Finite Group Databasebeta

← #14664155

Subgroups — #14664155

Order 2816.

470 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074500C211yesmaximal, characteristic
2#13066934C211yesmaximal, characteristic, complemented
3#13066642C212yesmaximal, complemented
4#13066618C212yesmaximal, complemented
5C4×C11×#100C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C2×C11×#100—21no—
9C4×C11×M16—21no—
10#10622836—21no—
11#10622826—21no—
12#10622824C411yescharacteristic
13C2×C22⋊(C11⋊C8)—21no—
14#10622604C2211yescharacteristic
15#10622599C2211yescharacteristic
16#10622573C411yescharacteristic
17#10622572—21no—
18#10622562C411yescharacteristic
19#10622553—21no—
20C11×#343C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×D44C2×C411yescharacteristic
29C2×C11×M16—22no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38#66983—41no—
39#66983—41no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×Dic11⋊C4—21no—
46C22×C11⋊C8—41no—
47C11×#100—24no—
48C11×#97—41no—
49C4×C8×C11—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—41no—
57#11737—111nomaximal, Sylow
58C24×C11C22⋊C411yescharacteristic
59C24×C11C22⋊C411yescharacteristic
60C23×D11—21no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—81no—
69C22×C4×C11—81no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—81no—
78C2×C22⋊D11—81no—
79C2×C22⋊D11—81no—
80C2×C22⋊D11—81no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C2×D44—41no—
85C2×D44—81no—
86C11×M16—24no—
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—81no—
95C22⋊Dic11—81no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—81no—
100(C2×D11)⋊C4—81no—
101C4⋊Dic11—41no—
102Dic11⋊C4—81no—
103C2×C11⋊C8—42no—
104C2×C11⋊C8—82no—
105#2635—111no—
106C4×#100D1111yescharacteristic, complemented
107#1459—111no—
108#1353—112no—
109#1345—112no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11#10412yes—
120C23×C11C2×C22⋊C411yescharacteristic
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128D4×C11—44no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11#9911yescharacteristic
144C2×C4×C11#13512yes—
145C22⋊D11—84no—
146C22⋊D11—84no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156D44—82no—
157C8×C11—44no—
158C11⋊C8—82no—
159C2×#121—111no—
160C2×C4×D4C2×D1111yescharacteristic
161C2×#100—21no—
162C2×C22⋊C8—221no—
163C4×M16—21no—
164#400—111no—
165#399—111no—
166#394—111no—
167#394—221no—
168#392—111no—
169#392—221no—
170#388—221no—
171#386—221no—
172#381—111no—
173#343C2×D1112yes—
174#324—112no—
175#323—221no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—22no—
179C22×C11—42no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11C2×#9911yescharacteristic
189C22×C11#41611yescharacteristic
190C22×C11C2×#10411yescharacteristic
191C2×D11—81no—
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—22no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204Dic11—81no—
205Dic11—81no—
206Dic11—81no—
207C22×D4—111no—
208C22×D4—221no—
209C22×D4—221no—
210C22×D4C22⋊D1111yescharacteristic
211C23×C4C4×D1111yescharacteristic
212C23×C4D4411yescharacteristic
213C2×M16—22no—
214C22×C8—441no—
215#121—441no—
216#121—441no—
217C4×D4—41no—
218C4×D4—41no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4C22×D1111yescharacteristic
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C22⋊C4—221no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4C4×D1111yescharacteristic
229C2×C22⋊C4D4411yescharacteristic
230C2×C42C22⋊D1111yescharacteristic
231#100—24no—
232C22⋊C8—222no—
233C22⋊C8—441no—
234#97—41no—
235C4×C8—41no—
236#95—111no—
237#95—111no—
238#95—221no—
239#95—221no—
240#95—221no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11—42no—
244C2×C11—81no—
245C2×C11#150111yescharacteristic
246C2×C11#212111yescharacteristic
247C2×C11#213411yescharacteristic
248D11—161no—
249C24—221no—
250C24(C2×D11)⋊C411yescharacteristic
251C24(C2×D11)⋊C411yescharacteristic
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—441no—
256C2×D4—442no—
257C2×D4—442no—
258C2×D4—881no—
259C2×D4—881no—
260C2×D4—881no—
261C2×D4—881no—
262C2×D4—881no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4(C2×D11)⋊C411yescharacteristic
273C22×C4(C2×D11)⋊C411yescharacteristic
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4C2×D4411yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277M16—24no—
278M16—42no—
279C2×C8—42no—
280C2×C8—442no—
281C2×C8—882no—
282C4⋊C4—41no—
283C4⋊C4—441no—
284C4⋊C4—881no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—442no—
290C22⋊C4—881no—
291C22⋊C4—881no—
292C22⋊C4—881no—
293C22⋊C4—881no—
294C42—21no—
295C42—21no—
296C11#1173711yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23#6686912yes—
314C23C2×(C2×D11)⋊C411yescharacteristic
315D4—44no—
316D4—882no—
317D4—884no—
318D4—884no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4#6687011yescharacteristic
342C2×C4#6687011yescharacteristic
343C2×C4#6700312yes—
344C8—44no—
345C8—882no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22C2×#6686911yescharacteristic
366C22C2×#6687011yescharacteristic
367C22#1062261511yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—881no—
375C4—881no—
376C4—881no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—81no—
381C2—1761no—
382C2#1306710511yescharacteristic
383C2#1307026311yescharacteristic
384C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC4×C11×#100C2
socleC22×C11C2×#99
prime radical#13074500C2
cosocleC2×C11×C4⋊C4C23
hypercenterC4×#100D11
hypocenterC11#11737
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. #13066934C2semidirect
3. #13066642C2semidirect
4. #13066618C2semidirect
5. C4×C11×#100C2semidirect
106. C4×#100D11semidirect
296. C11#11737semidirect

Maximal subgroups

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

subgroupindex
#130745002
#130669342
#130666422
#130666182
C4×C11×#1002
#1173711