Finite Group Databasebeta

← #14781616

Subgroups — #14781616

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×#10622737C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic, complemented
3#13077135C211yesmaximal, characteristic, complemented
4C2×#10622850C211yesmaximal, characteristic, complemented
5C2×#10622850C211yesmaximal, characteristic, complemented
6#13069893C214yesmaximal, complemented
7#13069886C214yesmaximal, complemented
8C2×#10622197C211yesmaximal, characteristic, complemented
9C2×C11×#575C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C11×#575—22no—
13C11×#575—22no—
14C11×#575—22no—
15C11×#575—22no—
16C2×C11×#137—21no—
17C2×C11×#137C2212yes—
18C2×C11×AGL(1,ℤ/8)—21no—
19C2×C11×AGL(1,ℤ/8)C2212yes—
20C2×C11×#135—22no—
21C22×C11×M16C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26#10622850—22no—
27#10622850—22no—
28#10622850—22no—
29#10622850C2214yes—
30#10622849—22no—
31#10622849C2214yes—
32C2×#66901—22no—
33#10622846—22no—
34#10622845—22no—
35C2×#66900—21no—
36C2×#66900C2212yescomplemented
37#10622838C2212yescomplemented
38C2×#66897—21no—
39C2×#66897C2212yescomplemented
40#10622828C2212yescomplemented
41#10622737—22no—
42#10622737C2214yescomplemented
43C2×#66886—22no—
44#10622197C2214yescomplemented
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×#41—21no—
63C2×C11×#41—21no—
64C2×C11×#41—21no—
65C2×C11×#41D412yes—
66C2×C11×#41D412yes—
67C2×C11×#41D412yes—
68C2×C11×#41C2312yes—
69C22×Q8×C11D411yescharacteristic
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11D411yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11—21no—
77C23×C4×C11C2311yescharacteristic
78C11×#137—24no—
79C11×#137—24no—
80C11×#137—24no—
81C11×#137—24no—
82C11×AGL(1,ℤ/8)—24no—
83C11×AGL(1,ℤ/8)—24no—
84C11×AGL(1,ℤ/8)—24no—
85C11×AGL(1,ℤ/8)—24no—
86C11×#135—28no—
87C11×#135—28no—
88C2×C11×Q16—22no—
89C2×C11×SD16—22no—
90C2×C11×SD16—22no—
91C2×C11×D8—22no—
92C2×C11×M16—21no—
93C2×C11×M16—21no—
94C2×C11×M16—21no—
95C2×C11×M16D412yes—
96C2×C11×M16D412yes—
97C2×C11×M16C2312yes—
98C22×C8×C11—21no—
99C2×C22⋊Dic11—21no—
100#66979—21no—
101#66979—21no—
102#66979—21no—
103#66979C2312yes—
104C2×C4⋊Dic11—21no—
105C2×C4×Dic11—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×#4318—21no—
119C2×#4318D412yes—
120C2×#4318D412yes—
121C2×#4318C2312yes—
122C2×#4318C2312yes—
123C2×#4318C2312yes—
124C22×C11⋊C8—21no—
125C22×C11⋊C8—21no—
126C22×C11⋊C8—21no—
127#66901—28no—
128#66900—24no—
129#66900—24no—
130#66899—24no—
131#66897—24no—
132#66897—24no—
133#66896—24no—
134#66886—28no—
135#23525—111nomaximal, Sylow
136C24×C11—21no—
137C24×C11—21no—
138C24×C11#4111yescharacteristic
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—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—22no—
151C11×#41—22no—
152C11×#41—22no—
153C11×#41—22no—
154C11×#41—22no—
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—
164C11×#41—41no—
165C11×#41—41no—
166C11×#41—41no—
167C11×#41—41no—
168C11×#41—41no—
169C11×#41—41no—
170C11×#41—41no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11C2×D412yes—
182C2×Q8×C11C2×D412yes—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
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—21no—
197C2×D4×C11—41no—
198C2×D4×C11—41no—
199C2×D4×C11—41no—
200C2×D4×C11—41no—
201C2×D4×C11—41no—
202C2×D4×C11—41no—
203C2×D4×C11—41no—
204C2×D4×C11—41no—
205C2×D4×C11C2×D412yes—
206C2×D4×C11C2×D412yes—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—41no—
214C22×C4×C11—41no—
215C22×C4×C11—41no—
216C22×C4×C11—41no—
217C22×C4×C11—41no—
218C22×C4×C11—41no—
219C22×C4×C11—41no—
220C22×C4×C11—41no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11#4111yescharacteristic
230C22×C4×C11#4111yescharacteristic
231C22×C4×C11#4111yescharacteristic
232C22×C4×C11#4111yescharacteristic
233C22×C4×C11#4111yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C22×Dic11—41no—
236C11×Q16—28no—
237C11×SD16—28no—
238C11×SD16—28no—
239C11×D8—28no—
240C11×M16—22no—
241C11×M16—22no—
242C11×M16—22no—
243C11×M16C2×D414yes—
244C2×C8×C11—22no—
245C2×C8×C11—22no—
246C2×C8×C11—22no—
247C22⋊Dic11—22no—
248C22⋊Dic11—41no—
249C4⋊Dic11—22no—
250C4⋊Dic11—41no—
251C4×Dic11—22no—
252C4×Dic11—41no—
253#4318—22no—
254#4318—22no—
255#4318—22no—
256#4318—22no—
257#4318—22no—
258#4318—22no—
259#4318—22no—
260#4318—41no—
261#4318—41no—
262#4318—41no—
263#4318—41no—
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—41no—
271C2×C11⋊C8—41no—
272C2×C11⋊C8—41no—
273C2×C11⋊C8—41no—
274C2×#575D1111yescharacteristic
275C2×#430—111no—
276C2×#421—111no—
277#2896—111no—
278C2×#413—111no—
279C2×#413—111no—
280#2049—114no—
281#2048—114no—
282C2×#344—111no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11—81no—
290C23×C11—82no—
291C23×C11—82no—
292C23×C11#12111yescharacteristic
293C23×C11#12111yescharacteristic
294C23×C11#12311yescharacteristic
295C23×C11#12311yescharacteristic
296C23×C11#12411yescharacteristic
297C23×C11#12411yescharacteristic
298C23×C11C2×#4111yescharacteristic
299Q8×C11—22no—
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—41no—
304Q8×C11—41no—
305Q8×C11—41no—
306Q8×C11—41no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—42no—
314D4×C11—42no—
315D4×C11—42no—
316D4×C11—42no—
317D4×C11—42no—
318D4×C11—42no—
319D4×C11—41no—
320D4×C11—41no—
321D4×C11—41no—
322D4×C11—41no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11#12011yescharacteristic
338C2×C4×C11#12011yescharacteristic
339C2×C4×C11#12011yescharacteristic
340C2×C4×C11#12011yescharacteristic
341C2×C4×C11#12111yescharacteristic
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#12311yescharacteristic
352C2×C4×C11#12311yescharacteristic
353C2×C4×C11#12311yescharacteristic
354C2×C4×C11#12311yescharacteristic
355C2×C4×C11#12311yescharacteristic
356C2×C4×C11#12311yescharacteristic
357C2×C4×C11#12411yescharacteristic
358C2×C4×C11#12411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C2×#4111yescharacteristic
364C2×C4×C11C2×#4111yescharacteristic
365C2×Dic11—42no—
366C2×Dic11—82no—
367C8×C11—24no—
368C11⋊C8—24no—
369C11⋊C8—42no—
370C11⋊C8—42no—
371C22×#41C2×D1111yescharacteristic
372C22×#41C2×D1111yescharacteristic
373#575—22no—
374#575—22no—
375#575—22no—
376#575—22no—
377C2×#137—21no—
378C2×#137C2×D1112yes—
379C2×AGL(1,ℤ/8)—21no—
380C2×AGL(1,ℤ/8)C2×D1112yes—
381C2×#135—22no—
382C22×M16—111no—
383C22×M16—111no—
384C22×M16—111no—
385C22×M16C2×D1111yescharacteristic
386C2×#117—111no—
387#430—114no—
388#430—222no—
389C2×#108—222no—
390#421—114no—
391#421—222no—
392C2×#104—222no—
393#419—112no—
394#418—112no—
395#417—222no—
396#416—222no—
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—42no—
415C22×C11—82no—
416C22×C11—82no—
417C22×C11—82no—
418C22×C11—82no—
419C22×C11—82no—
420C22×C11—82no—
421C22×C11#39411yescharacteristic
422C22×C11#39411yescharacteristic
423C22×C11#39411yescharacteristic
424C22×C11#39411yescharacteristic
425C22×C11C2×#12111yescharacteristic
426C22×C11C2×#12311yescharacteristic
427C22×C11C2×#12411yescharacteristic
428C4×C11—42no—
429C4×C11—42no—
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—82no—
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×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41C22⋊D1112yes—
460C2×#41C22⋊D1112yes—
461C2×#41C22⋊D1112yes—
462C2×#41C22×D1112yes—
463C22×Q8C22⋊D1111yescharacteristic
464C22×Q8C22×D1111yescharacteristic
465C22×D4—21no—
466C22×D4—21no—
467C22×D4C22⋊D1111yescharacteristic
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4C22×D1111yescharacteristic
472#137—24no—
473#137—24no—
474#137—24no—
475#137—24no—
476AGL(1,ℤ/8)—24no—
477AGL(1,ℤ/8)—24no—
478AGL(1,ℤ/8)—24no—
479AGL(1,ℤ/8)—24no—
480#135—28no—
481#135—28no—
482C2×Q16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×D8—22no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—112no—
490C2×M16—112no—
491C2×M16—112no—
492C2×M16—112no—
493C2×M16—112no—
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×M16—221no—
505C2×M16—221no—
506C2×M16—221no—
507C2×M16C22⋊D1112yes—
508C2×M16C22⋊D1112yes—
509C2×M16C22×D1112yes—
510C22×C8—21no—
511C22×C8—221no—
512C22×C8—221no—
513C22×C8—221no—
514#117—112no—
515#117—221no—
516#117—221no—
517#117—221no—
518C2×C4⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C42—221no—
521#108—228no—
522#104—228no—
523#103—224no—
524#102—224no—
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×C11—82no—
538C2×C11C2×#39411yescharacteristic
539C24—21no—
540C24—21no—
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—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×C22⋊D1112yes—
585C2×Q8C2×C22⋊D1112yes—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4C2×C22⋊D1112yes—
609C2×D4C2×C22⋊D1112yes—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—441no—
625C22×C4D4×D1111yescharacteristic
626C22×C4D4×D1111yescharacteristic
627C22×C4#434111yescharacteristic
628C22×C4#434111yescharacteristic
629C22×C4#434111yescharacteristic
630C22×C4#434111yescharacteristic
631C22×C4#434111yescharacteristic
632C22×C4C2×C22⋊D1111yescharacteristic
633C22×C4C2×C22⋊D1111yescharacteristic
634C22×C4C2×C22⋊D1111yescharacteristic
635C22×C4C2×C22⋊D1111yescharacteristic
636C22×C4C2×C22⋊D1111yescharacteristic
637C22×C4C2×C22⋊D1111yescharacteristic
638C22×C4C23×D1111yescharacteristic
639Q16—28no—
640SD16—28no—
641SD16—28no—
642D8—28no—
643M16—22no—
644M16—22no—
645M16—22no—
646M16—114no—
647M16—222no—
648M16—222no—
649M16—222no—
650M16—222no—
651M16—222no—
652M16—222no—
653M16—222no—
654M16—441no—
655M16—441no—
656M16—441no—
657M16—441no—
658M16C2×C22⋊D1114yes—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—222no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—222no—
666C2×C8—222no—
667C2×C8—441no—
668C2×C8—441no—
669C2×C8—441no—
670C2×C8—441no—
671C4⋊C4—222no—
672C4⋊C4—441no—
673C22⋊C4—222no—
674C22⋊C4—441no—
675C42—222no—
676C42—441no—
677C11#2352511yescharacteristic, complemented, Sylow
678C23—22no—
679C23—22no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—81no—
685C23—82no—
686C23—82no—
687C23#6698811yescharacteristic
688C23#6698811yescharacteristic
689C23#6698911yescharacteristic
690C23#6698911yescharacteristic
691C23#6699211yescharacteristic
692C23#6699211yescharacteristic
693C23C2×#434111yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—442no—
733C2×C4—882no—
734C2×C4#6698811yescharacteristic
735C2×C4#6698811yescharacteristic
736C2×C4#6698811yescharacteristic
737C2×C4#6698811yescharacteristic
738C2×C4#6698811yescharacteristic
739C2×C4#6698811yescharacteristic
740C2×C4#6698911yescharacteristic
741C2×C4#6698911yescharacteristic
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#6700611yescharacteristic
753C2×C4#6700611yescharacteristic
754C2×C4#6700611yescharacteristic
755C2×C4#6700611yescharacteristic
756C2×C4C2×D4×D1111yescharacteristic
757C2×C4C2×#434111yescharacteristic
758C2×C4C2×#434111yescharacteristic
759C2×C4C22×C22⋊D1111yescharacteristic
760C2×C4C22×C22⋊D1111yescharacteristic
761C2×C4C22×C22⋊D1111yescharacteristic
762C8—24no—
763C8—224no—
764C8—442no—
765C8—442no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22#1062283511yescharacteristic
782C22#1062283511yescharacteristic
783C22#1062283511yescharacteristic
784C22#1062283511yescharacteristic
785C22C2×#6698811yescharacteristic
786C22C2×#6698911yescharacteristic
787C22C2×#6699211yescharacteristic
788C4—42no—
789C4—42no—
790C4—882no—
791C4#1062283511yescharacteristic
792C4#1062283511yescharacteristic
793C4#1062283511yescharacteristic
794C4#1062283511yescharacteristic
795C4C2×#6698811yescharacteristic
796C4C2×#6699111yescharacteristic
797C4C2×#6699211yescharacteristic
798C4C2×#6700611yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—82no—
807C2—82no—
808C2C2×#1062283511yescharacteristic
subgroupG/H
centerC4#10622835
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#575C2
socleC2×C11C2×#394
hypercenterC2×#575D11
hypocenterC11#23525
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#10622737C2semidirect
2. C2×#10622849C2semidirect
3. #13077135C2semidirect
4. C2×#10622850C2semidirect
5. C2×#10622850C2semidirect
6. #13069893C2semidirect
7. #13069886C2semidirect
8. C2×#10622197C2semidirect
36. C2×#66900C22semidirect
37. #10622838C22semidirect
39. C2×#66897C22semidirect
40. #10622828C22semidirect
42. #10622737C22semidirect
44. #10622197C22semidirect
677. C11#23525semidirect

Maximal subgroups

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

subgroupindex
C2×#106227372
C2×#106228492
#130771352
C2×#106228502
#130698932
#130698862
C2×#106221972
C2×C11×#5752
#2352511