Finite Group Databasebeta

← #35323070

Subgroups — #35323070

Order 21248.

488 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912806C211yesmaximal, characteristic
2#24907455C211yesmaximal, characteristic
3#24905580C212yesmaximal
4#24905580C212yesmaximal
5C4×#99×C83C211yesmaximal, characteristic
6C22×Dic83⋊C4C411yescharacteristic, complemented
7#19127725—21no—
8C2×#14581709C2212yes—
9#19127634—21no—
10#19127624—21no—
11#19127585—21no—
12#19127581C2211yescharacteristic
13#19127581C2211yescharacteristic
14#19127574—21no—
15#19127573C411yescharacteristic, complemented
16#19127573C411yescharacteristic, complemented
17#19127561C411yescharacteristic, complemented
18#19127470—21no—
19C2×C4×D4×C83C2211yescharacteristic
20C2×#99×C83C2212yes—
21C4×C22⋊C4×C83—21no—
22#342×C83—21no—
23C23×Dic83C2×C411yescharacteristic
24C23×Dic83C2×C411yescharacteristic
25C2×#13050574—22no—
26C2×C4⋊Dic83—21no—
27C2×Dic83⋊C4—21no—
28C2×Dic83⋊C4—21no—
29C2×Dic83⋊C4—21no—
30C2×Dic83⋊C4—21no—
31C2×Dic83⋊C4—41no—
32C2×Dic83⋊C4—41no—
33C2×C22⋊Dic83—21no—
34C2×C22⋊Dic83—21no—
35C2×C22⋊Dic83C2×C411yescharacteristic
36C2×C22⋊Dic83C2×C411yescharacteristic
37C4⋊(C83⋊C8)—41no—
38C4⋊(C83⋊C8)—41no—
39#14581709—24no—
40C83⋊#95—21no—
41C83⋊#95—21no—
42C83⋊#95—21no—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C22×D4×C83C2311yescharacteristic
46C23×C4×C83C2×C411yescharacteristic
47C23×C4×C83D411yescharacteristic
48C4×D4×C83—41no—
49C4×D4×C83—41no—
50C2×C4⋊C4×C83D411yescharacteristic
51C2×C22⋊C4×C83—22no—
52C2×C22⋊C4×C83C2×C411yescharacteristic
53C2×C22⋊C4×C83D411yescharacteristic
54C2×C42×C83—41no—
55C2×C42×C83D411yescharacteristic
56#99×C83—22no—
57#99×C83Q814yes—
58#95×C83—41no—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—21no—
62C22×Dic83—21no—
63C22×Dic83—42no—
64C22×Dic83—41no—
65C22×Dic83—41no—
66C22×Dic83—81no—
67#13050574—42no—
68#13050574—42no—
69C2×C83⋊C8—42no—
70C4⋊Dic83—81no—
71Dic83⋊C4—42no—
72Dic83⋊C4—42no—
73Dic83⋊C4—41no—
74Dic83⋊C4—41no—
75Dic83⋊C4—81no—
76C22⋊Dic83—42no—
77C22⋊Dic83—41no—
78C22⋊Dic83—41no—
79C22⋊Dic83—81no—
80C24×C83C22×C411yescharacteristic
81C24×C83C2×D411yescharacteristic
82C2×D4×C83—41no—
83C2×D4×C83—41no—
84C2×D4×C83C2×Q812yes—
85C2×D4×C83#4112yes—
86C22×C4×C83—21no—
87C22×C4×C83—21no—
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—42no—
91C22×C4×C83—81no—
92C22×C4×C83—81no—
93C22×C4×C83C22⋊C411yescharacteristic
94C22×C4×C83C22⋊C411yescharacteristic
95C22×C4×C83C22⋊C411yescharacteristic
96C22×C4×C83C22⋊C411yescharacteristic
97C22×C4×C83C2×D411yescharacteristic
98C4⋊C4×C83—41no—
99C22⋊C4×C83—24no—
100C22⋊C4×C83—41no—
101C22⋊C4×C83—41no—
102C22⋊C4×C83—42no—
103C42×C83—21no—
104C42×C83—21no—
105C42×C83—82no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—41no—
111C23×C83—41no—
112C23×C83—41no—
113C23×C83—41no—
114C23×C83C2×C22⋊C411yescharacteristic
115C23×C83C4×Q812yes—
116C23×C83C22⋊Q812yes—
117D4×C83—42no—
118D4×C83—42no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—41no—
125C2×C4×C83—42no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—44no—
130C2×C4×C83—81no—
131C2×C4×C83—81no—
132C2×C4×C83—81no—
133C2×C4×C83—82no—
134C2×C4×C83—82no—
135C2×C4×C83#9911yescharacteristic
136C2×C4×C83#9911yescharacteristic
137C2×C4×C83#12411yescharacteristic
138C2×C4×C83C4⋊Q811yescharacteristic
139C2×Dic83—22no—
140C2×Dic83—41no—
141C2×Dic83—42no—
142C2×Dic83—41no—
143C2×Dic83—42no—
144C2×Dic83—41no—
145C2×Dic83—41no—
146C2×Dic83—41no—
147C2×Dic83—41no—
148C2×Dic83—41no—
149C2×Dic83—41no—
150C2×Dic83—41no—
151C2×Dic83—41no—
152C2×Dic83—41no—
153C2×Dic83—82no—
154C83⋊C8—82no—
155C22×C83—21no—
156C22×C83—21no—
157C22×C83—22no—
158C22×C83—22no—
159C22×C83—42no—
160C22×C83—42no—
161C22×C83—42no—
162C22×C83—41no—
163C22×C83—41no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—81no—
167C22×C83#39111yescharacteristic
168C22×C83C2×#9911yescharacteristic
169C22×C83#41011yescharacteristic
170C4×C83—21no—
171C4×C83—21no—
172C4×C83—21no—
173C4×C83—21no—
174C4×C83—41no—
175C4×C83—41no—
176C4×C83—41no—
177C4×C83—84no—
178Dic83—42no—
179Dic83—81no—
180Dic83—81no—
181Dic83—81no—
182#13297—831nomaximal, Sylow
183C2×C83—21no—
184C2×C83—21no—
185C2×C83—42no—
186C2×C83—42no—
187C2×C83#199611yescharacteristic
188C2×C83#212011yescharacteristic
189C2×C83#212111yescharacteristic
190#2579—831no—
191#1800—831no—
192C4×#99D8311yescharacteristic
193#1390—832no—
194#1390—832no—
195C83#1329711yescharacteristic, complemented, Sylow
196C2×C4×D4C2×D8311yescharacteristic
197C22×C4⋊C4—831no—
198#423—1661no—
199C2×#100—832no—
200C2×#99C2×D8312yes—
201#398—1661no—
202#396—1661no—
203#387—1661no—
204#386—831no—
205#386—831no—
206#385—831no—
207#385—831no—
208#385—1661no—
209#380—831no—
210C4×C22⋊C4—21no—
211#343—1661no—
212#342—21no—
213C22×D4C22×D8311yescharacteristic
214C23×C4—831no—
215C23×C4—831no—
216C23×C4C4×D8311yescharacteristic
217C23×C4C22⋊D8311yescharacteristic
218C2×M16—1662no—
219C4×D4—41no—
220C4×D4—41no—
221C2×C4⋊C4—3321no—
222C2×C4⋊C4—3321no—
223C2×C4⋊C4—1661no—
224C2×C4⋊C4—1661no—
225C2×C4⋊C4—1661no—
226C2×C4⋊C4—1661no—
227C2×C4⋊C4—1661no—
228C2×C4⋊C4D33211yescharacteristic
229C2×C22⋊C4—22no—
230C2×C22⋊C4—831no—
231C2×C22⋊C4—831no—
232C2×C22⋊C4—1661no—
233C2×C22⋊C4—1661no—
234C2×C22⋊C4C4×D8311yescharacteristic
235C2×C22⋊C4C22⋊D8311yescharacteristic
236C2×C42—41no—
237C2×C42D33211yescharacteristic
238C4⋊C8—3321no—
239C4⋊C8—3321no—
240#100—1664no—
241#99—22no—
242#99Dic16614yes—
243#95—41no—
244#95—1661no—
245#95—1661no—
246#95—1661no—
247#95—1661no—
248#95—1661no—
249C24C2×C4×D8311yescharacteristic
250C24C2×C22⋊D8311yescharacteristic
251C2×D4—41no—
252C2×D4—41no—
253C2×D4C2×Dic16612yes—
254C2×D4#1305059012yes—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—3321no—
263C22×C4—3322no—
264C22×C4—3321no—
265C22×C4—6641no—
266C22×C4—1661no—
267C22×C4—1661no—
268C22×C4—1661no—
269C22×C4—1661no—
270C22×C4(C2×D83)⋊C411yescharacteristic
271C22×C4(C2×D83)⋊C411yescharacteristic
272C22×C4(C2×D83)⋊C411yescharacteristic
273C22×C4(C2×D83)⋊C411yescharacteristic
274C22×C4C2×D33211yescharacteristic
275M16—3322no—
276M16—3322no—
277C2×C8—3322no—
278C4⋊C4—41no—
279C4⋊C4—3322no—
280C4⋊C4—3322no—
281C4⋊C4—3321no—
282C4⋊C4—3321no—
283C4⋊C4—6641no—
284C4⋊C4—6641no—
285C22⋊C4—24no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—3322no—
290C22⋊C4—3321no—
291C22⋊C4—3321no—
292C22⋊C4—6641no—
293C42—21no—
294C42—21no—
295C42—82no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23C2×(C2×D83)⋊C411yescharacteristic
305C23C4×Dic16612yes—
306C23#1458177112yes—
307D4—42no—
308D4—42no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—44no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—3321no—
326C2×C4—3322no—
327C2×C4—3321no—
328C2×C4—3322no—
329C2×C4—3321no—
330C2×C4—3321no—
331C2×C4—3321no—
332C2×C4—3321no—
333C2×C4—3321no—
334C2×C4—3321no—
335C2×C4—3321no—
336C2×C4—3321no—
337C2×C4—3321no—
338C2×C4—6642no—
339C2×C4—1662no—
340C2×C4#1458170611yescharacteristic
341C2×C4#1458170611yescharacteristic
342C2×C4#1458178011yescharacteristic
343C2×C4#1458179211yescharacteristic
344C8—6642no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—81no—
357C22#1912760711yescharacteristic
358C22C2×#1458170611yescharacteristic
359C22#1912767411yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—84no—
368C4—3322no—
369C4—6641no—
370C4—6641no—
371C4—6641no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—42no—
376C2#2490844811yescharacteristic
377C2#2490910211yescharacteristic
378C2#2490910711yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC24×C83C22×C4
FrattiniC22×D4C22×D83
FittingC4×#99×C83C2
socleC22×C83C2×#99
prime radical, cosocleC22×D4×C83C23
hypercenterC4×#99D83
hypocenterC83#13297
LCSG ▷ C24×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
6. C22×Dic83⋊C4C4semidirect
15. #19127573C4semidirect
16. #19127573C4semidirect
17. #19127561C4semidirect
195. C83#13297semidirect

Maximal subgroups

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

subgroupindex
#249128062
#249074552
#249055802
C4×#99×C832
#1329783