Finite Group Databasebeta

← #14913846

Subgroups — #14913846

Order 2816.

2518 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#117C211yesmaximal, characteristic
2#13071505C212yesmaximal, complemented
3#13071497C212yesmaximal, complemented
4#13071489C212yesmaximal, complemented
5#13071481C212yesmaximal, complemented
6#13071470C214yesmaximal, complemented
7#13071459C214yesmaximal
8#13071240C211yesmaximal, characteristic, complemented
9#13071236C211yesmaximal, characteristic, complemented
10#13071221C212yesmaximal, complemented
11#13071221C212yesmaximal, complemented
12#13071020C212yesmaximal, complemented
13#13071012C212yesmaximal, complemented
14#13070995C211yesmaximal, characteristic
15C2×#10622600C211yesmaximal, characteristic
16#13070972C211yesmaximal, characteristic, complemented
17C11×#2274C211yesmaximal, characteristic, complemented
18C23×C4×D11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C2×#66979C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26D11×#117C4116yescomplemented
27C2×#66945C2211yescharacteristic
28C2×#66945C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×C22⋊C4×D11C2212yes—
32C2×#66930C2212yes—
33C2×#66925C2214yes—
34C2×#66925C2212yes—
35C2×C42×D11C2212yes—
36C4×C11×C4⋊C4C2212yescomplemented
37C4×C11×C4⋊C4C2212yescomplemented
38C4×C11×C4⋊C4C2212yescomplemented
39C4×C11×C4⋊C4C2212yescomplemented
40C4×C11×C22⋊C4C2214yes—
41#10622823C2214yes—
42C2×C11⋊#95C2212yes—
43#10622600C2212yes—
44#10622600C2211yescharacteristic
45#10622600C2211yescharacteristic
46#10622600C2212yes—
47#10622600C2212yes—
48#10622600C2212yes—
49#10622600C2211yescharacteristic
50#10622600C2211yescharacteristic
51#10622590C2212yescomplemented
52#10622590C2212yescomplemented
53#10622589C2212yescomplemented
54#10622589C2212yescomplemented
55C4⋊C4×Dic11C2212yescomplemented
56C4⋊C4×Dic11C2212yescomplemented
57#10622586C2212yescomplemented
58#10622586C2212yescomplemented
59#10622568C2212yes—
60#10622559C2214yes—
61#10622556C2212yes—
62C22⋊C4×Dic11C2214yes—
63#10622553C2214yes—
64#10622553C2214yes—
65C4×(C2×D11)⋊C4C2214yes—
66C4×(C2×D11)⋊C4C2212yes—
67C4×(C2×D11)⋊C4C2212yes—
68C4×C4⋊Dic11C2212yescomplemented
69C4×C4⋊Dic11C2212yescomplemented
70#10622546C2214yescomplemented
71#10622546C2214yescomplemented
72#10622545C2214yescomplemented
73C4×Dic11⋊C4C2214yescomplemented
74#10622541C2212yescomplemented
75#10622541C2212yescomplemented
76#10622282C2214yes—
77#10622282C2214yes—
78#10622280C2214yes—
79#10622277C2214yes—
80#10622265C2214yescomplemented
81#10622265C2214yescomplemented
82#10622264C2214yescomplemented
83#10622263C2214yescomplemented
84C24×D11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2312yes—
89C22×C4×D11—24no—
90C22×C4×D11—24no—
91C22×C4×D11C2×C418yes—
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2312yes—
94C22×C4×D11C2311yescharacteristic
95C22×C4×D11C2311yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×C4×D11C2312yes—
98C11×#117—24no—
99C11×#117C2×C418yes—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C42×C11C2312yes—
110C2×C42×C11C2314yes—
111C2×C42×C11C2314yes—
112C2×C42×C11C2312yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2312yes—
115C2×(C2×D11)⋊C4—44no—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2312yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2312yes—
124#66979—24no—
125#66979C2×C418yes—
126C2×C4⋊Dic11—24no—
127C2×C4⋊Dic11C2312yes—
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2312yes—
145#66945C2×C418yescomplemented
146#66945C2×C418yescomplemented
147C4⋊C4×D11C2×C418yescomplemented
148C4⋊C4×D11C2×C418yescomplemented
149C22⋊C4×D11C2×C4116yes—
150#66930C2×C4116yes—
151#66925—48no—
152#66925C2×C4116yescomplemented
153C42×D11C2×C4116yescomplemented
154C11×#95C2314yes—
155C11×#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168#34180—111nomaximal, Sylow
169C24×C11C2411yescharacteristic
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—41no—
175C23×D11—41no—
176C23×D11C22×C414yes—
177C23×D11C2411yescharacteristic
178C23×D11C2411yescharacteristic
179C22×C4×C11—24no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11C22×C414yes—
183C22×C4×C11#4114yes—
184C22×C4×C11#4114yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2414yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—24no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11C22×C414yes—
198C22×Dic11C2412yes—
199C22×Dic11C2414yes—
200C22×Dic11C2412yes—
201C22×Dic11C2411yescharacteristic
202C22×Dic11C2411yescharacteristic
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C2×C4×D11—24no—
206C2×C4×D11—24no—
207C2×C4×D11—232no—
208C2×C4×D11—22no—
209C2×C4×D11—22no—
210C2×C4×D11—22no—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—22no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—42no—
217C2×C4×D11—42no—
218C2×C4×D11C22×C414yes—
219C2×C4×D11C22×C418yes—
220C2×C4×D11C22×C414yes—
221C2×C4×D11C22×C414yes—
222C2×C4×D11C22×C414yes—
223C2×C4×D11C22×C418yes—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4C22×C414yes—
229C11×C4⋊C4C22×C414yes—
230C11×C22⋊C4—24no—
231C11×C22⋊C4C22×C418yes—
232C42×C11—24no—
233C42×C11—44no—
234C42×C11—44no—
235C42×C11C22×C418yes—
236C22⋊Dic11—24no—
237C22⋊Dic11C22×C418yes—
238(C2×D11)⋊C4—24no—
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—44no—
242(C2×D11)⋊C4—42no—
243(C2×D11)⋊C4—42no—
244(C2×D11)⋊C4C22×C418yes—
245(C2×D11)⋊C4C22×C418yes—
246C4⋊Dic11—24no—
247C4⋊Dic11—24no—
248C4⋊Dic11—22no—
249C4⋊Dic11—22no—
250C4⋊Dic11C22×C414yes—
251C4⋊Dic11C22×C414yes—
252Dic11⋊C4—44no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256Dic11⋊C4C22×C418yes—
257Dic11⋊C4C22×C418yes—
258C4×Dic11—24no—
259C4×Dic11—44no—
260C4×Dic11—44no—
261C4×Dic11C22×C418yes—
262C4×Dic11C22×C418yes—
263C4×Dic11C22×C418yes—
264C22×#117—111no—
265#2347—112no—
266#2346—112no—
267#2345—112no—
268#2344—112no—
269#2343—114no—
270#2342—114no—
271#2317—111no—
272#2317—111no—
273#2314—112no—
274#2314—112no—
275#2285—112no—
276#2283—112no—
277#2280—111no—
278C2×#380—111no—
279#2274—111no—
280#2274D1111yescharacteristic, complemented
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11C23×C412yes—
286C23×C11C2×#4112yes—
287C23×C11C2×#4112yes—
288C23×C11C2511yescharacteristic
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—28no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—28no—
301C22×D11—44no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11C23×C412yes—
307C22×D11C23×C412yes—
308C22×D11H(5,𝔽2)12yes—
309C22×D112−1+412yes—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—22no—
323C2×C4×C11—84no—
324C2×C4×C11#117116yescomplemented
325C2×C4×C11C23×C414yes—
326C2×C4×C11C23×C414yes—
327C2×C4×C11C23×C412yes—
328C2×C4×C11C23×C412yes—
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2×#4112yes—
331C2×C4×C11C2×#4112yes—
332C2×C4×C11C2×#4112yes—
333C2×Dic11—28no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—24no—
345C2×Dic11—22no—
346C2×Dic11—24no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—24no—
350C2×Dic11—22no—
351C2×Dic11—84no—
352C2×Dic11C23×C412yes—
353C2×Dic11C23×C414yes—
354C2×Dic11C23×C414yes—
355C2×Dic11C23×C412yes—
356C4×D11—216no—
357C4×D11—28no—
358C4×D11—28no—
359C4×D11—28no—
360C4×D11—28no—
361C4×D11—48no—
362C24×C4—111no—
363C2×#117—111no—
364C2×#117—1116no—
365C2×#117—111no—
366C2×#117—111no—
367C2×#117—111no—
368C2×#117—112no—
369C2×#117—112no—
370C2×#117—114no—
371C2×#117C2×D1111yescharacteristic
372C2×#117C2×D1111yescharacteristic
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4—111no—
376C22×C4⋊C4C2×D1111yescharacteristic
377C22×C22⋊C4—112no—
378C22×C22⋊C4—112no—
379C22×C42—112no—
380#389—112no—
381#389—112no—
382#389—112no—
383#389—112no—
384#388—114no—
385#388—114no—
386#388—114no—
387#388—114no—
388#387—114no—
389#387—114no—
390#387—114no—
391#387—114no—
392#385—114no—
393#385—114no—
394#384—112no—
395#384—112no—
396#383—114no—
397#382—112no—
398#382—112no—
399#382—114no—
400#381—112no—
401#381—114no—
402#380—112no—
403#380—111no—
404#380—111no—
405#380—112no—
406#380—112no—
407#380—112no—
408#380—111no—
409#380—111no—
410#380—114no—
411#379—112no—
412C4×C4⋊C4—112no—
413C4×C4⋊C4—112no—
414C4×C4⋊C4—112no—
415C4×C4⋊C4—112no—
416C4×C4⋊C4—114no—
417C4×C4⋊C4C2×D1112yescomplemented
418C4×C4⋊C4C2×D1112yescomplemented
419C4×C4⋊C4C2×D1112yescomplemented
420C4×C4⋊C4C2×D1112yescomplemented
421C4×C22⋊C4—114no—
422C4×C22⋊C4—114no—
423C4×C22⋊C4—112no—
424C4×C22⋊C4—112no—
425C4×C22⋊C4C2×D1114yes—
426#376—114no—
427C2×#95—112no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11C2×#11714yes—
435C22×C11C24×C411yescharacteristic
436C22×C11C22×#4111yescharacteristic
437C22×C11C22×#4111yescharacteristic
438C22×C11C2×H(5,𝔽2)11yescharacteristic
439C22×C11C2×2−1+411yescharacteristic
440C22×C11#58511yescharacteristic
441C22×C11#58511yescharacteristic
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—416no—
452C2×D11—41no—
453C2×D11—41no—
454C2×D11—41no—
455C2×D11—41no—
456C2×D11#52014yes—
457C4×C11—24no—
458C4×C11—24no—
459C4×C11—42no—
460C4×C11—44no—
461C4×C11—42no—
462C4×C11C2×#11714yes—
463C4×C11C2×#11714yes—
464Dic11—22no—
465Dic11—22no—
466Dic11—24no—
467Dic11—24no—
468Dic11—42no—
469Dic11—44no—
470Dic11—42no—
471C25—111no—
472C23×C4—111no—
473C23×C4—118no—
474C23×C4—112no—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—112no—
480C23×C4—112no—
481C23×C4—224no—
482C23×C4—224no—
483C23×C4C22×D1112yes—
484C23×C4C22×D1111yescharacteristic
485#117—24no—
486#117—118no—
487#117—118no—
488#117—118no—
489#117—1116no—
490#117—1116no—
491#117—224no—
492#117—448no—
493#117C4×D1118yes—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—112no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—118no—
500C2×C4⋊C4—118no—
501C2×C4⋊C4—112no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—224no—
510C2×C4⋊C4C22×D1112yes—
511C2×C4⋊C4C22×D1112yes—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—112no—
517C2×C22⋊C4—112no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—1116no—
520C2×C22⋊C4—112no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—112no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—112no—
526C2×C22⋊C4—112no—
527C2×C22⋊C4—444no—
528C2×C22⋊C4C22×D1112yes—
529C2×C22⋊C4C22×D1112yes—
530C2×C42—112no—
531C2×C42—112no—
532C2×C42—112no—
533C2×C42—1116no—
534C2×C42—112no—
535C2×C42—114no—
536C2×C42—114no—
537C2×C42C22×D1112yes—
538C2×C42C22×D1114yes—
539C2×C42C22×D1114yes—
540C2×C42C22×D1112yes—
541#95—114no—
542#95—114no—
543#95—112no—
544#95—114no—
545#95—114no—
546#95—112no—
547#95—114no—
548#95—114no—
549#95—112no—
550#95—112no—
551#95—114no—
552#95—114no—
553#95C22×D1114yes—
554#95C22×D1114yes—
555C2×C11—24no—
556C2×C11C22×#11711yescharacteristic
557C2×C11C2×#52011yescharacteristic
558C2×C11#342811yescharacteristic
559C2×C11#349411yescharacteristic
560C2×C11#349411yescharacteristic
561C2×C11#349511yescharacteristic
562C2×C11#349511yescharacteristic
563D11—24no—
564D11—42no—
565C24—111no—
566C24—111no—
567C24—114no—
568C24—222no—
569C24—222no—
570C24—222no—
571C24—222no—
572C24—441no—
573C24—441no—
574C24C23×D1111yescharacteristic
575C22×C4—24no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—114no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—114no—
584C22×C4—118no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—114no—
588C22×C4—118no—
589C22×C4—112no—
590C22×C4—114no—
591C22×C4—112no—
592C22×C4—224no—
593C22×C4—224no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—2232no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—224no—
606C22×C4—442no—
607C22×C4—442no—
608C22×C4—442no—
609C22×C4—442no—
610C22×C4C2×C4×D1114yes—
611C22×C4#433914yes—
612C22×C4#433914yes—
613C22×C4C23×D1112yes—
614C22×C4C23×D1114yes—
615C22×C4C23×D1112yes—
616C22×C4C23×D1112yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619C22×C4C23×D1111yescharacteristic
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—118no—
625C4⋊C4—118no—
626C4⋊C4—114no—
627C4⋊C4—114no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—222no—
631C4⋊C4—222no—
632C4⋊C4—444no—
633C4⋊C4—444no—
634C4⋊C4—444no—
635C4⋊C4—444no—
636C4⋊C4C2×C4×D1114yes—
637C4⋊C4C2×C4×D1114yes—
638C22⋊C4—24no—
639C22⋊C4—118no—
640C22⋊C4—118no—
641C22⋊C4—118no—
642C22⋊C4—228no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—444no—
647C22⋊C4—442no—
648C22⋊C4—442no—
649C22⋊C4C2×C4×D1118yes—
650C42—24no—
651C42—44no—
652C42—44no—
653C42—118no—
654C42—118no—
655C42—118no—
656C42—224no—
657C42—444no—
658C42—444no—
659C42C2×C4×D1118yes—
660C11#3418011yescharacteristic, complemented, Sylow
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—112no—
666C23—112no—
667C23—112no—
668C23—112no—
669C23—228no—
670C23—221no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—228no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23—444no—
682C23—444no—
683C23—444no—
684C23—444no—
685C23—444no—
686C23C22×C4×D1112yes—
687C23C2×#433912yes—
688C23C2×#433912yes—
689C23C24×D1111yescharacteristic
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—84no—
704C2×C4—112no—
705C2×C4—114no—
706C2×C4—114no—
707C2×C4—112no—
708C2×C4—2216no—
709C2×C4—228no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—228no—
719C2×C4—228no—
720C2×C4—228no—
721C2×C4—228no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—224no—
725C2×C4—222no—
726C2×C4—224no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—224no—
731C2×C4—448no—
732C2×C4—884no—
733C2×C4#66925116yescomplemented
734C2×C4C22×C4×D1114yes—
735C2×C4C22×C4×D1114yes—
736C2×C4C22×C4×D1112yes—
737C2×C4C22×C4×D1112yes—
738C2×C4C2×#433912yes—
739C2×C4C2×#433912yes—
740C2×C4C2×#433912yes—
741C2×C4C2×#433912yes—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—114no—
749C22—222no—
750C22—222no—
751C22—222no—
752C22—222no—
753C22—222no—
754C22—222no—
755C22—222no—
756C22—222no—
757C22—222no—
758C22—4416no—
759C22—441no—
760C22—441no—
761C22—441no—
762C22—441no—
763C22C2×#6692514yes—
764C22C23×C4×D1111yescharacteristic
765C22C22×#433911yescharacteristic
766C22C22×#433911yescharacteristic
767C22D11×H(5,𝔽2)11yescharacteristic
768C22#1062345511yescharacteristic
769C22D11×2−1+411yescharacteristic
770C22#1062345711yescharacteristic
771C4—24no—
772C4—24no—
773C4—42no—
774C4—44no—
775C4—42no—
776C4—222no—
777C4—222no—
778C4—224no—
779C4—224no—
780C4—442no—
781C4—444no—
782C4—442no—
783C4C2×#6692514yes—
784C4C2×#6692514yes—
785C2—24no—
786C2—224no—
787C2—442no—
788C2C22×#6692511yescharacteristic
789C2D11×#52011yescharacteristic
790C2#1308181611yescharacteristic
791C2#1308234111yescharacteristic
792C2#1308235211yescharacteristic
793C2#1308235811yescharacteristic
794C2#1308236911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2274D11
hypocenterC11#34180
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. #13071505C2semidirect
3. #13071497C2semidirect
4. #13071489C2semidirect
5. #13071481C2semidirect
6. #13071470C2semidirect
8. #13071240C2semidirect
9. #13071236C2semidirect
10. #13071221C2semidirect
11. #13071221C2semidirect
12. #13071020C2semidirect
13. #13071012C2semidirect
16. #13070972C2semidirect
17. C11×#2274C2semidirect
26. D11×#117C4semidirect
36. C4×C11×C4⋊C4C22semidirect
37. C4×C11×C4⋊C4C22semidirect
38. C4×C11×C4⋊C4C22semidirect
39. C4×C11×C4⋊C4C22semidirect
51. #10622590C22semidirect
52. #10622590C22semidirect
53. #10622589C22semidirect
54. #10622589C22semidirect
55. C4⋊C4×Dic11C22semidirect
56. C4⋊C4×Dic11C22semidirect
57. #10622586C22semidirect
58. #10622586C22semidirect
68. C4×C4⋊Dic11C22semidirect
69. C4×C4⋊Dic11C22semidirect
70. #10622546C22semidirect
71. #10622546C22semidirect
72. #10622545C22semidirect
73. C4×Dic11⋊C4C22semidirect
74. #10622541C22semidirect
75. #10622541C22semidirect
80. #10622265C22semidirect
81. #10622265C22semidirect
82. #10622264C22semidirect
83. #10622263C22semidirect
145. #66945C2×C4semidirect
146. #66945C2×C4semidirect
147. C4⋊C4×D11C2×C4semidirect
148. C4⋊C4×D11C2×C4semidirect
152. #66925C2×C4semidirect
153. C42×D11C2×C4semidirect
280. #2274D11semidirect
324. C2×C4×C11#117semidirect
417. C4×C4⋊C4C2×D11semidirect
418. C4×C4⋊C4C2×D11semidirect
419. C4×C4⋊C4C2×D11semidirect
420. C4×C4⋊C4C2×D11semidirect
660. C11#34180semidirect
733. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1172
#130715052
#130714972
#130714892
#130714812
#130714702
#130714592
#130712402
#130712362
#130712212
#130710202
#130710122
#130709952
C2×#106226002
#130709722
C11×#22742
#3418011