Finite Group Databasebeta

← C2×#13069902 #14781627

Subgroups — C2×#13069902 #14781627

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C2×#10622537C211yesmaximal, characteristic, complemented
3C22×#66869C211yesmaximal, characteristic, complemented
4C2×#10622850C211yesmaximal, characteristic, complemented
5C2×#10622745C211yesmaximal, characteristic, complemented
6#13069902C218yesmaximal, direct product factor
7C2×C11⋊#338C211yesmaximal, characteristic, complemented
8C22×C11×#104C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
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
25C2×C11×#104—21no—
26C2×C11×#104—22no—
27C2×C11×#104—21no—
28C2×C11×#104C2214yescomplemented
29#10622850—22no—
30#10622850C2214yescomplemented
31C2×#66900—21no—
32C2×#66897—21no—
33C2×#66888—21no—
34#10622745—22no—
35#10622745C2214yescomplemented
36C2×#66887—21no—
37C2×#66869—21no—
38C2×#66869—22no—
39C2×#66869—21no—
40C2×#66869C2214yescomplemented
41#10622537—22no—
42#10622537C2214yescomplemented
43C2×C4⋊(C11⋊C8)—22no—
44C11⋊#338C2214yescomplemented
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×#41C2312yes—
57C22×Q8×C11D411yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11D411yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—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×#4339—21no—
74C2×#4339D412yes—
75C2×#4339C2312yes—
76C22×D44D411yescharacteristic
77C22×C4×D11—21no—
78C22×Dic22D411yescharacteristic
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16—21no—
82C2×C11×M16—21no—
83C2×C11×M16—21no—
84C2×C11×M16C2312yes—
85C22×C8×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11D411yescharacteristic
90C2×C42×C11D412yes—
91C2×C42×C11D411yescharacteristic
92C2×C42×C11C2312yes—
93#67004—24no—
94#67004—24no—
95#67003—28no—
96#67003—28no—
97#67002—24no—
98#67002—24no—
99C2×#4326—22no—
100#66995—24no—
101#66995—24no—
102C2×#4325—22no—
103C2×#4324—22no—
104#66985—24no—
105#66985—24no—
106C2×#4323—22no—
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×#4318—21no—
120C2×#4318—21no—
121C2×#4318D412yes—
122C2×#4318C2312yes—
123C2×#4318C2312yes—
124C2×#4318C2312yes—
125C22×C11⋊C8—21no—
126C22×C11⋊C8—21no—
127C22×C11⋊C8D412yes—
128C11×#104—24no—
129C11×#104—24no—
130#66900—24no—
131#66897—24no—
132#66888—24no—
133#66887—24no—
134#66869—24no—
135#66869—24no—
136C4⋊(C11⋊C8)—28no—
137C2×#2050—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11#4111yescharacteristic
140C23×D11—21no—
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—41no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C11×#41—41no—
156C11×#41—41no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11C2×D412yes—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—41no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11—41no—
174C2×D4×C11C2×D412yes—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—44no—
183C22×C4×C11—41no—
184C22×C4×C11—41no—
185C22×C4×C11—41no—
186C22×C4×C11—41no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11#4111yescharacteristic
196C22×C4×C11#4111yescharacteristic
197C22×C4×C11#4111yescharacteristic
198C22×C4×C11#4111yescharacteristic
199C22×C4×C11#4111yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—22no—
202C2×C22⋊D11—22no—
203C2×C22⋊D11—41no—
204C2×C22⋊D11—41no—
205C2×C22⋊D11—41no—
206C2×C22⋊D11—41no—
207C22×Dic11—21no—
208#4339—22no—
209#4339—22no—
210#4339—22no—
211#4339—22no—
212#4339—22no—
213#4339—22no—
214#4339—22no—
215#4339—22no—
216#4339—41no—
217#4339—41no—
218#4339—41no—
219#4339—41no—
220#4339—41no—
221#4339—41no—
222#4339—41no—
223#4339—41no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44C2×D412yes—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—41no—
233C2×C4×D11—41no—
234C2×C4×D11—41no—
235C2×C4×D11—41no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22C2×D412yes—
242C11×M16—22no—
243C11×M16—22no—
244C11×M16—41no—
245C11×M16—41no—
246C2×C8×C11—22no—
247C2×C8×C11—41no—
248C2×C8×C11—41no—
249C42×C11—21no—
250C42×C11—22no—
251C42×C11—21no—
252C42×C11—22no—
253C42×C11C2×D412yes—
254C42×C11C2×D412yes—
255#4326—28no—
256#4325—28no—
257#4324—28no—
258#4323—28no—
259#4318—22no—
260#4318—22no—
261#4318—22no—
262#4318—22no—
263#4318—22no—
264#4318—22no—
265#4318—22no—
266#4318—22no—
267#4318—41no—
268#4318—41no—
269#4318—41no—
270#4318—41no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—41no—
276C2×C11⋊C8—41no—
277C2×C11⋊C8—41no—
278C2×C11⋊C8—41no—
279C2×C11⋊C8C2×D414yes—
280C2×#575—111no—
281C2×#423—111no—
282C22×#104—111no—
283C22×#104D1111yescharacteristic, complemented
284C2×#413—111no—
285C2×#413—111no—
286#2050—118no—
287C2×#338—111no—
288C23×C11—22no—
289C23×C11—42no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—82no—
293C23×C11#12111yescharacteristic
294C23×C11#12111yescharacteristic
295C23×C11#12311yescharacteristic
296C23×C11#12311yescharacteristic
297C23×C11#12311yescharacteristic
298C23×C11#12311yescharacteristic
299C23×C11C2×#4111yescharacteristic
300C22×D11—22no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—82no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—41no—
307Q8×C11—41no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—42no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—42no—
314D4×C11—41no—
315D4×C11—41no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—42no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11#12011yescharacteristic
330C2×C4×C11#12011yescharacteristic
331C2×C4×C11#12011yescharacteristic
332C2×C4×C11#12011yescharacteristic
333C2×C4×C11#12111yescharacteristic
334C2×C4×C11#12111yescharacteristic
335C2×C4×C11#12111yescharacteristic
336C2×C4×C11#12111yescharacteristic
337C2×C4×C11#12111yescharacteristic
338C2×C4×C11#12111yescharacteristic
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12311yescharacteristic
344C2×C4×C11#12311yescharacteristic
345C2×C4×C11#12311yescharacteristic
346C2×C4×C11#12311yescharacteristic
347C2×C4×C11#12411yescharacteristic
348C2×C4×C11#12411yescharacteristic
349C2×C4×C11#12411yescharacteristic
350C2×C4×C11#12411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C22⋊D11—42no—
358C22⋊D11—42no—
359C22⋊D11—42no—
360C22⋊D11—42no—
361C2×Dic11—22no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364D44—22no—
365D44—22no—
366D44—41no—
367D44—41no—
368C4×D11—42no—
369C4×D11—42no—
370C4×D11—42no—
371C4×D11—42no—
372Dic22—22no—
373Dic22—22no—
374Dic22—41no—
375Dic22—41no—
376C8×C11—42no—
377C11⋊C8—24no—
378C11⋊C8—42no—
379C11⋊C8—42no—
380C22×#41—111no—
381C22×#41C2×D1111yescharacteristic
382#575—114no—
383#575—222no—
384#575—222no—
385#575—222no—
386C2×#137—221no—
387C2×#137—221no—
388C2×AGL(1,ℤ/8)—221no—
389C2×AGL(1,ℤ/8)—221no—
390C2×#135—222no—
391C22×M16—111no—
392C22×M16—111no—
393C22×M16—111no—
394C22×M16C2×D1111yescharacteristic
395C22×C42C2×D1111yescharacteristic
396#423—114no—
397#423—222no—
398C2×C4⋊C8—222no—
399C2×#104—21no—
400C2×#104—22no—
401C2×#104—21no—
402C2×#104—114no—
403C2×#104—221no—
404C2×#104—222no—
405C2×#104—221no—
406C2×#104C2×D1114yescomplemented
407#413—114no—
408#413—114no—
409#413—222no—
410#413—222no—
411C2×#101—221no—
412C2×#101—221no—
413C2×#100—221no—
414C2×#100—221no—
415#338—114no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—42no—
424C22×C11—82no—
425C22×C11—82no—
426C22×C11—82no—
427C22×C11#39411yescharacteristic
428C22×C11#39411yescharacteristic
429C22×C11#39411yescharacteristic
430C22×C11#39411yescharacteristic
431C22×C11C2×#12111yescharacteristic
432C22×C11C2×#12311yescharacteristic
433C22×C11C2×#12311yescharacteristic
434C2×D11—42no—
435C2×D11—82no—
436C2×D11—82no—
437C2×D11—82no—
438C4×C11—24no—
439C4×C11—42no—
440C4×C11—42no—
441C4×C11#39411yescharacteristic
442C4×C11#39411yescharacteristic
443C4×C11#39411yescharacteristic
444C4×C11#39411yescharacteristic
445C4×C11C2×#12011yescharacteristic
446C4×C11C2×#12111yescharacteristic
447C4×C11C2×#12111yescharacteristic
448C4×C11C2×#12411yescharacteristic
449Dic11—42no—
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×#41—21no—
460C2×#41—112no—
461C2×#41—112no—
462C2×#41—221no—
463C2×#41—221no—
464C2×#41—221no—
465C2×#41—221no—
466C2×#41—221no—
467C2×#41—221no—
468C2×#41—221no—
469C2×#41—221no—
470C2×#41—221no—
471C2×#41—221no—
472C2×#41D4412yes—
473C2×#41C22×D1112yes—
474C22×Q8—111no—
475C22×Q8D4411yescharacteristic
476C22×D4—21no—
477C22×D4—111no—
478C22×D4—221no—
479C22×D4D4411yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—221no—
483C23×C4C22×D1111yescharacteristic
484#137—224no—
485#137—224no—
486#137—224no—
487#137—224no—
488AGL(1,ℤ/8)—224no—
489AGL(1,ℤ/8)—224no—
490AGL(1,ℤ/8)—224no—
491AGL(1,ℤ/8)—224no—
492#135—228no—
493#135—228no—
494C2×Q16—222no—
495C2×SD16—222no—
496C2×SD16—222no—
497C2×D8—222no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—112no—
504C2×M16—112no—
505C2×M16—112no—
506C2×M16—112no—
507C2×M16—221no—
508C2×M16—221no—
509C2×M16—221no—
510C2×M16—221no—
511C2×M16—221no—
512C2×M16—221no—
513C2×M16—221no—
514C2×M16—221no—
515C2×M16—221no—
516C2×M16—221no—
517C2×M16—221no—
518C2×M16—221no—
519C2×M16—221no—
520C2×M16—221no—
521C2×M16C22×D1112yes—
522C22×C8—21no—
523C22×C8—112no—
524C22×C8—221no—
525C22×C8—221no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42C22⋊D1111yescharacteristic
530C2×C42C22⋊D1112yes—
531C2×C42C22⋊D1111yescharacteristic
532C2×C42C22×D1112yes—
533C4⋊C8—228no—
534#104—24no—
535#104—24no—
536#104—224no—
537#104—224no—
538#101—224no—
539#101—224no—
540#100—224no—
541#100—224no—
542C2×C11—21no—
543C2×C11—21no—
544C2×C11—21no—
545C2×C11—21no—
546C2×C11—21no—
547C2×C11—21no—
548C2×C11—82no—
549C2×C11#205012yescomplemented
550C2×C11C2×#39411yescharacteristic
551D11—82no—
552C24—21no—
553C24—221no—
554C24#434111yescharacteristic
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
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—222no—
572#41—222no—
573#41—222no—
574#41—222no—
575#41—222no—
576#41—222no—
577#41—222no—
578#41—222no—
579#41—441no—
580#41—441no—
581#41—441no—
582#41—441no—
583#41—441no—
584#41—441no—
585#41—441no—
586#41—441no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—112no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×Q8—221no—
598C2×Q8C2×D4412yes—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—112no—
611C2×D4—222no—
612C2×D4—222no—
613C2×D4—221no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—221no—
617C2×D4—221no—
618C2×D4—441no—
619C2×D4—441no—
620C2×D4—441no—
621C2×D4—441no—
622C2×D4C2×D4412yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—44no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—221no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—441no—
639C22×C4—441no—
640C22×C4—441no—
641C22×C4—441no—
642C22×C4C2×D4411yescharacteristic
643C22×C4C2×D4411yescharacteristic
644C22×C4#433911yescharacteristic
645C22×C4#433911yescharacteristic
646C22×C4D4×D1111yescharacteristic
647C22×C4D4×D1111yescharacteristic
648C22×C4D4×D1111yescharacteristic
649C22×C4D4×D1111yescharacteristic
650C22×C4#434111yescharacteristic
651C22×C4#434111yescharacteristic
652C22×C4#434111yescharacteristic
653C22×C4C2×C22⋊D1111yescharacteristic
654C22×C4C2×C22⋊D1111yescharacteristic
655C22×C4C23×D1111yescharacteristic
656Q16—228no—
657SD16—228no—
658SD16—228no—
659D8—228no—
660M16—22no—
661M16—22no—
662M16—41no—
663M16—41no—
664M16—222no—
665M16—222no—
666M16—222no—
667M16—222no—
668M16—222no—
669M16—222no—
670M16—222no—
671M16—222no—
672M16—441no—
673M16—441no—
674M16—441no—
675M16—441no—
676C2×C8—22no—
677C2×C8—41no—
678C2×C8—41no—
679C2×C8—114no—
680C2×C8—222no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8—441no—
685C2×C8—441no—
686C2×C8—441no—
687C2×C8—441no—
688C42—21no—
689C42—22no—
690C42—21no—
691C42—22no—
692C42C2×C22⋊D1112yes—
693C42C2×C22⋊D1112yes—
694C11C2×#205011yescharacteristic, complemented, Sylow
695C23—22no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—82no—
700C23—222no—
701C23—441no—
702C23—441no—
703C23—882no—
704C23#6693611yescharacteristic
705C23#6693611yescharacteristic
706C23#6693911yescharacteristic
707C23#6693911yescharacteristic
708C23#6699211yescharacteristic
709C23#6699211yescharacteristic
710C23C2×#434111yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—41no—
714Q8—41no—
715Q8—222no—
716Q8—222no—
717Q8—441no—
718Q8—441no—
719D4—22no—
720D4—22no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—41no—
726D4—41no—
727D4—222no—
728D4—222no—
729D4—442no—
730D4—442no—
731D4—442no—
732D4—442no—
733D4—441no—
734D4—441no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—222no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4#6693511yescharacteristic
756C2×C4#6693511yescharacteristic
757C2×C4#6693511yescharacteristic
758C2×C4#6693511yescharacteristic
759C2×C4#6693611yescharacteristic
760C2×C4#6693611yescharacteristic
761C2×C4#6693811yescharacteristic
762C2×C4#6693811yescharacteristic
763C2×C4#6693811yescharacteristic
764C2×C4#6693811yescharacteristic
765C2×C4#6693911yescharacteristic
766C2×C4#6693911yescharacteristic
767C2×C4#6698311yescharacteristic
768C2×C4#6698311yescharacteristic
769C2×C4#6698311yescharacteristic
770C2×C4#6698311yescharacteristic
771C2×C4#6699111yescharacteristic
772C2×C4#6699111yescharacteristic
773C2×C4#6699111yescharacteristic
774C2×C4#6699111yescharacteristic
775C2×C4#6699211yescharacteristic
776C2×C4#6699211yescharacteristic
777C2×C4C22×D4411yescharacteristic
778C2×C4C2×#433911yescharacteristic
779C2×C4C2×D4×D1111yescharacteristic
780C2×C4C2×D4×D1111yescharacteristic
781C2×C4C2×#434111yescharacteristic
782C2×C4C22×C22⋊D1111yescharacteristic
783C8—42no—
784C8—224no—
785C8—442no—
786C8—442no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—442no—
799C22—882no—
800C22—882no—
801C22—882no—
802C22#1062257411yescharacteristic
803C22#1062257411yescharacteristic
804C22#1062257411yescharacteristic
805C22#1062257411yescharacteristic
806C22C2×#6693611yescharacteristic
807C22C2×#6693911yescharacteristic
808C22C2×#6699211yescharacteristic
809C4—24no—
810C4—42no—
811C4—42no—
812C4—442no—
813C4#1062257411yescharacteristic
814C4#1062257411yescharacteristic
815C4#1062257411yescharacteristic
816C4#1062257411yescharacteristic
817C4C2×#6693511yescharacteristic
818C4C2×#6693811yescharacteristic
819C4C2×#6698311yescharacteristic
820C4C2×#6699111yescharacteristic
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—82no—
828C2—882no—
829C2#1306990212yesdirect product factor
830C2C2×#1062257411yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#104C2
socleC22×C11#394
prime radicalC2×#10623353C2
hypercenterC22×#104D11
hypocenterC11C2×#2050
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#10622537C2semidirect
3. C22×#66869C2semidirect
4. C2×#10622850C2semidirect
5. C2×#10622745C2semidirect
6. #13069902C2direct (N × H)
7. C2×C11⋊#338C2semidirect
8. C22×C11×#104C2semidirect
28. C2×C11×#104C22semidirect
30. #10622850C22semidirect
35. #10622745C22semidirect
40. C2×#66869C22semidirect
42. #10622537C22semidirect
44. C11⋊#338C22semidirect
283. C22×#104D11semidirect
406. C2×#104C2×D11semidirect
549. C2×C11#2050semidirect
694. C11C2×#2050semidirect
829. C2#13069902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106225372
C22×#668692
C2×#106228502
C2×#106227452
#130699022
C2×C11⋊#3382
C22×C11×#1042
C2×#205011