Finite Group Databasebeta

← #14664374

Subgroups — #14664374

Order 2816.

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

normal subgroups only

This group has 514 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#13073572C211yesmaximal, characteristic
2C4×#66897C211yesmaximal, characteristic, complemented
3#13066623C212yesmaximal, complemented
4#13066620C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66992—21no—
8C2×#66983C411yescharacteristic
9C11×#407—21no—
10C2×#66897—21no—
11#10622826—21no—
12C2×C11⋊#95C411yescharacteristic
13#10622604C2211yescharacteristic
14#10622596C2211yescharacteristic
15#10622573C411yescharacteristic
16#10622571—21no—
17#10622566C411yescharacteristic
18#10622553—21no—
19C4×#4318—21no—
20C11×#324C2212yes—
21C11×#323—21no—
22#10622168C2212yes—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C23×Dic11—21no—
29C22×D44C2×C411yescharacteristic
30C2×C11×M16—41no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38#66992—44no—
39#66983—41no—
40#66983—41no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×#4318—22no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—41no—
50#66897—24no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56#66867—41no—
57C4×C11⋊C8—41no—
58#11783—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C24×C11C22⋊C411yescharacteristic
61C23×D11—21no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—81no—
70C22×C4×C11—81no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—81no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C22×Dic11—81no—
88C2×D44—41no—
89C2×D44—81no—
90C11×M16—82no—
91C2×C8×C11—42no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—21no—
96C42×C11—21no—
97C22⋊Dic11—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—81no—
103C4⋊Dic11—41no—
104Dic11⋊C4—42no—
105#4318—24no—
106#4318—42no—
107C2×C11⋊C8—42no—
108#2543—111no—
109C4×#100—111no—
110#1465D1111yescharacteristic, complemented
111#1346—112no—
112#1345—112no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#10412yes—
123C23×C11C2×C22⋊C411yescharacteristic
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131D4×C11—44no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11#9911yescharacteristic
146C2×C4×C11#9911yescharacteristic
147C2×C4×C11AGL(1,ℤ/8)12yes—
148C22⋊D11—84no—
149C22⋊D11—84no—
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—84no—
160D44—82no—
161C8×C11—82no—
162C11⋊C8—44no—
163C2×#121—111no—
164C2×#121—221no—
165C2×C4×D4C2×D1111yescharacteristic
166C2×#100—221no—
167#407—21no—
168C4×M16—221no—
169#398—111no—
170#397—111no—
171#394—111no—
172#392—111no—
173#388—221no—
174#386—221no—
175#386—221no—
176C2×#95—111no—
177#343—112no—
178#324C2×D1112yes—
179#323—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—22no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—81no—
192C22×C11C2×#9911yescharacteristic
193C22×C11#41811yescharacteristic
194C22×C11C2×#10411yescharacteristic
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—22no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—41no—
208Dic11—42no—
209Dic11—81no—
210Dic11—81no—
211C22×D4—111no—
212C22×D4—221no—
213C22×D4—221no—
214C22×D4D4411yescharacteristic
215C23×C4—221no—
216C23×C4C4×D1111yescharacteristic
217C23×C4C22⋊D1111yescharacteristic
218C2×M16—41no—
219C2×M16—222no—
220#121—444no—
221#121—441no—
222#121—441no—
223C4×D4—41no—
224C4×D4—41no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4C22×D1111yescharacteristic
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4C4×D1111yescharacteristic
234C2×C22⋊C4C22⋊D1111yescharacteristic
235C2×C42D4411yescharacteristic
236#100—224no—
237C22⋊C8—22no—
238C22⋊C8—41no—
239#97—441no—
240C4×C8—441no—
241#95—111no—
242#95—111no—
243#95—221no—
244#95—221no—
245#95—221no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—42no—
249C2×C11—81no—
250C2×C11#150711yescharacteristic
251C2×C11#212111yescharacteristic
252C2×C11#213211yescharacteristic
253D11—161no—
254C24—221no—
255C24(C2×D11)⋊C411yescharacteristic
256C24(C2×D11)⋊C411yescharacteristic
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—41no—
260C2×D4—441no—
261C2×D4—442no—
262C2×D4—442no—
263C2×D4—442no—
264C2×D4—442no—
265C2×D4—442no—
266C2×D4—881no—
267C2×D4—881no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—81no—
273C22×C4—81no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—442no—
278C22×C4—442no—
279C22×C4—881no—
280C22×C4(C2×D11)⋊C411yescharacteristic
281C22×C4(C2×D11)⋊C411yescharacteristic
282C22×C4C2×C4×D1111yescharacteristic
283C22×C4C2×D4411yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285M16—82no—
286M16—224no—
287M16—442no—
288C2×C8—42no—
289C2×C8—442no—
290C4⋊C4—41no—
291C4⋊C4—441no—
292C4⋊C4—442no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—442no—
300C22⋊C4—881no—
301C42—21no—
302C42—21no—
303C11#1178311yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23—441no—
320C23#6688912yes—
321C23C2×(C2×D11)⋊C411yescharacteristic
322D4—44no—
323D4—882no—
324D4—884no—
325D4—884no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—222no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—884no—
349C2×C4#6687011yescharacteristic
350C2×C4#6687011yescharacteristic
351C2×C4#6696112yes—
352C8—82no—
353C8—444no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22—881no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22—881no—
371C22—881no—
372C22—881no—
373C22C2×#6687011yescharacteristic
374C22#1062274411yescharacteristic
375C22C2×#6688911yescharacteristic
376C4—22no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—442no—
383C4—881no—
384C4—881no—
385C2—21no—
386C2—21no—
387C2—42no—
388C2—81no—
389C2—1761no—
390C2#1306713311yescharacteristic
391C2#1307026011yescharacteristic
392C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1465C2
socleC22×C11C2×#99
prime radical#13073572C2
cosocleC2×C11×C4⋊C4C23
hypercenter#1465D11
hypocenterC11#11783
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. C4×#66897C2semidirect
3. #13066623C2semidirect
4. #13066620C2semidirect
5. C11×#1465C2semidirect
110. #1465D11semidirect
303. C11#11783semidirect

Maximal subgroups

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

subgroupindex
#130735722
C4×#668972
#130666232
#130666202
C11×#14652
#1178311