Finite Group Databasebeta

← #14654303

Subgroups — #14654303

Order 2816.

1160 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#10622649C212yesmaximal, complemented
2C2×#10622175C212yesmaximal, complemented
3#13066856C211yesmaximal, characteristic, complemented
4#13066459C211yesmaximal, characteristic, complemented
5C11×#2656C211yesmaximal, characteristic, complemented
6C23×D44C2211yescharacteristic
7C2×C11×#121—22no—
8C2×C11×#121C2212yes—
9C22×#4323—22no—
10C22×(C2×D11)⋊C4—22no—
11C11×#399—22no—
12C11×#392—22no—
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622649—24no—
17#10622649—24no—
18C2×#66873—22no—
19#10622175—24no—
20C24×D11—21no—
21C22×D4×C11—22no—
22C22×D4×C11—22no—
23C22×D4×C11D412yes—
24C23×C4×C11D412yes—
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—21no—
27C22×D44—22no—
28C22×D44—22no—
29C22×D44—21no—
30C22×D44—44no—
31C22×D44D412yescomplemented
32C11×#121—22no—
33C11×#121—22no—
34C11×#121—22no—
35C11×#121—22no—
36C11×#121—44no—
37C11×#121—44no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4D412yes—
40C2×C11×C22⋊C4—24no—
41C2×C11×C22⋊C4—22no—
42C2×#4323—28no—
43C2×#4323—48no—
44C2×(C2×D11)⋊C4—44no—
45C2×(C2×D11)⋊C4—44no—
46C2×(C2×D11)⋊C4—44no—
47C22×C11⋊C8—22no—
48C11×#95—22no—
49C11⋊#95—22no—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)D414yescomplemented
52#66873—28no—
53#9962—111nomaximal, Sylow
54C24×C11—22no—
55C24×C11C2×D411yescharacteristic
56C23×D11—24no—
57C23×D11—22no—
58C23×D11—42no—
59C23×D11—42no—
60C23×D11—42no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11—42no—
64C23×D11—42no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—44no—
68C2×D4×C11—44no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—44no—
72C2×D4×C11—44no—
73C2×D4×C11—82no—
74C2×D4×C11—82no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11D814yescomplemented
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D412yes—
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—22no—
87C22×Dic11—42no—
88C22×Dic11—41no—
89C22×Dic11—41no—
90C22×Dic11—42no—
91C2×D44—28no—
92C2×D44—24no—
93C2×D44—44no—
94C2×D44—44no—
95C2×D44—44no—
96C2×D44—48no—
97C2×D44—42no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—44no—
101C11×C22⋊C4—48no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—42no—
104#4323—416no—
105(C2×D11)⋊C4—416no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—44no—
108C2×#447—112no—
109#2656D1111yescharacteristic, complemented
110C2×#327—112no—
111#1438—111no—
112#1280—111no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—22no—
116C23×C11—42no—
117C23×C11—44no—
118C23×C11—42no—
119C23×C11—42no—
120C23×C11—44no—
121C23×C11#12011yescharacteristic
122C23×C11#12111yescharacteristic
123C23×C11#12711yescharacteristic
124C23×C11C2×D812yes—
125C23×C11AGL(1,ℤ/8)12yes—
126C22×D11—24no—
127C22×D11—44no—
128C22×D11—42no—
129C22×D11—44no—
130C22×D11—44no—
131C22×D11—44no—
132C22×D11—44no—
133C22×D11—44no—
134C22×D11—42no—
135C22×D11—44no—
136C22×D11—44no—
137C22×D11—82no—
138C22×D11—82no—
139C22×D11—82no—
140C22×D11—82no—
141C22×D11—82no—
142C22×D11—82no—
143C22×D11—81no—
144C22×D11—81no—
145C22×D11—81no—
146C22×D11—81no—
147D4×C11—44no—
148D4×C11—82no—
149D4×C11—88no—
150D4×C11—84no—
151D4×C11—82no—
152D4×C11—82no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—44no—
163C2×C4×C11—82no—
164C2×C4×C11#12012yes—
165C2×C4×C11#12112yes—
166C2×Dic11—44no—
167C2×Dic11—42no—
168C2×Dic11—82no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171D44—28no—
172D44—44no—
173D44—48no—
174C11⋊C8—44no—
175C23×D4—111no—
176C22×D8—222no—
177C2×#121—22no—
178C2×#121C2×D1112yes—
179C22×C22⋊C4—222no—
180#447—224no—
181#447—224no—
182C2×#102—222no—
183C2×C22⋊C8—112no—
184#399—22no—
185#392—22no—
186C2×#95—111no—
187C2×#95C2×D1111yescharacteristic
188#327—224no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—84no—
198C22×C11—84no—
199C22×C11—82no—
200C22×C11—82no—
201C22×C11—82no—
202C22×C11#39211yescharacteristic
203C22×C11#44712yes—
204C22×C11#45311yescharacteristic
205C22×C11#45411yescharacteristic
206C22×C11B(4,𝔽2)12yes—
207C22×C11#45912yes—
208C22×C11#49311yescharacteristic
209C22×C11#49611yescharacteristic
210C2×D11—48no—
211C2×D11—44no—
212C2×D11—84no—
213C2×D11—84no—
214C2×D11—84no—
215C2×D11—84no—
216C2×D11—84no—
217C2×D11—82no—
218C2×D11—82no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—44no—
222C4×C11—82no—
223Dic11—82no—
224C25—221no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—112no—
228C22×D4—222no—
229C22×D4—221no—
230C22×D4—222no—
231C22×D4—444no—
232C22×D4C22⋊D1112yes—
233C23×C4—221no—
234C23×C4C22⋊D1112yes—
235C23×C4C22×D1111yescharacteristic
236C2×D8—228no—
237C2×D8—448no—
238C22×C8—222no—
239#121—22no—
240#121—22no—
241#121—22no—
242#121—22no—
243#121—44no—
244#121—44no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4C22⋊D1112yes—
247C2×C22⋊C4—24no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—444no—
250C2×C22⋊C4—444no—
251C2×C22⋊C4—444no—
252#102—228no—
253C22⋊C8—114no—
254C22⋊C8—222no—
255#95—22no—
256#95—222no—
257C2×C11—21no—
258C2×C11—22no—
259C2×C11—21no—
260C2×C11—162no—
261C2×C11#159512yes—
262C2×C11#159812yes—
263C2×C11#200611yescharacteristic
264C2×C11#201111yescharacteristic
265C2×C11#202111yescharacteristic
266D11—84no—
267C24—22no—
268C24—224no—
269C24—222no—
270C24—442no—
271C24—442no—
272C24—442no—
273C24—442no—
274C24—442no—
275C24—441no—
276C24—441no—
277C24C2×C22⋊D1111yescharacteristic
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—44no—
281C2×D4—44no—
282C2×D4—44no—
283C2×D4—44no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—82no—
287C2×D4—82no—
288C2×D4—228no—
289C2×D4—224no—
290C2×D4—444no—
291C2×D4—444no—
292C2×D4—448no—
293C2×D4—444no—
294C2×D4—442no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—222no—
302C22×C4—442no—
303C22×C4—441no—
304C22×C4—442no—
305C22×C4—441no—
306C22×C4#432314yescomplemented
307C22×C4D4×D1111yescharacteristic
308C22×C4D4×D1112yes—
309C22×C4#434111yescharacteristic
310C22×C4C2×C22⋊D1112yes—
311D8—4416no—
312C2×C8—224no—
313C2×C8—444no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—44no—
317C22⋊C4—48no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—4416no—
321C11#996211yescharacteristic, complemented, Sylow
322C23—21no—
323C23—22no—
324C23—21no—
325C23—44no—
326C23—42no—
327C23—42no—
328C23—44no—
329C23—42no—
330C23—224no—
331C23—444no—
332C23—444no—
333C23—442no—
334C23—444no—
335C23—444no—
336C23—444no—
337C23—444no—
338C23—442no—
339C23—444no—
340C23—444no—
341C23—882no—
342C23—882no—
343C23—882no—
344C23—882no—
345C23—882no—
346C23—882no—
347C23—881no—
348C23—881no—
349C23—881no—
350C23—881no—
351C23C2×#432312yes—
352C23#6698512yes—
353C23#6699111yescharacteristic
354C23#6699311yescharacteristic
355C23#6700611yescharacteristic
356D4—44no—
357D4—82no—
358D4—88no—
359D4—84no—
360D4—82no—
361D4—82no—
362D4—228no—
363D4—444no—
364D4—448no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—82no—
376C2×C4—444no—
377C2×C4—442no—
378C2×C4—882no—
379C2×C4—881no—
380C2×C4—881no—
381C2×C4#6699012yes—
382C2×C4#6699212yes—
383C8—444no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—84no—
393C22—84no—
394C22—82no—
395C22—82no—
396C22—82no—
397C22—448no—
398C22—444no—
399C22—884no—
400C22—884no—
401C22—884no—
402C22—884no—
403C22—884no—
404C22—882no—
405C22—882no—
406C22#1062268512yes—
407C22#1062268611yescharacteristic
408C22#1062268711yescharacteristic
409C22#1062283012yes—
410C22#1062283611yescharacteristic
411C22#1062285411yescharacteristic
412C22#1062285712yes—
413C22#1062285811yescharacteristic
414C4—22no—
415C4—22no—
416C4—44no—
417C4—82no—
418C4—882no—
419C2—21no—
420C2—22no—
421C2—21no—
422C2—162no—
423C2—884no—
424C2#1306753412yes—
425C2#1306755112yes—
426C2#1306965811yescharacteristic
427C2#1306968711yescharacteristic
428C2#1306974011yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2656C2
socleC23×C11#120
hypercenter#2656D11
hypocenterC11#9962
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2656

Complements

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

NH ≅ G/Ntype
1. C2×#10622649C2semidirect
2. C2×#10622175C2semidirect
3. #13066856C2semidirect
4. #13066459C2semidirect
5. C11×#2656C2semidirect
31. C22×D44D4semidirect
51. C22⋊(C11⋊C8)D4semidirect
81. C22×C4×C11D8semidirect
109. #2656D11semidirect
306. C22×C4#4323semidirect
321. C11#9962semidirect

Maximal subgroups

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

subgroupindex
C2×#106226492
C2×#106221752
#130668562
#130664592
C11×#26562
#996211