Finite Group Databasebeta

← #14727893

Subgroups — #14727893

Order 2816.

1172 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1172 conjugacy classes of subgroups — too many to draw. Only its 183 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#13079418C212yesmaximal, complemented
2#13073547C211yesmaximal, characteristic
3#13067641C214yesmaximal, complemented
4#13067539C214yesmaximal, complemented
5#13067136C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic, complemented
7C2×C11×#543C211yesmaximal, characteristic, complemented
8C11×#543—24no—
9C11×#543—22no—
10C11×#543C2214yes—
11C2×C11×C22⋊Q8—22no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×C22⋊Q8C2212yes—
15C22×C11×C22⋊C4—21no—
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×#67006—21no—
18C2×#66983C2211yescharacteristic
19C2×#66982—21no—
20#10622840—22no—
21C4×C22⋊Dic11C2211yescharacteristic
22#10622820C2212yes—
23#10622662—24no—
24#10622659C2214yescomplemented
25#10622657C2214yescomplemented
26#10622580—22no—
27#10622573C2212yes—
28#10622570—22no—
29#10622562C2212yes—
30#10622176C2218yescomplemented
31#10622163C2214yes—
32C25×C11D411yescharacteristic
33C22×Q8×C11—21no—
34C22×Q8×C11D412yescomplemented
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—21no—
40C22×C22⋊D11—22no—
41C22×D44C2311yescharacteristic
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—28no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8D414yescomplemented
51C11×C22⋊Q8C2314yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D412yescomplemented
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D412yes—
63C2×C11×C22⋊C4C2312yes—
64#67006—44no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—22no—
67C2×#4325—24no—
68#66983—22no—
69#66983—22no—
70#66982—44no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—21no—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—21no—
76C2×#4318—22no—
77#66899—24no—
78C11⋊#95C2312yes—
79C22⋊(C11⋊C8)—22no—
80C22⋊(C11⋊C8)C2314yes—
81#66873—24no—
82#66871—24no—
83#18318—111nomaximal, Sylow
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—24no—
87C24×C11—42no—
88C24×C11—81no—
89C24×C11C2×D411yescharacteristic
90C24×C11C2×D412yes—
91C23×D11—21no—
92C2×Q8×C11—24no—
93C2×Q8×C11—22no—
94C2×Q8×C11—82no—
95C2×Q8×C11—82no—
96C2×Q8×C11C2×D414yes—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C22×C4×C11—81no—
105C22×C4×C11—82no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C2×C22⋊D11—42no—
113C2×C22⋊D11—42no—
114C2×C22⋊D11—44no—
115C2×C22⋊D11—41no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—44no—
118C2×C22⋊D11—82no—
119C22×Dic11—22no—
120C22×Dic11—21no—
121C2×D44—22no—
122C2×D44—81no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—28no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C22⋊Dic11—24no—
135C22⋊Dic11—44no—
136#4325—84no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—42no—
139C4⋊Dic11—22no—
140Dic11⋊C4—44no—
141C4×Dic11—81no—
142#4318—82no—
143C2×C11⋊C8—24no—
144C2×#543D1111yescharacteristic, complemented
145#3193—112no—
146#2539—111no—
147#1614—114no—
148#1596—114no—
149#1508—112no—
150#1462—111no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—41no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11—88no—
165C23×C11#12011yescharacteristic
166C23×C11#12011yescharacteristic
167C23×C11#13714yes—
168C23×C11C22×D411yescharacteristic
169C22×D11—41no—
170C22×D11—42no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—42no—
174Q8×C11—44no—
175Q8×C11—82no—
176Q8×C11—84no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—44no—
185C2×C4×C11—42no—
186C2×C4×C11—44no—
187C2×C4×C11—42no—
188C2×C4×C11—81no—
189C2×C4×C11—84no—
190C2×C4×C11—84no—
191C2×C4×C11#12012yes—
192C2×C4×C11C22×D412yes—
193C22⋊D11—88no—
194C22⋊D11—82no—
195C22⋊D11—82no—
196C2×Dic11—24no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202D44—44no—
203C11⋊C8—44no—
204#543—24no—
205#543—22no—
206#543C2×D1114yes—
207C2×#123—221no—
208C2×C22⋊Q8—22no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—22no—
211C2×C22⋊Q8C2×D1112yes—
212C2×#121—111no—
213C2×#120—221no—
214C22×C22⋊C4—21no—
215C22×C22⋊C4C2×D1111yescharacteristic
216#484—114no—
217#480—222no—
218#468—224no—
219#450—114no—
220#448—222no—
221#407—112no—
222#399—112no—
223#392—112no—
224#390—222no—
225C4×C22⋊C4—111no—
226#328—118no—
227#323—114no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—24no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—44no—
237C22×C11—44no—
238C22×C11—48no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—82no—
242C22×C11—84no—
243C22×C11#45312yes—
244C22×C11C2×#12011yescharacteristic
245C22×C11C2×#13712yes—
246C2×D11—82no—
247C2×D11—82no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—81no—
251C4×C11—22no—
252C4×C11—22no—
253C4×C11—42no—
254C4×C11—44no—
255C4×C11—44no—
256Dic11—44no—
257Dic11—81no—
258C25C22⋊D1111yescharacteristic
259C22×Q8—21no—
260C22×Q8C22⋊D1112yescomplemented
261C22×D4—111no—
262C22×D4—221no—
263C22×D4—222no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4C22⋊D1111yescharacteristic
267C23×C4C22×D1111yescharacteristic
268C2×SD16—224no—
269C2×M16—222no—
270#123—444no—
271C22⋊Q8—28no—
272C22⋊Q8—28no—
273C22⋊Q8—24no—
274C22⋊Q8—28no—
275C22⋊Q8—24no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—28no—
279C22⋊Q8C22⋊D1114yescomplemented
280C22⋊Q8C22×D1114yes—
281#121—222no—
282#121—222no—
283#120—444no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4C22⋊D1112yescomplemented
290C2×C22⋊C4—22no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4C22⋊D1112yes—
301C2×C22⋊C4C22×D1112yes—
302C2×C42—221no—
303#107—224no—
304#103—224no—
305#102—224no—
306C22⋊C8—114no—
307C22⋊C8—222no—
308#95—112no—
309C2×C11—22no—
310C2×C11—22no—
311C2×C11—41no—
312C2×C11—44no—
313C2×C11#300411yescharacteristic
314C2×C11C2×#45311yescharacteristic
315C2×C11#302611yescharacteristic
316D11—161no—
317C24—21no—
318C24—24no—
319C24—21no—
320C24—42no—
321C24—81no—
322C24—221no—
323C24C2×C22⋊D1111yescharacteristic
324C24C2×C22⋊D1112yes—
325C2×Q8—24no—
326C2×Q8—22no—
327C2×Q8—82no—
328C2×Q8—82no—
329C2×Q8C2×C22⋊D1114yes—
330C2×D4—222no—
331C2×D4—444no—
332C2×D4—442no—
333C2×D4—442no—
334C2×D4—444no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4—881no—
338C2×D4—882no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—21no—
345C22×C4—42no—
346C22×C4—81no—
347C22×C4—82no—
348C22×C4—82no—
349C22×C4—222no—
350C22×C4—221no—
351C22×C4C2×C22⋊D1112yes—
352C22×C4C2×C22⋊D1111yescharacteristic
353C22×C4C2×C22⋊D1112yes—
354C22×C4C2×C22⋊D1112yes—
355C22×C4C23×D1111yescharacteristic
356SD16—884no—
357M16—882no—
358C2×C8—224no—
359C4⋊C4—24no—
360C4⋊C4—28no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—24no—
364C4⋊C4—222no—
365C4⋊C4—444no—
366C4⋊C4C2×C22⋊D1114yes—
367C22⋊C4—28no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—224no—
373C22⋊C4—444no—
374C22⋊C4—444no—
375C22⋊C4—442no—
376C42—881no—
377C11#1831811yescharacteristic, complemented, Sylow
378C23—24no—
379C23—24no—
380C23—22no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—81no—
390C23—81no—
391C23—88no—
392C23—441no—
393C23—441no—
394C23—442no—
395C23—442no—
396C23—441no—
397C23#6699514yes—
398C23#6700611yescharacteristic
399C23#6700611yescharacteristic
400C23C22×C22⋊D1111yescharacteristic
401Q8—44no—
402Q8—82no—
403Q8—84no—
404D4—444no—
405D4—888no—
406D4—882no—
407D4—882no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—84no—
421C2×C4—84no—
422C2×C4—224no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4#6700612yes—
429C2×C4C22×C22⋊D1112yes—
430C8—444no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—44no—
440C22—44no—
441C22—48no—
442C22—42no—
443C22—42no—
444C22—82no—
445C22—84no—
446C22—882no—
447C22—882no—
448C22—881no—
449C22—881no—
450C22—881no—
451C22#1062285412yes—
452C22C2×#6699512yes—
453C22C2×#6700611yescharacteristic
454C4—22no—
455C4—22no—
456C4—42no—
457C4—44no—
458C4—44no—
459C4—444no—
460C4—881no—
461C2—22no—
462C2—22no—
463C2—41no—
464C2—44no—
465C2—1761no—
466C2#1307785011yescharacteristic
467C2C2×#1062285411yescharacteristic
468C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#543C2
socleC22×C11C2×#120
prime radical#13073547C2
hypercenterC2×#543D11
hypocenterC11#18318
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #13079418C2semidirect
3. #13067641C2semidirect
4. #13067539C2semidirect
5. #13067136C2semidirect
6. #13066943C2semidirect
7. C2×C11×#543C2semidirect
24. #10622659C22semidirect
25. #10622657C22semidirect
30. #10622176C22semidirect
34. C22×Q8×C11D4semidirect
50. C11×C22⋊Q8D4semidirect
55. C2×C11×C4⋊C4D4semidirect
144. C2×#543D11semidirect
260. C22×Q8C22⋊D11semidirect
279. C22⋊Q8C22⋊D11semidirect
289. C2×C4⋊C4C22⋊D11semidirect
377. C11#18318semidirect

Maximal subgroups

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

subgroupindex
#130794182
#130735472
#130676412
#130675392
#130671362
#130669432
C2×C11×#5432
#1831811