Finite Group Databasebeta

← #35302613

Subgroups — #35302613

Order 21248.

444 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908257C211yesmaximal, characteristic
2#24907330C211yesmaximal, characteristic, complemented
3C4×#14581714C211yesmaximal, characteristic
4C2×#19127452C211yesmaximal, characteristic, complemented
5C2×#19127430C211yesmaximal, characteristic
6#24905303C211yesmaximal, characteristic, complemented
7C83×#1273C211yesmaximal, characteristic, complemented
8C2×C4×D332C2211yescharacteristic
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×#14581714C411yescharacteristic
12C2×#14581714C411yescharacteristic
13C2×(C2×D83)⋊C8—21no—
14C2×(C2×D83)⋊C8—21no—
15C2×#14581702—21no—
16C4×C4⋊Dic83C2211yescharacteristic
17#19127464C411yescharacteristic
18#19127464C411yescharacteristic
19#19127455—21no—
20#19127452—22no—
21#19127430—22no—
22C2×C4×C8×C83C2211yescharacteristic
23C2×C4×C8×C83C2211yescharacteristic
24C2×C4×C8×C83C2211yescharacteristic
25C22×D332C2×C411yescharacteristic
26C22×C4×D83—21no—
27C22×C83⋊C8—21no—
28C22×C83⋊C8—21no—
29C4×D332—21no—
30C4×D332—21no—
31C4×D332—21no—
32C4×D332—21no—
33C2×C4⋊Dic83C2×C411yescharacteristic
34C2×C4⋊Dic83C2×C411yescharacteristic
35C2×C4⋊Dic83C2×C411yescharacteristic
36C2×(C2×D83)⋊C4—21no—
37C2×C4×Dic83—21no—
38C4⋊(C83⋊C8)—21no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)—21no—
41C4⋊(C83⋊C8)D412yes—
42#14581714—22no—
43#14581714—22no—
44(C2×D83)⋊C8—42no—
45(C2×D83)⋊C8—42no—
46#14581702—42no—
47C83⋊#95—21no—
48C22×C8×C83—21no—
49C22×C8×C83C2×C411yescharacteristic
50C22×C8×C83C2×C411yescharacteristic
51C22×C8×C83D411yescharacteristic
52C22×C8×C83D411yescharacteristic
53C2×C42×C83C2311yescharacteristic
54C4×C8×C83—21no—
55C4×C8×C83—21no—
56C4×C8×C83—21no—
57C4×C8×C83—21no—
58C4×C8×C83—21no—
59C4×C8×C83—21no—
60C23×D83—21no—
61C2×D332—21no—
62C2×D332—21no—
63C2×D332—21no—
64C2×D332—21no—
65C2×D332—21no—
66C2×D332M1612yes—
67C22×Dic83—21no—
68C22×Dic83—21no—
69C22×Dic83—21no—
70C2×C4×D83—41no—
71C2×C4×D83—41no—
72C2×C4×D83—41no—
73C2×C4×D83—41no—
74C2×C4×D83—41no—
75C2×C4×D83—41no—
76C2×C83⋊C8—22no—
77C2×C83⋊C8—41no—
78C2×C83⋊C8—41no—
79C2×C83⋊C8—41no—
80C2×C83⋊C8—41no—
81C2×C83⋊C8—41no—
82C4⋊Dic83—21no—
83C4⋊Dic83—21no—
84C4⋊Dic83—21no—
85C4⋊Dic83—21no—
86C4⋊Dic83—21no—
87C4⋊Dic83—21no—
88(C2×D83)⋊C4—41no—
89(C2×D83)⋊C4—41no—
90C4×Dic83—41no—
91C4×Dic83—41no—
92C22×C4×C83C22×C411yescharacteristic
93C22×C4×C83C2×D411yescharacteristic
94C22×C4×C83#4111yescharacteristic
95C2×C8×C83—21no—
96C2×C8×C83—21no—
97C2×C8×C83—21no—
98C2×C8×C83—21no—
99C2×C8×C83—22no—
100C2×C8×C83—21no—
101C2×C8×C83—21no—
102C2×C8×C83—21no—
103C2×C8×C83—21no—
104C2×C8×C83—21no—
105C2×C8×C83—21no—
106C2×C8×C83—41no—
107C2×C8×C83—41no—
108C2×C8×C83M1612yes—
109C2×C8×C83SD1612yes—
110C42×C83C2×D411yescharacteristic
111C42×C83#4111yescharacteristic
112C42×C83#4111yescharacteristic
113C42×C83#4111yescharacteristic
114C23×C83C4×D411yescharacteristic
115C22×D83—22no—
116C22×D83—41no—
117C22×D83—41no—
118C22×D83—41no—
119C22×D83—41no—
120C22×D83—41no—
121C22×D83—41no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83#11711yescharacteristic
125C2×C4×C83C4×D411yescharacteristic
126C2×C4×C83#12111yescharacteristic
127C2×C4×C83#12311yescharacteristic
128C2×C4×C83#12411yescharacteristic
129C2×C4×C83#12611yescharacteristic
130C2×C4×C83C2×M1611yescharacteristic
131C2×C4×C83C2×M1611yescharacteristic
132C2×C4×C83#13111yescharacteristic
133C2×C4×C83#13111yescharacteristic
134C2×C4×C83C2×SD1611yescharacteristic
135C2×C4×C83#13511yescharacteristic
136C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
138C2×Dic83—41no—
139C2×Dic83—41no—
140C2×Dic83—41no—
141C2×Dic83—41no—
142C2×Dic83—41no—
143C2×Dic83—41no—
144C2×Dic83—41no—
145C2×Dic83—41no—
146C2×Dic83—41no—
147D332—22no—
148D332—22no—
149D332—41no—
150D332—41no—
151C4×D83—81no—
152C4×D83—81no—
153C4×D83—81no—
154C4×D83—81no—
155C8×C83—22no—
156C8×C83—22no—
157C8×C83—42no—
158C8×C83—41no—
159C8×C83—41no—
160C83⋊C8—42no—
161C83⋊C8—81no—
162C22×C83#38811yescharacteristic
163C22×C83#43511yescharacteristic
164C22×C83#43611yescharacteristic
165C22×C83C4×SD1611yescharacteristic
166C22×C83#44211yescharacteristic
167C22×C83#44311yescharacteristic
168C22×C83#44411yescharacteristic
169C2×D83—42no—
170C2×D83—42no—
171C2×D83—42no—
172C2×D83—81no—
173C2×D83—81no—
174C2×D83—81no—
175C2×D83—81no—
176C4×C83—21no—
177C4×C83—21no—
178C4×C83#43211yescharacteristic
179C4×C83#43311yescharacteristic
180C4×C83#43511yescharacteristic
181C4×C83#43511yescharacteristic
182C4×C83#46011yescharacteristic
183C4×C83#46311yescharacteristic
184C4×C83#48111yescharacteristic
185C4×C83#48211yescharacteristic
186Dic83—81no—
187Dic83—81no—
188Dic83—81no—
189#9546—831nomaximal, Sylow
190C2×C83#158211yescharacteristic
191C2×C83#158611yescharacteristic
192C2×C83#159011yescharacteristic
193C2×C83#159411yescharacteristic
194C2×C83#192411yescharacteristic
195C2×C83#192611yescharacteristic
196C2×C83#192911yescharacteristic
197D83—82no—
198#1954—831no—
199#1770—831no—
200C4×#102—831no—
201C2×#334—831no—
202C2×D4⋊C8—831no—
203#1279—831no—
204#1273D8311yescharacteristic, complemented
205C83#954611yescharacteristic, complemented, Sylow
206C2×C4×D4—831no—
207C2×C4⋊C8—831no—
208C2×C4⋊C8—831no—
209C2×#102—831no—
210C2×#102—831no—
211C2×C22⋊C8—1661no—
212C2×C22⋊C8—1661no—
213C2×#97—1661no—
214C2×C4×C8C2×D8311yescharacteristic
215C2×C4×C8C2×D8311yescharacteristic
216C2×C4×C8C2×D8311yescharacteristic
217C4×C4⋊C4—831no—
218#340—831no—
219#340—831no—
220#336—1661no—
221#334—1662no—
222D4⋊C8—1662no—
223C22×D4—831no—
224C23×C4—1661no—
225C22×C8—21no—
226C22×C8—1661no—
227C22×C8—1661no—
228C22×C8C4×D8311yescharacteristic
229C22×C8C4×D8311yescharacteristic
230C22×C8D33211yescharacteristic
231C22×C8D33211yescharacteristic
232C4×D4—1661no—
233C4×D4—1661no—
234C4×D4—1661no—
235C4×D4—1661no—
236C2×C4⋊C4—831no—
237C2×C4⋊C4—831no—
238C2×C4⋊C4—831no—
239C2×C22⋊C4—1661no—
240C2×C42—1661no—
241C2×C42C22×D8311yescharacteristic
242C4⋊C8—832no—
243C4⋊C8—1661no—
244C4⋊C8—1661no—
245C4⋊C8—1661no—
246#102—1662no—
247#102—1662no—
248C22⋊C8—3322no—
249C22⋊C8—3322no—
250#97—3322no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—21no—
257#95—1661no—
258C24—1661no—
259C2×D4—832no—
260C2×D4—1661no—
261C2×D4—1661no—
262C2×D4—1661no—
263C2×D4—1661no—
264C2×D4—1661no—
265C22×C4—3321no—
266C22×C4—3321no—
267C22×C4—3321no—
268C22×C4—3321no—
269C22×C4—3321no—
270C22×C4—3321no—
271C22×C4—1661no—
272C22×C4—1661no—
273C22×C4—1661no—
274C22×C4C2×C4×D8311yescharacteristic
275C22×C4C2×D33211yescharacteristic
276C22×C4#1305059011yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—3321no—
291C2×C8—3321no—
292C2×C8—3321no—
293C2×C8—3321no—
294C2×C8—3321no—
295C2×C8—1662no—
296C2×C8#1305057312yes—
297C2×C8#1305057912yes—
298C4⋊C4—1661no—
299C4⋊C4—1661no—
300C4⋊C4—1661no—
301C4⋊C4—1661no—
302C4⋊C4—1661no—
303C4⋊C4—1661no—
304C22⋊C4—3321no—
305C22⋊C4—3321no—
306C42—3321no—
307C42—3321no—
308C42D4×D8311yescharacteristic
309C42#1305058911yescharacteristic
310C42#1305058911yescharacteristic
311C42#1305059111yescharacteristic
312C23—3321no—
313C23—3321no—
314C23—3321no—
315C23—3321no—
316C23—3321no—
317C23—3321no—
318C23—1662no—
319C23C4×D33211yescharacteristic
320D4—3321no—
321D4—3321no—
322D4—1662no—
323D4—1662no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—3321no—
327C2×C4—3321no—
328C2×C4—3321no—
329C2×C4—3321no—
330C2×C4—3321no—
331C2×C4—3321no—
332C2×C4—3321no—
333C2×C4—3321no—
334C2×C4—3321no—
335C2×C4—6641no—
336C2×C4—6641no—
337C2×C4—6641no—
338C2×C4—6641no—
339C2×C4#1458175011yescharacteristic
340C2×C4(C22⋊D83)⋊C411yescharacteristic
341C2×C4#1458176711yescharacteristic
342C2×C4#1458177611yescharacteristic
343C2×C4#1458177811yescharacteristic
344C2×C4#1458178711yescharacteristic
345C2×C4M16×D8311yescharacteristic
346C2×C4C2×#1305057311yescharacteristic
347C2×C4#1458179811yescharacteristic
348C2×C4#1458180011yescharacteristic
349C2×C4C2×#1305057911yescharacteristic
350C2×C4#1458181411yescharacteristic
351C2×C4#1458182011yescharacteristic
352C2×C4#1458182011yescharacteristic
353C8—22no—
354C8—22no—
355C8—42no—
356C8—41no—
357C8—41no—
358C8—3322no—
359C8—6641no—
360C22—3322no—
361C22—3322no—
362C22—3322no—
363C22—6641no—
364C22—6641no—
365C22—6641no—
366C22—6641no—
367C22#1912759311yescharacteristic
368C22#1912777411yescharacteristic
369C22#1912778011yescharacteristic
370C22C4×#1305057911yescharacteristic
371C22#1912781411yescharacteristic
372C22#1912781911yescharacteristic
373C22#1912782411yescharacteristic
374C4—21no—
375C4—21no—
376C4—6641no—
377C4—6641no—
378C4—6641no—
379C4#1912775711yescharacteristic
380C4#1912776111yescharacteristic
381C4#1912776911yescharacteristic
382C4#1912777511yescharacteristic
383C4#1912790211yescharacteristic
384C4#1912791711yescharacteristic
385C4#1912802011yescharacteristic
386C4#1912802611yescharacteristic
387C2—6642no—
388C2#2490630111yescharacteristic
389C2#2490632911yescharacteristic
390C2#2490635511yescharacteristic
391C2#2490637811yescharacteristic
392C2#2490807711yescharacteristic
393C2#2490809111yescharacteristic
394C2#2490811211yescharacteristic
subgroupG/H
centerC22×C4C2×D332
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1273C2
socleC23×C83C4×D4
prime radicalC22×D332C2×C4
cosocleC2×C42×C83C23
hypercenter#1273D83
hypocenterC83#9546
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1273

Complements

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

NH ≅ G/Ntype
2. #24907330C2semidirect
4. C2×#19127452C2semidirect
6. #24905303C2semidirect
7. C83×#1273C2semidirect
204. #1273D83semidirect
205. C83#9546semidirect

Maximal subgroups

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

subgroupindex
#249082572
#249073302
C4×#145817142
C2×#191274522
C2×#191274302
#249053032
C83×#12732
#954683