Finite Group Databasebeta

← C2×#13080206 #15628839

Subgroups — C2×#13080206 #15628839

Order 2816.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66962C211yesmaximal, characteristic, complemented
2C22×#66957C211yesmaximal, characteristic, complemented
3C2×#10623084C211yesmaximal, characteristic, complemented
4C2×#10623083C211yesmaximal, characteristic, complemented
5#13080206C2116yesmaximal, direct product factor
6C2×#10622325C211yesmaximal, characteristic, complemented
7C2×#10622748C211yesmaximal, characteristic, complemented
8C2×#10622727C211yesmaximal, characteristic, complemented
9C2×#10622458C211yesmaximal, characteristic, complemented
10C2×#10622461C211yesmaximal, characteristic, complemented
11C2×#10622346C211yesmaximal, characteristic, complemented
12C2×#10622347C211yesmaximal, characteristic, complemented
13C2×#10622347C211yesmaximal, characteristic, complemented
14C2×#10622351C211yesmaximal, characteristic, complemented
15C2×#10622329C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×#66993—21no—
25C2×#66992—21no—
26C2×#66983C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C2×#66983C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C2×#66962—28no—
31C2×#66962C2218yescomplemented
32C22×Dic44C2211yescharacteristic
33C22×Dic44C2211yescharacteristic
34C2×#66957—28no—
35C2×#66957C2218yescomplemented
36C22×D88C2211yescharacteristic
37C22×D88C2211yescharacteristic
38C22×#4314C2211yescharacteristic
39C22×#4314C2211yescharacteristic
40C22×#4314C2211yescharacteristic
41C22×#4314C2211yescharacteristic
42C22×#4314C2211yescharacteristic
43#10623084—24no—
44#10623084C2218yescomplemented
45#10623083—24no—
46#10623083C2218yescomplemented
47C2×#66949—21no—
48C2×#66946—21no—
49C2×#66938—21no—
50C2×#66937—21no—
51C2×#66937—21no—
52C2×(C22⋊D11)⋊C4—21no—
53C2×#66928C2211yescharacteristic
54C2×#66927C2211yescharacteristic
55C2×C4×Dic22C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic
57C11×#435C2218yescomplemented
58C2×C11×C4⋊C8C2211yescharacteristic
59C2×C11×C22⋊C8C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C2×C11×#97C2211yescharacteristic
62#10622748C2218yescomplemented
63#10622727C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66885C2211yescharacteristic
66C2×#66885C2211yescharacteristic
67C2×#66881C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69C2×#66880C2211yescharacteristic
70C2×#66880C2211yescharacteristic
71#10622461C2218yescomplemented
72#10622458C2218yescomplemented
73#10622351C2218yescomplemented
74#10622347C2218yescomplemented
75#10622347C2218yescomplemented
76#10622346C2218yescomplemented
77#10622329C2218yescomplemented
78#10622325C2218yescomplemented
79C22×D4×C11D411yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C23×Dic11—21no—
89C2×#4339—22no—
90C2×#4339—22no—
91C2×#4339—22no—
92C2×#4339—24no—
93C2×#4339—24no—
94C2×#4339—24no—
95C2×#4339—42no—
96C2×#4339—42no—
97C2×#4339—42no—
98C2×#4339C2314yes—
99C2×#4339C2314yes—
100C2×#4339C2314yes—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44C2311yescharacteristic
104C22×D44C2311yescharacteristic
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11—21no—
109C22×Dic22—24no—
110C22×Dic22—21no—
111C22×Dic22—22no—
112C22×Dic22—42no—
113C22×Dic22C2311yescharacteristic
114C22×Dic22C2314yes—
115C22×Dic22C2311yescharacteristic
116C22×Dic22C2311yescharacteristic
117C2×C11×M16—24no—
118C2×C11×M16C2314yes—
119C22×C8×C11—24no—
120C22×C8×C11C2311yescharacteristic
121C22×C8×C11C2311yescharacteristic
122C22×C8×C11C2314yes—
123C22×C8×C11C2311yescharacteristic
124C22×C8×C11C2311yescharacteristic
125C4×D4×C11D414yes—
126C4×D4×C11C2314yes—
127C2×C11×C4⋊C4D411yescharacteristic
128C2×C11×C22⋊C4D411yescharacteristic
129C2×C11×C22⋊C4D411yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C2×C22⋊Dic11—21no—
132#66993—28no—
133#66992—28no—
134#66983—22no—
135#66983—22no—
136#66983—22no—
137#66983C2314yes—
138#66983C2314yes—
139#66983C2314yes—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147#66977—22no—
148#66977C2314yes—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11—21no—
154#66962—232no—
155C2×Dic44—24no—
156C2×Dic44D418yescomplemented
157C2×Dic44C2314yes—
158C2×Dic44C2314yes—
159#66957—232no—
160C2×D88—24no—
161C2×D88—42no—
162C2×D88C2314yes—
163C2×D88C2314yes—
164C2×#4314—24no—
165C2×#4314—24no—
166C2×#4314—24no—
167C2×#4314—24no—
168C2×#4314—42no—
169C2×#4314C2314yes—
170C2×#4314C2314yes—
171C2×#4314C2314yes—
172C2×#4314C2314yes—
173C2×#4314C2314yes—
174#66949—28no—
175#66946—28no—
176#66938—28no—
177#66937—28no—
178#66937—28no—
179(C22⋊D11)⋊C4—28no—
180#66928—22no—
181#66928C2314yes—
182#66927—22no—
183#66927C2314yes—
184C4×Dic22—22no—
185C4×Dic22—22no—
186C4×Dic22C2314yes—
187C4×Dic22C2314yes—
188C11×C4⋊C8C2314yes—
189C11×C22⋊C8C2314yes—
190C11×C22⋊C8C2314yes—
191C11×#97C2314yes—
192#66885C2314yes—
193#66885C2314yes—
194#66885C2314yes—
195#66881C2314yes—
196#66880C2314yes—
197#66880C2314yes—
198#66880C2314yes—
199C2×#3271—111nomaximal, Sylow
200C24×C11C2×D411yescharacteristic
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C2×D4×C11—42no—
206C2×D4×C11C2×D414yes—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—82no—
231C2×C22⋊D11—82no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—24no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—44no—
239#4339—28no—
240#4339—28no—
241#4339—28no—
242#4339—44no—
243#4339—44no—
244#4339—44no—
245#4339—48no—
246#4339—48no—
247#4339—48no—
248C2×D44—21no—
249C2×D44—21no—
250C2×D44—24no—
251C2×D44—21no—
252C2×D44—24no—
253C2×D44—22no—
254C2×D44—22no—
255C2×D44—22no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44—22no—
259C2×D44—44no—
260C2×D44—82no—
261C2×D44C2412yes—
262C2×D44C2412yes—
263C2×D44C2412yes—
264C2×C4×D11—24no—
265C2×C4×D11—24no—
266C2×C4×D11—24no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×Dic22—28no—
271C2×Dic22—21no—
272C2×Dic22—21no—
273C2×Dic22—22no—
274C2×Dic22—21no—
275C2×Dic22—24no—
276C2×Dic22—22no—
277C2×Dic22—22no—
278C2×Dic22—22no—
279C2×Dic22—44no—
280C2×Dic22—48no—
281C2×Dic22—44no—
282C2×Dic22C2×D414yes—
283C2×Dic22C2×D414yes—
284C2×Dic22C2412yes—
285C2×Dic22C2412yes—
286C2×Dic22C2412yes—
287C11×M16—28no—
288C2×C8×C11—28no—
289C2×C8×C11—22no—
290C2×C8×C11—22no—
291C2×C8×C11—22no—
292C2×C8×C11C2×D414yes—
293C2×C8×C11C2412yes—
294C2×C8×C11C2412yes—
295C2×C8×C11C2412yes—
296C2×C8×C11C2412yes—
297C11×C4⋊C4C2×D414yes—
298C11×C22⋊C4C2×D414yes—
299C11×C22⋊C4C2×D414yes—
300C42×C11C2×D412yes—
301C42×C11C2412yes—
302C22⋊Dic11—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11C2412yes—
311C4⋊Dic11C2412yes—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314Dic11⋊C4—24no—
315C4×Dic11—24no—
316C4×Dic11—24no—
317Dic44—28no—
318Dic44C2×D4116yescomplemented
319D88—28no—
320D88—44no—
321#4314—28no—
322#4314—28no—
323#4314—28no—
324#4314—28no—
325#4314—44no—
326C22×#137—111no—
327C22×#135—111no—
328C2×#550—111no—
329C2×#548—111no—
330#3271—1116no—
331C2×#496—111no—
332C2×#469—111no—
333C2×#465—111no—
334C2×#464—111no—
335C2×#460—111no—
336C2×#452—111no—
337C2×#449—111no—
338C2×#449—111no—
339C2×#448—111no—
340C2×#441—111no—
341C2×#435D1111yescharacteristic, complemented
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11C22×D412yes—
349C23×C11C22×D412yes—
350C23×C11C22×D411yescharacteristic
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—42no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11—42no—
363D4×C11—44no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—24no—
369C2×C4×C11—24no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11C22×D412yes—
375C2×C4×C11C22×D412yes—
376C2×C4×C11C22×D412yes—
377C2×C4×C11C22×D412yes—
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D412yes—
380C2×C4×C11H(5,𝔽2)12yes—
381C2×C4×C11C2511yescharacteristic
382C22⋊D11—48no—
383C22⋊D11—48no—
384C22⋊D11—48no—
385C22⋊D11—48no—
386C22⋊D11—84no—
387C22⋊D11—84no—
388C2×Dic11—24no—
389C2×Dic11—24no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—48no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399D44—22no—
400D44—22no—
401D44—22no—
402D44—22no—
403D44—22no—
404D44—22no—
405D44—48no—
406D44—42no—
407D44—42no—
408D44—42no—
409D44—84no—
410C4×D11—48no—
411C4×D11—48no—
412C4×D11—48no—
413Dic22—24no—
414Dic22—24no—
415Dic22—22no—
416Dic22—22no—
417Dic22—22no—
418Dic22—22no—
419Dic22—48no—
420Dic22—42no—
421Dic22C22×D414yes—
422Dic22C22×D414yes—
423C8×C11—22no—
424C8×C11—22no—
425C8×C11—22no—
426C8×C11C22×D414yes—
427C22×#41—111no—
428C22×#41—111no—
429C22×#41—111no—
430C23×Q8—111no—
431C2×#137—118no—
432C2×#137—228no—
433C2×#135—118no—
434C2×#135—228no—
435C22×Q16—111no—
436C22×Q16—111no—
437C22×SD16—111no—
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16—111no—
441C22×SD16—111no—
442C22×D8—111no—
443C22×D8—111no—
444C22×M16C2×D1111yescharacteristic
445C23×C8C2×D1111yescharacteristic
446#550—118no—
447#550—224no—
448#548—118no—
449#548—224no—
450C2×#127—111no—
451C2×#127—221no—
452C2×#124—111no—
453C2×#124—221no—
454C2×C22⋊Q8—111no—
455C2×C22⋊Q8—221no—
456C2×#121—111no—
457C2×#121—111no—
458C2×#121—111no—
459C2×#121—221no—
460C2×#121—221no—
461C2×#121—221no—
462C2×C4×Q8—111no—
463C2×C4×Q8—111no—
464C2×C4×D4—221no—
465C2×C4×D4—221no—
466C2×C4×D4C2×D1111yescharacteristic
467#496—118no—
468#469—118no—
469#465—118no—
470#464—118no—
471#460—118no—
472#452—118no—
473#449—118no—
474#449—118no—
475#448—118no—
476#441—118no—
477#435C2×D1118yescomplemented
478C2×#106—111no—
479C2×C4⋊C8C2×D1111yescharacteristic
480C2×#103—111no—
481C2×#103—111no—
482C2×#103—111no—
483C2×#102—111no—
484C2×#102—111no—
485C2×#102—111no—
486C2×C22⋊C8C2×D1111yescharacteristic
487C2×C22⋊C8C2×D1111yescharacteristic
488C2×#97C2×D1111yescharacteristic
489C22×C11—22no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—22no—
495C22×C11—44no—
496C22×C11—44no—
497C22×C11D4212yes—
498C22×C11#57512yes—
499C22×C11#57712yes—
500C22×C11C23×D411yescharacteristic
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—84no—
511C2×D11—84no—
512C2×D11—84no—
513C4×C11—22no—
514C4×C11—22no—
515C4×C11—22no—
516C4×C11—22no—
517C4×C11D4212yes—
518C4×C11C23×D411yescharacteristic
519C4×C11C2×H(5,𝔽2)11yescharacteristic
520Dic11—24no—
521Dic11—24no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525C2×#41—114no—
526C2×#41—114no—
527C2×#41—114no—
528C2×#41—224no—
529C2×#41—224no—
530C2×#41—224no—
531C2×#41—222no—
532C2×#41—222no—
533C2×#41—222no—
534C2×#41—442no—
535C2×#41—442no—
536C2×#41—442no—
537C22×Q8—111no—
538C22×Q8—111no—
539C22×Q8—111no—
540C22×Q8—114no—
541C22×Q8—224no—
542C22×Q8—221no—
543C22×Q8—222no—
544C22×Q8—442no—
545C22×D4—111no—
546C22×D4—111no—
547C22×D4—111no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4—221no—
554C22×D4—221no—
555C22×D4—221no—
556C22×D4D4411yescharacteristic
557C23×C4—221no—
558C23×C4—221no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563#137—2232no—
564#135—2232no—
565C2×Q16—118no—
566C2×Q16—114no—
567C2×Q16—114no—
568C2×Q16—224no—
569C2×SD16—114no—
570C2×SD16—114no—
571C2×SD16—114no—
572C2×SD16—114no—
573C2×SD16—114no—
574C2×SD16—224no—
575C2×SD16—224no—
576C2×SD16—224no—
577C2×SD16—224no—
578C2×SD16—442no—
579C2×D8—114no—
580C2×D8—114no—
581C2×D8—224no—
582C2×D8—442no—
583C2×M16—24no—
584C2×M16C22×D1114yes—
585C22×C8—24no—
586C22×C8C22×D1111yescharacteristic
587C22×C8C22×D1114yes—
588C22×C8C22×D1111yescharacteristic
589C22×C8C22×D1111yescharacteristic
590C22×C8C22×D1111yescharacteristic
591#127—114no—
592#127—228no—
593#127—222no—
594#124—114no—
595#124—228no—
596#124—222no—
597C22⋊Q8—114no—
598C22⋊Q8—222no—
599C22⋊Q8—228no—
600#121—114no—
601#121—114no—
602#121—114no—
603#121—228no—
604#121—222no—
605#121—222no—
606#121—222no—
607#121—228no—
608#121—228no—
609C4×Q8—114no—
610C4×Q8—114no—
611C4×Q8—222no—
612C4×Q8—222no—
613C4×D4—228no—
614C4×D4—228no—
615C4×D4D4414yes—
616C4×D4C22×D1114yes—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C4⋊C4D4411yescharacteristic
623C2×C22⋊C4—221no—
624C2×C22⋊C4—221no—
625C2×C22⋊C4—221no—
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4D4411yescharacteristic
630C2×C22⋊C4D4411yescharacteristic
631C2×C42—221no—
632C2×C42—221no—
633C2×C42C22×D1111yescharacteristic
634#106—114no—
635C4⋊C8C22×D1114yes—
636#103—114no—
637#103—114no—
638#103—114no—
639#102—114no—
640#102—114no—
641#102—114no—
642C22⋊C8C22×D1114yes—
643C22⋊C8C22×D1114yes—
644#97C22×D1114yes—
645C2×C11—42no—
646C2×C11—42no—
647C2×C11#327114yescomplemented
648C2×C11C2×D4211yescharacteristic
649C2×C11C2×#57511yescharacteristic
650C2×C11C2×#57711yescharacteristic
651D11—82no—
652D11—82no—
653D11—82no—
654C24—221no—
655C24—221no—
656C24—221no—
657C24C2×D4411yescharacteristic
658C24C2×D4411yescharacteristic
659#41—228no—
660#41—228no—
661#41—228no—
662#41—444no—
663#41—444no—
664#41—444no—
665#41—448no—
666#41—448no—
667#41—448no—
668C2×Q8—114no—
669C2×Q8—114no—
670C2×Q8—112no—
671C2×Q8—112no—
672C2×Q8—112no—
673C2×Q8—228no—
674C2×Q8—221no—
675C2×Q8—221no—
676C2×Q8—224no—
677C2×Q8—221no—
678C2×Q8—222no—
679C2×Q8—222no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8—444no—
683C2×Q8—444no—
684C2×Q8—448no—
685C2×D4—42no—
686C2×D4—112no—
687C2×D4—112no—
688C2×D4—112no—
689C2×D4—224no—
690C2×D4—224no—
691C2×D4—224no—
692C2×D4—224no—
693C2×D4—224no—
694C2×D4—224no—
695C2×D4—224no—
696C2×D4—221no—
697C2×D4—221no—
698C2×D4—221no—
699C2×D4—224no—
700C2×D4—222no—
701C2×D4—222no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—222no—
706C2×D4—444no—
707C2×D4—444no—
708C2×D4—444no—
709C2×D4—444no—
710C2×D4—444no—
711C2×D4—882no—
712C2×D4—882no—
713C2×D4—882no—
714C2×D4C2×D4414yes—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—224no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—224no—
726C22×C4—224no—
727C22×C4—224no—
728C22×C4—444no—
729C22×C4—444no—
730C22×C4—444no—
731C22×C4—444no—
732C22×C4C2×D4412yes—
733C22×C4C2×D4412yes—
734C22×C4C2×D4411yescharacteristic
735C22×C4C2×D4411yescharacteristic
736C22×C4C2×D4411yescharacteristic
737C22×C4C2×D4411yescharacteristic
738C22×C4C23×D1112yes—
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—1116no—
742Q16—228no—
743SD16—228no—
744SD16—228no—
745SD16—228no—
746SD16—228no—
747SD16—444no—
748D8—228no—
749D8—444no—
750M16—28no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—28no—
755C2×C8D4×D1114yes—
756C2×C8C23×D1112yes—
757C2×C8C23×D1112yes—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—112no—
761C4⋊C4—112no—
762C4⋊C4—221no—
763C4⋊C4—221no—
764C4⋊C4—224no—
765C4⋊C4—224no—
766C4⋊C4—224no—
767C4⋊C4C2×D4414yes—
768C22⋊C4—224no—
769C22⋊C4—224no—
770C22⋊C4—224no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4C2×D4414yes—
775C22⋊C4C2×D4414yes—
776C42—224no—
777C42—224no—
778C42C2×D4412yes—
779C42C23×D1112yes—
780C11C2×#327111yescharacteristic, complemented, Sylow
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—442no—
791C23—442no—
792C23—442no—
793C23—442no—
794C23—442no—
795C23—442no—
796C23—442no—
797C23—442no—
798C23—442no—
799C23C22×D4412yes—
800C23C22×D4412yes—
801C23C22×D4411yescharacteristic
802Q8—114no—
803Q8—114no—
804Q8—224no—
805Q8—224no—
806Q8—222no—
807Q8—222no—
808Q8—222no—
809Q8—222no—
810Q8—448no—
811Q8—442no—
812D4—44no—
813D4—222no—
814D4—222no—
815D4—222no—
816D4—222no—
817D4—222no—
818D4—222no—
819D4—448no—
820D4—448no—
821D4—448no—
822D4—448no—
823D4—448no—
824D4—442no—
825D4—442no—
826D4—442no—
827D4—884no—
828D4—884no—
829D4—884no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—224no—
841C2×C4—224no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—448no—
848C2×C4—448no—
849C2×C4—448no—
850C2×C4—448no—
851C2×C4—442no—
852C2×C4—442no—
853C2×C4—442no—
854C2×C4C22×D4412yes—
855C2×C4C22×D4412yes—
856C2×C4C22×D4412yes—
857C2×C4C22×D4412yes—
858C2×C4C22×D4411yescharacteristic
859C2×C4C2×D4×D1112yes—
860C2×C4#6704212yes—
861C2×C4C24×D1111yescharacteristic
862C8—22no—
863C8—22no—
864C8—22no—
865C8C2×D4×D1114yes—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—44no—
874C22—442no—
875C22—442no—
876C22—442no—
877C22—442no—
878C22—442no—
879C22—442no—
880C22—442no—
881C22—442no—
882C22—442no—
883C22—884no—
884C22—884no—
885C22—884no—
886C22D4×D4412yes—
887C22#1062327912yes—
888C22#1062328212yes—
889C22C23×D4411yescharacteristic
890C4—22no—
891C4—22no—
892C4—22no—
893C4—22no—
894C4—224no—
895C4—224no—
896C4—442no—
897C4—442no—
898C4—442no—
899C4D4×D4412yes—
900C4C22×D4×D1111yescharacteristic
901C4C2×#6704211yescharacteristic
902C2—42no—
903C2—42no—
904C2—882no—
905C2—882no—
906C2—882no—
907C2#1308020614yesdirect product factor
908C2C2×D4×D4411yescharacteristic
909C2C2×#1062327911yescharacteristic
910C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
hypercenterC2×#435D11
hypocenterC11C2×#3271
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#66962C2semidirect
2. C22×#66957C2semidirect
3. C2×#10623084C2semidirect
4. C2×#10623083C2semidirect
5. #13080206C2direct (N × H)
6. C2×#10622325C2semidirect
7. C2×#10622748C2semidirect
8. C2×#10622727C2semidirect
9. C2×#10622458C2semidirect
10. C2×#10622461C2semidirect
11. C2×#10622346C2semidirect
12. C2×#10622347C2semidirect
13. C2×#10622347C2semidirect
14. C2×#10622351C2semidirect
15. C2×#10622329C2semidirect
16. C2×C11×#435C2semidirect
31. C2×#66962C22semidirect
35. C2×#66957C22semidirect
44. #10623084C22semidirect
46. #10623083C22semidirect
57. C11×#435C22semidirect
62. #10622748C22semidirect
63. #10622727C22semidirect
71. #10622461C22semidirect
72. #10622458C22semidirect
73. #10622351C22semidirect
74. #10622347C22semidirect
75. #10622347C22semidirect
76. #10622346C22semidirect
77. #10622329C22semidirect
78. #10622325C22semidirect
156. C2×Dic44D4semidirect
318. Dic44C2×D4semidirect
341. C2×#435D11semidirect
477. #435C2×D11semidirect
647. C2×C11#3271semidirect
780. C11C2×#3271semidirect
907. C2#13080206direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C22×#669572
C2×#106230842
C2×#106230832
#130802062
C2×#106223252
C2×#106227482
C2×#106227272
C2×#106224582
C2×#106224612
C2×#106223462
C2×#106223472
C2×#106223512
C2×#106223292
C2×C11×#4352
C2×#327111