Finite Group Databasebeta

← #14651694

Subgroups — #14651694

Order 2816.

660 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 93 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#13072894C211yesmaximal, characteristic
2#13071212C211yesmaximal, characteristic
3#13068690C211yesmaximal, characteristic
4#13068688C211yesmaximal, characteristic
5C11⋊#1304C211yesmaximal, characteristic
6C11⋊#1304C211yesmaximal, characteristic
7C11×#1819C211yesmaximal, characteristic
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic11C2211yescharacteristic
10C11×#379C2211yescharacteristic
11C11×#379C2211yescharacteristic
12#10622860C2211yescharacteristic
13#10622860C2211yescharacteristic
14#10622860C2211yescharacteristic
15#10622824C412yescomplemented
16#10622823C412yescomplemented
17#10622565—22no—
18#10622559—21no—
19#10622558—22no—
20#10622557—22no—
21#10622556—21no—
22#10622555—21no—
23C22⋊C4×Dic11—21no—
24C11×#342—22no—
25#10622165—22no—
26#10622164—22no—
27C25×C11C2311yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4D412yes—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11C2×C412yes—
56C2×C22⋊Dic11C2×C412yes—
57C2×C22⋊Dic11D412yes—
58C2×C22⋊Dic11D412yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×C4×Dic11—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67#9500—111nomaximal, Sylow
68C24×C11—42no—
69C24×C11—42no—
70C24×C11—81no—
71C24×C11C22×C411yescharacteristic
72C24×C11C2×D411yescharacteristic
73C24×C11C2×D411yescharacteristic
74C24×C11C2×D411yescharacteristic
75C24×C11C2×D411yescharacteristic
76C24×C11#4111yescharacteristic
77C24×C11#4111yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—42no—
86C22×C4×C11—41no—
87C22×C4×C11—81no—
88C22×Dic11—22no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—22no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—42no—
95C22×Dic11—41no—
96C22×Dic11—81no—
97C22×Dic11C22⋊C412yes—
98C22×Dic11C22⋊C412yes—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—81no—
108C11×C22⋊C4—81no—
109C22⋊Dic11—22no—
110C22⋊Dic11—22no—
111C22⋊Dic11—22no—
112C22⋊Dic11—22no—
113C22⋊Dic11—42no—
114C22⋊Dic11—42no—
115C22⋊Dic11—42no—
116C22⋊Dic11—42no—
117C22⋊Dic11—42no—
118C22⋊Dic11—42no—
119C22⋊Dic11—81no—
120C22⋊Dic11—81no—
121C22⋊Dic11—81no—
122Dic11⋊C4—82no—
123Dic11⋊C4—82no—
124C4×Dic11—82no—
125#2483—111no—
126#2312—111no—
127#1819—111no—
128#1819—111no—
129#1819D1111yescharacteristic
130#1304—111no—
131#1304—111no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—88no—
154C23×C11C2×C22⋊C411yescharacteristic
155C23×C11C4×D411yescharacteristic
156C23×C11C4×D411yescharacteristic
157C23×C11#12011yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12111yescharacteristic
160C23×C11#12311yescharacteristic
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—81no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192C22×C22⋊C4—111no—
193C22×C22⋊C4C2×D1111yescharacteristic
194#397—222no—
195#388—222no—
196#388—222no—
197#385—112no—
198#385—221no—
199#381—112no—
200#381—221no—
201#380—221no—
202#379—111no—
203#379—111no—
204#379—111no—
205#379C2×D1111yescharacteristic
206#379C2×D1111yescharacteristic
207C4×C22⋊C4—221no—
208#342—22no—
209#342—222no—
210#342—222no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—44no—
231C22×C11—44no—
232C22×C11—82no—
233C22×C11—82no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11#38611yescharacteristic
238C22×C11#41012yes—
239C22×C11#45812yes—
240C4×C11—82no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11—161no—
244Dic11—42no—
245Dic11—42no—
246Dic11—82no—
247Dic11—82no—
248Dic11—161no—
249C25C22×D1111yescharacteristic
250C23×C4—111no—
251C23×C4—111no—
252C23×C4C4×D1111yescharacteristic
253C23×C4C4×D1111yescharacteristic
254C2×C4⋊C4—222no—
255C2×C4⋊C4—222no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—112no—
268C2×C22⋊C4—112no—
269C2×C22⋊C4—112no—
270C2×C22⋊C4—112no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—221no—
274C2×C22⋊C4—221no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—221no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4C22⋊D1112yes—
283C2×C42—222no—
284#95—222no—
285#95—222no—
286#95—222no—
287#95—222no—
288#95—222no—
289C2×C11—22no—
290C2×C11—22no—
291C2×C11—41no—
292C2×C11—41no—
293C2×C11—41no—
294C2×C11—41no—
295C2×C11—41no—
296C2×C11#189011yescharacteristic
297C2×C11#189911yescharacteristic
298C2×C11#191311yescharacteristic
299C24—42no—
300C24—42no—
301C24—81no—
302C24C2×C4×D1111yescharacteristic
303C24#433911yescharacteristic
304C24D4×D1111yescharacteristic
305C24D4×D1111yescharacteristic
306C24D4×D1111yescharacteristic
307C24#434111yescharacteristic
308C24C2×C22⋊D1111yescharacteristic
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—81no—
319C22×C4—112no—
320C22×C4—112no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—222no—
326C22×C4—222no—
327C22×C4—442no—
328C22×C4—441no—
329C22×C4—881no—
330C4⋊C4—882no—
331C4⋊C4—882no—
332C22⋊C4—42no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—81no—
341C22⋊C4—81no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—222no—
345C22⋊C4—222no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C22⋊C4—442no—
352C22⋊C4—881no—
353C22⋊C4—881no—
354C22⋊C4—881no—
355C42—882no—
356C11#950011yescharacteristic, complemented, Sylow
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—22no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—88no—
379C23C22⋊C4×D1111yescharacteristic
380C23(C22⋊D11)⋊C411yescharacteristic
381C23#6693611yescharacteristic
382C23#6693711yescharacteristic
383C23C4×C22⋊D1111yescharacteristic
384C23#6699011yescharacteristic
385C23#6699111yescharacteristic
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—881no—
413C2×C4—881no—
414C2×C4—881no—
415C2×C4—881no—
416C2×C4—881no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—44no—
437C22—44no—
438C22—82no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22#1062235312yes—
444C22#1062256911yescharacteristic
445C22#1062266612yes—
446C4—82no—
447C4—81no—
448C4—81no—
449C4—161no—
450C4—442no—
451C4—442no—
452C4—882no—
453C4—882no—
454C4—1761no—
455C2—22no—
456C2—22no—
457C2—41no—
458C2—41no—
459C2—41no—
460C2—41no—
461C2—41no—
462C2#1306902611yescharacteristic
463C2#1306907111yescharacteristic
464C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#1819C2
socleC22×C11#386
prime radical, cosocleC25×C11C23
hypercenter#1819D11
hypocenterC11#9500
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
15. #10622824C4semidirect
16. #10622823C4semidirect
356. C11#9500semidirect

Maximal subgroups

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

subgroupindex
#130728942
#130712122
#130686902
#130686882
C11⋊#13042
C11×#18192
#950011