661no—
251C2×#95—1661no—
252#327—1664no—
253C22×D4—831no—
254C22×D4—1661no—
255C23×C4—1662no—
256C23×C4D33211yescharacteristic
257C23×C4D33211yescharacteristic
258C23×C4C22×D8311yescharacteristic
259C22×C8—22no—
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×C42C22⋊D8311yescharacteristic
280C2×C42C22⋊D8311yescharacteristic
281C4⋊C8—24no—
282C22⋊C8—22no—
283C22⋊C8C22⋊D8314yes—
284C4×C8—24no—
285#95—3322no—
286#95—1664no—
287#95—1662no—
288#95—1662no—
289#95—1661no—
290#95—1661no—
291#95—1661no—
292C24—1661no—
293C24C2×D33211yescharacteristic
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—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—3322no—
309C22×C4—3322no—
310C22×C4—3322no—
311C22×C4—3322no—
312C22×C4—3322no—
313C22×C4—3322no—
314C22×C4—1664no—
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×C4D66412yes—
323C22×C4#1305057912yes—
324C22×C4C2×C4×D8311yescharacteristic
325C22×C4C2×C22⋊D8311yescharacteristic
326C22×C4C2×C22⋊D8312yes—
327C22×C4#1305059012yes—
328C2×C8—24no—
329C2×C8—42no—
330C2×C8—42no—
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#1458176612yes—
363C23C2×D66411yescharacteristic
364C23C2×#1305057911yescharacteristic
365C23#1458181412yes—
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—3324no—
388C2×C4—3324no—
389C2×C4—3324no—
390C2×C4—3321no—
391C2×C4—3321no—
392C2×C4—3321no—
393C2×C4—3321no—
394C2×C4—3321no—
395C2×C4—3321no—
396C2×C4—3321no—
397C2×C4—3321no—
398C2×C4—3321no—
399C2×C4—6642no—
400C2×C4—6642no—
401C2×C4—6642no—
402C2×C4—6642no—
403C2×C4#1458171412yes—
404C2×C4#1458171412yes—
405C2×C4#1458171812yes—
406C2×C4C4×C22⋊D8312yes—
407C2×C4#1458176111yescharacteristic
408C2×C4#1458177511yescharacteristic
409C8—44no—
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#1912758011yescharacteristic
426C22#1912767411yescharacteristic
427C22#1912767411yescharacteristic
428C22C2×#1458171411yescharacteristic
429C22#1912769811yescharacteristic
430C22C2×#1458171811yescharacteristic
431C22#1912771711yescharacteristic
432C22#1912793012yes—
433C22#1912793712yes—
434C4—22no—
435C4—22no—
436C4—21no—
437C4—21no—
438C4—22no—
439C4—22no—
440C4—41no—
441C4—6644no—
442C4—6641no—
443C4—6641no—
444C4—6641no—
445C2—22no—
446C2—22no—
447C2—13281no—
448C2#2490595011yescharacteristic
449C2#2490595911yescharacteristic
450C2#2490602411yescharacteristic
451C2#2490604111yescharacteristic
452C2#2490776511yescharacteristic
453C2#2490789111yescharacteristic
454C2#2490792111yescharacteristic
subgroupG/H
centerC23C2×(C2×D83)⋊C4
commutatorC22×C4×C83C22×C4
FrattiniC23×C4C22×D83
FittingC2×#431×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC2×#14581766C22
cosocleC23×C4×C83C23
hypercenterC2×#431D83
hypocenterC83#9114
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #24905690C2semidirect
4. #24905343C2semidirect
5. C2×#431×C83C2semidirect
8. #19127603C4semidirect
9. #19127603C4semidirect
10. #19127599C4semidirect
11. #19127599C4semidirect
228. C2×#431D83semidirect
233. C83#9114semidirect

Maximal subgroups

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

subgroupindex
#249157942
C2×#191274362
#249056902
#249053432
C2×#431×C832
#911483