Finite Group Databasebeta

← #35295299

Subgroups — #35295299

Order 21248.

804 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14581766C211yesmaximal, characteristic
2#24907225C211yesmaximal, characteristic, complemented
3C2×#19127434C212yesmaximal
4#24905342C212yesmaximal, complemented
5C4×#95×C83C211yesmaximal, characteristic, complemented
6C2×#14581766C2211yescharacteristic
7C2×C4×D332C411yescharacteristic, complemented
8C2×C4×C22⋊D83—21no—
9C2×C22⋊(C83⋊C8)C2212yes—
10C2×#14581703—21no—
11#19127603C411yescharacteristic, complemented
12#19127599C411yescharacteristic, complemented
13#19127592—21no—
14#19127580—21no—
15#19127561C2211yescharacteristic
16C4×C4⋊Dic83C411yescharacteristic, complemented
17C4×(C2×D83)⋊C4—21no—
18#19127456—21no—
19#19127434C418yescomplemented
20C22×C42×C83—21no—
21C22×C42×C83C2211yescharacteristic
22C2×#95×C83—21no—
23C2×#95×C83C2212yes—
24C22×D332C2×C411yescharacteristic
25C22×C22⋊D83—21no—
26C22×C4×D83—21no—
27C22×C83⋊C8—22no—
28#14581766—22no—
29#14581766C2×C414yes—
30C4×D332—42no—
31C4×C22⋊D83—44no—
32C2×C4⋊Dic83C2×C411yescharacteristic
33C2×C4⋊Dic83C2×C411yescharacteristic
34C2×C4⋊Dic83C2×C411yescharacteristic
35C2×Dic83⋊C4—21no—
36C2×C22⋊Dic83—21no—
37C2×(C2×D83)⋊C4—21no—
38C2×(C2×D83)⋊C4—21no—
39C2×(C2×D83)⋊C4—21no—
40C2×(C2×D83)⋊C4—21no—
41C2×C4×Dic83—21no—
42C22⋊(C83⋊C8)—22no—
43C22⋊(C83⋊C8)C2×C414yescomplemented
44#14581703—42no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C83⋊#95—21no—
48C23×C4×C83—22no—
49C23×C4×C83D411yescharacteristic
50C23×C4×C83D411yescharacteristic
51C23×C4×C83C2311yescharacteristic
52C2×C42×C83—24no—
53C2×C42×C83—42no—
54C2×C42×C83—42no—
55C2×C42×C83—42no—
56C2×C42×C83C2×C411yescharacteristic
57C2×C42×C83C2×C411yescharacteristic
58C2×C42×C83D411yescharacteristic
59C2×C42×C83D411yescharacteristic
60#95×C83—24no—
61#95×C83—22no—
62#95×C83C2×C414yescomplemented
63C23×D83—21no—
64C2×D332—21no—
65C2×D332—41no—
66C2×D332—41no—
67C2×D332C4212yescomplemented
68C2×C22⋊D83—24no—
69C2×C22⋊D83—41no—
70C2×C22⋊D83—42no—
71C2×C22⋊D83—41no—
72C22×Dic83—21no—
73C22×Dic83—21no—
74C22×Dic83—21no—
75C2×C4×D83—42no—
76C2×C4×D83—42no—
77C2×C4×D83—42no—
78C2×C83⋊C8—24no—
79C2×C83⋊C8—42no—
80C2×C83⋊C8—42no—
81C4⋊Dic83—21no—
82C4⋊Dic83—41no—
83C4⋊Dic83—41no—
84C4⋊Dic83C4212yescomplemented
85Dic83⋊C4—42no—
86C22⋊Dic83—42no—
87(C2×D83)⋊C4—24no—
88(C2×D83)⋊C4—42no—
89(C2×D83)⋊C4—42no—
90(C2×D83)⋊C4—42no—
91C4×Dic83—42no—
92C24×C83C2×D411yescharacteristic
93C22×C4×C83—21no—
94C22×C4×C83—21no—
95C22×C4×C83—22no—
96C22×C4×C83—22no—
97C22×C4×C83—24no—
98C22×C4×C83—24no—
99C22×C4×C83—24no—
100C22×C4×C83—22no—
101C22×C4×C83—22no—
102C22×C4×C83—41no—
103C22×C4×C83—41no—
104C22×C4×C83—41no—
105C22×C4×C83—42no—
106C22×C4×C83—42no—
107C22×C4×C83—42no—
108C22×C4×C83—42no—
109C22×C4×C83C22⋊C411yescharacteristic
110C22×C4×C83C22⋊C411yescharacteristic
111C22×C4×C83C22⋊C411yescharacteristic
112C22×C4×C83C22⋊C411yescharacteristic
113C22×C4×C83C22×C411yescharacteristic
114C22×C4×C83C22×C412yes—
115C22×C4×C83C2×D411yescharacteristic
116C22×C4×C83#4112yes—
117C42×C83—22no—
118C42×C83—22no—
119C42×C83—41no—
120C42×C83—41no—
121C42×C83—48no—
122C23×C83—21no—
123C23×C83—21no—
124C23×C83—21no—
125C23×C83—21no—
126C23×C83C2×C22⋊C411yescharacteristic
127C23×C83C4×D412yes—
128C23×C83AGL(1,ℤ/8)12yes—
129C23×C83AGL(1,ℤ/8)11yescharacteristic
130C23×C83#13711yescharacteristic
131C22×D83—22no—
132C22×D83—41no—
133C22×D83—41no—
134C22×D83—41no—
135C22×D83—41no—
136C22×D83—41no—
137C22×D83—41no—
138C2×C4×C83—24no—
139C2×C4×C83—24no—
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—21no—
149C2×C4×C83—21no—
150C2×C4×C83—28no—
151C2×C4×C83—21no—
152C2×C4×C83—21no—
153C2×C4×C83—21no—
154C2×C4×C83—42no—
155C2×C4×C83—42no—
156C2×C4×C83—44no—
157C2×C4×C83—44no—
158C2×C4×C83—44no—
159C2×C4×C83—44no—
160C2×C4×C83—44no—
161C2×C4×C83—44no—
162C2×C4×C83—44no—
163C2×C4×C83#9912yes—
164C2×C4×C83#10412yes—
165C2×C4×C83#10412yes—
166C2×C4×C83C2×C4211yescharacteristic
167C2×C4×C83#11711yescharacteristic
168C2×C4×C83C4×D412yes—
169C22⋊D83—44no—
170C22⋊D83—44no—
171C2×Dic83—22no—
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—42no—
181D332—42no—
182C4×D83—84no—
183C83⋊C8—44no—
184C22×C83—22no—
185C22×C83—22no—
186C22×C83—21no—
187C22×C83—21no—
188C22×C83—22no—
189C22×C83—22no—
190C22×C83—21no—
191C22×C83—21no—
192C22×C83C4×C22⋊C411yescharacteristic
193C22×C83C2×#9911yescharacteristic
194C22×C83#41011yescharacteristic
195C22×C83#41711yescharacteristic
196C22×C83#41811yescharacteristic
197C22×C83C2×#10411yescharacteristic
198C22×C83C2×#10411yescharacteristic
199C22×C83#44012yes—
200C22×C83#44212yes—
201C2×D83—42no—
202C2×D83—42no—
203C2×D83—42no—
204C2×D83—81no—
205C2×D83—81no—
206C2×D83—81no—
207C2×D83—81no—
208C4×C83—22no—
209C4×C83—21no—
210C4×C83—21no—
211C4×C83—22no—
212C4×C83—22no—
213C4×C83—22no—
214C4×C83—48no—
215C4×C83—41no—
216Dic83—42no—
217Dic83—81no—
218Dic83—81no—
219#8218—831nomaximal, Sylow
220C2×C83—22no—
221C2×C83—22no—
222C2×C83#150411yescharacteristic
223C2×C83#150511yescharacteristic
224C2×C83#150711yescharacteristic
225C2×C83#150911yescharacteristic
226C2×C83C4×#9911yescharacteristic
227C2×C83C4×#10411yescharacteristic
228C2×C83#176211yescharacteristic
229D83—82no—
230C4×#121—831no—
231#1749—831no—
232C2×#327—832no—
233C4×#95D8311yescharacteristic, complemented
234#1294—832no—
235C83#821811yescharacteristic, complemented, Sylow
236C2×#121—831no—
237C2×C4×D4—831no—
238C2×C4×D4—1661no—
239C22×C42—21no—
240C22×C42C2×D8311yescharacteristic
241C2×C22⋊C8—832no—
242C2×#97—1661no—
243#390—831no—
244#389—831no—
245#388—1661no—
246#386—1661no—
247#380—831no—
248C4×C4⋊C4—831no—
249C4×C22⋊C4—1661no—
250C2×#95—21no—
251C2×#95C2×D8312yes—
252#336—1661no—
253#327—838no—
254C22×D4—831no—
255C22×D4—1661no—
256C23×C4—22no—
257C23×C4—1661no—
258C23×C4C22⋊D8311yescharacteristic
259C23×C4C22⋊D8311yescharacteristic
260C23×C4C22×D8311yescharacteristic
261C22×C8—1662no—
262#121—834no—
263#121—1662no—
264C4×D4—3322no—
265C4×D4—3324no—
266C2×C4⋊C4—831no—
267C2×C4⋊C4—831no—
268C2×C4⋊C4—831no—
269C2×C4⋊C4—1661no—
270C2×C22⋊C4—1661no—
271C2×C22⋊C4—1661no—
272C2×C22⋊C4—1661no—
273C2×C22⋊C4—1661no—
274C2×C22⋊C4—1661no—
275C2×C42—24no—
276C2×C42—42no—
277C2×C42—42no—
278C2×C42—42no—
279C2×C42—1661no—
280C2×C42C4×D8311yescharacteristic
281C2×C42C4×D8311yescharacteristic
282C2×C42D33211yescharacteristic
283C2×C42D33211yescharacteristic
284C22⋊C8—834no—
285C22⋊C8—1662no—
286#97—3322no—
287#95—24no—
288#95—22no—
289#95—1661no—
290#95—1661no—
291#95—1661no—
292#95C4×D8314yescomplemented
293C24—1661no—
294C24C2×C22⋊D8311yescharacteristic
295C2×D4—3321no—
296C2×D4—3321no—
297C2×D4—3322no—
298C2×D4—3321no—
299C2×D4—3321no—
300C2×D4—832no—
301C2×D4—1664no—
302C2×D4—1661no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—22no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—3322no—
320C22×C4—3322no—
321C22×C4—3322no—
322C22×C4—1661no—
323C22×C4—1661no—
324C22×C4—1661no—
325C22×C4(C2×D83)⋊C411yescharacteristic
326C22×C4(C2×D83)⋊C411yescharacteristic
327C22×C4(C2×D83)⋊C411yescharacteristic
328C22×C4(C2×D83)⋊C411yescharacteristic
329C22×C4C2×C4×D8311yescharacteristic
330C22×C4C2×C4×D8312yes—
331C22×C4C2×D33211yescharacteristic
332C22×C4#1305059012yes—
333C2×C8—3322no—
334C2×C8—3322no—
335C2×C8—1664no—
336C4⋊C4—3321no—
337C4⋊C4—3321no—
338C4⋊C4—3322no—
339C4⋊C4—832no—
340C4⋊C4—1661no—
341C22⋊C4—3322no—
342C22⋊C4—3322no—
343C22⋊C4—3322no—
344C22⋊C4—3322no—
345C22⋊C4—1664no—
346C42—22no—
347C42—22no—
348C42—41no—
349C42—41no—
350C42—48no—
351C42—3322no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—3321no—
357C23—3321no—
358C23—3321no—
359C23—3321no—
360C23—3321no—
361C23—3321no—
362C23—1662no—
363C23C2×(C2×D83)⋊C411yescharacteristic
364C23C4×C22⋊D8312yes—
365C23#1458181712yes—
366C23#1458181811yescharacteristic
367C23#1458182311yescharacteristic
368D4—3322no—
369D4—3322no—
370D4—3324no—
371D4—3324no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—28no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—3321no—
398C2×C4—3321no—
399C2×C4—3321no—
400C2×C4—3321no—
401C2×C4—3321no—
402C2×C4—3321no—
403C2×C4—3321no—
404C2×C4—3321no—
405C2×C4—6644no—
406C2×C4—1662no—
407C2×C4#1458170612yes—
408C2×C4#1458172012yes—
409C2×C4#1458172012yes—
410C2×C4C42×D8311yescharacteristic
411C2×C4#1458174911yescharacteristic
412C2×C4C4×D33212yes—
413C8—3324no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—3322no—
423C22—3322no—
424C22—3322no—
425C22—6641no—
426C22—6641no—
427C22—6641no—
428C22—6641no—
429C22C4×(C2×D83)⋊C411yescharacteristic
430C22C2×#1458170611yescharacteristic
431C22#1912767411yescharacteristic
432C22#1912770011yescharacteristic
433C22#1912770511yescharacteristic
434C22C2×#1458172011yescharacteristic
435C22C2×#1458172011yescharacteristic
436C22#1912779912yes—
437C22#1912781112yes—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—21no—
443C4—22no—
444C4—48no—
445C4—41no—
446C4—3322no—
447C4—6641no—
448C4—6641no—
449C2—22no—
450C2—22no—
451C2—6642no—
452C2#2490596511yescharacteristic
453C2#2490597011yescharacteristic
454C2#2490597811yescharacteristic
455C2#2490598611yescharacteristic
456C2C4×#1458170611yescharacteristic
457C2C4×#1458172011yescharacteristic
458C2#2490729111yescharacteristic
subgroupG/H
centerC23C2×(C2×D83)⋊C4
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC4×#95×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC2×#14581766C22
cosocleC23×C4×C83C23
hypercenterC4×#95D83
hypocenterC83#8218
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. #24907225C2semidirect
4. #24905342C2semidirect
5. C4×#95×C83C2semidirect
7. C2×C4×D332C4semidirect
11. #19127603C4semidirect
12. #19127599C4semidirect
16. C4×C4⋊Dic83C4semidirect
19. #19127434C4semidirect
43. C22⋊(C83⋊C8)C2×C4semidirect
62. #95×C83C2×C4semidirect
67. C2×D332C42semidirect
84. C4⋊Dic83C42semidirect
233. C4×#95D83semidirect
235. C83#8218semidirect
292. #95C4×D83semidirect

Maximal subgroups

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

subgroupindex
C4×#145817662
#249072252
C2×#191274342
#249053422
C4×#95×C832
#821883