Finite Group Databasebeta

← #14664272

Subgroups — #14664272

Order 2816.

622 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 87 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#13071951C211yesmaximal, characteristic
2#13066946C211yesmaximal, characteristic, complemented
3#13066645C212yesmaximal, complemented
4#13066618C212yesmaximal, complemented
5C2×C11×#343C211yesmaximal, characteristic, complemented
6C22×#4339C411yescharacteristic
7C22×C11×M16—21no—
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66982—21no—
10#10622826—21no—
11#10622824C411yescharacteristic
12#10622820—21no—
13#10622604C411yescharacteristic
14#10622604C2211yescharacteristic
15#10622602—21no—
16#10622602—21no—
17#10622592C411yescharacteristic
18#10622592C2211yescharacteristic
19C11×#343—21no—
20C11×#343C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C2×#4339—41no—
28C2×#4339—41no—
29C2×#4339—44no—
30C22×D44C2×C411yescharacteristic
31C22×C4×D11—21no—
32C22×Dic22C2×C411yescharacteristic
33C2×C11×M16—24no—
34C2×C11×M16—22no—
35C2×C11×M16—41no—
36C2×C11×M16—42no—
37C22×C8×C11—41no—
38C2×C11×C4⋊C4—41no—
39C2×C11×C4⋊C4—41no—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C22⋊Dic11—21no—
45#66982—44no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×#4318—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—41no—
60#11762—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C23×D11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×C22⋊D11—24no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87#4339—44no—
88#4339—44no—
89#4339—44no—
90#4339—44no—
91C2×D44—41no—
92C2×D44—42no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C4×D11—42no—
96C2×Dic22—41no—
97C2×Dic22—42no—
98C11×M16—24no—
99C11×M16—44no—
100C11×M16—42no—
101C2×C8×C11—44no—
102C2×C8×C11—42no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C22⋊Dic11—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113Dic11⋊C4—42no—
114Dic11⋊C4—42no—
115#4318—82no—
116C2×C11⋊C8—42no—
117#2406—111no—
118C2×#343D1111yescharacteristic, complemented
119#1463—111no—
120#1354—112no—
121#1345—112no—
122C23×C11—22no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—41no—
126C23×C11#9911yescharacteristic
127C23×C11#9911yescharacteristic
128C23×C11C2×C22⋊C411yescharacteristic
129C22×D11—22no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11#10412yes—
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C22⋊D11—44no—
160C22⋊D11—44no—
161C2×Dic11—22no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170D44—42no—
171D44—42no—
172C4×D11—48no—
173Dic22—42no—
174Dic22—42no—
175C8×C11—44no—
176C11⋊C8—82no—
177C22×#41—111no—
178C22×M16—21no—
179C2×#123—221no—
180C22×C4⋊C4C2×D1111yescharacteristic
181#407—221no—
182#395—111no—
183#395—111no—
184#394—111no—
185#394—111no—
186#386—221no—
187#385—221no—
188#385—221no—
189#381—111no—
190#343—21no—
191#343C2×D1112yes—
192#324—112no—
193#324—221no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11AΣL(1,𝔽16)12yes—
204C22×C11C2×#9911yescharacteristic
205C22×C11#41711yescharacteristic
206C22×C11C2×#10411yescharacteristic
207C2×D11—42no—
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C4×C11—22no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—41no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—41no—
221Dic11—42no—
222Dic11—81no—
223Dic11—81no—
224C2×#41—441no—
225C2×#41—441no—
226C2×#41—444no—
227C22×Q8—111no—
228C22×D4—111no—
229C22×D4—221no—
230C23×C4—221no—
231C23×C4C4×D1111yescharacteristic
232C23×C4D4411yescharacteristic
233C23×C4C22⋊D1111yescharacteristic
234C2×M16—24no—
235C2×M16—22no—
236C2×M16—41no—
237C2×M16—42no—
238C2×M16—441no—
239C22×C8—41no—
240#123—444no—
241C2×C4⋊C4—41no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4C4×D1111yescharacteristic
246C2×C4⋊C4D4411yescharacteristic
247C2×C4⋊C4C22⋊D1111yescharacteristic
248C2×C4⋊C4C22×D1111yescharacteristic
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C22⋊C8—222no—
255C22⋊C8—441no—
256#95—111no—
257#95—111no—
258#95—221no—
259#95—221no—
260#95—221no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—22no—
264C2×C11—41no—
265C2×C11#150411yescharacteristic
266C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
267C2×C11#213311yescharacteristic
268D11—82no—
269C24—221no—
270C24(C2×D11)⋊C411yescharacteristic
271#41—444no—
272#41—444no—
273#41—444no—
274#41—444no—
275C2×Q8—441no—
276C2×Q8—442no—
277C2×D4—224no—
278C2×D4—441no—
279C2×D4—442no—
280C2×D4—442no—
281C2×D4—441no—
282C2×D4—441no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—442no—
298C22×C4—442no—
299C22×C4—442no—
300C22×C4(C2×D11)⋊C411yescharacteristic
301C22×C4(C2×D11)⋊C411yescharacteristic
302C22×C4(C2×D11)⋊C411yescharacteristic
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4C2×D4411yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306M16—24no—
307M16—44no—
308M16—42no—
309M16—882no—
310C2×C8—44no—
311C2×C8—42no—
312C2×C8—442no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—442no—
322C22⋊C4—442no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C11#1176211yescharacteristic, complemented, Sylow
326C23—21no—
327C23—21no—
328C23—22no—
329C23—41no—
330C23—222no—
331C23—441no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23#6687011yescharacteristic
338C23#6687011yescharacteristic
339C23C2×(C2×D11)⋊C411yescharacteristic
340Q8—442no—
341Q8—442no—
342D4—442no—
343D4—442no—
344D4—444no—
345D4—444no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—222no—
367C2×C4—448no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4#6686912yes—
377C2×C4#6698511yescharacteristic
378C2×C4#6699511yescharacteristic
379C8—44no—
380C8—882no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—42no—
389C22—42no—
390C22—442no—
391C22—442no—
392C22—442no—
393C22—881no—
394C22—881no—
395C22—881no—
396C22—881no—
397C22#1062211312yes—
398C22C2×#6686911yescharacteristic
399C22C2×#6687011yescharacteristic
400C22#1062257911yescharacteristic
401C4—21no—
402C4—22no—
403C4—21no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—442no—
409C4—881no—
410C4—881no—
411C2—21no—
412C2—21no—
413C2—22no—
414C2—41no—
415C2—882no—
416C2#1306711811yescharacteristic
417C2C2×#1062211311yescharacteristic
418C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC2×C11×#343C2
socleC22×C11C2×#99
prime radicalC22×#4339C4
cosocleC2×C11×C4⋊C4C23
hypercenterC2×#343D11
hypocenterC11#11762
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. #13066946C2semidirect
3. #13066645C2semidirect
4. #13066618C2semidirect
5. C2×C11×#343C2semidirect
118. C2×#343D11semidirect
325. C11#11762semidirect

Maximal subgroups

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

subgroupindex
#130719512
#130669462
#130666452
#130666182
C2×C11×#3432
#1176211