Finite Group Databasebeta

← #15622236

Subgroups — #15622236

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×#10623155C211yesmaximal, characteristic, complemented
2C2×#41×Dic11C211yesmaximal, characteristic, complemented
3#13078788C212yesmaximal, complemented
4#13078755C212yesmaximal, complemented
5#13078726C214yesmaximal, complemented
6#13078697C212yesmaximal, complemented
7#13078664C212yesmaximal, complemented
8#13078635C214yesmaximal, complemented
9#13078560C211yesmaximal, characteristic, complemented
10#13078557C211yesmaximal, characteristic, complemented
11#13078436C212yesmaximal, complemented
12#13078112C212yesmaximal, complemented
13#13077868C211yesmaximal, characteristic
14#137×Dic11C212yesmaximal, complemented
15#13077429C212yesmaximal, complemented
16#13077245C211yesmaximal, characteristic, complemented
17C11×#3007C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C2×C11×#137C2212yes—
20C2×C11×C22⋊Q8C2211yescharacteristic
21#41×Dic11—21no—
22#41×Dic11—21no—
23#41×Dic11—21no—
24#41×Dic11—21no—
25#41×Dic11C2212yes—
26#41×Dic11C2212yes—
27#41×Dic11C2212yescomplemented
28#41×Dic11C2212yescomplemented
29C2×#67002C2212yes—
30C2×#67000C2211yescharacteristic, complemented
31C2×Q8×Dic11C2211yescharacteristic, complemented
32C2×Q8×Dic11C2211yescharacteristic, complemented
33C2×Q8×Dic11C2211yescharacteristic, complemented
34C2×D4×Dic11—21no—
35C2×D4×Dic11—21no—
36C2×D4×Dic11C2211yescharacteristic, complemented
37C2×D4×Dic11C2211yescharacteristic, complemented
38C2×#66983C2211yescharacteristic
39C2×#66979—21no—
40C2×#66979C2211yescharacteristic
41C22×C4×Dic11—21no—
42C22×C4×Dic11C2211yescharacteristic
43#10623155—21no—
44#10623155—21no—
45#10623155—21no—
46#10623155—21no—
47#10623155C2212yes—
48#10623155C2212yes—
49#10623155C2212yescomplemented
50#10623155C2212yescomplemented
51C2×#66951—21no—
52C2×#66946C2211yescharacteristic, complemented
53C2×#66945—21no—
54C2×#66943C2211yescharacteristic, complemented
55C2×#66939—21no—
56C2×(C22⋊D11)⋊C4—21no—
57C11×#452C2214yescomplemented
58C11×#451C2212yescomplemented
59C11×#450C2212yescomplemented
60C11×#417C2212yes—
61C11×#407C2211yescharacteristic
62#10622851C2214yes—
63#10622845C2212yes—
64#10622840C2212yes—
65#10622838C2212yescomplemented
66#10622830C2212yes—
67#10622820C2211yescharacteristic
68#10622798C2214yescomplemented
69#10622798C2214yescomplemented
70#10622797C2214yescomplemented
71Q16×Dic11C2214yescomplemented
72#10622778C2214yescomplemented
73#10622778C2214yescomplemented
74#10622777C2214yescomplemented
75SD16×Dic11C2214yescomplemented
76#10622744C2212yescomplemented
77#10622734C2212yescomplemented
78#10622731C2212yescomplemented
79M16×Dic11C2212yescomplemented
80#10622658C2214yescomplemented
81#10622657C2212yescomplemented
82#10622656C2212yescomplemented
83#10622577C2212yescomplemented
84#10622430C2214yescomplemented
85#10622412C2214yescomplemented
86#10622409C2214yescomplemented
87#10622401C2214yescomplemented
88#10622398C2214yescomplemented
89#10622379C2214yescomplemented
90#10622376C2214yescomplemented
91#10622369C2214yescomplemented
92#10622350C2214yescomplemented
93#10622349C2212yes—
94#10622348C2212yes—
95#10622332C2212yescomplemented
96#10622332C2212yescomplemented
97#10622331C2212yescomplemented
98#10622331C2212yescomplemented
99C2×C11×#41—28no—
100C2×C11×#41—21no—
101C2×C11×#41—21no—
102C2×C11×#41C2312yes—
103C2×C11×#41C2312yes—
104C22×Q8×C11C2311yescharacteristic
105C22×Q8×C11C2311yescharacteristic
106C22×D4×C11—21no—
107C22×D4×C11C2311yescharacteristic
108C23×C4×C11—21no—
109C23×C4×C11C2311yescharacteristic
110C22×C22⋊D11—21no—
111C23×Dic11—21no—
112C23×Dic11—21no—
113C23×Dic11D411yescharacteristic
114C23×Dic11D411yescharacteristic
115C22×D44C2311yescharacteristic
116C22×C4×D11—21no—
117C11×#137—28no—
118C2×C11×Q16C2314yes—
119C2×C11×SD16C2314yes—
120C2×C11×M16C2312yes—
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8C2312yes—
124C11×C22⋊Q8C2312yes—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11—21no—
131#67002—28no—
132#67000—21no—
133#67000—21no—
134#67000C2312yes—
135#67000C2312yes—
136Q8×Dic11—21no—
137Q8×Dic11—21no—
138Q8×Dic11—21no—
139Q8×Dic11—21no—
140Q8×Dic11—21no—
141Q8×Dic11—21no—
142Q8×Dic11C2312yes—
143Q8×Dic11C2312yes—
144Q8×Dic11C2312yes—
145Q8×Dic11C2312yes—
146Q8×Dic11C2312yes—
147Q8×Dic11C2312yes—
148C2×#4325C2314yes—
149D4×Dic11—22no—
150D4×Dic11—22no—
151D4×Dic11—22no—
152D4×Dic11—22no—
153D4×Dic11—22no—
154D4×Dic11—22no—
155D4×Dic11—22no—
156D4×Dic11—22no—
157D4×Dic11—21no—
158D4×Dic11—21no—
159D4×Dic11—21no—
160D4×Dic11—21no—
161D4×Dic11C2312yes—
162D4×Dic11C2312yes—
163D4×Dic11C2312yes—
164D4×Dic11C2312yes—
165C2×#4323C2314yes—
166#66983—21no—
167#66983—21no—
168#66983C2312yes—
169#66983C2312yes—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—21no—
172C2×(C2×D11)⋊C4—21no—
173C2×(C2×D11)⋊C4—21no—
174#66979—21no—
175#66979—21no—
176#66979—22no—
177#66979—22no—
178#66979—22no—
179#66979—22no—
180#66979C2312yes—
181#66979C2312yes—
182C2×C4⋊Dic11—21no—
183C2×C4⋊Dic11—21no—
184C2×C4⋊Dic11—21no—
185C2×C4⋊Dic11—21no—
186C2×C4⋊Dic11C2311yescharacteristic
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2311yescharacteristic
189C2×Dic11⋊C4—21no—
190C2×C4×Dic11—21no—
191C2×C4×Dic11—21no—
192C2×C4×Dic11—21no—
193C2×C4×Dic11—21no—
194C2×C4×Dic11—22no—
195C2×C4×Dic11—22no—
196C2×C4×Dic11—22no—
197C2×C4×Dic11—22no—
198C2×C4×Dic11D411yescharacteristic
199C2×C4×Dic11D411yescharacteristic
200C2×C4×Dic11D411yescharacteristic
201C2×C4×Dic11D411yescharacteristic
202C2×C4×Dic11D411yescharacteristic
203C2×C4×Dic11D411yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×#4318C2312yes—
211#66951—22no—
212#66951—22no—
213#66951—22no—
214#66951—22no—
215#66946—21no—
216#66946—21no—
217#66946C2312yes—
218#66946C2312yes—
219#66945—22no—
220#66945—22no—
221#66945—22no—
222#66945—22no—
223#66943—21no—
224#66943—21no—
225#66943C2312yes—
226#66943C2312yes—
227#66939—22no—
228#66939—22no—
229#66939—22no—
230#66939—22no—
231(C22⋊D11)⋊C4—22no—
232(C22⋊D11)⋊C4—22no—
233(C22⋊D11)⋊C4—22no—
234(C22⋊D11)⋊C4—22no—
235C11×#103C2314yes—
236C11×#102C2314yes—
237C11×C22⋊C8C2312yes—
238C11×C22⋊C8C2312yes—
239#66899C2314yes—
240#66899C2314yes—
241#66899C2314yes—
242#66896C2314yes—
243C22⋊(C11⋊C8)C2312yes—
244C22⋊(C11⋊C8)C2312yes—
245#66885C2314yes—
246#66885C2314yes—
247#66882C2314yes—
248#66881C2314yes—
249#66879C2314yes—
250Dic11⋊C8C2314yes—
251Dic11⋊C8C2314yes—
252C8×Dic11C2314yes—
253#66872C2314yes—
254#66871C2314yes—
255#60563—111nomaximal, Sylow
256C24×C11—21no—
257C24×C11C2×D411yescharacteristic
258C23×D11—21no—
259C11×#41—28no—
260C11×#41—28no—
261C11×#41—24no—
262C11×#41—24no—
263C11×#41—24no—
264C11×#41#4118yes—
265C2×Q8×C11—24no—
266C2×Q8×C11—21no—
267C2×Q8×C11—21no—
268C2×Q8×C11—24no—
269C2×Q8×C11C2412yes—
270C2×Q8×C11C2412yes—
271C2×D4×C11—28no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—24no—
275C2×D4×C11—21no—
276C2×D4×C11C2412yes—
277C22×C4×C11—28no—
278C22×C4×C11—21no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—24no—
282C22×C4×C11—21no—
283C22×C4×C11—21no—
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C2×C22⋊D11—22no—
291C2×C22⋊D11—22no—
292C2×C22⋊D11—44no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—42no—
301C22×Dic11—42no—
302C22×Dic11—44no—
303C22×Dic11—44no—
304C22×Dic11C2×D411yescharacteristic
305C22×Dic11C2×D411yescharacteristic
306C22×Dic11C2×D411yescharacteristic
307C22×Dic11C2×D411yescharacteristic
308C22×Dic11C2×D411yescharacteristic
309C22×Dic11C2×D411yescharacteristic
310C22×Dic11C2×D411yescharacteristic
311C22×Dic11C2×D411yescharacteristic
312C22×Dic11C2×D411yescharacteristic
313C22×Dic11C2×D411yescharacteristic
314C22×Dic11C2×D411yescharacteristic
315C22×Dic11C2×D411yescharacteristic
316C2×D44—21no—
317C2×D44—24no—
318C2×D44C2412yes—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—44no—
322C11×Q16—28no—
323C11×SD16—28no—
324C11×M16—24no—
325C2×C8×C11C2414yes—
326C11×C4⋊C4—21no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—22no—
329C11×C4⋊C4C2412yes—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—22no—
332C22⋊Dic11—22no—
333C22⋊Dic11—22no—
334C22⋊Dic11—22no—
335C22⋊Dic11—22no—
336C22⋊Dic11—22no—
337C22⋊Dic11—22no—
338#4325—28no—
339#4323—28no—
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—
348C4⋊Dic11—22no—
349C4⋊Dic11—22no—
350C4⋊Dic11—22no—
351C4⋊Dic11—22no—
352C4⋊Dic11—22no—
353C4⋊Dic11—22no—
354C4⋊Dic11—22no—
355C4⋊Dic11—22no—
356C4⋊Dic11—21no—
357C4⋊Dic11—21no—
358C4⋊Dic11—21no—
359C4⋊Dic11C2412yes—
360C4⋊Dic11C2412yes—
361C4⋊Dic11C2412yes—
362Dic11⋊C4—22no—
363Dic11⋊C4—22no—
364C4×Dic11—22no—
365C4×Dic11—22no—
366C4×Dic11—22no—
367C4×Dic11—22no—
368C4×Dic11—22no—
369C4×Dic11—22no—
370C4×Dic11—22no—
371C4×Dic11—22no—
372C4×Dic11C2×D411yescharacteristic
373C4×Dic11C2×D411yescharacteristic
374C4×Dic11C2×D411yescharacteristic
375C4×Dic11C2×D411yescharacteristic
376C4×Dic11C2×D411yescharacteristic
377C4×Dic11C2×D411yescharacteristic
378C4×Dic11C2×D411yescharacteristic
379C4×Dic11C2×D411yescharacteristic
380C4×Dic11C2×D411yescharacteristic
381C4×Dic11C2×D411yescharacteristic
382C4×Dic11C2×D411yescharacteristic
383C4×Dic11C2×D411yescharacteristic
384C4×Dic11C2411yescharacteristic
385C4×Dic11C2411yescharacteristic
386C4×Dic11C2411yescharacteristic
387C4×Dic11C2411yescharacteristic
388#4318—24no—
389C2×C11⋊C8C2414yes—
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#3007D1111yescharacteristic, complemented
403#3006—111no—
404C4×#137—112no—
405C4×AGL(1,ℤ/8)—112no—
406#2920—111no—
407C23×C11—24no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—41no—
412C23×C11—42no—
413C23×C11—42no—
414C23×C11C22×D411yescharacteristic
415C23×C11C22×D411yescharacteristic
416C23×C11C22×D411yescharacteristic
417C22×D11—22no—
418C22×D11—42no—
419C22×D11—42no—
420C22×D11—42no—
421Q8×C11—24no—
422Q8×C11—22no—
423Q8×C11—24no—
424Q8×C11—42no—
425Q8×C11C2×#4114yes—
426D4×C11—28no—
427D4×C11—24no—
428D4×C11—28no—
429D4×C11—22no—
430D4×C11C2×#4114yes—
431C2×C4×C11—24no—
432C2×C4×C11—28no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—28no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—42no—
443C2×C4×C11—42no—
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11C22×D411yescharacteristic
446C2×C4×C11C22×D411yescharacteristic
447C2×C4×C11C2×#4114yes—
448C2×C4×C11C2511yescharacteristic
449C22⋊D11—44no—
450C22⋊D11—44no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—44no—
467C2×Dic11—44no—
468C2×Dic11—44no—
469C2×Dic11—42no—
470C2×Dic11—42no—
471C2×Dic11—42no—
472C2×Dic11—44no—
473C2×Dic11C22×D411yescharacteristic
474C2×Dic11C22×D411yescharacteristic
475C2×Dic11C22×D411yescharacteristic
476C2×Dic11C22×D411yescharacteristic
477C2×Dic11C22×D411yescharacteristic
478C2×Dic11C22×D411yescharacteristic
479C2×Dic11C22×D411yescharacteristic
480C2×Dic11C22×D411yescharacteristic
481D44—24no—
482D44—42no—
483C4×D11—44no—
484C4×D11—44no—
485C8×C11—24no—
486C11⋊C8—24no—
487C22×#41C2×D1111yescharacteristic
488C2×#137C2×D1112yes—
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⋊Q8C2×D1111yescharacteristic
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—111no—
525C22×C42—221no—
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#452C2×D1114yescomplemented
541#451C2×D1112yescomplemented
542#450C2×D1112yescomplemented
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#432—112no—
555#432—112no—
556#431—112no—
557#431—112no—
558#428—112no—
559#428—112no—
560#423—112no—
561#419—112no—
562#418—112no—
563#417—112no—
564#417C2×D1112yes—
565#407—111no—
566#407C2×D1111yescharacteristic
567C4×M16—112no—
568C22×C11—21no—
569C22×C11—21no—
570C22×C11—21no—
571C22×C11—21no—
572C22×C11—21no—
573C22×C11—24no—
574C22×C11—21no—
575C22×C11—21no—
576C22×C11—44no—
577C22×C11—48no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11#52512yes—
581C22×C11#57512yes—
582C22×C11C23×D411yescharacteristic
583C2×D11—42no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—84no—
587C4×C11—21no—
588C4×C11—24no—
589C4×C11—21no—
590C4×C11—42no—
591C4×C11—42no—
592C4×C11#52512yes—
593C4×C11C22×#4112yes—
594Dic11—21no—
595Dic11—21no—
596Dic11—21no—
597Dic11—21no—
598Dic11—21no—
599Dic11—21no—
600Dic11—21no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11#57512yes—
605C2×#41—28no—
606C2×#41—21no—
607C2×#41—21no—
608C2×#41C22×D1112yes—
609C2×#41C22×D1112yes—
610C22×Q8C22×D1111yescharacteristic
611C22×Q8C22×D1111yescharacteristic
612C22×D4—21no—
613C22×D4—111no—
614C22×D4—221no—
615C22×D4C22×D1111yescharacteristic
616C23×C4—21no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—221no—
620C23×C4—221no—
621C23×C4—221no—
622C23×C4C22×D1111yescharacteristic
623#137—28no—
624AGL(1,ℤ/8)—228no—
625C2×Q16C22×D1114yes—
626C2×SD16—114no—
627C2×SD16C22×D1114yes—
628C2×D8—114no—
629C2×M16—112no—
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—21no—
648C22⋊Q8—21no—
649C22⋊Q8C22×D1112yes—
650C22⋊Q8C22×D1112yes—
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—221no—
674C4×D4—221no—
675C4×D4—221no—
676C4×D4—221no—
677C4×D4—221no—
678C4×D4—221no—
679C4×D4—222no—
680C4×D4—222no—
681C4×D4—222no—
682C4×D4—222no—
683C4×D4—222no—
684C4×D4—222no—
685C4×D4—222no—
686C4×D4—222no—
687C4×D4—222no—
688C4×D4—222no—
689C4×D4—222no—
690C4×D4—222no—
691#117—112no—
692#117—112no—
693#117—222no—
694#117—222no—
695#117—222no—
696#117—222no—
697#117—222no—
698#117—222no—
699#117—222no—
700#117—222no—
701#117—221no—
702#117—221no—
703C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
713C2×C22⋊C4—21no—
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—111no—
722C2×C42—111no—
723C2×C42—111no—
724C2×C42—111no—
725C2×C42—111no—
726C2×C42—111no—
727C2×C42—111no—
728C2×C42—111no—
729C2×C42—111no—
730C2×C42—111no—
731C2×C42—111no—
732C2×C42—111no—
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—222no—
736C2×C42—222no—
737C2×C42—221no—
738C2×C42—221no—
739C2×C42—221no—
740C2×C42—221no—
741#107—114no—
742#107—114no—
743#106—114no—
744#106—114no—
745C4⋊C8—114no—
746C4⋊C8—114no—
747#103—114no—
748#103—114no—
749#103—114no—
750#103C22×D1114yes—
751#102—114no—
752#102—114no—
753#102—114no—
754#102C22×D1114yes—
755C22⋊C8—112no—
756C22⋊C8—112no—
757C22⋊C8C22×D1112yes—
758C22⋊C8C22×D1112yes—
759#97—114no—
760C4×C8—114no—
761C2×C11—22no—
762C2×C11—22no—
763C2×C11—41no—
764C2×C11—44no—
765C2×C11C2×#52511yescharacteristic
766C2×C11C2×#57511yescharacteristic
767C2×C11C2×#57511yescharacteristic
768D11—82no—
769C24—21no—
770C24—221no—
771C24D4×D1111yescharacteristic
772#41—28no—
773#41—28no—
774#41—24no—
775#41—24no—
776#41—24no—
777#41#434118yes—
778C2×Q8—24no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—24no—
782C2×Q8C23×D1112yes—
783C2×Q8C23×D1112yes—
784C2×D4—28no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—24no—
788C2×D4—21no—
789C2×D4—112no—
790C2×D4—222no—
791C2×D4—222no—
792C2×D4—221no—
793C2×D4—224no—
794C2×D4—444no—
795C2×D4C23×D1112yes—
796C22×C4—28no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—24no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—111no—
804C22×C4—111no—
805C22×C4—111no—
806C22×C4—111no—
807C22×C4—111no—
808C22×C4—111no—
809C22×C4—111no—
810C22×C4—111no—
811C22×C4—111no—
812C22×C4—111no—
813C22×C4—111no—
814C22×C4—111no—
815C22×C4—222no—
816C22×C4—222no—
817C22×C4—222no—
818C22×C4—222no—
819C22×C4—222no—
820C22×C4—222no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—444no—
825C22×C4—442no—
826C22×C4—442no—
827C22×C4—444no—
828C22×C4—444no—
829C22×C4D4×D1111yescharacteristic
830C22×C4D4×D1111yescharacteristic
831C22×C4D4×D1111yescharacteristic
832C22×C4C23×D1111yescharacteristic
833C22×C4C23×D1111yescharacteristic
834C22×C4C23×D1111yescharacteristic
835Q16—28no—
836SD16—28no—
837SD16—228no—
838D8—228no—
839M16—24no—
840M16—224no—
841C2×C8—114no—
842C2×C8C23×D1114yes—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—21no—
846C4⋊C4—112no—
847C4⋊C4—112no—
848C4⋊C4—112no—
849C4⋊C4—222no—
850C4⋊C4—222no—
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—221no—
860C4⋊C4—221no—
861C4⋊C4—221no—
862C4⋊C4C23×D1112yes—
863C22⋊C4—22no—
864C22⋊C4—22no—
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—111no—
880C42—111no—
881C42—111no—
882C42—111no—
883C42—111no—
884C42—111no—
885C42—111no—
886C42—111no—
887C42—111no—
888C42—111no—
889C42—111no—
890C42—111no—
891C42—111no—
892C42—111no—
893C42—111no—
894C42—111no—
895C42—222no—
896C42—222no—
897C42—222no—
898C42—222no—
899C42—222no—
900C42—222no—
901C42—222no—
902C42—222no—
903C11#6056311yescharacteristic, complemented, Sylow
904C23—24no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—42no—
911C23—222no—
912C23—442no—
913C23—442no—
914C23—442no—
915C23C2×D4×D1111yescharacteristic
916C23C2×D4×D1111yescharacteristic
917C23C2×D4×D1111yescharacteristic
918Q8—24no—
919Q8—22no—
920Q8—24no—
921Q8—42no—
922Q8C2×#434114yes—
923D4—28no—
924D4—24no—
925D4—28no—
926D4—22no—
927D4—224no—
928D4—444no—
929D4—444no—
930D4—442no—
931D4C2×#434114yes—
932C2×C4—24no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—28no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—111no—
946C2×C4—111no—
947C2×C4—111no—
948C2×C4—111no—
949C2×C4—111no—
950C2×C4—111no—
951C2×C4—111no—
952C2×C4—111no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—444no—
962C2×C4—444no—
963C2×C4—444no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—444no—
972C2×C4—444no—
973C2×C4—444no—
974C2×C4—442no—
975C2×C4—442no—
976C2×C4—442no—
977C2×C4C2×D4×D1111yescharacteristic
978C2×C4C2×D4×D1111yescharacteristic
979C2×C4C2×D4×D1111yescharacteristic
980C2×C4C2×#434114yes—
981C2×C4C24×D1111yescharacteristic
982C8—24no—
983C8—224no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—24no—
992C22—44no—
993C22—48no—
994C22—42no—
995C22—42no—
996C22—442no—
997C22—442no—
998C22—442no—
999C22—884no—
1000C22#1062311712yes—
1001C22#1062330812yes—
1002C22C22×D4×D1111yescharacteristic
1003C4—21no—
1004C4—24no—
1005C4—21no—
1006C4—42no—
1007C4—42no—
1008C4—112no—
1009C4—221no—
1010C4—221no—
1011C4—221no—
1012C4—221no—
1013C4—221no—
1014C4—221no—
1015C4—221no—
1016C4—442no—
1017C4—442no—
1018C4—442no—
1019C4#1062311712yes—
1020C4C22×#434112yes—
1021C2—22no—
1022C2—22no—
1023C2—41no—
1024C2—44no—
1025C2—882no—
1026C2C2×#1062311711yescharacteristic
1027C2D11×#57511yescharacteristic
1028C2C2×#1062330811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3007C2
socleC22×C11C23×D4
prime radical#13077868C2
hypercenter#3007D11
hypocenterC11#60563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C2×#10623155C2semidirect
2. C2×#41×Dic11C2semidirect
3. #13078788C2semidirect
4. #13078755C2semidirect
5. #13078726C2semidirect
6. #13078697C2semidirect
7. #13078664C2semidirect
8. #13078635C2semidirect
9. #13078560C2semidirect
10. #13078557C2semidirect
11. #13078436C2semidirect
12. #13078112C2semidirect
14. #137×Dic11C2semidirect
15. #13077429C2semidirect
16. #13077245C2semidirect
17. C11×#3007C2semidirect
27. #41×Dic11C22semidirect
28. #41×Dic11C22semidirect
30. C2×#67000C22semidirect
31. C2×Q8×Dic11C22semidirect
32. C2×Q8×Dic11C22semidirect
33. C2×Q8×Dic11C22semidirect
36. C2×D4×Dic11C22semidirect
37. C2×D4×Dic11C22semidirect
49. #10623155C22semidirect
50. #10623155C22semidirect
52. C2×#66946C22semidirect
54. C2×#66943C22semidirect
57. C11×#452C22semidirect
58. C11×#451C22semidirect
59. C11×#450C22semidirect
65. #10622838C22semidirect
68. #10622798C22semidirect
69. #10622798C22semidirect
70. #10622797C22semidirect
71. Q16×Dic11C22semidirect
72. #10622778C22semidirect
73. #10622778C22semidirect
74. #10622777C22semidirect
75. SD16×Dic11C22semidirect
76. #10622744C22semidirect
77. #10622734C22semidirect
78. #10622731C22semidirect
79. M16×Dic11C22semidirect
80. #10622658C22semidirect
81. #10622657C22semidirect
82. #10622656C22semidirect
83. #10622577C22semidirect
84. #10622430C22semidirect
85. #10622412C22semidirect
86. #10622409C22semidirect
87. #10622401C22semidirect
88. #10622398C22semidirect
89. #10622379C22semidirect
90. #10622376C22semidirect
91. #10622369C22semidirect
92. #10622350C22semidirect
95. #10622332C22semidirect
96. #10622332C22semidirect
97. #10622331C22semidirect
98. #10622331C22semidirect
402. #3007D11semidirect
540. #452C2×D11semidirect
541. #451C2×D11semidirect
542. #450C2×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×#106231552
C2×#41×Dic112
#130787882
#130787552
#130787262
#130786972
#130786642
#130786352
#130785602
#130785572
#130784362
#130781122
#130778682
#137×Dic112
#130774292
#130772452
C11×#30072
#6056311