Finite Group Databasebeta

← C2×#13066874 #14675461

Subgroups — C2×#13066874 #14675461

Order 2816.

2942 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic11⋊C4C211yesmaximal, characteristic
2C22×C11⋊#95C211yesmaximal, characteristic
3C22×C11⋊#95C211yesmaximal, characteristic
4C22×C11⋊#95C211yesmaximal, characteristic
5C22×C11⋊#95C211yesmaximal, characteristic
6C22×C11⋊#95C211yesmaximal, characteristic
7#13066874C218yesmaximal, direct product factor
8C22×C11×#95C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×Dic11⋊C4—24no—
17C22×Dic11⋊C4—24no—
18C22×Dic11⋊C4—24no—
19C22×Dic11⋊C4C2214yes—
20C2×C11×#95—24no—
21C2×C11×#95C2214yes—
22C2×C11⋊#95—24no—
23C2×C11⋊#95—24no—
24C2×C11⋊#95—24no—
25C2×C11⋊#95—24no—
26C2×C11⋊#95C418yescomplemented
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32C25×C11C2311yescharacteristic
33C23×C4×C11—22no—
34C23×C4×C11—22no—
35C23×C4×C11—22no—
36C23×C4×C11—22no—
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11C2×C414yes—
52C23×C4×C11D414yes—
53C23×C4×C11Q814yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×Dic11—22no—
58C23×Dic11—22no—
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11C2×C414yes—
80C23×Dic11C2×C414yes—
81C23×Dic11D414yes—
82C23×Dic11D414yes—
83C23×Dic11D414yes—
84C23×Dic11Q814yes—
85C23×Dic11C2312yes—
86C23×Dic11C2312yes—
87C23×Dic11C2312yes—
88C23×Dic11C2312yes—
89C2×Dic11⋊C4—232no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—28no—
93C11×#95—28no—
94C11⋊#95—28no—
95C11⋊#95—28no—
96C11⋊#95—28no—
97C11⋊#95—28no—
98C11⋊#95C2×C4116yescomplemented
99C2×#1442—111nomaximal, Sylow
100C24×C11C22×C412yes—
101C24×C11C2×D412yes—
102C24×C11C2×D412yes—
103C24×C11C2×D412yes—
104C24×C11C2×D412yes—
105C24×C11C2×Q812yes—
106C24×C11C2×Q812yes—
107C24×C11#4112yes—
108C24×C11#4112yes—
109C24×C11#4112yes—
110C24×C11#4112yes—
111C24×C11#4112yes—
112C24×C11#4112yes—
113C24×C11#4112yes—
114C24×C11#4112yes—
115C24×C11C2411yescharacteristic
116C22×C4×C11—28no—
117C22×C4×C11—28no—
118C22×C4×C11—28no—
119C22×C4×C11—28no—
120C22×C4×C11—28no—
121C22×C4×C11—28no—
122C22×C4×C11—28no—
123C22×C4×C11—28no—
124C22×C4×C11—28no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11—44no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11C22×C414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×Q814yes—
158C22×Dic11—28no—
159C22×Dic11—28no—
160C22×Dic11—28no—
161C22×Dic11—28no—
162C22×Dic11—28no—
163C22×Dic11—28no—
164C22×Dic11—28no—
165C22×Dic11—28no—
166C22×Dic11—28no—
167C22×Dic11—28no—
168C22×Dic11—28no—
169C22×Dic11—28no—
170C22×Dic11—28no—
171C22×Dic11—28no—
172C22×Dic11—28no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—44no—
196C22×Dic11—44no—
197C22×Dic11—44no—
198C22×Dic11—44no—
199C22×Dic11—44no—
200C22×Dic11—44no—
201C22×Dic11—44no—
202C22×Dic11—44no—
203C22×Dic11—44no—
204C22×Dic11—44no—
205C22×Dic11—44no—
206C22×Dic11—44no—
207C22×Dic11C4⋊C4116yes—
208C22×Dic11C22×C414yes—
209C22×Dic11C22×C414yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D414yes—
213C22×Dic11C2×Q814yes—
214Dic11⋊C4—232no—
215C23×C4⋊C4—111no—
216C22×#95—111no—
217C22×#95—111no—
218C22×#95—111no—
219C22×#95—111no—
220C22×#95—111no—
221C22×#95D1111yescharacteristic
222#1442—118no—
223C23×C11C2×C4⋊C414yes—
224C23×C11#11714yes—
225C23×C11#11714yes—
226C23×C11C4×D414yes—
227C23×C11C4×D414yes—
228C23×C11C4×D414yes—
229C23×C11C4×Q814yes—
230C23×C11#12014yes—
231C23×C11#12114yes—
232C23×C11#12114yes—
233C23×C11#12114yes—
234C23×C11C22⋊Q814yes—
235C23×C11C22⋊Q814yes—
236C23×C11C22⋊Q814yes—
237C23×C11C22⋊Q814yes—
238C23×C11C22⋊Q814yes—
239C23×C11#12314yes—
240C23×C11#12314yes—
241C23×C11#12314yes—
242C23×C11#12314yes—
243C23×C11#12314yes—
244C23×C11#12414yes—
245C23×C11#12414yes—
246C23×C11#12414yes—
247C23×C11#12414yes—
248C23×C11#12514yes—
249C23×C11#12514yes—
250C23×C11#12514yes—
251C23×C11#12514yes—
252C23×C11#12514yes—
253C23×C11#12614yes—
254C23×C11#12614yes—
255C23×C11#12614yes—
256C23×C11#12614yes—
257C23×C11C4⋊Q814yes—
258C23×C11C23×C411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C22×D411yescharacteristic
262C23×C11C22×D411yescharacteristic
263C23×C11C22×Q811yescharacteristic
264C23×C11C22×Q811yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11C2×#4111yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—416no—
295C2×C4×C11—416no—
296C2×C4×C11—416no—
297C2×Dic11—24no—
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—232no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—42no—
314C2×Dic11—42no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—416no—
326C2×Dic11—416no—
327C2×Dic11—416no—
328C2×Dic11C2×C4⋊C418yes—
329C24×C4—111no—
330C24×C4—111no—
331C24×C4—111no—
332C24×C4—111no—
333C24×C4C2×D1111yescharacteristic
334C24×C4C2×D1111yescharacteristic
335C24×C4C2×D1111yescharacteristic
336C22×C4⋊C4—114no—
337C22×C4⋊C4—224no—
338C22×C4⋊C4—224no—
339C22×C4⋊C4—224no—
340C2×#95—24no—
341C2×#95—114no—
342C2×#95—118no—
343C2×#95—114no—
344C2×#95—114no—
345C2×#95—114no—
346C2×#95—114no—
347C2×#95—224no—
348C2×#95—224no—
349C2×#95—224no—
350C2×#95—224no—
351C2×#95C2×D1114yes—
352C22×C11#38218yes—
353C22×C11#38518yes—
354C22×C11#38718yes—
355C22×C11#38718yes—
356C22×C11#38818yes—
357C22×C11#38818yes—
358C22×C11#38918yes—
359C22×C11#39318yes—
360C22×C11#39418yes—
361C22×C11#39718yes—
362C22×C11#39818yes—
363C22×C11#39818yes—
364C22×C11#40018yes—
365C22×C11#40018yes—
366C22×C11#40018yes—
367C22×C11C22×C4⋊C411yescharacteristic
368C22×C11C2×#11711yescharacteristic
369C22×C11C2×#11711yescharacteristic
370C22×C11C2×C4×D411yescharacteristic
371C22×C11C2×C4×D411yescharacteristic
372C22×C11C2×C4×D411yescharacteristic
373C22×C11C2×C4×Q811yescharacteristic
374C22×C11C2×#12011yescharacteristic
375C22×C11C2×#12111yescharacteristic
376C22×C11C2×#12111yescharacteristic
377C22×C11C2×#12111yescharacteristic
378C22×C11C2×C22⋊Q811yescharacteristic
379C22×C11C2×C22⋊Q811yescharacteristic
380C22×C11C2×C22⋊Q811yescharacteristic
381C22×C11C2×C22⋊Q811yescharacteristic
382C22×C11C2×C22⋊Q811yescharacteristic
383C22×C11C2×#12311yescharacteristic
384C22×C11C2×#12311yescharacteristic
385C22×C11C2×#12311yescharacteristic
386C22×C11C2×#12311yescharacteristic
387C22×C11C2×#12311yescharacteristic
388C22×C11C2×#12411yescharacteristic
389C22×C11C2×#12411yescharacteristic
390C22×C11C2×#12411yescharacteristic
391C22×C11C2×#12411yescharacteristic
392C22×C11C2×#12511yescharacteristic
393C22×C11C2×#12511yescharacteristic
394C22×C11C2×#12511yescharacteristic
395C22×C11C2×#12511yescharacteristic
396C22×C11C2×#12511yescharacteristic
397C22×C11C2×#12611yescharacteristic
398C22×C11C2×#12611yescharacteristic
399C22×C11C2×#12611yescharacteristic
400C22×C11C2×#12611yescharacteristic
401C22×C11C2×C4⋊Q811yescharacteristic
402C4×C11—44no—
403C4×C11—44no—
404C4×C11—44no—
405Dic11—28no—
406Dic11—44no—
407Dic11—44no—
408Dic11—44no—
409C25C22×D1111yescharacteristic
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—114no—
429C23×C4—114no—
430C23×C4—114no—
431C23×C4—112no—
432C23×C4—114no—
433C23×C4—114no—
434C23×C4—114no—
435C23×C4—112no—
436C23×C4—112no—
437C23×C4—112no—
438C23×C4—222no—
439C23×C4—222no—
440C23×C4—222no—
441C23×C4—222no—
442C23×C4—222no—
443C23×C4—222no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4—222no—
449C23×C4—222no—
450C23×C4—222no—
451C23×C4—222no—
452C23×C4—222no—
453C23×C4—222no—
454C23×C4—222no—
455C23×C4—222no—
456C23×C4—222no—
457C23×C4—222no—
458C23×C4—222no—
459C23×C4—222no—
460C23×C4Dic2214yes—
461C23×C4C4×D1114yes—
462C23×C4C22⋊D1114yes—
463C23×C4C22×D1112yes—
464C23×C4C22×D1112yes—
465C23×C4C22×D1112yes—
466C2×C4⋊C4—228no—
467C2×C4⋊C4—228no—
468C2×C4⋊C4—2232no—
469C2×C4⋊C4—228no—
470#95—28no—
471#95—1116no—
472#95—228no—
473#95—228no—
474#95—228no—
475#95—228no—
476C2×C11#1442116yescomplemented
477C2×C11C2×#38211yescharacteristic
478C2×C11C2×#38511yescharacteristic
479C2×C11C2×#38711yescharacteristic
480C2×C11C2×#38711yescharacteristic
481C2×C11C2×#38811yescharacteristic
482C2×C11C2×#38811yescharacteristic
483C2×C11C2×#38911yescharacteristic
484C2×C11C2×#39311yescharacteristic
485C2×C11C2×#39411yescharacteristic
486C2×C11C2×#39711yescharacteristic
487C2×C11C2×#39811yescharacteristic
488C2×C11C2×#39811yescharacteristic
489C2×C11C2×#40011yescharacteristic
490C2×C11C2×#40011yescharacteristic
491C2×C11C2×#40011yescharacteristic
492C24C2×Dic2212yes—
493C24C2×C4×D1112yes—
494C24#433912yes—
495C24#433912yes—
496C24#433912yes—
497C24#433912yes—
498C24D4×D1112yes—
499C24D4×D1112yes—
500C24D4×D1112yes—
501C24#434112yes—
502C24#434112yes—
503C24#434112yes—
504C24Q8×D1112yes—
505C24#434312yes—
506C24C2×C22⋊D1112yes—
507C24C23×D1111yescharacteristic
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—1116no—
548C22×C4—114no—
549C22×C4—114no—
550C22×C4—114no—
551C22×C4—114no—
552C22×C4—114no—
553C22×C4—114no—
554C22×C4—228no—
555C22×C4—228no—
556C22×C4—228no—
557C22×C4—228no—
558C22×C4—228no—
559C22×C4—228no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—228no—
565C22×C4—228no—
566C22×C4—228no—
567C22×C4—228no—
568C22×C4—228no—
569C22×C4—228no—
570C22×C4—228no—
571C22×C4—228no—
572C22×C4—228no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—444no—
592C22×C4—444no—
593C22×C4—444no—
594C22×C4—444no—
595C22×C4—444no—
596C22×C4—444no—
597C22×C4—444no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4—444no—
601C22×C4—444no—
602C22×C4—444no—
603C22×C4C2×Dic2214yes—
604C22×C4C2×C4×D1114yes—
605C22×C4C2×C22⋊D1114yes—
606C4⋊C4—2232no—
607C11C2×#144211yescharacteristic, complemented, Sylow
608C23C4×Dic2214yes—
609C23#6692314yes—
610C23#6692514yes—
611C23#6692914yes—
612C23#6693014yes—
613C23#6693114yes—
614C23#6693114yes—
615C23#6693214yes—
616C23(C22⋊D11)⋊C414yes—
617C23#6693614yes—
618C23#6693614yes—
619C23#6693714yes—
620C23#6693714yes—
621C23#6693814yes—
622C23#6693814yes—
623C23#6693814yes—
624C23#6694114yes—
625C23#6694214yes—
626C23#6694214yes—
627C23#6694214yes—
628C23#6694314yes—
629C23C4⋊C4×D1114yes—
630C23#6694614yes—
631C23#6694714yes—
632C23#6694714yes—
633C23#6694914yes—
634C23#6695114yes—
635C23#6695114yes—
636C23#6697714yes—
637C23C4×C22⋊D1114yes—
638C23#6698214yes—
639C23#6698914yes—
640C23#6699014yes—
641C23#6699214yes—
642C23#6699914yes—
643C23C22×Dic2211yescharacteristic
644C23C22×C4×D1111yescharacteristic
645C23C2×#433911yescharacteristic
646C23C2×#433911yescharacteristic
647C23C2×#433911yescharacteristic
648C23C2×#433911yescharacteristic
649C23C2×D4×D1111yescharacteristic
650C23C2×D4×D1111yescharacteristic
651C23C2×D4×D1111yescharacteristic
652C23C2×#434111yescharacteristic
653C23C2×#434111yescharacteristic
654C23C2×#434111yescharacteristic
655C23C2×Q8×D1111yescharacteristic
656C23C2×#434311yescharacteristic
657C23C22×C22⋊D1111yescharacteristic
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—416no—
676C2×C4—416no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—416no—
682C2×C4—118no—
683C2×C4—224no—
684C2×C4—224no—
685C2×C4—224no—
686C2×C4—224no—
687C2×C4—224no—
688C2×C4—224no—
689C2×C4—2232no—
690C2×C4—224no—
691C2×C4—224no—
692C2×C4—224no—
693C2×C4—224no—
694C2×C4—224no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—4416no—
710C2×C4—4416no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—4416no—
714C22#1062226018yes—
715C22#1062226318yes—
716C22#1062226718yes—
717C22#1062227018yes—
718C22#1062227118yes—
719C22#1062227318yes—
720C22#1062228218yes—
721C22#1062228818yes—
722C22#1062254618yes—
723C22#1062255818yes—
724C22#1062256018yes—
725C22#1062257218yes—
726C22#1062259518yes—
727C22#1062259718yes—
728C22#1062260218yes—
729C22C2×C4×Dic2211yescharacteristic
730C22C2×#6692311yescharacteristic
731C22C2×#6692511yescharacteristic
732C22C2×#6692911yescharacteristic
733C22C2×#6693011yescharacteristic
734C22C2×#6693111yescharacteristic
735C22C2×#6693111yescharacteristic
736C22C2×#6693211yescharacteristic
737C22C2×(C22⋊D11)⋊C411yescharacteristic
738C22C2×#6693611yescharacteristic
739C22C2×#6693611yescharacteristic
740C22C2×#6693711yescharacteristic
741C22C2×#6693711yescharacteristic
742C22C2×#6693811yescharacteristic
743C22C2×#6693811yescharacteristic
744C22C2×#6693811yescharacteristic
745C22C2×#6694111yescharacteristic
746C22C2×#6694211yescharacteristic
747C22C2×#6694211yescharacteristic
748C22C2×#6694211yescharacteristic
749C22C2×#6694311yescharacteristic
750C22C2×C4⋊C4×D1111yescharacteristic
751C22C2×#6694611yescharacteristic
752C22C2×#6694711yescharacteristic
753C22C2×#6694711yescharacteristic
754C22C2×#6694911yescharacteristic
755C22C2×#6695111yescharacteristic
756C22C2×#6695111yescharacteristic
757C22C2×#6697711yescharacteristic
758C22C2×C4×C22⋊D1111yescharacteristic
759C22C2×#6698211yescharacteristic
760C22C2×#6698911yescharacteristic
761C22C2×#6699011yescharacteristic
762C22C2×#6699211yescharacteristic
763C22C2×#6699911yescharacteristic
764C4—44no—
765C4—44no—
766C4—44no—
767C4—228no—
768C4—444no—
769C4—444no—
770C4—444no—
771C2#13066874116yesdirect product factor
772C2C2×#1062226311yescharacteristic
773C2C2×#1062260211yescharacteristic
774C2C2×#1062226711yescharacteristic
775C2C2×#1062254611yescharacteristic
776C2C2×#1062228211yescharacteristic
777C2C2×#1062255811yescharacteristic
778C2C2×#1062226011yescharacteristic
779C2C2×#1062256011yescharacteristic
780C2C2×#1062257211yescharacteristic
781C2C2×#1062228811yescharacteristic
782C2C2×#1062259711yescharacteristic
783C2C2×#1062227011yescharacteristic
784C2C2×#1062259511yescharacteristic
785C2C2×#1062227111yescharacteristic
786C2C2×#1062227311yescharacteristic
subgroupG/H
centerC25C22×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC22×C11×#95C2
socle, prime radicalC25×C11C23
cosocleC24×C11C24
hypercenterC22×#95D11
hypocenterC11C2×#1442
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
7. #13066874C2direct (N × H)
26. C2×C11⋊#95C4semidirect
98. C11⋊#95C2×C4semidirect
476. C2×C11#1442semidirect
607. C11C2×#1442semidirect
771. C2#13066874direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C22×C11⋊#952
#130668742
C22×C11×#952
C2×#144211