Finite Group Databasebeta

← #15622191

Subgroups — #15622191

Order 2816.

2138 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic
2#13078787C214yesmaximal, complemented
3#13078746C212yesmaximal, complemented
4#13078738C212yesmaximal, complemented
5#13078696C214yesmaximal, complemented
6#13078655C212yesmaximal, complemented
7#13078647C212yesmaximal, complemented
8#13078539C212yesmaximal, complemented
9#13078421C212yesmaximal, complemented
10#13078088C212yesmaximal, complemented
11#13077850C212yesmaximal, complemented
12C4×#66995C214yesmaximal, complemented
13#13077249C211yesmaximal, characteristic, complemented
14C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
15C23×Q8×C11C2211yescharacteristic
16C2×C4×Q8×C11—21no—
17C2×C4×Q8×C11—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2212yes—
23C2×C4×Q8×C11C2212yes—
24C2×C4×Q8×C11C2212yes—
25C2×C4×Q8×C11C2212yes—
26C2×C4×Q8×C11C2212yes—
27C2×C4×Q8×C11C2212yes—
28C22×C11×C4⋊C4—21no—
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C42×C11—21no—
31C22×C42×C11C2211yescharacteristic
32C2×#66995C2214yes—
33#10623322—21no—
34#10623322—21no—
35#10623322C2212yes—
36#10623010—21no—
37#10623010—21no—
38#10623010—21no—
39#10623010—21no—
40#10623010C2212yes—
41#10623010C2212yes—
42#10623008C2211yescharacteristic
43#10623008C2211yescharacteristic
44#10623008C2211yescharacteristic
45C4×#4339—21no—
46C4×#4339—21no—
47C4×#4339C2212yes—
48#10623001C2211yescharacteristic
49#10623001C2211yescharacteristic
50#10623001C2211yescharacteristic
51#10622841C2214yes—
52#10622841C2214yes—
53#10622840C2214yes—
54#10622840C2214yes—
55#10622838C2214yes—
56#10622820C2212yes—
57#10622644C2214yescomplemented
58#10622643C2218yescomplemented
59C4×#4326C2218yescomplemented
60#10622641C2218yescomplemented
61#10622640C2214yescomplemented
62#10622639C2218yescomplemented
63C4×#4325C2218yescomplemented
64#10622635C2218yescomplemented
65#10622634C2214yescomplemented
66#10622633C2214yescomplemented
67#10622584C2214yes—
68#10622583C2214yes—
69#10622581C2214yes—
70#10622580C2214yes—
71#10622579C2214yes—
72#10622577C2214yes—
73#10622539C2212yes—
74#10622539C2212yes—
75#10622538C2212yes—
76#10622538C2212yes—
77#10622537C2212yes—
78C4×#4318C2212yes—
79C22×Q8×C11—28no—
80C22×Q8×C11—21no—
81C22×Q8×C11—21no—
82C22×Q8×C11—21no—
83C22×Q8×C11C2312yes—
84C22×Q8×C11C2312yes—
85C22×Q8×C11C2312yes—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11D411yescharacteristic
89C23×C4×C11D411yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C2×#4339—21no—
92C2×#4339—21no—
93C2×#4339C2312yes—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11—22no—
98C4×Q8×C11—22no—
99C4×Q8×C11—22no—
100C4×Q8×C11—22no—
101C4×Q8×C11—22no—
102C4×Q8×C11—22no—
103C4×Q8×C11—22no—
104C4×Q8×C11—22no—
105C4×Q8×C11—22no—
106C4×Q8×C11C2314yes—
107C4×Q8×C11C2314yes—
108C4×Q8×C11C2314yes—
109C4×Q8×C11C2314yes—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2312yes—
122C2×C42×C11—22no—
123C2×C42×C11—22no—
124C2×C42×C11—22no—
125C2×C42×C11—22no—
126C2×C42×C11—22no—
127C2×C42×C11—22no—
128C2×C42×C11D411yescharacteristic
129C2×C42×C11D411yescharacteristic
130C2×C42×C11D411yescharacteristic
131C2×C42×C11D411yescharacteristic
132C2×C42×C11D411yescharacteristic
133C2×C42×C11D411yescharacteristic
134C2×C42×C11C2311yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C2×C42×C11C2311yescharacteristic
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2311yescharacteristic
140#67006—22no—
141C2×#4326C2318yes—
142#66995—216no—
143C2×#4325C2318yes—
144#66983—21no—
145#66983—21no—
146#66983—21no—
147#66983—21no—
148#66983C2312yes—
149#66983C2312yes—
150#66982—22no—
151#66982—22no—
152#66982—22no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11—22no—
156C4×C22⋊D11—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159#66979—21no—
160#66979—21no—
161#66979C2312yes—
162#66977—21no—
163#66977—21no—
164#66977—21no—
165#66977—21no—
166#66977C2312yes—
167#66977C2312yes—
168C2×#4318C2314yes—
169#66929—22no—
170#66929—22no—
171#66928—21no—
172#66928—21no—
173#66928C2312yes—
174#66927C2311yescharacteristic
175C4×D44—21no—
176C4×D44—21no—
177C4×D44—21no—
178C4×D44—21no—
179C4×D44C2312yes—
180C4×D44C2312yes—
181#66925—22no—
182#66925—22no—
183#66925—22no—
184C42×D11—22no—
185#66923—21no—
186#66923—21no—
187#66923C2312yes—
188#66922C2311yescharacteristic
189#66922C2311yescharacteristic
190#66922C2311yescharacteristic
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22—21no—
194C4×Dic22—21no—
195C4×Dic22C2312yes—
196C4×Dic22C2312yes—
197#66899C2318yes—
198#66899C2318yes—
199C22⋊(C11⋊C8)C2314yes—
200C22⋊(C11⋊C8)C2314yes—
201#66874C2318yes—
202#66873C2318yes—
203#66872C2318yes—
204#66871C2318yes—
205C4⋊(C11⋊C8)C2314yes—
206C4⋊(C11⋊C8)C2314yes—
207#66867C2314yes—
208C4×C11⋊C8C2314yes—
209#60560—111nomaximal, Sylow
210C24×C11C2×D411yescharacteristic
211C2×Q8×C11—28no—
212C2×Q8×C11—28no—
213C2×Q8×C11—28no—
214C2×Q8×C11—28no—
215C2×Q8×C11—28no—
216C2×Q8×C11—22no—
217C2×Q8×C11—22no—
218C2×Q8×C11—22no—
219C2×Q8×C11—24no—
220C2×Q8×C11#4118yescomplemented
221C2×Q8×C11C2414yes—
222C22×C4×C11—28no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—24no—
227C22×C4×C11—24no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—42no—
232C22×C4×C11—44no—
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—22no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—22no—
254#4339—28no—
255#4339—44no—
256#4339—44no—
257C2×D44—21no—
258C2×D44—21no—
259C2×D44C2412yes—
260C2×C4×D11—22no—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×Dic22—21no—
264C2×Dic22—21no—
265C2×Dic22C2412yes—
266C11×C4⋊C4—24no—
267C11×C4⋊C4—24no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4C2414yes—
274C42×C11—24no—
275C42×C11—24no—
276C42×C11—24no—
277C42×C11—24no—
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2411yescharacteristic
291C42×C11C2411yescharacteristic
292C42×C11C2411yescharacteristic
293C42×C11C2411yescharacteristic
294C22⋊Dic11—22no—
295C22⋊Dic11—22no—
296C22⋊Dic11—22no—
297#4326—216no—
298#4325—216no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4—22no—
301(C2×D11)⋊C4—22no—
302(C2×D11)⋊C4—22no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—22no—
305C4⋊Dic11—21no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11—21no—
309C4⋊Dic11C2412yes—
310C4⋊Dic11C2412yes—
311Dic11⋊C4—22no—
312Dic11⋊C4—22no—
313Dic11⋊C4—22no—
314Dic11⋊C4—22no—
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317C4×Dic11—22no—
318C4×Dic11—22no—
319C4×Dic11—22no—
320#4318—28no—
321C2×C11⋊C8C2418yes—
322#3444—111no—
323C22×C4×Q8D1111yescharacteristic, complemented
324#3117—114no—
325#3113—112no—
326#3112—112no—
327#3108—114no—
328#3104—112no—
329#3103—112no—
330#3092—112no—
331#3078—112no—
332#3037—112no—
333#3004—112no—
334C4×#137—114no—
335#2920—111no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11C22×D411yescharacteristic
340C23×C11C22×D411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C22×D11—22no—
343Q8×C11—28no—
344Q8×C11—28no—
345Q8×C11—28no—
346Q8×C11—24no—
347Q8×C11C2×#4118yes—
348C2×C4×C11—28no—
349C2×C4×C11—28no—
350C2×C4×C11—28no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—24no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—24no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—44no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11#13714yescomplemented
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2×#4114yes—
385C2×C4×C11C2511yescharacteristic
386C22⋊D11—44no—
387C22⋊D11—44no—
388C22⋊D11—44no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392D44—24no—
393D44—42no—
394D44—42no—
395C4×D11—44no—
396C4×D11—44no—
397C4×D11—44no—
398Dic22—24no—
399Dic22—42no—
400Dic22—42no—
401C11⋊C8—28no—
402C23×Q8C2×D1111yescharacteristic
403C2×#137—114no—
404#533—111no—
405#533—111no—
406#533—111no—
407#532—111no—
408#532—111no—
409#532—111no—
410#529—112no—
411#529—112no—
412#529—221no—
413#529—221no—
414#529—221no—
415#529—221no—
416#525—112no—
417#525—221no—
418#525—221no—
419C4×#41—112no—
420C4×#41—221no—
421C4×#41—221no—
422C2×C4×Q8—21no—
423C2×C4×Q8—21no—
424C2×C4×Q8—21no—
425C2×C4×Q8—21no—
426C2×C4×Q8—21no—
427C2×C4×Q8—21no—
428C2×C4×Q8C2×D1112yes—
429C2×C4×Q8C2×D1112yes—
430C2×C4×Q8C2×D1112yes—
431C2×C4×Q8C2×D1112yes—
432C2×C4×Q8C2×D1112yes—
433C2×C4×Q8C2×D1112yes—
434C22×C4⋊C4—21no—
435C22×C4⋊C4C2×D1111yescharacteristic
436C22×C42—21no—
437C22×C42C2×D1111yescharacteristic
438#484—114no—
439#483—114no—
440#481—114no—
441#480—114no—
442#479—118no—
443#477—114no—
444#475—114no—
445#464—118no—
446#462—114no—
447#460—114no—
448#451—114no—
449#451—114no—
450#448—114no—
451#448—114no—
452#441—118no—
453#440—118no—
454C4×Q16—118no—
455C4×SD16—118no—
456#432—112no—
457#432—112no—
458#431—112no—
459#431—112no—
460#428—114no—
461#423—112no—
462#419—114no—
463#417—114no—
464#407—112no—
465C4×M16—112no—
466C22×C11—28no—
467C22×C11—21no—
468C22×C11—21no—
469C22×C11—21no—
470C22×C11—21no—
471C22×C11—21no—
472C22×C11—21no—
473C22×C11#52512yes—
474C22×C11C2×#13712yes—
475C22×C11#57512yes—
476C22×C11C23×D411yescharacteristic
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C4×C11—28no—
481C4×C11—21no—
482C4×C11—21no—
483C4×C11—21no—
484C4×C11—21no—
485C4×C11—21no—
486C4×C11—21no—
487C4×C11—21no—
488C4×C11—21no—
489C4×C11—44no—
490C4×C11#52512yes—
491C4×C11C2×#13712yes—
492C4×C11C2×#13712yes—
493C4×C11C22×#4112yes—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C2×#41—112no—
498C2×#41—221no—
499C2×#41—221no—
500C22×Q8—28no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8C22×D1112yes—
505C22×Q8C22×D1112yes—
506C22×Q8C22×D1112yes—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C22⋊D1111yescharacteristic
510C23×C4C22⋊D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512#137—2216no—
513C2×Q16—118no—
514C2×SD16—118no—
515C2×M16—114no—
516C4⋊Q8—111no—
517C4⋊Q8—111no—
518C4⋊Q8—111no—
519#127—111no—
520#126—222no—
521#126—222no—
522#125—112no—
523#125—221no—
524#125—221no—
525#124—112no—
526#124—221no—
527#124—221no—
528#123—222no—
529#123—222no—
530#123—222no—
531C22⋊Q8—112no—
532C22⋊Q8—112no—
533C22⋊Q8—221no—
534C22⋊Q8—221no—
535C22⋊Q8—221no—
536C22⋊Q8—221no—
537#121—112no—
538#121—112no—
539#121—221no—
540#121—221no—
541#121—221no—
542#121—221no—
543#120—222no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—22no—
556C4×Q8—112no—
557C4×Q8—112no—
558C4×Q8—221no—
559C4×Q8—221no—
560C4×Q8—221no—
561C4×Q8—221no—
562C4×Q8C22×D1114yes—
563C4×Q8C22×D1114yes—
564C4×Q8C22×D1114yes—
565C4×Q8C22×D1114yes—
566C4×D4—112no—
567C4×D4—112no—
568C4×D4—222no—
569C4×D4—222no—
570C4×D4—222no—
571C4×D4—222no—
572C4×D4—222no—
573C4×D4—222no—
574C4×D4—221no—
575C4×D4—221no—
576C4×D4—221no—
577C4×D4—221no—
578#117—112no—
579#117—221no—
580#117—221no—
581#117—222no—
582#117—222no—
583#117—222no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4C22×D1112yes—
594C2×C4⋊C4C22×D1112yes—
595C2×C4⋊C4C22×D1112yes—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—222no—
603C2×C42C22⋊D1111yescharacteristic
604C2×C42C22⋊D1111yescharacteristic
605C2×C42C22⋊D1111yescharacteristic
606C2×C42C22⋊D1111yescharacteristic
607C2×C42C22⋊D1111yescharacteristic
608C2×C42C22⋊D1111yescharacteristic
609C2×C42C22×D1111yescharacteristic
610C2×C42C22×D1111yescharacteristic
611C2×C42C22×D1111yescharacteristic
612C2×C42C22×D1111yescharacteristic
613C2×C42C22×D1111yescharacteristic
614C2×C42C22×D1111yescharacteristic
615#107—118no—
616#106—118no—
617C4⋊C8—114no—
618C4⋊C8—114no—
619#103—118no—
620#103—118no—
621#103—118no—
622#102—118no—
623C22⋊C8—114no—
624C22⋊C8—114no—
625#97—114no—
626C4×C8—114no—
627C2×C11—22no—
628C2×C11—22no—
629C2×C11—22no—
630C2×C11C2×#52511yescharacteristic
631C2×C11C22×#13711yescharacteristic
632C2×C11C2×#57511yescharacteristic
633D11—82no—
634C24C2×C22⋊D1111yescharacteristic
635#41—228no—
636#41—444no—
637#41—444no—
638C2×Q8—28no—
639C2×Q8—28no—
640C2×Q8—28no—
641C2×Q8—28no—
642C2×Q8—28no—
643C2×Q8—24no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—112no—
648C2×Q8—221no—
649C2×Q8—221no—
650C2×Q8#433918yescomplemented
651C2×Q8C23×D1114yes—
652C2×D4—112no—
653C2×D4—222no—
654C2×D4—222no—
655C2×D4—222no—
656C2×D4—221no—
657C2×D4—221no—
658C22×C4—28no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—42no—
668C22×C4—44no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4C2×C22⋊D1111yescharacteristic
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683C22×C4C2×C22⋊D1111yescharacteristic
684C22×C4C2×C22⋊D1111yescharacteristic
685C22×C4C2×C22⋊D1111yescharacteristic
686C22×C4C2×C22⋊D1111yescharacteristic
687C22×C4C23×D1111yescharacteristic
688C22×C4C23×D1111yescharacteristic
689C22×C4C23×D1111yescharacteristic
690Q16—2216no—
691SD16—2216no—
692M16—228no—
693C2×C8—118no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—112no—
702C4⋊C4—112no—
703C4⋊C4—222no—
704C4⋊C4—222no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—222no—
710C4⋊C4—222no—
711C4⋊C4—222no—
712C4⋊C4—222no—
713C4⋊C4C23×D1114yes—
714C22⋊C4—222no—
715C22⋊C4—222no—
716C22⋊C4—222no—
717C22⋊C4—222no—
718C22⋊C4—222no—
719C22⋊C4—222no—
720C22⋊C4—222no—
721C22⋊C4—222no—
722C22⋊C4—222no—
723C42—24no—
724C42—24no—
725C42—24no—
726C42—24no—
727C42—222no—
728C42—222no—
729C42—222no—
730C42C2×C22⋊D1111yescharacteristic
731C42C2×C22⋊D1111yescharacteristic
732C42C2×C22⋊D1111yescharacteristic
733C42C2×C22⋊D1111yescharacteristic
734C42C2×C22⋊D1111yescharacteristic
735C42C2×C22⋊D1111yescharacteristic
736C42C2×C22⋊D1111yescharacteristic
737C42C2×C22⋊D1111yescharacteristic
738C42C2×C22⋊D1111yescharacteristic
739C42C2×C22⋊D1111yescharacteristic
740C42C2×C22⋊D1111yescharacteristic
741C42C2×C22⋊D1111yescharacteristic
742C42C23×D1111yescharacteristic
743C42C23×D1111yescharacteristic
744C42C23×D1111yescharacteristic
745C42C23×D1111yescharacteristic
746C11#6056011yescharacteristic, complemented, Sylow
747C23—22no—
748C23—22no—
749C23—22no—
750C23—222no—
751C23C22×C22⋊D1111yescharacteristic
752C23C22×C22⋊D1111yescharacteristic
753C23C22×C22⋊D1111yescharacteristic
754Q8—28no—
755Q8—28no—
756Q8—28no—
757Q8—24no—
758Q8—224no—
759Q8—442no—
760Q8—442no—
761Q8C2×#433918yes—
762D4—224no—
763D4—442no—
764D4—444no—
765D4—444no—
766D4—444no—
767D4—442no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—444no—
796C2×C4—444no—
797C2×C4—444no—
798C2×C4#6699514yescomplemented
799C2×C4C2×#433914yes—
800C2×C4C22×C22⋊D1111yescharacteristic
801C2×C4C22×C22⋊D1111yescharacteristic
802C2×C4C22×C22⋊D1111yescharacteristic
803C2×C4C22×C22⋊D1111yescharacteristic
804C2×C4C22×C22⋊D1111yescharacteristic
805C2×C4C22×C22⋊D1111yescharacteristic
806C2×C4C22×C22⋊D1111yescharacteristic
807C2×C4C22×C22⋊D1111yescharacteristic
808C2×C4C22×C22⋊D1111yescharacteristic
809C2×C4C22×C22⋊D1111yescharacteristic
810C2×C4C22×C22⋊D1111yescharacteristic
811C2×C4C24×D1111yescharacteristic
812C8—228no—
813C22—28no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22#1062332212yes—
824C22C2×#6699512yes—
825C22#1062335312yes—
826C22C23×C22⋊D1111yescharacteristic
827C4—28no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—44no—
837C4—442no—
838C4—442no—
839C4—442no—
840C4#1062332212yes—
841C4C2×#6699512yes—
842C4C2×#6699512yes—
843C4C22×#433912yes—
844C2—22no—
845C2—22no—
846C2—22no—
847C2—882no—
848C2C2×#1062332211yescharacteristic
849C2C22×#6699511yescharacteristic
850C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C4×Q8×C11C2
socleC22×C11C23×D4
prime radical#13081912C2
hypercenterC22×C4×Q8D11
hypocenterC11#60560
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13078787C2semidirect
3. #13078746C2semidirect
4. #13078738C2semidirect
5. #13078696C2semidirect
6. #13078655C2semidirect
7. #13078647C2semidirect
8. #13078539C2semidirect
9. #13078421C2semidirect
10. #13078088C2semidirect
11. #13077850C2semidirect
12. C4×#66995C2semidirect
13. #13077249C2semidirect
14. C22×C4×Q8×C11C2semidirect
57. #10622644C22semidirect
58. #10622643C22semidirect
59. C4×#4326C22semidirect
60. #10622641C22semidirect
61. #10622640C22semidirect
62. #10622639C22semidirect
63. C4×#4325C22semidirect
64. #10622635C22semidirect
65. #10622634C22semidirect
66. #10622633C22semidirect
220. C2×Q8×C11#41semidirect
323. C22×C4×Q8D11semidirect
372. C2×C4×C11#137semidirect
650. C2×Q8#4339semidirect
746. C11#60560semidirect
798. C2×C4#66995semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130787872
#130787462
#130787382
#130786962
#130786552
#130786472
#130785392
#130784212
#130780882
#130778502
C4×#669952
#130772492
C22×C4×Q8×C112
#6056011