Finite Group Databasebeta

← #15626791

Subgroups — #15626791

Order 2816.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2C2×#10623010C211yesmaximal, characteristic, complemented
3#13080017C214yesmaximal, complemented
4#13079990C212yesmaximal, complemented
5#13079979C212yesmaximal, complemented
6#13079968C214yesmaximal, complemented
7#13079954C212yesmaximal, complemented
8#13079943C212yesmaximal, complemented
9#13078439C212yesmaximal, complemented
10#13078423C211yesmaximal, characteristic, complemented
11#13078415C211yesmaximal, characteristic, complemented
12#13078246C212yesmaximal, complemented
13#13078235C212yesmaximal, complemented
14#13078111C212yesmaximal, complemented
15#13078090C211yesmaximal, characteristic, complemented
16#13078082C211yesmaximal, characteristic, complemented
17C2×C11×#423C211yesmaximal, characteristic, complemented
18C22×C11×M16C2212yes—
19C22×C42×C11C2211yescharacteristic
20#10623322—21no—
21#10623322—21no—
22#10623322C2212yes—
23C2×#66983C2211yescharacteristic
24C2×#66982—21no—
25C2×C4×C22⋊D11—21no—
26C2×#66977C2211yescharacteristic
27C2×#66962C2212yes—
28C2×#66961C2212yes—
29#10623010—21no—
30#10623010—21no—
31#10623010—21no—
32#10623010—21no—
33#10623010—21no—
34#10623010—21no—
35#10623010—21no—
36#10623010—21no—
37#10623010C2212yes—
38#10623010C2212yes—
39#10623010C2212yes—
40#10623010C2212yes—
41#10623010C2212yescomplemented
42#10623010C2212yescomplemented
43C2×#66929—21no—
44#10623008C2211yescharacteristic
45#10623008C2211yescharacteristic, complemented
46#10623008C2211yescharacteristic, complemented
47C2×#66928C2211yescharacteristic
48C4×#4339—21no—
49C4×#4339—21no—
50C4×#4339C2212yes—
51C2×C4×D44C2211yescharacteristic
52C2×#66925—21no—
53#10623001C2211yescharacteristic
54#10623001C2211yescharacteristic, complemented
55#10623001C2211yescharacteristic, complemented
56C2×#66923C2211yescharacteristic
57C2×C4×Dic22C2211yescharacteristic
58C11×#423C2211yescharacteristic
59C11×#423C2211yescharacteristic
60C11×#423C2212yes—
61C11×#423C2212yescomplemented
62C11×#423C2212yescomplemented
63C2×C11×C4⋊C8C2212yescomplemented
64C2×C11×C4⋊C8C2212yescomplemented
65#10622750C2214yescomplemented
66#10622748C2214yes—
67#10622747C2214yes—
68#10622747C2214yescomplemented
69#10622746C2212yes—
70#10622746C2212yes—
71#10622744C2212yes—
72#10622734C2212yes—
73#10622734C2212yes—
74#10622733C2212yes—
75#10622729C2214yescomplemented
76#10622728C2214yes—
77#10622727C2214yes—
78#10622727C2214yescomplemented
79#10622464C2212yescomplemented
80#10622463C2212yescomplemented
81#10622462C2212yescomplemented
82#10622461C2212yescomplemented
83#10622460C2214yescomplemented
84#10622460C2214yescomplemented
85#10622460C2214yescomplemented
86#10622459C2212yescomplemented
87#10622458C2214yescomplemented
88#10622458C2214yescomplemented
89#10622458C2214yescomplemented
90#10622457C2214yescomplemented
91#10622457C2214yescomplemented
92#10622457C2214yescomplemented
93#10622456C2212yescomplemented
94#10622455C2212yescomplemented
95#10622454C2212yescomplemented
96#10622442C2214yescomplemented
97#10622442C2214yescomplemented
98#10622442C2214yescomplemented
99C23×C4×C11D411yescharacteristic
100C23×C4×C11D411yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C22×C22⋊D11—21no—
103C2×#4339—21no—
104C2×#4339—21no—
105C2×#4339C2312yes—
106C22×D44C2311yescharacteristic
107C22×C4×D11—21no—
108C22×Dic22C2311yescharacteristic
109C2×C11×M16—44no—
110C2×C11×M16C2312yes—
111C2×C11×M16C2312yes—
112C2×C11×M16C2314yes—
113C22×C8×C11C2314yes—
114C2×C42×C11D411yescharacteristic
115C2×C42×C11D411yescharacteristic
116C2×C42×C11D411yescharacteristic
117C2×C42×C11D411yescharacteristic
118C2×C42×C11D411yescharacteristic
119C2×C42×C11D411yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126#67006—22no—
127C2×C22⋊Dic11—21no—
128#66983—21no—
129#66983—21no—
130#66983—21no—
131#66983—21no—
132#66983—21no—
133#66983—21no—
134#66983C2312yes—
135#66983C2312yes—
136#66983C2312yes—
137#66983C2312yes—
138#66982—22no—
139#66982—22no—
140#66982—22no—
141#66982—22no—
142#66982—22no—
143#66982—22no—
144#66982—22no—
145C4×C22⋊D11—22no—
146C4×C22⋊D11—22no—
147C4×C22⋊D11—22no—
148C4×C22⋊D11—22no—
149C4×C22⋊D11—22no—
150C4×C22⋊D11—22no—
151C4×C22⋊D11—22no—
152C4×C22⋊D11—22no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155C2×(C2×D11)⋊C4—21no—
156C2×(C2×D11)⋊C4—21no—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4—21no—
159#66979—21no—
160#66979—21no—
161#66979C2312yes—
162C2×C4⋊Dic11C2311yescharacteristic
163C2×C4⋊Dic11C2311yescharacteristic
164#66977—21no—
165#66977—21no—
166#66977—21no—
167#66977—21no—
168#66977—21no—
169#66977—21no—
170#66977C2312yes—
171#66977C2312yes—
172#66977C2312yes—
173#66977C2312yes—
174C2×Dic11⋊C4—21no—
175C2×Dic11⋊C4—21no—
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4—21no—
178C2×C4×Dic11—21no—
179#66962—44no—
180#66961—44no—
181C2×Dic44C2314yes—
182C2×D88C2314yes—
183C2×#4314C2314yes—
184C2×#4314C2314yes—
185#66929—22no—
186#66929—22no—
187#66929—22no—
188#66929—22no—
189#66929—22no—
190#66929—22no—
191#66928—21no—
192#66928—21no—
193#66928—21no—
194#66928—21no—
195#66928C2312yes—
196#66928C2312yes—
197#66928C2312yes—
198#66927C2311yescharacteristic
199C4×D44—21no—
200C4×D44—21no—
201C4×D44—21no—
202C4×D44—21no—
203C4×D44—21no—
204C4×D44—21no—
205C4×D44C2312yes—
206C4×D44C2312yes—
207C4×D44C2312yes—
208C4×D44C2312yes—
209#66925—22no—
210#66925—22no—
211#66925—22no—
212#66925—22no—
213#66925—22no—
214#66925—22no—
215#66925—22no—
216C42×D11—22no—
217#66923—21no—
218#66923—21no—
219#66923—21no—
220#66923—21no—
221#66923C2312yes—
222#66923C2312yes—
223#66923C2312yes—
224#66922C2311yescharacteristic
225#66922C2311yescharacteristic
226#66922C2311yescharacteristic
227C4×Dic22—21no—
228C4×Dic22—21no—
229C4×Dic22—21no—
230C4×Dic22—21no—
231C4×Dic22—21no—
232C4×Dic22—21no—
233C4×Dic22C2312yes—
234C4×Dic22C2312yes—
235C4×Dic22C2312yes—
236C4×Dic22C2312yes—
237C11×C4⋊C8C2312yes—
238C11×C4⋊C8C2312yes—
239C11×C4⋊C8C2314yes—
240C11×C4⋊C8C2314yes—
241C11×C4⋊C8C2312yes—
242C11×C4⋊C8C2312yes—
243#66885C2314yes—
244#66885C2314yes—
245#66885C2314yes—
246#66885C2314yes—
247#66882C2314yes—
248#66882C2314yes—
249#66881C2314yes—
250#66881C2314yes—
251#66880C2314yes—
252#66880C2314yes—
253#66880C2314yes—
254#66880C2314yes—
255#60917—111nomaximal, Sylow
256C24×C11C2×D411yescharacteristic
257C23×D11—21no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—42no—
261C22×C4×C11—42no—
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C2×C22⋊D11—22no—
281C2×C22⋊D11—22no—
282C2×C22⋊D11—22no—
283C2×C22⋊D11—22no—
284C2×C22⋊D11—22no—
285C2×C22⋊D11—44no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289#4339—24no—
290#4339—24no—
291#4339—44no—
292#4339—44no—
293C2×D44—21no—
294C2×D44—21no—
295C2×D44—21no—
296C2×D44—22no—
297C2×D44—22no—
298C2×D44C2412yes—
299C2×D44C2412yes—
300C2×C4×D11—22no—
301C2×C4×D11—22no—
302C2×C4×D11—22no—
303C2×C4×D11—22no—
304C2×C4×D11—22no—
305C2×C4×D11—44no—
306C2×Dic22—21no—
307C2×Dic22—21no—
308C2×Dic22—21no—
309C2×Dic22—22no—
310C2×Dic22—22no—
311C2×Dic22C2412yes—
312C2×Dic22C2412yes—
313C11×M16—24no—
314C11×M16—24no—
315C11×M16—44no—
316C2×C8×C11—44no—
317C2×C8×C11C2414yes—
318C2×C8×C11C2414yes—
319C42×C11C2×D411yescharacteristic
320C42×C11C2×D411yescharacteristic
321C42×C11C2×D411yescharacteristic
322C42×C11C2×D411yescharacteristic
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D411yescharacteristic
326C42×C11C2×D411yescharacteristic
327C42×C11C2×D411yescharacteristic
328C42×C11C2×D411yescharacteristic
329C42×C11C2×D411yescharacteristic
330C42×C11C2×D411yescharacteristic
331C42×C11C2411yescharacteristic
332C42×C11C2411yescharacteristic
333C42×C11C2411yescharacteristic
334C42×C11C2411yescharacteristic
335C22⋊Dic11—22no—
336C22⋊Dic11—22no—
337C22⋊Dic11—22no—
338C22⋊Dic11—22no—
339C22⋊Dic11—22no—
340(C2×D11)⋊C4—22no—
341(C2×D11)⋊C4—22no—
342(C2×D11)⋊C4—22no—
343(C2×D11)⋊C4—22no—
344(C2×D11)⋊C4—22no—
345(C2×D11)⋊C4—22no—
346(C2×D11)⋊C4—22no—
347(C2×D11)⋊C4—22no—
348(C2×D11)⋊C4—22no—
349(C2×D11)⋊C4—22no—
350(C2×D11)⋊C4—22no—
351(C2×D11)⋊C4—22no—
352(C2×D11)⋊C4—22no—
353(C2×D11)⋊C4—22no—
354C4⋊Dic11—21no—
355C4⋊Dic11—21no—
356C4⋊Dic11—21no—
357C4⋊Dic11—21no—
358C4⋊Dic11—21no—
359C4⋊Dic11—21no—
360C4⋊Dic11C2412yes—
361C4⋊Dic11C2412yes—
362C4⋊Dic11C2412yes—
363C4⋊Dic11C2412yes—
364Dic11⋊C4—22no—
365Dic11⋊C4—22no—
366Dic11⋊C4—22no—
367Dic11⋊C4—22no—
368Dic11⋊C4—22no—
369Dic11⋊C4—22no—
370Dic11⋊C4—22no—
371Dic11⋊C4—22no—
372Dic11⋊C4—22no—
373Dic11⋊C4—22no—
374Dic11⋊C4—22no—
375Dic11⋊C4—22no—
376Dic11⋊C4—22no—
377Dic11⋊C4—22no—
378C4×Dic11—22no—
379C4×Dic11—22no—
380C4×Dic11—22no—
381C4×Dic11—22no—
382C4×Dic11—22no—
383Dic44—44no—
384D88—44no—
385#4314—44no—
386#4314—44no—
387#3444—111no—
388C2×#529—111no—
389#3256—114no—
390#3252—112no—
391#3251—112no—
392#3250—114no—
393#3248—112no—
394#3247—112no—
395#3080—112no—
396#3078—111no—
397#3077—111no—
398#3056—112no—
399#3055—112no—
400#3040—112no—
401#3037—111no—
402#3036—111no—
403C2×#423D1111yescharacteristic, complemented
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—41no—
407C23×C11C22×D411yescharacteristic
408C23×C11C22×D411yescharacteristic
409C23×C11C22×D411yescharacteristic
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—42no—
413C22×D11—42no—
414C22×D11—42no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11C22×D411yescharacteristic
435C2×C4×C11C22×D411yescharacteristic
436C2×C4×C11C22×D411yescharacteristic
437C2×C4×C11C22×D411yescharacteristic
438C2×C4×C11C22×D411yescharacteristic
439C2×C4×C11C22×D411yescharacteristic
440C2×C4×C11C22×D411yescharacteristic
441C2×C4×C11C22×D411yescharacteristic
442C2×C4×C11C22×D411yescharacteristic
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11H(5,𝔽2)12yes—
446C2×C4×C112−1+412yes—
447C2×C4×C11C2511yescharacteristic
448C22⋊D11—44no—
449C22⋊D11—44no—
450C22⋊D11—44no—
451C22⋊D11—44no—
452C22⋊D11—44no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—42no—
460C2×Dic11—42no—
461C2×Dic11—42no—
462D44—22no—
463D44—22no—
464D44—22no—
465D44—22no—
466D44—42no—
467D44—42no—
468D44—42no—
469C4×D11—44no—
470C4×D11—44no—
471C4×D11—44no—
472C4×D11—44no—
473C4×D11—44no—
474Dic22—22no—
475Dic22—22no—
476Dic22—22no—
477Dic22—22no—
478Dic22—42no—
479Dic22—42no—
480Dic22—42no—
481C8×C11—24no—
482C8×C11—24no—
483C2×#137—112no—
484C2×AGL(1,ℤ/8)—112no—
485C22×M16C2×D1112yes—
486#533—111no—
487#533—111no—
488#533—111no—
489#532—111no—
490#532—111no—
491#532—111no—
492#529—112no—
493#529—112no—
494#529—112no—
495#529—112no—
496#529—112no—
497#529—112no—
498#529—221no—
499#529—221no—
500#529—221no—
501#529—221no—
502#529—221no—
503#529—221no—
504#529—221no—
505#529—221no—
506C2×#126—221no—
507C2×#125—111no—
508C2×#124—111no—
509#525—112no—
510#525—221no—
511#525—221no—
512C2×#123—221no—
513C2×C22⋊Q8—111no—
514C2×#121—111no—
515C4×#41—112no—
516C4×#41—221no—
517C4×#41—221no—
518C2×C4×Q8—111no—
519C2×C4×D4—111no—
520C2×C4×D4—221no—
521C2×#117—221no—
522C22×C42C2×D1111yescharacteristic
523#479—114no—
524#479—114no—
525#479—114no—
526#478—114no—
527#478—114no—
528#478—114no—
529#477—112no—
530#476—112no—
531#475—112no—
532#474—112no—
533#470—114no—
534#469—114no—
535#468—114no—
536#468—114no—
537#467—114no—
538#466—114no—
539#465—114no—
540#465—114no—
541#464—114no—
542#464—114no—
543#464—114no—
544#463—114no—
545#463—114no—
546#463—114no—
547#462—112no—
548#461—112no—
549#460—112no—
550#459—112no—
551#428—112no—
552#428—112no—
553#423C2×D1111yescharacteristic
554#423C2×D1111yescharacteristic
555#423C2×D1112yes—
556#423C2×D1112yescomplemented
557#423C2×D1112yescomplemented
558C2×C4⋊C8C2×D1112yescomplemented
559C2×C4⋊C8C2×D1112yescomplemented
560#419—112no—
561#418—112no—
562#417—112no—
563#417—112no—
564C22×C11—21no—
565C22×C11—21no—
566C22×C11—21no—
567C22×C11—21no—
568C22×C11—21no—
569C22×C11—21no—
570C22×C11—21no—
571C22×C11—44no—
572C22×C11#53712yes—
573C22×C11#57512yes—
574C22×C11C23×D411yescharacteristic
575C2×D11—42no—
576C2×D11—42no—
577C2×D11—42no—
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—84no—
582C4×C11—21no—
583C4×C11—21no—
584C4×C11—21no—
585C4×C11—21no—
586C4×C11—21no—
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—21no—
590C4×C11—21no—
591C4×C11#53712yes—
592C4×C11#57512yes—
593C4×C11C2×H(5,𝔽2)11yescharacteristic
594C4×C11C2×2−1+411yescharacteristic
595Dic11—42no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599Dic11—42no—
600Dic11—42no—
601C2×#41—112no—
602C2×#41—221no—
603C2×#41—221no—
604C22×Q8—111no—
605C22×D4—111no—
606C22×D4—221no—
607C23×C4—221no—
608C23×C4D4411yescharacteristic
609C23×C4D4411yescharacteristic
610C23×C4C22×D1111yescharacteristic
611#137—444no—
612AGL(1,ℤ/8)—444no—
613C2×Q16—114no—
614C2×SD16—114no—
615C2×SD16—114no—
616C2×D8—114no—
617C2×M16—44no—
618C2×M16C22×D1112yes—
619C2×M16C22×D1112yes—
620C2×M16C22×D1114yes—
621C22×C8C22×D1114yes—
622C4⋊Q8—111no—
623C4⋊Q8—111no—
624C4⋊Q8—111no—
625#127—111no—
626#126—222no—
627#126—222no—
628#126—222no—
629#126—222no—
630#126—222no—
631#126—222no—
632#125—112no—
633#125—112no—
634#125—112no—
635#125—221no—
636#125—221no—
637#125—221no—
638#125—221no—
639#124—112no—
640#124—112no—
641#124—112no—
642#124—221no—
643#124—221no—
644#124—221no—
645#124—221no—
646#123—222no—
647#123—222no—
648#123—222no—
649#123—222no—
650#123—222no—
651#123—222no—
652#123—222no—
653C22⋊Q8—112no—
654C22⋊Q8—112no—
655C22⋊Q8—112no—
656C22⋊Q8—112no—
657C22⋊Q8—221no—
658C22⋊Q8—221no—
659C22⋊Q8—221no—
660C22⋊Q8—221no—
661C22⋊Q8—221no—
662C22⋊Q8—221no—
663#121—112no—
664#121—112no—
665#121—112no—
666#121—112no—
667#121—221no—
668#121—221no—
669#121—221no—
670#121—221no—
671#121—221no—
672#121—221no—
673#120—222no—
674C4×Q8—112no—
675C4×Q8—112no—
676C4×Q8—112no—
677C4×Q8—112no—
678C4×Q8—221no—
679C4×Q8—221no—
680C4×Q8—221no—
681C4×Q8—221no—
682C4×Q8—221no—
683C4×Q8—221no—
684C4×D4—112no—
685C4×D4—112no—
686C4×D4—112no—
687C4×D4—112no—
688C4×D4—222no—
689C4×D4—222no—
690C4×D4—222no—
691C4×D4—222no—
692C4×D4—222no—
693C4×D4—222no—
694C4×D4—222no—
695C4×D4—222no—
696C4×D4—222no—
697C4×D4—222no—
698C4×D4—221no—
699C4×D4—221no—
700C4×D4—221no—
701C4×D4—221no—
702C4×D4—221no—
703C4×D4—221no—
704#117—112no—
705#117—221no—
706#117—221no—
707#117—222no—
708#117—222no—
709#117—222no—
710#117—222no—
711#117—222no—
712#117—222no—
713#117—222no—
714C2×C4⋊C4—111no—
715C2×C4⋊C4—111no—
716C2×C4⋊C4—221no—
717C2×C4⋊C4—221no—
718C2×C4⋊C4—221no—
719C2×C4⋊C4—221no—
720C2×C22⋊C4—221no—
721C2×C22⋊C4—221no—
722C2×C22⋊C4—221no—
723C2×C22⋊C4—221no—
724C2×C22⋊C4—221no—
725C2×C42—221no—
726C2×C42—222no—
727C2×C42D4411yescharacteristic
728C2×C42D4411yescharacteristic
729C2×C42D4411yescharacteristic
730C2×C42D4411yescharacteristic
731C2×C42D4411yescharacteristic
732C2×C42D4411yescharacteristic
733C2×C42C22×D1111yescharacteristic
734C2×C42C22×D1111yescharacteristic
735C2×C42C22×D1111yescharacteristic
736C2×C42C22×D1111yescharacteristic
737C2×C42C22×D1111yescharacteristic
738C2×C42C22×D1111yescharacteristic
739#107—114no—
740#107—114no—
741#106—114no—
742#106—114no—
743C4⋊C8C22×D1112yes—
744C4⋊C8C22×D1112yes—
745C4⋊C8C22×D1112yes—
746C4⋊C8C22×D1114yes—
747C4⋊C8C22×D1114yes—
748C4⋊C8C22×D1112yes—
749#103—114no—
750#103—114no—
751#103—114no—
752#103—114no—
753#102—114no—
754#102—114no—
755#102—114no—
756#102—114no—
757C2×C11—22no—
758C2×C11—22no—
759C2×C11—41no—
760C2×C11C2×#53711yescharacteristic
761C2×C11C2×#57511yescharacteristic
762C2×C11C2×#57511yescharacteristic
763D11—82no—
764D11—82no—
765C24—221no—
766C24C2×D4411yescharacteristic
767#41—224no—
768#41—224no—
769#41—444no—
770#41—444no—
771C2×Q8—112no—
772C2×Q8—112no—
773C2×Q8—221no—
774C2×Q8—221no—
775C2×Q8—221no—
776C2×Q8—222no—
777C2×Q8—222no—
778C2×D4—112no—
779C2×D4—112no—
780C2×D4—222no—
781C2×D4—222no—
782C2×D4—222no—
783C2×D4—222no—
784C2×D4—222no—
785C2×D4—221no—
786C2×D4—221no—
787C2×D4—221no—
788C2×D4—222no—
789C2×D4—222no—
790C2×D4—444no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—222no—
799C22×C4—222no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—444no—
804C22×C4C2×D4411yescharacteristic
805C22×C4C2×D4411yescharacteristic
806C22×C4C2×D4411yescharacteristic
807C22×C4C2×D4411yescharacteristic
808C22×C4C2×D4411yescharacteristic
809C22×C4C2×D4411yescharacteristic
810C22×C4C2×D4411yescharacteristic
811C22×C4C2×D4411yescharacteristic
812C22×C4C2×D4411yescharacteristic
813C22×C4C2×D4411yescharacteristic
814C22×C4C2×D4411yescharacteristic
815C22×C4C2×D4411yescharacteristic
816C22×C4C2×D4411yescharacteristic
817C22×C4C2×D4411yescharacteristic
818C22×C4C2×D4411yescharacteristic
819C22×C4C23×D1111yescharacteristic
820C22×C4C23×D1111yescharacteristic
821C22×C4C23×D1111yescharacteristic
822Q16—444no—
823SD16—444no—
824SD16—444no—
825D8—444no—
826M16—24no—
827M16—24no—
828M16—44no—
829C2×C8—44no—
830C2×C8C23×D1114yes—
831C2×C8C23×D1114yes—
832C4⋊C4—112no—
833C4⋊C4—112no—
834C4⋊C4—112no—
835C4⋊C4—112no—
836C4⋊C4—221no—
837C4⋊C4—221no—
838C4⋊C4—222no—
839C4⋊C4—222no—
840C4⋊C4—222no—
841C4⋊C4—222no—
842C4⋊C4—222no—
843C4⋊C4—222no—
844C4⋊C4—222no—
845C4⋊C4—222no—
846C4⋊C4—222no—
847C4⋊C4—222no—
848C4⋊C4—221no—
849C4⋊C4—221no—
850C4⋊C4—221no—
851C4⋊C4—221no—
852C4⋊C4—222no—
853C4⋊C4—222no—
854C4⋊C4—222no—
855C4⋊C4—222no—
856C22⋊C4—222no—
857C22⋊C4—222no—
858C22⋊C4—222no—
859C22⋊C4—222no—
860C22⋊C4—222no—
861C22⋊C4—222no—
862C22⋊C4—222no—
863C22⋊C4—222no—
864C22⋊C4—222no—
865C22⋊C4—222no—
866C22⋊C4—222no—
867C22⋊C4—222no—
868C22⋊C4—222no—
869C22⋊C4—222no—
870C22⋊C4—222no—
871C22⋊C4—222no—
872C22⋊C4—222no—
873C22⋊C4—222no—
874C22⋊C4—222no—
875C42—222no—
876C42—222no—
877C42—222no—
878C42—222no—
879C42—222no—
880C42C2×D4411yescharacteristic
881C42C2×D4411yescharacteristic
882C42C2×D4411yescharacteristic
883C42C2×D4411yescharacteristic
884C42C2×D4411yescharacteristic
885C42C2×D4411yescharacteristic
886C42C2×D4411yescharacteristic
887C42C2×D4411yescharacteristic
888C42C2×D4411yescharacteristic
889C42C2×D4411yescharacteristic
890C42C2×D4411yescharacteristic
891C42C2×D4411yescharacteristic
892C42C23×D1111yescharacteristic
893C42C23×D1111yescharacteristic
894C42C23×D1111yescharacteristic
895C42C23×D1111yescharacteristic
896C11#6091711yescharacteristic, complemented, Sylow
897C23—22no—
898C23—22no—
899C23—41no—
900C23—222no—
901C23—222no—
902C23—442no—
903C23—442no—
904C23—442no—
905C23C22×D4411yescharacteristic
906C23C22×D4411yescharacteristic
907C23C22×D4411yescharacteristic
908Q8—222no—
909Q8—222no—
910Q8—222no—
911Q8—222no—
912Q8—442no—
913Q8—442no—
914Q8—442no—
915D4—222no—
916D4—222no—
917D4—222no—
918D4—222no—
919D4—442no—
920D4—444no—
921D4—444no—
922D4—444no—
923D4—444no—
924D4—444no—
925D4—442no—
926D4—442no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—444no—
953C2×C4—444no—
954C2×C4—444no—
955C2×C4—442no—
956C2×C4—442no—
957C2×C4—442no—
958C2×C4—444no—
959C2×C4—444no—
960C2×C4C22×D4411yescharacteristic
961C2×C4C22×D4411yescharacteristic
962C2×C4C22×D4411yescharacteristic
963C2×C4C22×D4411yescharacteristic
964C2×C4C22×D4411yescharacteristic
965C2×C4C22×D4411yescharacteristic
966C2×C4C22×D4411yescharacteristic
967C2×C4C22×D4411yescharacteristic
968C2×C4C22×D4411yescharacteristic
969C2×C4C22×D4411yescharacteristic
970C2×C4C22×D4411yescharacteristic
971C2×C4#6703712yes—
972C2×C4#6704012yes—
973C2×C4C24×D1111yescharacteristic
974C8—24no—
975C8—24no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—44no—
984C22—442no—
985C22—442no—
986C22—442no—
987C22—442no—
988C22—442no—
989C22—442no—
990C22—884no—
991C22#1062304112yes—
992C22#1062327912yes—
993C22C23×D4411yescharacteristic
994C4—21no—
995C4—21no—
996C4—21no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—21no—
1001C4—21no—
1002C4—21no—
1003C4—442no—
1004C4—442no—
1005C4—442no—
1006C4—442no—
1007C4—442no—
1008C4—442no—
1009C4#1062304112yes—
1010C4#1062327912yes—
1011C4C2×#6703711yescharacteristic
1012C4C2×#6704011yescharacteristic
1013C2—22no—
1014C2—22no—
1015C2—41no—
1016C2—882no—
1017C2—882no—
1018C2C2×#1062304111yescharacteristic
1019C2C2×#1062327911yescharacteristic
1020C2C2×#1062327911yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#423C2
socleC22×C11C23×D4
hypercenterC2×#423D11
hypocenterC11#60917
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. C2×#10623010C2semidirect
3. #13080017C2semidirect
4. #13079990C2semidirect
5. #13079979C2semidirect
6. #13079968C2semidirect
7. #13079954C2semidirect
8. #13079943C2semidirect
9. #13078439C2semidirect
10. #13078423C2semidirect
11. #13078415C2semidirect
12. #13078246C2semidirect
13. #13078235C2semidirect
14. #13078111C2semidirect
15. #13078090C2semidirect
16. #13078082C2semidirect
17. C2×C11×#423C2semidirect
41. #10623010C22semidirect
42. #10623010C22semidirect
45. #10623008C22semidirect
46. #10623008C22semidirect
54. #10623001C22semidirect
55. #10623001C22semidirect
61. C11×#423C22semidirect
62. C11×#423C22semidirect
63. C2×C11×C4⋊C8C22semidirect
64. C2×C11×C4⋊C8C22semidirect
65. #10622750C22semidirect
68. #10622747C22semidirect
75. #10622729C22semidirect
78. #10622727C22semidirect
79. #10622464C22semidirect
80. #10622463C22semidirect
81. #10622462C22semidirect
82. #10622461C22semidirect
83. #10622460C22semidirect
84. #10622460C22semidirect
85. #10622460C22semidirect
86. #10622459C22semidirect
87. #10622458C22semidirect
88. #10622458C22semidirect
89. #10622458C22semidirect
90. #10622457C22semidirect
91. #10622457C22semidirect
92. #10622457C22semidirect
93. #10622456C22semidirect
94. #10622455C22semidirect
95. #10622454C22semidirect
96. #10622442C22semidirect
97. #10622442C22semidirect
98. #10622442C22semidirect
403. C2×#423D11semidirect
556. #423C2×D11semidirect
557. #423C2×D11semidirect
558. C2×C4⋊C8C2×D11semidirect
559. C2×C4⋊C8C2×D11semidirect
896. C11#60917semidirect

Maximal subgroups

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

subgroupindex
#130819122
C2×#106230102
#130800172
#130799902
#130799792
#130799682
#130799542
#130799432
#130784392
#130784232
#130784152
#130782462
#130782352
#130781112
#130780902
#130780822
C2×C11×#4232
#6091711