Finite Group Databasebeta

← C2×#13080771 #15630458

Subgroups — C2×#13080771 #15630458

Order 2816.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623265C211yesmaximal, characteristic, complemented
2C2×#10623207C211yesmaximal, characteristic, complemented
3#13080771C2116yesmaximal, direct product factor
4C2×#10622428C211yesmaximal, characteristic, complemented
5C2×#10622392C211yesmaximal, characteristic, complemented
6C2×#10622700C211yesmaximal, characteristic, complemented
7C2×#10622425C211yesmaximal, characteristic, complemented
8C2×#10622388C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622424C211yesmaximal, characteristic, complemented
11C2×#10622386C211yesmaximal, characteristic, complemented
12C2×#10622324C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622383C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#489C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic, complemented
20C2×C11×#124C2211yescharacteristic
21C2×#67000—21no—
22C2×#67000—21no—
23C2×#66999C2211yescharacteristic
24C22×#4325C2211yescharacteristic, complemented
25C2×#66991C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×D88C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29C22×C8×D11C2211yescharacteristic, complemented
30#10623265—24no—
31#10623265C2218yescomplemented
32#10623207—24no—
33#10623207C2218yescomplemented
34C2×#66948—21no—
35C2×#66948C2211yescharacteristic
36C2×#66948C2211yescharacteristic, complemented
37C2×#66945—21no—
38C2×#66945C2211yescharacteristic
39C2×#66945C2211yescharacteristic, complemented
40C2×#66937—21no—
41C2×#66936—21no—
42C2×#66935—21no—
43C2×C22⋊C4×D11—21no—
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic, complemented
47C11×#489C2218yescomplemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#97C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic, complemented
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
59C2×#66881C2211yescharacteristic, complemented
60#10622700C2218yescomplemented
61#10622670C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66871C2211yescharacteristic, complemented
65C2×#66871C2211yescharacteristic, complemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622428C2218yescomplemented
68#10622425C2218yescomplemented
69#10622424C2218yescomplemented
70#10622417C2218yescomplemented
71#10622392C2218yescomplemented
72#10622388C2218yescomplemented
73#10622386C2218yescomplemented
74#10622383C2218yescomplemented
75#10622324C2218yescomplemented
76#10622319C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×#4343—22no—
84C2×#4343—24no—
85C2×#4343—42no—
86C2×#4343C2314yes—
87C2×D4×D11—24no—
88C2×D4×D11—22no—
89C2×D4×D11—42no—
90C2×D4×D11C2314yes—
91C22×D44—21no—
92C22×D44—21no—
93C22×D44—21no—
94C22×D44D411yescharacteristic
95C22×D44C2311yescharacteristic
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C22×C4×D11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C11×C4⋊Q8—22no—
105C11×C4⋊Q8C2314yescomplemented
106C11×#124—22no—
107C11×#124C2314yes—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115#67000—28no—
116#67000—28no—
117#66999—22no—
118#66999C2314yes—
119C2×#4325—42no—
120C2×#4325C2314yescomplemented
121#66991—22no—
122#66991C2314yes—
123C2×#4323—42no—
124C2×#4323C2314yes—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4D411yescharacteristic
133C2×(C2×D11)⋊C4D411yescharacteristic
134C2×C4⋊Dic11D411yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C2×D88—24no—
143C2×D88C2314yes—
144C2×#4313—42no—
145C2×#4313C2314yes—
146C2×C8×D11—42no—
147C2×C8×D11C2314yescomplemented
148#66948—28no—
149#66948—22no—
150#66948—22no—
151#66948C2314yes—
152#66948C2314yescomplemented
153#66945—22no—
154#66945—22no—
155#66945—28no—
156#66945C2314yes—
157#66945C2314yescomplemented
158#66937—28no—
159#66936—28no—
160#66935—28no—
161C22⋊C4×D11—28no—
162C4×D44—22no—
163C4×D44—22no—
164C4×D44D414yes—
165C4×D44C2314yes—
166C4×D44C2314yes—
167C4×D44C2314yescomplemented
168C11×#103C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#102C2314yes—
171C11×#102C2314yes—
172C11×#97C2314yescomplemented
173#66899C2314yescomplemented
174#66896C2314yes—
175#66885C2314yes—
176#66885C2314yescomplemented
177(C2×D11)⋊C8C2314yes—
178(C2×D11)⋊C8C2314yescomplemented
179#66881C2314yescomplemented
180#66873C2314yes—
181#66873C2314yes—
182#66871C2314yescomplemented
183#66871C2314yescomplemented
184C4⋊(C11⋊C8)C2314yescomplemented
185C2×#3319—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—24no—
190C23×D11—44no—
191C23×D11—44no—
192C23×D11—82no—
193C23×D11C2×D411yescharacteristic
194C23×D11C2×D411yescharacteristic
195C2×Q8×C11—21no—
196C2×Q8×C11—24no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—82no—
200C2×Q8×C11C2412yes—
201C2×D4×C11—21no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11C2412yes—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—82no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219#4343—28no—
220#4343—44no—
221#4343—48no—
222D4×D11—28no—
223D4×D11—44no—
224D4×D11—48no—
225C2×D44—24no—
226C2×D44—24no—
227C2×D44—24no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44—42no—
234C2×D44—44no—
235C2×D44—82no—
236C2×D44—82no—
237C2×D44C2×D414yes—
238C2×D44#4114yes—
239C2×D44C2412yes—
240C2×D44C2412yes—
241C2×C4×D11—24no—
242C2×C4×D11—24no—
243C2×C4×D11—24no—
244C2×C4×D11—22no—
245C2×C4×D11—22no—
246C2×C4×D11—22no—
247C2×C4×D11—22no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—82no—
251C2×C4×D11C2×D412yes—
252C2×C4×D11C2×D412yes—
253C2×C4×D11C2412yes—
254C2×C4×D11C2412yes—
255C2×C8×C11—22no—
256C2×C8×C11—22no—
257C2×C8×C11C2412yes—
258C2×C8×C11C2412yes—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4C2412yes—
263C11×C4⋊C4C2412yes—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C42×C11C2×D412yes—
267C42×C11C2412yes—
268C22⋊Dic11—24no—
269#4325—44no—
270#4323—44no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4C2×D414yes—
279(C2×D11)⋊C4C2×D414yes—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11C2×D414yes—
283C4⋊Dic11C2412yes—
284C4⋊Dic11C2412yes—
285Dic11⋊C4—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292D88—28no—
293#4313—44no—
294C8×D11—44no—
295C2×#555—111no—
296C2×#546—111no—
297#3319—1116no—
298C2×#489D1111yescharacteristic, complemented
299C2×#485—111no—
300C2×#482—111no—
301C2×#474—111no—
302C2×#468—111no—
303C2×#466—111no—
304C2×#463—111no—
305C2×#449—111no—
306C2×#447—111no—
307C2×#442—111no—
308C2×#435—111no—
309C2×#418—111no—
310C2×#416—111no—
311C23×C11—22no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11C22×D411yescharacteristic
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—24no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—48no—
326C22×D11—48no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—84no—
333C22×D11—816no—
334C22×D11C22×D412yes—
335C22×D11C22×D412yes—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—42no—
339Q8×C11—84no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—42no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4112yes—
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C11C2511yescharacteristic
357C22⋊D11—48no—
358C22⋊D11—84no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11C22×D412yes—
366C2×Dic11C22×D412yes—
367D44—24no—
368D44—22no—
369D44—22no—
370D44—22no—
371D44—44no—
372D44—48no—
373D44—42no—
374D44—84no—
375D44—84no—
376D44C2×#4114yes—
377C4×D11—24no—
378C4×D11—24no—
379C4×D11—22no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—48no—
384C4×D11—48no—
385C4×D11—84no—
386C8×C11—22no—
387C8×C11—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41—111no—
391C23×D4—111no—
392C22×SD16—111no—
393C22×D8—111no—
394C22×D8—111no—
395C22×M16—111no—
396C23×C8—111no—
397#555—118no—
398#555—224no—
399#546—118no—
400#546—224no—
401C2×C4⋊Q8C2×D1111yescharacteristic, complemented
402C2×#124—221no—
403C2×#124—221no—
404C2×#124C2×D1111yescharacteristic
405C2×#123—221no—
406C2×C22⋊Q8—111no—
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#121—221no—
412C2×#120—221no—
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—111no—
416C2×#117—111no—
417C2×#117—111no—
418C2×#117—221no—
419C22×C22⋊C4—221no—
420#489C2×D1118yescomplemented
421#485—118no—
422#482—118no—
423#474—118no—
424#468—118no—
425#466—118no—
426#463—118no—
427#449—118no—
428#447—118no—
429#442—118no—
430#435—118no—
431C2×#107—111no—
432C2×#107—111no—
433C2×#106—111no—
434C2×C4⋊C8—111no—
435#418—118no—
436#416—118no—
437C2×#103—111no—
438C2×#103C2×D1111yescharacteristic, complemented
439C2×#103C2×D1111yescharacteristic, complemented
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102C2×D1111yescharacteristic
446C2×#102C2×D1111yescharacteristic
447C2×C22⋊C8—111no—
448C2×C22⋊C8—111no—
449C2×#97C2×D1111yescharacteristic, complemented
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—84no—
454C22×C11#54612yes—
455C22×C11#57512yes—
456C22×C11#57612yes—
457C22×C11C23×D411yescharacteristic
458C2×D11—24no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—44no—
466C2×D11—44no—
467C2×D11—48no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—816no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11—42no—
480C4×C11#54612yes—
481C4×C11C22×#4111yescharacteristic
482C4×C11C2×H(5,𝔽2)11yescharacteristic
483Dic11—22no—
484Dic11—22no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—114no—
489C2×#41—222no—
490C2×#41—224no—
491C2×#41—442no—
492C22×Q8—21no—
493C22×Q8C22×D1111yescharacteristic
494C22×D4—114no—
495C22×D4—111no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—221no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—222no—
502C22×D4—221no—
503C22×D4—224no—
504C22×D4—221no—
505C22×D4—442no—
506C22×D4C22×D1111yescharacteristic
507C23×C4—111no—
508C23×C4—111no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4—221no—
512C2×SD16—114no—
513C2×SD16—442no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—224no—
517C2×D8—442no—
518C2×M16—114no—
519C2×M16—442no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—114no—
523C22×C8—442no—
524C22×C8C22×D1111yescharacteristic
525C22×C8C22×D1111yescharacteristic
526C4⋊Q8—22no—
527C4⋊Q8C22×D1114yescomplemented
528#124—22no—
529#124—228no—
530#124—228no—
531#124C22×D1114yes—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—222no—
535#121—114no—
536#121—114no—
537#121—114no—
538#121—228no—
539#121—222no—
540#121—222no—
541#121—228no—
542#121—222no—
543#120—228no—
544C4×D4—114no—
545C4×D4—114no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—222no—
549C4×D4—222no—
550#117—114no—
551#117—114no—
552#117—228no—
553#117—222no—
554#117—222no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4C22×D1111yescharacteristic
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—111no—
565C2×C22⋊C4—111no—
566C2×C22⋊C4—228no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C42—221no—
576C2×C42—221no—
577C2×C42C22×D1111yescharacteristic
578#107—114no—
579#107—114no—
580#106—114no—
581C4⋊C8—114no—
582#103—114no—
583#103C22×D1114yescomplemented
584#103C22×D1114yescomplemented
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590#102C22×D1114yes—
591#102C22×D1114yes—
592C22⋊C8—114no—
593C22⋊C8—114no—
594#97C22×D1114yescomplemented
595C2×C11—82no—
596C2×C11#331914yescomplemented
597C2×C11C2×#54611yescharacteristic
598C2×C11C2×#57511yescharacteristic
599C2×C11C2×#57611yescharacteristic
600D11—42no—
601D11—42no—
602D11—44no—
603D11—82no—
604C24—21no—
605C24—111no—
606C24—111no—
607C24—224no—
608C24—221no—
609C24—221no—
610C24—444no—
611C24—444no—
612C24—882no—
613#41—228no—
614#41—444no—
615#41—448no—
616C2×Q8—21no—
617C2×Q8—24no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—82no—
621C2×Q8C23×D1112yes—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—114no—
626C2×D4—114no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—224no—
633C2×D4—228no—
634C2×D4—224no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—222no—
638C2×D4—222no—
639C2×D4—222no—
640C2×D4—442no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—448no—
644C2×D4—444no—
645C2×D4—882no—
646C2×D4—882no—
647C2×D4—882no—
648C2×D4C23×D1112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—224no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—224no—
666C22×C4—224no—
667C22×C4—444no—
668C22×C4—444no—
669C22×C4—882no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—444no—
674D8—228no—
675D8—444no—
676M16—444no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—444no—
684C2×C8C23×D1112yes—
685C2×C8C23×D1112yes—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—114no—
690C4⋊C4—112no—
691C4⋊C4—112no—
692C4⋊C4—224no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4C23×D1112yes—
696C4⋊C4C23×D1112yes—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—114no—
700C22⋊C4—114no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C42—224no—
710C42—224no—
711C42D4×D1112yes—
712C42C23×D1112yes—
713C11C2×#331911yescharacteristic, complemented, Sylow
714C23—22no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—112no—
719C23—112no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—224no—
728C23—222no—
729C23—448no—
730C23—448no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23—442no—
735C23—442no—
736C23—884no—
737C23—8816no—
738C23C2×D4×D1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742Q8—84no—
743D4—22no—
744D4—22no—
745D4—42no—
746D4—114no—
747D4—222no—
748D4—222no—
749D4—222no—
750D4—224no—
751D4—444no—
752D4—448no—
753D4—448no—
754D4—442no—
755D4—884no—
756D4—884no—
757D4—884no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—112no—
767C2×C4—112no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—224no—
775C2×C4—224no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—448no—
779C2×C4—448no—
780C2×C4—442no—
781C2×C4—442no—
782C2×C4—884no—
783C2×C4C2×D4×D1112yes—
784C2×C4C2×D4×D1112yes—
785C2×C4C2×D4×D1111yescharacteristic
786C2×C4#41×D1112yes—
787C2×C4#6704212yes—
788C2×C4C24×D1111yescharacteristic
789C8—22no—
790C8—22no—
791C8—222no—
792C8—222no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—84no—
797C22—222no—
798C22—222no—
799C22—224no—
800C22—222no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—444no—
805C22—444no—
806C22—448no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—442no—
812C22—8816no—
813C22—884no—
814C22#1062320712yes—
815C22#1062330512yes—
816C22#1062330812yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—222no—
824C4—222no—
825C4—442no—
826C4—442no—
827C4#1062320712yes—
828C4C2×#41×D1111yescharacteristic
829C4C2×#6704211yescharacteristic
830C2—82no—
831C2—442no—
832C2—442no—
833C2—444no—
834C2—882no—
835C2#1308077114yesdirect product factor
836C2C2×#1062320711yescharacteristic
837C2C2×#1062330811yescharacteristic
838C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
hypercenterC2×#489D11
hypocenterC11C2×#3319
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623265C2semidirect
2. C2×#10623207C2semidirect
3. #13080771C2direct (N × H)
4. C2×#10622428C2semidirect
5. C2×#10622392C2semidirect
6. C2×#10622700C2semidirect
7. C2×#10622425C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622424C2semidirect
11. C2×#10622386C2semidirect
12. C2×#10622324C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622383C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#489C2semidirect
19. C2×C11×C4⋊Q8C22semidirect
24. C22×#4325C22semidirect
29. C22×C8×D11C22semidirect
31. #10623265C22semidirect
33. #10623207C22semidirect
36. C2×#66948C22semidirect
39. C2×#66945C22semidirect
46. C2×C4×D44C22semidirect
47. C11×#489C22semidirect
48. C2×C11×#103C22semidirect
49. C2×C11×#103C22semidirect
52. C2×C11×#97C22semidirect
53. C2×#66899C22semidirect
56. C2×#66885C22semidirect
58. C2×(C2×D11)⋊C8C22semidirect
59. C2×#66881C22semidirect
60. #10622700C22semidirect
61. #10622670C22semidirect
64. C2×#66871C22semidirect
65. C2×#66871C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. #10622428C22semidirect
68. #10622425C22semidirect
69. #10622424C22semidirect
70. #10622417C22semidirect
71. #10622392C22semidirect
72. #10622388C22semidirect
73. #10622386C22semidirect
74. #10622383C22semidirect
75. #10622324C22semidirect
76. #10622319C22semidirect
105. C11×C4⋊Q8C23semidirect
120. C2×#4325C23semidirect
147. C2×C8×D11C23semidirect
152. #66948C23semidirect
157. #66945C23semidirect
167. C4×D44C23semidirect
168. C11×#103C23semidirect
169. C11×#103C23semidirect
172. C11×#97C23semidirect
173. #66899C23semidirect
176. #66885C23semidirect
178. (C2×D11)⋊C8C23semidirect
179. #66881C23semidirect
182. #66871C23semidirect
183. #66871C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
298. C2×#489D11semidirect
401. C2×C4⋊Q8C2×D11semidirect
420. #489C2×D11semidirect
438. C2×#103C2×D11semidirect
439. C2×#103C2×D11semidirect
449. C2×#97C2×D11semidirect
527. C4⋊Q8C22×D11semidirect
583. #103C22×D11semidirect
584. #103C22×D11semidirect
594. #97C22×D11semidirect
596. C2×C11#3319semidirect
713. C11C2×#3319semidirect
835. C2#13080771direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106232072
#130807712
C2×#106224282
C2×#106223922
C2×#106227002
C2×#106224252
C2×#106223882
C2×#106226702
C2×#106224242
C2×#106223862
C2×#106223242
C2×#106223192
C2×#106223832
C2×#106224172
C2×C11×#4892
C2×#331911