Finite Group Databasebeta

← #14781633

Subgroups — #14781633

Order 2816.

1336 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2#13077180C211yesmaximal, characteristic, complemented
3C2×#10622618C211yesmaximal, characteristic, complemented
4C2×#10622850C211yesmaximal, characteristic, complemented
5C2×#10622745C211yesmaximal, characteristic, complemented
6#13069902C218yesmaximal, complemented
7C2×C11⋊#338C211yesmaximal, characteristic, complemented
8C2×C11×#421C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
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—
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C11×#421—22no—
26C11×#421—22no—
27C2×C11×#104C2214yescomplemented
28#10622850—22no—
29#10622850C2214yescomplemented
30C2×#66900—21no—
31C2×#66897—21no—
32C2×#66888—21no—
33#10622745—22no—
34#10622745C2214yescomplemented
35C2×#66887—21no—
36#10622618—22no—
37#10622618—22no—
38#10622612—22no—
39#10622612—22no—
40C2×#66869C2214yescomplemented
41#10622537C2214yescomplemented
42C11⋊#338C2214yescomplemented
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
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16C2312yes—
82C22×C8×C11—21no—
83C11×#117—21no—
84C11×#117—21no—
85C11×#117D412yes—
86C11×#117D412yes—
87C2×C11×C4⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11C2312yes—
90#67004—24no—
91#67004—24no—
92#67003—28no—
93#67003—28no—
94#67002—24no—
95#67002—24no—
96C2×#4326—22no—
97#66995—24no—
98#66995—24no—
99C2×#4325—22no—
100C2×#4324—22no—
101#66985—24no—
102#66985—24no—
103C2×#4323—22no—
104C2×#4318—21no—
105C2×#4318—21no—
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×#4318—21no—
118C2×#4318D412yes—
119C2×#4318C2312yes—
120C2×#4318C2312yes—
121C2×#4318C2312yes—
122C22×C11⋊C8—21no—
123C22×C11⋊C8—21no—
124C22×C11⋊C8D412yes—
125C11×#104—28no—
126#66900—24no—
127#66897—24no—
128#66888—24no—
129#66887—24no—
130#66869—28no—
131C4⋊(C11⋊C8)—28no—
132#23527—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11#4111yescharacteristic
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×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×C11C2×D411yescharacteristic
186C22×C4×C11#4111yescharacteristic
187C22×C4×C11#4111yescharacteristic
188C22×C4×C11#4111yescharacteristic
189C22×C4×C11#4111yescharacteristic
190C22×C4×C11#4111yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11—41no—
195C2×C22⋊D11—41no—
196C2×C22⋊D11—41no—
197C2×C22⋊D11—41no—
198C22×Dic11—21no—
199#4339—22no—
200#4339—22no—
201#4339—22no—
202#4339—22no—
203#4339—22no—
204#4339—22no—
205#4339—22no—
206#4339—22no—
207#4339—41no—
208#4339—41no—
209#4339—41no—
210#4339—41no—
211#4339—41no—
212#4339—41no—
213#4339—41no—
214#4339—41no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44C2×D412yes—
221C2×C4×D11—22no—
222C2×C4×D11—22no—
223C2×C4×D11—41no—
224C2×C4×D11—41no—
225C2×C4×D11—41no—
226C2×C4×D11—41no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22C2×D412yes—
233C11×M16—22no—
234C11×M16—22no—
235C11×M16—41no—
236C11×M16—41no—
237C2×C8×C11—22no—
238C2×C8×C11—41no—
239C2×C8×C11—41no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—22no—
244C42×C11—22no—
245C42×C11C2×D414yes—
246#4326—28no—
247#4325—28no—
248#4324—28no—
249#4323—28no—
250#4318—22no—
251#4318—22no—
252#4318—22no—
253#4318—22no—
254#4318—22no—
255#4318—22no—
256#4318—22no—
257#4318—22no—
258#4318—41no—
259#4318—41no—
260#4318—41no—
261#4318—41no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—41no—
267C2×C11⋊C8—41no—
268C2×C11⋊C8—41no—
269C2×C11⋊C8—41no—
270C2×C11⋊C8C2×D414yes—
271C2×#575—111no—
272#2905—111no—
273C2×#421—111no—
274C2×#421D1111yescharacteristic, complemented
275C2×#413—111no—
276C2×#413—111no—
277#2050—118no—
278C2×#338—111no—
279C23×C11—22no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—81no—
283C23×C11—82no—
284C23×C11#12111yescharacteristic
285C23×C11#12111yescharacteristic
286C23×C11#12311yescharacteristic
287C23×C11#12311yescharacteristic
288C23×C11#12311yescharacteristic
289C23×C11#12311yescharacteristic
290C23×C11C2×#4111yescharacteristic
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—82no—
316C2×C4×C11#12011yescharacteristic
317C2×C4×C11#12011yescharacteristic
318C2×C4×C11#12011yescharacteristic
319C2×C4×C11#12011yescharacteristic
320C2×C4×C11#12111yescharacteristic
321C2×C4×C11#12111yescharacteristic
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#12111yescharacteristic
329C2×C4×C11#12111yescharacteristic
330C2×C4×C11#12311yescharacteristic
331C2×C4×C11#12311yescharacteristic
332C2×C4×C11#12311yescharacteristic
333C2×C4×C11#12311yescharacteristic
334C2×C4×C11#12411yescharacteristic
335C2×C4×C11#12411yescharacteristic
336C2×C4×C11#12411yescharacteristic
337C2×C4×C11#12411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C22⋊D11—42no—
345C22⋊D11—42no—
346C22⋊D11—42no—
347C22⋊D11—42no—
348C2×Dic11—22no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351D44—22no—
352D44—22no—
353D44—41no—
354D44—41no—
355C4×D11—42no—
356C4×D11—42no—
357C4×D11—42no—
358C4×D11—42no—
359Dic22—22no—
360Dic22—22no—
361Dic22—41no—
362Dic22—41no—
363C8×C11—42no—
364C11⋊C8—24no—
365C11⋊C8—42no—
366C11⋊C8—42no—
367C22×#41—111no—
368C22×#41C2×D1111yescharacteristic
369#575—114no—
370#575—222no—
371#575—222no—
372#575—222no—
373C2×#137—221no—
374C2×#137—221no—
375C2×AGL(1,ℤ/8)—221no—
376C2×AGL(1,ℤ/8)—221no—
377C2×#135—222no—
378C22×M16—111no—
379C22×M16—111no—
380C22×M16—111no—
381C22×M16C2×D1111yescharacteristic
382C2×#117C2×D1111yescharacteristic
383#424—222no—
384#424—222no—
385#423—114no—
386#421—22no—
387#421—22no—
388#421—222no—
389#421—222no—
390C2×#104—114no—
391C2×#104C2×D1114yescomplemented
392#413—114no—
393#413—114no—
394#413—222no—
395#413—222no—
396C2×#101—221no—
397C2×#101—221no—
398C2×#100—221no—
399C2×#100—221no—
400#338—114no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—42no—
409C22×C11—82no—
410C22×C11—82no—
411C22×C11—82no—
412C22×C11#39411yescharacteristic
413C22×C11#39411yescharacteristic
414C22×C11#39411yescharacteristic
415C22×C11#39411yescharacteristic
416C22×C11C2×#12111yescharacteristic
417C22×C11C2×#12311yescharacteristic
418C22×C11C2×#12311yescharacteristic
419C2×D11—42no—
420C2×D11—82no—
421C2×D11—82no—
422C2×D11—82no—
423C4×C11—44no—
424C4×C11—42no—
425C4×C11#39411yescharacteristic
426C4×C11#39411yescharacteristic
427C4×C11#39411yescharacteristic
428C4×C11#39411yescharacteristic
429C4×C11C2×#12011yescharacteristic
430C4×C11C2×#12111yescharacteristic
431C4×C11C2×#12111yescharacteristic
432C4×C11C2×#12411yescharacteristic
433Dic11—42no—
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—112no—
445C2×#41—112no—
446C2×#41—221no—
447C2×#41—221no—
448C2×#41—221no—
449C2×#41—221no—
450C2×#41—221no—
451C2×#41—221no—
452C2×#41—221no—
453C2×#41—221no—
454C2×#41—221no—
455C2×#41—221no—
456C2×#41D4412yes—
457C2×#41C22×D1112yes—
458C22×Q8—111no—
459C22×Q8D4411yescharacteristic
460C22×D4—21no—
461C22×D4—111no—
462C22×D4—221no—
463C22×D4D4411yescharacteristic
464C23×C4—21no—
465C23×C4—221no—
466C23×C4C22×D1111yescharacteristic
467#137—224no—
468#137—224no—
469#137—224no—
470#137—224no—
471AGL(1,ℤ/8)—224no—
472AGL(1,ℤ/8)—224no—
473AGL(1,ℤ/8)—224no—
474AGL(1,ℤ/8)—224no—
475#135—228no—
476#135—228no—
477C2×Q16—222no—
478C2×SD16—222no—
479C2×SD16—222no—
480C2×D8—222no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—112no—
487C2×M16—112no—
488C2×M16—112no—
489C2×M16—112no—
490C2×M16—221no—
491C2×M16—221no—
492C2×M16—221no—
493C2×M16—221no—
494C2×M16—221no—
495C2×M16—221no—
496C2×M16—221no—
497C2×M16—221no—
498C2×M16—221no—
499C2×M16—221no—
500C2×M16—221no—
501C2×M16—221no—
502C2×M16—221no—
503C2×M16—221no—
504C2×M16C22×D1112yes—
505C22×C8—21no—
506C22×C8—112no—
507C22×C8—221no—
508C22×C8—221no—
509#117—21no—
510#117—21no—
511#117C22⋊D1112yes—
512#117C22⋊D1112yes—
513C2×C4⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C42C22×D1112yes—
516C4⋊C8—228no—
517#104—28no—
518#104—228no—
519#101—224no—
520#101—224no—
521#100—224no—
522#100—224no—
523C2×C11—21no—
524C2×C11—21no—
525C2×C11—21no—
526C2×C11—21no—
527C2×C11—21no—
528C2×C11—21no—
529C2×C11—21no—
530C2×C11—82no—
531C2×C11C2×#39411yescharacteristic
532D11—82no—
533C24—21no—
534C24—221no—
535C24#434111yescharacteristic
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
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—222no—
553#41—222no—
554#41—222no—
555#41—222no—
556#41—222no—
557#41—222no—
558#41—222no—
559#41—222no—
560#41—441no—
561#41—441no—
562#41—441no—
563#41—441no—
564#41—441no—
565#41—441no—
566#41—441no—
567#41—441no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—112no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—221no—
579C2×Q8C2×D4412yes—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—112no—
592C2×D4—222no—
593C2×D4—222no—
594C2×D4—221no—
595C2×D4—221no—
596C2×D4—221no—
597C2×D4—221no—
598C2×D4—221no—
599C2×D4—441no—
600C2×D4—441no—
601C2×D4—441no—
602C2×D4—441no—
603C2×D4C2×D4412yes—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—221no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—441no—
616C22×C4—441no—
617C22×C4—441no—
618C22×C4—441no—
619C22×C4C2×D4411yescharacteristic
620C22×C4C2×D4411yescharacteristic
621C22×C4#433911yescharacteristic
622C22×C4#433911yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4D4×D1111yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4D4×D1111yescharacteristic
627C22×C4#434111yescharacteristic
628C22×C4#434111yescharacteristic
629C22×C4#434111yescharacteristic
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C2×C22⋊D1111yescharacteristic
632C22×C4C23×D1111yescharacteristic
633Q16—228no—
634SD16—228no—
635SD16—228no—
636D8—228no—
637M16—22no—
638M16—22no—
639M16—41no—
640M16—41no—
641M16—222no—
642M16—222no—
643M16—222no—
644M16—222no—
645M16—222no—
646M16—222no—
647M16—222no—
648M16—222no—
649M16—441no—
650M16—441no—
651M16—441no—
652M16—441no—
653C2×C8—22no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—114no—
657C2×C8—222no—
658C2×C8—222no—
659C2×C8—222no—
660C2×C8—222no—
661C2×C8—441no—
662C2×C8—441no—
663C2×C8—441no—
664C2×C8—441no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C42—22no—
670C42C2×C22⋊D1114yes—
671C11#2352711yescharacteristic, complemented, Sylow
672C23—22no—
673C23—41no—
674C23—41no—
675C23—81no—
676C23—82no—
677C23—222no—
678C23—441no—
679C23—441no—
680C23—882no—
681C23#6693611yescharacteristic
682C23#6693611yescharacteristic
683C23#6693911yescharacteristic
684C23#6693911yescharacteristic
685C23#6699211yescharacteristic
686C23#6699211yescharacteristic
687C23C2×#434111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—41no—
691Q8—41no—
692Q8—222no—
693Q8—222no—
694Q8—441no—
695Q8—441no—
696D4—22no—
697D4—22no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—41no—
703D4—41no—
704D4—222no—
705D4—222no—
706D4—442no—
707D4—442no—
708D4—442no—
709D4—442no—
710D4—441no—
711D4—441no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—82no—
721C2×C4—222no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4#6693511yescharacteristic
729C2×C4#6693511yescharacteristic
730C2×C4#6693511yescharacteristic
731C2×C4#6693511yescharacteristic
732C2×C4#6693611yescharacteristic
733C2×C4#6693611yescharacteristic
734C2×C4#6693811yescharacteristic
735C2×C4#6693811yescharacteristic
736C2×C4#6693811yescharacteristic
737C2×C4#6693811yescharacteristic
738C2×C4#6693911yescharacteristic
739C2×C4#6693911yescharacteristic
740C2×C4#6698311yescharacteristic
741C2×C4#6698311yescharacteristic
742C2×C4#6698311yescharacteristic
743C2×C4#6698311yescharacteristic
744C2×C4#6699111yescharacteristic
745C2×C4#6699111yescharacteristic
746C2×C4#6699111yescharacteristic
747C2×C4#6699111yescharacteristic
748C2×C4#6699211yescharacteristic
749C2×C4#6699211yescharacteristic
750C2×C4C22×D4411yescharacteristic
751C2×C4C2×#433911yescharacteristic
752C2×C4C2×D4×D1111yescharacteristic
753C2×C4C2×D4×D1111yescharacteristic
754C2×C4C2×#434111yescharacteristic
755C2×C4C22×C22⋊D1111yescharacteristic
756C8—42no—
757C8—224no—
758C8—442no—
759C8—442no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—442no—
772C22—882no—
773C22—882no—
774C22—882no—
775C22#1062257411yescharacteristic
776C22#1062257411yescharacteristic
777C22#1062257411yescharacteristic
778C22#1062257411yescharacteristic
779C22C2×#6693611yescharacteristic
780C22C2×#6693911yescharacteristic
781C22C2×#6699211yescharacteristic
782C4—44no—
783C4—42no—
784C4—442no—
785C4#1062257411yescharacteristic
786C4#1062257411yescharacteristic
787C4#1062257411yescharacteristic
788C4#1062257411yescharacteristic
789C4C2×#6693511yescharacteristic
790C4C2×#6693811yescharacteristic
791C4C2×#6698311yescharacteristic
792C4C2×#6699111yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—82no—
801C2—882no—
802C2C2×#1062257411yescharacteristic
subgroupG/H
centerC4C2×#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#421C2
socleC2×C11C2×#394
prime radicalC2×#10623353C2
hypercenterC2×#421D11
hypocenterC11#23527
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #13077180C2semidirect
3. C2×#10622618C2semidirect
4. C2×#10622850C2semidirect
5. C2×#10622745C2semidirect
6. #13069902C2semidirect
7. C2×C11⋊#338C2semidirect
8. C2×C11×#421C2semidirect
27. C2×C11×#104C22semidirect
29. #10622850C22semidirect
34. #10622745C22semidirect
40. C2×#66869C22semidirect
41. #10622537C22semidirect
42. C11⋊#338C22semidirect
274. C2×#421D11semidirect
391. C2×#104C2×D11semidirect
671. C11#23527semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
#130771802
C2×#106226182
C2×#106228502
C2×#106227452
#130699022
C2×C11⋊#3382
C2×C11×#4212
#2352711