Finite Group Databasebeta

← #14660549

Subgroups — #14660549

Order 2816.

1338 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×#10622849C211yesmaximal, characteristic, complemented
3C22×#66869C211yesmaximal, characteristic, complemented
4C2×#10622619C211yesmaximal, characteristic, complemented
5C2×#10622171C211yesmaximal, characteristic, complemented
6C2×#10622161C211yesmaximal, characteristic, complemented
7C11×#2297C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C2×#67004C412yescomplemented
13#10623353—22no—
14#10623353—22no—
15#10623353—22no—
16#10623353—22no—
17C2×#67003—22no—
18C2×#67002C412yescomplemented
19C2×#66995—21no—
20C2×#66985—21no—
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C11×#391—21no—
25C11×#390—21no—
26C11×#386—22no—
27C4×C11×C22⋊C4—22no—
28#10622849—22no—
29#10622849—22no—
30C2×#66901—22no—
31#10622619—22no—
32#10622619—22no—
33C2×#66870—22no—
34C2×#66869—22no—
35C2×#66869—22no—
36C2×#66869—22no—
37#10622171—22no—
38#10622161—22no—
39C2×C11×#41—21no—
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×#41C2×C412yes—
50C2×C11×#41D412yes—
51C22×Q8×C11D411yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11D411yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C2×#4339—21no—
59C2×#4339—21no—
60C2×#4339—21no—
61C2×#4339—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—21no—
68C2×#4339D412yes—
69C2×#4339D412yes—
70C22×D44C2×C411yescharacteristic
71C22×C4×D11—21no—
72C22×Dic22C2×C411yescharacteristic
73C11×#117—21no—
74C11×#117—21no—
75C11×#117—21no—
76C11×#117—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4D412yes—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11D412yes—
87C2×C22⋊Dic11—21no—
88#67004—24no—
89#67004—24no—
90#67003—28no—
91#67003—28no—
92#67002—24no—
93#67002—24no—
94C2×#4326—22no—
95#66995—24no—
96#66995—24no—
97C2×#4325—22no—
98C2×#4324—22no—
99#66985—24no—
100#66985—24no—
101C2×#4323—22no—
102#66979—21no—
103#66979—21no—
104#66979—21no—
105#66979D412yes—
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×#4318C2×C412yes—
117C2×#4318D412yes—
118C2×#4318D412yes—
119C2×#4318D412yes—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—21no—
122C11×#95—24no—
123#66901—28no—
124#66870—28no—
125#66869—28no—
126#11019—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C11×#41—22no—
131C11×#41—22no—
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—41no—
139C11×#41—41no—
140C11×#41—41no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C22⋊C412yes—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11C22⋊C412yes—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—44no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
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
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—41no—
193C2×C22⋊D11—41no—
194C2×C22⋊D11—41no—
195C2×C22⋊D11—41no—
196C22×Dic11—21no—
197C22×Dic11—41no—
198#4339—22no—
199#4339—22no—
200#4339—22no—
201#4339—22no—
202#4339—22no—
203#4339—22no—
204#4339—22no—
205#4339—22no—
206#4339—41no—
207#4339—41no—
208#4339—41no—
209#4339—41no—
210#4339—41no—
211#4339—41no—
212#4339—41no—
213#4339—41no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44C22⋊C412yescomplemented
220C2×C4×D11—22no—
221C2×C4×D11—22no—
222C2×C4×D11—41no—
223C2×C4×D11—41no—
224C2×C4×D11—41no—
225C2×C4×D11—41no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22C22⋊C412yescomplemented
232C11×C4⋊C4—41no—
233C11×C4⋊C4—41no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—48no—
237C42×C11—22no—
238C42×C11—22no—
239C42×C11—41no—
240C42×C11—41no—
241C42×C11—41no—
242C42×C11—41no—
243C22⋊Dic11—22no—
244C22⋊Dic11—41no—
245#4326—28no—
246#4325—28no—
247#4324—28no—
248#4323—28no—
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—41no—
259#4318—41no—
260#4318C22⋊C414yescomplemented
261C2×C11⋊C8—22no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—41no—
266C2×C11⋊C8—41no—
267C2×#575—111no—
268C2×#421—111no—
269C22×#104—111no—
270C2×#410—111no—
271#2297D1111yescharacteristic, complemented
272C2×#344—111no—
273C2×#339—111no—
274C23×C11—22no—
275C23×C11—42no—
276C23×C11—44no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11C4×D411yescharacteristic
280C23×C11#12011yescharacteristic
281C23×C11#12011yescharacteristic
282C23×C11#12111yescharacteristic
283C23×C11#12111yescharacteristic
284C23×C11#12111yescharacteristic
285C23×C11#12711yescharacteristic
286C22×D11—22no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—82no—
290Q8×C11—22no—
291Q8×C11—22no—
292Q8×C11—41no—
293Q8×C11—41no—
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—42no—
297D4×C11—42no—
298D4×C11—42no—
299D4×C11—42no—
300D4×C11—41no—
301D4×C11—41no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—42no—
305C2×C4×C11—44no—
306C2×C4×C11—44no—
307C2×C4×C11—42no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—44no—
315C2×C4×C11—42no—
316C2×C4×C11C2×C22⋊C411yescharacteristic
317C2×C4×C11C2×C22⋊C411yescharacteristic
318C2×C4×C11C2×C22⋊C411yescharacteristic
319C2×C4×C11C4×D411yescharacteristic
320C2×C4×C11C4×D411yescharacteristic
321C2×C4×C11C4×D411yescharacteristic
322C2×C4×C11#12011yescharacteristic
323C2×C4×C11#12011yescharacteristic
324C2×C4×C11#12011yescharacteristic
325C2×C4×C11#12011yescharacteristic
326C2×C4×C11#12011yescharacteristic
327C2×C4×C11#12011yescharacteristic
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#12111yescharacteristic
335C2×C4×C11#12111yescharacteristic
336C2×C4×C11#12111yescharacteristic
337C2×C4×C11#12311yescharacteristic
338C2×C4×C11#12311yescharacteristic
339C2×C4×C11#12311yescharacteristic
340C2×C4×C11#12311yescharacteristic
341C2×C4×C11#12411yescharacteristic
342C2×C4×C11#12411yescharacteristic
343C2×C4×C11#12711yescharacteristic
344C22⋊D11—42no—
345C22⋊D11—42no—
346C22⋊D11—42no—
347C22⋊D11—42no—
348C2×Dic11—22no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—42no—
352C2×Dic11—82no—
353D44—22no—
354D44—22no—
355D44—41no—
356D44—41no—
357C4×D11—42no—
358C4×D11—42no—
359C4×D11—42no—
360C4×D11—42no—
361Dic22—22no—
362Dic22—22no—
363Dic22—41no—
364Dic22—41no—
365C11⋊C8—24no—
366C11⋊C8—42no—
367C22×#41—111no—
368C22×#41C2×D1111yescharacteristic
369#575—222no—
370#575—222no—
371#575—222no—
372#575—222no—
373C2×#137—112no—
374C2×#137—221no—
375C2×AGL(1,ℤ/8)—112no—
376C2×AGL(1,ℤ/8)—221no—
377C2×#135—222no—
378C22×M16—111no—
379C22×M16—111no—
380C2×#117—111no—
381C2×#117C2×D1111yescharacteristic
382C22×C42C2×D1111yescharacteristic
383#421—222no—
384#421—222no—
385C2×#104—222no—
386C2×#104—222no—
387C2×#104—222no—
388C2×#104—222no—
389#410—222no—
390#410—222no—
391C2×#99—222no—
392#391—21no—
393#390—21no—
394#386—22no—
395C4×C22⋊C4—22no—
396#344—222no—
397#339—222no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—44no—
406C22×C11—42no—
407C22×C11—82no—
408C22×C11—82no—
409C22×C11#38611yescharacteristic
410C22×C11#38611yescharacteristic
411C22×C11#39011yescharacteristic
412C22×C11#39211yescharacteristic
413C22×C11#39211yescharacteristic
414C22×C11#39211yescharacteristic
415C22×C11#39411yescharacteristic
416C2×D11—42no—
417C2×D11—82no—
418C2×D11—82no—
419C2×D11—82no—
420C4×C11—44no—
421C4×C11—42no—
422C4×C11—82no—
423C4×C11#37911yescharacteristic
424C4×C11#38611yescharacteristic
425C4×C11#38611yescharacteristic
426C4×C11#39011yescharacteristic
427C4×C11#39211yescharacteristic
428C4×C11#39411yescharacteristic
429C4×C11#39411yescharacteristic
430C4×C11#39411yescharacteristic
431Dic11—42no—
432Dic11—82no—
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—112no—
444C2×#41—112no—
445C2×#41—221no—
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×#41C4×D1112yes—
456C2×#41D4412yes—
457C22×Q8—111no—
458C22×Q8C22⋊D1111yescharacteristic
459C22×D4—21no—
460C22×D4—111no—
461C22×D4—221no—
462C22×D4C22⋊D1111yescharacteristic
463C23×C4—21no—
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—112no—
482C2×M16—112no—
483C2×M16—112no—
484C2×M16—112no—
485C2×M16—221no—
486C2×M16—221no—
487C2×M16—221no—
488C2×M16—221no—
489C2×M16—221no—
490C2×M16—221no—
491C2×M16—221no—
492C2×M16—221no—
493C22×C8—221no—
494C22×C8—221no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—112no—
500#117—221no—
501#117—221no—
502#117—221no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—221no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4C22⋊D1112yes—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—221no—
515C2×C42C22⋊D1112yes—
516#104—228no—
517#104—228no—
518#99—228no—
519#95—24no—
520C2×C11—21no—
521C2×C11—21no—
522C2×C11—21no—
523C2×C11—21no—
524C2×C11—21no—
525C2×C11—21no—
526C2×C11—82no—
527C2×C11#143811yescharacteristic
528C2×C11#190612yes—
529D11—82no—
530C24—21no—
531C24—221no—
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—222no—
550#41—222no—
551#41—222no—
552#41—222no—
553#41—222no—
554#41—222no—
555#41—222no—
556#41—222no—
557#41—441no—
558#41—441no—
559#41—441no—
560#41—441no—
561#41—441no—
562#41—441no—
563#41—441no—
564#41—441no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—112no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×Q8—221no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8(C2×D11)⋊C412yes—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—112no—
589C2×D4—222no—
590C2×D4—222no—
591C2×D4—221no—
592C2×D4—221no—
593C2×D4—221no—
594C2×D4—221no—
595C2×D4—221no—
596C2×D4—441no—
597C2×D4—441no—
598C2×D4—441no—
599C2×D4—441no—
600C2×D4(C2×D11)⋊C412yes—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—44no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—221no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—441no—
617C22×C4—441no—
618C22×C4—441no—
619C22×C4—441no—
620C22×C4—441no—
621C22×C4C2×C4×D1111yescharacteristic
622C22×C4C2×D4411yescharacteristic
623C22×C4#433911yescharacteristic
624C22×C4#433911yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4D4×D1111yescharacteristic
627C22×C4D4×D1111yescharacteristic
628C22×C4D4×D1111yescharacteristic
629C22×C4D4×D1111yescharacteristic
630C22×C4D4×D1111yescharacteristic
631C22×C4#434111yescharacteristic
632C22×C4#434111yescharacteristic
633C22×C4C2×C22⋊D1111yescharacteristic
634C22×C4C2×C22⋊D1111yescharacteristic
635Q16—228no—
636SD16—228no—
637SD16—228no—
638D8—228no—
639M16—114no—
640M16—222no—
641M16—222no—
642M16—222no—
643M16—222no—
644M16—222no—
645M16—441no—
646M16—441no—
647C2×C8—222no—
648C2×C8—222no—
649C2×C8—222no—
650C2×C8—222no—
651C2×C8—441no—
652C2×C8—441no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—222no—
656C4⋊C4—441no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—48no—
660C22⋊C4—222no—
661C22⋊C4—441no—
662C42—22no—
663C42—22no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—222no—
669C42—441no—
670C11#1101911yescharacteristic, complemented, Sylow
671C23—22no—
672C23—42no—
673C23—44no—
674C23—41no—
675C23—41no—
676C23—222no—
677C23—441no—
678C23—441no—
679C23—882no—
680C23C4×C22⋊D1111yescharacteristic
681C23#6698311yescharacteristic
682C23#6699011yescharacteristic
683C23#6699111yescharacteristic
684C23#6699211yescharacteristic
685C23#6699311yescharacteristic
686C23#6700611yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—41no—
690Q8—41no—
691Q8—222no—
692Q8—222no—
693Q8—441no—
694Q8—441no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—222no—
704D4—222no—
705D4—442no—
706D4—442no—
707D4—442no—
708D4—442no—
709D4—441no—
710D4—441no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—222no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—882no—
734C2×C4C22⋊C4×D1111yescharacteristic
735C2×C4C22⋊C4×D1111yescharacteristic
736C2×C4(C22⋊D11)⋊C411yescharacteristic
737C2×C4(C22⋊D11)⋊C411yescharacteristic
738C2×C4#6693511yescharacteristic
739C2×C4#6693511yescharacteristic
740C2×C4#6693511yescharacteristic
741C2×C4#6693611yescharacteristic
742C2×C4#6693611yescharacteristic
743C2×C4#6693711yescharacteristic
744C2×C4#6693711yescharacteristic
745C2×C4#6693711yescharacteristic
746C2×C4#6693711yescharacteristic
747C2×C4#6693811yescharacteristic
748C2×C4#6693811yescharacteristic
749C2×C4#6693911yescharacteristic
750C2×C4C2×(C2×D11)⋊C411yescharacteristic
751C2×C4C4×C22⋊D1111yescharacteristic
752C2×C4#6698211yescharacteristic
753C2×C4#6698311yescharacteristic
754C2×C4#6699011yescharacteristic
755C2×C4#6699011yescharacteristic
756C2×C4#6699011yescharacteristic
757C2×C4#6699111yescharacteristic
758C2×C4#6699211yescharacteristic
759C2×C4#6699211yescharacteristic
760C2×C4#6699211yescharacteristic
761C2×C4#6699311yescharacteristic
762C8—224no—
763C8—442no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—44no—
772C22—42no—
773C22—82no—
774C22—82no—
775C22—442no—
776C22—882no—
777C22—882no—
778C22—882no—
779C22#1062256911yescharacteristic
780C22#1062257011yescharacteristic
781C22#1062257311yescharacteristic
782C22#1062257411yescharacteristic
783C22#1062282611yescharacteristic
784C22#1062283611yescharacteristic
785C22#1062283611yescharacteristic
786C4—44no—
787C4—42no—
788C4—82no—
789C4—442no—
790C4—882no—
791C4#1062256811yescharacteristic
792C4#1062256911yescharacteristic
793C4#1062257011yescharacteristic
794C4#1062257111yescharacteristic
795C4#1062257211yescharacteristic
796C4#1062257211yescharacteristic
797C4#1062257311yescharacteristic
798C4#1062257411yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—82no—
806C2—882no—
807C2#1306685511yescharacteristic
808C2#1306911712yes—
subgroupG/H
centerC2×C4#66983
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2297C2
socleC22×C11#386
prime radicalC2×#10623353C2
cosocleC23×C4×C11C23
hypercenter#2297D11
hypocenterC11#11019
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C2×#10622849C2semidirect
3. C22×#66869C2semidirect
4. C2×#10622619C2semidirect
5. C2×#10622171C2semidirect
6. C2×#10622161C2semidirect
7. C11×#2297C2semidirect
12. C2×#67004C4semidirect
18. C2×#67002C4semidirect
219. C2×D44C22⋊C4semidirect
231. C2×Dic22C22⋊C4semidirect
260. #4318C22⋊C4semidirect
271. #2297D11semidirect
670. C11#11019semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106228492
C22×#668692
C2×#106226192
C2×#106221712
C2×#106221612
C11×#22972
#1101911