Finite Group Databasebeta

← #14660328

Subgroups — #14660328

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10622849C211yesmaximal, characteristic, complemented
3C2×#10622619C211yesmaximal, characteristic, complemented
4#13077060C211yesmaximal, characteristic, complemented
5C2×#10622193C211yesmaximal, characteristic, complemented
6C2×#10622170C211yesmaximal, characteristic, complemented
7C2×C11×#421C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12#10623363—22no—
13#10623363—22no—
14#10623363—22no—
15#10623363—22no—
16C2×#67000C411yescharacteristic, complemented
17C2×#66997C411yescharacteristic, complemented
18C2×#66993C411yescharacteristic, complemented
19C2×#66992—22no—
20C2×#66989C411yescharacteristic, complemented
21C2×C4×C22⋊D11—22no—
22C2×#66979C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C11×#421—22no—
26C11×#421—22no—
27C2×C11×#104—22no—
28#10622849—22no—
29#10622849—22no—
30C2×#66901—22no—
31#10622742—22no—
32#10622739—22no—
33#10622723—22no—
34#10622619—22no—
35#10622619—22no—
36C2×#66870—22no—
37#10622193—22no—
38#10622170—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×#41D412yes—
50C2×C11×#41D412yes—
51C22×Q8×C11C2×C411yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2×C411yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—22no—
57C22×C22⋊D11D412yes—
58C23×Dic11—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×#4339—21no—
69C2×#4339—21no—
70C2×#4339—21no—
71C22×D44C2×C411yescharacteristic
72C22×C4×D11D412yes—
73C22×Dic22C2×C411yescharacteristic
74C2×C11×M16—21no—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16D412yescomplemented
80C22×C8×C11—21no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117—21no—
84C11×#117D412yescomplemented
85C2×C11×C4⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—21no—
90#67000—22no—
91#67000—22no—
92#66997—22no—
93#66997—22no—
94#66993—22no—
95#66993—22no—
96#66992—28no—
97#66992—28no—
98#66989—22no—
99#66989—22no—
100C4×C22⋊D11—28no—
101C4×C22⋊D11—28no—
102C2×(C2×D11)⋊C4—22no—
103#66979—21no—
104#66979—21no—
105#66979—21no—
106#66979D412yescomplemented
107C2×C4⋊Dic11—21no—
108C2×Dic11⋊C4—22no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11C2×C411yescharacteristic
114C2×C4×Dic11C2×C411yescharacteristic
115C2×C4×Dic11D412yes—
116C2×C4×Dic11D412yes—
117C2×#4318—21no—
118C2×#4318—21no—
119C2×#4318—21no—
120C2×#4318—21no—
121C2×#4318—21no—
122C2×#4318D412yescomplemented
123C22×C11⋊C8—21no—
124C11×#104—28no—
125#66901—28no—
126(C2×D11)⋊C8—28no—
127#66870—28no—
128#10979—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C2×D411yescharacteristic
131C23×D11C22⋊C412yes—
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—41no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C22⋊C412yes—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11C22⋊C412yes—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
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×C11#4111yescharacteristic
185C22×C4×C11#4111yescharacteristic
186C22×C4×C11#4111yescharacteristic
187C22×C4×C11#4111yescharacteristic
188C2×C22⋊D11—28no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11—22no—
195C2×C22⋊D11—48no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—44no—
201C22×Dic11—41no—
202C22×Dic11C22⋊C412yes—
203#4339—41no—
204#4339—41no—
205#4339—41no—
206#4339—41no—
207#4339—41no—
208#4339—41no—
209#4339—41no—
210#4339—41no—
211#4339—41no—
212#4339—41no—
213#4339—41no—
214#4339—41no—
215#4339—41no—
216#4339—41no—
217#4339—41no—
218#4339—41no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×C4×D11—22no—
226C2×C4×D11—22no—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×Dic22—21no—
232C2×Dic22—21no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C11×M16—22no—
238C11×M16—22no—
239C11×M16—41no—
240C11×M16—41no—
241C2×C8×C11—22no—
242C2×C8×C11—41no—
243C2×C8×C11—41no—
244C11×C4⋊C4—22no—
245C11×C4⋊C4—41no—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—41no—
248C42×C11—22no—
249C42×C11—41no—
250C22⋊Dic11—28no—
251C22⋊Dic11—22no—
252C22⋊Dic11—41no—
253(C2×D11)⋊C4—28no—
254C4⋊Dic11—22no—
255C4⋊Dic11—41no—
256Dic11⋊C4—28no—
257C4×Dic11—21no—
258C4×Dic11—21no—
259C4×Dic11—22no—
260C4×Dic11—22no—
261C4×Dic11—22no—
262C4×Dic11—41no—
263C4×Dic11C22⋊C412yes—
264C4×Dic11C22⋊C412yes—
265#4318—22no—
266#4318—22no—
267#4318—41no—
268#4318—41no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8—41no—
271C2×C11⋊C8—41no—
272C2×#532—111no—
273C2×#421—111no—
274C2×#421D1111yescharacteristic, complemented
275C2×#410—111no—
276#2879—111no—
277C2×#339—111no—
278C2×#339—111no—
279C23×C11—22no—
280C23×C11—42no—
281C23×C11—44no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11C2×C22⋊C411yescharacteristic
285C23×C11#12011yescharacteristic
286C23×C11#12011yescharacteristic
287C23×C11#12011yescharacteristic
288C23×C11#12111yescharacteristic
289C23×C11#12111yescharacteristic
290C23×C11#12311yescharacteristic
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—44no—
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—22no—
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—42no—
315C2×C4×C11—82no—
316C2×C4×C11C2×C22⋊C411yescharacteristic
317C2×C4×C11C2×C22⋊C411yescharacteristic
318C2×C4×C11C4×D411yescharacteristic
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#12111yescharacteristic
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#12411yescharacteristic
341C2×C4×C11#12411yescharacteristic
342C2×C4×C11#12711yescharacteristic
343C2×C4×C11#12711yescharacteristic
344C22⋊D11—416no—
345C22⋊D11—42no—
346C22⋊D11—42no—
347C22⋊D11—42no—
348C22⋊D11—42no—
349C2×Dic11—24no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—44no—
356C2×Dic11—44no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—82no—
360D44—41no—
361D44—41no—
362D44—41no—
363D44—41no—
364C4×D11—42no—
365C4×D11—42no—
366C4×D11—42no—
367C4×D11—42no—
368Dic22—41no—
369Dic22—41no—
370Dic22—41no—
371Dic22—41no—
372C8×C11—42no—
373C11⋊C8—42no—
374C22×#41—111no—
375C22×#41C2×D1111yescharacteristic
376C22×M16—111no—
377C22×M16C2×D1111yescharacteristic
378#532—222no—
379#532—222no—
380#532—222no—
381#532—222no—
382C2×C4⋊Q8—111no—
383C2×#127—111no—
384C2×#124—111no—
385C2×#124—111no—
386C2×#121—222no—
387C2×C4×D4—222no—
388C2×#117—111no—
389C2×#117C2×D1111yescharacteristic
390C22×C42—111no—
391#421—22no—
392#421—22no—
393#421—222no—
394#421—222no—
395C2×#104—22no—
396C2×#104—222no—
397#410—222no—
398#410—222no—
399C2×#99—222no—
400#408—222no—
401#408—222no—
402#407—222no—
403#339—222no—
404#339—222no—
405C22×C11—22no—
406C22×C11—22no—
407C22×C11—22no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—44no—
413C22×C11—42no—
414C22×C11—82no—
415C22×C11—82no—
416C22×C11#37911yescharacteristic
417C22×C11#38611yescharacteristic
418C22×C11#38611yescharacteristic
419C22×C11#39211yescharacteristic
420C22×C11#39211yescharacteristic
421C22×C11#39411yescharacteristic
422C22×C11#39411yescharacteristic
423C2×D11—44no—
424C2×D11—44no—
425C2×D11—42no—
426C2×D11—82no—
427C4×C11—42no—
428C4×C11—82no—
429C4×C11#38611yescharacteristic
430C4×C11#38611yescharacteristic
431C4×C11#39011yescharacteristic
432C4×C11#39011yescharacteristic
433C4×C11#39211yescharacteristic
434C4×C11#39211yescharacteristic
435C4×C11#39411yescharacteristic
436C4×C11#39411yescharacteristic
437Dic11—24no—
438Dic11—42no—
439Dic11—42no—
440Dic11—82no—
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—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×#41—221no—
461C2×#41—221no—
462C2×#41—221no—
463C2×#41D4412yes—
464C2×#41C22⋊D1112yes—
465C22×Q8—111no—
466C22×Q8C4×D1111yescharacteristic
467C22×D4—21no—
468C22×D4—112no—
469C22×D4—111no—
470C22×D4—222no—
471C22×D4C4×D1111yescharacteristic
472C23×C4—21no—
473C23×C4—112no—
474C23×C4—221no—
475C23×C4C22×D1111yescharacteristic
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—112no—
482C2×M16—221no—
483C2×M16—221no—
484C2×M16—221no—
485C2×M16—221no—
486C2×M16—221no—
487C2×M16C22⋊D1112yescomplemented
488C22×C8—21no—
489C22×C8—221no—
490C4⋊Q8—222no—
491C4⋊Q8—222no—
492#127—222no—
493#127—222no—
494#124—222no—
495#124—222no—
496#124—222no—
497#124—222no—
498#121—228no—
499#121—228no—
500C4×D4—228no—
501C4×D4—228no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—112no—
506#117—221no—
507#117—221no—
508#117—221no—
509#117C22⋊D1112yescomplemented
510C2×C4⋊C4—21no—
511C2×C4⋊C4—222no—
512C2×C4⋊C4—221no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—222no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—221no—
517C2×C42—21no—
518C2×C42—111no—
519C2×C42—111no—
520C2×C42—112no—
521C2×C42—112no—
522C2×C42—221no—
523C2×C42—221no—
524C2×C42—221no—
525C2×C42—221no—
526#104—28no—
527#104—228no—
528#99—228no—
529C22⋊C8—228no—
530C2×C11—21no—
531C2×C11—21no—
532C2×C11—21no—
533C2×C11—21no—
534C2×C11—21no—
535C2×C11—21no—
536C2×C11—82no—
537C2×C11#143811yescharacteristic
538C2×C11#188412yes—
539D11—82no—
540C24—21no—
541C24—112no—
542C24D4×D1111yescharacteristic
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—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—441no—
560#41—441no—
561#41—441no—
562#41—441no—
563#41—441no—
564#41—441no—
565#41—441no—
566#41—441no—
567#41—441no—
568#41—441no—
569#41—441no—
570#41—441no—
571#41—441no—
572#41—441no—
573#41—441no—
574#41—441no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8—221no—
583C2×Q8—221no—
584C2×Q8—221no—
585C2×Q8—221no—
586C2×Q8(C2×D11)⋊C412yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—228no—
599C2×D4—222no—
600C2×D4—222no—
601C2×D4—222no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—222no—
605C2×D4—221no—
606C2×D4—221no—
607C2×D4—221no—
608C2×D4—221no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—448no—
612C2×D4(C2×D11)⋊C412yes—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—112no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—444no—
633C22×C4—441no—
634C22×C4C2×C4×D1111yescharacteristic
635C22×C4C2×D4411yescharacteristic
636C22×C4#433911yescharacteristic
637C22×C4#433911yescharacteristic
638C22×C4D4×D1111yescharacteristic
639C22×C4D4×D1111yescharacteristic
640C22×C4D4×D1111yescharacteristic
641C22×C4D4×D1111yescharacteristic
642C22×C4D4×D1111yescharacteristic
643C22×C4#434111yescharacteristic
644C22×C4#434111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C2×C22⋊D1111yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648M16—22no—
649M16—22no—
650M16—41no—
651M16—41no—
652M16—222no—
653M16—222no—
654M16—441no—
655M16—441no—
656C2×C8—22no—
657C2×C8—41no—
658C2×C8—41no—
659C2×C8—222no—
660C2×C8—441no—
661C2×C8—441no—
662C4⋊C4—22no—
663C4⋊C4—41no—
664C4⋊C4—228no—
665C4⋊C4—222no—
666C4⋊C4—441no—
667C22⋊C4—22no—
668C22⋊C4—41no—
669C22⋊C4—228no—
670C22⋊C4—228no—
671C22⋊C4—222no—
672C22⋊C4—441no—
673C42—22no—
674C42—41no—
675C42—112no—
676C42—112no—
677C42—222no—
678C42—221no—
679C42—221no—
680C42—222no—
681C42—222no—
682C42—441no—
683C11#1097911yescharacteristic, complemented, Sylow
684C23—22no—
685C23—42no—
686C23—44no—
687C23—41no—
688C23—41no—
689C23—222no—
690C23—222no—
691C23—222no—
692C23—444no—
693C23C22⋊C4×D1111yescharacteristic
694C23#6693511yescharacteristic
695C23#6693611yescharacteristic
696C23#6693711yescharacteristic
697C23#6699011yescharacteristic
698C23#6699011yescharacteristic
699C23#6699111yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704Q8—441no—
705Q8—441no—
706Q8—441no—
707Q8—441no—
708D4—22no—
709D4—22no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—41no—
715D4—41no—
716D4—4416no—
717D4—442no—
718D4—442no—
719D4—442no—
720D4—442no—
721D4—441no—
722D4—441no—
723D4—441no—
724D4—441no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4—224no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—444no—
741C2×C4—444no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—882no—
749C2×C4C22⋊C4×D1111yescharacteristic
750C2×C4(C22⋊D11)⋊C411yescharacteristic
751C2×C4(C22⋊D11)⋊C411yescharacteristic
752C2×C4#6693511yescharacteristic
753C2×C4#6693511yescharacteristic
754C2×C4#6693611yescharacteristic
755C2×C4#6693711yescharacteristic
756C2×C4#6693711yescharacteristic
757C2×C4#6693711yescharacteristic
758C2×C4#6693811yescharacteristic
759C2×C4#6693811yescharacteristic
760C2×C4#6693911yescharacteristic
761C2×C4C2×(C2×D11)⋊C411yescharacteristic
762C2×C4C4×C22⋊D1111yescharacteristic
763C2×C4C4×C22⋊D1111yescharacteristic
764C2×C4#6698211yescharacteristic
765C2×C4#6698311yescharacteristic
766C2×C4#6698311yescharacteristic
767C2×C4#6699011yescharacteristic
768C2×C4#6699011yescharacteristic
769C2×C4#6699111yescharacteristic
770C2×C4#6699211yescharacteristic
771C2×C4#6699211yescharacteristic
772C2×C4#6699211yescharacteristic
773C2×C4#6699211yescharacteristic
774C2×C4#6699311yescharacteristic
775C2×C4#6699311yescharacteristic
776C2×C4#6700611yescharacteristic
777C8—42no—
778C8—442no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—44no—
787C22—42no—
788C22—82no—
789C22—82no—
790C22—444no—
791C22—442no—
792C22—444no—
793C22—882no—
794C22#1062256811yescharacteristic
795C22#1062256911yescharacteristic
796C22#1062256911yescharacteristic
797C22#1062257211yescharacteristic
798C22#1062257311yescharacteristic
799C22#1062257411yescharacteristic
800C22#1062283611yescharacteristic
801C4—42no—
802C4—82no—
803C4—224no—
804C4—442no—
805C4—442no—
806C4—882no—
807C4#1062257011yescharacteristic
808C4#1062257011yescharacteristic
809C4#1062257111yescharacteristic
810C4#1062257211yescharacteristic
811C4#1062257311yescharacteristic
812C4#1062257411yescharacteristic
813C4#1062282611yescharacteristic
814C4#1062283611yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—82no—
822C2—882no—
823C2#1306685511yescharacteristic
824C2#1306899612yes—
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#421C2
socleC22×C11#386
prime radicalC2×#10623363C2
cosocleC23×C4×C11C23
hypercenterC2×#421D11
hypocenterC11#10979
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#10622849C2semidirect
3. C2×#10622619C2semidirect
4. #13077060C2semidirect
5. C2×#10622193C2semidirect
6. C2×#10622170C2semidirect
7. C2×C11×#421C2semidirect
16. C2×#67000C4semidirect
17. C2×#66997C4semidirect
18. C2×#66993C4semidirect
20. C2×#66989C4semidirect
79. C2×C11×M16D4semidirect
84. C11×#117D4semidirect
106. #66979D4semidirect
122. C2×#4318D4semidirect
274. C2×#421D11semidirect
487. C2×M16C22⋊D11semidirect
509. #117C22⋊D11semidirect
683. C11#10979semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106228492
C2×#106226192
#130770602
C2×#106221932
C2×#106221702
C2×C11×#4212
#1097911