Finite Group Databasebeta

← C4×#10622396 #14759405

Subgroups — C4×#10622396 #14759405

Order 2816.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C2×#10622396C211yesmaximal, characteristic
3C2×C4×Dic44C211yesmaximal, characteristic, complemented
4C2×C4×#4324C211yesmaximal, characteristic, complemented
5C4×#66950C211yesmaximal, characteristic, complemented
6#13068958C211yesmaximal, characteristic, complemented
7#13068948C211yesmaximal, characteristic, complemented
8#13068927C211yesmaximal, characteristic, complemented
9#13068885C211yesmaximal, characteristic, complemented
10#13068865C211yesmaximal, characteristic, complemented
11#13068818C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic
13C4×#66874C211yesmaximal, characteristic, complemented
14C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C22×C4×Dic11—21no—
22C22×Dic44C2211yescharacteristic
23C4×#4341—24no—
24C4×#4341—24no—
25C2×#66950C2211yescharacteristic
26C2×#66945C2211yescharacteristic
27C2×#66940C2211yescharacteristic
28C2×(C22⋊D11)⋊C4—21no—
29C2×#66930—21no—
30C2×C42×D11C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×#66882C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C4×#4324—24no—
44#10622600C2211yescharacteristic
45#10622598C2211yescharacteristic
46#10622587C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C4×(C2×D11)⋊C4—21no—
52C4×C4⋊Dic11—21no—
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622396C418yesdirect product factor
55C4×Dic44—24no—
56#10622281—21no—
57#10622266—21no—
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C22×C22⋊D11—21no—
67C23×Dic11—21no—
68C23×Dic11—21no—
69C2×#4341—22no—
70C2×#4341—22no—
71C2×#4341—22no—
72C2×#4341—22no—
73C2×#4341—22no—
74C2×#4341C2×C414yes—
75C22×C4×D11D411yescharacteristic
76C22×C4×D11D411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×Dic22C2311yescharacteristic
79C22×Dic22C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C4×D4×C11—22no—
83C4×D4×C11D414yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—21no—
91D4×Dic11—22no—
92D4×Dic11—22no—
93C2×#4324—22no—
94C2×#4324—22no—
95C2×#4324C2×C414yescomplemented
96C4×C22⋊D11—28no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11—28no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11D411yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×Dic44—22no—
118C2×Dic44—22no—
119C2×Dic44C2×C414yescomplemented
120#66950—22no—
121#66950C2×C414yescomplemented
122#66945—22no—
123#66945—22no—
124#66940—22no—
125#66940—22no—
126(C22⋊D11)⋊C4—28no—
127#66930—28no—
128C42×D11—22no—
129C42×D11—22no—
130C4×Dic22—22no—
131C4×Dic22—22no—
132C4×Dic22—22no—
133C4×Dic22D414yes—
134C11×#102—22no—
135C11×#102C2×C414yescomplemented
136C4×C8×C11—22no—
137C11×#95—21no—
138#66896—22no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143(C2×D11)⋊C8—22no—
144(C2×D11)⋊C8C2×C414yescomplemented
145#66882—22no—
146#66880—22no—
147#66880—22no—
148#66874—22no—
149#66874—22no—
150#66874C2×C414yescomplemented
151#66872—22no—
152C4×C11⋊C8—22no—
153C4×#452—111nomaximal, Sylow
154C24×C11—21no—
155C23×D11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11C22×C412yes—
160C2×D4×C11C2×D412yes—
161C2×D4×C11#4112yes—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—24no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C2×C22⋊D11—24no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187#4341—28no—
188#4341—28no—
189#4341—28no—
190#4341—28no—
191C2×C4×D11—22no—
192C2×C4×D11—22no—
193C2×C4×D11—22no—
194C2×C4×D11—22no—
195C2×C4×D11—22no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—41no—
201C2×C4×D11C22×C412yes—
202C2×C4×D11#4112yes—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22C22×C412yes—
212C2×Dic22C22×C412yes—
213C2×Dic22C2×D412yes—
214C2×Dic22#4112yes—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—21no—
220C2×C8×C11C22×C412yes—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4C22×C412yes—
226C11×C4⋊C4C2×D412yes—
227C11×C22⋊C4—24no—
228C42×C11—42no—
229C42×C11C2×D412yes—
230C42×C11C2×D412yes—
231C22⋊Dic11—24no—
232#4324—28no—
233(C2×D11)⋊C4—24no—
234(C2×D11)⋊C4—24no—
235(C2×D11)⋊C4—42no—
236C4⋊Dic11—24no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—42no—
241C4⋊Dic11C2×D412yes—
242Dic11⋊C4—24no—
243Dic11⋊C4—24no—
244Dic11⋊C4—42no—
245C4×Dic11—24no—
246C4×Dic11—24no—
247C4×Dic11—24no—
248C4×Dic11—22no—
249C4×Dic11—22no—
250C4×Dic11—21no—
251C4×Dic11—21no—
252C4×Dic11—42no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8C22×C412yes—
259Dic44—28no—
260C2×C4×#41—111no—
261C2×#452—111no—
262C2×C4×Q16—111no—
263C2×C4×SD16—111no—
264C4×C22⋊Q8—111no—
265#1878—111no—
266#1877—111no—
267#1873—111no—
268#1865—111no—
269#1862—111no—
270#1854—111no—
271#1788—111no—
272C4×#103—111no—
273C4×#102D1111yescharacteristic, complemented
274C4×C22⋊C8—111no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11C22×D411yescharacteristic
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11C4×D412yes—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—22no—
293D4×C11C4×D414yes—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—48no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11#12012yes—
307C2×C4×C11#12012yes—
308C2×C4×C11#13512yes—
309C2×C4×C11#13712yes—
310C2×C4×C11C23×C411yescharacteristic
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C22⋊D11—216no—
317C2×Dic11—216no—
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—22no—
326C2×Dic11—21no—
327C2×Dic11—22no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—48no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11C4×D412yes—
339C2×Dic11#13512yes—
340C4×D11—22no—
341C4×D11—22no—
342C4×D11—22no—
343C4×D11—22no—
344C4×D11—44no—
345C4×D11—44no—
346Dic22—22no—
347Dic22—22no—
348Dic22—22no—
349Dic22—22no—
350Dic22—22no—
351Dic22—41no—
352Dic22—41no—
353Dic22C4×D414yes—
354C8×C11—22no—
355C8×C11—41no—
356C11⋊C8—22no—
357C11⋊C8—41no—
358C22×#41—111no—
359C22×Q16—111no—
360C22×SD16—111no—
361C2×C22⋊Q8—111no—
362C4×#41—224no—
363C4×#41—224no—
364C2×C4×Q8—111no—
365C2×C4×Q8—111no—
366C2×C4×Q8—111no—
367C2×C4×D4—111no—
368C2×C4×D4—221no—
369C2×C4×D4—221no—
370C2×C4×D4C2×D1111yescharacteristic
371C2×#117—111no—
372C2×#117—221no—
373C22×C42—111no—
374C22×C42—221no—
375#452—118no—
376C4×Q16—224no—
377C4×SD16—224no—
378C2×#107—111no—
379C2×#106—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#103—111no—
384C2×#103—111no—
385C2×#102—111no—
386C2×#102C2×D1111yescharacteristic
387C2×#102C2×D1111yescharacteristic
388C2×C22⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C4×C8—111no—
391C2×C4×C8C2×D1111yescharacteristic
392#391—111no—
393#389—111no—
394#387—221no—
395#385—221no—
396#380—111no—
397C4×C4⋊C4—221no—
398C4×C4⋊C4C2×D1111yescharacteristic
399C4×C22⋊C4—221no—
400#340—111no—
401#340—111no—
402#340C2×D1111yescharacteristic
403#340C2×D1111yescharacteristic
404#336—111no—
405#336—111no—
406C22×C11—24no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C2×#12011yescharacteristic
415C22×C11#52511yescharacteristic
416C22×C11C2×#13511yescharacteristic
417C22×C11C2×#13511yescharacteristic
418C22×C11C2×#13711yescharacteristic
419C22×C11#57511yescharacteristic
420C2×D11—22no—
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—41no—
424C2×D11—41no—
425C2×D11—41no—
426C2×D11—41no—
427C4×C11—22no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—81no—
431C4×C11#45214yescomplemented
432C4×C11C2×C4×D411yescharacteristic
433C4×C11C2×C4×D411yescharacteristic
434C4×C11#52511yescharacteristic
435C4×C11#52511yescharacteristic
436Dic11—22no—
437Dic11—24no—
438Dic11—22no—
439Dic11—41no—
440Dic11—42no—
441Dic11—42no—
442Dic11—81no—
443C2×#41—114no—
444C2×#41—222no—
445C2×#41—222no—
446C2×#41—222no—
447C2×#41—222no—
448C2×#41—222no—
449C22×Q8—111no—
450C22×Q8—111no—
451C22×D4—221no—
452C22×D4C22×D1111yescharacteristic
453C23×C4—21no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—221no—
458C23×C4—221no—
459C2×Q16—114no—
460C2×Q16—222no—
461C2×Q16—222no—
462C2×SD16—114no—
463C2×SD16—222no—
464C2×SD16—222no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8C22×D1111yescharacteristic
468C22×C8C22×D1111yescharacteristic
469C22⋊Q8—114no—
470C22⋊Q8—222no—
471C4×Q8—114no—
472C4×Q8—222no—
473C4×Q8—222no—
474C4×Q8—222no—
475C4×Q8—222no—
476C4×Q8—222no—
477C4×D4—22no—
478C4×D4—228no—
479C4×D4—222no—
480C4×D4—228no—
481C4×D4—222no—
482C4×D4D4414yes—
483#117—228no—
484#117—222no—
485#117—222no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C42—21no—
502C2×C42—111no—
503C2×C42—111no—
504C2×C42—111no—
505C2×C42—221no—
506C2×C42—221no—
507C2×C42—228no—
508C2×C42—221no—
509C2×C42—222no—
510C2×C42—222no—
511C2×C42—221no—
512C2×C42C22×D1111yescharacteristic
513#107—222no—
514#106—222no—
515#103—114no—
516#103—222no—
517#103—222no—
518#103—222no—
519#103—222no—
520#102—22no—
521#102—222no—
522#102C4×D1114yescomplemented
523C22⋊C8—114no—
524C22⋊C8—222no—
525C4×C8—22no—
526C4×C8—222no—
527#95—21no—
528#95—221no—
529#95—221no—
530#95—221no—
531#95—221no—
532C2×C11—44no—
533C2×C11C4×#12011yescharacteristic
534C2×C11C4×#13511yescharacteristic
535C2×C11C4×#13711yescharacteristic
536C2×C11C2×#45211yescharacteristic
537C2×C11#300211yescharacteristic
538C2×C11#310211yescharacteristic
539C2×C11#310711yescharacteristic
540D11—42no—
541C24—21no—
542C24—111no—
543#41—228no—
544#41—228no—
545#41—228no—
546#41—228no—
547C2×Q8—112no—
548C2×Q8—112no—
549C2×Q8—112no—
550C2×Q8—112no—
551C2×Q8—221no—
552C2×Q8—221no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—221no—
557C2×Q8—221no—
558C2×Q8—221no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—224no—
563C2×D4—224no—
564C2×D4—224no—
565C2×D4C2×C4×D1112yes—
566C2×D4C2×D4412yes—
567C2×D4#433912yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—111no—
579C22×C4—222no—
580C22×C4—224no—
581C22×C4—224no—
582C22×C4—224no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—224no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—221no—
596C22×C4—441no—
597C22×C4—442no—
598C22×C4—442no—
599C22×C4D4×D1111yescharacteristic
600C22×C4D4×D1111yescharacteristic
601C22×C4C23×D1111yescharacteristic
602Q16—228no—
603SD16—228no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—112no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8C2×C4×D1112yes—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—112no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—221no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—442no—
628C4⋊C4—442no—
629C4⋊C4C2×C4×D1112yes—
630C4⋊C4C2×D4412yes—
631C22⋊C4—24no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—442no—
636C42—42no—
637C42—224no—
638C42—224no—
639C42—222no—
640C42—222no—
641C42—224no—
642C42—221no—
643C42—221no—
644C42—442no—
645C42C2×D4412yes—
646C42D4×D1112yes—
647C11C4×#45211yescharacteristic, complemented, Sylow
648C23—22no—
649C23—22no—
650C23—22no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—112no—
656C23—221no—
657C23—221no—
658C23—221no—
659C23—221no—
660C23—221no—
661C23—221no—
662C23C2×D4×D1111yescharacteristic
663Q8—114no—
664Q8—222no—
665Q8—222no—
666Q8—222no—
667Q8—222no—
668Q8—222no—
669Q8—441no—
670Q8—441no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—2216no—
675D4C4×D4414yes—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—48no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—112no—
689C2×C4—112no—
690C2×C4—2216no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—222no—
694C2×C4—221no—
695C2×C4—222no—
696C2×C4—221no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—221no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—222no—
707C2×C4—444no—
708C2×C4—448no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—444no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4#6693512yes—
718C2×C4#6693512yes—
719C2×C4#6696512yes—
720C2×C4#6696812yes—
721C2×C4C22×C4×D1111yescharacteristic
722C2×C4C22×D4411yescharacteristic
723C2×C4C2×#433911yescharacteristic
724C2×C4C2×D4×D1111yescharacteristic
725C2×C4#41×D1111yescharacteristic
726C2×C4#41×D1111yescharacteristic
727C8—22no—
728C8—41no—
729C8—222no—
730C8—441no—
731C22—24no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—222no—
739C22—222no—
740C22—222no—
741C22—441no—
742C22—441no—
743C22—441no—
744C22—441no—
745C22C2×#6693511yescharacteristic
746C22C4×D4×D1111yescharacteristic
747C22#1062307811yescharacteristic
748C22C2×#6696511yescharacteristic
749C22C2×#6696811yescharacteristic
750C22D11×#13511yescharacteristic
751C22#1062329911yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—81no—
756C4—222no—
757C4—224no—
758C4—222no—
759C4—442no—
760C4—441no—
761C4—442no—
762C4—881no—
763C4#1062239614yesdirect product factor
764C4C2×C4×D4411yescharacteristic
765C4#1062305511yescharacteristic
766C4C4×D4×D1111yescharacteristic
767C4#1062307811yescharacteristic
768C2—44no—
769C2—442no—
770C2C4×#6693511yescharacteristic
771C2C4×#6696511yescharacteristic
772C2C4×#6696811yescharacteristic
773C2C2×#1062239611yescharacteristic
774C2#1307783611yescharacteristic
775C2#1307863011yescharacteristic
776C2#1307868311yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11C4×#452
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic44C2semidirect
4. C2×C4×#4324C2semidirect
5. C4×#66950C2semidirect
6. #13068958C2semidirect
7. #13068948C2semidirect
8. #13068927C2semidirect
9. #13068885C2semidirect
10. #13068865C2semidirect
11. #13068818C2semidirect
13. C4×#66874C2semidirect
14. C4×(C2×D11)⋊C8C2semidirect
15. C4×C11×#102C2semidirect
54. #10622396C4direct (N × H)
95. C2×#4324C2×C4semidirect
119. C2×Dic44C2×C4semidirect
121. #66950C2×C4semidirect
135. C11×#102C2×C4semidirect
144. (C2×D11)⋊C8C2×C4semidirect
150. #66874C2×C4semidirect
273. C4×#102D11semidirect
431. C4×C11#452semidirect
522. #102C4×D11semidirect
647. C11C4×#452semidirect
763. C4#10622396direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C2×#106223962
C2×C4×Dic442
C2×C4×#43242
C4×#669502
#130689582
#130689482
#130689272
#130688852
#130688652
#130688182
#130685532
C4×#668742
C4×(C2×D11)⋊C82
C4×C11×#1022
C4×#45211