Finite Group Databasebeta

← #14649818

Subgroups — #14649818

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#13074431C211yesmaximal, characteristic
2#13071233C211yesmaximal, characteristic
3#13067188C211yesmaximal, characteristic
4C2×#10622107C211yesmaximal, characteristic
5#13066484C211yesmaximal, characteristic
6#13066483C211yesmaximal, characteristic
7C11×#1520C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×#66930—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622842C412yescomplemented
14#10622825C2211yescharacteristic
15#10622825C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622597—22no—
18#10622595C412yescomplemented
19#10622585—22no—
20#10622559—21no—
21#10622556—21no—
22#10622555—21no—
23#10622260—22no—
24C11×#328—22no—
25#10622176—22no—
26#10622107—22no—
27C22×Q8×C11C2×C411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C23×Dic11D411yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×C8×C11—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—22no—
50C2×Dic11⋊C4—22no—
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×#95D412yes—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95C2×C412yes—
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#9200—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—81no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—81no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—81no—
93C22×Dic11C22⋊C412yes—
94C22×Dic11C22⋊C412yes—
95C22×Dic11SD1612yes—
96C22×Dic11Q1612yes—
97C2×C8×C11—41no—
98C2×C8×C11—81no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—81no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C4⋊Dic11—81no—
113C4⋊Dic11—81no—
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116Dic11⋊C4—22no—
117Dic11⋊C4—22no—
118Dic11⋊C4—44no—
119Dic11⋊C4—82no—
120Dic11⋊C4—82no—
121C4×Dic11—44no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—81no—
124#2627—111no—
125#2316—111no—
126#1520—111no—
127#1520D1111yescharacteristic
128C2×#324—111no—
129#1289—111no—
130#1289—111no—
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
140Q8×C11—81no—
141Q8×C11—81no—
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—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—22no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—81no—
175C2×Dic11#10314yes—
176C8×C11—81no—
177C11⋊C8—81no—
178C2×C22⋊Q8C2×D1111yescharacteristic
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—111no—
192#380—221no—
193#380C2×D1111yescharacteristic
194#328—22no—
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—81no—
220C4×C11—81no—
221Dic11—24no—
222Dic11—42no—
223Dic11—82no—
224Dic11—82no—
225C22×Q8C4×D1111yescharacteristic
226C23×C4—111no—
227C23×C4—111no—
228C23×C4C22×D1111yescharacteristic
229C22×C8—21no—
230C22×C8—221no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
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—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—222no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4C4×D1111yescharacteristic
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—112no—
262#95—222no—
263#95—222no—
264#95—222no—
265#95—222no—
266#95C22⋊D1112yes—
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—21no—
278C2×Q8—21no—
279C2×Q8—81no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—81no—
284C22×C4—112no—
285C22×C4—112no—
286C22×C4—112no—
287C22×C4—112no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—881no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4#433911yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4#434111yescharacteristic
302C22×C4C2×C22⋊D1111yescharacteristic
303C2×C8—41no—
304C2×C8—81no—
305C2×C8—441no—
306C2×C8—881no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—81no—
312C4⋊C4—222no—
313C4⋊C4—222no—
314C4⋊C4—222no—
315C4⋊C4—222no—
316C4⋊C4—444no—
317C4⋊C4—882no—
318C4⋊C4—882no—
319C4⋊C4—881no—
320C4⋊C4—881no—
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#6693611yescharacteristic
335C23SD16×D1111yescharacteristic
336C23#6696711yescharacteristic
337C23Q16×D1111yescharacteristic
338C23#6697111yescharacteristic
339C23#6699011yescharacteristic
340Q8—81no—
341Q8—81no—
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—41no—
354C2×C4—41no—
355C2×C4—114no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—881no—
372C2×C4(C22⋊D11)⋊C411yescharacteristic
373C2×C4#6693711yescharacteristic
374C2×C4C4×C22⋊D1111yescharacteristic
375C2×C4#6699111yescharacteristic
376C8—81no—
377C8—881no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22D11×#10311yescharacteristic
389C22#1062241611yescharacteristic
390C22#1062241811yescharacteristic
391C22#1062242211yescharacteristic
392C22#1062256911yescharacteristic
393C22#1062278211yescharacteristic
394C22#1062279911yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—81no—
401C4—81no—
402C4—224no—
403C4—442no—
404C4—882no—
405C4—882no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2—21no—
410C2—21no—
411C2—21no—
412C2#1306892011yescharacteristic
413C2#1306915011yescharacteristic
414C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1520D11
hypocenterC11#9200
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
13. #10622842C4semidirect
18. #10622595C4semidirect
330. C11#9200semidirect

Maximal subgroups

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

subgroupindex
#130744312
#130712332
#130671882
C2×#106221072
#130664842
#130664832
C11×#15202
#920011