Finite Group Databasebeta

← #14656926

Subgroups — #14656926

Order 2816.

466 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 95 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#13073628C211yesmaximal, characteristic
2#13069602C211yesmaximal, characteristic
3C2×#10622176C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066483C211yesmaximal, characteristic
6#13066463C211yesmaximal, characteristic
7C11×#1520C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66931—21no—
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12#10622825C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14C2×C11⋊#95C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16#10622597—21no—
17#10622592—21no—
18#10622559—21no—
19#10622260—21no—
20#10622259—21no—
21C11×#328—21no—
22C11×#328—21no—
23#10622176—21no—
24#10622176—21no—
25#10622164—21no—
26#10622164—21no—
27C22×Q8×C11Q811yescharacteristic, complemented
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C22×Dic22—21no—
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⋊C4Q811yescharacteristic, complemented
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11D411yescharacteristic
43C2×C22⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C22×C11⋊C8—21no—
52#66931—42no—
53#66931—42no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95D411yescharacteristic
64C11⋊#95D411yescharacteristic
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#10375—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—81no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—81no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×Q811yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—42no—
88C22×Dic11—41no—
89C22×Dic11—41no—
90C22×Dic11—41no—
91C22×Dic11—81no—
92C2×Dic22—42no—
93C2×Dic22—42no—
94C2×Dic22—81no—
95C2×C8×C11—41no—
96C2×C8×C11—81no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—81no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C22⋊Dic11—21no—
107C22⋊Dic11—21no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11SD1612yes—
111C22⋊Dic11Q1612yes—
112C4⋊Dic11—42no—
113C4⋊Dic11—81no—
114Dic11⋊C4—42no—
115Dic11⋊C4—42no—
116Dic11⋊C4—42no—
117Dic11⋊C4—81no—
118C4×Dic11—81no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—81no—
121#2549—111no—
122#1996—111no—
123#1520D1111yescharacteristic
124C2×#328—111no—
125#1294—111no—
126#1289—111no—
127#1282—111no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11#12011yescharacteristic
131C23×C11C22⋊Q811yescharacteristic
132C23×C11#12411yescharacteristic
133C23×C11C2×SD1611yescharacteristic
134C23×C11C2×Q1611yescharacteristic
135C23×C11AGL(1,ℤ/8)11yescharacteristic
136C23×C11#13711yescharacteristic
137Q8×C11—81no—
138Q8×C11—81no—
139C2×C4×C11—41no—
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—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11C22⋊Q811yescharacteristic
156C2×C4×C11C22⋊Q811yescharacteristic
157C2×C4×C11#12411yescharacteristic
158C2×C4×C11#12411yescharacteristic
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—82no—
172C2×Dic11—82no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176Dic22—84no—
177C8×C11—81no—
178C11⋊C8—81no—
179C2×C22⋊Q8—221no—
180C2×C22⋊Q8C2×D1111yescharacteristic
181C2×C22⋊C8—111no—
182C2×C22⋊C8C2×D1111yescharacteristic
183#398—221no—
184#395—221no—
185#391—221no—
186#389—221no—
187#385—221no—
188#380—111no—
189#380C2×D1111yescharacteristic
190C4×C22⋊C4—111no—
191C2×#95—111no—
192#342—221no—
193#342—221no—
194#328—21no—
195#328—21no—
196#328—221no—
197#328—221no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11#39311yescharacteristic
209C22×C11#45011yescharacteristic
210C22×C11#45111yescharacteristic
211C22×C11#47511yescharacteristic
212C22×C11#47711yescharacteristic
213C22×C11#48711yescharacteristic
214C22×C11#48911yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11—81no—
223Dic11—42no—
224Dic11—42no—
225Dic11—42no—
226Dic11—81no—
227Dic11—161no—
228C22×Q8—221no—
229C22×Q8Dic2211yescharacteristic, complemented
230C23×C4—221no—
231C23×C4C22×D1111yescharacteristic
232C22×C8—21no—
233C22×C8—221no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—442no—
239C22⋊Q8—442no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4Dic2211yescharacteristic, complemented
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—111no—
253C2×C22⋊C4—221no—
254C2×C42—221no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—221no—
258C22⋊C8—221no—
259#95—111no—
260#95—111no—
261#95—221no—
262#95—221no—
263#95—221no—
264#95—221no—
265#95—221no—
266#95C22⋊D1111yescharacteristic
267#95C22⋊D1111yescharacteristic
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—21no—
274C2×C11#202411yescharacteristic
275C2×C11#203111yescharacteristic
276C2×C11#203211yescharacteristic
277C24D4×D1111yescharacteristic
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—81no—
281C2×Q8—442no—
282C2×Q8—442no—
283C2×Q8—881no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—81no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—442no—
294C22×C4—441no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4—881no—
298C22×C4C2×Dic2211yescharacteristic
299C22×C4#433911yescharacteristic
300C22×C4D4×D1111yescharacteristic
301C22×C4#434111yescharacteristic
302C22×C4#434111yescharacteristic
303C22×C4C2×C22⋊D1111yescharacteristic
304C2×C8—41no—
305C2×C8—81no—
306C2×C8—441no—
307C2×C8—881no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—81no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C4⋊C4—442no—
317C4⋊C4—881no—
318C4⋊C4—881no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—112no—
324C22⋊C4—112no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42—881no—
330C11#1037511yescharacteristic, complemented, Sylow
331C23—41no—
332C23—41no—
333C23#6693111yescharacteristic
334C23#6693811yescharacteristic
335C23SD16×D1111yescharacteristic
336C23#6696711yescharacteristic
337C23Q16×D1111yescharacteristic
338C23#6697111yescharacteristic
339C23#6699011yescharacteristic
340Q8—81no—
341Q8—81no—
342Q8—884no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—882no—
372C2×C4—882no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4—881no—
376C2×C4#6693111yescharacteristic
377C2×C4#6693811yescharacteristic
378C2×C4#6697711yescharacteristic
379C2×C4#6698911yescharacteristic
380C8—81no—
381C8—881no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#1062240411yescharacteristic
393C22#1062240511yescharacteristic
394C22#1062240711yescharacteristic
395C22#1062240811yescharacteristic
396C22#1062256011yescharacteristic
397C22#1062278211yescharacteristic
398C22#1062279911yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—81no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4—442no—
408C4—442no—
409C4—442no—
410C4—881no—
411C4—1761no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—21no—
416C2—21no—
417C2—21no—
418C2#1306975511yescharacteristic
419C2#1306978611yescharacteristic
420C2#1306979311yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#393
prime radicalC24×C11C2×D4
hypercenter#1520D11
hypocenterC11#10375
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
27. C22×Q8×C11Q8semidirect
38. C2×C11×C4⋊C4Q8semidirect
229. C22×Q8Dic22semidirect
248. C2×C4⋊C4Dic22semidirect
330. C11#10375semidirect

Maximal subgroups

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

subgroupindex
#130736282
#130696022
C2×#106221762
#130664962
#130664832
#130664632
C11×#15202
#1037511