Finite Group Databasebeta

← #14669264

Subgroups — #14669264

Order 2816.

1098 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10623363C211yesmaximal, characteristic
2C2×#10622111C212yesmaximal, complemented
3C2×#10622112C212yesmaximal, complemented
4#13068534C211yesmaximal, characteristic, complemented
5C11×#1782C211yesmaximal, characteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C22×#4339C411yescharacteristic, complemented
8#10623363—24no—
9#10623363—24no—
10C2×#67000C411yescharacteristic, complemented
11C2×#66997C411yescharacteristic, complemented
12C2×#66993C2211yescharacteristic
13C2×#66992—21no—
14C2×#66992—21no—
15C2×#66989C2211yescharacteristic
16C2×C4×C22⋊D11—21no—
17C2×C4×C22⋊D11—21no—
18C22×C4×Dic11C411yescharacteristic, complemented
19C2×C11×#99—21no—
20C2×C11×#99C2212yes—
21C11×#381—21no—
22C2×#66898—21no—
23C2×#66898C2212yes—
24#10622824—21no—
25#10622112—24no—
26#10622111—24no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—42no—
30C2×C11×#41—42no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×D4×C11C2311yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C22×C22⋊D11—21no—
39C22×C22⋊D11—21no—
40C22×C22⋊D11—21no—
41C23×Dic11—21no—
42C2×#4339—22no—
43C2×#4339—22no—
44C2×#4339—42no—
45C2×#4339—42no—
46C22×D44C2×C411yescharacteristic
47C22×C4×D11—21no—
48C22×Dic22C2×C411yescharacteristic
49C2×C11×C22⋊C4—22no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—22no—
53#67000—22no—
54#67000—22no—
55#66997—22no—
56#66997—22no—
57#66993—22no—
58#66993D414yes—
59#66992—28no—
60#66992—28no—
61#66989—22no—
62#66989D414yes—
63C4×C22⋊D11—28no—
64C4×C22⋊D11—28no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11C2×C411yescharacteristic
74C11×#99—22no—
75C11×#99—22no—
76C11×#99—42no—
77C11×#95—42no—
78#66898—22no—
79#66898—22no—
80#66898—42no—
81C11⋊#95—42no—
82#12695—111nomaximal, Sylow
83C24×C11C22⋊C411yescharacteristic
84C24×C11C2×D411yescharacteristic
85C24×C11C2×D411yescharacteristic
86C23×D11—21no—
87C11×#41—48no—
88C11×#41—48no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—41no—
92C2×Q8×C11—41no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11C2×D412yes—
102C2×D4×C11C2×D412yes—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11—42no—
114C22×C4×C11C22⋊C411yescharacteristic
115C22×C4×C11C22⋊C411yescharacteristic
116C22×C4×C11C22⋊C411yescharacteristic
117C22×C4×C11C22×C411yescharacteristic
118C2×C22⋊D11—24no—
119C2×C22⋊D11—24no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—42no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—44no—
124C2×C22⋊D11—42no—
125C22×Dic11—24no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—42no—
130C22×Dic11—44no—
131#4339—48no—
132#4339—48no—
133C2×D44—21no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44C22⋊C412yes—
137C2×C4×D11—24no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×Dic22—21no—
141C2×Dic22—41no—
142C2×Dic22—41no—
143C2×Dic22C22⋊C412yes—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—42no—
146C22⋊Dic11—24no—
147C22⋊Dic11—24no—
148C22⋊Dic11—42no—
149C22⋊Dic11—42no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152Dic11⋊C4—24no—
153Dic11⋊C4—24no—
154C4×Dic11—24no—
155C4×Dic11—21no—
156C4×Dic11—21no—
157C4×Dic11C22⋊C412yes—
158C4×Dic11C22⋊C412yes—
159C2×#532—111no—
160C2×#354—112no—
161C2×#353—112no—
162#1782—111no—
163#1782D1111yescharacteristic, complemented
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11#9912yes—
174C23×C11C2×C22⋊C411yescharacteristic
175C23×C11#12012yes—
176C23×C11#12012yes—
177C22×D11—22no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—41no—
181C22×D11—41no—
182Q8×C11—42no—
183Q8×C11—42no—
184D4×C11—42no—
185D4×C11—42no—
186D4×C11—44no—
187D4×C11—44no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—44no—
201C2×C4×C11—44no—
202C2×C4×C11—82no—
203C2×C4×C11—84no—
204C2×C4×C11#9912yes—
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C22⋊D11—48no—
208C22⋊D11—48no—
209C22⋊D11—48no—
210C2×Dic11—24no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—48no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—82no—
219C2×Dic11—84no—
220D44—42no—
221D44—42no—
222C4×D11—48no—
223Dic22—42no—
224Dic22—42no—
225C22×#41—111no—
226C22×#41C2×D1111yescharacteristic
227#532—224no—
228#532—224no—
229C2×C4⋊Q8—111no—
230C2×#127—111no—
231C2×#124—111no—
232C2×#124—111no—
233C2×#121—221no—
234C2×#121—221no—
235C2×C4×D4—221no—
236C2×C4×D4—221no—
237C22×C42—111no—
238C2×#99—21no—
239C2×#99—112no—
240C2×#99—221no—
241C2×#99C2×D1112yes—
242#381—21no—
243#381—221no—
244#354—224no—
245#353—224no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11#37911yescharacteristic
260C22×C11C2×#9911yescharacteristic
261C22×C11C2×#9911yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—82no—
266C2×D11—82no—
267C4×C11—22no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—41no—
271C4×C11—41no—
272C4×C11—162no—
273Dic11—24no—
274Dic11—42no—
275Dic11—42no—
276Dic11—162no—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—42no—
280C2×#41—42no—
281C2×#41—222no—
282C2×#41—222no—
283C2×#41—442no—
284C2×#41—442no—
285C22×Q8—111no—
286C22×Q8C4×D1111yescharacteristic
287C22×D4—111no—
288C22×D4—221no—
289C22×D4—221no—
290C22×D4—221no—
291C22×D4D4411yescharacteristic
292C22×D4C22⋊D1111yescharacteristic
293C22×D4C22×D1111yescharacteristic
294C23×C4—221no—
295C23×C4—221no—
296C23×C4C4×D1111yescharacteristic
297C23×C4D4411yescharacteristic
298C23×C4C22⋊D1111yescharacteristic
299C4⋊Q8—222no—
300C4⋊Q8—222no—
301#127—114no—
302#127—222no—
303#124—114no—
304#124—222no—
305#124—222no—
306#124—222no—
307#121—228no—
308#121—228no—
309C4×D4—228no—
310C4×D4—228no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—221no—
315C2×C22⋊C4—221no—
316C2×C22⋊C4—221no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—222no—
319C2×C42—111no—
320C2×C42—111no—
321C2×C42—222no—
322C2×C42—222no—
323C2×C42—221no—
324#99—22no—
325#99—22no—
326#99—42no—
327#99—222no—
328#99—222no—
329#99—442no—
330#95—42no—
331#95—442no—
332C2×C11—21no—
333C2×C11—21no—
334C2×C11—42no—
335C2×C11—42no—
336C2×C11—42no—
337C2×C11#178111yescharacteristic
338C2×C11#212612yes—
339D11—82no—
340C24—221no—
341C24(C2×D11)⋊C411yescharacteristic
342C24C2×D4411yescharacteristic
343C24C2×C22⋊D1111yescharacteristic
344#41—48no—
345#41—48no—
346#41—448no—
347#41—448no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—41no—
351C2×Q8—41no—
352C2×Q8—112no—
353C2×Q8—221no—
354C2×Q8—441no—
355C2×Q8—441no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—112no—
365C2×D4—224no—
366C2×D4—224no—
367C2×D4—224no—
368C2×D4—221no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—444no—
372C2×D4—444no—
373C2×D4—442no—
374C2×D4—442no—
375C2×D4D4×D1112yes—
376C2×D4D4×D1112yes—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—42no—
388C22×C4—224no—
389C22×C4—221no—
390C22×C4—224no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—442no—
394C22×C4—444no—
395C22×C4—442no—
396C22×C4—442no—
397C22×C4(C2×D11)⋊C411yescharacteristic
398C22×C4(C2×D11)⋊C411yescharacteristic
399C22×C4(C2×D11)⋊C411yescharacteristic
400C22×C4C2×C4×D1111yescharacteristic
401C4⋊C4—224no—
402C4⋊C4—224no—
403C22⋊C4—42no—
404C22⋊C4—42no—
405C22⋊C4—224no—
406C22⋊C4—224no—
407C22⋊C4—224no—
408C22⋊C4—224no—
409C22⋊C4—442no—
410C22⋊C4—442no—
411C42—112no—
412C42—112no—
413C42—224no—
414C42—221no—
415C42—221no—
416C11#1269511yescharacteristic, complemented, Sylow
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—222no—
427C23—442no—
428C23—442no—
429C23—441no—
430C23—441no—
431C23#6687012yes—
432C23#6693512yes—
433C23C2×(C2×D11)⋊C411yescharacteristic
434C23#6699012yes—
435Q8—42no—
436Q8—42no—
437Q8—442no—
438Q8—442no—
439D4—42no—
440D4—42no—
441D4—44no—
442D4—44no—
443D4—442no—
444D4—442no—
445D4—448no—
446D4—448no—
447D4—448no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—82no—
463C2×C4—84no—
464C2×C4—224no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—448no—
469C2×C4—448no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—882no—
474C2×C4—884no—
475C2×C4#6687012yes—
476C2×C4C22⋊C4×D1111yescharacteristic
477C2×C4C22⋊C4×D1111yescharacteristic
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—81no—
490C22—81no—
491C22—442no—
492C22—442no—
493C22—442no—
494C22—882no—
495C22—882no—
496C22C2×#6687011yescharacteristic
497C22C2×#6687011yescharacteristic
498C22#1062256811yescharacteristic
499C4—22no—
500C4—21no—
501C4—21no—
502C4—41no—
503C4—41no—
504C4—162no—
505C4—224no—
506C4—442no—
507C4—442no—
508C4—1762no—
509C2—21no—
510C2—21no—
511C2—42no—
512C2—42no—
513C2—42no—
514C2—882no—
515C2#1306853011yescharacteristic
516C2#1307027912yes—
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1782C2
socleC22×C11C2×#99
prime radicalC2×#10623363C2
cosocleC22×D4×C11C23
hypercenter#1782D11
hypocenterC11#12695
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. C2×#10622111C2semidirect
3. C2×#10622112C2semidirect
4. #13068534C2semidirect
5. C11×#1782C2semidirect
7. C22×#4339C4semidirect
10. C2×#67000C4semidirect
11. C2×#66997C4semidirect
18. C22×C4×Dic11C4semidirect
163. #1782D11semidirect
416. C11#12695semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106221112
C2×#106221122
#130685342
C11×#17822
#1269511