Finite Group Databasebeta

← #15620752

Subgroups — #15620752

Order 2816.

2750 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623279C211yesmaximal, characteristic, complemented
2C2×#10623353C211yesmaximal, characteristic, complemented
3#13081945C211yesmaximal, characteristic, complemented
4C2×#10623035C211yesmaximal, characteristic, complemented
5#13078171C214yesmaximal, complemented
6#13078165C214yesmaximal, complemented
7#13078160C214yesmaximal, complemented
8#13078154C214yesmaximal, complemented
9#13078087C214yesmaximal, complemented
10#13078079C214yesmaximal, complemented
11#13077179C211yesmaximal, characteristic, complemented
12C2×#10622579C211yesmaximal, characteristic, complemented
13C2×C11×#417C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19#10623364—21no—
20#10623364—21no—
21#10623363C2214yes—
22#10623361C2212yescomplemented
23#10623359—22no—
24#10623356C2212yescomplemented
25C2×#67004C2212yescomplemented
26#10623353—28no—
27C2×#67003C2214yes—
28C2×#67002C2212yescomplemented
29#10623347C2212yescomplemented
30C2×#66995C2212yescomplemented
31#10623336C2212yescomplemented
32#10623335—22no—
33C2×#66985C2212yescomplemented
34#10623322—22no—
35C2×C4×C22⋊D11—22no—
36C2×#66979C2211yescharacteristic
37C22×#4318C2211yescharacteristic
38#10623279—28no—
39C2×#66962C2212yescomplemented
40C2×#66962C2212yescomplemented
41C2×#66961C2212yescomplemented
42C2×#66961C2212yescomplemented
43C2×#66957C2214yes—
44#10623035—22no—
45#10623035—22no—
46#10623035C2214yescomplemented
47#10623035C2214yescomplemented
48C2×#66946C2212yescomplemented
49C2×#66945—21no—
50C2×C4⋊C4×D11—21no—
51C2×#66940C2212yescomplemented
52C11×#417C2214yescomplemented
53C11×#417C2214yescomplemented
54C2×C11×#103C2212yescomplemented
55C2×C11×#102C2212yescomplemented
56#10622732C2214yescomplemented
57#10622731C2214yescomplemented
58#10622715C2214yescomplemented
59C2×#66874C2212yescomplemented
60#10622579C2214yescomplemented
61#10622579C2214yescomplemented
62C2×#66873C2212yescomplemented
63#10622432C2218yescomplemented
64#10622431C2218yescomplemented
65#10622411C2218yescomplemented
66#10622406C2218yescomplemented
67#10622400C2218yescomplemented
68#10622399C2218yescomplemented
69#10622380C2218yescomplemented
70#10622375C2218yescomplemented
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—24no—
74C2×C11×#41—24no—
75C2×C11×#41C2312yes—
76C2×C11×#41C2312yes—
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C2×#4339—21no—
86C2×#4339—21no—
87C2×#4339—24no—
88C2×#4339—21no—
89C2×#4339—21no—
90C2×#4339—24no—
91C2×#4339—24no—
92C2×#4339D418yescomplemented
93C2×#4339C2312yes—
94C2×#4339C2312yes—
95C2×#4339C2312yes—
96C2×#4339C2312yes—
97C22×D44C2311yescharacteristic
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11—22no—
102C22×Dic22C2311yescharacteristic
103C22×Dic22C2311yescharacteristic
104C2×C11×M16—24no—
105C2×C11×M16C2312yes—
106C2×C11×M16C2312yes—
107C22×C8×C11C2312yes—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2312yes—
114#67006—24no—
115C2×C22⋊Dic11D412yes—
116#67004—28no—
117#67003—216no—
118#67002—28no—
119#67000C2314yes—
120#66999—22no—
121#66999—22no—
122#66997C2314yes—
123C2×#4326C2314yes—
124#66995—28no—
125C2×#4325C2314yes—
126#66993C2314yes—
127#66992—24no—
128#66992—24no—
129#66991—22no—
130#66991—22no—
131#66990—24no—
132#66989C2314yes—
133#66988—24no—
134C2×#4324C2314yes—
135#66985—28no—
136C2×#4323C2314yes—
137#66983—22no—
138#66983—22no—
139#66982—24no—
140C4×C22⋊D11—28no—
141C4×C22⋊D11—28no—
142C4×C22⋊D11—24no—
143C4×C22⋊D11—24no—
144C2×(C2×D11)⋊C4—22no—
145#66979D412yes—
146#66979D412yes—
147#66979C2312yes—
148#66979C2312yes—
149C2×C4⋊Dic11D411yescharacteristic
150C2×C4⋊Dic11D411yescharacteristic
151#66977—22no—
152#66977—22no—
153C2×Dic11⋊C4—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11C2312yes—
156C2×#4318—24no—
157C2×#4318C2312yes—
158C2×#4318C2312yes—
159C22×C11⋊C8C2312yes—
160#66962—28no—
161#66962—28no—
162#66961—28no—
163#66961—28no—
164C2×Dic44C2314yes—
165#66957—216no—
166C2×D88C2314yes—
167C2×#4314C2314yes—
168C2×#4314C2314yes—
169#66946—24no—
170#66946C2318yes—
171#66945—24no—
172#66945—24no—
173C4⋊C4×D11—24no—
174C4⋊C4×D11—24no—
175#66940—24no—
176#66940C2318yes—
177C11×#103C2318yes—
178C11×#102C2318yes—
179Dic11⋊C8C2318yes—
180Dic11⋊C8C2318yes—
181#66874C2318yes—
182#66873C2318yes—
183#60425—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11C2×D411yescharacteristic
186C23×D11—21no—
187C23×D11—21no—
188C11×#41—24no—
189C11×#41—24no—
190C11×#41—24no—
191C11×#41—24no—
192C11×#41—44no—
193C11×#41—44no—
194C2×Q8×C11—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11C2412yes—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—21no—
202C2×D4×C11—22no—
203C2×D4×C11—44no—
204C2×D4×C11C2412yes—
205C22×C4×C11—22no—
206C22×C4×C11—21no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—44no—
212C22×C4×C11—82no—
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D414yes—
217C22×C4×C11#4114yes—
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—28no—
224C2×C22⋊D11—22no—
225C2×C22⋊D11—22no—
226C2×C22⋊D11—22no—
227C2×C22⋊D11—22no—
228C2×C22⋊D11—44no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11C2×D412yes—
232C22×Dic11C2×D412yes—
233#4339—28no—
234#4339—28no—
235#4339—24no—
236#4339—24no—
237#4339—24no—
238#4339—24no—
239#4339—24no—
240#4339—24no—
241#4339—44no—
242#4339—44no—
243#4339C2×D418yes—
244#4339C2×D418yes—
245C2×D44—21no—
246C2×D44—21no—
247C2×D44—22no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44C2×D414yes—
251C2×D44C2412yes—
252C2×D44C2412yes—
253C2×C4×D11—28no—
254C2×C4×D11—28no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—22no—
258C2×C4×D11—22no—
259C2×C4×D11—44no—
260C2×C4×D11—84no—
261C2×Dic22—21no—
262C2×Dic22—22no—
263C2×Dic22—21no—
264C2×Dic22—22no—
265C2×Dic22—22no—
266C2×Dic22C2×D414yes—
267C2×Dic22C2412yes—
268C2×Dic22C2412yes—
269C11×M16—24no—
270C11×M16—24no—
271C2×C8×C11—24no—
272C2×C8×C11C2414yes—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4C2414yes—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279C22⋊Dic11C2×D414yes—
280C22⋊Dic11C2×D414yes—
281#4326—28no—
282#4325—28no—
283#4324—28no—
284#4323—28no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288C4⋊Dic11C2×D412yes—
289C4⋊Dic11C2×D412yes—
290C4⋊Dic11C2×D412yes—
291C4⋊Dic11C2×D412yes—
292Dic11⋊C4—28no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295C4×Dic11—28no—
296C4×Dic11C2×D414yes—
297C4×Dic11C2414yes—
298#4318—24no—
299#4318—24no—
300C2×C11⋊C8—24no—
301C2×C11⋊C8C2414yes—
302Dic44—28no—
303D88—28no—
304#4314—28no—
305#4314—28no—
306C2×#575—111no—
307C2×#575—111no—
308#3449—111no—
309C2×#520—111no—
310#3046—114no—
311#3046—114no—
312#3045—114no—
313#3045—114no—
314#3037—114no—
315#3036—114no—
316#2905—111no—
317C2×#417—111no—
318C2×#417D1111yescharacteristic, complemented
319C23×C11—22no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—42no—
323C23×C11—81no—
324C23×C11—81no—
325C23×C11#12114yes—
326C23×C11C22×D411yescharacteristic
327C23×C11C22×D411yescharacteristic
328C23×C11C22×D411yescharacteristic
329C22×D11—24no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—81no—
336C22×D11—81no—
337Q8×C11—22no—
338Q8×C11—22no—
339Q8×C11—42no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—44no—
343D4×C11—44no—
344D4×C11—42no—
345C2×C4×C11—24no—
346C2×C4×C11—22no—
347C2×C4×C11—44no—
348C2×C4×C11—42no—
349C2×C4×C11—44no—
350C2×C4×C11—44no—
351C2×C4×C11—82no—
352C2×C4×C11—82no—
353C2×C4×C11#12114yes—
354C2×C4×C11#12114yes—
355C2×C4×C11#12114yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D412yes—
362C2×C4×C11C2×#4112yes—
363C2×C4×C11C2×#4112yes—
364C2×C4×C11C2×#4112yes—
365C2×C4×C11C2511yescharacteristic
366C22⋊D11—28no—
367C22⋊D11—28no—
368C22⋊D11—44no—
369C22⋊D11—44no—
370C22⋊D11—84no—
371C22⋊D11—84no—
372C2×Dic11—24no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—42no—
376C2×Dic11—42no—
377C2×Dic11—42no—
378C2×Dic11C22×D414yes—
379C2×Dic11C22×D414yes—
380D44—24no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—42no—
385D44C22×D414yes—
386C4×D11—28no—
387C4×D11—28no—
388C4×D11—44no—
389C4×D11—44no—
390C4×D11—88no—
391Dic22—24no—
392Dic22—22no—
393Dic22—22no—
394Dic22—22no—
395Dic22—42no—
396Dic22C22×D414yes—
397C8×C11—24no—
398C11⋊C8—24no—
399C22×#41—111no—
400C22×#41—111no—
401C22×#41C2×D1111yescharacteristic
402#575—228no—
403#575—228no—
404C2×#137—112no—
405C2×#137—112no—
406C2×#137—112no—
407C2×#137—112no—
408C2×AGL(1,ℤ/8)—112no—
409C2×AGL(1,ℤ/8)—112no—
410C2×AGL(1,ℤ/8)—112no—
411C2×AGL(1,ℤ/8)—112no—
412C2×#135—114no—
413C2×#135—114no—
414C22×M16—111no—
415C22×M16C2×D1111yescharacteristic
416#537—221no—
417#537—221no—
418#536—112no—
419#536—112no—
420#535—112no—
421#535—112no—
422#534—222no—
423#532—114no—
424#525—222no—
425#525—222no—
426#520—114no—
427#520—114no—
428#520—222no—
429#520—222no—
430C2×C4×Q8—112no—
431C2×C4×D4—112no—
432C2×C4×D4—222no—
433C2×#117—111no—
434C2×#117—221no—
435C22×C4⋊C4—221no—
436C22×C4⋊C4C2×D1111yescharacteristic
437#464—118no—
438#464—118no—
439#463—118no—
440#463—118no—
441#462—118no—
442#461—118no—
443#460—118no—
444#459—118no—
445#424—114no—
446#424—114no—
447#423—114no—
448#417—114no—
449#417—114no—
450#417C2×D1114yescomplemented
451#417C2×D1114yescomplemented
452C2×#103—112no—
453C2×#103C2×D1112yescomplemented
454C2×#102—112no—
455C2×#102C2×D1112yescomplemented
456C22×C11—21no—
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—21no—
460C22×C11—21no—
461C22×C11—21no—
462C22×C11—44no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—84no—
467C22×C11C2×#12112yes—
468C22×C11C2×#12112yes—
469C22×C11C2×#12112yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—24no—
472C2×D11—48no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—84no—
479C4×C11—44no—
480C4×C11—42no—
481C4×C11C2×#12112yes—
482C4×C11C2×#12112yes—
483C4×C11C2×#12112yes—
484C4×C11C23×D411yescharacteristic
485C4×C11C22×#4111yescharacteristic
486Dic11—24no—
487Dic11—24no—
488Dic11—24no—
489Dic11—42no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—24no—
493C2×#41—24no—
494C2×#41—118no—
495C2×#41—112no—
496C2×#41—112no—
497C2×#41—112no—
498C2×#41—112no—
499C2×#41—224no—
500C2×#41—221no—
501C2×#41—221no—
502C2×#41—221no—
503C2×#41—221no—
504C2×#41—224no—
505C2×#41—224no—
506C2×#41C22×D1112yes—
507C2×#41C22×D1112yes—
508C22×Q8—111no—
509C22×Q8—111no—
510C22×Q8C22×D1111yescharacteristic
511C22×D4—21no—
512C22×D4—111no—
513C22×D4—111no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4C22×D1111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—222no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523#137—228no—
524#137—228no—
525#137—228no—
526#137—228no—
527AGL(1,ℤ/8)—228no—
528AGL(1,ℤ/8)—228no—
529AGL(1,ℤ/8)—228no—
530AGL(1,ℤ/8)—228no—
531#135—2216no—
532#135—2216no—
533C2×Q16—114no—
534C2×Q16—114no—
535C2×SD16—114no—
536C2×SD16—114no—
537C2×SD16—114no—
538C2×SD16—114no—
539C2×D8—114no—
540C2×D8—114no—
541C2×M16—24no—
542C2×M16—112no—
543C2×M16—112no—
544C2×M16—224no—
545C2×M16C22×D1112yes—
546C2×M16C22×D1112yes—
547C22×C8—112no—
548C22×C8C22×D1112yes—
549C4⋊Q8—114no—
550#127—114no—
551#124—114no—
552#124—114no—
553#123—224no—
554#123—224no—
555C22⋊Q8—222no—
556C22⋊Q8—222no—
557C22⋊Q8—222no—
558C22⋊Q8—222no—
559#121—222no—
560#121—222no—
561#121—222no—
562#121—222no—
563#121—224no—
564#121—224no—
565#120—224no—
566#120—224no—
567C4×Q8—118no—
568C4×Q8—224no—
569C4×D4—118no—
570C4×D4—224no—
571C4×D4—224no—
572C4×D4—224no—
573C4×D4—228no—
574C4×D4—228no—
575#117—112no—
576#117—112no—
577#117—112no—
578#117—112no—
579#117—224no—
580#117—224no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—111no—
585C2×C4⋊C4—111no—
586C2×C4⋊C4—224no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—222no—
589C2×C4⋊C4C22×D1112yes—
590C2×C4⋊C4C22×D1112yes—
591C2×C4⋊C4C22×D1112yes—
592C2×C22⋊C4—112no—
593C2×C22⋊C4—222no—
594C2×C42—112no—
595C2×C42—222no—
596C4⋊C8—118no—
597C4⋊C8—118no—
598#103—118no—
599#103C22×D1118yes—
600#102—118no—
601#102C22×D1118yes—
602C2×C11—22no—
603C2×C11—22no—
604C2×C11—22no—
605C2×C11—82no—
606C2×C11C22×#12111yescharacteristic
607C2×C11#358511yescharacteristic
608C2×C11#358611yescharacteristic
609D11—44no—
610D11—82no—
611C24—21no—
612C24—221no—
613C24—221no—
614C24D4×D1111yescharacteristic
615#41—24no—
616#41—24no—
617#41—24no—
618#41—24no—
619#41—44no—
620#41—44no—
621#41—118no—
622#41—118no—
623#41—228no—
624#41—228no—
625#41—224no—
626#41—224no—
627#41—224no—
628#41—224no—
629#41—224no—
630#41—224no—
631#41—444no—
632#41—444no—
633C2×Q8—21no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—114no—
637C2×Q8—112no—
638C2×Q8—112no—
639C2×Q8—222no—
640C2×Q8—221no—
641C2×Q8—221no—
642C2×Q8—222no—
643C2×Q8—222no—
644C2×Q8C23×D1112yes—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—44no—
651C2×D4—114no—
652C2×D4—112no—
653C2×D4—112no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—228no—
657C2×D4—222no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4—222no—
661C2×D4—222no—
662C2×D4—222no—
663C2×D4—221no—
664C2×D4—222no—
665C2×D4—221no—
666C2×D4—444no—
667C2×D4C23×D1112yes—
668C22×C4—22no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—44no—
675C22×C4—82no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—228no—
679C22×C4—221no—
680C22×C4—228no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—221no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—444no—
687C22×C4—884no—
688C22×C4#433914yes—
689C22×C4D4×D1111yescharacteristic
690C22×C4D4×D1111yescharacteristic
691C22×C4D4×D1111yescharacteristic
692C22×C4D4×D1114yes—
693C22×C4C23×D1111yescharacteristic
694C22×C4C23×D1111yescharacteristic
695C22×C4C23×D1111yescharacteristic
696Q16—228no—
697Q16—228no—
698SD16—228no—
699SD16—228no—
700SD16—228no—
701SD16—228no—
702D8—228no—
703D8—228no—
704M16—24no—
705M16—24no—
706M16—224no—
707M16—224no—
708C2×C8—24no—
709C2×C8—114no—
710C2×C8—224no—
711C2×C8C23×D1114yes—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—112no—
716C4⋊C4—112no—
717C4⋊C4—112no—
718C4⋊C4—112no—
719C4⋊C4—228no—
720C4⋊C4—224no—
721C4⋊C4—224no—
722C4⋊C4C23×D1114yes—
723C22⋊C4—114no—
724C22⋊C4—114no—
725C22⋊C4—228no—
726C22⋊C4—224no—
727C22⋊C4—224no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C42—114no—
731C42—114no—
732C42—228no—
733C11#6042511yescharacteristic, complemented, Sylow
734C23—22no—
735C23—41no—
736C23—41no—
737C23—42no—
738C23—81no—
739C23—81no—
740C23—224no—
741C23—222no—
742C23—222no—
743C23—442no—
744C23—442no—
745C23—442no—
746C23—881no—
747C23—881no—
748C23#6693714yes—
749C23C2×D4×D1111yescharacteristic
750C23C2×D4×D1111yescharacteristic
751C23C2×D4×D1111yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—114no—
756Q8—224no—
757Q8—222no—
758Q8—222no—
759Q8—222no—
760Q8—442no—
761D4—22no—
762D4—22no—
763D4—44no—
764D4—44no—
765D4—42no—
766D4—114no—
767D4—228no—
768D4—228no—
769D4—224no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—444no—
774D4—444no—
775D4—442no—
776D4—884no—
777D4—884no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—114no—
787C2×C4—114no—
788C2×C4—224no—
789C2×C4—222no—
790C2×C4—228no—
791C2×C4—228no—
792C2×C4—222no—
793C2×C4—442no—
794C2×C4—442no—
795C2×C4—442no—
796C2×C4—444no—
797C2×C4—444no—
798C2×C4—888no—
799C2×C4#6693714yes—
800C2×C4#6693714yes—
801C2×C4#6693714yes—
802C2×C4C2×#433912yes—
803C2×C4C2×#433912yes—
804C2×C4C2×#433912yes—
805C2×C4C2×D4×D1111yescharacteristic
806C2×C4C2×D4×D1111yescharacteristic
807C2×C4C2×D4×D1111yescharacteristic
808C2×C4C2×D4×D1112yes—
809C2×C4C2×D4×D1112yes—
810C2×C4C2×D4×D1112yes—
811C2×C4C24×D1111yescharacteristic
812C8—24no—
813C8—224no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—44no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—84no—
825C22—224no—
826C22—448no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—884no—
833C22C2×#6693712yes—
834C22C2×#6693712yes—
835C22C2×#6693712yes—
836C22C22×D4×D1111yescharacteristic
837C4—44no—
838C4—42no—
839C4—224no—
840C4—224no—
841C4—224no—
842C4—442no—
843C4C2×#6693712yes—
844C4C2×#6693712yes—
845C4C2×#6693712yes—
846C4C22×#433911yescharacteristic
847C4C22×D4×D1111yescharacteristic
848C2—22no—
849C2—22no—
850C2—22no—
851C2—82no—
852C2—444no—
853C2—882no—
854C2C22×#6693711yescharacteristic
855C2#1308339211yescharacteristic
856C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC22×C11C23×D4
hypercenterC2×#417D11
hypocenterC11#60425
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10623279C2semidirect
2. C2×#10623353C2semidirect
3. #13081945C2semidirect
4. C2×#10623035C2semidirect
5. #13078171C2semidirect
6. #13078165C2semidirect
7. #13078160C2semidirect
8. #13078154C2semidirect
9. #13078087C2semidirect
10. #13078079C2semidirect
11. #13077179C2semidirect
12. C2×#10622579C2semidirect
13. C2×C11×#417C2semidirect
22. #10623361C22semidirect
24. #10623356C22semidirect
25. C2×#67004C22semidirect
28. C2×#67002C22semidirect
29. #10623347C22semidirect
30. C2×#66995C22semidirect
31. #10623336C22semidirect
33. C2×#66985C22semidirect
39. C2×#66962C22semidirect
40. C2×#66962C22semidirect
41. C2×#66961C22semidirect
42. C2×#66961C22semidirect
46. #10623035C22semidirect
47. #10623035C22semidirect
48. C2×#66946C22semidirect
51. C2×#66940C22semidirect
52. C11×#417C22semidirect
53. C11×#417C22semidirect
54. C2×C11×#103C22semidirect
55. C2×C11×#102C22semidirect
56. #10622732C22semidirect
57. #10622731C22semidirect
58. #10622715C22semidirect
59. C2×#66874C22semidirect
60. #10622579C22semidirect
61. #10622579C22semidirect
62. C2×#66873C22semidirect
63. #10622432C22semidirect
64. #10622431C22semidirect
65. #10622411C22semidirect
66. #10622406C22semidirect
67. #10622400C22semidirect
68. #10622399C22semidirect
69. #10622380C22semidirect
70. #10622375C22semidirect
92. C2×#4339D4semidirect
318. C2×#417D11semidirect
450. #417C2×D11semidirect
451. #417C2×D11semidirect
453. C2×#103C2×D11semidirect
455. C2×#102C2×D11semidirect
733. C11#60425semidirect

Maximal subgroups

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

subgroupindex
C2×#106232792
C2×#106233532
#130819452
C2×#106230352
#130781712
#130781652
#130781602
#130781542
#130780872
#130780792
#130771792
C2×#106225792
C2×C11×#4172
#6042511