Finite Group Databasebeta

← #14647283

Subgroups — #14647283

Order 2816.

538 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 83 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#13071212C211yesmaximal, characteristic
2#13068688C211yesmaximal, characteristic
3#13068688C211yesmaximal, characteristic
4C11⋊#1304C211yesmaximal, characteristic
5C11⋊#1304C211yesmaximal, characteristic
6C11⋊#1304C211yesmaximal, characteristic
7C11×#1304C211yesmaximal, characteristic
8C22×C22⋊Dic11C2211yescharacteristic
9C11×#379C2211yescharacteristic
10C11×#379C2211yescharacteristic
11C11×#379C2211yescharacteristic
12#10622860C2211yescharacteristic
13#10622860C2211yescharacteristic
14#10622860C2211yescharacteristic
15#10622558—22no—
16#10622557—22no—
17#10622555C412yescomplemented
18C22⋊C4×Dic11C412yescomplemented
19#10622165—22no—
20#10622165—22no—
21C25×C11C2311yescharacteristic
22C23×Dic11C2×C411yescharacteristic
23C23×Dic11C2×C411yescharacteristic
24C2×C11×C22⋊C4—21no—
25C2×C11×C22⋊C4—21no—
26C2×C11×C22⋊C4—21no—
27C2×C11×C22⋊C4—21no—
28C2×C11×C22⋊C4—21no—
29C2×C11×C22⋊C4—21no—
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4C2×C412yes—
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11C2×C412yes—
46C2×C22⋊Dic11D412yes—
47C2×C22⋊Dic11D412yes—
48C2×Dic11⋊C4—22no—
49C2×C4×Dic11—22no—
50C11⋊#95—22no—
51C11⋊#95—22no—
52#8750—111nomaximal, Sylow
53C24×C11—42no—
54C24×C11—81no—
55C24×C11—81no—
56C24×C11C22×C411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C24×C11C2×D411yescharacteristic
59C24×C11#4111yescharacteristic
60C24×C11#4111yescharacteristic
61C24×C11#4111yescharacteristic
62C24×C11#4111yescharacteristic
63C22×C4×C11—22no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×Dic11—22no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—41no—
72C22×Dic11—41no—
73C22×Dic11—81no—
74C22×Dic11—81no—
75C22×Dic11C22⋊C412yes—
76C22×Dic11C22⋊C412yes—
77C11×C22⋊C4—42no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—81no—
81C11×C22⋊C4—81no—
82C11×C22⋊C4—81no—
83C11×C22⋊C4—81no—
84C11×C22⋊C4—81no—
85C11×C22⋊C4—81no—
86C22⋊Dic11—22no—
87C22⋊Dic11—22no—
88C22⋊Dic11—22no—
89C22⋊Dic11—22no—
90C22⋊Dic11—42no—
91C22⋊Dic11—42no—
92C22⋊Dic11—42no—
93C22⋊Dic11—81no—
94C22⋊Dic11—81no—
95C22⋊Dic11—81no—
96C22⋊Dic11—81no—
97C22⋊Dic11—81no—
98C22⋊Dic11—81no—
99Dic11⋊C4—82no—
100C4×Dic11—82no—
101#2312—111no—
102#1819—111no—
103#1819—111no—
104#1304—111no—
105#1304—111no—
106#1304—111no—
107#1304D1111yescharacteristic
108C23×C11—22no—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—88no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#11711yescharacteristic
132C23×C11#11711yescharacteristic
133C23×C11#12311yescharacteristic
134C23×C11#12311yescharacteristic
135C23×C11#12311yescharacteristic
136C23×C11#12311yescharacteristic
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×Dic11—22no—
147C2×Dic11—22no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163C22×C22⋊C4—111no—
164#388—222no—
165#388—222no—
166#380—112no—
167#379—111no—
168#379—111no—
169#379—111no—
170#379C2×D1111yescharacteristic
171#379C2×D1111yescharacteristic
172#379C2×D1111yescharacteristic
173C4×C22⋊C4—112no—
174#342—222no—
175#342—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—44no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11—82no—
203C22×C11#38111yescharacteristic
204C22×C11#41012yes—
205C4×C11—82no—
206C4×C11—161no—
207C4×C11—161no—
208Dic11—42no—
209Dic11—42no—
210Dic11—82no—
211Dic11—161no—
212Dic11—161no—
213C25C22×D1111yescharacteristic
214C23×C4—111no—
215C23×C4—111no—
216C2×C4⋊C4—222no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—112no—
226C2×C22⋊C4—112no—
227C2×C22⋊C4—112no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4C4×D1112yes—
241C2×C42—222no—
242#95—222no—
243#95—222no—
244C2×C11—22no—
245C2×C11—41no—
246C2×C11—41no—
247C2×C11—41no—
248C2×C11—41no—
249C2×C11—41no—
250C2×C11—41no—
251C2×C11#182011yescharacteristic
252C2×C11#182811yescharacteristic
253C2×C11#182811yescharacteristic
254C24—42no—
255C24—81no—
256C24—81no—
257C24C2×C4×D1111yescharacteristic
258C24#433911yescharacteristic
259C24#433911yescharacteristic
260C24D4×D1111yescharacteristic
261C24D4×D1111yescharacteristic
262C24#434111yescharacteristic
263C24#434311yescharacteristic
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—112no—
268C22×C4—112no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—222no—
274C22×C4—441no—
275C22×C4—441no—
276C22×C4—881no—
277C22×C4—881no—
278C4⋊C4—882no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—81no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C22⋊C4—81no—
286C22⋊C4—81no—
287C22⋊C4—81no—
288C22⋊C4—222no—
289C22⋊C4—222no—
290C22⋊C4—222no—
291C22⋊C4—222no—
292C22⋊C4—442no—
293C22⋊C4—442no—
294C22⋊C4—442no—
295C22⋊C4—881no—
296C22⋊C4—881no—
297C22⋊C4—881no—
298C22⋊C4—881no—
299C22⋊C4—881no—
300C22⋊C4—881no—
301C42—882no—
302C11#875011yescharacteristic, complemented, Sylow
303C23—22no—
304C23—22no—
305C23—22no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—88no—
325C23#6692511yescharacteristic
326C23C22⋊C4×D1111yescharacteristic
327C23#6693611yescharacteristic
328C23#6693611yescharacteristic
329C23#6694511yescharacteristic
330C23#6694711yescharacteristic
331C23#6694711yescharacteristic
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—222no—
342C2×C4—222no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—881no—
349C2×C4—881no—
350C2×C4—881no—
351C2×C4—881no—
352C2×C4—881no—
353C2×C4—881no—
354C2×C4—881no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4—881no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22#1062227711yescharacteristic
386C22#1062235312yes—
387C4—82no—
388C4—161no—
389C4—161no—
390C4—442no—
391C4—442no—
392C4—882no—
393C4—1761no—
394C4—1761no—
395C2—22no—
396C2—41no—
397C2—41no—
398C2—41no—
399C2—41no—
400C2—41no—
401C2—41no—
402C2#1306869211yescharacteristic
403C2#1306872311yescharacteristic
404C2#1306872311yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#1304C2
socleC22×C11#381
prime radical, cosocleC25×C11C23
hypercenter#1304D11
hypocenterC11#8750
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
17. #10622555C4semidirect
18. C22⋊C4×Dic11C4semidirect
302. C11#8750semidirect

Maximal subgroups

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

subgroupindex
#130712122
#130686882
C11⋊#13042
C11×#13042
#875011