Finite Group Databasebeta

← #14649820

Subgroups — #14649820

Order 2816.

560 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 113 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#13074432C211yesmaximal, characteristic
2#13071233C211yesmaximal, characteristic
3#13067189C211yesmaximal, characteristic
4#13067187C211yesmaximal, characteristic
5C2×#10622107C211yesmaximal, characteristic
6#13066483C211yesmaximal, characteristic
7C11×#1289C211yesmaximal, characteristic
8C2×#66977C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×#66930—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C11×#380C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16#10622596—22no—
17#10622585—22no—
18#10622563—21no—
19#10622556—21no—
20#10622555—21no—
21#10622272C412yescomplemented
22#10622269C412yescomplemented
23#10622260—22no—
24#10622107—22no—
25#10622105—22no—
26#10622090—22no—
27C23×C4×C11C2311yescharacteristic
28C23×Dic11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×Dic22C2×C411yescharacteristic
31C22×C8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41#66977—21no—
42#66977—21no—
43#66977—21no—
44#66977—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—22no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4C2×C412yes—
53C2×Dic11⋊C4D412yes—
54C2×C4×Dic11—22no—
55C22×C11⋊C8—21no—
56#66930—42no—
57#66930—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95C2×C412yes—
61C11×#95D412yes—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#9200—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—81no—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—22no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—81no—
90C22×Dic11C22⋊C412yes—
91C22×Dic11C22⋊C412yes—
92C22×Dic11SD1612yes—
93C22×Dic11Q1612yes—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—81no—
97C2×C8×C11—41no—
98C2×C8×C11—81no—
99C11×C4⋊C4—81no—
100C11×C4⋊C4—81no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—81no—
112C4⋊Dic11—82no—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116Dic11⋊C4—22no—
117Dic11⋊C4—44no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—82no—
121C4×Dic11—44no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—81no—
124#2627—111no—
125#2316—111no—
126#1520—111no—
127#1520—111no—
128C2×#324—111no—
129#1289—111no—
130#1289D1111yescharacteristic
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#12011yescharacteristic
135C23×C11#12311yescharacteristic
136C23×C11C2×SD1611yescharacteristic
137C23×C11C2×Q1611yescharacteristic
138C23×C11AGL(1,ℤ/8)11yescharacteristic
139C23×C11#13711yescharacteristic
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11C4×D411yescharacteristic
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—81no—
173C2×Dic11#10314yes—
174Dic22—81no—
175Dic22—81no—
176C8×C11—81no—
177C11⋊C8—81no—
178C2×C22⋊Q8—111no—
179C2×#117—221no—
180C22×C4⋊C4—111no—
181C2×C22⋊C8—111no—
182C2×C22⋊C8C2×D1111yescharacteristic
183#400—112no—
184#398—222no—
185#395—112no—
186#389—222no—
187#389—222no—
188#385—221no—
189#381—221no—
190#380—111no—
191#380—221no—
192#380C2×D1111yescharacteristic
193#380C2×D1111yescharacteristic
194#328—222no—
195#328—222no—
196#324—222no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11#38611yescharacteristic
208C22×C11C2×#10311yescharacteristic
209C22×C11#41711yescharacteristic
210C22×C11#45011yescharacteristic
211C22×C11#45111yescharacteristic
212C22×C11#48311yescharacteristic
213C22×C11#48411yescharacteristic
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—82no—
219C4×C11—82no—
220Dic11—24no—
221Dic11—42no—
222Dic11—82no—
223Dic11—81no—
224Dic11—81no—
225C22×Q8—111no—
226C23×C4—111no—
227C23×C4—111no—
228C23×C4C22×D1111yescharacteristic
229C22×C8—21no—
230C22×C8—221no—
231C22⋊Q8—221no—
232C22⋊Q8—221no—
233C22⋊Q8—221no—
234C22⋊Q8—221no—
235#117—442no—
236#117—442no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—112no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—222no—
249C2×C4⋊C4—222no—
250C2×C4⋊C4—221no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C42—222no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260#95—112no—
261#95—222no—
262#95—222no—
263#95—222no—
264#95—222no—
265#95C4×D1112yes—
266#95D4412yes—
267C2×C11—21no—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11#187211yescharacteristic
274C2×C11#191211yescharacteristic
275C2×C11#191311yescharacteristic
276C24D4×D1111yescharacteristic
277C2×Q8—221no—
278C2×Q8—221no—
279C2×Q8—881no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—81no—
283C22×C4—112no—
284C22×C4—112no—
285C22×C4—112no—
286C22×C4—112no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—222no—
296C22×C4—881no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4C2×D4411yescharacteristic
299C22×C4#433911yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4D4×D1111yescharacteristic
302C22×C4#434311yescharacteristic
303C2×C8—41no—
304C2×C8—81no—
305C2×C8—441no—
306C2×C8—881no—
307C4⋊C4—81no—
308C4⋊C4—81no—
309C4⋊C4—222no—
310C4⋊C4—222no—
311C4⋊C4—222no—
312C4⋊C4—222no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—444no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—882no—
319C4⋊C4—881no—
320C4⋊C4—882no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42—444no—
330C11#920011yescharacteristic, complemented, Sylow
331C23—41no—
332C23—41no—
333C23C22⋊C4×D1111yescharacteristic
334C23#6693511yescharacteristic
335C23#6694711yescharacteristic
336C23#6696411yescharacteristic
337C23SD16×D1111yescharacteristic
338C23#6696811yescharacteristic
339C23Q16×D1111yescharacteristic
340Q8—881no—
341Q8—881no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—114no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—442no—
371C2×C4—881no—
372C2×C4C4×D4411yescharacteristic
373C2×C4#6693711yescharacteristic
374C2×C4#6694611yescharacteristic
375C2×C4#6694811yescharacteristic
376C8—81no—
377C8—881no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22#1062227811yescharacteristic
389C22#1062238411yescharacteristic
390C22#1062238911yescharacteristic
391C22D11×#10311yescharacteristic
392C22#1062242111yescharacteristic
393C22#1062247511yescharacteristic
394C22#1062249711yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—82no—
401C4—224no—
402C4—442no—
403C4—882no—
404C4—881no—
405C4—881no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2—21no—
411C2—21no—
412C2#1306892211yescharacteristic
413C2#1306915211yescharacteristic
414C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1289C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1289D11
hypocenterC11#9200
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
21. #10622272C4semidirect
22. #10622269C4semidirect
330. C11#9200semidirect

Maximal subgroups

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

subgroupindex
#130744322
#130712332
#130671892
#130671872
C2×#106221072
#130664832
C11×#12892
#920011