Finite Group Databasebeta

← #14663351

Subgroups — #14663351

Order 2816.

408 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 69 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#13073077C211yesmaximal, characteristic
2#13066949C211yesmaximal, characteristic, complemented
3#13066929C211yesmaximal, characteristic, complemented
4#13066561C211yesmaximal, characteristic, complemented
5#13066561C211yesmaximal, characteristic, complemented
6#13066548C211yesmaximal, characteristic, complemented
7C11×#1318C211yesmaximal, characteristic, complemented
8C2×#66991C411yescharacteristic
9C2×#66945C2211yescharacteristic
10C11×#390C2211yescharacteristic
11#10622834C411yescharacteristic
12#10622589C2211yescharacteristic
13#10622572—21no—
14#10622572—21no—
15#10622558—21no—
16#10622558—21no—
17C4×(C2×D11)⋊C4C411yescharacteristic
18#10622549C411yescharacteristic
19#10622332—21no—
20#10622331—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622106—21no—
26#10622106—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C4×D11C2×C411yescharacteristic
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37#66991—41no—
38#66991—41no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4D411yescharacteristic
41C2×(C2×D11)⋊C4D411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49#66945—41no—
50#66945—41no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66879—41no—
59Dic11⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11554—111nomaximal, Sylow
63C24×C11—21no—
64C23×D11C22⋊C411yescharacteristic
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—81no—
75C2×C22⋊D11—81no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11C22⋊C411yescharacteristic
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—81no—
90C11×C22⋊C4—81no—
91C42×C11—41no—
92C22⋊Dic11—42no—
93C22⋊Dic11—42no—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—42no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101Dic11⋊C4—81no—
102Dic11⋊C4—81no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2500—111no—
112#1464—111no—
113#1458—111no—
114#1325—111no—
115#1325—111no—
116#1318—111no—
117#1318D1111yescharacteristic, complemented
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11C2×C22⋊C411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—41no—
130C22×D11—41no—
131D4×C11—81no—
132D4×C11—81no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11#13111yescharacteristic
143C2×C4×C11#13111yescharacteristic
144C22⋊D11—84no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—22no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11#9911yescharacteristic
158C2×Dic11#9911yescharacteristic
159C4×D11—41no—
160C4×D11—41no—
161C4×D11—41no—
162C4×D11—41no—
163C8×C11—81no—
164C8×C11—81no—
165C11⋊C8—81no—
166C11⋊C8—81no—
167C2×#121—111no—
168C2×#117—111no—
169#432—221no—
170#431—221no—
171#394—221no—
172#394—221no—
173#390—111no—
174#390C2×D1111yescharacteristic
175#388—221no—
176#388—221no—
177#384—111no—
178#382—111no—
179C4×C22⋊C4—111no—
180#324—111no—
181#324—111no—
182#324C2×D1111yescharacteristic
183#324C2×D1111yescharacteristic
184#323—221no—
185#323—221no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11#40811yescharacteristic
196C22×C11C2×#9911yescharacteristic
197C22×C11#41311yescharacteristic
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—81no—
208Dic11—21no—
209Dic11—21no—
210Dic11—42no—
211Dic11—41no—
212Dic11—41no—
213Dic11—81no—
214C22×D4—221no—
215C22×D4C4×D1111yescharacteristic
216C23×C4—111no—
217#121—441no—
218#121—441no—
219#117—441no—
220#117—441no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4C22×D1111yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42C4×D1111yescharacteristic
238C4⋊C8—441no—
239C4⋊C8—441no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—221no—
243C22⋊C8—221no—
244#97—441no—
245C4×C8—441no—
246#95—221no—
247#95—221no—
248#95—221no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11—161no—
252C2×C11#146811yescharacteristic
253C2×C11#212811yescharacteristic
254C2×C11#213211yescharacteristic
255D11—81no—
256C24—21no—
257C24—111no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—442no—
263C2×D4—881no—
264C2×D4—881no—
265C22×C4—21no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—441no—
276C22×C4C2×C4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—441no—
282C2×C8—441no—
283C4⋊C4—41no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—881no—
287C4⋊C4—881no—
288C22⋊C4—81no—
289C22⋊C4—81no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C22⋊C4—442no—
293C22⋊C4—441no—
294C22⋊C4—441no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C42—41no—
298C42—221no—
299C42—221no—
300C42—221no—
301C42—221no—
302C42—221no—
303C42—221no—
304C11#1155411yescharacteristic, complemented, Sylow
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—221no—
313C23—221no—
314C23—221no—
315C23—441no—
316C23—441no—
317C23C22⋊C4×D1111yescharacteristic
318D4—81no—
319D4—81no—
320D4—884no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—111no—
331C2×C4—111no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—222no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
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#6695411yescharacteristic
349C2×C4#6696011yescharacteristic
350C8—81no—
351C8—81no—
352C8—881no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—441no—
364C22—441no—
365C22—441no—
366C22—881no—
367C22—881no—
368C22#1062234011yescharacteristic
369C22D11×#9911yescharacteristic
370C22#1062235811yescharacteristic
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—221no—
377C4—221no—
378C4—442no—
379C4—441no—
380C4—441no—
381C4—881no—
382C2—21no—
383C2—21no—
384C2—161no—
385C2—881no—
386C2#1306696111yescharacteristic
387C2#1307028611yescharacteristic
388C2#1307029811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1318C2
socleC22×C11C2×#99
prime radicalC2×#66991C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1318D11
hypocenterC11#11554
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #13066949C2semidirect
3. #13066929C2semidirect
4. #13066561C2semidirect
5. #13066561C2semidirect
6. #13066548C2semidirect
7. C11×#1318C2semidirect
117. #1318D11semidirect
304. C11#11554semidirect

Maximal subgroups

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

subgroupindex
#130730772
#130669492
#130669292
#130665612
#130665482
C11×#13182
#1155411