Finite Group Databasebeta

← #14663431

Subgroups — #14663431

Order 2816.

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

normal subgroups only

This group has 416 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#13073815C211yesmaximal, characteristic
2#13066953C211yesmaximal, characteristic
3#13066933C211yesmaximal, characteristic
4#13066561C211yesmaximal, characteristic, complemented
5#13066561C211yesmaximal, characteristic, complemented
6#13066560C211yesmaximal, characteristic, complemented
7C11×#1324C211yesmaximal, characteristic, complemented
8C2×#66946C2211yescharacteristic
9C2×#66943C411yescharacteristic
10C11×#382C2211yescharacteristic
11#10622601C411yescharacteristic
12#10622589C2211yescharacteristic
13#10622552C411yescharacteristic
14C4×Dic11⋊C4C411yescharacteristic
15#10622339—21no—
16D11×C22⋊C8—21no—
17#10622289—21no—
18#10622289—21no—
19#10622281—21no—
20#10622281—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622106—21no—
26#10622106—21no—
27C22×D44C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4D411yescharacteristic
38C2×(C2×D11)⋊C4D411yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×#4313—41no—
48C2×C8×D11—41no—
49#66946—41no—
50#66946—41no—
51#66943—41no—
52#66943—41no—
53C11×C22⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60(C2×D11)⋊C8—41no—
61(C2×D11)⋊C8—41no—
62#11572—111nomaximal, Sylow
63C23×D11C22⋊C411yescharacteristic
64C23×D11C22⋊C411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×D44—22no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—41no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—81no—
83C2×C4×D11—81no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11—21no—
89C42×C11—21no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—81no—
95(C2×D11)⋊C4—81no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99Dic11⋊C4—42no—
100Dic11⋊C4—42no—
101Dic11⋊C4—81no—
102Dic11⋊C4—81no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#4313—82no—
110C8×D11—82no—
111#2566—111no—
112#1465—111no—
113#1459—111no—
114#1325—111no—
115#1325—111no—
116#1324—111no—
117#1324D1111yescharacteristic, complemented
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11#10112yes—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
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—41no—
140C2×C4×C11—41no—
141C2×C4×C11#13111yescharacteristic
142C2×C4×C11#13111yescharacteristic
143C2×Dic11—22no—
144C2×Dic11—21no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11#9911yescharacteristic
153C2×Dic11#9911yescharacteristic
154D44—42no—
155D44—42no—
156C4×D11—42no—
157C4×D11—42no—
158C4×D11—81no—
159C4×D11—81no—
160C8×C11—81no—
161C8×C11—81no—
162C11⋊C8—81no—
163C11⋊C8—81no—
164C2×#125—111no—
165C2×C4×D4—111no—
166#407—221no—
167C2×C22⋊C8—221no—
168#396—221no—
169#396—221no—
170#390—111no—
171#390—111no—
172#385—221no—
173#385—221no—
174#384—111no—
175#382C2×D1111yescharacteristic
176C4×C4⋊C4—111no—
177#324—111no—
178#324—111no—
179#324C2×D1111yescharacteristic
180#324C2×D1111yescharacteristic
181#323—221no—
182#323—221no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#40811yescharacteristic
186C22×C11C2×#9911yescharacteristic
187C22×C11C2×#10111yescharacteristic
188C2×D11—22no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—42no—
192C2×D11—42no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—81no—
203C4×C11—81no—
204Dic11—21no—
205Dic11—21no—
206Dic11—42no—
207Dic11—41no—
208Dic11—81no—
209C22×D4—111no—
210C23×C4—111no—
211C23×C4—111no—
212C2×M16—441no—
213C22×C8—441no—
214#125—441no—
215#125—441no—
216C4×D4—441no—
217C4×D4—441no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4C4×D1111yescharacteristic
225C2×C4⋊C4C22×D1111yescharacteristic
226C2×C22⋊C4—111no—
227C2×C22⋊C4—111no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C42—111no—
233C2×C42—111no—
234C2×C42C4×D1111yescharacteristic
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—221no—
238C22⋊C8—221no—
239C22⋊C8—441no—
240C22⋊C8—441no—
241#95—21no—
242#95—21no—
243#95—221no—
244C2×C11—21no—
245C2×C11—21no—
246C2×C11#147211yescharacteristic
247C2×C11#212711yescharacteristic
248C2×C11#213211yescharacteristic
249D11—42no—
250D11—81no—
251C24—111no—
252C24—111no—
253C2×D4—222no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—441no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—881no—
268C22×C4—881no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4D4×D1111yescharacteristic
272M16—882no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—441no—
276C2×C8—441no—
277C2×C8—882no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C4⋊C4—881no—
286C4⋊C4—881no—
287C22⋊C4—441no—
288C22⋊C4—441no—
289C22⋊C4—442no—
290C22⋊C4—442no—
291C22⋊C4—881no—
292C22⋊C4—881no—
293C42—21no—
294C42—21no—
295C42—221no—
296C42—221no—
297C42—221no—
298C42—221no—
299C11#1157211yescharacteristic, complemented, Sylow
300C23—112no—
301C23—221no—
302C23—221no—
303C23—221no—
304C23—221no—
305C23—221no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23C22⋊C4×D1111yescharacteristic
311D4—442no—
312D4—442no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—222no—
328C2×C4—221no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4#6695411yescharacteristic
341C2×C4#6696011yescharacteristic
342C8—81no—
343C8—81no—
344C8—881no—
345C8—881no—
346C22—21no—
347C22—21no—
348C22—222no—
349C22—442no—
350C22—442no—
351C22—441no—
352C22—441no—
353C22—441no—
354C22—441no—
355C22—441no—
356C22—881no—
357C22—881no—
358C22#1062234011yescharacteristic
359C22D11×#9911yescharacteristic
360C22D11×#10111yescharacteristic
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—221no—
368C4—221no—
369C4—442no—
370C4—441no—
371C4—881no—
372C2—21no—
373C2—21no—
374C2—442no—
375C2—881no—
376C2#1306697811yescharacteristic
377C2#1307028411yescharacteristic
378C2#1307029811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1324D11
hypocenterC11#11572
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
4. #13066561C2semidirect
5. #13066561C2semidirect
6. #13066560C2semidirect
7. C11×#1324C2semidirect
117. #1324D11semidirect
299. C11#11572semidirect

Maximal subgroups

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

subgroupindex
#130738152
#130669532
#130669332
#130665612
#130665602
C11×#13242
#1157211