Finite Group Databasebeta

← #14660437

Subgroups — #14660437

Order 2816.

1292 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622849C211yesmaximal, characteristic, complemented
2#13077135C211yesmaximal, characteristic, complemented
3C2×#10622850C211yesmaximal, characteristic, complemented
4C2×#10622853C211yesmaximal, characteristic, complemented
5#13068326C211yesmaximal, characteristic, complemented
6C2×#10622169C211yesmaximal, characteristic, complemented
7C11×#3449C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C22×C11×#41C2211yescharacteristic
10C11×#537—22no—
11C11×#536—21no—
12C11×#536—21no—
13C11×#535—21no—
14C11×#535—21no—
15C11×#534—22no—
16C11×#532—22no—
17C11×#525—22no—
18C11×#525C414yescomplemented
19C2×C11×#117C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24#10622853—22no—
25#10622853—22no—
26#10622850—22no—
27#10622850—22no—
28#10622849—22no—
29#10622849—22no—
30C2×#66901—22no—
31#10622846—22no—
32#10622845—22no—
33C2×#66900—21no—
34#10622838—21no—
35C2×#66898—22no—
36C2×#66897—21no—
37#10622828—21no—
38#10622169—22no—
39#10622161—22no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C2×C11×#41—21no—
62C2×C11×#41C2×C412yes—
63C2×C11×#41D412yes—
64C22×Q8×C11D411yescharacteristic
65C22×Q8×C11D411yescharacteristic
66C22×D4×C11—21no—
67C22×D4×C11D412yes—
68C22×D4×C11D411yescharacteristic
69C22×D4×C11D411yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2×C412yes—
72C23×C4×C11C2311yescharacteristic
73C11×C4⋊Q8—22no—
74C11×#127—22no—
75C11×#124—22no—
76C11×#124—22no—
77C11×#123—24no—
78C11×#123—24no—
79C11×C22⋊Q8—24no—
80C11×C22⋊Q8—24no—
81C11×#121—24no—
82C11×#121—28no—
83C11×#121—24no—
84C11×#120—24no—
85C11×#120—24no—
86C4×D4×C11—28no—
87C11×#117—21no—
88C11×#117—21no—
89C11×#117C2×C412yes—
90C11×#117D412yes—
91C2×C11×C4⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C42×C11D412yes—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96#66979—21no—
97#66979—21no—
98#66979—21no—
99#66979—21no—
100#66979—21no—
101#66979—21no—
102#66979D412yescomplemented
103#66979D412yescomplemented
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×#4318—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318—21no—
116C2×#4318—21no—
117C2×#4318—21no—
118C2×#4318D412yescomplemented
119C2×#4318D412yescomplemented
120C22×C11⋊C8—21no—
121C22×C11⋊C8—21no—
122#66901—28no—
123#66900—24no—
124#66899—24no—
125#66898—28no—
126#66897—24no—
127#66896—24no—
128#11000—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C22⋊C412yes—
131C24×C11C2×D411yescharacteristic
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—41no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C11×#41—41no—
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C11×#41—41no—
156C11×#41—41no—
157C11×#41—41no—
158C11×#41—41no—
159C11×#41—41no—
160C11×#41—41no—
161C11×#41—41no—
162C11×#41—41no—
163C11×#41—41no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11C22⋊C412yes—
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—22no—
182C2×D4×C11—22no—
183C2×D4×C11—22no—
184C2×D4×C11—28no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—41no—
197C2×D4×C11—41no—
198C2×D4×C11—41no—
199C2×D4×C11—41no—
200C2×D4×C11C22⋊C412yes—
201C22×C4×C11—21no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—41no—
212C22×C4×C11—41no—
213C22×C4×C11—41no—
214C22×C4×C11—41no—
215C22×C4×C11C22⋊C412yes—
216C22×C4×C11C22×C411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11#4111yescharacteristic
227C22×C4×C11#4111yescharacteristic
228C22×C4×C11#4111yescharacteristic
229C22×C4×C11#4111yescharacteristic
230C22×Dic11—41no—
231C22×Dic11—41no—
232C11×C4⋊C4—28no—
233C11×C4⋊C4—22no—
234C11×C4⋊C4—22no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—28no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—22no—
239C42×C11—22no—
240C42×C11C22⋊C414yes—
241C22⋊Dic11—22no—
242C22⋊Dic11—22no—
243C22⋊Dic11—41no—
244C22⋊Dic11—41no—
245C4⋊Dic11—22no—
246C4⋊Dic11—22no—
247C4⋊Dic11—41no—
248C4⋊Dic11—41no—
249C4×Dic11—22no—
250C4×Dic11—22no—
251C4×Dic11—41no—
252C4×Dic11—41no—
253#4318—22no—
254#4318—22no—
255#4318—22no—
256#4318—22no—
257#4318—41no—
258#4318—41no—
259#4318—41no—
260#4318—41no—
261C2×C11⋊C8—22no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—41no—
264C2×C11⋊C8—41no—
265C2×C11⋊C8—41no—
266C2×C11⋊C8—41no—
267#3449D1111yescharacteristic
268C2×#421—111no—
269#2896—111no—
270C2×#413—111no—
271C2×#410—111no—
272#1733—111no—
273C2×H(3,ℤ/4)—111no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—81no—
281C23×C11—82no—
282C23×C11—82no—
283C23×C11C2×C22⋊C411yescharacteristic
284C23×C11#12011yescharacteristic
285C23×C11#12011yescharacteristic
286C23×C11#12011yescharacteristic
287C23×C11#12111yescharacteristic
288C23×C11#12111yescharacteristic
289C23×C11#12311yescharacteristic
290Q8×C11—22no—
291Q8×C11—22no—
292Q8×C11—41no—
293Q8×C11—41no—
294Q8×C11—41no—
295Q8×C11—41no—
296Q8×C11—41no—
297Q8×C11—41no—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—42no—
301D4×C11—42no—
302D4×C11—42no—
303D4×C11—42no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—42no—
308D4×C11—41no—
309D4×C11—41no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—41no—
314D4×C11—88no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—82no—
331C2×C4×C11C2×C22⋊C411yescharacteristic
332C2×C4×C11C2×C22⋊C411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11C4×D411yescharacteristic
335C2×C4×C11C4×D411yescharacteristic
336C2×C4×C11C4×D411yescharacteristic
337C2×C4×C11#12011yescharacteristic
338C2×C4×C11#12011yescharacteristic
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12011yescharacteristic
341C2×C4×C11#12011yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12111yescharacteristic
344C2×C4×C11#12111yescharacteristic
345C2×C4×C11#12111yescharacteristic
346C2×C4×C11#12111yescharacteristic
347C2×C4×C11#12111yescharacteristic
348C2×C4×C11#12111yescharacteristic
349C2×C4×C11#12111yescharacteristic
350C2×C4×C11#12111yescharacteristic
351C2×C4×C11#12111yescharacteristic
352C2×C4×C11#12311yescharacteristic
353C2×C4×C11#12311yescharacteristic
354C2×C4×C11#12311yescharacteristic
355C2×C4×C11#12411yescharacteristic
356C2×C4×C11#12411yescharacteristic
357C2×C4×C11#12711yescharacteristic
358C2×C4×C11#12711yescharacteristic
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—82no—
362C2×Dic11—82no—
363C11⋊C8—42no—
364C11⋊C8—42no—
365C22×#41C2×D1111yescharacteristic
366C22×#41C2×D1111yescharacteristic
367C22×M16—111no—
368C22×M16—111no—
369#537—22no—
370#536—21no—
371#536—21no—
372#535—21no—
373#535—21no—
374#534—22no—
375#532—22no—
376#525—22no—
377#525Dic1114yescomplemented
378C2×#117—111no—
379C2×#117—111no—
380C2×#117C2×D1111yescharacteristic
381#421—222no—
382#421—222no—
383C2×#104—222no—
384#419—221no—
385#418—221no—
386#417—222no—
387#416—222no—
388#413—222no—
389#413—222no—
390C2×#101—221no—
391C2×#100—221no—
392#410—222no—
393#410—222no—
394C2×#99—222no—
395#339—222no—
396H(3,ℤ/4)—222no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—44no—
405C22×C11—44no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—82no—
409C22×C11—82no—
410C22×C11—82no—
411C22×C11—82no—
412C22×C11#37911yescharacteristic
413C22×C11#38611yescharacteristic
414C22×C11#38611yescharacteristic
415C22×C11#39211yescharacteristic
416C22×C11#39211yescharacteristic
417C22×C11#39411yescharacteristic
418C22×C11#39411yescharacteristic
419C4×C11—44no—
420C4×C11—42no—
421C4×C11—42no—
422C4×C11#38611yescharacteristic
423C4×C11#38611yescharacteristic
424C4×C11#39011yescharacteristic
425C4×C11#39011yescharacteristic
426C4×C11#39211yescharacteristic
427C4×C11#39211yescharacteristic
428C4×C11#39411yescharacteristic
429C4×C11#39411yescharacteristic
430Dic11—82no—
431Dic11—82no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41C2×Dic1112yes—
455C2×#41C22⋊D1112yes—
456C22×Q8C22⋊D1111yescharacteristic
457C22×Q8C22⋊D1111yescharacteristic
458C22×D4—21no—
459C22×D4C22⋊D1112yes—
460C22×D4C22⋊D1111yescharacteristic
461C22×D4C22⋊D1111yescharacteristic
462C23×C4—21no—
463C23×C4C2×Dic1112yes—
464C23×C4C22×D1111yescharacteristic
465C2×M16—112no—
466C2×M16—112no—
467C2×M16—221no—
468C2×M16—221no—
469C2×M16—221no—
470C2×M16—221no—
471C2×M16—221no—
472C2×M16—221no—
473C2×M16—221no—
474C2×M16—221no—
475C2×M16—221no—
476C2×M16—221no—
477C22×C8—221no—
478C22×C8—221no—
479C4⋊Q8—22no—
480#127—22no—
481#124—22no—
482#124—22no—
483#123—24no—
484#123—24no—
485C22⋊Q8—24no—
486C22⋊Q8—24no—
487#121—24no—
488#121—28no—
489#121—24no—
490#120—24no—
491#120—24no—
492C4×D4—28no—
493#117—21no—
494#117—21no—
495#117—112no—
496#117—112no—
497#117—221no—
498#117—221no—
499#117—221no—
500#117—221no—
501#117—221no—
502#117—221no—
503#117C2×Dic1112yes—
504#117C22⋊D1112yes—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C42—221no—
512C2×C42—221no—
513C2×C42C22⋊D1112yes—
514#104—228no—
515#103—224no—
516#102—224no—
517#101—224no—
518#100—224no—
519#99—228no—
520C2×C11—21no—
521C2×C11—21no—
522C2×C11—21no—
523C2×C11—21no—
524C2×C11—21no—
525C2×C11—21no—
526C2×C11—21no—
527C2×C11—82no—
528C2×C11—82no—
529C2×C11#143811yescharacteristic
530C24—21no—
531C24C22⋊Dic1112yes—
532C24C2×C22⋊D1111yescharacteristic
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8C22⋊Dic1112yes—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—28no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4C22⋊Dic1112yes—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—441no—
617C22×C4—441no—
618C22×C4C22⋊Dic1112yes—
619C22×C4D4×D1111yescharacteristic
620C22×C4D4×D1111yescharacteristic
621C22×C4D4×D1111yescharacteristic
622C22×C4D4×D1111yescharacteristic
623C22×C4#434111yescharacteristic
624C22×C4#434111yescharacteristic
625C22×C4#434111yescharacteristic
626C22×C4#434111yescharacteristic
627C22×C4C22×Dic1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629C22×C4C2×C22⋊D1111yescharacteristic
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C2×C22⋊D1111yescharacteristic
632C22×C4C2×C22⋊D1111yescharacteristic
633M16—222no—
634M16—222no—
635M16—222no—
636M16—222no—
637M16—441no—
638M16—441no—
639M16—441no—
640M16—441no—
641C2×C8—222no—
642C2×C8—222no—
643C2×C8—441no—
644C2×C8—441no—
645C2×C8—441no—
646C2×C8—441no—
647C4⋊C4—28no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—222no—
651C4⋊C4—222no—
652C4⋊C4—441no—
653C4⋊C4—441no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—222no—
659C22⋊C4—222no—
660C22⋊C4—441no—
661C22⋊C4—441no—
662C42—22no—
663C42—222no—
664C42—222no—
665C42—441no—
666C42—441no—
667C42C22⋊Dic1114yes—
668C11#1100011yescharacteristic, complemented, Sylow
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—81no—
676C23—82no—
677C23—82no—
678C23#6698811yescharacteristic
679C23#6699011yescharacteristic
680C23#6699211yescharacteristic
681C23#6699211yescharacteristic
682C23C2×C22⋊Dic1111yescharacteristic
683C23#6700611yescharacteristic
684C23#6700611yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—88no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—82no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—882no—
729C2×C4—882no—
730C2×C4D4×Dic1111yescharacteristic
731C2×C4D4×Dic1111yescharacteristic
732C2×C4D4×Dic1111yescharacteristic
733C2×C4D4×Dic1111yescharacteristic
734C2×C4#6698811yescharacteristic
735C2×C4#6698811yescharacteristic
736C2×C4#6698811yescharacteristic
737C2×C4#6698911yescharacteristic
738C2×C4#6698911yescharacteristic
739C2×C4#6699011yescharacteristic
740C2×C4#6699011yescharacteristic
741C2×C4#6699011yescharacteristic
742C2×C4#6699111yescharacteristic
743C2×C4#6699111yescharacteristic
744C2×C4#6699111yescharacteristic
745C2×C4#6699111yescharacteristic
746C2×C4#6699211yescharacteristic
747C2×C4#6699211yescharacteristic
748C2×C4#6699211yescharacteristic
749C2×C4#6699211yescharacteristic
750C2×C4#6699211yescharacteristic
751C2×C4#6699211yescharacteristic
752C2×C4#6699311yescharacteristic
753C2×C4#6699311yescharacteristic
754C2×C4C2×C22⋊Dic1111yescharacteristic
755C2×C4C2×C22⋊Dic1111yescharacteristic
756C2×C4#6700611yescharacteristic
757C2×C4#6700611yescharacteristic
758C8—442no—
759C8—442no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22#1062283311yescharacteristic
776C22#1062283311yescharacteristic
777C22#1062283511yescharacteristic
778C22#1062283511yescharacteristic
779C22#1062283611yescharacteristic
780C22#1062283611yescharacteristic
781C22#1062286011yescharacteristic
782C4—44no—
783C4—42no—
784C4—42no—
785C4—882no—
786C4—882no—
787C4#1062283311yescharacteristic
788C4#1062283311yescharacteristic
789C4#1062283411yescharacteristic
790C4#1062283411yescharacteristic
791C4#1062283511yescharacteristic
792C4#1062283511yescharacteristic
793C4#1062283611yescharacteristic
794C4#1062283611yescharacteristic
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—82no—
803C2—82no—
804C2#1306685711yescharacteristic
subgroupG/H
centerC4#10622834
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3449C2
socleC2×C11#1438
cosocleC23×C4×C11C23
hypercenter#3449D11
hypocenterC11#11000
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#10622849C2semidirect
2. #13077135C2semidirect
3. C2×#10622850C2semidirect
4. C2×#10622853C2semidirect
5. #13068326C2semidirect
6. C2×#10622169C2semidirect
18. C11×#525C4semidirect
102. #66979D4semidirect
103. #66979D4semidirect
118. C2×#4318D4semidirect
119. C2×#4318D4semidirect
377. #525Dic11semidirect
668. C11#11000semidirect

Maximal subgroups

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

subgroupindex
C2×#106228492
#130771352
C2×#106228502
C2×#106228532
#130683262
C2×#106221692
C11×#34492
#1100011