Finite Group Databasebeta

← C2×#13080821 #15630574

Subgroups — C2×#13080821 #15630574

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×#10623145C211yesmaximal, characteristic, complemented
2C2×#10623337C211yesmaximal, characteristic, complemented
3#13080821C2116yesmaximal, direct product factor
4C2×#10622381C211yesmaximal, characteristic, complemented
5C2×#10622336C211yesmaximal, characteristic, complemented
6C2×#10622387C211yesmaximal, characteristic, complemented
7C2×#10622376C211yesmaximal, characteristic, complemented
8C2×#10622772C211yesmaximal, characteristic, complemented
9C2×#10622655C211yesmaximal, characteristic, complemented
10C2×#10622766C211yesmaximal, characteristic, complemented
11C2×#10622771C211yesmaximal, characteristic, complemented
12C2×D8×Dic11C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×#10622828C211yesmaximal, characteristic, complemented
16C2×C11×#447C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×#67006—21no—
23C22×C22⋊Dic11—21no—
24#10623337—24no—
25#10623337C2218yescomplemented
26C2×#66992—21no—
27C2×#66991—21no—
28C2×#66991C2211yescharacteristic
29C2×#66991C2211yescharacteristic, complemented
30C2×#66989C2211yescharacteristic
31C2×#66988—21no—
32C2×#66988—21no—
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2211yescharacteristic, complemented
35C22×#4324C2211yescharacteristic, complemented
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×#66979C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39C22×#4318C2211yescharacteristic
40C22×#4313C2211yescharacteristic, complemented
41#10623145—24no—
42#10623145C2218yescomplemented
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×#66943C2211yescharacteristic, complemented
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66932—21no—
47C11×#447C2218yescomplemented
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51#10622828C2218yescomplemented
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic, complemented
57#10622772C2218yescomplemented
58#10622771C2218yescomplemented
59#10622766C2218yescomplemented
60D8×Dic11C2218yescomplemented
61C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
62C2×#66882C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66880C2211yescharacteristic, complemented
65C2×#66880C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic11C2211yescharacteristic, complemented
68#10622655C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622387C2218yescomplemented
72#10622384C2218yescomplemented
73#10622381C2218yescomplemented
74#10622376C2218yescomplemented
75#10622342C2218yescomplemented
76#10622336C2218yescomplemented
77C25×C11—21no—
78C22×D4×C11—24no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11—22no—
82C22×D4×C11—42no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2314yes—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11D411yescharacteristic
92C23×Dic11—21no—
93C23×Dic11—21no—
94C23×Dic11—21no—
95C2×#4341—24no—
96C2×#4341—22no—
97C2×#4341—42no—
98C2×#4341C2314yes—
99C22×C4×D11—21no—
100C22×C4×D11C2311yescharacteristic
101C22×Dic22C2311yescharacteristic
102C2×C11×D8—24no—
103C2×C11×D8—42no—
104C2×C11×D8C2314yes—
105C2×C11×D8C2314yes—
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×#121—22no—
109C11×#121C2314yes—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112#67006—28no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—28no—
122C2×C22⋊Dic11D411yescharacteristic
123#66992—28no—
124#66991—28no—
125#66991—22no—
126#66991—22no—
127#66991C2314yes—
128#66991C2314yescomplemented
129#66989—22no—
130#66989C2314yes—
131#66988—28no—
132#66988—28no—
133D4×Dic11—22no—
134D4×Dic11—22no—
135D4×Dic11C2314yes—
136D4×Dic11C2314yescomplemented
137C2×#4324—42no—
138C2×#4324C2314yescomplemented
139C4×C22⋊D11D414yes—
140C4×C22⋊D11C2314yes—
141C2×(C2×D11)⋊C4D411yescharacteristic
142#66979—22no—
143#66979C2314yes—
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11C2311yescharacteristic
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⋊C4D411yescharacteristic
154C2×C4×Dic11—21no—
155C2×C4×Dic11C2311yescharacteristic
156C2×#4318—42no—
157C2×#4318C2314yes—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×#4313—42no—
161C2×#4313C2314yescomplemented
162C4⋊C4×D11—22no—
163C4⋊C4×D11C2314yescomplemented
164#66943—22no—
165#66943C2314yescomplemented
166(C22⋊D11)⋊C4—28no—
167#66932—28no—
168C11×#102C2314yes—
169C11×#102C2314yes—
170C11×C22⋊C8C2314yes—
171#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yescomplemented
176(C2×D11)⋊C8C2314yescomplemented
177#66882C2314yescomplemented
178#66881C2314yescomplemented
179#66880C2314yescomplemented
180#66880C2314yescomplemented
181Dic11⋊C8C2314yescomplemented
182C8×Dic11C2314yescomplemented
183#66874C2314yescomplemented
184#66871C2314yescomplemented
185C2×#3322—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—24no—
190C24×C11—44no—
191C24×C11—44no—
192C24×C11—82no—
193C24×C11C2×D411yescharacteristic
194C23×D11C2×D411yescharacteristic
195C2×D4×C11—28no—
196C2×D4×C11—24no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—24no—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—22no—
206C2×D4×C11—44no—
207C2×D4×C11—48no—
208C2×D4×C11—44no—
209C2×D4×C11—82no—
210C2×D4×C11#4114yes—
211C2×D4×C11C2412yes—
212C2×D4×C11C2412yes—
213C2×D4×C11C2412yes—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
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—42no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11C2×D414yes—
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—24no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—44no—
237C22×Dic11—82no—
238C22×Dic11—82no—
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241C22×Dic11C2×D411yescharacteristic
242#4341—28no—
243#4341—44no—
244#4341—48no—
245C2×C4×D11—24no—
246C2×C4×D11—22no—
247C2×C4×D11—22no—
248C2×C4×D11—82no—
249C2×C4×D11C2×D412yes—
250C2×C4×D11C2412yes—
251C2×Dic22—21no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22C2412yes—
255C11×D8—28no—
256C11×D8—44no—
257C2×C8×C11—22no—
258C2×C8×C11—22no—
259C2×C8×C11C2412yes—
260C2×C8×C11C2412yes—
261C11×C4⋊C4—21no—
262C11×C4⋊C4C2412yes—
263C11×C22⋊C4—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—24no—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272C22⋊Dic11C2×D414yes—
273#4324—44no—
274(C2×D11)⋊C4C2×D414yes—
275C4⋊Dic11—24no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11C2412yes—
280C4⋊Dic11C2412yes—
281C4⋊Dic11C2412yes—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4C2×D414yes—
286C4×Dic11—24no—
287C4×Dic11C2×D412yes—
288C4×Dic11C2412yes—
289#4318—44no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294#4313—44no—
295C2×#553—111no—
296C2×#546—111no—
297#3322—1116no—
298C2×#488—111no—
299C2×#485—111no—
300C2×#480—111no—
301C2×#478—111no—
302C2×#469—111no—
303C2×#468—111no—
304C2×#463—111no—
305C2×#449—111no—
306C2×#447D1111yescharacteristic, complemented
307C2×C4×D8—111no—
308C2×#436—111no—
309C2×#417—111no—
310C2×#418—111no—
311C23×C11—24no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—48no—
319C23×C11—48no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—84no—
329C23×C11—816no—
330C23×C11C22×D412yes—
331C23×C11C22×D411yescharacteristic
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11C22×D412yes—
336D4×C11—24no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—48no—
343D4×C11—42no—
344D4×C11—42no—
345D4×C11—84no—
346D4×C11C2×#4114yes—
347C2×C4×C11—22no—
348C2×C4×C11—24no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—42no—
353C2×C4×C11C22×D412yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4112yes—
356C2×C4×C11H(5,𝔽2)12yes—
357C2×C4×C11C2511yescharacteristic
358C22⋊D11—44no—
359C22⋊D11—48no—
360C22⋊D11—48no—
361C22⋊D11—84no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—48no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11—84no—
375C2×Dic11—84no—
376C2×Dic11C22×D412yes—
377C2×Dic11C22×D412yes—
378C2×Dic11C22×D412yes—
379C4×D11—24no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—84no—
383Dic22—22no—
384Dic22—22no—
385Dic22—42no—
386C8×C11—22no—
387C8×C11—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41—111no—
391C23×D4C2×D1111yescharacteristic
392C22×SD16—111no—
393C22×D8C2×D1111yescharacteristic
394C22×D8C2×D1111yescharacteristic
395C22×M16—111no—
396C22×M16—111no—
397#553—118no—
398#553—224no—
399#546—118no—
400#546—224no—
401C2×#126—221no—
402C2×#125—111no—
403C2×#124—111no—
404C2×#123—221no—
405C2×#123—221no—
406C2×C22⋊Q8—111no—
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#121—221no—
411C2×#121C2×D1111yescharacteristic
412C2×#120—221no—
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—111no—
416C2×C4×D4—221no—
417C2×#117—111no—
418C22×C4⋊C4—111no—
419C22×C22⋊C4—221no—
420#488—118no—
421#485—118no—
422#480—118no—
423#478—118no—
424#469—118no—
425#468—118no—
426#463—118no—
427#449—118no—
428#447C2×D1118yescomplemented
429C4×D8—118no—
430#436—118no—
431C2×#107—111no—
432C2×#107—111no—
433C2×#106—111no—
434C2×C4⋊C8—111no—
435#418—118no—
436#417—118no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103—111no—
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⋊C8C2×D1111yescharacteristic
449C2×C4×C8—111no—
450C22×C11—22no—
451C22×C11—24no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—44no—
455C22×C11—48no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—816no—
465C22×C11—84no—
466C22×C11—84no—
467C22×C11#54612yes—
468C22×C11#57512yes—
469C22×C11#57612yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—44no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11#54612yes—
478C4×C11C22×#4111yescharacteristic
479C4×C11C2×H(5,𝔽2)11yescharacteristic
480Dic11—22no—
481Dic11—22no—
482Dic11—22no—
483Dic11—42no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487C25—21no—
488C2×#41—114no—
489C2×#41—222no—
490C2×#41—224no—
491C2×#41—442no—
492C22×Q8—111no—
493C22×D4—24no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—42no—
498C22×D4—111no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4C22×D1111yescharacteristic
503C22×D4C22×D1111yescharacteristic
504C22×D4C22×D1114yes—
505C22×D4C22×D1111yescharacteristic
506C23×C4—111no—
507C23×C4—221no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—442no—
514C2×D8—24no—
515C2×D8—42no—
516C2×D8C22×D1114yes—
517C2×D8C22×D1114yes—
518C2×M16—114no—
519C2×M16—114no—
520C2×M16—442no—
521C2×M16—442no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8C22×D1111yescharacteristic
525C22×C8C22×D1111yescharacteristic
526#126—228no—
527#125—114no—
528#125—222no—
529#124—114no—
530#124—222no—
531#123—228no—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—222no—
535#121—22no—
536#121—114no—
537#121—114no—
538#121—228no—
539#121—222no—
540#121—222no—
541#121—228no—
542#121C22×D1114yes—
543#120—228no—
544C4×D4—114no—
545C4×D4—114no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—222no—
549C4×D4—222no—
550C4×D4—228no—
551#117—114no—
552#117—222no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—222no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4C22×D1111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—111no—
566C2×C22⋊C4—111no—
567C2×C22⋊C4—228no—
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×C22⋊C4—221no—
576C2×C42—111no—
577C2×C42—221no—
578#107—114no—
579#107—114no—
580#106—114no—
581C4⋊C8—114no—
582#103—114no—
583#103—114no—
584#103—114no—
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⋊C8C22×D1114yes—
594C4×C8—114no—
595C2×C11—42no—
596C2×C11—44no—
597C2×C11—82no—
598C2×C11—82no—
599C2×C11#332214yescomplemented
600C2×C11C2×#54611yescharacteristic
601C2×C11C2×#57511yescharacteristic
602C2×C11C2×#57611yescharacteristic
603D11—42no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—44no—
609C24—44no—
610C24—82no—
611C24—111no—
612C24D4×D1111yescharacteristic
613#41—228no—
614#41—444no—
615#41—448no—
616C2×Q8—112no—
617C2×Q8—221no—
618C2×Q8—222no—
619C2×Q8—222no—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—44no—
632C2×D4—48no—
633C2×D4—44no—
634C2×D4—82no—
635C2×D4—114no—
636C2×D4—224no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—442no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—882no—
643C2×D4#434114yes—
644C2×D4C23×D1112yes—
645C2×D4C23×D1112yes—
646C2×D4C23×D1112yes—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—21no—
650C22×C4—111no—
651C22×C4—111no—
652C22×C4—111no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—224no—
656C22×C4—224no—
657C22×C4—224no—
658C22×C4—224no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—444no—
666C22×C4—882no—
667C22×C4—882no—
668C22×C4—882no—
669C22×C4D4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—444no—
674D8—28no—
675D8—44no—
676M16—444no—
677M16—444no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8C23×D1112yes—
685C2×C8C23×D1112yes—
686C4⋊C4—21no—
687C4⋊C4—114no—
688C4⋊C4—112no—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—224no—
698C4⋊C4C23×D1112yes—
699C22⋊C4—24no—
700C22⋊C4—114no—
701C22⋊C4—114no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—224no—
710C42—112no—
711C42—112no—
712C42—224no—
713C11C2×#332211yescharacteristic, complemented, Sylow
714C23—22no—
715C23—22no—
716C23—22no—
717C23—24no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—48no—
722C23—48no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—84no—
732C23—816no—
733C23—112no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23C2×D4×D1112yes—
738C23C2×D4×D1111yescharacteristic
739Q8—222no—
740Q8—222no—
741Q8—442no—
742D4—24no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—22no—
747D4—22no—
748D4—48no—
749D4—42no—
750D4—42no—
751D4—84no—
752D4—444no—
753D4—448no—
754D4—448no—
755D4—884no—
756D4C2×#434114yes—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—42no—
763C2×C4—112no—
764C2×C4—112no—
765C2×C4—112no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—224no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—448no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4—442no—
781C2×C4—884no—
782C2×C4—884no—
783C2×C4—884no—
784C2×C4C2×D4×D1112yes—
785C2×C4C2×D4×D1111yescharacteristic
786C2×C4C2×#434112yes—
787C2×C4#6703712yes—
788C2×C4C24×D1111yescharacteristic
789C8—22no—
790C8—22no—
791C8—222no—
792C8—222no—
793C22—22no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—48no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—816no—
808C22—84no—
809C22—84no—
810C22—222no—
811C22—222no—
812C22—222no—
813C22—444no—
814C22#1062312212yes—
815C22#1062328812yes—
816C22#1062330412yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—42no—
820C4—222no—
821C4—222no—
822C4—222no—
823C4—442no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4#1062312212yes—
828C4C22×#434111yescharacteristic
829C4C2×#6703711yescharacteristic
830C2—42no—
831C2—44no—
832C2—82no—
833C2—82no—
834C2—442no—
835C2#1308082114yesdirect product factor
836C2C2×#1062312211yescharacteristic
837C2C2×#1062330411yescharacteristic
838C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC23×C11C22×D4
hypercenterC2×#447D11
hypocenterC11C2×#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#10623145C2semidirect
2. C2×#10623337C2semidirect
3. #13080821C2direct (N × H)
4. C2×#10622381C2semidirect
5. C2×#10622336C2semidirect
6. C2×#10622387C2semidirect
7. C2×#10622376C2semidirect
8. C2×#10622772C2semidirect
9. C2×#10622655C2semidirect
10. C2×#10622766C2semidirect
11. C2×#10622771C2semidirect
12. C2×D8×Dic11C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622384C2semidirect
15. C2×#10622828C2semidirect
16. C2×C11×#447C2semidirect
25. #10623337C22semidirect
29. C2×#66991C22semidirect
34. C2×D4×Dic11C22semidirect
35. C22×#4324C22semidirect
40. C22×#4313C22semidirect
42. #10623145C22semidirect
43. C2×C4⋊C4×D11C22semidirect
44. C2×#66943C22semidirect
47. C11×#447C22semidirect
51. #10622828C22semidirect
56. C2×#66896C22semidirect
57. #10622772C22semidirect
58. #10622771C22semidirect
59. #10622766C22semidirect
60. D8×Dic11C22semidirect
61. C2×(C2×D11)⋊C8C22semidirect
62. C2×#66882C22semidirect
63. C2×#66881C22semidirect
64. C2×#66880C22semidirect
65. C2×#66880C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×C8×Dic11C22semidirect
68. #10622655C22semidirect
69. C2×#66874C22semidirect
70. C2×#66871C22semidirect
71. #10622387C22semidirect
72. #10622384C22semidirect
73. #10622381C22semidirect
74. #10622376C22semidirect
75. #10622342C22semidirect
76. #10622336C22semidirect
128. #66991C23semidirect
136. D4×Dic11C23semidirect
138. C2×#4324C23semidirect
161. C2×#4313C23semidirect
163. C4⋊C4×D11C23semidirect
165. #66943C23semidirect
175. #66896C23semidirect
176. (C2×D11)⋊C8C23semidirect
177. #66882C23semidirect
178. #66881C23semidirect
179. #66880C23semidirect
180. #66880C23semidirect
181. Dic11⋊C8C23semidirect
182. C8×Dic11C23semidirect
183. #66874C23semidirect
184. #66871C23semidirect
306. C2×#447D11semidirect
428. #447C2×D11semidirect
599. C2×C11#3322semidirect
713. C11C2×#3322semidirect
835. C2#13080821direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231452
C2×#106233372
#130808212
C2×#106223812
C2×#106223362
C2×#106223872
C2×#106223762
C2×#106227722
C2×#106226552
C2×#106227662
C2×#106227712
C2×D8×Dic112
C2×#106223422
C2×#106223842
C2×#106228282
C2×C11×#4472
C2×#332211