Finite Group Databasebeta

← #14663454

Subgroups — #14663454

Order 2816.

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

normal subgroups only

This group has 424 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#13073968C211yesmaximal, characteristic
2#13066951C211yesmaximal, characteristic
3#13066935C211yesmaximal, characteristic
4#13066565C211yesmaximal, characteristic, complemented
5#13066564C211yesmaximal, characteristic, complemented
6#13066563C211yesmaximal, characteristic, complemented
7C11×#1326C211yesmaximal, characteristic, complemented
8C22×Dic11⋊C4C411yescharacteristic
9C2×(C22⋊D11)⋊C4C2211yescharacteristic
10C11×#385C2211yescharacteristic
11#10622826C411yescharacteristic
12#10622602—21no—
13#10622593—21no—
14#10622571C411yescharacteristic
15#10622559C2211yescharacteristic
16#10622555C411yescharacteristic
17#10622339—21no—
18#10622331—21no—
19#10622289—21no—
20#10622265—21no—
21C11×#323C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622107—21no—
26#10622106—21no—
27C23×C4×C11C2×C411yescharacteristic
28C22×C22⋊D11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C23×Dic11C2×C411yescharacteristic
31C22×C4×D11D411yescharacteristic
32C2×C11×C4⋊C4—21no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C22⋊Dic11C2×C411yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—41no—
44C2×Dic11⋊C4—41no—
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×#4313—41no—
48(C22⋊D11)⋊C4—41no—
49(C22⋊D11)⋊C4—41no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)—21no—
59(C2×D11)⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11577—111nomaximal, Sylow
63C24×C11C22×C411yescharacteristic
64C23×D11C22⋊C411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11—81no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C22⋊D11—22no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11—41no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—41no—
80C22×Dic11—42no—
81C22×Dic11—81no—
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—81no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—81no—
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C11×C22⋊C4—41no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—81no—
99Dic11⋊C4—41no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—81no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#4313—82no—
110#2579—111no—
111#1465—111no—
112#1460—111no—
113#1326—111no—
114#1326—111no—
115#1326—111no—
116#1326D1111yescharacteristic, complemented
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11#13111yescharacteristic
123C23×C11#13111yescharacteristic
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—41no—
128C22×D11—41no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—82no—
140C22⋊D11—42no—
141C22⋊D11—42no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—22no—
145C2×Dic11—21no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11#9911yescharacteristic
158C2×Dic11#9911yescharacteristic
159C2×Dic11#10112yes—
160C4×D11—42no—
161C4×D11—81no—
162C8×C11—81no—
163C8×C11—81no—
164C11⋊C8—81no—
165C11⋊C8—81no—
166C2×C4×D4—111no—
167C22×C4⋊C4—111no—
168#431—221no—
169#407—221no—
170#398—221no—
171#396—221no—
172#387—221no—
173#386—111no—
174#386—111no—
175#385—111no—
176#385—221no—
177#385C2×D1111yescharacteristic
178#380—111no—
179#324—221no—
180#323—111no—
181#323—111no—
182#323—221no—
183#323C2×D1111yescharacteristic
184#323C2×D1111yescharacteristic
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—42no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11#40811yescharacteristic
195C22×C11C2×#9911yescharacteristic
196C22×C11C2×#10111yescharacteristic
197C2×D11—42no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—81no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11—81no—
205C4×C11—81no—
206Dic11—21no—
207Dic11—21no—
208Dic11—22no—
209Dic11—42no—
210Dic11—41no—
211Dic11—81no—
212C22×D4—111no—
213C23×C4—111no—
214C23×C4—111no—
215C23×C4—111no—
216C23×C4C4×D1111yescharacteristic
217C2×M16—441no—
218C4×D4—441no—
219C4×D4—441no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—441no—
227C2×C4⋊C4—441no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4C4×D1111yescharacteristic
233C2×C22⋊C4C22×D1111yescharacteristic
234C2×C42—111no—
235C4⋊C8—441no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—221no—
239C22⋊C8—221no—
240C22⋊C8—441no—
241C4×C8—441no—
242#95—21no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95—221no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—41no—
250C2×C11—41no—
251C2×C11#147211yescharacteristic
252C2×C11#212011yescharacteristic
253C2×C11#212111yescharacteristic
254D11—81no—
255C24—111no—
256C24C2×C4×D1111yescharacteristic
257C2×D4—222no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—441no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—81no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—442no—
275C22×C4—441no—
276C22×C4—881no—
277C22×C4—881no—
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280M16—882no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—441no—
284C2×C8—441no—
285C4⋊C4—81no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—442no—
290C4⋊C4—442no—
291C4⋊C4—881no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—41no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—441no—
298C22⋊C4—442no—
299C22⋊C4—881no—
300C42—221no—
301C42—221no—
302C11#1157711yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—221no—
308C23—221no—
309C23—221no—
310C23—441no—
311C23—441no—
312C23C22⋊C4×D1111yescharacteristic
313C23#6695411yescharacteristic
314C23#6696011yescharacteristic
315D4—442no—
316D4—442no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—82no—
328C2×C4—111no—
329C2×C4—111no—
330C2×C4—112no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—222no—
334C2×C4—221no—
335C2×C4—442no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—442no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—442no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—881no—
346C2×C4—881no—
347C2×C4—881no—
348C8—81no—
349C8—81no—
350C8—881no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—41no—
360C22—41no—
361C22—442no—
362C22—441no—
363C22—441no—
364C22—441no—
365C22—881no—
366C22#1062234011yescharacteristic
367C22D11×#9911yescharacteristic
368C22D11×#10111yescharacteristic
369C4—41no—
370C4—41no—
371C4—81no—
372C4—81no—
373C4—221no—
374C4—221no—
375C4—222no—
376C4—442no—
377C4—441no—
378C4—881no—
379C2—21no—
380C2—21no—
381C2—41no—
382C2—41no—
383C2—881no—
384C2#1306697811yescharacteristic
385C2#1307025611yescharacteristic
386C2#1307025911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1326C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1326D11
hypocenterC11#11577
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1326

Complements

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

NH ≅ G/Ntype
4. #13066565C2semidirect
5. #13066564C2semidirect
6. #13066563C2semidirect
7. C11×#1326C2semidirect
116. #1326D11semidirect
302. C11#11577semidirect

Maximal subgroups

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

subgroupindex
#130739682
#130669512
#130669352
#130665652
#130665642
#130665632
C11×#13262
#1157711