Finite Group Databasebeta

← #14664288

Subgroups — #14664288

Order 2816.

470 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 71 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#13074298C211yesmaximal, characteristic
2#13068353C211yesmaximal, characteristic, complemented
3#13066949C211yesmaximal, characteristic, complemented
4#13066646C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C2×#67000C411yescharacteristic
9C2×M16×D11—21no—
10C2×#66945C2211yescharacteristic
11C11×#395C2211yescharacteristic
12#10622844C411yescharacteristic
13#10622604C2211yescharacteristic
14#10622603—21no—
15#10622601—21no—
16#10622332—21no—
17#10622284C411yescharacteristic
18#10622283—21no—
19#10622278—21no—
20#10622261C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×D44—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2311yescharacteristic
34#67000—41no—
35#67000—41no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4C2×C411yescharacteristic
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4×Dic11—21no—
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49M16×D11—24no—
50M16×D11—42no—
51C2×#4313—41no—
52C2×C8×D11—41no—
53#66945—41no—
54#66945—41no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66879—41no—
63Dic11⋊C8—41no—
64#11765—111nomaximal, Sylow
65C23×D11—21no—
66C23×D11C22⋊C411yescharacteristic
67C2×Q8×C11—41no—
68C2×Q8×C11—81no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C2×D44—42no—
79C2×D44—41no—
80C2×D44—42no—
81C2×D44—81no—
82C2×D44—81no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—22no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C11×M16—22no—
89C11×M16—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—81no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—81no—
103(C2×D11)⋊C4—81no—
104C4⋊Dic11—41no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—42no—
110#4318—22no—
111#4318—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#4313—44no—
115C8×D11—44no—
116#2610—111no—
117#1742—111no—
118#1464—111no—
119#1354—111no—
120#1354D1111yescharacteristic, complemented
121#1345—111no—
122#1345—111no—
123C23×C11C2×C22⋊C411yescharacteristic
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11#10412yes—
136Q8×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11#9911yescharacteristic
161C2×Dic11#9911yescharacteristic
162D44—84no—
163D44—82no—
164C4×D11—22no—
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—22no—
168C8×C11—42no—
169C8×C11—81no—
170C11⋊C8—42no—
171C11⋊C8—81no—
172C22×M16—221no—
173C2×#124—111no—
174C2×#117—111no—
175#432—221no—
176#395C2×D1111yescharacteristic
177#394—111no—
178#393—111no—
179#392—111no—
180#390—221no—
181#388—221no—
182#388—221no—
183#386—221no—
184#376—111no—
185#343—111no—
186#343—221no—
187#343C2×D1111yescharacteristic
188#324—111no—
189#324C2×D1111yescharacteristic
190#323—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11C2×#9911yescharacteristic
194C22×C11#41711yescharacteristic
195C22×C11C2×#10411yescharacteristic
196C2×D11—22no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—42no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—42no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—81no—
214Dic11—21no—
215Dic11—21no—
216Dic11—41no—
217Dic11—41no—
218Dic11—81no—
219C22×Q8C4×D1111yescharacteristic
220C22×D4—111no—
221C22×D4—221no—
222C23×C4—111no—
223C2×M16—21no—
224C2×M16—224no—
225C2×M16—221no—
226C2×M16—441no—
227C2×M16—442no—
228C22×C8—441no—
229#124—441no—
230#124—441no—
231#117—441no—
232#117—441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4C22×D1111yescharacteristic
236C2×C22⋊C4—111no—
237C2×C22⋊C4—111no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C42—111no—
245C2×C42—111no—
246C2×C42—221no—
247C4⋊C8—441no—
248C22⋊C8—21no—
249C22⋊C8—221no—
250#97—441no—
251#95—21no—
252#95—111no—
253#95—221no—
254#95—221no—
255#95C4×D1111yescharacteristic
256C2×C11—21no—
257C2×C11—21no—
258C2×C11#150411yescharacteristic
259C2×C11#212211yescharacteristic
260C2×C11#213211yescharacteristic
261D11—42no—
262D11—161no—
263C24—111no—
264C24—221no—
265C2×Q8—41no—
266C2×Q8—81no—
267C2×D4—441no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—881no—
271C2×D4—881no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—222no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4C2×C4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286M16—22no—
287M16—41no—
288M16—222no—
289M16—444no—
290M16—441no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—444no—
294C2×C8—441no—
295C2×C8—441no—
296C4⋊C4—41no—
297C4⋊C4—81no—
298C4⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—442no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—881no—
308C22⋊C4—881no—
309C42—221no—
310C42—221no—
311C42—221no—
312C42—221no—
313C42—442no—
314C11#1176511yescharacteristic, complemented, Sylow
315C23—112no—
316C23—221no—
317C23—221no—
318C23—441no—
319C23—441no—
320C23—441no—
321C23—441no—
322C23—441no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23C22⋊C4×D1111yescharacteristic
328Q8—82no—
329D4—884no—
330D4—882no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—222no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4#6696711yescharacteristic
359C2×C4#6697111yescharacteristic
360C8—42no—
361C8—81no—
362C8—442no—
363C8—881no—
364C22—21no—
365C22—21no—
366C22—222no—
367C22—442no—
368C22—441no—
369C22—441no—
370C22—881no—
371C22—881no—
372C22—881no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22—881no—
378C22D11×#9911yescharacteristic
379C22#1062241611yescharacteristic
380C22D11×#10411yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—221no—
388C4—221no—
389C4—441no—
390C4—441no—
391C4—881no—
392C2—21no—
393C2—21no—
394C2—442no—
395C2—1761no—
396C2#1306711911yescharacteristic
397C2#1307026411yescharacteristic
398C2#1307030011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radical#10622284C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11765
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
2. #13068353C2semidirect
3. #13066949C2semidirect
4. #13066646C2semidirect
5. #13066620C2semidirect
6. #13066618C2semidirect
7. C11×#1354C2semidirect
120. #1354D11semidirect
314. C11#11765semidirect

Maximal subgroups

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

subgroupindex
#130742982
#130683532
#130669492
#130666462
#130666202
#130666182
C11×#13542
#1176511