Finite Group Databasebeta

← #14672437

Subgroups — #14672437

Order 2816.

488 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 99 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#13073959C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic
3#13066735C212yesmaximal
4#13066735C212yesmaximal
5C11×#1800C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C22×Dic11⋊C4C411yescharacteristic, complemented
8C11×#423—21no—
9C2×C11×#100C2212yes—
10#10622833C2211yescharacteristic
11#10622833C2211yescharacteristic
12C2×#66898C2212yes—
13#10622825C411yescharacteristic, complemented
14#10622823—21no—
15C4×C22⋊Dic11—21no—
16#10622597—21no—
17#10622561—21no—
18#10622559C411yescharacteristic, complemented
19#10622559C411yescharacteristic, complemented
20#10622546—21no—
21C11×#343—21no—
22#10622164—21no—
23C22×D4×C11C2311yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11C2×C411yescharacteristic
27C23×Dic11C2×C411yescharacteristic
28C2×C11×M16—22no—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11C2×C411yescharacteristic
39C2×C22⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—41no—
46C2×Dic11⋊C4—41no—
47C2×C4×Dic11—41no—
48C11×C4⋊C8—41no—
49C11×C4⋊C8—41no—
50C11×#100—24no—
51#66898—22no—
52#66898Q814yes—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—41no—
59#13297—111nomaximal, Sylow
60C24×C11C22×C411yescharacteristic
61C24×C11C2×D411yescharacteristic
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11C2×Q812yes—
65C2×D4×C11#4112yes—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—81no—
71C22×C4×C11—81no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82C22×Dic11—42no—
83C22×Dic11—41no—
84C22×Dic11—42no—
85C22×Dic11—81no—
86C11×M16—42no—
87C11×M16—42no—
88C2×C8×C11—42no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11—21no—
93C42×C11—21no—
94C22⋊Dic11—24no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97C22⋊Dic11—42no—
98C22⋊Dic11—42no—
99C22⋊Dic11—81no—
100C4⋊Dic11—81no—
101Dic11⋊C4—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—81no—
106C4×Dic11—82no—
107#2579—111no—
108#1800D1111yescharacteristic
109C4×#99—111no—
110#1390—112no—
111#1390—112no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11C2×C22⋊C411yescharacteristic
121C23×C11C4×Q812yes—
122C23×C11C22⋊Q812yes—
123D4×C11—42no—
124D4×C11—42no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11#9911yescharacteristic
139C2×C4×C11#9911yescharacteristic
140C2×C4×C11#12411yescharacteristic
141C2×C4×C11C4⋊Q811yescharacteristic
142C2×Dic11—22no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—44no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—82no—
158C2×Dic11—82no—
159C2×Dic11—82no—
160C8×C11—82no—
161C2×C4×D4C2×D1111yescharacteristic
162C22×C4⋊C4—111no—
163#423—21no—
164C2×#100C2×D1112yes—
165C2×#99—112no—
166#398—221no—
167#396—221no—
168#387—221no—
169#386—111no—
170#386—111no—
171#385—111no—
172#385—111no—
173#385—221no—
174#380—111no—
175C4×C22⋊C4—221no—
176#343—21no—
177#342—221no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—81no—
190C22×C11#39111yescharacteristic
191C22×C11C2×#9911yescharacteristic
192C22×C11#41011yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200Dic11—42no—
201Dic11—81no—
202Dic11—81no—
203Dic11—84no—
204Dic11—81no—
205C22×D4C22×D1111yescharacteristic
206C23×C4—111no—
207C23×C4—111no—
208C23×C4C4×D1111yescharacteristic
209C23×C4D4411yescharacteristic
210C2×M16—22no—
211C4×D4—41no—
212C4×D4—41no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—441no—
219C2×C4⋊C4—441no—
220C2×C4⋊C4C22⋊D1111yescharacteristic
221C2×C22⋊C4—111no—
222C2×C22⋊C4—111no—
223C2×C22⋊C4—222no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4C4×D1111yescharacteristic
227C2×C22⋊C4D4411yescharacteristic
228C2×C42—441no—
229C2×C42C22⋊D1111yescharacteristic
230C4⋊C8—41no—
231C4⋊C8—41no—
232#100—24no—
233#99—114no—
234#99—222no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—441no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—42no—
244C2×C11—42no—
245C2×C11#199611yescharacteristic
246C2×C11#212011yescharacteristic
247C2×C11#212111yescharacteristic
248C24C2×C4×D1111yescharacteristic
249C24C2×D4411yescharacteristic
250C2×D4—41no—
251C2×D4—41no—
252C2×D4#434112yes—
253C2×D4Q8×D1112yes—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—442no—
265C22×C4—441no—
266C22×C4—442no—
267C22×C4—441no—
268C22×C4—881no—
269C22×C4(C2×D11)⋊C411yescharacteristic
270C22×C4(C2×D11)⋊C411yescharacteristic
271C22×C4(C2×D11)⋊C411yescharacteristic
272C22×C4(C2×D11)⋊C411yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274M16—42no—
275M16—42no—
276C2×C8—42no—
277C4⋊C4—41no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—881no—
283C4⋊C4—881no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—224no—
287C22⋊C4—442no—
288C22⋊C4—442no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C22⋊C4—881no—
292C42—21no—
293C42—21no—
294C42—882no—
295C11#1329711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23#6694012yes—
305C23#6695012yes—
306C23C2×(C2×D11)⋊C411yescharacteristic
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—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—222no—
323C2×C4—441no—
324C2×C4—442no—
325C2×C4—441no—
326C2×C4—442no—
327C2×C4—444no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—882no—
338C2×C4—882no—
339C2×C4—882no—
340C2×C4#6687011yescharacteristic
341C2×C4#6687011yescharacteristic
342C2×C4#6698911yescharacteristic
343C2×C4#6699711yescharacteristic
344C8—82no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—81no—
357C22C2×#6687011yescharacteristic
358C22#1062258711yescharacteristic
359C22#1062261911yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—442no—
368C4—881no—
369C4—881no—
370C4—884no—
371C4—881no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—42no—
376C2#1306960011yescharacteristic
377C2#1307025811yescharacteristic
378C2#1307026311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1800C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#1800D11
hypocenterC11#13297
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
7. C22×Dic11⋊C4C4semidirect
13. #10622825C4semidirect
18. #10622559C4semidirect
19. #10622559C4semidirect
295. C11#13297semidirect

Maximal subgroups

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

subgroupindex
#130739592
C4×#668982
#130667352
C11×#18002
#1329711