Finite Group Databasebeta

← #35308613

Subgroups — #35308613

Order 21248.

554 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128075C211yesmaximal, characteristic
2#24908416C211yesmaximal, characteristic, complemented
3#24908389C211yesmaximal, characteristic
4#24908179C211yesmaximal, characteristic, complemented
5C2×#19127444C211yesmaximal, characteristic
6#24905297C211yesmaximal, characteristic, complemented
7C2×#332×C83C211yesmaximal, characteristic, complemented
8C22×#13050577—21no—
9C22×#13050577—21no—
10C2×#14581789C2211yescharacteristic
11#19128075—22no—
12#19128075—22no—
13C2×C4⋊(C83⋊C8)C2211yescharacteristic
14C2×Dic83⋊C8—21no—
15C2×#14581714—21no—
16C2×#14581714—21no—
17C2×C4×C83⋊C8C2211yescharacteristic
18C4×C4⋊Dic83C2211yescharacteristic
19#19127463—21no—
20#19127463—21no—
21#19127455—21no—
22#19127444—22no—
23C2×C4⋊Q8×C83C2211yescharacteristic
24C2×C4⋊C8×C83C2211yescharacteristic
25C2×C4⋊C8×C83C2211yescharacteristic
26#332×C83—22no—
27C22×D332—21no—
28C22×D332—21no—
29C22×D332—21no—
30C2×#13050577—24no—
31C2×#13050577—24no—
32C2×#13050577—42no—
33C2×#13050577—42no—
34C2×#13050577—42no—
35C2×#13050577—42no—
36C22×C83⋊C8—21no—
37C22×C83⋊C8D411yescharacteristic
38C22×C83⋊C8D411yescharacteristic
39#14581789—21no—
40#14581789—21no—
41#14581789—21no—
42#14581789D412yes—
43C2×C4⋊Dic83D411yescharacteristic
44C2×C4⋊Dic83D411yescharacteristic
45C2×C4×Dic83—21no—
46C4⋊(C83⋊C8)—21no—
47C4⋊(C83⋊C8)—21no—
48Dic83⋊C8—42no—
49#14581714—42no—
50#14581714—42no—
51C4×C83⋊C8—21no—
52C4×C83⋊C8—21no—
53C83⋊#95—21no—
54C22×Q8×C83—21no—
55C22×C8×C83—21no—
56C22×C8×C83—21no—
57C4⋊Q8×C83—21no—
58C4⋊Q8×C83—21no—
59C4⋊Q8×C83—21no—
60C4⋊Q8×C83D412yes—
61C2×C4⋊C4×C83—21no—
62C2×C4⋊C4×C83—21no—
63C2×C42×C83C2311yescharacteristic
64C4⋊C8×C83—21no—
65C4⋊C8×C83—21no—
66C4⋊C8×C83—21no—
67C4⋊C8×C83—21no—
68C23×D83—41no—
69C2×D332—22no—
70C2×D332—22no—
71C2×D332—22no—
72C2×D332—41no—
73C2×D332—41no—
74C2×D332—41no—
75C2×D332—41no—
76C2×D332—41no—
77C2×D332—41no—
78C2×D332—41no—
79C2×D332—41no—
80C2×D332—41no—
81C2×D332—41no—
82C2×D332—41no—
83C2×D332—81no—
84C2×D332—81no—
85C22×Dic83—21no—
86C22×Dic83—21no—
87#13050577—48no—
88#13050577—48no—
89C2×C83⋊C8—21no—
90C2×C83⋊C8—21no—
91C2×C83⋊C8—21no—
92C2×C83⋊C8—21no—
93C2×C83⋊C8—41no—
94C2×C83⋊C8—41no—
95C2×C83⋊C8—41no—
96C2×C83⋊C8D812yes—
97C2×C83⋊C8SD1612yes—
98C4⋊Dic83—21no—
99C4⋊Dic83—21no—
100C4⋊Dic83—21no—
101C4⋊Dic83SD1612yescomplemented
102C4×Dic83—41no—
103C4×Dic83—41no—
104C2×Q8×C83—22no—
105C2×Q8×C83—41no—
106C2×Q8×C83—41no—
107C2×Q8×C83—41no—
108C2×Q8×C83—41no—
109C2×Q8×C83—41no—
110C22×C4×C83—41no—
111C22×C4×C83C2×D411yescharacteristic
112C22×C4×C83C2×D411yescharacteristic
113C22×C4×C83#4111yescharacteristic
114C2×C8×C83—41no—
115C2×C8×C83—41no—
116C2×C8×C83—41no—
117C2×C8×C83—41no—
118C2×C8×C83—41no—
119C2×C8×C83—41no—
120C4⋊C4×C83—22no—
121C4⋊C4×C83—22no—
122C4⋊C4×C83—41no—
123C4⋊C4×C83—41no—
124C42×C83C2×D411yescharacteristic
125C42×C83C2×D411yescharacteristic
126C42×C83#4111yescharacteristic
127C42×C83#4111yescharacteristic
128C23×C83#12111yescharacteristic
129C22×D83—42no—
130C22×D83—81no—
131C22×D83—81no—
132C22×D83—81no—
133C22×D83—81no—
134C22×D83—81no—
135C22×D83—81no—
136Q8×C83—42no—
137Q8×C83—42no—
138Q8×C83—81no—
139Q8×C83—81no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—42no—
143C2×C4×C83—81no—
144C2×C4×C83—81no—
145C2×C4×C83#12011yescharacteristic
146C2×C4×C83#12111yescharacteristic
147C2×C4×C83#12111yescharacteristic
148C2×C4×C83#12311yescharacteristic
149C2×C4×C83#12311yescharacteristic
150C2×C4×C83#12411yescharacteristic
151C2×C4×C83C2×D811yescharacteristic
152C2×C4×C83C2×SD1611yescharacteristic
153C2×C4×C83C2×SD1611yescharacteristic
154C2×C4×C83#13511yescharacteristic
155C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C83#13711yescharacteristic
159C2×Dic83—22no—
160C2×Dic83—41no—
161C2×Dic83—41no—
162C2×Dic83—41no—
163C2×Dic83—41no—
164C2×Dic83—41no—
165D332—42no—
166D332—42no—
167D332—42no—
168D332—42no—
169D332—82no—
170D332—82no—
171D332—81no—
172D332—81no—
173D332—81no—
174D332—81no—
175C8×C83—81no—
176C8×C83—81no—
177C83⋊C8—22no—
178C83⋊C8—22no—
179C83⋊C8—81no—
180C22×C83#39411yescharacteristic
181C22×C83#45911yescharacteristic
182C22×C83#46011yescharacteristic
183C22×C83#46511yescharacteristic
184C22×C83#46811yescharacteristic
185C22×C83#47111yescharacteristic
186C22×C83#47111yescharacteristic
187C2×D83—82no—
188C2×D83—82no—
189C2×D83—82no—
190C2×D83—161no—
191C2×D83—161no—
192C2×D83—161no—
193C2×D83—161no—
194C4×C83—21no—
195C4×C83—21no—
196C4×C83—82no—
197C4×C83#44711yescharacteristic
198C4×C83#45011yescharacteristic
199C4×C83#46011yescharacteristic
200C4×C83#46111yescharacteristic
201C4×C83#46311yescharacteristic
202C4×C83#46411yescharacteristic
203C4×C83#48611yescharacteristic
204C4×C83#49011yescharacteristic
205Dic83—42no—
206Dic83—81no—
207#10537—831nomaximal, Sylow
208C2×C83#166511yescharacteristic
209C2×C83#166611yescharacteristic
210C2×C83#168511yescharacteristic
211C2×C83#168611yescharacteristic
212C2×C83#204111yescharacteristic
213C2×C83#204611yescharacteristic
214C2×C83#205511yescharacteristic
215D83—162no—
216C2×#492—831no—
217#1988—831no—
218#1982—831no—
219#1939—831no—
220C2×#332D8311yescharacteristic, complemented
221C2×#331—831no—
222#1277—831no—
223C83#1053711yescharacteristic, complemented, Sylow
224C22×SD16—1661no—
225C22×SD16—1661no—
226C2×C4⋊Q8C2×D8311yescharacteristic
227C2×#127—831no—
228#492—1662no—
229#492—1662no—
230C2×C4⋊C8—831no—
231C2×C4⋊C8—1661no—
232C2×C4⋊C8C2×D8311yescharacteristic
233C2×C4⋊C8C2×D8311yescharacteristic
234C2×#102—1661no—
235C2×#102—1661no—
236C2×C4×C8—831no—
237C4×C4⋊C4—831no—
238#340—1661no—
239#340—1661no—
240#336—1661no—
241#332—22no—
242#331—1662no—
243C22×Q8—21no—
244C22×D4—1661no—
245C22×D4—1661no—
246C22×D4—1661no—
247C2×SD16—3322no—
248C2×SD16—3322no—
249C2×SD16—3322no—
250C2×SD16—3322no—
251C2×SD16—1664no—
252C2×SD16—1664no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—831no—
256C22×C8—831no—
257C22×C8—1661no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8C22⋊D8312yes—
262#127—832no—
263#127—1661no—
264#127—1661no—
265#127—1661no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—831no—
269C2×C4⋊C4—831no—
270C2×C42—1661no—
271C2×C42C22×D8311yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—3322no—
277C4⋊C8—1661no—
278C4⋊C8—1661no—
279#102—3322no—
280#102—3322no—
281C4×C8—1661no—
282C4×C8—1661no—
283#95—1661no—
284C24—3321no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×D4—3321no—
292C2×D4—3321no—
293C2×D4—3321no—
294C2×D4—3321no—
295C2×D4—3321no—
296C2×D4—3321no—
297C2×D4—3321no—
298C2×D4—3321no—
299C2×D4—3321no—
300C2×D4—3321no—
301C2×D4—3321no—
302C2×D4—6641no—
303C2×D4—6641no—
304C2×D4—1662no—
305C2×D4—1662no—
306C2×D4—1662no—
307C22×C4—41no—
308C22×C4—1661no—
309C22×C4—1661no—
310C22×C4D4×D8311yescharacteristic
311C22×C4D4×D8311yescharacteristic
312C22×C4#1305059011yescharacteristic
313SD16—3328no—
314SD16—3328no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—3321no—
322C2×C8—3321no—
323C2×C8—3321no—
324C2×C8—832no—
325C2×C8—832no—
326C2×C8—1661no—
327C2×C8—1661no—
328C2×C8—1661no—
329C2×C8—1661no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—832no—
335C4⋊C4—1661no—
336C4⋊C4—1661no—
337C4⋊C4—1661no—
338C42—3321no—
339C42—3321no—
340C42D4×D8311yescharacteristic
341C42C2×C22⋊D8311yescharacteristic
342C42#1305058911yescharacteristic
343C42#1305059011yescharacteristic
344C23—3322no—
345C23—6641no—
346C23—6641no—
347C23—6641no—
348C23—6641no—
349C23—6641no—
350C23—6641no—
351C23#1458176511yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—81no—
355Q8—81no—
356D4—3322no—
357D4—3322no—
358D4—3322no—
359D4—3322no—
360D4—6642no—
361D4—6642no—
362D4—6641no—
363D4—6641no—
364D4—6641no—
365D4—6641no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—3321no—
372C2×C4—3321no—
373C2×C4—3321no—
374C2×C4—3321no—
375C2×C4—3321no—
376C2×C4—1662no—
377C2×C4#1458176011yescharacteristic
378C2×C4#1458176411yescharacteristic
379C2×C4#1458176511yescharacteristic
380C2×C4#1458177411yescharacteristic
381C2×C4#1458177511yescharacteristic
382C2×C4#1458177811yescharacteristic
383C2×C4D8×D8311yescharacteristic
384C2×C4SD16×D8311yescharacteristic
385C2×C4SD16×D8311yescharacteristic
386C2×C4#1458181511yescharacteristic
387C2×C4#1458181611yescharacteristic
388C2×C4#1458181911yescharacteristic
389C2×C4#1458181911yescharacteristic
390C2×C4#1458182411yescharacteristic
391C8—81no—
392C8—81no—
393C8—6641no—
394C8—1662no—
395C8—1662no—
396C22—13281no—
397C22—13281no—
398C22—13281no—
399C22—13281no—
400C22—6642no—
401C22—6642no—
402C22—6642no—
403C22#1912761611yescharacteristic
404C22#1912789511yescharacteristic
405C22#1912790011yescharacteristic
406C22#1912793311yescharacteristic
407C22#1912795011yescharacteristic
408C22#1912796711yescharacteristic
409C22#1912796711yescharacteristic
410C4—21no—
411C4—21no—
412C4—82no—
413C4—3322no—
414C4—6641no—
415C4#1912783311yescharacteristic
416C4#1912785011yescharacteristic
417C4#1912789911yescharacteristic
418C4#1912790511yescharacteristic
419C4#1912791911yescharacteristic
420C4#1912792511yescharacteristic
421C4#1912804611yescharacteristic
422C4#1912806411yescharacteristic
423C2—13282no—
424C2#2490680711yescharacteristic
425C2#2490681411yescharacteristic
426C2#2490693111yescharacteristic
427C2#2490693811yescharacteristic
428C2#2490869511yescharacteristic
429C2#2490872211yescharacteristic
430C2#2490877711yescharacteristic
subgroupG/H
centerC23#14581765
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC2×#332×C83C2
socleC23×C83#121
prime radicalC2×#14581789C22
hypercenterC2×#332D83
hypocenterC83#10537
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #24908416C2semidirect
4. #24908179C2semidirect
6. #24905297C2semidirect
7. C2×#332×C83C2semidirect
101. C4⋊Dic83SD16semidirect
220. C2×#332D83semidirect
223. C83#10537semidirect

Maximal subgroups

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

subgroupindex
C2×#191280752
#249084162
#249083892
#249081792
C2×#191274442
#249052972
C2×#332×C832
#1053783