Finite Group Databasebeta

← C2×#13078273 #15620971

Subgroups — C2×#13078273 #15620971

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66969C211yesmaximal, characteristic, complemented
2C22×#66954C211yesmaximal, characteristic, complemented
3C2×#10623160C211yesmaximal, characteristic, complemented
4C2×#10623139C211yesmaximal, characteristic, complemented
5#13078273C2116yesmaximal, direct product factor
6C2×#10622429C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622652C211yesmaximal, characteristic, complemented
10C2×#10622477C211yesmaximal, characteristic, complemented
11C2×#10622727C211yesmaximal, characteristic, complemented
12C2×#10622784C211yesmaximal, characteristic, complemented
13C2×D11×#106C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×#10622384C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C2×#66992—21no—
27C2×#66991—21no—
28C2×#66991C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C2×#66969—28no—
34C2×#66969C2218yescomplemented
35C22×#4314C2211yescharacteristic
36C2×#66954—28no—
37C2×#66954C2218yescomplemented
38C22×#4313C2211yescharacteristic
39C22×#4313C2211yescharacteristic
40C22×C8×D11C2211yescharacteristic
41C22×C8×D11C2211yescharacteristic
42#10623160—24no—
43#10623160C2218yescomplemented
44#10623139—24no—
45#10623139C2218yescomplemented
46C2×#66950C2211yescharacteristic
47C2×#66949—21no—
48C2×#66948—21no—
49C2×#66948C2211yescharacteristic
50C2×C4⋊C4×D11C2211yescharacteristic
51C2×C4⋊C4×D11C2211yescharacteristic
52C2×#66937—21no—
53C2×#66937—21no—
54C2×#66937—21no—
55C2×#66931—21no—
56C11×#465C2218yescomplemented
57C2×C11×#106C2211yescharacteristic
58C2×C11×#103C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62#10622784C2218yescomplemented
63#10622727C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67#10622665C2218yescomplemented
68#10622652C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66872C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73#10622477C2218yescomplemented
74D11×#106C2218yescomplemented
75#10622429C2218yescomplemented
76#10622416C2218yescomplemented
77#10622395C2218yescomplemented
78#10622384C2218yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11D411yescharacteristic
87C22×C22⋊D11D411yescharacteristic
88C23×Dic11—21no—
89C2×#4343—22no—
90C2×#4343—24no—
91C2×#4343—24no—
92C2×#4343C2314yes—
93C2×#4341—24no—
94C2×#4341—22no—
95C2×#4341—24no—
96C2×#4341C2314yes—
97C2×#4339—24no—
98C2×#4339—24no—
99C2×#4339D414yes—
100C2×#4339C2314yes—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44D411yescharacteristic
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11C2311yescharacteristic
109C22×C4×D11C2311yescharacteristic
110C22×Dic22D411yescharacteristic
111C22×Dic22C2311yescharacteristic
112C2×C11×SD16—24no—
113C2×C11×SD16C2314yes—
114C22×C8×C11—24no—
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2314yes—
117C22×C8×C11C2311yescharacteristic
118C11×C22⋊Q8—22no—
119C11×C22⋊Q8C2314yes—
120C11×#121—22no—
121C11×#121C2314yes—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129#66999—22no—
130#66999C2314yes—
131C2×#4326—24no—
132C2×#4326C2314yes—
133#66992—28no—
134#66991—28no—
135#66991—22no—
136#66991C2314yes—
137C2×#4323—24no—
138C2×#4323C2314yes—
139#66983—22no—
140#66983C2314yes—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148#66977—22no—
149#66977C2314yes—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×#4318—24no—
155C2×#4318C2314yes—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158#66969—232no—
159C2×#4314—24no—
160C2×#4314C2314yes—
161#66954—232no—
162C2×#4313—24no—
163C2×#4313—24no—
164C2×#4313C2314yes—
165C2×#4313C2314yes—
166C2×C8×D11—24no—
167C2×C8×D11D418yescomplemented
168C2×C8×D11C2314yes—
169C2×C8×D11C2314yes—
170#66950—22no—
171#66950C2314yes—
172#66949—28no—
173#66948—28no—
174#66948—22no—
175#66948C2314yes—
176C4⋊C4×D11—22no—
177C4⋊C4×D11—22no—
178C4⋊C4×D11C2314yes—
179C4⋊C4×D11C2314yes—
180#66937—28no—
181#66937—28no—
182#66937—28no—
183#66931—28no—
184C11×#106C2314yes—
185C11×#103C2314yes—
186C11×#102C2314yes—
187#66899C2314yes—
188#66896C2314yes—
189#66885C2314yes—
190#66881C2314yes—
191#66880C2314yes—
192#66874C2314yes—
193#66873C2314yes—
194#66872C2314yes—
195#66872C2314yes—
196C2×#3060—111nomaximal, Sylow
197C24×C11—21no—
198C24×C11C2×D411yescharacteristic
199C23×D11—21no—
200C23×D11C2×D411yescharacteristic
201C23×D11C2×D411yescharacteristic
202C2×Q8×C11—21no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11C2412yes—
206C2×D4×C11—24no—
207C2×D4×C11—22no—
208C2×D4×C11—21no—
209C2×D4×C11—22no—
210C2×D4×C11—82no—
211C2×D4×C11C2412yes—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11—82no—
229C2×C22⋊D11C2×D414yes—
230C2×C22⋊D11C2×D414yes—
231C22×Dic11—24no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—44no—
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238#4343—28no—
239#4343—28no—
240#4343—48no—
241#4341—28no—
242#4341—28no—
243#4341—48no—
244#4339—216no—
245#4339—28no—
246#4339—28no—
247C2×D44—24no—
248C2×D44—24no—
249C2×D44—24no—
250C2×D44—21no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—44no—
254C2×D44—82no—
255C2×D44C2×D414yes—
256C2×D44C2412yes—
257C2×C4×D11—24no—
258C2×C4×D11—24no—
259C2×C4×D11—24no—
260C2×C4×D11—22no—
261C2×C4×D11—22no—
262C2×C4×D11—44no—
263C2×C4×D11—82no—
264C2×C4×D11—82no—
265C2×C4×D11C2×D414yes—
266C2×C4×D11C2×D412yes—
267C2×C4×D11C2×D412yes—
268C2×C4×D11#4114yes—
269C2×C4×D11C2412yes—
270C2×C4×D11C2412yes—
271C2×Dic22—24no—
272C2×Dic22—22no—
273C2×Dic22—21no—
274C2×Dic22—22no—
275C2×Dic22C2×D414yes—
276C2×Dic22C2412yes—
277C11×SD16—28no—
278C2×C8×C11—28no—
279C2×C8×C11—22no—
280C2×C8×C11C2×D414yes—
281C2×C8×C11C2412yes—
282C2×C8×C11C2412yes—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—24no—
286C11×C4⋊C4C2412yes—
287C11×C4⋊C4C2412yes—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—24no—
290C22⋊Dic11—24no—
291C22⋊Dic11—24no—
292#4326—28no—
293#4323—28no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—24no—
298C4⋊Dic11—24no—
299C4⋊Dic11—21no—
300C4⋊Dic11—21no—
301C4⋊Dic11C2412yes—
302C4⋊Dic11C2412yes—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307#4318—28no—
308C2×C11⋊C8—22no—
309C2×C11⋊C8C2×D414yes—
310C2×C11⋊C8C2412yes—
311C2×C11⋊C8C2412yes—
312#4314—28no—
313#4313—28no—
314#4313—28no—
315C8×D11—28no—
316C8×D11C2×D4116yescomplemented
317C22×#135—111no—
318C22×#131—111no—
319C2×#537—111no—
320C2×#537—111no—
321#3060—1116no—
322C2×#470—111no—
323C2×#470—111no—
324C2×#469—111no—
325C2×#469—111no—
326C2×#465—111no—
327C2×#465—111no—
328C2×#465—111no—
329C2×#465D1111yescharacteristic, complemented
330C22×#106—111no—
331C2×#417—111no—
332C2×#417—111no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11—42no—
340C23×C11C22×D412yes—
341C23×C11C22×D411yescharacteristic
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11#12114yes—
352C22×D11C22×D412yes—
353C22×D11C22×D412yes—
354Q8×C11—22no—
355Q8×C11—22no—
356Q8×C11—42no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—42no—
360D4×C11—84no—
361C2×C4×C11—22no—
362C2×C4×C11—24no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
371C2×C4×C11C22×D412yes—
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D412yes—
374C2×C4×C11C2×#4112yes—
375C2×C4×C11C2511yescharacteristic
376C22⋊D11—28no—
377C22⋊D11—28no—
378C22⋊D11—48no—
379C22⋊D11—84no—
380C22⋊D11—84no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11—48no—
389C2×Dic11#12114yes—
390C2×Dic11C22×D412yes—
391C2×Dic11C22×D412yes—
392D44—28no—
393D44—22no—
394D44—22no—
395D44—48no—
396D44—42no—
397D44—84no—
398C4×D11—24no—
399C4×D11—22no—
400C4×D11—22no—
401C4×D11—48no—
402C4×D11—84no—
403C4×D11—84no—
404C4×D11#12118yes—
405C4×D11C22×D414yes—
406C4×D11C2×#4114yes—
407Dic22—28no—
408Dic22—22no—
409Dic22—22no—
410Dic22—42no—
411C8×C11—22no—
412C8×C11C22×D414yes—
413C11⋊C8—22no—
414C11⋊C8C22×D414yes—
415C22×#41—111no—
416C22×#41—111no—
417C22×#41—111no—
418C2×#135—118no—
419C2×#135—228no—
420C22×Q16—111no—
421C22×SD16—111no—
422C22×SD16C2×D1111yescharacteristic
423C22×D8—111no—
424C2×#131—118no—
425C2×#131—228no—
426C22×M16—111no—
427C22×M16—111no—
428C22×M16—111no—
429C23×C8—111no—
430C23×C8—111no—
431C23×C8C2×D1111yescharacteristic
432#537—118no—
433#537—118no—
434#537—224no—
435#537—224no—
436C2×C22⋊Q8—111no—
437C2×C22⋊Q8—111no—
438C2×C22⋊Q8—111no—
439C2×C22⋊Q8—221no—
440C2×C22⋊Q8—221no—
441C2×C22⋊Q8C2×D1111yescharacteristic
442C2×#121—111no—
443C2×#121—111no—
444C2×#121—111no—
445C2×#121—221no—
446C2×#121—221no—
447C2×#121—221no—
448C2×#121—221no—
449C2×#121—221no—
450C2×#121—221no—
451C2×#121C2×D1111yescharacteristic
452C22×C4⋊C4—111no—
453C22×C4⋊C4—111no—
454#470—118no—
455#470—118no—
456#469—118no—
457#469—118no—
458#465—118no—
459#465—118no—
460#465—118no—
461#465C2×D1118yescomplemented
462C2×#106—111no—
463C2×#106—111no—
464C2×#106—111no—
465C2×#106—118no—
466C2×#106C2×D1111yescharacteristic
467#417—118no—
468#417—118no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103—111no—
472C2×#103C2×D1111yescharacteristic
473C2×#102—111no—
474C2×#102—111no—
475C2×#102—111no—
476C2×#102C2×D1111yescharacteristic
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—44no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—84no—
485C22×C11C2×#12112yes—
486C22×C11#57712yes—
487C22×C11#57712yes—
488C22×C11C23×D411yescharacteristic
489C2×D11—28no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—22no—
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—44no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—84no—
500C2×D11C2×#12114yes—
501C4×C11—22no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11C2×#12112yes—
506C4×C11C23×D411yescharacteristic
507C4×C11C22×#4111yescharacteristic
508Dic11—22no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11C2×#12114yes—
513C2×#41—114no—
514C2×#41—114no—
515C2×#41—114no—
516C2×#41—114no—
517C2×#41—224no—
518C2×#41—224no—
519C2×#41—222no—
520C2×#41—222no—
521C2×#41—224no—
522C2×#41—224no—
523C2×#41—224no—
524C2×#41—224no—
525C22×Q8—111no—
526C22×Q8—111no—
527C22×Q8C22×D1111yescharacteristic
528C22×D4—21no—
529C22×D4—111no—
530C22×D4—111no—
531C22×D4—111no—
532C22×D4—111no—
533C22×D4—221no—
534C22×D4—221no—
535C22×D4—221no—
536C22×D4—221no—
537C22×D4—221no—
538C22×D4C22×D1111yescharacteristic
539C23×C4—111no—
540C23×C4—111no—
541C23×C4—221no—
542C23×C4—221no—
543C23×C4—221no—
544C23×C4—221no—
545C23×C4C22×D1111yescharacteristic
546#135—2232no—
547C2×Q16—114no—
548C2×Q16—224no—
549C2×SD16—24no—
550C2×SD16—114no—
551C2×SD16—224no—
552C2×SD16C22×D1114yes—
553C2×D8—114no—
554C2×D8—224no—
555#131—2232no—
556C2×M16—114no—
557C2×M16—114no—
558C2×M16—114no—
559C2×M16—224no—
560C2×M16—224no—
561C2×M16—224no—
562C22×C8—24no—
563C22×C8—111no—
564C22×C8—118no—
565C22×C8—114no—
566C22×C8—111no—
567C22×C8—114no—
568C22×C8—224no—
569C22×C8C22×D1111yescharacteristic
570C22×C8C22×D1114yes—
571C22×C8C22×D1111yescharacteristic
572C22⋊Q8—22no—
573C22⋊Q8—114no—
574C22⋊Q8—114no—
575C22⋊Q8—114no—
576C22⋊Q8—228no—
577C22⋊Q8—222no—
578C22⋊Q8—228no—
579C22⋊Q8—222no—
580C22⋊Q8—222no—
581C22⋊Q8C22×D1114yes—
582#121—22no—
583#121—114no—
584#121—114no—
585#121—114no—
586#121—228no—
587#121—228no—
588#121—228no—
589#121—222no—
590#121—228no—
591#121—222no—
592#121—228no—
593#121—228no—
594#121—222no—
595#121C22×D1114yes—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—114no—
600C2×C4⋊C4—114no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—221no—
605C2×C4⋊C4—221no—
606C2×C4⋊C4—221no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4C22×D1111yescharacteristic
609C2×C4⋊C4C22×D1111yescharacteristic
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C22⋊C4—221no—
618#106—114no—
619#106—114no—
620#106—114no—
621#106C22×D1114yes—
622#103—114no—
623#103—114no—
624#103—114no—
625#103C22×D1114yes—
626#102—114no—
627#102—114no—
628#102—114no—
629#102C22×D1114yes—
630C2×C11—42no—
631C2×C11—82no—
632C2×C11#306014yescomplemented
633C2×C11C22×#12111yescharacteristic
634C2×C11C2×#57711yescharacteristic
635C2×C11C2×#57711yescharacteristic
636D11—24no—
637D11—42no—
638D11—82no—
639C24—21no—
640C24—111no—
641C24—111no—
642C24—221no—
643C24D4×D1111yescharacteristic
644#41—228no—
645#41—2216no—
646#41—228no—
647#41—228no—
648#41—228no—
649#41—228no—
650#41—228no—
651#41—448no—
652#41—448no—
653C2×Q8—21no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—114no—
657C2×Q8—112no—
658C2×Q8—224no—
659C2×Q8—221no—
660C2×Q8—222no—
661C2×Q8—222no—
662C2×Q8C23×D1112yes—
663C2×D4—24no—
664C2×D4—22no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—82no—
668C2×D4—114no—
669C2×D4—114no—
670C2×D4—114no—
671C2×D4—112no—
672C2×D4—224no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—224no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—222no—
681C2×D4—221no—
682C2×D4—222no—
683C2×D4—444no—
684C2×D4—444no—
685C2×D4—882no—
686C2×D4—882no—
687C2×D4—882no—
688C2×D4C23×D1112yes—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—111no—
695C22×C4—112no—
696C22×C4—114no—
697C22×C4—114no—
698C22×C4—112no—
699C22×C4—111no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—224no—
703C22×C4—224no—
704C22×C4—224no—
705C22×C4—224no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—444no—
712C22×C4—444no—
713C22×C4—882no—
714C22×C4—882no—
715C22×C4D4×D1112yes—
716C22×C4D4×D1111yescharacteristic
717C22×C4C23×D1112yes—
718C22×C4C23×D1111yescharacteristic
719Q16—228no—
720SD16—28no—
721SD16—228no—
722D8—228no—
723M16—228no—
724M16—228no—
725M16—228no—
726C2×C8—22no—
727C2×C8—28no—
728C2×C8—114no—
729C2×C8—112no—
730C2×C8—1116no—
731C2×C8—112no—
732C2×C8—222no—
733C2×C8—228no—
734C2×C8D4×D1114yes—
735C2×C8C23×D1112yes—
736C2×C8C23×D1112yes—
737C4⋊C4—24no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—112no—
741C4⋊C4—112no—
742C4⋊C4—224no—
743C4⋊C4—224no—
744C4⋊C4—224no—
745C4⋊C4—224no—
746C4⋊C4—221no—
747C4⋊C4—221no—
748C4⋊C4—224no—
749C4⋊C4C23×D1112yes—
750C4⋊C4C23×D1112yes—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—224no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C11C2×#306011yescharacteristic, complemented, Sylow
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—114no—
768C23—112no—
769C23—112no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—442no—
777C23—442no—
778C23—442no—
779C23C2×D4×D1112yes—
780C23C2×D4×D1111yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—42no—
784Q8—228no—
785Q8—222no—
786Q8—222no—
787Q8—442no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—84no—
792D4—228no—
793D4—228no—
794D4—228no—
795D4—222no—
796D4—222no—
797D4—448no—
798D4—448no—
799D4—442no—
800D4—884no—
801D4—884no—
802D4—884no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—114no—
814C2×C4—112no—
815C2×C4—118no—
816C2×C4—114no—
817C2×C4—114no—
818C2×C4—112no—
819C2×C4—222no—
820C2×C4—224no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—448no—
827C2×C4—448no—
828C2×C4—442no—
829C2×C4—442no—
830C2×C4—442no—
831C2×C4—884no—
832C2×C4—884no—
833C2×C4C2×D4×D1112yes—
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4C2×D4×D1112yes—
836C2×C4#41×D1112yes—
837C2×C4C24×D1111yescharacteristic
838C8—22no—
839C8—114no—
840C8—222no—
841C8C2×D4×D1114yes—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—84no—
850C22—114no—
851C22—228no—
852C22—222no—
853C22—222no—
854C22—222no—
855C22—222no—
856C22—222no—
857C22—444no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—884no—
862C22D11×#12112yes—
863C22#1062329312yes—
864C22#1062330112yes—
865C22C22×D4×D1111yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—114no—
871C4—222no—
872C4—442no—
873C4—442no—
874C4—442no—
875C4D11×#12112yes—
876C4C22×D4×D1111yescharacteristic
877C4C2×#41×D1111yescharacteristic
878C2—42no—
879C2—82no—
880C2—224no—
881C2—442no—
882C2—882no—
883C2#1307827314yesdirect product factor
884C2C2×D11×#12111yescharacteristic
885C2C2×#1062329311yescharacteristic
886C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
hypercenterC2×#465D11
hypocenterC11C2×#3060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#66969C2semidirect
2. C22×#66954C2semidirect
3. C2×#10623160C2semidirect
4. C2×#10623139C2semidirect
5. #13078273C2direct (N × H)
6. C2×#10622429C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622652C2semidirect
10. C2×#10622477C2semidirect
11. C2×#10622727C2semidirect
12. C2×#10622784C2semidirect
13. C2×D11×#106C2semidirect
14. C2×#10622416C2semidirect
15. C2×#10622384C2semidirect
16. C2×C11×#465C2semidirect
34. C2×#66969C22semidirect
37. C2×#66954C22semidirect
43. #10623160C22semidirect
45. #10623139C22semidirect
56. C11×#465C22semidirect
62. #10622784C22semidirect
63. #10622727C22semidirect
67. #10622665C22semidirect
68. #10622652C22semidirect
73. #10622477C22semidirect
74. D11×#106C22semidirect
75. #10622429C22semidirect
76. #10622416C22semidirect
77. #10622395C22semidirect
78. #10622384C22semidirect
167. C2×C8×D11D4semidirect
316. C8×D11C2×D4semidirect
329. C2×#465D11semidirect
461. #465C2×D11semidirect
632. C2×C11#3060semidirect
759. C11C2×#3060semidirect
883. C2#13078273direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669692
C22×#669542
C2×#106231602
C2×#106231392
#130782732
C2×#106224292
C2×#106226652
C2×#106223952
C2×#106226522
C2×#106224772
C2×#106227272
C2×#106227842
C2×D11×#1062
C2×#106224162
C2×#106223842
C2×C11×#4652
C2×#306011