Finite Group Databasebeta

← #35293946

Subgroups — #35293946

Order 21248.

614 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127753C211yesmaximal, characteristic
2C2×#19127752C211yesmaximal, characteristic
3#24909859C211yesmaximal, characteristic
4#24905304C211yesmaximal, characteristic, complemented
5#24905303C211yesmaximal, characteristic, complemented
6#24905302C211yesmaximal, characteristic, complemented
7C83×#1279C211yesmaximal, characteristic, complemented
8C2×C42×D83C2211yescharacteristic
9#19127753—22no—
10#19127753C414yescomplemented
11#19127752—22no—
12#19127752C414yescomplemented
13C2×C4⋊(C83⋊C8)C2211yescharacteristic
14C2×Dic83⋊C8—21no—
15C2×(C2×D83)⋊C8—21no—
16C2×(C2×D83)⋊C8—21no—
17C2×C4×C83⋊C8C2211yescharacteristic
18C2×C8×Dic83—21no—
19#19127568—21no—
20#19127566C412yes—
21#19127563—21no—
22#19127558C412yes—
23C4×C4⋊Dic83C2211yescharacteristic
24C4×(C2×D83)⋊C4—21no—
25#19127547—21no—
26C2×C4⋊C8×C83C2211yescharacteristic
27C2×C4×C8×C83C2211yescharacteristic
28C4×C4⋊C4×C83C2211yescharacteristic
29C22×C4×D83C2×C411yescharacteristic
30C22×C4×D83D411yescharacteristic
31C22×C4×D83D411yescharacteristic
32C22×C83⋊C8—21no—
33C22×C83⋊C8—21no—
34C2×C4⋊Dic83C2×C412yes—
35C2×(C2×D83)⋊C4—22no—
36C2×C4×Dic83—21no—
37C2×C4×Dic83C2×C411yescharacteristic
38C2×C4×Dic83D411yescharacteristic
39C2×C4×Dic83D411yescharacteristic
40C42×D83C2×C412yes—
41C42×D83C2×C412yes—
42C42×D83D412yes—
43C42×D83Q812yes—
44C4⋊(C83⋊C8)—21no—
45C4⋊(C83⋊C8)C2×C412yes—
46Dic83⋊C8—24no—
47(C2×D83)⋊C8—24no—
48(C2×D83)⋊C8—24no—
49C4×C83⋊C8—21no—
50C4×C83⋊C8C2×C412yes—
51C8×Dic83—24no—
52C83⋊#95—22no—
53C83⋊#95—22no—
54C83⋊#95—22no—
55C83⋊#95—21no—
56C22×C8×C83—21no—
57C22×C8×C83—21no—
58C2×C4⋊C4×C83C2×C412yes—
59C2×C42×C83—21no—
60C2×C42×C83C2311yescharacteristic
61C4⋊C8×C83—21no—
62C4⋊C8×C83C2×C412yes—
63C4×C8×C83—21no—
64C4×C8×C83C2×C412yes—
65#95×C83—21no—
66C23×D83C22⋊C411yescharacteristic
67C22×Dic83—22no—
68C22×Dic83C22⋊C411yescharacteristic
69C22×Dic83C22⋊C411yescharacteristic
70C22×Dic83C22⋊C411yescharacteristic
71C2×C4×D83—22no—
72C2×C4×D83—22no—
73C2×C4×D83—21no—
74C2×C4×D83—21no—
75C2×C4×D83—21no—
76C2×C4×D83—21no—
77C2×C4×D83—42no—
78C2×C4×D83C4212yes—
79C2×C4×D83C22⋊C412yes—
80C2×C4×D83C22⋊C412yes—
81C2×C4×D83C4⋊C412yes—
82C2×C4×D83C4⋊C412yes—
83C2×C4×D83C4⋊C412yes—
84C2×C83⋊C8—22no—
85C2×C83⋊C8—22no—
86C2×C83⋊C8—42no—
87C2×C83⋊C8—41no—
88C2×C83⋊C8—41no—
89C4⋊Dic83—22no—
90C4⋊Dic83—22no—
91(C2×D83)⋊C4—44no—
92C4×Dic83—41no—
93C4×Dic83—41no—
94C4×Dic83C4212yes—
95C4×Dic83C22⋊C412yes—
96C4×Dic83C22⋊C412yes—
97C4×Dic83C4⋊C412yes—
98C4×Dic83C4⋊C412yes—
99C4×Dic83C4⋊C412yes—
100C22×C4×C83—22no—
101C22×C4×C83C22×C411yescharacteristic
102C22×C4×C83C2×D411yescharacteristic
103C22×C4×C83C2×D411yescharacteristic
104C2×C8×C83—22no—
105C2×C8×C83—22no—
106C2×C8×C83—42no—
107C2×C8×C83—41no—
108C2×C8×C83—41no—
109C4⋊C4×C83—22no—
110C4⋊C4×C83—22no—
111C42×C83—41no—
112C42×C83—41no—
113C42×C83C22×C411yescharacteristic
114C42×C83C22×C411yescharacteristic
115C42×C83C2×D411yescharacteristic
116C42×C83C2×Q811yescharacteristic
117C23×C83C2×C22⋊C411yescharacteristic
118C22×D83—22no—
119C22×D83—21no—
120C22×D83—21no—
121C22×D83—22no—
122C22×D83#9512yes—
123C2×C4×C83—22no—
124C2×C4×C83—42no—
125C2×C4×C83—42no—
126C2×C4×C83—42no—
127C2×C4×C83C2×C4211yescharacteristic
128C2×C4×C83C2×C22⋊C411yescharacteristic
129C2×C4×C83C2×C22⋊C411yescharacteristic
130C2×C4×C83C2×C4⋊C411yescharacteristic
131C2×C4×C83C2×C4⋊C411yescharacteristic
132C2×C4×C83C2×C4⋊C411yescharacteristic
133C2×C4×C83#13112yes—
134C2×C4×C83#13112yes—
135C2×C4×C83#13511yescharacteristic
136C2×C4×C83#13511yescharacteristic
137C2×C4×C83#13511yescharacteristic
138C2×C4×C83#13511yescharacteristic
139C2×Dic83—22no—
140C2×Dic83—21no—
141C2×Dic83—21no—
142C2×Dic83—22no—
143C2×Dic83—42no—
144C2×Dic83—42no—
145C2×Dic83—42no—
146C2×Dic83#9512yes—
147C2×Dic83#9512yes—
148C2×Dic83#9512yes—
149C4×D83—22no—
150C4×D83—22no—
151C4×D83—22no—
152C4×D83—22no—
153C4×D83—24no—
154C4×D83—22no—
155C4×D83—22no—
156C4×D83—42no—
157C4×D83—42no—
158C8×C83—42no—
159C8×C83—42no—
160C83⋊C8—42no—
161C83⋊C8—42no—
162C22×C83C2×#9511yescharacteristic
163C22×C83#40812yes—
164C22×C83#41611yescharacteristic
165C22×C83#41611yescharacteristic
166C22×C83#42112yes—
167C2×D83—22no—
168C2×D83—22no—
169C2×D83—22no—
170C2×D83—42no—
171C2×D83—42no—
172C4×C83—21no—
173C4×C83—21no—
174C4×C83—82no—
175C4×C83#40511yescharacteristic
176C4×C83#40511yescharacteristic
177C4×C83#41611yescharacteristic
178C4×C83#41611yescharacteristic
179C4×C83#42412yes—
180C4×C83#42711yescharacteristic
181C4×C83#42711yescharacteristic
182Dic83—22no—
183Dic83—22no—
184Dic83—22no—
185Dic83—82no—
186#7894—831nomaximal, Sylow
187C2×C83#148212yes—
188C2×C83#148212yes—
189C2×C83#172911yescharacteristic
190C2×C83#173311yescharacteristic
191C2×C83#173511yescharacteristic
192D83—42no—
193C2×#431—831no—
194C2×#431—831no—
195#2283—831no—
196#1279—831no—
197#1279—831no—
198#1279—831no—
199#1279D8311yescharacteristic, complemented
200C83#789411yescharacteristic, complemented, Sylow
201C22×C42—831no—
202#431—834no—
203#431—834no—
204#431—1662no—
205#431—1662no—
206C2×C4⋊C8—831no—
207C2×C4⋊C8—1661no—
208C2×C4⋊C8C2×D8311yescharacteristic
209C2×C22⋊C8—1661no—
210C2×C22⋊C8—1661no—
211C2×C4×C8—831no—
212C2×C4×C8—1661no—
213C2×C4×C8C2×D8311yescharacteristic
214#383—1661no—
215#382—832no—
216#381—1661no—
217#380—832no—
218C4×C4⋊C4—831no—
219C4×C4⋊C4C2×D8311yescharacteristic
220C4×C22⋊C4—1661no—
221#376—1661no—
222C23×C4—831no—
223C23×C4—831no—
224C23×C4—831no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—1661no—
228C22×C8—1661no—
229C2×C4⋊C4—832no—
230C2×C4⋊C4C4×D8312yes—
231C2×C22⋊C4—1662no—
232C2×C42—21no—
233C2×C42—831no—
234C2×C42—831no—
235C2×C42—831no—
236C2×C42—832no—
237C2×C42—832no—
238C2×C42—832no—
239C2×C42—832no—
240C2×C42—1661no—
241C2×C42C22×D8311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—832no—
244C4⋊C8—1664no—
245C4⋊C8—1661no—
246C4⋊C8C4×D8312yes—
247C22⋊C8—1664no—
248C22⋊C8—1664no—
249C4×C8—21no—
250C4×C8—832no—
251C4×C8—1664no—
252C4×C8—1661no—
253C4×C8C4×D8312yes—
254#95—21no—
255#95—1662no—
256#95—1662no—
257#95—1662no—
258#95—1661no—
259C24—831no—
260C22×C4—22no—
261C22×C4—3322no—
262C22×C4—832no—
263C22×C4—832no—
264C22×C4—831no—
265C22×C4—831no—
266C22×C4—831no—
267C22×C4—832no—
268C22×C4—832no—
269C22×C4—832no—
270C22×C4—832no—
271C22×C4—1662no—
272C22×C4—1662no—
273C22×C4—1662no—
274C22×C4—1661no—
275C22×C4—1661no—
276C22×C4—1661no—
277C22×C4—1661no—
278C22×C4C2×C4×D8311yescharacteristic
279C22×C4D4×D8311yescharacteristic
280C22×C4D4×D8311yescharacteristic
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—42no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—3322no—
287C2×C8—3321no—
288C2×C8—3321no—
289C2×C8—1662no—
290C2×C8—1662no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—1662no—
294C4⋊C4—1662no—
295C22⋊C4—3324no—
296C42—41no—
297C42—41no—
298C42—3321no—
299C42—3321no—
300C42—832no—
301C42—832no—
302C42—832no—
303C42—832no—
304C42—832no—
305C42—832no—
306C42C2×C4×D8311yescharacteristic
307C42C2×C4×D8311yescharacteristic
308C42D4×D8311yescharacteristic
309C42Q8×D8311yescharacteristic
310C23—832no—
311C23—1662no—
312C23—1661no—
313C23—1661no—
314C23—1662no—
315C23C22⋊C4×D8311yescharacteristic
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—3322no—
321C2×C4—3322no—
322C2×C4—3322no—
323C2×C4—3322no—
324C2×C4—3322no—
325C2×C4—832no—
326C2×C4—832no—
327C2×C4—832no—
328C2×C4—1662no—
329C2×C4—1661no—
330C2×C4—1661no—
331C2×C4—1662no—
332C2×C4—1662no—
333C2×C4—1662no—
334C2×C4—1662no—
335C2×C4—1662no—
336C2×C4—1664no—
337C2×C4—1662no—
338C2×C4—1662no—
339C2×C4C42×D8311yescharacteristic
340C2×C4C22⋊C4×D8311yescharacteristic
341C2×C4C22⋊C4×D8311yescharacteristic
342C2×C4C4⋊C4×D8311yescharacteristic
343C2×C4C4⋊C4×D8311yescharacteristic
344C2×C4C4⋊C4×D8311yescharacteristic
345C2×C4#1458179812yes—
346C2×C4#1458180012yes—
347C2×C4#1458181111yescharacteristic
348C2×C4#1458181311yescharacteristic
349C2×C4#1458181311yescharacteristic
350C2×C4#1458181511yescharacteristic
351C8—42no—
352C8—42no—
353C8—3322no—
354C8—3322no—
355C22—3322no—
356C22—3322no—
357C22—1662no—
358C22—1662no—
359C22—1662no—
360C22#95×D8311yescharacteristic
361C22#1912766612yes—
362C22#1912769411yescharacteristic
363C22#1912769611yescharacteristic
364C22#1912771612yes—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—6642no—
369C4—1662no—
370C4—1662no—
371C4—1662no—
372C4#1912765511yescharacteristic
373C4#1912765811yescharacteristic
374C4#1912769411yescharacteristic
375C4#1912769611yescharacteristic
376C4#1912772612yes—
377C4#1912773611yescharacteristic
378C4#1912773811yescharacteristic
379C2—3322no—
380C2#2490586812yes—
381C2#2490587012yes—
382C2#2490715811yescharacteristic
383C2#2490717111yescharacteristic
384C2#2490717811yescharacteristic
subgroupG/H
centerC22×C4D4×D83
commutatorC2×C4×C83C2×C42
FrattiniC2×C42C22×D83
FittingC83×#1279C2
socleC23×C83C2×C22⋊C4
prime radicalC23×D83C22⋊C4
cosocleC2×C42×C83C23
hypercenter#1279D83
hypocenterC83#7894
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #24905304C2semidirect
5. #24905303C2semidirect
6. #24905302C2semidirect
7. C83×#1279C2semidirect
10. #19127753C4semidirect
12. #19127752C4semidirect
199. #1279D83semidirect
200. C83#7894semidirect

Maximal subgroups

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

subgroupindex
C2×#191277532
C2×#191277522
#249098592
#249053042
#249053032
#249053022
C83×#12792
#789483