Finite Group Databasebeta

← #35315564

Subgroups — #35315564

Order 21248.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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#24912639C211yesmaximal, characteristic
2#24907455C211yesmaximal, characteristic
3#24905494C212yesmaximal, complemented
4#24905491C212yesmaximal, complemented
5C83×#1459C211yesmaximal, characteristic
6C2×#14581771C411yescharacteristic
7#19127725—21no—
8C2×#14581709—21no—
9#19127640C2211yescharacteristic
10#19127637C411yescharacteristic
11#19127621C2211yescharacteristic
12#19127613C411yescharacteristic
13#19127585—21no—
14#19127581—21no—
15#19127574—21no—
16#19127559—21no—
17C2×C83⋊#95C411yescharacteristic
18#19127470C2212yes—
19C2×C4×D4×C83C2211yescharacteristic
20C2×C22⋊C8×C83—21no—
21#324×C83C2212yes—
22#323×C83—21no—
23C22×Dic166C2×C411yescharacteristic
24C23×Dic83—21no—
25C2×#13050574—22no—
26#14581771—41no—
27#14581771—41no—
28C2×C4⋊Dic83C2×C411yescharacteristic
29C2×Dic83⋊C4—21no—
30C2×Dic83⋊C4—21no—
31C2×Dic83⋊C4—21no—
32C2×C22⋊Dic83—21no—
33C2×C22⋊Dic83—21no—
34C2×C22⋊Dic83—21no—
35C4⋊(C83⋊C8)—41no—
36C4⋊(C83⋊C8)—41no—
37#14581709—42no—
38C83⋊#95—21no—
39C83⋊#95—21no—
40C83⋊#95—21no—
41C83⋊#95—21no—
42C83⋊#95—21no—
43C83⋊#95C2×C411yescharacteristic
44C83⋊#95C2×C411yescharacteristic
45C22×D4×C83D411yescharacteristic
46C23×C4×C83C2×C411yescharacteristic
47C23×C4×C83D411yescharacteristic
48C22×C8×C83—41no—
49C4×D4×C83—41no—
50C4×D4×C83—41no—
51C2×C4⋊C4×C83C2311yescharacteristic
52C2×C22⋊C4×C83C2×C411yescharacteristic
53C2×C22⋊C4×C83D411yescharacteristic
54C2×C42×C83D411yescharacteristic
55C22⋊C8×C83—22no—
56C22⋊C8×C83—41no—
57C2×Dic166—41no—
58C2×Dic166—81no—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—21no—
62C22×Dic83—21no—
63C22×Dic83—42no—
64C22×Dic83—42no—
65C22×Dic83—81no—
66#13050574—42no—
67#13050574—42no—
68C2×C83⋊C8—42no—
69C4⋊Dic83—41no—
70Dic83⋊C4—42no—
71Dic83⋊C4—41no—
72Dic83⋊C4—41no—
73Dic83⋊C4—81no—
74C22⋊Dic83—42no—
75C22⋊Dic83—42no—
76C22⋊Dic83—81no—
77C24×C83C22⋊C411yescharacteristic
78C24×C83C22⋊C411yescharacteristic
79C2×D4×C83—41no—
80C2×D4×C83—41no—
81C2×D4×C83SD1612yes—
82C2×D4×C83Q1612yes—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83—81no—
88C22×C4×C83—81no—
89C22×C4×C83C22⋊C411yescharacteristic
90C22×C4×C83C22⋊C411yescharacteristic
91C22×C4×C83C22×C411yescharacteristic
92C22×C4×C83C2×D411yescharacteristic
93C22×C4×C83C2×D411yescharacteristic
94C2×C8×C83—42no—
95C2×C8×C83—82no—
96C4⋊C4×C83—41no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—41no—
99C42×C83—21no—
100C42×C83—21no—
101C23×C83—21no—
102C23×C83—21no—
103C23×C83—21no—
104C23×C83—21no—
105C23×C83—41no—
106C23×C83—41no—
107C23×C83—41no—
108C23×C83—41no—
109C23×C83#10312yes—
110C23×C83#10312yes—
111C23×C83C2×C22⋊C411yescharacteristic
112D4×C83—42no—
113D4×C83—42no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—41no—
120C2×C4×C83—42no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83—81no—
125C2×C4×C83—81no—
126C2×C4×C83—81no—
127C2×C4×C83#9911yescharacteristic
128C2×C4×C83#9911yescharacteristic
129C2×C4×C83C2×SD1611yescharacteristic
130C2×C4×C83C2×Q1611yescharacteristic
131C2×Dic83—22no—
132C2×Dic83—41no—
133C2×Dic83—41no—
134C2×Dic83—41no—
135C2×Dic83—41no—
136C2×Dic83—41no—
137C2×Dic83—41no—
138C2×Dic83—41no—
139C2×Dic83—41no—
140C2×Dic83—41no—
141C2×Dic83—41no—
142C2×Dic83—41no—
143C2×Dic83—84no—
144Dic166—82no—
145C8×C83—82no—
146C83⋊C8—82no—
147C22×C83—21no—
148C22×C83—21no—
149C22×C83—22no—
150C22×C83—22no—
151C22×C83—42no—
152C22×C83—42no—
153C22×C83—42no—
154C22×C83—41no—
155C22×C83—41no—
156C22×C83—41no—
157C22×C83—41no—
158C22×C83—81no—
159C22×C83C2×#9911yescharacteristic
160C22×C83C2×#10311yescharacteristic
161C22×C83#42111yescharacteristic
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—21no—
165C4×C83—21no—
166C4×C83—41no—
167C4×C83—41no—
168C4×C83—41no—
169Dic83—42no—
170Dic83—81no—
171Dic83—81no—
172Dic83—81no—
173#11906—831nomaximal, Sylow
174C2×C83—21no—
175C2×C83—21no—
176C2×C83—42no—
177C2×C83—42no—
178C2×C83#152011yescharacteristic
179C2×C83#212111yescharacteristic
180C2×C83#213211yescharacteristic
181#2564—831no—
182#1800—831no—
183#1459D8311yescharacteristic
184#1354—832no—
185#1353—832no—
186C83#1190611yescharacteristic, complemented, Sylow
187C2×C22⋊Q8—831no—
188C2×C4×D4C2×D8311yescharacteristic
189#423—1661no—
190C2×#100—1661no—
191C2×C22⋊C8—21no—
192#400—831no—
193#399—831no—
194#395—831no—
195#393—831no—
196#387—1661no—
197#386—1661no—
198#385—1661no—
199#380—1661no—
200C2×#95—831no—
201#343—832no—
202#324C2×D8312yes—
203#323—21no—
204C22×Q8—831no—
205C22×D4D33211yescharacteristic
206C23×C4—1661no—
207C23×C4C4×D8311yescharacteristic
208C23×C4C22⋊D8311yescharacteristic
209C2×M16—1662no—
210C22×C8—41no—
211C22⋊Q8—3321no—
212C22⋊Q8—3321no—
213C4×D4—41no—
214C4×D4—41no—
215C2×C4⋊C4—831no—
216C2×C4⋊C4—1661no—
217C2×C4⋊C4—1661no—
218C2×C4⋊C4—1661no—
219C2×C4⋊C4C22×D8311yescharacteristic
220C2×C22⋊C4—1661no—
221C2×C22⋊C4—1661no—
222C2×C22⋊C4—1661no—
223C2×C22⋊C4C4×D8311yescharacteristic
224C2×C22⋊C4C22⋊D8311yescharacteristic
225C2×C42D33211yescharacteristic
226C4⋊C8—3321no—
227C4⋊C8—3321no—
228#100—3322no—
229C22⋊C8—22no—
230C22⋊C8—41no—
231#95—831no—
232#95—831no—
233#95—1661no—
234#95—1661no—
235#95—1661no—
236#95—1661no—
237#95—1661no—
238C24(C2×D83)⋊C411yescharacteristic
239C24(C2×D83)⋊C411yescharacteristic
240C2×Q8—3321no—
241C2×Q8—6641no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4#1305057912yes—
245C2×D4Dic33212yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—3322no—
253C22×C4—3322no—
254C22×C4—6641no—
255C22×C4—1661no—
256C22×C4—1661no—
257C22×C4—1661no—
258C22×C4—1661no—
259C22×C4(C2×D83)⋊C411yescharacteristic
260C22×C4(C2×D83)⋊C411yescharacteristic
261C22×C4C2×C4×D8311yescharacteristic
262C22×C4C2×C22⋊D8311yescharacteristic
263C22×C4C2×D33211yescharacteristic
264M16—3322no—
265M16—3322no—
266C2×C8—42no—
267C2×C8—82no—
268C2×C8—3322no—
269C4⋊C4—41no—
270C4⋊C4—3321no—
271C4⋊C4—3322no—
272C4⋊C4—3321no—
273C4⋊C4—3321no—
274C4⋊C4—6641no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—3322no—
278C22⋊C4—3322no—
279C22⋊C4—6641no—
280C42—21no—
281C42—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23#1458171712yes—
291C23#1458171712yes—
292C23C2×(C2×D83)⋊C411yescharacteristic
293Q8—6642no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—3321no—
310C2×C4—3321no—
311C2×C4—3321no—
312C2×C4—3321no—
313C2×C4—3321no—
314C2×C4—3321no—
315C2×C4—3321no—
316C2×C4—3321no—
317C2×C4—3321no—
318C2×C4—3321no—
319C2×C4—3321no—
320C2×C4—6644no—
321C2×C4—1662no—
322C2×C4#1458170611yescharacteristic
323C2×C4#1458170611yescharacteristic
324C2×C4C2×#1305057911yescharacteristic
325C2×C4C2×Dic33211yescharacteristic
326C8—82no—
327C8—6642no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22C2×#1458170611yescharacteristic
341C22C2×#1458171711yescharacteristic
342C22#1912771711yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—3322no—
351C4—6641no—
352C4—6641no—
353C4—6641no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—42no—
358C2#2490603611yescharacteristic
359C2#2490910711yescharacteristic
360C2#2490914611yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#1459C2
socleC22×C83C2×#99
prime radicalC22×D4×C83D4
cosocleC2×C4⋊C4×C83C23
hypercenter#1459D83
hypocenterC83#11906
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #24905494C2semidirect
4. #24905491C2semidirect
186. C83#11906semidirect

Maximal subgroups

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

subgroupindex
#249126392
#249074552
#249054942
#249054912
C83×#14592
#1190683