Finite Group Databasebeta

← #35308637

Subgroups — #35308637

Order 21248.

506 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128048C211yesmaximal, characteristic
2#24908389C211yesmaximal, characteristic
3#24908385C211yesmaximal, characteristic, complemented
4#24908181C211yesmaximal, characteristic, complemented
5C2×#19127448C211yesmaximal, characteristic, complemented
6C2×#19127444C211yesmaximal, characteristic
7C83×#1277C211yesmaximal, characteristic, complemented
8C2×#14581792C2211yescharacteristic
9C2×#14581789C2211yescharacteristic
10#19128048—22no—
11#19128048—22no—
12C2×C4⋊(C83⋊C8)C2211yescharacteristic
13C2×Dic83⋊C8—21no—
14C2×#14581717—21no—
15C2×#14581717—21no—
16C2×#14581714—21no—
17C2×#14581714—21no—
18C2×#14581714—21no—
19C2×#14581714—21no—
20C4×C4⋊Dic83C2211yescharacteristic
21#19127455—21no—
22#19127448—22no—
23#19127444—22no—
24C2×C4⋊C8×C83C2211yescharacteristic
25C2×C4⋊C8×C83C2211yescharacteristic
26C2×C4×C8×C83C2211yescharacteristic
27C22×Dic166—21no—
28C22×D332—21no—
29C22×D332—21no—
30C22×D332—21no—
31C22×C83⋊C8—21no—
32#14581792—21no—
33#14581792—21no—
34#14581792—21no—
35#14581792D412yes—
36#14581789—21no—
37#14581789—21no—
38#14581789—21no—
39#14581789D412yes—
40C2×C4⋊Dic83—21no—
41C2×C4⋊Dic83—21no—
42C2×C4⋊Dic83D411yescharacteristic
43C2×C4⋊Dic83D411yescharacteristic
44C2×C4×Dic83—21no—
45C4⋊(C83⋊C8)—21no—
46C4⋊(C83⋊C8)—21no—
47Dic83⋊C8—42no—
48#14581717—42no—
49#14581717—42no—
50#14581714—24no—
51#14581714—24no—
52#14581714—42no—
53#14581714—42no—
54C83⋊#95—21no—
55C22×C8×C83—21no—
56C22×C8×C83—21no—
57C22×C8×C83D411yescharacteristic
58C22×C8×C83D411yescharacteristic
59C2×C42×C83C2311yescharacteristic
60C4⋊C8×C83—21no—
61C4⋊C8×C83—21no—
62C4⋊C8×C83—21no—
63C4⋊C8×C83—21no—
64C4×C8×C83—21no—
65C4×C8×C83—21no—
66C23×D83—41no—
67C2×Dic166—22no—
68C2×Dic166—41no—
69C2×Dic166—41no—
70C2×Dic166—41no—
71C2×Dic166—41no—
72C2×Dic166—41no—
73C2×D332—22no—
74C2×D332—22no—
75C2×D332—22no—
76C2×D332—41no—
77C2×D332—41no—
78C2×D332—41no—
79C2×D332—41no—
80C2×D332—41no—
81C2×D332—41no—
82C2×D332—41no—
83C2×D332—41no—
84C2×D332—41no—
85C2×D332—41no—
86C2×D332—41no—
87C2×D332—81no—
88C2×D332—81no—
89C22×Dic83—21no—
90C22×Dic83—21no—
91C22×Dic83—41no—
92C2×C83⋊C8—41no—
93C2×C83⋊C8—41no—
94C2×C83⋊C8—41no—
95C4⋊Dic83—21no—
96C4⋊Dic83—22no—
97C4⋊Dic83—22no—
98C4⋊Dic83—21no—
99C4⋊Dic83—21no—
100C4⋊Dic83—41no—
101C4⋊Dic83—41no—
102C4⋊Dic83D812yes—
103C4×Dic83—41no—
104C4×Dic83—41no—
105C22×C4×C83C2×D411yescharacteristic
106C22×C4×C83C2×D411yescharacteristic
107C22×C4×C83#4111yescharacteristic
108C2×C8×C83—21no—
109C2×C8×C83—21no—
110C2×C8×C83—21no—
111C2×C8×C83—21no—
112C2×C8×C83—21no—
113C2×C8×C83—21no—
114C2×C8×C83—41no—
115C2×C8×C83—41no—
116C2×C8×C83—41no—
117C2×C8×C83—41no—
118C2×C8×C83—41no—
119C2×C8×C83—41no—
120C42×C83C2×D411yescharacteristic
121C42×C83C2×D411yescharacteristic
122C42×C83#4111yescharacteristic
123C42×C83#4111yescharacteristic
124C23×C83#12111yescharacteristic
125C22×D83—42no—
126C22×D83—81no—
127C22×D83—81no—
128C22×D83—81no—
129C22×D83—81no—
130C22×D83—81no—
131C22×D83—81no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83#12011yescharacteristic
135C2×C4×C83#12111yescharacteristic
136C2×C4×C83#12111yescharacteristic
137C2×C4×C83#12311yescharacteristic
138C2×C4×C83#12311yescharacteristic
139C2×C4×C83#12411yescharacteristic
140C2×C4×C83C2×D811yescharacteristic
141C2×C4×C83#13511yescharacteristic
142C2×C4×C83#13511yescharacteristic
143C2×C4×C83#13511yescharacteristic
144C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C83#13711yescharacteristic
148C2×Dic83—22no—
149C2×Dic83—41no—
150C2×Dic83—41no—
151C2×Dic83—42no—
152C2×Dic83—41no—
153C2×Dic83—41no—
154C2×Dic83—41no—
155C2×Dic83—81no—
156C2×Dic83—81no—
157D332—42no—
158D332—42no—
159D332—42no—
160D332—42no—
161D332—82no—
162D332—82no—
163D332—81no—
164D332—81no—
165D332—81no—
166D332—81no—
167Dic166—42no—
168Dic166—42no—
169Dic166—81no—
170Dic166—81no—
171C8×C83—41no—
172C8×C83—41no—
173C8×C83—81no—
174C8×C83—81no—
175C83⋊C8—81no—
176C22×C83#39411yescharacteristic
177C22×C83#46311yescharacteristic
178C22×C83#46411yescharacteristic
179C22×C83#46611yescharacteristic
180C22×C83#46911yescharacteristic
181C22×C83#47111yescharacteristic
182C22×C83#47111yescharacteristic
183C2×D83—82no—
184C2×D83—82no—
185C2×D83—82no—
186C2×D83—161no—
187C2×D83—161no—
188C2×D83—161no—
189C2×D83—161no—
190C4×C83—21no—
191C4×C83—21no—
192C4×C83#44911yescharacteristic
193C4×C83#45211yescharacteristic
194C4×C83#45911yescharacteristic
195C4×C83#45911yescharacteristic
196C4×C83#46311yescharacteristic
197C4×C83#46311yescharacteristic
198C4×C83#48811yescharacteristic
199C4×C83#48911yescharacteristic
200Dic83—42no—
201Dic83—82no—
202Dic83—81no—
203#10540—831nomaximal, Sylow
204C2×C83#168111yescharacteristic
205C2×C83#168211yescharacteristic
206C2×C83#170111yescharacteristic
207C2×C83#170211yescharacteristic
208C2×C83#204211yescharacteristic
209C2×C83#204611yescharacteristic
210C2×C83#205411yescharacteristic
211D83—162no—
212C2×#486—831no—
213#1982—831no—
214#1981—831no—
215#1939—831no—
216C2×#332—831no—
217C2×#331—831no—
218#1277D8311yescharacteristic, complemented
219C83#1054011yescharacteristic, complemented, Sylow
220C2×C4⋊Q8—831no—
221C2×#127—831no—
222#486—1662no—
223#486—1662no—
224C2×C4⋊C8—831no—
225C2×C4⋊C8—1661no—
226C2×C4⋊C8C2×D8311yescharacteristic
227C2×C4⋊C8C2×D8311yescharacteristic
228C2×#103—1661no—
229C2×#103—1661no—
230C2×#102—1661no—
231C2×#102—1661no—
232C2×#102—1661no—
233C2×#102—1661no—
234C2×C4×C8C2×D8311yescharacteristic
235C4×C4⋊C4—831no—
236#336—1661no—
237#332—1662no—
238#331—1662no—
239C22×Q8—1661no—
240C22×D4—1661no—
241C22×D4—1661no—
242C22×D4—1661no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—1661no—
246C22×C8D33211yescharacteristic
247C22×C8D33211yescharacteristic
248C4⋊Q8—832no—
249C4⋊Q8—1661no—
250C4⋊Q8—1661no—
251C4⋊Q8—1661no—
252#127—832no—
253#127—1661no—
254#127—1661no—
255#127—1661no—
256C2×C4⋊C4—831no—
257C2×C4⋊C4—831no—
258C2×C4⋊C4—1661no—
259C2×C4⋊C4—1661no—
260C2×C42—1661no—
261C2×C42C22×D8311yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—3322no—
267C4⋊C8—1661no—
268C4⋊C8—1661no—
269#103—3322no—
270#103—3322no—
271#102—3322no—
272#102—3322no—
273#102—1664no—
274#102—1664no—
275C4×C8—21no—
276C4×C8—21no—
277#95—1661no—
278C24—3321no—
279C2×Q8—3321no—
280C2×Q8—3321no—
281C2×Q8—3321no—
282C2×Q8—3321no—
283C2×Q8—3321no—
284C2×Q8—1662no—
285C2×D4—3321no—
286C2×D4—3321no—
287C2×D4—3321no—
288C2×D4—3321no—
289C2×D4—3321no—
290C2×D4—3321no—
291C2×D4—3321no—
292C2×D4—3321no—
293C2×D4—3321no—
294C2×D4—3321no—
295C2×D4—3321no—
296C2×D4—6641no—
297C2×D4—6641no—
298C2×D4—1662no—
299C2×D4—1662no—
300C2×D4—1662no—
301C22×C4—3321no—
302C22×C4—1661no—
303C22×C4—1661no—
304C22×C4D4×D8311yescharacteristic
305C22×C4C2×D33211yescharacteristic
306C22×C4#1305059111yescharacteristic
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—3321no—
320C2×C8—3321no—
321C2×C8—3321no—
322C4⋊C4—3321no—
323C4⋊C4—3321no—
324C4⋊C4—832no—
325C4⋊C4—1662no—
326C4⋊C4—1662no—
327C4⋊C4—1661no—
328C4⋊C4—1661no—
329C4⋊C4—1661no—
330C42—3321no—
331C42—3321no—
332C42D4×D8311yescharacteristic
333C42D4×D8311yescharacteristic
334C42#1305059011yescharacteristic
335C42#1305059011yescharacteristic
336C23—3322no—
337C23—6641no—
338C23—6641no—
339C23—6641no—
340C23—6641no—
341C23—6641no—
342C23—6641no—
343C23#1458176711yescharacteristic
344Q8—3322no—
345Q8—3322no—
346Q8—6641no—
347Q8—6641no—
348D4—3322no—
349D4—3322no—
350D4—3322no—
351D4—3322no—
352D4—6642no—
353D4—6642no—
354D4—6641no—
355D4—6641no—
356D4—6641no—
357D4—6641no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—3321no—
361C2×C4—3321no—
362C2×C4—3322no—
363C2×C4—3321no—
364C2×C4—3321no—
365C2×C4—3321no—
366C2×C4—6641no—
367C2×C4—6641no—
368C2×C4—1662no—
369C2×C4#1458176211yescharacteristic
370C2×C4#1458176511yescharacteristic
371C2×C4#1458176511yescharacteristic
372C2×C4#1458177711yescharacteristic
373C2×C4#1458177711yescharacteristic
374C2×C4#1458178011yescharacteristic
375C2×C4D8×D8311yescharacteristic
376C2×C4#1458181411yescharacteristic
377C2×C4#1458181411yescharacteristic
378C2×C4#1458181511yescharacteristic
379C2×C4#1458181911yescharacteristic
380C2×C4#1458181911yescharacteristic
381C2×C4#1458182011yescharacteristic
382C2×C4#1458182511yescharacteristic
383C8—41no—
384C8—41no—
385C8—81no—
386C8—81no—
387C8—6641no—
388C22—13281no—
389C22—13281no—
390C22—13281no—
391C22—13281no—
392C22—6642no—
393C22—6642no—
394C22—6642no—
395C22#1912761911yescharacteristic
396C22#1912791711yescharacteristic
397C22#1912792411yescharacteristic
398C22#1912793811yescharacteristic
399C22#1912795511yescharacteristic
400C22#1912796511yescharacteristic
401C22#1912796511yescharacteristic
402C4—21no—
403C4—21no—
404C4—3322no—
405C4—6641no—
406C4—6642no—
407C4#1912784811yescharacteristic
408C4#1912786511yescharacteristic
409C4#1912789511yescharacteristic
410C4#1912789511yescharacteristic
411C4#1912791911yescharacteristic
412C4#1912791911yescharacteristic
413C4#1912805611yescharacteristic
414C4#1912806111yescharacteristic
415C2—13282no—
416C2#2490690111yescharacteristic
417C2#2490690811yescharacteristic
418C2#2490702511yescharacteristic
419C2#2490703211yescharacteristic
420C2#2490870511yescharacteristic
421C2#2490872711yescharacteristic
422C2#2490877511yescharacteristic
subgroupG/H
centerC23#14581767
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1277C2
socleC23×C83#121
prime radicalC2×#14581789C22
hypercenter#1277D83
hypocenterC83#10540
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
3. #24908385C2semidirect
4. #24908181C2semidirect
5. C2×#19127448C2semidirect
7. C83×#1277C2semidirect
218. #1277D83semidirect
219. C83#10540semidirect

Maximal subgroups

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

subgroupindex
C2×#191280482
#249083892
#249083852
#249081812
C2×#191274482
C2×#191274442
C83×#12772
#1054083