Finite Group Databasebeta

← #35323049

Subgroups — #35323049

Order 21248.

484 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 111 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#24907451C211yesmaximal, characteristic
2C4×#14581709C211yesmaximal, characteristic
3#24905581C214yesmaximal
4C83×#2487C211yesmaximal, characteristic
5C2×#14581709C2212yes—
6C2×#14581707C2212yes—
7C4×#13050574—21no—
8#19127561—21no—
9#19127470—21no—
10#19127468—21no—
11C2×C4×D4×C83C2211yescharacteristic
12C22×C4⋊C4×C83C411yescharacteristic, complemented
13#400×C83—21no—
14#399×C83—21no—
15#389×C83—21no—
16#386×C83C2212yes—
17#385×C83C412yescomplemented
18#380×C83—21no—
19#380×C83C411yescharacteristic, complemented
20C2×#13050574—22no—
21C2×C4⋊Dic83—41no—
22C2×C22⋊Dic83—22no—
23#14581709—22no—
24#14581709Q814yes—
25#14581707—24no—
26#14581703—41no—
27C4×C83⋊C8—41no—
28C83⋊#95—41no—
29C22×D4×C83C2311yescharacteristic
30C23×C4×C83C2×C411yescharacteristic
31C23×C4×C83C2×C412yes—
32C23×C4×C83D411yescharacteristic
33C4×D4×C83—41no—
34C4×D4×C83—41no—
35C2×C4⋊C4×C83—21no—
36C2×C4⋊C4×C83—21no—
37C2×C4⋊C4×C83—21no—
38C2×C4⋊C4×C83—22no—
39C2×C4⋊C4×C83—41no—
40C2×C4⋊C4×C83—41no—
41C2×C4⋊C4×C83D411yescharacteristic
42C2×C22⋊C4×C83—22no—
43C2×C22⋊C4×C83C2×C412yes—
44C2×C22⋊C4×C83C2×C411yescharacteristic
45C2×C22⋊C4×C83D411yescharacteristic
46C2×C42×C83D411yescharacteristic
47#95×C83—22no—
48#95×C83—21no—
49#95×C83—22no—
50C22×Dic83—42no—
51#13050574—24no—
52#13050574—42no—
53C2×C83⋊C8—42no—
54C4⋊Dic83—82no—
55C22⋊Dic83—42no—
56C22⋊Dic83—42no—
57C24×C83C22×C411yescharacteristic
58C24×C83C2×D411yescharacteristic
59C2×D4×C83—41no—
60C2×D4×C83—41no—
61C2×D4×C83C2×Q812yes—
62C2×D4×C83#4112yes—
63C22×C4×C83—21no—
64C22×C4×C83—21no—
65C22×C4×C83—21no—
66C22×C4×C83—21no—
67C22×C4×C83—22no—
68C22×C4×C83—22no—
69C22×C4×C83—42no—
70C22×C4×C83—42no—
71C22×C4×C83—42no—
72C22×C4×C83—82no—
73C22×C4×C83C22⋊C411yescharacteristic
74C22×C4×C83C22⋊C411yescharacteristic
75C22×C4×C83C22⋊C411yescharacteristic
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C2×D411yescharacteristic
78C4⋊C4×C83—41no—
79C4⋊C4×C83—42no—
80C4⋊C4×C83—42no—
81C4⋊C4×C83—41no—
82C4⋊C4×C83—41no—
83C4⋊C4×C83—82no—
84C22⋊C4×C83—41no—
85C22⋊C4×C83—41no—
86C22⋊C4×C83—42no—
87C22⋊C4×C83—82no—
88C42×C83—21no—
89C42×C83—21no—
90C23×C83—21no—
91C23×C83—21no—
92C23×C83—21no—
93C23×C83—21no—
94C23×C83—41no—
95C23×C83—41no—
96C23×C83—41no—
97C23×C83—41no—
98C23×C83C2×C22⋊C411yescharacteristic
99C23×C83C4×Q812yes—
100C23×C83#12411yescharacteristic
101C23×C83C4⋊Q811yescharacteristic
102D4×C83—42no—
103D4×C83—42no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—22no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—42no—
111C2×C4×C83—42no—
112C2×C4×C83—42no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—42no—
117C2×C4×C83—42no—
118C2×C4×C83—42no—
119C2×C4×C83—42no—
120C2×C4×C83—42no—
121C2×C4×C83—42no—
122C2×C4×C83—81no—
123C2×C4×C83—84no—
124C2×C4×C83#9911yescharacteristic
125C2×C4×C83#9911yescharacteristic
126C2×C4×C83C22⋊Q812yes—
127C2×Dic83—82no—
128C2×Dic83—82no—
129C2×Dic83—82no—
130C83⋊C8—44no—
131C22×C83—21no—
132C22×C83—21no—
133C22×C83—21no—
134C22×C83—22no—
135C22×C83—21no—
136C22×C83—42no—
137C22×C83—41no—
138C22×C83—41no—
139C22×C83—42no—
140C22×C83—41no—
141C22×C83—41no—
142C22×C83—41no—
143C22×C83—41no—
144C22×C83—81no—
145C22×C83#39111yescharacteristic
146C22×C83C2×#9911yescharacteristic
147C22×C83#41011yescharacteristic
148C4×C83—21no—
149C4×C83—22no—
150C4×C83—41no—
151C4×C83—41no—
152C4×C83—41no—
153C4×C83—82no—
154C4×C83—82no—
155C4×C83#35212yes—
156Dic83—162no—
157#13292—831nomaximal, Sylow
158C2×C83—21no—
159C2×C83—21no—
160C2×C83—41no—
161C2×C83—42no—
162C2×C83—41no—
163C2×C83#199611yescharacteristic
164C2×C83C2×#35211yescharacteristic
165C2×C83#212211yescharacteristic
166#2487D8311yescharacteristic
167#1799—831no—
168C4×#100—831no—
169#1390—834no—
170C83#1329211yescharacteristic, complemented, Sylow
171C2×C4×D4C2×D8311yescharacteristic
172C22×C4⋊C4Dic8311yescharacteristic, complemented
173C2×#100—832no—
174C2×#99—832no—
175C4×M16—1661no—
176#400—21no—
177#399—21no—
178#389—21no—
179#386C2×D8312yes—
180#385Dic8312yescomplemented
181#380—21no—
182#380—1661no—
183#380Dic8311yescharacteristic, complemented
184#343—1661no—
185#342—1661no—
186C22×D4C22×D8311yescharacteristic
187C23×C4C2×Dic8311yescharacteristic
188C23×C4C2×Dic8312yes—
189C23×C4C22⋊D8311yescharacteristic
190C2×M16—1662no—
191C4×D4—41no—
192C4×D4—41no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—3321no—
200C2×C4⋊C4C22⋊D8311yescharacteristic
201C2×C22⋊C4—22no—
202C2×C22⋊C4—1662no—
203C2×C22⋊C4C2×Dic8312yes—
204C2×C22⋊C4C2×Dic8311yescharacteristic
205C2×C22⋊C4C22⋊D8311yescharacteristic
206C2×C42C22⋊D8311yescharacteristic
207#100—834no—
208#100—1662no—
209#99—1664no—
210#97—3321no—
211C4×C8—3321no—
212#95—22no—
213#95—21no—
214#95—22no—
215#95—3321no—
216C24C22×Dic8311yescharacteristic
217C24C2×C22⋊D8311yescharacteristic
218C2×D4—41no—
219C2×D4—41no—
220C2×D4Q8×D8312yes—
221C2×D4#1305059112yes—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—82no—
232C22×C4—3322no—
233C22×C4C22⋊Dic8311yescharacteristic
234C22×C4C22⋊Dic8311yescharacteristic
235C22×C4C22⋊Dic8311yescharacteristic
236C22×C4C22⋊Dic8311yescharacteristic
237C22×C4C2×C22⋊D8311yescharacteristic
238M16—3322no—
239M16—1664no—
240C2×C8—3322no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—82no—
247C4⋊C4—6642no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—82no—
252C22⋊C4—3322no—
253C22⋊C4—3322no—
254C42—21no—
255C42—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23C2×C22⋊Dic8311yescharacteristic
265C23Q8×Dic8312yes—
266C23#1458178111yescharacteristic
267C23#1458179011yescharacteristic
268D4—42no—
269D4—42no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4—84no—
290C2×C4—6642no—
291C2×C4—6642no—
292C2×C4—6642no—
293C2×C4#1458170711yescharacteristic
294C2×C4#1458170711yescharacteristic
295C2×C4#1458176812yes—
296C8—3324no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22#1912760811yescharacteristic
312C22C2×#1458170711yescharacteristic
313C22#1912767511yescharacteristic
314C4—21no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—82no—
320C4—82no—
321C4—13282no—
322C4#1912749112yes—
323C2—21no—
324C2—21no—
325C2—41no—
326C2—42no—
327C2—41no—
328C2#2490844911yescharacteristic
329C2C2×#1912749111yescharacteristic
330C2#2490911311yescharacteristic
subgroupG/H
centerC22C2×#14581707
commutatorC24×C83C22×C4
FrattiniC22×D4C22×D83
FittingC83×#2487C2
socleC22×C83C2×#99
prime radical, cosocleC22×D4×C83C23
hypercenter#2487D83
hypocenterC83#13292
LCSG ▷ C24×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
12. C22×C4⋊C4×C83C4semidirect
17. #385×C83C4semidirect
19. #380×C83C4semidirect
170. C83#13292semidirect
172. C22×C4⋊C4Dic83semidirect
180. #385Dic83semidirect
183. #380Dic83semidirect

Maximal subgroups

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

subgroupindex
#249074512
C4×#145817092
#249055812
C83×#24872
#1329283