Finite Group Databasebeta

← #14781695

Subgroups — #14781695

Order 2816.

1352 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2#13077180C211yesmaximal, characteristic, complemented
3#13077135C211yesmaximal, characteristic, complemented
4#13077133C211yesmaximal, characteristic, complemented
5C2×#10622619C211yesmaximal, characteristic, complemented
6#13069921C218yesmaximal, complemented
7C2×#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#410C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#67004—21no—
14#10623353—22no—
15#10623353—22no—
16#10623353—22no—
17#10623353C2214yes—
18C2×#67003—22no—
19C2×#67002—21no—
20C2×#66995—21no—
21C2×#66985—21no—
22C2×#66979C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C11×#410—22no—
26C11×#410C2214yescomplemented
27C2×C11×#99—22no—
28#10622846C2214yescomplemented
29#10622845—22no—
30#10622838—21no—
31#10622828—21no—
32#10622619—22no—
33#10622619C2214yescomplemented
34#10622617—21no—
35#10622615C2214yescomplemented
36#10622614—21no—
37#10622612—22no—
38#10622612C2214yescomplemented
39#10622579—22no—
40C2×#66870—22no—
41#10622537—22no—
42#10622169C2214yescomplemented
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×#41D412yes—
54C2×C11×#41C2312yes—
55C22×Q8×C11D411yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11D411yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C2×#4339—21no—
62C2×#4339—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×#4339D412yes—
72C2×#4339C2312yes—
73C22×D44D411yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22D411yescharacteristic
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117D412yes—
82C11×#117C2312yes—
83C11×#117C2312yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C22⋊Dic11—21no—
91#67004—24no—
92#67004—24no—
93#67003—28no—
94#67003—28no—
95#67002—24no—
96#67002—24no—
97C2×#4326—22no—
98#66995—24no—
99#66995—24no—
100C2×#4325—22no—
101C2×#4324—22no—
102#66985—24no—
103#66985—24no—
104C2×#4323—22no—
105#66979—21no—
106#66979—21no—
107#66979—21no—
108#66979C2312yes—
109C2×C4⋊Dic11—21no—
110C2×C4×Dic11—21no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318—21no—
116C2×#4318—21no—
117C2×#4318—21no—
118C2×#4318—21no—
119C2×#4318—21no—
120C2×#4318—21no—
121C2×#4318D412yes—
122C2×#4318C2312yes—
123C22×C11⋊C8D412yes—
124C22×C11⋊C8C2312yes—
125C11×#99—28no—
126#66899—24no—
127#66896—24no—
128#66874—24no—
129#66873—24no—
130#66870—28no—
131C4⋊(C11⋊C8)—28no—
132#23535—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—22no—
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C11×#41—41no—
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—41no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11C2×D412yes—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—41no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C2×D4×C11—41no—
169C2×D4×C11C2×D412yes—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
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×C11C2×D411yescharacteristic
186C22×C4×C11#4111yescharacteristic
187C22×C4×C11#4111yescharacteristic
188C22×C4×C11#4111yescharacteristic
189C22×C4×C11#4111yescharacteristic
190C22×C4×C11#4111yescharacteristic
191C22×C4×C11#4111yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—22no—
194C2×C22⋊D11—22no—
195C2×C22⋊D11—41no—
196C2×C22⋊D11—41no—
197C2×C22⋊D11—41no—
198C2×C22⋊D11—41no—
199C22×Dic11—21no—
200C22×Dic11—41no—
201#4339—22no—
202#4339—22no—
203#4339—22no—
204#4339—22no—
205#4339—22no—
206#4339—22no—
207#4339—22no—
208#4339—22no—
209#4339—41no—
210#4339—41no—
211#4339—41no—
212#4339—41no—
213#4339—41no—
214#4339—41no—
215#4339—41no—
216#4339—41no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44C2×D412yes—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—41no—
226C2×C4×D11—41no—
227C2×C4×D11—41no—
228C2×C4×D11—41no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22C2×D412yes—
235C11×C4⋊C4—22no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4—41no—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—41no—
242C11×C22⋊C4C2×D414yes—
243C42×C11—22no—
244C42×C11—22no—
245C42×C11—22no—
246C42×C11—41no—
247C22⋊Dic11—22no—
248C22⋊Dic11—41no—
249#4326—28no—
250#4325—28no—
251#4324—28no—
252#4323—28no—
253C4⋊Dic11—22no—
254C4⋊Dic11—41no—
255C4×Dic11—22no—
256C4×Dic11—41no—
257#4318—22no—
258#4318—22no—
259#4318—22no—
260#4318—22no—
261#4318—41no—
262#4318—41no—
263#4318—41no—
264#4318—41no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8C2×D414yes—
271C2×#575—111no—
272#2905—111no—
273#2896—111no—
274#2896—111no—
275C2×#410—111no—
276C2×#410D1111yescharacteristic, complemented
277#2053—118no—
278C2×H(3,ℤ/4)—111no—
279C23×C11—22no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—81no—
283C23×C11—82no—
284C23×C11#12111yescharacteristic
285C23×C11#12111yescharacteristic
286C23×C11#12111yescharacteristic
287C23×C11#12111yescharacteristic
288C23×C11#12111yescharacteristic
289C23×C11#12111yescharacteristic
290C23×C11C22×D411yescharacteristic
291C22×D11—22no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—82no—
295Q8×C11—22no—
296Q8×C11—22no—
297Q8×C11—41no—
298Q8×C11—41no—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—42no—
302D4×C11—42no—
303D4×C11—42no—
304D4×C11—42no—
305D4×C11—41no—
306D4×C11—41no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—82no—
317C2×C4×C11—82no—
318C2×C4×C11#12011yescharacteristic
319C2×C4×C11#12011yescharacteristic
320C2×C4×C11#12011yescharacteristic
321C2×C4×C11#12011yescharacteristic
322C2×C4×C11#12111yescharacteristic
323C2×C4×C11#12111yescharacteristic
324C2×C4×C11#12111yescharacteristic
325C2×C4×C11#12111yescharacteristic
326C2×C4×C11#12111yescharacteristic
327C2×C4×C11#12111yescharacteristic
328C2×C4×C11#12311yescharacteristic
329C2×C4×C11#12311yescharacteristic
330C2×C4×C11#12311yescharacteristic
331C2×C4×C11#12311yescharacteristic
332C2×C4×C11#12311yescharacteristic
333C2×C4×C11#12311yescharacteristic
334C2×C4×C11#12311yescharacteristic
335C2×C4×C11#12311yescharacteristic
336C2×C4×C11#12411yescharacteristic
337C2×C4×C11#12411yescharacteristic
338C2×C4×C11#12411yescharacteristic
339C2×C4×C11#12411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11C2×#4111yescharacteristic
345C2×C4×C11C2×#4111yescharacteristic
346C22⋊D11—42no—
347C22⋊D11—42no—
348C22⋊D11—42no—
349C22⋊D11—42no—
350C2×Dic11—22no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—42no—
354C2×Dic11—82no—
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—
367C11⋊C8—24no—
368C11⋊C8—42no—
369C22×#41—111no—
370C22×#41C2×D1111yescharacteristic
371#575—114no—
372#575—222no—
373#575—222no—
374#575—222no—
375C2×#137—221no—
376C2×#137—221no—
377C2×AGL(1,ℤ/8)—221no—
378C2×AGL(1,ℤ/8)—221no—
379C2×#135—222no—
380C22×M16—111no—
381C22×M16—111no—
382C2×#117—111no—
383C2×#117C2×D1111yescharacteristic
384C2×#117C2×D1111yescharacteristic
385#424—114no—
386#424—222no—
387#423—222no—
388#419—221no—
389#419—221no—
390#418—221no—
391#418—221no—
392#417—222no—
393#417—222no—
394#416—114no—
395#416—114no—
396#410—22no—
397#410—114no—
398#410—222no—
399#410C2×D1114yescomplemented
400C2×#99—22no—
401C2×#99—222no—
402H(3,ℤ/4)—114no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—42no—
411C22×C11—82no—
412C22×C11—82no—
413C22×C11—82no—
414C22×C11#39411yescharacteristic
415C22×C11#39411yescharacteristic
416C22×C11#39411yescharacteristic
417C22×C11#39411yescharacteristic
418C22×C11C2×#12111yescharacteristic
419C22×C11C2×#12111yescharacteristic
420C22×C11C2×#12111yescharacteristic
421C2×D11—42no—
422C2×D11—82no—
423C2×D11—82no—
424C2×D11—82no—
425C4×C11—44no—
426C4×C11—42no—
427C4×C11—82no—
428C4×C11#39411yescharacteristic
429C4×C11#39411yescharacteristic
430C4×C11#39411yescharacteristic
431C4×C11#39411yescharacteristic
432C4×C11C2×#12011yescharacteristic
433C4×C11C2×#12311yescharacteristic
434C4×C11C2×#12311yescharacteristic
435C4×C11C2×#12411yescharacteristic
436Dic11—42no—
437Dic11—82no—
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—112no—
449C2×#41—112no—
450C2×#41—221no—
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×#41D4412yes—
461C2×#41C22×D1112yes—
462C22×Q8—111no—
463C22×Q8D4411yescharacteristic
464C22×D4—21no—
465C22×D4—111no—
466C22×D4—221no—
467C22×D4D4411yescharacteristic
468C23×C4—21no—
469C23×C4—221no—
470C23×C4C22×D1111yescharacteristic
471#137—224no—
472#137—224no—
473#137—224no—
474#137—224no—
475AGL(1,ℤ/8)—224no—
476AGL(1,ℤ/8)—224no—
477AGL(1,ℤ/8)—224no—
478AGL(1,ℤ/8)—224no—
479#135—228no—
480#135—228no—
481C2×Q16—222no—
482C2×SD16—222no—
483C2×SD16—222no—
484C2×D8—222no—
485C2×M16—112no—
486C2×M16—112no—
487C2×M16—221no—
488C2×M16—221no—
489C2×M16—221no—
490C2×M16—221no—
491C2×M16—221no—
492C2×M16—221no—
493C2×M16—221no—
494C2×M16—221no—
495C2×M16—221no—
496C2×M16—221no—
497C22×C8—112no—
498C22×C8—112no—
499#117—21no—
500#117—21no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—112no—
505#117—221no—
506#117—221no—
507#117—221no—
508#117C22⋊D1112yes—
509#117C22×D1112yes—
510#117C22×D1112yes—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—221no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4C22⋊D1112yes—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42—221no—
520C4⋊C8—228no—
521#103—224no—
522#103—224no—
523#102—224no—
524#102—224no—
525#99—28no—
526#99—228no—
527C2×C11—21no—
528C2×C11—21no—
529C2×C11—21no—
530C2×C11—21no—
531C2×C11—21no—
532C2×C11—21no—
533C2×C11—21no—
534C2×C11—82no—
535C2×C11C2×#39411yescharacteristic
536D11—82no—
537C24—21no—
538C24—221no—
539C24C2×C22⋊D1111yescharacteristic
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
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—222no—
557#41—222no—
558#41—222no—
559#41—222no—
560#41—222no—
561#41—222no—
562#41—222no—
563#41—222no—
564#41—441no—
565#41—441no—
566#41—441no—
567#41—441no—
568#41—441no—
569#41—441no—
570#41—441no—
571#41—441no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—112no—
578C2×Q8—221no—
579C2×Q8—221no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8—221no—
583C2×Q8C2×D4412yes—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—112no—
596C2×D4—222no—
597C2×D4—222no—
598C2×D4—221no—
599C2×D4—221no—
600C2×D4—221no—
601C2×D4—221no—
602C2×D4—221no—
603C2×D4—441no—
604C2×D4—441no—
605C2×D4—441no—
606C2×D4—441no—
607C2×D4C2×D4412yes—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—221no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—441no—
621C22×C4—441no—
622C22×C4—441no—
623C22×C4—441no—
624C22×C4—441no—
625C22×C4C2×D4411yescharacteristic
626C22×C4C2×D4411yescharacteristic
627C22×C4#433911yescharacteristic
628C22×C4#433911yescharacteristic
629C22×C4D4×D1111yescharacteristic
630C22×C4D4×D1111yescharacteristic
631C22×C4D4×D1111yescharacteristic
632C22×C4D4×D1111yescharacteristic
633C22×C4#434111yescharacteristic
634C22×C4#434111yescharacteristic
635C22×C4#434111yescharacteristic
636C22×C4#434111yescharacteristic
637C22×C4C2×C22⋊D1111yescharacteristic
638C22×C4C23×D1111yescharacteristic
639Q16—228no—
640SD16—228no—
641SD16—228no—
642D8—228no—
643M16—222no—
644M16—222no—
645M16—222no—
646M16—222no—
647M16—441no—
648M16—441no—
649M16—441no—
650M16—441no—
651C2×C8—114no—
652C2×C8—222no—
653C2×C8—222no—
654C2×C8—222no—
655C2×C8—222no—
656C2×C8—222no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—41no—
661C4⋊C4—222no—
662C4⋊C4—441no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—41no—
666C22⋊C4—222no—
667C22⋊C4—441no—
668C22⋊C4C2×C22⋊D1114yes—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—41no—
673C42—222no—
674C42—441no—
675C11#2353511yescharacteristic, complemented, Sylow
676C23—22no—
677C23—41no—
678C23—41no—
679C23—81no—
680C23—82no—
681C23—222no—
682C23—441no—
683C23—441no—
684C23—882no—
685C23#6698311yescharacteristic
686C23#6698311yescharacteristic
687C23#6699111yescharacteristic
688C23#6699111yescharacteristic
689C23#6699211yescharacteristic
690C23#6699211yescharacteristic
691C23C22×C22⋊D1111yescharacteristic
692Q8—22no—
693Q8—22no—
694Q8—41no—
695Q8—41no—
696Q8—222no—
697Q8—222no—
698Q8—441no—
699Q8—441no—
700D4—22no—
701D4—22no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—41no—
707D4—41no—
708D4—222no—
709D4—222no—
710D4—442no—
711D4—442no—
712D4—442no—
713D4—442no—
714D4—441no—
715D4—441no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—82no—
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—442no—
735C2×C4—882no—
736C2×C4#6693511yescharacteristic
737C2×C4#6693511yescharacteristic
738C2×C4#6693511yescharacteristic
739C2×C4#6693511yescharacteristic
740C2×C4#6693611yescharacteristic
741C2×C4#6693611yescharacteristic
742C2×C4#6693611yescharacteristic
743C2×C4#6693611yescharacteristic
744C2×C4#6693811yescharacteristic
745C2×C4#6693811yescharacteristic
746C2×C4#6693811yescharacteristic
747C2×C4#6693811yescharacteristic
748C2×C4#6693911yescharacteristic
749C2×C4#6693911yescharacteristic
750C2×C4#6693911yescharacteristic
751C2×C4#6693911yescharacteristic
752C2×C4#6698311yescharacteristic
753C2×C4#6698311yescharacteristic
754C2×C4#6699111yescharacteristic
755C2×C4#6699111yescharacteristic
756C2×C4#6699211yescharacteristic
757C2×C4#6699211yescharacteristic
758C2×C4C22×D4411yescharacteristic
759C2×C4C2×#433911yescharacteristic
760C2×C4C2×D4×D1111yescharacteristic
761C2×C4C2×D4×D1111yescharacteristic
762C2×C4C2×#434111yescharacteristic
763C2×C4C2×#434111yescharacteristic
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#1062257411yescharacteristic
782C22#1062257411yescharacteristic
783C22#1062257411yescharacteristic
784C22#1062257411yescharacteristic
785C22C2×#6698311yescharacteristic
786C22C2×#6699111yescharacteristic
787C22C2×#6699211yescharacteristic
788C4—44no—
789C4—42no—
790C4—82no—
791C4—442no—
792C4—882no—
793C4#1062257411yescharacteristic
794C4#1062257411yescharacteristic
795C4#1062257411yescharacteristic
796C4#1062257411yescharacteristic
797C4C2×#6693511yescharacteristic
798C4C2×#6693611yescharacteristic
799C4C2×#6693811yescharacteristic
800C4C2×#6693911yescharacteristic
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—82no—
809C2—882no—
810C2C2×#1062257411yescharacteristic
subgroupG/H
centerC4C2×#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#410C2
socleC2×C11C2×#394
prime radicalC2×#10623353C2
hypercenterC2×#410D11
hypocenterC11#23535
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #13077180C2semidirect
3. #13077135C2semidirect
4. #13077133C2semidirect
5. C2×#10622619C2semidirect
6. #13069921C2semidirect
7. C2×#10622169C2semidirect
8. C2×C11×#410C2semidirect
26. C11×#410C22semidirect
28. #10622846C22semidirect
33. #10622619C22semidirect
35. #10622615C22semidirect
38. #10622612C22semidirect
42. #10622169C22semidirect
276. C2×#410D11semidirect
399. #410C2×D11semidirect
675. C11#23535semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
#130771802
#130771352
#130771332
C2×#106226192
#130699212
C2×#106221692
C2×C11×#4102
#2353511