Finite Group Databasebeta

← #15622237

Subgroups — #15622237

Order 2816.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic, complemented
2C2×C4×#4339C211yesmaximal, characteristic, complemented
3#13078789C212yesmaximal, complemented
4#13078756C212yesmaximal, complemented
5#13078727C214yesmaximal, complemented
6#13078698C212yesmaximal, complemented
7#13078665C212yesmaximal, complemented
8#13078636C214yesmaximal, complemented
9#13078565C211yesmaximal, characteristic, complemented
10#13078557C211yesmaximal, characteristic, complemented
11#13078439C212yesmaximal, complemented
12#13078111C212yesmaximal, complemented
13#13077878C211yesmaximal, characteristic, complemented
14#13077870C211yesmaximal, characteristic
15C4×#66962C212yesmaximal, complemented
16C4×#66961C212yesmaximal, complemented
17C11×#2920C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66982—21no—
22C2×C4×C22⋊D11—21no—
23C2×C4×C22⋊D11—21no—
24C2×C4×C22⋊D11—21no—
25C2×#66979C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C2×#66962C2212yes—
28C2×#66961C2212yes—
29#10623010—21no—
30#10623010—21no—
31#10623010—21no—
32#10623010—21no—
33#10623010C2212yes—
34#10623010C2212yes—
35#10623010C2212yescomplemented
36#10623010C2212yescomplemented
37C2×#66929—21no—
38C2×#66928C2211yescharacteristic, complemented
39C4×#4339—21no—
40C4×#4339—21no—
41C4×#4339—21no—
42C4×#4339—21no—
43C4×#4339C2212yes—
44C4×#4339C2212yes—
45C4×#4339C2212yescomplemented
46C4×#4339C2212yescomplemented
47C2×C4×D44C2211yescharacteristic, complemented
48C2×C4×D44C2211yescharacteristic, complemented
49C2×C4×D44C2211yescharacteristic, complemented
50C2×#66925—21no—
51C2×#66925—21no—
52C2×C42×D11—21no—
53C2×#66923C2211yescharacteristic, complemented
54C2×C4×Dic22C2211yescharacteristic, complemented
55C2×C4×Dic22C2211yescharacteristic, complemented
56C2×C4×Dic22C2211yescharacteristic, complemented
57C11×#432C2212yescomplemented
58C11×#432C2212yescomplemented
59C11×#431C2212yescomplemented
60C11×#431C2212yescomplemented
61C11×#423C2212yescomplemented
62C11×#407C2211yescharacteristic
63C11×#407C2211yescharacteristic
64C4×C11×M16C2212yescomplemented
65#10622746C2212yes—
66#10622746C2212yes—
67#10622744C2212yescomplemented
68#10622734C2212yescomplemented
69#10622734C2212yescomplemented
70#10622733C2212yescomplemented
71#10622460C2214yescomplemented
72#10622460C2214yescomplemented
73#10622458C2214yescomplemented
74#10622458C2214yescomplemented
75#10622457C2214yescomplemented
76#10622457C2214yescomplemented
77#10622442C2214yescomplemented
78#10622442C2214yescomplemented
79#10622352C2212yescomplemented
80#10622351C2212yes—
81#10622350C2214yescomplemented
82#10622349C2212yes—
83#10622348C2212yes—
84#10622347C2214yes—
85#10622346C2214yescomplemented
86#10622345C2212yes—
87#10622344C2212yescomplemented
88#10622336C2214yescomplemented
89#10622335C2212yescomplemented
90#10622334C2212yescomplemented
91#10622329C2214yescomplemented
92#10622324C2214yescomplemented
93#10622323C2214yescomplemented
94#10622323C2214yescomplemented
95C4×Dic44C2214yescomplemented
96C4×D88C2214yescomplemented
97C4×#4314C2214yescomplemented
98C4×#4314C2214yescomplemented
99C23×C4×C11D411yescharacteristic
100C23×C4×C11D411yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C22×C22⋊D11—21no—
103C22×C22⋊D11—21no—
104C2×#4339—21no—
105C2×#4339—21no—
106C2×#4339—28no—
107C2×#4339C2312yes—
108C2×#4339C2312yes—
109C22×D44C2311yescharacteristic
110C22×D44C2311yescharacteristic
111C22×C4×D11—21no—
112C22×C4×D11—21no—
113C22×C4×D11—21no—
114C22×C4×D11—21no—
115C22×Dic22C2311yescharacteristic
116C22×Dic22C2311yescharacteristic
117C2×C11×M16C2312yes—
118C2×C11×M16C2312yes—
119C2×C42×C11D411yescharacteristic
120C2×C42×C11D411yescharacteristic
121C2×C42×C11D411yescharacteristic
122C2×C42×C11D411yescharacteristic
123C2×C42×C11D411yescharacteristic
124C2×C42×C11D411yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C2×C42×C11C2311yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11—21no—
133#66983—21no—
134#66983—21no—
135#66983C2312yes—
136#66983C2312yes—
137#66982—22no—
138#66982—22no—
139#66982—22no—
140#66982—22no—
141C4×C22⋊D11—22no—
142C4×C22⋊D11—22no—
143C4×C22⋊D11—22no—
144C4×C22⋊D11—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—
153C2×(C2×D11)⋊C4—21no—
154C2×(C2×D11)⋊C4—21no—
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—
162#66979C2312yes—
163C2×C4⋊Dic11C2311yescharacteristic
164C2×C4⋊Dic11C2311yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167#66977—21no—
168#66977—21no—
169#66977C2312yes—
170#66977C2312yes—
171C2×Dic11⋊C4—21no—
172C2×Dic11⋊C4—21no—
173C2×Dic11⋊C4—21no—
174C2×Dic11⋊C4—21no—
175C2×Dic11⋊C4—21no—
176C2×Dic11⋊C4—21no—
177C2×C4×Dic11—21no—
178C2×C4×Dic11—21no—
179C2×C4×Dic11—21no—
180C2×C4×Dic11—21no—
181#66962—28no—
182#66961—28no—
183C2×Dic44C2314yes—
184C2×D88C2314yes—
185C2×#4314C2314yes—
186C2×#4314C2314yes—
187#66929—22no—
188#66929—22no—
189#66929—22no—
190#66929—22no—
191#66928—21no—
192#66928—21no—
193#66928C2312yes—
194#66928C2312yes—
195C4×D44—21no—
196C4×D44—21no—
197C4×D44—21no—
198C4×D44—21no—
199C4×D44—21no—
200C4×D44—21no—
201C4×D44C2312yes—
202C4×D44C2312yes—
203C4×D44C2312yes—
204C4×D44C2312yes—
205C4×D44C2312yes—
206C4×D44C2312yes—
207#66925—22no—
208#66925—22no—
209#66925—22no—
210#66925—22no—
211#66925—22no—
212#66925—22no—
213#66925—22no—
214#66925—22no—
215C42×D11—22no—
216C42×D11—22no—
217C42×D11—22no—
218C42×D11—22no—
219#66923—21no—
220#66923—21no—
221#66923C2312yes—
222#66923C2312yes—
223C4×Dic22—21no—
224C4×Dic22—21no—
225C4×Dic22—21no—
226C4×Dic22—21no—
227C4×Dic22—21no—
228C4×Dic22—21no—
229C4×Dic22C2312yes—
230C4×Dic22C2312yes—
231C4×Dic22C2312yes—
232C4×Dic22C2312yes—
233C4×Dic22C2312yes—
234C4×Dic22C2312yes—
235C11×C4⋊C8C2314yes—
236C11×C4⋊C8C2314yes—
237C11×C22⋊C8C2312yes—
238C11×C22⋊C8C2312yes—
239C11×C22⋊C8C2312yes—
240C11×C22⋊C8C2312yes—
241C11×#97C2314yes—
242C4×C8×C11C2314yes—
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#60563—111nomaximal, Sylow
256C24×C11C2×D411yescharacteristic
257C23×D11—21no—
258C23×D11—21no—
259C22×C4×C11—24no—
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—28no—
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—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292#4339—28no—
293#4339—28no—
294#4339—24no—
295#4339—24no—
296#4339—24no—
297#4339#4118yes—
298C2×D44—24no—
299C2×D44—21no—
300C2×D44—21no—
301C2×D44—24no—
302C2×D44C2412yes—
303C2×D44C2412yes—
304C2×C4×D11—28no—
305C2×C4×D11—22no—
306C2×C4×D11—22no—
307C2×C4×D11—22no—
308C2×C4×D11—22no—
309C2×C4×D11—22no—
310C2×C4×D11—22no—
311C2×C4×D11—22no—
312C2×C4×D11—22no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×Dic22—24no—
317C2×Dic22—21no—
318C2×Dic22—21no—
319C2×Dic22—24no—
320C2×Dic22C2412yes—
321C2×Dic22C2412yes—
322C11×M16—24no—
323C11×M16—24no—
324C2×C8×C11C2414yes—
325C2×C8×C11C2414yes—
326C42×C11C2×D411yescharacteristic
327C42×C11C2×D411yescharacteristic
328C42×C11C2×D411yescharacteristic
329C42×C11C2×D411yescharacteristic
330C42×C11C2×D411yescharacteristic
331C42×C11C2×D411yescharacteristic
332C42×C11C2×D411yescharacteristic
333C42×C11C2×D411yescharacteristic
334C42×C11C2×D411yescharacteristic
335C42×C11C2×D411yescharacteristic
336C42×C11C2×D411yescharacteristic
337C42×C11C2×D411yescharacteristic
338C42×C11C2411yescharacteristic
339C42×C11C2411yescharacteristic
340C42×C11C2411yescharacteristic
341C42×C11C2411yescharacteristic
342C22⋊Dic11—22no—
343C22⋊Dic11—22no—
344C22⋊Dic11—22no—
345C22⋊Dic11—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—
354(C2×D11)⋊C4—22no—
355(C2×D11)⋊C4—22no—
356(C2×D11)⋊C4—22no—
357(C2×D11)⋊C4—22no—
358C4⋊Dic11—21no—
359C4⋊Dic11—21no—
360C4⋊Dic11—21no—
361C4⋊Dic11—21no—
362C4⋊Dic11C2412yes—
363C4⋊Dic11C2412yes—
364C4⋊Dic11C2412yes—
365C4⋊Dic11C2412yes—
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—
383C4×Dic11—22no—
384C4×Dic11—22no—
385C4×Dic11—22no—
386Dic44—28no—
387D88—28no—
388#4314—28no—
389#4314—28no—
390C2×#529—111no—
391C2×C4×#41—111no—
392#3117—112no—
393#3114—112no—
394#3111—114no—
395#3108—112no—
396#3105—112no—
397#3102—114no—
398#3095—111no—
399#3094—111no—
400#3080—112no—
401#3040—112no—
402#3007—111no—
403#3006—111no—
404C4×#137—112no—
405C4×AGL(1,ℤ/8)—112no—
406#2920D1111yescharacteristic, complemented
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—41no—
410C23×C11C22×D411yescharacteristic
411C23×C11C22×D411yescharacteristic
412C23×C11C22×D411yescharacteristic
413C22×D11—24no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—42no—
417C22×D11—42no—
418C22×D11—42no—
419C22×D11—42no—
420C22×D11—42no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
446C2×C4×C11C22×D411yescharacteristic
447C2×C4×C11C22×D411yescharacteristic
448C2×C4×C11C22×D411yescharacteristic
449C2×C4×C11C2×#4114yes—
450C2×C4×C11C2511yescharacteristic
451C22⋊D11—28no—
452C22⋊D11—28no—
453C22⋊D11—44no—
454C22⋊D11—44no—
455C2×Dic11—24no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—42no—
463C2×Dic11—42no—
464C2×Dic11—42no—
465C2×Dic11—42no—
466C2×Dic11—42no—
467D44—24no—
468D44—22no—
469D44—24no—
470D44—42no—
471D44C2×#4114yes—
472C4×D11—28no—
473C4×D11—28no—
474C4×D11—44no—
475C4×D11—44no—
476C4×D11—44no—
477C4×D11—44no—
478C4×D11—44no—
479C4×D11—44no—
480Dic22—24no—
481Dic22—22no—
482Dic22—24no—
483Dic22—42no—
484Dic22C2×#4114yes—
485C8×C11—24no—
486C8×C11—24no—
487C22×#41—111no—
488C2×#137—112no—
489C2×AGL(1,ℤ/8)—112no—
490#529—112no—
491#529—112no—
492#529—112no—
493#529—112no—
494#529—221no—
495#529—221no—
496#529—221no—
497#529—221no—
498C2×#126—221no—
499C2×#125—111no—
500C2×#124—111no—
501C2×#123—221no—
502C2×C22⋊Q8—111no—
503C2×#121—111no—
504C4×#41—112no—
505C4×#41—112no—
506C4×#41—112no—
507C4×#41—112no—
508C4×#41—221no—
509C4×#41—221no—
510C4×#41—221no—
511C4×#41—221no—
512C2×C4×Q8—111no—
513C2×C4×Q8—111no—
514C2×C4×Q8—111no—
515C2×C4×D4—111no—
516C2×C4×D4—111no—
517C2×C4×D4—111no—
518C2×C4×D4—221no—
519C2×C4×D4—221no—
520C2×C4×D4—221no—
521C2×#117—111no—
522C2×#117—221no—
523C2×#117—221no—
524C22×C42—221no—
525C22×C42C2×D1111yescharacteristic
526#485—114no—
527#484—112no—
528#483—112no—
529#482—114no—
530#481—112no—
531#480—112no—
532#479—114no—
533#479—114no—
534#478—114no—
535#478—114no—
536#464—114no—
537#464—114no—
538#463—114no—
539#463—114no—
540#452—114no—
541#451—112no—
542#450—112no—
543#449—114no—
544#448—112no—
545#447—112no—
546#442—114no—
547#441—114no—
548#440—114no—
549#440—114no—
550C4×Q16—114no—
551C4×SD16—114no—
552C4×SD16—114no—
553C4×D8—114no—
554#432C2×D1112yescomplemented
555#432C2×D1112yescomplemented
556#431C2×D1112yescomplemented
557#431C2×D1112yescomplemented
558#428—112no—
559#428—112no—
560#423C2×D1112yescomplemented
561#419—112no—
562#418—112no—
563#417—112no—
564#417—112no—
565#407C2×D1111yescharacteristic
566#407C2×D1111yescharacteristic
567C4×M16C2×D1112yescomplemented
568C22×C11—21no—
569C22×C11—21no—
570C22×C11—21no—
571C22×C11—21no—
572C22×C11—21no—
573C22×C11—21no—
574C22×C11—21no—
575C22×C11—44no—
576C22×C11#52512yes—
577C22×C11#57512yes—
578C22×C11C23×D411yescharacteristic
579C2×D11—24no—
580C2×D11—48no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—84no—
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—21no—
590C4×C11—21no—
591C4×C11—21no—
592C4×C11—21no—
593C4×C11—21no—
594C4×C11—21no—
595C4×C11—21no—
596C4×C11#52512yes—
597C4×C11#57512yes—
598C4×C11C22×#4112yes—
599Dic11—24no—
600Dic11—42no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11—42no—
605C2×#41—112no—
606C2×#41—112no—
607C2×#41—228no—
608C2×#41—221no—
609C2×#41—221no—
610C22×Q8—111no—
611C22×Q8—111no—
612C22×D4—111no—
613C22×D4—111no—
614C22×D4—221no—
615C22×D4—221no—
616C23×C4—221no—
617C23×C4—221no—
618C23×C4—221no—
619C23×C4—221no—
620C23×C4D4411yescharacteristic
621C23×C4D4411yescharacteristic
622C23×C4C22×D1111yescharacteristic
623#137—228no—
624AGL(1,ℤ/8)—228no—
625C2×Q16—114no—
626C2×SD16—114no—
627C2×SD16—114no—
628C2×D8—114no—
629C2×M16C22×D1112yes—
630C2×M16C22×D1112yes—
631#126—222no—
632#126—222no—
633#126—222no—
634#126—222no—
635#125—112no—
636#125—112no—
637#125—221no—
638#125—221no—
639#124—112no—
640#124—112no—
641#124—221no—
642#124—221no—
643#123—222no—
644#123—222no—
645#123—222no—
646#123—222no—
647C22⋊Q8—112no—
648C22⋊Q8—112no—
649C22⋊Q8—221no—
650C22⋊Q8—221no—
651#121—112no—
652#121—112no—
653#121—221no—
654#121—221no—
655C4×Q8—112no—
656C4×Q8—112no—
657C4×Q8—112no—
658C4×Q8—112no—
659C4×Q8—112no—
660C4×Q8—112no—
661C4×Q8—221no—
662C4×Q8—221no—
663C4×Q8—221no—
664C4×Q8—221no—
665C4×Q8—221no—
666C4×Q8—221no—
667C4×D4—112no—
668C4×D4—112no—
669C4×D4—112no—
670C4×D4—112no—
671C4×D4—112no—
672C4×D4—112no—
673C4×D4—222no—
674C4×D4—222no—
675C4×D4—222no—
676C4×D4—222no—
677C4×D4—222no—
678C4×D4—222no—
679C4×D4—222no—
680C4×D4—222no—
681C4×D4—222no—
682C4×D4—222no—
683C4×D4—222no—
684C4×D4—222no—
685C4×D4—221no—
686C4×D4—221no—
687C4×D4—221no—
688C4×D4—221no—
689C4×D4—221no—
690C4×D4—221no—
691#117—112no—
692#117—112no—
693#117—221no—
694#117—221no—
695#117—222no—
696#117—222no—
697#117—222no—
698#117—222no—
699#117—222no—
700#117—222no—
701#117—222no—
702#117—222no—
703C2×C4⋊C4—111no—
704C2×C4⋊C4—111no—
705C2×C4⋊C4—111no—
706C2×C4⋊C4—111no—
707C2×C4⋊C4—221no—
708C2×C4⋊C4—221no—
709C2×C4⋊C4—221no—
710C2×C4⋊C4—221no—
711C2×C4⋊C4—221no—
712C2×C4⋊C4—221no—
713C2×C22⋊C4—221no—
714C2×C22⋊C4—221no—
715C2×C22⋊C4—221no—
716C2×C22⋊C4—221no—
717C2×C22⋊C4—221no—
718C2×C22⋊C4—221no—
719C2×C22⋊C4—221no—
720C2×C22⋊C4—221no—
721C2×C42—221no—
722C2×C42—221no—
723C2×C42—221no—
724C2×C42—221no—
725C2×C42—222no—
726C2×C42—222no—
727C2×C42—222no—
728C2×C42—222no—
729C2×C42D4411yescharacteristic
730C2×C42D4411yescharacteristic
731C2×C42D4411yescharacteristic
732C2×C42D4411yescharacteristic
733C2×C42D4411yescharacteristic
734C2×C42D4411yescharacteristic
735C2×C42C22×D1111yescharacteristic
736C2×C42C22×D1111yescharacteristic
737C2×C42C22×D1111yescharacteristic
738C2×C42C22×D1111yescharacteristic
739C2×C42C22×D1111yescharacteristic
740C2×C42C22×D1111yescharacteristic
741#107—114no—
742#107—114no—
743#106—114no—
744#106—114no—
745C4⋊C8C22×D1114yes—
746C4⋊C8C22×D1114yes—
747#103—114no—
748#103—114no—
749#103—114no—
750#103—114no—
751#102—114no—
752#102—114no—
753#102—114no—
754#102—114no—
755C22⋊C8C22×D1112yes—
756C22⋊C8C22×D1112yes—
757C22⋊C8C22×D1112yes—
758C22⋊C8C22×D1112yes—
759#97C22×D1114yes—
760C4×C8C22×D1114yes—
761C2×C11—22no—
762C2×C11—22no—
763C2×C11—41no—
764C2×C11C2×#52511yescharacteristic
765C2×C11C2×#57511yescharacteristic
766C2×C11C2×#57511yescharacteristic
767D11—44no—
768D11—82no—
769C24—221no—
770C24—221no—
771C24C2×D4411yescharacteristic
772#41—118no—
773#41—224no—
774#41—224no—
775#41—228no—
776#41—228no—
777#41—224no—
778C2×Q8—112no—
779C2×Q8—112no—
780C2×Q8—224no—
781C2×Q8—221no—
782C2×Q8—221no—
783C2×Q8—224no—
784C2×D4—112no—
785C2×D4—112no—
786C2×D4—224no—
787C2×D4—228no—
788C2×D4—222no—
789C2×D4—222no—
790C2×D4—222no—
791C2×D4—222no—
792C2×D4—221no—
793C2×D4—221no—
794C2×D4—224no—
795C2×D4—444no—
796C22×C4—24no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—228no—
800C22×C4—221no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—221no—
804C22×C4—221no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—222no—
809C22×C4—222no—
810C22×C4—222no—
811C22×C4—222no—
812C22×C4—222no—
813C22×C4—222no—
814C22×C4—444no—
815C22×C4—444no—
816C22×C4—444no—
817C22×C4C2×D4411yescharacteristic
818C22×C4C2×D4411yescharacteristic
819C22×C4C2×D4411yescharacteristic
820C22×C4C2×D4411yescharacteristic
821C22×C4C2×D4411yescharacteristic
822C22×C4C2×D4411yescharacteristic
823C22×C4C2×D4411yescharacteristic
824C22×C4C2×D4411yescharacteristic
825C22×C4C2×D4411yescharacteristic
826C22×C4C2×D4411yescharacteristic
827C22×C4C2×D4411yescharacteristic
828C22×C4C2×D4411yescharacteristic
829C22×C4C2×D4411yescharacteristic
830C22×C4C2×D4411yescharacteristic
831C22×C4C2×D4411yescharacteristic
832C22×C4C23×D1111yescharacteristic
833C22×C4C23×D1111yescharacteristic
834C22×C4C23×D1111yescharacteristic
835Q16—228no—
836SD16—228no—
837SD16—228no—
838D8—228no—
839M16—24no—
840M16—24no—
841C2×C8C23×D1114yes—
842C2×C8C23×D1114yes—
843C4⋊C4—112no—
844C4⋊C4—112no—
845C4⋊C4—112no—
846C4⋊C4—112no—
847C4⋊C4—221no—
848C4⋊C4—221no—
849C4⋊C4—221no—
850C4⋊C4—221no—
851C4⋊C4—222no—
852C4⋊C4—222no—
853C4⋊C4—222no—
854C4⋊C4—222no—
855C4⋊C4—222no—
856C4⋊C4—222no—
857C4⋊C4—222no—
858C4⋊C4—222no—
859C4⋊C4—222no—
860C4⋊C4—222no—
861C4⋊C4—222no—
862C4⋊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—
875C22⋊C4—222no—
876C22⋊C4—222no—
877C22⋊C4—222no—
878C22⋊C4—222no—
879C42—222no—
880C42—222no—
881C42—222no—
882C42—222no—
883C42—222no—
884C42—222no—
885C42—222no—
886C42—222no—
887C42C2×D4411yescharacteristic
888C42C2×D4411yescharacteristic
889C42C2×D4411yescharacteristic
890C42C2×D4411yescharacteristic
891C42C2×D4411yescharacteristic
892C42C2×D4411yescharacteristic
893C42C2×D4411yescharacteristic
894C42C2×D4411yescharacteristic
895C42C2×D4411yescharacteristic
896C42C2×D4411yescharacteristic
897C42C2×D4411yescharacteristic
898C42C2×D4411yescharacteristic
899C42C23×D1111yescharacteristic
900C42C23×D1111yescharacteristic
901C42C23×D1111yescharacteristic
902C42C23×D1111yescharacteristic
903C11#6056311yescharacteristic, complemented, Sylow
904C23—22no—
905C23—22no—
906C23—41no—
907C23—224no—
908C23—222no—
909C23—222no—
910C23—442no—
911C23—442no—
912C23—442no—
913C23—442no—
914C23—442no—
915C23C22×D4411yescharacteristic
916C23C22×D4411yescharacteristic
917C23C22×D4411yescharacteristic
918Q8—114no—
919Q8—224no—
920Q8—222no—
921Q8—224no—
922Q8—442no—
923D4—114no—
924D4—224no—
925D4—228no—
926D4—228no—
927D4—222no—
928D4—224no—
929D4—444no—
930D4—444no—
931D4—442no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—228no—
950C2×C4—224no—
951C2×C4—222no—
952C2×C4—228no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—444no—
959C2×C4—444no—
960C2×C4—444no—
961C2×C4—444no—
962C2×C4—442no—
963C2×C4—442no—
964C2×C4—442no—
965C2×C4—442no—
966C2×C4—442no—
967C2×C4—444no—
968C2×C4—444no—
969C2×C4C22×D4411yescharacteristic
970C2×C4C22×D4411yescharacteristic
971C2×C4C22×D4411yescharacteristic
972C2×C4C22×D4411yescharacteristic
973C2×C4C22×D4411yescharacteristic
974C2×C4C22×D4411yescharacteristic
975C2×C4C22×D4411yescharacteristic
976C2×C4C22×D4411yescharacteristic
977C2×C4C22×D4411yescharacteristic
978C2×C4C22×D4411yescharacteristic
979C2×C4C22×D4411yescharacteristic
980C2×C4#41×D1114yes—
981C2×C4C24×D1111yescharacteristic
982C8—24no—
983C8—24no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—44no—
992C22—224no—
993C22—448no—
994C22—442no—
995C22—442no—
996C22—442no—
997C22—442no—
998C22—442no—
999C22—884no—
1000C22#1062305512yes—
1001C22#1062327912yes—
1002C22C23×D4411yescharacteristic
1003C4—21no—
1004C4—21no—
1005C4—21no—
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—21no—
1011C4—21no—
1012C4—224no—
1013C4—442no—
1014C4—442no—
1015C4—442no—
1016C4—442no—
1017C4—442no—
1018C4#1062305512yes—
1019C4#1062327912yes—
1020C4C2×#41×D1112yes—
1021C2—22no—
1022C2—22no—
1023C2—41no—
1024C2—444no—
1025C2—882no—
1026C2C2×#1062305511yescharacteristic
1027C2C2×#1062327911yescharacteristic
1028C2C2×#1062327911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2920C2
socleC22×C11C23×D4
prime radical#13077870C2
hypercenter#2920D11
hypocenterC11#60563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#10623010C2semidirect
2. C2×C4×#4339C2semidirect
3. #13078789C2semidirect
4. #13078756C2semidirect
5. #13078727C2semidirect
6. #13078698C2semidirect
7. #13078665C2semidirect
8. #13078636C2semidirect
9. #13078565C2semidirect
10. #13078557C2semidirect
11. #13078439C2semidirect
12. #13078111C2semidirect
13. #13077878C2semidirect
15. C4×#66962C2semidirect
16. C4×#66961C2semidirect
17. C11×#2920C2semidirect
35. #10623010C22semidirect
36. #10623010C22semidirect
38. C2×#66928C22semidirect
45. C4×#4339C22semidirect
46. C4×#4339C22semidirect
47. C2×C4×D44C22semidirect
48. C2×C4×D44C22semidirect
49. C2×C4×D44C22semidirect
53. C2×#66923C22semidirect
54. C2×C4×Dic22C22semidirect
55. C2×C4×Dic22C22semidirect
56. C2×C4×Dic22C22semidirect
57. C11×#432C22semidirect
58. C11×#432C22semidirect
59. C11×#431C22semidirect
60. C11×#431C22semidirect
61. C11×#423C22semidirect
64. C4×C11×M16C22semidirect
67. #10622744C22semidirect
68. #10622734C22semidirect
69. #10622734C22semidirect
70. #10622733C22semidirect
71. #10622460C22semidirect
72. #10622460C22semidirect
73. #10622458C22semidirect
74. #10622458C22semidirect
75. #10622457C22semidirect
76. #10622457C22semidirect
77. #10622442C22semidirect
78. #10622442C22semidirect
79. #10622352C22semidirect
81. #10622350C22semidirect
85. #10622346C22semidirect
87. #10622344C22semidirect
88. #10622336C22semidirect
89. #10622335C22semidirect
90. #10622334C22semidirect
91. #10622329C22semidirect
92. #10622324C22semidirect
93. #10622323C22semidirect
94. #10622323C22semidirect
95. C4×Dic44C22semidirect
96. C4×D88C22semidirect
97. C4×#4314C22semidirect
98. C4×#4314C22semidirect
406. #2920D11semidirect
554. #432C2×D11semidirect
555. #432C2×D11semidirect
556. #431C2×D11semidirect
557. #431C2×D11semidirect
560. #423C2×D11semidirect
567. C4×M16C2×D11semidirect
903. C11#60563semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C2×C4×#43392
#130787892
#130787562
#130787272
#130786982
#130786652
#130786362
#130785652
#130785572
#130784392
#130781112
#130778782
#130778702
C4×#669622
C4×#669612
C11×#29202
#6056311