Finite Group Databasebeta

← #14664266

Subgroups — #14664266

Order 2816.

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

normal subgroups only

This group has 484 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#13074177C211yesmaximal, characteristic
2#13068353C211yesmaximal, characteristic, complemented
3#13066949C211yesmaximal, characteristic, complemented
4#13066644C211yesmaximal, characteristic, complemented
5#13066642C211yesmaximal, characteristic, complemented
6#13066619C211yesmaximal, characteristic, complemented
7C11×#1345C211yesmaximal, characteristic, complemented
8C2×D4×Dic11C411yescharacteristic
9C2×M16×D11—21no—
10C2×#66945C2211yescharacteristic
11C11×#394C2211yescharacteristic
12#10622836C411yescharacteristic
13#10622599C2211yescharacteristic
14#10622571—21no—
15#10622569—21no—
16#10622564—21no—
17#10622563—21no—
18#10622332—21no—
19#10622290C411yescharacteristic
20#10622264C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11—21no—
30C22×C4×D11D411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37D4×Dic11—41no—
38D4×Dic11—41no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4C2×C411yescharacteristic
41C2×(C2×D11)⋊C4D411yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×#4318—21no—
48M16×D11—24no—
49M16×D11—42no—
50C2×#4313—41no—
51C2×C8×D11—41no—
52#66945—41no—
53#66945—41no—
54C11×C22⋊C8—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66879—41no—
63Dic11⋊C8—41no—
64#11761—111nomaximal, Sylow
65C24×C11—21no—
66C23×D11C22⋊C411yescharacteristic
67C2×D4×C11—41no—
68C2×D4×C11—42no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—42no—
75C2×C22⋊D11—81no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—42no—
79C22×Dic11—81no—
80C22×Dic11—81no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—22no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C11×M16—22no—
90C11×M16—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99C22⋊Dic11—81no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—81no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—81no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110#4318—22no—
111#4318—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#4313—44no—
115C8×D11—44no—
116#2598—111no—
117#1742—111no—
118#1464—111no—
119#1353—111no—
120#1353—111no—
121#1345—111no—
122#1345D1111yescharacteristic, complemented
123C23×C11—22no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11C2×C22⋊C411yescharacteristic
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11#10412yes—
136D4×C11—42no—
137D4×C11—42no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
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×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C22⋊D11—84no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—84no—
163C2×Dic11#9911yescharacteristic
164C2×Dic11#9911yescharacteristic
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—22no—
168C4×D11—22no—
169C8×C11—42no—
170C8×C11—81no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173C22×M16—221no—
174C2×C4×D4—111no—
175C2×#117—111no—
176#432—221no—
177#400—111no—
178#399—111no—
179#394C2×D1111yescharacteristic
180#392—111no—
181#388—221no—
182#386—221no—
183#386—221no—
184#385—221no—
185#383—111no—
186#343—111no—
187#343—221no—
188#343C2×D1111yescharacteristic
189#324—111no—
190#324C2×D1111yescharacteristic
191#323—221no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11C2×#9911yescharacteristic
202C22×C11#41711yescharacteristic
203C22×C11C2×#10411yescharacteristic
204C2×D11—22no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—42no—
208C2×D11—81no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—81no—
214Dic11—21no—
215Dic11—21no—
216Dic11—41no—
217Dic11—41no—
218Dic11—81no—
219Dic11—81no—
220C22×D4—221no—
221C22×D4C4×D1111yescharacteristic
222C23×C4—111no—
223C23×C4—221no—
224C2×M16—21no—
225C2×M16—224no—
226C2×M16—221no—
227C2×M16—441no—
228C2×M16—442no—
229C22×C8—441no—
230C4×D4—441no—
231C4×D4—441no—
232#117—441no—
233#117—441no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4C22×D1111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—111no—
241C2×C22⋊C4—111no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C42—111no—
246C2×C42—111no—
247C4⋊C8—441no—
248C22⋊C8—21no—
249C22⋊C8—221no—
250#97—441no—
251#95—111no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95C4×D1111yescharacteristic
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—82no—
260C2×C11#150411yescharacteristic
261C2×C11#212011yescharacteristic
262C2×C11#213411yescharacteristic
263D11—42no—
264C24—21no—
265C24—111no—
266C2×D4—41no—
267C2×D4—42no—
268C2×D4—442no—
269C2×D4—442no—
270C2×D4—881no—
271C22×C4—21no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—222no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—442no—
283C22×C4—881no—
284C22×C4—881no—
285C22×C4C2×C4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288M16—22no—
289M16—41no—
290M16—222no—
291M16—444no—
292M16—441no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—444no—
296C2×C8—441no—
297C2×C8—441no—
298C4⋊C4—41no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—881no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—881no—
310C22⋊C4—881no—
311C42—221no—
312C42—221no—
313C42—221no—
314C42—221no—
315C11#1176111yescharacteristic, complemented, Sylow
316C23—22no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—112no—
324C23—221no—
325C23—221no—
326C23—441no—
327C23—441no—
328C23C22⋊C4×D1111yescharacteristic
329D4—42no—
330D4—42no—
331D4—884no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—111no—
342C2×C4—111no—
343C2×C4—222no—
344C2×C4—222no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—884no—
360C2×C4#6696411yescharacteristic
361C2×C4#6696811yescharacteristic
362C8—42no—
363C8—81no—
364C8—442no—
365C8—881no—
366C22—21no—
367C22—21no—
368C22—42no—
369C22—42no—
370C22—42no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—222no—
376C22—442no—
377C22—441no—
378C22—441no—
379C22—881no—
380C22D11×#9911yescharacteristic
381C22#1062238411yescharacteristic
382C22D11×#10411yescharacteristic
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—221no—
389C4—221no—
390C4—441no—
391C4—441no—
392C4—881no—
393C4—881no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—442no—
398C2#1306711711yescharacteristic
399C2#1307025411yescharacteristic
400C2#1307030611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1345C2
socleC22×C11C2×#99
prime radical#10622836C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1345D11
hypocenterC11#11761
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #13068353C2semidirect
3. #13066949C2semidirect
4. #13066644C2semidirect
5. #13066642C2semidirect
6. #13066619C2semidirect
7. C11×#1345C2semidirect
122. #1345D11semidirect
315. C11#11761semidirect

Maximal subgroups

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

subgroupindex
#130741772
#130683532
#130669492
#130666442
#130666422
#130666192
C11×#13452
#1176111