Finite Group Databasebeta

← #35308614

Subgroups — #35308614

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#24908390C211yesmaximal, characteristic
3#24908182C211yesmaximal, characteristic, complemented
4C2×#19127447C211yesmaximal, characteristic, complemented
5C2×#19127444C211yesmaximal, characteristic
6#24905297C211yesmaximal, characteristic, complemented
7C83×#1988C211yesmaximal, characteristic, complemented
8C22×#13050577—21no—
9C22×#13050577—21no—
10C2×#14581789C2211yescharacteristic
11#19128075—22no—
12#19128075—22no—
13C2×C4⋊(C83⋊C8)—21no—
14C2×C4⋊(C83⋊C8)C2211yescharacteristic
15C2×C4⋊(C83⋊C8)C2211yescharacteristic
16C2×#14581712—21no—
17C2×#14581712—21no—
18C2×C4×C83⋊C8C2211yescharacteristic
19#19127456—21no—
20#19127447—22no—
21#19127444—22no—
22C2×C4⋊Q8×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24C4×C4⋊C4×C83C2211yescharacteristic
25#340×C83—21no—
26#340×C83—21no—
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⋊C8—21no—
38C22×C83⋊C8D411yescharacteristic
39C22×C83⋊C8D411yescharacteristic
40#14581789—21no—
41#14581789—21no—
42#14581789—21no—
43#14581789D412yes—
44C4⋊(C83⋊C8)—21no—
45C4⋊(C83⋊C8)—21no—
46C4⋊(C83⋊C8)—21no—
47C4⋊(C83⋊C8)—21no—
48C4⋊(C83⋊C8)—42no—
49#14581712—42no—
50#14581712—42no—
51C4×C83⋊C8—21no—
52C4×C83⋊C8—21no—
53C22×Q8×C83—21no—
54C22×C8×C83—21no—
55C4⋊Q8×C83—21no—
56C4⋊Q8×C83—21no—
57C4⋊Q8×C83—21no—
58C4⋊Q8×C83D412yes—
59C2×C4⋊C4×C83—21no—
60C2×C4⋊C4×C83—21no—
61C2×C4⋊C4×C83D411yescharacteristic
62C2×C4⋊C4×C83D411yescharacteristic
63C2×C42×C83—21no—
64C2×C42×C83C2311yescharacteristic
65C4⋊C8×C83—21no—
66C4⋊C8×C83—21no—
67#95×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—
85#13050577—48no—
86#13050577—48no—
87C2×C83⋊C8—21no—
88C2×C83⋊C8—21no—
89C2×C83⋊C8—21no—
90C2×C83⋊C8—21no—
91C2×C83⋊C8—41no—
92C2×C83⋊C8—41no—
93C2×C83⋊C8—41no—
94C2×C83⋊C8—41no—
95C2×C83⋊C8—41no—
96C2×C83⋊C8—41no—
97C2×C83⋊C8D812yes—
98C2×C83⋊C8SD1612yes—
99C2×Q8×C83—22no—
100C2×Q8×C83—41no—
101C2×Q8×C83—41no—
102C2×Q8×C83—41no—
103C2×Q8×C83—41no—
104C2×Q8×C83—41no—
105C22×C4×C83—21no—
106C22×C4×C83—21no—
107C22×C4×C83—41no—
108C22×C4×C83C2×D411yescharacteristic
109C22×C4×C83C2×D411yescharacteristic
110C22×C4×C83#4111yescharacteristic
111C2×C8×C83—41no—
112C2×C8×C83—41no—
113C2×C8×C83—41no—
114C4⋊C4×C83—21no—
115C4⋊C4×C83—22no—
116C4⋊C4×C83—22no—
117C4⋊C4×C83—21no—
118C4⋊C4×C83—21no—
119C4⋊C4×C83—41no—
120C4⋊C4×C83—41no—
121C4⋊C4×C83SD1612yescomplemented
122C42×C83—41no—
123C42×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—22no—
143C2×C4×C83—41no—
144C2×C4×C83—41no—
145C2×C4×C83—42no—
146C2×C4×C83—41no—
147C2×C4×C83—41no—
148C2×C4×C83—41no—
149C2×C4×C83—81no—
150C2×C4×C83—81no—
151C2×C4×C83#12011yescharacteristic
152C2×C4×C83#12111yescharacteristic
153C2×C4×C83#12111yescharacteristic
154C2×C4×C83#12311yescharacteristic
155C2×C4×C83#12311yescharacteristic
156C2×C4×C83#12411yescharacteristic
157C2×C4×C83C2×D811yescharacteristic
158C2×C4×C83C2×SD1611yescharacteristic
159C2×C4×C83C2×SD1611yescharacteristic
160C2×C4×C83#13511yescharacteristic
161C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C83#13711yescharacteristic
165D332—42no—
166D332—42no—
167D332—42no—
168D332—42no—
169D332—82no—
170D332—82no—
171D332—81no—
172D332—81no—
173D332—81no—
174D332—81no—
175C8×C83—81no—
176C83⋊C8—22no—
177C83⋊C8—22no—
178C83⋊C8—81no—
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—42no—
197C4×C83—81no—
198C4×C83—82no—
199C4×C83#44711yescharacteristic
200C4×C83#45011yescharacteristic
201C4×C83#46011yescharacteristic
202C4×C83#46111yescharacteristic
203C4×C83#46311yescharacteristic
204C4×C83#46411yescharacteristic
205C4×C83#48611yescharacteristic
206C4×C83#49011yescharacteristic
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#1988D8311yescharacteristic, complemented
218#1982—831no—
219#1939—831no—
220C2×#332—831no—
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—831no—
232C2×C4⋊C8—1661no—
233C2×C4⋊C8C2×D8311yescharacteristic
234C2×#102—1661no—
235C2×#102—1661no—
236C2×C4×C8—831no—
237C4×C4⋊C4C2×D8311yescharacteristic
238#340—21no—
239#340—21no—
240#336—1661no—
241#332—1662no—
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—831no—
255C22×C8—831no—
256C22×C8—1661no—
257C22×C8—1661no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8D33212yes—
262#127—832no—
263#127—1661no—
264#127—1661no—
265#127—1661no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4C22⋊D8311yescharacteristic
269C2×C4⋊C4C22⋊D8311yescharacteristic
270C2×C42—21no—
271C2×C42C22×D8311yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—3322no—
275C4⋊C8—1661no—
276C4⋊C8—1661no—
277C4⋊C8—1661no—
278C4⋊C8—1661no—
279#102—3322no—
280#102—3322no—
281C4×C8—1661no—
282C4×C8—1661no—
283#95—21no—
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—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4D4×D8311yescharacteristic
311C22×C4C2×C22⋊D8311yescharacteristic
312C22×C4#1305058911yescharacteristic
313SD16—3328no—
314SD16—3328no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—3321no—
319C2×C8—3321no—
320C2×C8—3321no—
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—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4#1305057712yescomplemented
338C42—41no—
339C42—41no—
340C42D4×D8311yescharacteristic
341C42C2×D33211yescharacteristic
342C42#1305058911yescharacteristic
343C42#1305059011yescharacteristic
344C23—3322no—
345C23—6641no—
346C23—6641no—
347C23—6641no—
348C23—6641no—
349C23—6641no—
350C23—6641no—
351C23#1458176411yescharacteristic
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—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4#1458176211yescharacteristic
378C2×C4#1458176311yescharacteristic
379C2×C4#1458176611yescharacteristic
380C2×C4#1458177411yescharacteristic
381C2×C4#1458177611yescharacteristic
382C2×C4#1458177811yescharacteristic
383C2×C4D8×D8311yescharacteristic
384C2×C4SD16×D8311yescharacteristic
385C2×C4C2×#1305057711yescharacteristic
386C2×C4#1458181211yescharacteristic
387C2×C4#1458181611yescharacteristic
388C2×C4#1458181711yescharacteristic
389C2×C4#1458181911yescharacteristic
390C2×C4#1458182311yescharacteristic
391C8—81no—
392C8—6641no—
393C8—6641no—
394C8—1662no—
395C8—1662no—
396C22—13281no—
397C22—13281no—
398C22—13281no—
399C22—13281no—
400C22—6642no—
401C22—6642no—
402C22—6642no—
403C22#1912761711yescharacteristic
404C22#1912789411yescharacteristic
405C22#1912789911yescharacteristic
406C22#1912793211yescharacteristic
407C22#1912794911yescharacteristic
408C22#1912796611yescharacteristic
409C22#1912796611yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—82no—
414C4—81no—
415C4#1912783611yescharacteristic
416C4#1912785311yescharacteristic
417C4#1912790111yescharacteristic
418C4#1912790311yescharacteristic
419C4#1912791311yescharacteristic
420C4#1912792311yescharacteristic
421C4#1912804611yescharacteristic
422C4#1912806411yescharacteristic
423C2—13282no—
424C2#2490680611yescharacteristic
425C2#2490681311yescharacteristic
426C2#2490693011yescharacteristic
427C2#2490693711yescharacteristic
428C2#2490869611yescharacteristic
429C2#2490872311yescharacteristic
430C2#2490877811yescharacteristic
subgroupG/H
centerC23#14581764
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1988C2
socleC23×C83#121
prime radicalC2×#14581789C22
hypercenter#1988D83
hypocenterC83#10537
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
3. #24908182C2semidirect
4. C2×#19127447C2semidirect
6. #24905297C2semidirect
7. C83×#1988C2semidirect
121. C4⋊C4×C83SD16semidirect
217. #1988D83semidirect
223. C83#10537semidirect
337. C4⋊C4#13050577semidirect

Maximal subgroups

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

subgroupindex
C2×#191280752
#249083902
#249081822
C2×#191274472
C2×#191274442
#249052972
C83×#19882
#1053783