Finite Group Databasebeta

← #14666877

Subgroups — #14666877

Order 2816.

468 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069780C211yesmaximal, characteristic
2#13067606C211yesmaximal, characteristic, complemented
3#13067572C211yesmaximal, characteristic, complemented
4#13066637C211yesmaximal, characteristic, complemented
5#13066616C211yesmaximal, characteristic, complemented
6#13066544C211yesmaximal, characteristic
7C11×#2736C211yesmaximal, characteristic
8#10623014C2211yescharacteristic
9C11×#397—21no—
10C11×#397C2211yescharacteristic
11C11×#393—21no—
12C11×#393C2211yescharacteristic
13C11×#388—21no—
14C11×#388—21no—
15C11×#388—21no—
16C11×#379—21no—
17C11×#379C2211yescharacteristic
18#10622860—21no—
19#10622841—21no—
20#10622584—21no—
21#10622165—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622090—21no—
26#10622090—21no—
27C25×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4—21no—
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⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C42×C11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—41no—
45C2×C22⋊Dic11—41no—
46C2×#4326—41no—
47#66977—21no—
48#66977—21no—
49#66931—41no—
50#66931—41no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95D411yescharacteristic
56C11×#95D411yescharacteristic
57#66899—41no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66874—41no—
61#66872—41no—
62#12264—111nomaximal, Sylow
63C24×C11—21no—
64C24×C11—21no—
65C24×C11—21no—
66C24×C11—41no—
67C24×C11—41no—
68C24×C11—42no—
69C24×C11—81no—
70C24×C11C2×D411yescharacteristic
71C2×Q8×C11—41no—
72C2×Q8×C11—81no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—81no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—42no—
89C11×C22⋊C4—42no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—81no—
94C11×C22⋊C4—81no—
95C11×C22⋊C4—81no—
96C11×C22⋊C4—81no—
97C11×C22⋊C4—81no—
98C42×C11—81no—
99C22⋊Dic11—41no—
100C22⋊Dic11—41no—
101C22⋊Dic11—41no—
102C22⋊Dic11—41no—
103C22⋊Dic11—82no—
104C22⋊Dic11—82no—
105#4326—82no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#2736D1111yescharacteristic
113#2029—111no—
114#1608—111no—
115#1602—111no—
116#1351—111no—
117#1344—111no—
118#1316—111no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—22no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—81no—
134C23×C11—82no—
135C23×C11—81no—
136C23×C11—82no—
137C23×C11—84no—
138C23×C11—81no—
139C23×C11#12011yescharacteristic
140C23×C11#13511yescharacteristic
141C23×C11#13711yescharacteristic
142Q8×C11—42no—
143Q8×C11—81no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
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—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170Dic22—81no—
171Dic22—81no—
172C11⋊C8—81no—
173C11⋊C8—81no—
174#543—111no—
175#483—221no—
176#451—221no—
177#397—21no—
178#397C2×D1111yescharacteristic
179#393—21no—
180#393C2×D1111yescharacteristic
181#388—21no—
182#388—21no—
183#388—21no—
184#379—21no—
185#379—221no—
186#379C2×D1111yescharacteristic
187#342—111no—
188#342—221no—
189#328—221no—
190#328—221no—
191#323—111no—
192#323—111no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—42no—
200C22×C11—42no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—44no—
204C22×C11—42no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11#45211yescharacteristic
214C22×C11#45511yescharacteristic
215C22×C11B(4,𝔽2)11yescharacteristic
216C4×C11—41no—
217C4×C11—41no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11—81no—
223Dic11—81no—
224Dic11—81no—
225Dic11—161no—
226C25C22⋊D1111yescharacteristic
227C22×Q8C22⋊D1111yescharacteristic
228C2×Q16—441no—
229C22⋊Q8—221no—
230C22⋊Q8—221no—
231C22⋊Q8—441no—
232C22⋊Q8—441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C22⋊D1111yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—441no—
246C2×C22⋊C4—441no—
247C2×C22⋊C4C22⋊D1111yescharacteristic
248C2×C22⋊C4C22×D1111yescharacteristic
249C2×C42—21no—
250#106—441no—
251#103—441no—
252#103—441no—
253C22⋊C8—221no—
254C22⋊C8—221no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95C22⋊D1111yescharacteristic
260#95C22⋊D1111yescharacteristic
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—41no—
264C2×C11—41no—
265C2×C11—82no—
266C2×C11#160611yescharacteristic
267C2×C11#219711yescharacteristic
268C2×C11#219911yescharacteristic
269C24—21no—
270C24—21no—
271C24—21no—
272C24—41no—
273C24—41no—
274C24—42no—
275C24—81no—
276C24C2×C22⋊D1111yescharacteristic
277C2×Q8—41no—
278C2×Q8—81no—
279C2×Q8—221no—
280C2×Q8—221no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—441no—
289C22×C4C2×C22⋊D1111yescharacteristic
290C22×C4C2×C22⋊D1111yescharacteristic
291Q16—882no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—41no—
295C4⋊C4—81no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—41no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—81no—
307C22⋊C4—81no—
308C22⋊C4—81no—
309C22⋊C4—81no—
310C22⋊C4—81no—
311C22⋊C4—441no—
312C22⋊C4—441no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—882no—
316C22⋊C4—882no—
317C42—81no—
318C11#1226411yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—81no—
334C23—82no—
335C23—81no—
336C23—82no—
337C23—84no—
338C23—81no—
339C23#6700311yescharacteristic
340C23#6700411yescharacteristic
341C23#6700611yescharacteristic
342Q8—42no—
343Q8—81no—
344Q8—881no—
345Q8—881no—
346C2×C4—21no—
347C2×C4—21no—
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—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—881no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4—881no—
371C2×C4—881no—
372C8—881no—
373C8—881no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—42no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—44no—
385C22—42no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—81no—
393C22—81no—
394C22#1062285211yescharacteristic
395C22#1062285511yescharacteristic
396C22#1062285711yescharacteristic
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—881no—
405C4—881no—
406C4—1761no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—82no—
412C2#1306759611yescharacteristic
413C2#1307060611yescharacteristic
414C2#1307061711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2736C2
socleC22×C11B(4,𝔽2)
prime radicalC25×C11D4
hypercenter#2736D11
hypocenterC11#12264
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2736

Complements

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

NH ≅ G/Ntype
2. #13067606C2semidirect
3. #13067572C2semidirect
4. #13066637C2semidirect
5. #13066616C2semidirect
318. C11#12264semidirect

Maximal subgroups

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

subgroupindex
#130697802
#130676062
#130675722
#130666372
#130666162
#130665442
C11×#27362
#1226411