Finite Group Databasebeta

← #14642345

Subgroups — #14642345

Order 2816.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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#13076965C211yesmaximal, characteristic
2#13068683C211yesmaximal, characteristic
3#13068377C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic, complemented
5#13066441C211yesmaximal, characteristic, complemented
6#13066441C211yesmaximal, characteristic, complemented
7C11×#1272C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic
9C2×#66997C411yescharacteristic
10C2×#66950C411yescharacteristic
11C2×C42×D11C2211yescharacteristic
12C11×#391C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×#66879—21no—
16#10622589C411yescharacteristic
17#10622542C2211yescharacteristic
18#10622280—21no—
19#10622280—21no—
20#10622260—21no—
21#10622260—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11C2×C411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36#66999—42no—
37#66997—42no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52#66950—42no—
53C42×D11—42no—
54C11×#95—21no—
55C11×#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58(C2×D11)⋊C8—24no—
59(C2×D11)⋊C8—42no—
60#66879—42no—
61#7707—111nomaximal, Sylow
62C23×D11C22⋊C411yescharacteristic
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—41no—
100C42×C11—41no—
101(C2×D11)⋊C4—42no—
102(C2×D11)⋊C4—42no—
103C4⋊Dic11—41no—
104C4⋊Dic11—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109Dic11⋊C4—42no—
110C4×Dic11—22no—
111C4×Dic11—22no—
112C4×Dic11—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#2857—111no—
120#1817—111no—
121#1749—111no—
122#1272—111no—
123#1272—111no—
124#1272—111no—
125#1272D1111yescharacteristic, complemented
126C23×C11C2×C22⋊C411yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11#10012yes—
134Q8×C11—81no—
135Q8×C11—81no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
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×C11—41no—
148C2×C4×C11#13111yescharacteristic
149C2×C4×C11#13111yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11#9912yes—
168C2×Dic11#10412yes—
169C4×D11—42no—
170C4×D11—42no—
171C4×D11—42no—
172C4×D11—42no—
173C4×D11—42no—
174C4×D11—42no—
175Dic22—81no—
176Dic22—81no—
177C8×C11—42no—
178C8×C11—81no—
179C11⋊C8—42no—
180C11⋊C8—81no—
181C2×C4⋊Q8—111no—
182C2×C22⋊Q8—111no—
183C2×C22⋊Q8—111no—
184C22×C42—111no—
185C2×C22⋊C8—221no—
186C2×C22⋊C8—221no—
187C2×#97—221no—
188#391—111no—
189#391C2×D1111yescharacteristic
190#389—221no—
191#389—221no—
192#384—111no—
193#380—221no—
194#380—221no—
195#336—111no—
196#336—111no—
197#336—221no—
198#336C2×D1111yescharacteristic
199#336C2×D1111yescharacteristic
200C22×C11#40811yescharacteristic
201C22×C11C2×#9911yescharacteristic
202C22×C11C2×#10011yescharacteristic
203C22×C11#41911yescharacteristic
204C22×C11#41911yescharacteristic
205C22×C11C2×#10411yescharacteristic
206C22×C11#42111yescharacteristic
207C2×D11—22no—
208C2×D11—22no—
209C2×D11—22no—
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C2×D11—41no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—81no—
221C4×C11—81no—
222Dic11—22no—
223Dic11—22no—
224Dic11—41no—
225Dic11—81no—
226Dic11—81no—
227C22×Q8—111no—
228C22×Q8C4×D1111yescharacteristic
229C23×C4—111no—
230C23×C4—111no—
231C23×C4—111no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—221no—
235C22×C8—221no—
236C4⋊Q8—442no—
237C22⋊Q8—442no—
238C22⋊Q8—442no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4C4×D1111yescharacteristic
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C42—111no—
250C2×C42—111no—
251C2×C42—111no—
252C2×C42—442no—
253C2×C42C22×D1111yescharacteristic
254C22⋊C8—224no—
255C22⋊C8—442no—
256#97—442no—
257#95—21no—
258#95—21no—
259#95—221no—
260#95—221no—
261C2×C11#147111yescharacteristic
262C2×C11#148511yescharacteristic
263C2×C11#149711yescharacteristic
264C2×C11#150811yescharacteristic
265C2×C11#151111yescharacteristic
266C2×C11#153011yescharacteristic
267C2×C11#155811yescharacteristic
268D11—42no—
269C24—111no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—221no—
275C2×Q8—221no—
276C2×Q8—441no—
277C2×Q8—441no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—222no—
284C22×C4—222no—
285C22×C4—222no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—222no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—441no—
310C2×C8—441no—
311C2×C8—441no—
312C4⋊C4—41no—
313C4⋊C4—441no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C4⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4—442no—
322C42—41no—
323C42—222no—
324C42—222no—
325C42—441no—
326C11#770711yescharacteristic, complemented, Sylow
327C23—112no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23—221no—
334C23C22⋊C4×D1111yescharacteristic
335Q8—81no—
336Q8—81no—
337Q8—881no—
338Q8—881no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—112no—
352C2×C4—112no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4#6695411yescharacteristic
373C2×C4#6696011yescharacteristic
374C2×C4#6696811yescharacteristic
375C2×C4#6696811yescharacteristic
376C2×C4#6697111yescharacteristic
377C2×C4#6697111yescharacteristic
378C8—42no—
379C8—81no—
380C8—442no—
381C8—881no—
382C22—222no—
383C22—222no—
384C22—222no—
385C22—441no—
386C22—441no—
387C22—441no—
388C22—441no—
389C22#1062234011yescharacteristic
390C22D11×#9911yescharacteristic
391C22D11×#10011yescharacteristic
392C22#1062241511yescharacteristic
393C22#1062241511yescharacteristic
394C22D11×#10411yescharacteristic
395C22#1062243411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—222no—
405C4—222no—
406C4—441no—
407C4—881no—
408C4—881no—
409C2—442no—
410C2#1306697411yescharacteristic
411C2#1306703511yescharacteristic
412C2#1306708711yescharacteristic
413C2#1306713411yescharacteristic
414C2#1306714711yescharacteristic
415C2#1306722511yescharacteristic
416C2#1306734011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1272D11
hypocenterC11#7707
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #13066442C2semidirect
5. #13066441C2semidirect
6. #13066441C2semidirect
7. C11×#1272C2semidirect
125. #1272D11semidirect
326. C11#7707semidirect

Maximal subgroups

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

subgroupindex
#130769652
#130686832
#130683772
#130664422
#130664412
C11×#12722
#770711