Finite Group Databasebeta

← #35299479

Subgroups — #35299479

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#24916548C211yesmaximal, characteristic
2C4×#14581711C211yesmaximal, characteristic
3#24905910C212yesmaximal
4#24905356C212yesmaximal
5C83×#2399C211yesmaximal, characteristic
6#19127832—24no—
7#19127758—21no—
8#19127758C2212yes—
9#19127754—21no—
10C2×#14581711—21no—
11C4×#13050574C2212yes—
12#19127470—21no—
13Q8⋊(C83⋊C8)—24no—
14C2×C4×Q8×C83C2211yescharacteristic
15C2×C4×Q8×C83C2211yescharacteristic
16#398×C83—21no—
17#398×C83C411yescharacteristic
18#398×C83C411yescharacteristic
19#395×C83—21no—
20#395×C83C411yescharacteristic
21#395×C83C411yescharacteristic
22C4×C4⋊C4×C83—21no—
23C4×C4⋊C4×C83—21no—
24#376×C83C2211yescharacteristic
25C2×#13050574—22no—
26C4⋊(C83⋊C8)—22no—
27C4⋊(C83⋊C8)—22no—
28C4⋊(C83⋊C8)D414yes—
29#14581711—24no—
30C22⋊(C83⋊C8)—22no—
31#14581703—22no—
32#14581703—22no—
33#14581703—22no—
34C4×C83⋊C8—22no—
35C4×C83⋊C8—22no—
36C22×Q8×C83C2×C411yescharacteristic
37C22×Q8×C83D411yescharacteristic
38C4×Q8×C83—22no—
39C4×Q8×C83—22no—
40C4×Q8×C83—22no—
41C4×Q8×C83—22no—
42C2×C4⋊C4×C83—21no—
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83C2×C411yescharacteristic
48C2×C4⋊C4×C83C2×C411yescharacteristic
49C2×C4⋊C4×C83C2×C411yescharacteristic
50C2×C4⋊C4×C83D411yescharacteristic
51C2×C42×C83—21no—
52C2×C42×C83—21no—
53C2×C42×C83D411yescharacteristic
54C2×C42×C83D411yescharacteristic
55C2×C42×C83C2311yescharacteristic
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61#95×C83C2×C411yescharacteristic
62#95×C83C2×C411yescharacteristic
63#13050574—24no—
64#13050574—42no—
65C2×C83⋊C8—24no—
66C2×C83⋊C8—42no—
67C2×Q8×C83—22no—
68C2×Q8×C83—22no—
69C2×Q8×C83—22no—
70C2×Q8×C83—41no—
71C2×Q8×C83—42no—
72C22×C4×C83—21no—
73C22×C4×C83—21no—
74C22×C4×C83—21no—
75C22×C4×C83—21no—
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C22⋊C411yescharacteristic
78C22×C4×C83C22⋊C411yescharacteristic
79C22×C4×C83C22⋊C411yescharacteristic
80C22×C4×C83C22×C411yescharacteristic
81C22×C4×C83C2×D411yescharacteristic
82C22×C4×C83C2×D411yescharacteristic
83C4⋊C4×C83—22no—
84C4⋊C4×C83—22no—
85C4⋊C4×C83—22no—
86C4⋊C4×C83—22no—
87C4⋊C4×C83—42no—
88C4⋊C4×C83—42no—
89C4⋊C4×C83—42no—
90C4⋊C4×C83—42no—
91C4⋊C4×C83—42no—
92C42×C83—24no—
93C42×C83—21no—
94C42×C83—21no—
95C42×C83—21no—
96C42×C83—21no—
97C42×C83—41no—
98C42×C83—41no—
99C42×C83C2×D412yes—
100C42×C83#4112yes—
101C23×C83C2×C22⋊C411yescharacteristic
102Q8×C83—24no—
103Q8×C83—44no—
104Q8×C83—42no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—22no—
110C2×C4×C83—22no—
111C2×C4×C83—22no—
112C2×C4×C83—22no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—41no—
119C2×C4×C83—41no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83—41no—
125C2×C4×C83—41no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83#10412yes—
131C2×C4×C83C4×D412yes—
132C2×C4×C83#12011yescharacteristic
133C2×C4×C83#12112yes—
134C2×C4×C83#12311yescharacteristic
135C83⋊C8—44no—
136C83⋊C8—44no—
137C22×C83—21no—
138C22×C83—21no—
139C22×C83#38611yescharacteristic
140C22×C83C2×#10411yescharacteristic
141C22×C83#42111yescharacteristic
142C4×C83—22no—
143C4×C83—22no—
144C4×C83—21no—
145C4×C83—22no—
146C4×C83—42no—
147C4×C83—42no—
148C4×C83—41no—
149C4×C83—41no—
150C4×C83—41no—
151C4×C83—42no—
152C4×C83—81no—
153C4×C83#45612yes—
154#9030—831nomaximal, Sylow
155C2×C83—21no—
156C2×C83—21no—
157C2×C83#187111yescharacteristic
158C2×C83#188611yescharacteristic
159C2×C83#189111yescharacteristic
160#2983—831no—
161#2399D8311yescharacteristic
162C4×#101—831no—
163#1491—832no—
164#1300—832no—
165C83#903011yescharacteristic, complemented, Sylow
166C2×C4×Q8C2×D8311yescharacteristic
167C2×C4×Q8C2×D8311yescharacteristic
168#446—1664no—
169#432—832no—
170#432—1661no—
171#431—1661no—
172C2×#101—1661no—
173C4×M16—832no—
174#398—21no—
175#398Dic8311yescharacteristic
176#398Dic8311yescharacteristic
177#395—21no—
178#395Dic8311yescharacteristic
179#395Dic8311yescharacteristic
180C4×C4⋊C4—21no—
181C4×C4⋊C4—21no—
182#376C2×D8311yescharacteristic
183#343—1661no—
184Q8⋊C8—1664no—
185C22×Q8C2×Dic8311yescharacteristic
186C22×Q8C22⋊D8311yescharacteristic
187C2×M16—1662no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×Q8—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×Dic8311yescharacteristic
198C2×C4⋊C4C2×Dic8311yescharacteristic
199C2×C4⋊C4C2×Dic8311yescharacteristic
200C2×C4⋊C4C22⋊D8311yescharacteristic
201C2×C42—21no—
202C2×C42—21no—
203C2×C42C22⋊D8311yescharacteristic
204C2×C42C22⋊D8311yescharacteristic
205C2×C42C22×D8311yescharacteristic
206C4⋊C8—834no—
207C4⋊C8—1662no—
208C4⋊C8—1662no—
209#101—1664no—
210C22⋊C8—1662no—
211#97—1662no—
212#97—1662no—
213#97—1662no—
214C4×C8—1662no—
215C4×C8—1662no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95C2×Dic8311yescharacteristic
222#95C2×Dic8311yescharacteristic
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—42no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4C22⋊Dic8311yescharacteristic
233C22×C4C22⋊Dic8311yescharacteristic
234C22×C4C22⋊Dic8311yescharacteristic
235C22×C4C22⋊Dic8311yescharacteristic
236C22×C4C22×Dic8311yescharacteristic
237C22×C4C2×C22⋊D8311yescharacteristic
238C22×C4C2×C22⋊D8311yescharacteristic
239M16—3322no—
240M16—1664no—
241C2×C8—3322no—
242C2×C8—1664no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C42—24no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—41no—
258C42—41no—
259C42D4×D8312yes—
260C42#1305058912yes—
261C23C2×C22⋊Dic8311yescharacteristic
262Q8—24no—
263Q8—44no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4#1458171912yes—
291C2×C4D4×Dic8312yes—
292C2×C4#1458176011yescharacteristic
293C2×C4#1458176412yes—
294C2×C4#1458177311yescharacteristic
295C8—3324no—
296C8—3324no—
297C22—21no—
298C22—21no—
299C22#1912758111yescharacteristic
300C22C2×#1458171911yescharacteristic
301C22#1912771811yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4#1912788312yes—
314C2—21no—
315C2—21no—
316C2#2490776611yescharacteristic
317C2#2490785711yescharacteristic
318C2#2490788211yescharacteristic
subgroupG/H
centerC2×C4#14581760
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2399C2
socleC22×C83#386
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenter#2399D83
hypocenterC83#9030
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
165. C83#9030semidirect

Maximal subgroups

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

subgroupindex
#249165482
C4×#145817112
#249059102
#249053562
C83×#23992
#903083