Finite Group Databasebeta

← #14660482

Subgroups — #14660482

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C22×#66885C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5C2×#10622188C211yesmaximal, characteristic, complemented
6#13066845C211yesmaximal, characteristic, complemented
7C22×C11×#102C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C23×C22⋊D11—22no—
10C23×D44C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66993—22no—
14C2×#66993—22no—
15C2×#66993—22no—
16C2×#66993—22no—
17C2×#66993—22no—
18C2×#66993C414yescomplemented
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×C11×#102—22no—
23C2×C11×#102—22no—
24C2×C11×#102—22no—
25C2×#66896—22no—
26C2×#66896—22no—
27C2×#66896—22no—
28C2×C11⋊#95—22no—
29C2×#66885—22no—
30C2×#66885—22no—
31C2×#66885—22no—
32C2×#66873—22no—
33C2×#66873—22no—
34C2×#66873—22no—
35#10622188—22no—
36C25×C11—21no—
37C24×D11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2×C412yes—
50C22×D4×C11D412yes—
51C22×D4×C11D412yes—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—28no—
55C22×C22⋊D11—28no—
56C22×C22⋊D11—28no—
57C22×C22⋊D11—44no—
58C22×C22⋊D11—44no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11—44no—
61C23×Dic11—21no—
62C23×Dic11D412yes—
63C22×D44—21no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44—21no—
68C22×D44—21no—
69C22×D44—21no—
70C22×D44—21no—
71C22×D44—21no—
72C22×D44—21no—
73C22×D44—21no—
74C22×D44C2×C412yes—
75C22×D44D412yes—
76C22×D44D412yes—
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C22×C8×C11—21no—
82C22×C8×C11—21no—
83C22×C8×C11D412yescomplemented
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D412yescomplemented
90#66993—28no—
91#66993—28no—
92#66993—28no—
93#66993—28no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11D412yescomplemented
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2×C412yes—
105C2×C4×Dic11D412yes—
106C22×C11⋊C8—21no—
107C22×C11⋊C8—21no—
108C22×C11⋊C8—21no—
109C22×C11⋊C8—21no—
110C22×C11⋊C8—21no—
111C22×C11⋊C8—21no—
112C22×C11⋊C8D412yescomplemented
113C11×#102—28no—
114#66896—28no—
115C11⋊#95—44no—
116#66885—28no—
117#66873—28no—
118#11008—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—41no—
123C24×C11—41no—
124C24×C11—41no—
125C24×C11—41no—
126C24×C11—42no—
127C24×C11—42no—
128C24×C11—42no—
129C24×C11—42no—
130C24×C11C2×D411yescharacteristic
131C23×D11—22no—
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—41no—
135C23×D11—41no—
136C23×D11—41no—
137C23×D11—41no—
138C23×D11—42no—
139C23×D11—42no—
140C23×D11—42no—
141C23×D11—42no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C2×D4×C11—41no—
169C2×D4×C11C22⋊C414yes—
170C22×C4×C11—22no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11#4111yescharacteristic
186C22×C4×C11#4111yescharacteristic
187C22×C4×C11#4111yescharacteristic
188C22×C4×C11#4111yescharacteristic
189C2×C22⋊D11—232no—
190C2×C22⋊D11—416no—
191C2×C22⋊D11—416no—
192C2×C22⋊D11—416no—
193C2×C22⋊D11—416no—
194C2×C22⋊D11—416no—
195C2×C22⋊D11—416no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—41no—
202C22×Dic11—41no—
203C22×Dic11—42no—
204C22×Dic11—42no—
205C22×Dic11C22⋊C414yes—
206C22×Dic11D814yes—
207C22×Dic11SD1614yes—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44—22no—
223C2×D44—41no—
224C2×D44—41no—
225C2×D44—41no—
226C2×D44—41no—
227C2×D44—41no—
228C2×D44—41no—
229C2×D44—41no—
230C2×D44—41no—
231C2×D44—41no—
232C2×D44—41no—
233C2×D44—41no—
234C2×D44—41no—
235C2×D44C22⋊C414yes—
236C2×C8×C11—22no—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11—41no—
240C2×C8×C11—41no—
241C2×C8×C11—41no—
242C2×C8×C11—41no—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—41no—
246C11×C4⋊C4—41no—
247C4⋊Dic11—22no—
248C4⋊Dic11—22no—
249C4⋊Dic11—41no—
250C4⋊Dic11—41no—
251C4×Dic11—22no—
252C4×Dic11—22no—
253C4×Dic11—22no—
254C4×Dic11—22no—
255C2×C11⋊C8—22no—
256C2×C11⋊C8—22no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—41no—
259C2×C11⋊C8—41no—
260C2×C11⋊C8—41no—
261C2×C11⋊C8—41no—
262C22×#127—111no—
263C22×#102—111no—
264C22×#102—111no—
265C22×#102—111no—
266C22×#102D1111yescharacteristic, complemented
267C2×#336—111no—
268C4⋊#95—111no—
269C23×C11—24no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—82no—
283C23×C11—82no—
284C23×C11—82no—
285C23×C11—82no—
286C23×C11—82no—
287C23×C11—82no—
288C23×C11—81no—
289C23×C11—81no—
290C23×C11—81no—
291C23×C11—81no—
292C23×C11C2×C22⋊C411yescharacteristic
293C23×C11#12011yescharacteristic
294C23×C11#12011yescharacteristic
295C23×C11#12111yescharacteristic
296C23×C11#12111yescharacteristic
297C23×C11#12411yescharacteristic
298C23×C11#12711yescharacteristic
299C23×C11C2×D812yes—
300C23×C11C2×SD1612yes—
301C23×C11AGL(1,ℤ/8)12yes—
302C23×C11AGL(1,ℤ/8)12yes—
303C22×D11—24no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—44no—
311C22×D11—44no—
312C22×D11—44no—
313C22×D11—44no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11—82no—
317C22×D11—82no—
318C22×D11—82no—
319C22×D11—82no—
320C22×D11—82no—
321C22×D11—82no—
322C22×D11—81no—
323C22×D11—81no—
324C22×D11—81no—
325C22×D11—81no—
326D4×C11—24no—
327D4×C11—24no—
328D4×C11—42no—
329D4×C11—42no—
330D4×C11—42no—
331D4×C11—42no—
332D4×C11—42no—
333D4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—44no—
336C2×C4×C11—82no—
337C2×C4×C11—81no—
338C2×C4×C11—81no—
339C2×C4×C11C2×C22⋊C411yescharacteristic
340C2×C4×C11C2×C22⋊C411yescharacteristic
341C2×C4×C11C4×D411yescharacteristic
342C2×C4×C11C4×D411yescharacteristic
343C2×C4×C11C4×D411yescharacteristic
344C2×C4×C11C4×D411yescharacteristic
345C2×C4×C11#12011yescharacteristic
346C2×C4×C11#12011yescharacteristic
347C2×C4×C11#12011yescharacteristic
348C2×C4×C11#12011yescharacteristic
349C2×C4×C11#12011yescharacteristic
350C2×C4×C11#12011yescharacteristic
351C2×C4×C11#12111yescharacteristic
352C2×C4×C11#12111yescharacteristic
353C2×C4×C11#12111yescharacteristic
354C2×C4×C11#12111yescharacteristic
355C2×C4×C11#12111yescharacteristic
356C2×C4×C11#12111yescharacteristic
357C2×C4×C11#12111yescharacteristic
358C2×C4×C11#12111yescharacteristic
359C2×C4×C11#12111yescharacteristic
360C2×C4×C11#12111yescharacteristic
361C2×C4×C11#12311yescharacteristic
362C2×C4×C11#12311yescharacteristic
363C2×C4×C11#12311yescharacteristic
364C2×C4×C11#12311yescharacteristic
365C2×C4×C11#12411yescharacteristic
366C2×C4×C11#12711yescharacteristic
367C22⋊D11—464no—
368C2×Dic11—24no—
369C2×Dic11—24no—
370C2×Dic11—24no—
371C2×Dic11—24no—
372C2×Dic11—24no—
373C2×Dic11—24no—
374C2×Dic11—42no—
375C2×Dic11—44no—
376C2×Dic11—82no—
377C2×Dic11—81no—
378C2×Dic11—81no—
379C2×Dic11#10218yescomplemented
380D44—24no—
381D44—24no—
382D44—42no—
383D44—42no—
384D44—42no—
385D44—42no—
386D44—42no—
387D44—42no—
388C8×C11—42no—
389C11⋊C8—42no—
390C23×D4—111no—
391C23×D4—222no—
392C23×D4C2×D1111yescharacteristic
393C23×C8—111no—
394C23×C8C2×D1111yescharacteristic
395C2×#127—114no—
396C2×#127—222no—
397C2×#127—222no—
398C2×#127—222no—
399C2×#127—222no—
400C2×#127—222no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4C2×D1111yescharacteristic
403C22×C42—111no—
404C2×#102—22no—
405C2×#102—22no—
406C2×#102—22no—
407C2×#102—222no—
408C2×#102—222no—
409C2×#102—222no—
410C2×#102—222no—
411C2×#102—222no—
412C2×#102—222no—
413C2×#102—222no—
414C2×#102—222no—
415C2×#102—222no—
416C2×#95—222no—
417#336—222no—
418C22×C11—44no—
419C22×C11—48no—
420C22×C11—82no—
421C22×C11—82no—
422C22×C11—84no—
423C22×C11—82no—
424C22×C11—82no—
425C22×C11—82no—
426C22×C11—82no—
427C22×C11—84no—
428C22×C11—84no—
429C22×C11#37911yescharacteristic
430C22×C11#39011yescharacteristic
431C22×C11#39011yescharacteristic
432C22×C11#39211yescharacteristic
433C22×C11#39211yescharacteristic
434C22×C11#39411yescharacteristic
435C22×C11#39411yescharacteristic
436C22×C11C2×#10212yes—
437C22×C11#41812yes—
438C22×C11#44712yes—
439C22×C11#44712yes—
440C22×C11#45012yes—
441C22×C11#45012yes—
442C22×C11#45912yes—
443C22×C11#45912yes—
444C22×C11#46012yes—
445C22×C11#46012yes—
446C22×C11#48612yes—
447C22×C11#49012yes—
448C22×C11#49211yescharacteristic
449C22×C11#49311yescharacteristic
450C22×C11#49611yescharacteristic
451C22×C11#49611yescharacteristic
452C2×D11—44no—
453C2×D11—48no—
454C2×D11—82no—
455C2×D11—82no—
456C2×D11—84no—
457C2×D11—82no—
458C2×D11—82no—
459C2×D11—82no—
460C2×D11—82no—
461C2×D11—84no—
462C2×D11—84no—
463C4×C11—82no—
464C4×C11#38611yescharacteristic
465C4×C11#38611yescharacteristic
466C4×C11#38611yescharacteristic
467C4×C11#38611yescharacteristic
468C4×C11#39211yescharacteristic
469C4×C11#39211yescharacteristic
470C4×C11#39411yescharacteristic
471C4×C11#39411yescharacteristic
472Dic11—28no—
473Dic11—82no—
474C25—21no—
475C25—221no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—112no—
488C22×D4—112no—
489C22×D4—112no—
490C22×D4—228no—
491C22×D4—228no—
492C22×D4—228no—
493C22×D4—221no—
494C22×D4—221no—
495C22×D4—221no—
496C22×D4—221no—
497C22×D4—221no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—221no—
504C22×D4—444no—
505C22×D4—444no—
506C22×D4—444no—
507C22×D4—444no—
508C22×D4C4×D1112yes—
509C22×D4D4412yes—
510C22×D4C22⋊D1112yes—
511C23×C4—21no—
512C23×C4—112no—
513C23×C4—221no—
514C23×C4C22×D1111yescharacteristic
515C22×C8—21no—
516C22×C8—21no—
517C22×C8—21no—
518C22×C8—21no—
519C22×C8—21no—
520C22×C8—21no—
521C22×C8—112no—
522C22×C8—221no—
523C22×C8—221no—
524C22×C8—221no—
525C22×C8—221no—
526C22×C8—221no—
527C22×C8—221no—
528C22×C8C22⋊D1112yescomplemented
529#127—228no—
530#127—228no—
531#127—228no—
532#127—228no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4—221no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4C22⋊D1112yescomplemented
545C2×C42—112no—
546C2×C42—112no—
547C2×C42—221no—
548C2×C42—221no—
549C2×C42—221no—
550C2×C42—221no—
551#102—28no—
552#102—228no—
553#102—228no—
554#102—228no—
555#95—444no—
556C2×C11—84no—
557C2×C11#143811yescharacteristic
558C2×C11#178612yes—
559C2×C11#195711yescharacteristic
560C2×C11#196111yescharacteristic
561C2×C11#198212yes—
562C2×C11#201111yescharacteristic
563C2×C11#201111yescharacteristic
564C2×C11#201411yescharacteristic
565C2×C11#201411yescharacteristic
566C2×C11#204112yes—
567C2×C11#204112yes—
568D11—84no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—41no—
573C24—41no—
574C24—42no—
575C24—42no—
576C24—42no—
577C24—42no—
578C24—41no—
579C24—41no—
580C24—222no—
581C24—222no—
582C24—222no—
583C24—441no—
584C24—441no—
585C24—442no—
586C24—442no—
587C24—442no—
588C24—442no—
589C24—441no—
590C24—441no—
591C24D4×D1111yescharacteristic
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—114no—
620C2×D4—2232no—
621C2×D4—222no—
622C2×D4—222no—
623C2×D4—222no—
624C2×D4—222no—
625C2×D4—222no—
626C2×D4—222no—
627C2×D4—222no—
628C2×D4—222no—
629C2×D4—222no—
630C2×D4—222no—
631C2×D4—222no—
632C2×D4—222no—
633C2×D4—222no—
634C2×D4—222no—
635C2×D4—222no—
636C2×D4—4416no—
637C2×D4—4416no—
638C2×D4—4416no—
639C2×D4—4416no—
640C2×D4—4416no—
641C2×D4—4416no—
642C2×D4—441no—
643C2×D4—441no—
644C2×D4—441no—
645C2×D4—441no—
646C2×D4—441no—
647C2×D4—441no—
648C2×D4—441no—
649C2×D4—441no—
650C2×D4—441no—
651C2×D4—441no—
652C2×D4—441no—
653C2×D4—441no—
654C2×D4(C2×D11)⋊C414yes—
655C22×C4—22no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—114no—
661C22×C4—114no—
662C22×C4—114no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—441no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—441no—
672C22×C4C2×C4×D1111yescharacteristic
673C22×C4C2×D4411yescharacteristic
674C22×C4#433911yescharacteristic
675C22×C4#433911yescharacteristic
676C22×C4D4×D1111yescharacteristic
677C22×C4D4×D1111yescharacteristic
678C22×C4D4×D1111yescharacteristic
679C22×C4D4×D1111yescharacteristic
680C22×C4D4×D1111yescharacteristic
681C22×C4#434111yescharacteristic
682C22×C4#434111yescharacteristic
683C22×C4C2×C22⋊D1111yescharacteristic
684C22×C4C2×C22⋊D1111yescharacteristic
685C22×C4C2×C22⋊D1111yescharacteristic
686C2×C8—22no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—41no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—41no—
693C2×C8—222no—
694C2×C8—222no—
695C2×C8—222no—
696C2×C8—441no—
697C2×C8—441no—
698C2×C8—441no—
699C2×C8—441no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—41no—
703C4⋊C4—41no—
704C4⋊C4—222no—
705C4⋊C4—222no—
706C4⋊C4—441no—
707C4⋊C4—441no—
708C42—222no—
709C42—222no—
710C42—222no—
711C42—222no—
712C11#1100811yescharacteristic, complemented, Sylow
713C23—24no—
714C23—44no—
715C23—44no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—82no—
727C23—81no—
728C23—81no—
729C23—82no—
730C23—81no—
731C23—81no—
732C23—82no—
733C23—82no—
734C23—82no—
735C23—82no—
736C23—224no—
737C23—444no—
738C23—444no—
739C23—442no—
740C23—442no—
741C23—442no—
742C23—442no—
743C23—442no—
744C23—442no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—882no—
750C23—881no—
751C23—881no—
752C23—882no—
753C23—881no—
754C23—881no—
755C23—882no—
756C23—882no—
757C23—882no—
758C23—882no—
759C23C22⋊C4×D1111yescharacteristic
760C23#6693511yescharacteristic
761C23#6693711yescharacteristic
762C23#6693811yescharacteristic
763C23D8×D1112yes—
764C23#6696412yes—
765C23SD16×D1112yes—
766C23#6696712yes—
767C23#6699011yescharacteristic
768C23#6699211yescharacteristic
769C23#6699311yescharacteristic
770D4—24no—
771D4—24no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—224no—
779D4—224no—
780D4—4464no—
781D4—442no—
782D4—442no—
783D4—442no—
784D4—442no—
785D4—442no—
786D4—442no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—82no—
792C2×C4—118no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—224no—
796C2×C4—224no—
797C2×C4—224no—
798C2×C4—224no—
799C2×C4—442no—
800C2×C4—444no—
801C2×C4—881no—
802C2×C4—881no—
803C2×C4—882no—
804C2×C4C22⋊C4×D1111yescharacteristic
805C2×C4(C22⋊D11)⋊C411yescharacteristic
806C2×C4(C22⋊D11)⋊C411yescharacteristic
807C2×C4#6693511yescharacteristic
808C2×C4#6693511yescharacteristic
809C2×C4#6693611yescharacteristic
810C2×C4#6693611yescharacteristic
811C2×C4#6693711yescharacteristic
812C2×C4#6693711yescharacteristic
813C2×C4#6693711yescharacteristic
814C2×C4#6693811yescharacteristic
815C2×C4#6693911yescharacteristic
816C2×C4C2×(C2×D11)⋊C411yescharacteristic
817C2×C4C4×C22⋊D1111yescharacteristic
818C2×C4C4×C22⋊D1111yescharacteristic
819C2×C4#6698211yescharacteristic
820C2×C4#6698311yescharacteristic
821C2×C4#6698311yescharacteristic
822C2×C4#6699011yescharacteristic
823C2×C4#6699011yescharacteristic
824C2×C4#6699011yescharacteristic
825C2×C4#6699111yescharacteristic
826C2×C4#6699111yescharacteristic
827C2×C4#6699211yescharacteristic
828C2×C4#6699211yescharacteristic
829C2×C4#6699211yescharacteristic
830C2×C4#6699311yescharacteristic
831C2×C4#6700611yescharacteristic
832C8—42no—
833C8—442no—
834C22—48no—
835C22—44no—
836C22—84no—
837C22—84no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—84no—
845C22—448no—
846C22—444no—
847C22—884no—
848C22—884no—
849C22—882no—
850C22—882no—
851C22—882no—
852C22—882no—
853C22—882no—
854C22—882no—
855C22—884no—
856C22#1062237312yes—
857C22#1062237512yes—
858C22#1062237712yes—
859C22D11×#10212yes—
860C22#1062238312yes—
861C22#1062238612yes—
862C22#1062238912yes—
863C22#1062239912yes—
864C22#1062256811yescharacteristic
865C22#1062257011yescharacteristic
866C22#1062257011yescharacteristic
867C22#1062257211yescharacteristic
868C22#1062257311yescharacteristic
869C22#1062257411yescharacteristic
870C22#1062276312yes—
871C22#1062276411yescharacteristic
872C22#1062276711yescharacteristic
873C22#1062276912yes—
874C22#1062277612yes—
875C22#1062278212yes—
876C22#1062278811yescharacteristic
877C22#1062278911yescharacteristic
878C22#1062283611yescharacteristic
879C4—82no—
880C4—228no—
881C4—882no—
882C4#1062256911yescharacteristic
883C4#1062256911yescharacteristic
884C4#1062257111yescharacteristic
885C4#1062257211yescharacteristic
886C4#1062257311yescharacteristic
887C4#1062257411yescharacteristic
888C4#1062282611yescharacteristic
889C4#1062283611yescharacteristic
890C2—84no—
891C2—884no—
892C2#1306685511yescharacteristic
893C2#1306854512yes—
894C2#1306942011yescharacteristic
895C2#1306943811yescharacteristic
896C2#1306954112yes—
897C2#1306968511yescharacteristic
898C2#1306968811yescharacteristic
899C2#1306970211yescharacteristic
900C2#1306970511yescharacteristic
901C2#1306984812yes—
902C2#1306984912yes—
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC22×#66993C2
cosocleC23×C4×C11C23
hypercenterC22×#102D11
hypocenterC11#11008
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#66885C2semidirect
3. C22×#66896C2semidirect
4. C22×#66873C2semidirect
5. C2×#10622188C2semidirect
6. #13066845C2semidirect
7. C22×C11×#102C2semidirect
18. C2×#66993C4semidirect
83. C22×C8×C11D4semidirect
89. C2×C11×C4⋊C4D4semidirect
99. C2×C4⋊Dic11D4semidirect
112. C22×C11⋊C8D4semidirect
266. C22×#102D11semidirect
379. C2×Dic11#102semidirect
528. C22×C8C22⋊D11semidirect
544. C2×C4⋊C4C22⋊D11semidirect
712. C11#11008semidirect

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#668852
C22×#668962
C22×#668732
C2×#106221882
#130668452
C22×C11×#1022
#1100811