Finite Group Databasebeta

← #14651693

Subgroups — #14651693

Order 2816.

956 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 956 conjugacy classes of subgroups — too many to draw. Only its 115 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#13071194C211yesmaximal, characteristic
2#13068690C212yesmaximal, complemented
3#13068531C211yesmaximal, characteristic
4C11⋊#1304C212yesmaximal, complemented
5C11×#2405C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C2×C11×#123C412yescomplemented
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic11—21no—
10C11×#394—22no—
11C11×#386C412yescomplemented
12C11×#385—21no—
13C11×#379—21no—
14C11×#379C2211yescharacteristic
15#10622860C2212yes—
16#10622860C2212yes—
17#10622833—24no—
18C2×#66898—22no—
19#10622824—21no—
20#10622164—24no—
21C25×C11D411yescharacteristic
22C25×C11C2311yescharacteristic
23C22×D4×C11—22no—
24C22×D4×C11—22no—
25C22×D4×C11—44no—
26C22×D4×C11C2×C412yes—
27C22×D4×C11D412yes—
28C23×C4×C11C2×C411yescharacteristic, complemented
29C23×C4×C11C2×C411yescharacteristic, complemented
30C23×C4×C11D411yescharacteristic
31C23×Dic11—22no—
32C11×#123—44no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4C2×C412yescomplemented
43C2×C22⋊Dic11—22no—
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—44no—
50C2×C22⋊Dic11D414yes—
51C11×#95—22no—
52#66898—44no—
53C11⋊#95—24no—
54#9499—111nomaximal, Sylow
55C24×C11—21no—
56C24×C11—24no—
57C24×C11—21no—
58C24×C11—42no—
59C24×C11—42no—
60C24×C11—42no—
61C24×C11—81no—
62C24×C11—81no—
63C24×C11C22⋊C412yes—
64C24×C11C22×C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C24×C11C2×D411yescharacteristic
67C24×C11C2×D412yes—
68C24×C11#4112yes—
69C2×D4×C11—24no—
70C2×D4×C11—24no—
71C2×D4×C11—24no—
72C2×D4×C11—24no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11—44no—
76C2×D4×C11—44no—
77C2×D4×C11—48no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—81no—
88C22×C4×C11C22⋊C412yes—
89C22×Dic11—24no—
90C22×Dic11—44no—
91C22×Dic11—42no—
92C22×Dic11—82no—
93C22×Dic11—82no—
94C11×C4⋊C4—44no—
95C11×C22⋊C4—42no—
96C11×C22⋊C4—44no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—82no—
103C22⋊Dic11—44no—
104C22⋊Dic11—44no—
105C22⋊Dic11—44no—
106C22⋊Dic11—44no—
107C22⋊Dic11—44no—
108C22⋊Dic11—82no—
109C22⋊Dic11—82no—
110#2405D1111yescharacteristic
111#2308—111no—
112#1819—112no—
113#1781—111no—
114#1304—112no—
115C23×C11—22no—
116C23×C11—22no—
117C23×C11—24no—
118C23×C11—22no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—24no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—41no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11—41no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—81no—
140C23×C11—81no—
141C23×C11—88no—
142C23×C11—88no—
143C23×C11#9914yes—
144C23×C11C2×C22⋊C411yescharacteristic
145C23×C11C4×D412yes—
146C23×C11#12011yescharacteristic
147C23×C11#12112yes—
148C23×C11#12311yescharacteristic
149D4×C11—48no—
150D4×C11—48no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168C2×Dic11—88no—
169C2×Dic11—82no—
170C2×Dic11—82no—
171C2×Dic11—82no—
172C23×D4C2×D1111yescharacteristic
173C2×#123Dic1112yescomplemented
174C22×C22⋊C4—221no—
175C22×C22⋊C4C2×D1111yescharacteristic
176C2×#99—222no—
177#394—22no—
178#386—224no—
179#386Dic1112yescomplemented
180#385—21no—
181#381—221no—
182#379—21no—
183#379—112no—
184#379—112no—
185#379C2×D1111yescharacteristic
186#342—224no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—21no—
195C22×C11—22no—
196C22×C11—24no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—21no—
200C22×C11—22no—
201C22×C11—44no—
202C22×C11—44no—
203C22×C11—44no—
204C22×C11—44no—
205C22×C11—44no—
206C22×C11—42no—
207C22×C11—42no—
208C22×C11—84no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—84no—
212C22×C11—84no—
213C22×C11#38611yescharacteristic
214C22×C11C2×#9912yes—
215C22×C11#45812yes—
216C4×C11—42no—
217C4×C11—82no—
218C4×C11—81no—
219C4×C11—81no—
220Dic11—84no—
221Dic11—162no—
222C25C22⋊D1111yescharacteristic
223C25C22×D1111yescharacteristic
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—44no—
227C22×D4C2×Dic1112yes—
228C22×D4C22⋊D1112yes—
229C23×C4—222no—
230C23×C4C2×Dic1111yescharacteristic, complemented
231C23×C4C2×Dic1111yescharacteristic, complemented
232C23×C4C22⋊D1111yescharacteristic
233#123—44no—
234C2×C4⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—114no—
244C2×C22⋊C4—222no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4—222no—
247C2×C22⋊C4—222no—
248C2×C22⋊C4—222no—
249C2×C22⋊C4—222no—
250C2×C22⋊C4—444no—
251C2×C22⋊C4C2×Dic1112yescomplemented
252#99—444no—
253#95—22no—
254#95—224no—
255C2×C11—22no—
256C2×C11—22no—
257C2×C11—42no—
258C2×C11—42no—
259C2×C11—41no—
260C2×C11—44no—
261C2×C11#189011yescharacteristic
262C2×C11#189811yescharacteristic
263C2×C11#191311yescharacteristic
264C24—21no—
265C24—24no—
266C24—21no—
267C24—42no—
268C24—42no—
269C24—42no—
270C24—81no—
271C24—81no—
272C24C22⋊Dic1112yes—
273C24D4×D1112yes—
274C24#434112yes—
275C24C22×Dic1111yescharacteristic
276C24C2×C22⋊D1111yescharacteristic
277C24C2×C22⋊D1111yescharacteristic
278C2×D4—24no—
279C2×D4—24no—
280C2×D4—24no—
281C2×D4—24no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—44no—
285C2×D4—44no—
286C2×D4—48no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—81no—
297C22×C4—224no—
298C22×C4—444no—
299C22×C4—442no—
300C22×C4—882no—
301C22×C4—882no—
302C22×C4C22⋊Dic1112yes—
303C4⋊C4—44no—
304C22⋊C4—42no—
305C22⋊C4—44no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—81no—
311C22⋊C4—82no—
312C22⋊C4—444no—
313C22⋊C4—444no—
314C22⋊C4—444no—
315C22⋊C4—444no—
316C22⋊C4—444no—
317C22⋊C4—882no—
318C22⋊C4—882no—
319C11#949911yescharacteristic, complemented, Sylow
320C23—22no—
321C23—22no—
322C23—24no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—22no—
329C23—24no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23—41no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—81no—
346C23—88no—
347C23—88no—
348C23#6689814yes—
349C23D4×Dic1112yes—
350C23#6698811yescharacteristic
351C23#6699011yescharacteristic
352C23#6699212yes—
353C23C2×C22⋊Dic1111yescharacteristic
354D4—48no—
355D4—48no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—444no—
371C2×C4—444no—
372C2×C4—444no—
373C2×C4—888no—
374C2×C4—882no—
375C2×C4—882no—
376C2×C4—882no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—22no—
383C22—22no—
384C22—24no—
385C22—22no—
386C22—22no—
387C22—21no—
388C22—22no—
389C22—21no—
390C22—22no—
391C22—44no—
392C22—44no—
393C22—44no—
394C22—44no—
395C22—44no—
396C22—42no—
397C22—42no—
398C22—82no—
399C22—82no—
400C22—84no—
401C22—84no—
402C22—84no—
403C22#1062266612yes—
404C22C2×#6689812yes—
405C22#1062283311yescharacteristic
406C4—42no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—884no—
411C4—1762no—
412C2—22no—
413C2—22no—
414C2—42no—
415C2—41no—
416C2—42no—
417C2—44no—
418C2#1306903011yescharacteristic
419C2#1306907011yescharacteristic
420C2#1306915911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#2405C2
socleC22×C11#386
prime radicalC23×D4×C11C22
cosocleC25×C11C23
hypercenter#2405D11
hypocenterC11#9499
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2405

Complements

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

NH ≅ G/Ntype
2. #13068690C2semidirect
4. C11⋊#1304C2semidirect
7. C2×C11×#123C4semidirect
11. C11×#386C4semidirect
28. C23×C4×C11C2×C4semidirect
29. C23×C4×C11C2×C4semidirect
42. C2×C11×C22⋊C4C2×C4semidirect
173. C2×#123Dic11semidirect
179. #386Dic11semidirect
230. C23×C4C2×Dic11semidirect
231. C23×C4C2×Dic11semidirect
251. C2×C22⋊C4C2×Dic11semidirect
319. C11#9499semidirect

Maximal subgroups

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

subgroupindex
#130711942
#130686902
#130685312
C11⋊#13042
C11×#24052
#949911