Finite Group Databasebeta

← #14781617

Subgroups — #14781617

Order 2816.

1332 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C2×#10622737C211yesmaximal, characteristic, complemented
3C2×#10622618C211yesmaximal, characteristic, complemented
4C2×#10622850C211yesmaximal, characteristic, complemented
5C2×#10622745C211yesmaximal, characteristic, complemented
6#13069894C214yesmaximal, complemented
7#13069887C214yesmaximal, complemented
8C2×#10622171C211yesmaximal, characteristic, complemented
9C11×#2896C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#67004—21no—
15#10623353—22no—
16#10623353—22no—
17#10623353—22no—
18#10623353—22no—
19C2×#67003—22no—
20C2×#67002—21no—
21C2×#66995C2212yes—
22C2×#66985C2212yes—
23C22×#4318C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C11×#419C2212yescomplemented
27C11×#418C2212yescomplemented
28C11×#417—22no—
29C11×#416—22no—
30#10622850—22no—
31#10622850—22no—
32C2×#66900C2212yescomplemented
33C2×#66897C2212yescomplemented
34C2×#66888—21no—
35#10622745—22no—
36#10622745C2214yes—
37C2×#66887—21no—
38#10622737—22no—
39#10622737C2214yescomplemented
40C2×#66886—22no—
41#10622618—22no—
42#10622618C2214yes—
43C2×#66869—22no—
44#10622171C2214yescomplemented
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×#41D412yes—
56C2×C11×#41D412yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—21no—
68C2×#4339—21no—
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339—21no—
72C2×#4339—21no—
73C2×#4339D412yes—
74C2×#4339C2312yes—
75C22×D44D411yescharacteristic
76C22×C4×D11—21no—
77C22×Dic22D411yescharacteristic
78C2×C11×M16—21no—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16—21no—
82C2×C11×M16—21no—
83C2×C11×M16C2312yes—
84C22×C8×C11—21no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117—21no—
88C11×#117C2312yes—
89C2×C11×C4⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C42×C11—21no—
92#67004—24no—
93#67004—24no—
94#67003—28no—
95#67003—28no—
96#67002—24no—
97#67002—24no—
98C2×#4326—22no—
99#66995—24no—
100#66995—24no—
101C2×#4325—22no—
102C2×#4324—22no—
103#66985—24no—
104#66985—24no—
105C2×#4323—22no—
106C2×#4318—21no—
107C2×#4318—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×#4318D412yes—
118C2×#4318D412yes—
119C2×#4318D412yes—
120C2×#4318D412yes—
121C2×#4318C2312yes—
122C2×#4318C2312yes—
123C2×#4318C2312yes—
124C22×C11⋊C8—21no—
125C22×C11⋊C8—21no—
126C22×C11⋊C8—21no—
127C11×#103—24no—
128C11×#102—24no—
129#66900—24no—
130#66897—24no—
131#66888—24no—
132#66887—24no—
133#66886—28no—
134#66869—28no—
135#23525—111nomaximal, Sylow
136C24×C11—21no—
137C24×C11#4111yescharacteristic
138C23×D11—21no—
139C11×#41—22no—
140C11×#41—22no—
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—41no—
148C11×#41—41no—
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C2×D412yes—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—41no—
169C2×D4×C11—41no—
170C2×D4×C11—41no—
171C2×D4×C11—41no—
172C2×D4×C11C2×D412yes—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11#4111yescharacteristic
190C22×C4×C11#4111yescharacteristic
191C22×C4×C11#4111yescharacteristic
192C22×C4×C11#4111yescharacteristic
193C22×C4×C11#4111yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—22no—
196C2×C22⋊D11—22no—
197C2×C22⋊D11—41no—
198C2×C22⋊D11—41no—
199C2×C22⋊D11—41no—
200C2×C22⋊D11—41no—
201C22×Dic11—21no—
202#4339—22no—
203#4339—22no—
204#4339—22no—
205#4339—22no—
206#4339—22no—
207#4339—22no—
208#4339—22no—
209#4339—22no—
210#4339—41no—
211#4339—41no—
212#4339—41no—
213#4339—41no—
214#4339—41no—
215#4339—41no—
216#4339—41no—
217#4339—41no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44C2×D412yes—
224C2×C4×D11—22no—
225C2×C4×D11—22no—
226C2×C4×D11—41no—
227C2×C4×D11—41no—
228C2×C4×D11—41no—
229C2×C4×D11—41no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22C2×D412yes—
236C11×M16—22no—
237C11×M16—22no—
238C11×M16—41no—
239C11×M16—41no—
240C2×C8×C11—22no—
241C2×C8×C11—41no—
242C2×C8×C11—41no—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—41no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—41no—
247C42×C11—22no—
248C42×C11—41no—
249#4326—28no—
250#4325—28no—
251#4324—28no—
252#4323—28no—
253#4318—22no—
254#4318—22no—
255#4318—22no—
256#4318—22no—
257#4318—22no—
258#4318—22no—
259#4318—22no—
260#4318—22no—
261#4318—41no—
262#4318—41no—
263#4318C2×D414yes—
264#4318C2×D414yes—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—41no—
273C2×C11⋊C8—41no—
274C2×#575—111no—
275C2×#430—111no—
276C2×#421—111no—
277#2896D1111yescharacteristic, complemented
278C2×#413—111no—
279C2×#413—111no—
280#2049—114no—
281#2048—114no—
282C2×#344—111no—
283C23×C11—22no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—81no—
287C23×C11—82no—
288C23×C11#12111yescharacteristic
289C23×C11#12111yescharacteristic
290C23×C11#12311yescharacteristic
291C23×C11#12311yescharacteristic
292C23×C11#12411yescharacteristic
293C23×C11#12411yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C22×D11—22no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—82no—
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—41no—
302Q8×C11—41no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—42no—
308D4×C11—42no—
309D4×C11—41no—
310D4×C11—41no—
311C2×C4×C11—22no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—82no—
320C2×C4×C11#12011yescharacteristic
321C2×C4×C11#12011yescharacteristic
322C2×C4×C11#12011yescharacteristic
323C2×C4×C11#12011yescharacteristic
324C2×C4×C11#12111yescharacteristic
325C2×C4×C11#12111yescharacteristic
326C2×C4×C11#12111yescharacteristic
327C2×C4×C11#12111yescharacteristic
328C2×C4×C11#12111yescharacteristic
329C2×C4×C11#12111yescharacteristic
330C2×C4×C11#12111yescharacteristic
331C2×C4×C11#12111yescharacteristic
332C2×C4×C11#12111yescharacteristic
333C2×C4×C11#12111yescharacteristic
334C2×C4×C11#12311yescharacteristic
335C2×C4×C11#12311yescharacteristic
336C2×C4×C11#12311yescharacteristic
337C2×C4×C11#12311yescharacteristic
338C2×C4×C11#12311yescharacteristic
339C2×C4×C11#12311yescharacteristic
340C2×C4×C11#12411yescharacteristic
341C2×C4×C11#12411yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11C22×D411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4111yescharacteristic
347C2×C4×C11C2×#4111yescharacteristic
348C22⋊D11—42no—
349C22⋊D11—42no—
350C22⋊D11—42no—
351C22⋊D11—42no—
352C2×Dic11—22no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355D44—22no—
356D44—22no—
357D44—41no—
358D44—41no—
359C4×D11—42no—
360C4×D11—42no—
361C4×D11—42no—
362C4×D11—42no—
363Dic22—22no—
364Dic22—22no—
365Dic22—41no—
366Dic22—41no—
367C8×C11—42no—
368C11⋊C8—24no—
369C11⋊C8—24no—
370C11⋊C8—42no—
371C22×#41—111no—
372C22×#41C2×D1111yescharacteristic
373#575—222no—
374#575—222no—
375#575—222no—
376#575—222no—
377C2×#137—112no—
378C2×#137—221no—
379C2×AGL(1,ℤ/8)—112no—
380C2×AGL(1,ℤ/8)—221no—
381C2×#135—222no—
382C22×M16—111no—
383C22×M16—111no—
384C22×M16—111no—
385C22×M16C2×D1111yescharacteristic
386C2×#117C2×D1111yescharacteristic
387#430—114no—
388#430—222no—
389C2×#108—222no—
390#421—114no—
391#421—222no—
392C2×#104—222no—
393#419C2×D1112yescomplemented
394#418C2×D1112yescomplemented
395#417—22no—
396#416—22no—
397#413—114no—
398#413—222no—
399#413—222no—
400#413—222no—
401C2×#101—112no—
402C2×#101—221no—
403C2×#100—112no—
404C2×#100—221no—
405#344—114no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—42no—
414C22×C11—82no—
415C22×C11—82no—
416C22×C11—82no—
417C22×C11#39411yescharacteristic
418C22×C11#39411yescharacteristic
419C22×C11#39411yescharacteristic
420C22×C11#39411yescharacteristic
421C22×C11C2×#12111yescharacteristic
422C22×C11C2×#12311yescharacteristic
423C22×C11C2×#12411yescharacteristic
424C2×D11—42no—
425C2×D11—82no—
426C2×D11—82no—
427C2×D11—82no—
428C4×C11—42no—
429C4×C11—82no—
430C4×C11#39411yescharacteristic
431C4×C11#39411yescharacteristic
432C4×C11#39411yescharacteristic
433C4×C11#39411yescharacteristic
434C4×C11C2×#12011yescharacteristic
435C4×C11C2×#12111yescharacteristic
436C4×C11C2×#12111yescharacteristic
437C4×C11C2×#12311yescharacteristic
438Dic11—42no—
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—112no—
450C2×#41—112no—
451C2×#41—221no—
452C2×#41—221no—
453C2×#41—221no—
454C2×#41—221no—
455C2×#41—221no—
456C2×#41—221no—
457C2×#41—221no—
458C2×#41—221no—
459C2×#41—221no—
460C2×#41—221no—
461C2×#41C22⋊D1112yes—
462C2×#41C22⋊D1112yes—
463C22×Q8—111no—
464C22×Q8C22×D1111yescharacteristic
465C22×D4—21no—
466C22×D4—111no—
467C22×D4—221no—
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—221no—
471C23×C4C22×D1111yescharacteristic
472#137—224no—
473#137—224no—
474#137—224no—
475#137—224no—
476AGL(1,ℤ/8)—224no—
477AGL(1,ℤ/8)—224no—
478AGL(1,ℤ/8)—224no—
479AGL(1,ℤ/8)—224no—
480#135—228no—
481#135—228no—
482C2×Q16—222no—
483C2×SD16—222no—
484C2×SD16—222no—
485C2×D8—222no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—112no—
492C2×M16—112no—
493C2×M16—112no—
494C2×M16—112no—
495C2×M16—112no—
496C2×M16—112no—
497C2×M16—112no—
498C2×M16—221no—
499C2×M16—221no—
500C2×M16—221no—
501C2×M16—221no—
502C2×M16—221no—
503C2×M16—221no—
504C2×M16—221no—
505C2×M16—221no—
506C2×M16—221no—
507C2×M16—221no—
508C2×M16—221no—
509C2×M16C22×D1112yes—
510C22×C8—21no—
511C22×C8—221no—
512C22×C8—221no—
513C22×C8—221no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117C22×D1112yes—
518C2×C4⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C42—21no—
521#108—228no—
522#104—228no—
523#103—24no—
524#102—24no—
525#101—224no—
526#101—224no—
527#100—224no—
528#100—224no—
529C2×C11—21no—
530C2×C11—21no—
531C2×C11—21no—
532C2×C11—21no—
533C2×C11—21no—
534C2×C11—21no—
535C2×C11—21no—
536C2×C11—82no—
537C2×C11C2×#39411yescharacteristic
538D11—82no—
539C24—21no—
540C24—221no—
541C24#434111yescharacteristic
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
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—222no—
559#41—222no—
560#41—222no—
561#41—222no—
562#41—222no—
563#41—222no—
564#41—222no—
565#41—222no—
566#41—441no—
567#41—441no—
568#41—441no—
569#41—441no—
570#41—441no—
571#41—441no—
572#41—441no—
573#41—441no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—112no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8—221no—
583C2×Q8—221no—
584C2×Q8—221no—
585C2×Q8C2×C22⋊D1112yes—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—112no—
598C2×D4—222no—
599C2×D4—222no—
600C2×D4—221no—
601C2×D4—221no—
602C2×D4—221no—
603C2×D4—221no—
604C2×D4—221no—
605C2×D4—441no—
606C2×D4—441no—
607C2×D4—441no—
608C2×D4—441no—
609C2×D4C2×C22⋊D1112yes—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—221no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—441no—
622C22×C4—441no—
623C22×C4—441no—
624C22×C4—441no—
625C22×C4#433911yescharacteristic
626C22×C4#433911yescharacteristic
627C22×C4#433911yescharacteristic
628C22×C4#433911yescharacteristic
629C22×C4D4×D1111yescharacteristic
630C22×C4D4×D1111yescharacteristic
631C22×C4D4×D1111yescharacteristic
632C22×C4D4×D1111yescharacteristic
633C22×C4D4×D1111yescharacteristic
634C22×C4D4×D1111yescharacteristic
635C22×C4#434111yescharacteristic
636C22×C4C2×C22⋊D1111yescharacteristic
637C22×C4C2×C22⋊D1111yescharacteristic
638C22×C4C23×D1111yescharacteristic
639Q16—228no—
640SD16—228no—
641SD16—228no—
642D8—228no—
643M16—22no—
644M16—22no—
645M16—41no—
646M16—41no—
647M16—114no—
648M16—114no—
649M16—222no—
650M16—222no—
651M16—222no—
652M16—222no—
653M16—222no—
654M16—222no—
655M16—222no—
656M16—222no—
657M16—441no—
658M16—441no—
659C2×C8—22no—
660C2×C8—41no—
661C2×C8—41no—
662C2×C8—222no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8—222no—
667C2×C8—222no—
668C2×C8—222no—
669C2×C8—441no—
670C2×C8—441no—
671C4⋊C4—22no—
672C4⋊C4—41no—
673C22⋊C4—22no—
674C22⋊C4—41no—
675C42—22no—
676C42—41no—
677C11#2352511yescharacteristic, complemented, Sylow
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—82no—
683C23—222no—
684C23—441no—
685C23—441no—
686C23—882no—
687C23#6693611yescharacteristic
688C23#6693611yescharacteristic
689C23#6693811yescharacteristic
690C23#6693811yescharacteristic
691C23#6699211yescharacteristic
692C23#6699211yescharacteristic
693C23C2×#434111yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—222no—
699Q8—222no—
700Q8—441no—
701Q8—441no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4—222no—
711D4—222no—
712D4—442no—
713D4—442no—
714D4—442no—
715D4—442no—
716D4—441no—
717D4—441no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—82no—
727C2×C4—222no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4#6693611yescharacteristic
735C2×C4#6693611yescharacteristic
736C2×C4#6693711yescharacteristic
737C2×C4#6693711yescharacteristic
738C2×C4#6693711yescharacteristic
739C2×C4#6693711yescharacteristic
740C2×C4#6693711yescharacteristic
741C2×C4#6693711yescharacteristic
742C2×C4#6693711yescharacteristic
743C2×C4#6693711yescharacteristic
744C2×C4#6693811yescharacteristic
745C2×C4#6693811yescharacteristic
746C2×C4#6698211yescharacteristic
747C2×C4#6698211yescharacteristic
748C2×C4#6698211yescharacteristic
749C2×C4#6698211yescharacteristic
750C2×C4#6699011yescharacteristic
751C2×C4#6699011yescharacteristic
752C2×C4#6699011yescharacteristic
753C2×C4#6699011yescharacteristic
754C2×C4#6699211yescharacteristic
755C2×C4#6699211yescharacteristic
756C2×C4C2×#433911yescharacteristic
757C2×C4C2×#433911yescharacteristic
758C2×C4C2×D4×D1111yescharacteristic
759C2×C4C2×D4×D1111yescharacteristic
760C2×C4C2×D4×D1111yescharacteristic
761C2×C4C22×C22⋊D1111yescharacteristic
762C8—42no—
763C8—224no—
764C8—224no—
765C8—442no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—442no—
778C22—882no—
779C22—882no—
780C22—882no—
781C22#1062257211yescharacteristic
782C22#1062257211yescharacteristic
783C22#1062257211yescharacteristic
784C22#1062257211yescharacteristic
785C22C2×#6693611yescharacteristic
786C22C2×#6693811yescharacteristic
787C22C2×#6699211yescharacteristic
788C4—42no—
789C4—82no—
790C4—442no—
791C4#1062257211yescharacteristic
792C4#1062257211yescharacteristic
793C4#1062257211yescharacteristic
794C4#1062257211yescharacteristic
795C4C2×#6693711yescharacteristic
796C4C2×#6693711yescharacteristic
797C4C2×#6698211yescharacteristic
798C4C2×#6699011yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—82no—
807C2—882no—
808C2C2×#1062257211yescharacteristic
subgroupG/H
centerC4#10622572
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2896C2
socleC2×C11C2×#394
prime radicalC2×#10623353C2
hypercenter#2896D11
hypocenterC11#23525
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. C2×#10622737C2semidirect
3. C2×#10622618C2semidirect
4. C2×#10622850C2semidirect
5. C2×#10622745C2semidirect
6. #13069894C2semidirect
7. #13069887C2semidirect
8. C2×#10622171C2semidirect
9. C11×#2896C2semidirect
26. C11×#419C22semidirect
27. C11×#418C22semidirect
32. C2×#66900C22semidirect
33. C2×#66897C22semidirect
39. #10622737C22semidirect
44. #10622171C22semidirect
277. #2896D11semidirect
393. #419C2×D11semidirect
394. #418C2×D11semidirect
677. C11#23525semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106227372
C2×#106226182
C2×#106228502
C2×#106227452
#130698942
#130698872
C2×#106221712
C11×#28962
#2352511