Finite Group Databasebeta

← C4×#11718900 #15868549

Subgroups — C4×#11718900 #15868549

Order 3328.

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×#11718900C211yesmaximal, characteristic
2C2×C4×#6107C211yesmaximal, characteristic, complemented
3C2×C4×#6105C211yesmaximal, characteristic, complemented
4C4×#88178C211yesmaximal, characteristic, complemented
5#13115177C211yesmaximal, characteristic, complemented
6#13115170C211yesmaximal, characteristic, complemented
7#13115148C211yesmaximal, characteristic, complemented
8#13115104C211yesmaximal, characteristic, complemented
9#13115083C211yesmaximal, characteristic, complemented
10#13115035C211yesmaximal, characteristic, complemented
11#13114776C211yesmaximal, characteristic
12C4×#88075C211yesmaximal, characteristic, complemented
13C4×#88072C211yesmaximal, characteristic, complemented
14C4×C22⋊#1055C211yesmaximal, characteristic, complemented
15C2×C4×C13×#41C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C4×C13×#41—24no—
18C4×C13×#41—24no—
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13—21no—
22C2×C4×D4×C13—21no—
23C2×C4×D4×C13C2211yescharacteristic
24C2×C4×D4×C13C2211yescharacteristic
25C2×C13×#117—21no—
26C2×C13×#117C2211yescharacteristic
27C22×C42×C13—21no—
28C22×C42×C13C2211yescharacteristic
29C22×#6107C2211yescharacteristic
30C22×#6105C2211yescharacteristic
31C2×#88178C2211yescharacteristic
32C2×C4×Dic26C2211yescharacteristic
33#11718900C418yesdirect product factor
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40#11718873C2211yescharacteristic
41#11718871—21no—
42C4×C22⋊Dic13—21no—
43C2×C22⋊#1055C2211yescharacteristic
44C2×C22⋊#1055C2211yescharacteristic
45C4×#6107—24no—
46C4×#6105—24no—
47C2×#88050C2211yescharacteristic
48C2×#88050C2211yescharacteristic
49C2×#88048C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51C4×C4⋊Dic13C2211yescharacteristic
52#11718594—21no—
53C4×#6101—21no—
54#11718590C2211yescharacteristic
55#11718589C2211yescharacteristic
56C2×C4×#1055C2211yescharacteristic
57C2×C4×#1055C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718116C2211yescharacteristic
63#11718116C2211yescharacteristic
64C2×C13×#41—22no—
65C2×C13×#41—22no—
66C2×C13×#41—22no—
67C2×C13×#41—22no—
68C2×C13×#41—22no—
69C2×C13×#41C2×C414yes—
70C22×Q8×C13C2311yescharacteristic
71C22×D4×C13—21no—
72C22×D4×C13C2311yescharacteristic
73C23×C4×C13—21no—
74C23×C4×C13—21no—
75C23×C4×C13—21no—
76C23×C4×C13D411yescharacteristic
77C23×C4×C13D411yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×Dic26C2311yescharacteristic
80C4×Q8×C13—22no—
81C4×Q8×C13—22no—
82C4×Q8×C13—22no—
83C4×Q8×C13D414yes—
84C4×D4×C13—28no—
85C4×D4×C13—28no—
86C4×D4×C13—22no—
87C4×D4×C13—22no—
88C4×D4×C13—22no—
89C4×D4×C13D414yes—
90C13×#117—28no—
91C13×#117—22no—
92C13×#117—22no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C42×C13—28no—
101C2×C42×C13—21no—
102C2×C42×C13—21no—
103C2×C42×C13—21no—
104C2×C42×C13—22no—
105C2×C42×C13—22no—
106C2×C42×C13D411yescharacteristic
107C2×C42×C13D411yescharacteristic
108C2×C42×C13C2311yescharacteristic
109C2×C42×C13C2311yescharacteristic
110C2×C22⋊Dic13—21no—
111C2×C22⋊Dic13—21no—
112C2×#6107—22no—
113C2×#6107—22no—
114C2×#6107C2×C414yescomplemented
115C2×#6105—22no—
116C2×#6105—22no—
117C2×#6105C2×C414yescomplemented
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4⋊Dic13C2311yescharacteristic
121#88178—22no—
122#88178C2×C414yescomplemented
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C4×Dic26—22no—
133C4×Dic26—22no—
134#88075—22no—
135#88075—22no—
136#88075C2×C414yescomplemented
137#88072—22no—
138#88072—22no—
139#88072C2×C414yescomplemented
140#88071—21no—
141#88071—21no—
142#88071—21no—
143#88071—21no—
144#88071—21no—
145C22⋊#1055—22no—
146C22⋊#1055C2×C414yescomplemented
147#88050—22no—
148#88050—22no—
149#88048—22no—
150#88047—22no—
151C4×#1055—22no—
152C4×#1055—22no—
153C4×#452—131nomaximal, Sylow
154C24×C13—21no—
155C24×C13C2×D411yescharacteristic
156C13×#41—28no—
157C13×#41—28no—
158C13×#41—28no—
159C13×#41—28no—
160C2×Q8×C13—21no—
161C2×Q8×C13—21no—
162C2×Q8×C13—21no—
163C2×Q8×C13C22×C412yes—
164C2×Q8×C13C2×D412yes—
165C2×Q8×C13#4112yes—
166C2×D4×C13—24no—
167C2×D4×C13—24no—
168C2×D4×C13—24no—
169C2×D4×C13—21no—
170C2×D4×C13—21no—
171C2×D4×C13—21no—
172C2×D4×C13C22×C412yes—
173C2×D4×C13C2×D412yes—
174C2×D4×C13#4112yes—
175C22×C4×C13—24no—
176C22×C4×C13—24no—
177C22×C4×C13—21no—
178C22×C4×C13—24no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—24no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—22no—
187C22×C4×C13—22no—
188C22×C4×C13—24no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—22no—
192C22×C4×C13—41no—
193C22×C4×C13—42no—
194C22×C4×C13—42no—
195C22×C4×C13—42no—
196C22×C4×C13—42no—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D411yescharacteristic
202C22×C4×C13C2×D411yescharacteristic
203C22×C4×C13#4112yes—
204C22×C4×C13C2411yescharacteristic
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C2×Dic26—21no—
210C2×Dic26—21no—
211C2×Dic26—21no—
212C2×Dic26—21no—
213C2×Dic26—21no—
214C2×Dic26C22×C412yes—
215C13×C4⋊C4—24no—
216C13×C4⋊C4—24no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4C2×D412yes—
220C13×C4⋊C4C2×D412yes—
221C13×C22⋊C4—24no—
222C13×C22⋊C4—24no—
223C13×C22⋊C4—24no—
224C42×C13—24no—
225C42×C13—24no—
226C42×C13—22no—
227C42×C13—24no—
228C42×C13—22no—
229C42×C13—21no—
230C42×C13—21no—
231C42×C13C2×D412yes—
232C42×C13C2×D412yes—
233C22⋊Dic13—24no—
234C22⋊Dic13—42no—
235#6107—28no—
236#6105—28no—
237C4⋊Dic13—21no—
238C4⋊Dic13—21no—
239C4⋊Dic13—21no—
240C4⋊Dic13—21no—
241C4⋊Dic13—21no—
242C4⋊Dic13C22×C412yes—
243#6101—24no—
244#6101—42no—
245#6101—42no—
246C4×Dic13—42no—
247C4×Dic13—42no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055—21no—
251C2×#1055—21no—
252C2×#1055—21no—
253C2×#1055—21no—
254C2×#1055—21no—
255C2×#1055—21no—
256C2×#1055—21no—
257C2×#1055—21no—
258C2×#1055C22×C412yes—
259C2×#1055C22×C412yes—
260C2×C4×#41D1311yescharacteristic
261C2×#452—131no—
262C2×C4×Q16—131no—
263C2×C4×SD16—131no—
264C4×C22⋊Q8—131no—
265#1878—131no—
266#1877—131no—
267#1873—131no—
268#1865—131no—
269#1862—131no—
270#1854—131no—
271#1788—131no—
272C4×#103—131no—
273C4×#102—131no—
274C4×C22⋊C8—131no—
275C23×C13—22no—
276C23×C13—21no—
277C23×C13—22no—
278C23×C13—21no—
279C23×C13—22no—
280C23×C13—21no—
281C23×C13—21no—
282C23×C13—21no—
283C23×C13—21no—
284C23×C13—41no—
285C23×C13—41no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13C4×D412yes—
289C23×C13C22×D411yescharacteristic
290Q8×C13—22no—
291Q8×C13—22no—
292Q8×C13—22no—
293Q8×C13C4×D414yes—
294D4×C13—216no—
295D4×C13—22no—
296D4×C13—22no—
297D4×C13—22no—
298D4×C13C4×D414yes—
299C2×C4×C13—216no—
300C2×C4×C13—22no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—22no—
304C2×C4×C13—21no—
305C2×C4×C13—22no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—21no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—44no—
319C2×C4×C13—48no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—44no—
325C2×C4×C13—48no—
326C2×C4×C13C4×D412yes—
327C2×C4×C13#12012yes—
328C2×C4×C13#12012yes—
329C2×C4×C13#13512yes—
330C2×C4×C13#13512yes—
331C2×C4×C13#13712yes—
332C2×C4×C13C23×C411yescharacteristic
333C2×C4×C13C22×D411yescharacteristic
334C2×C4×C13C22×D411yescharacteristic
335C2×C4×C13C2×#4111yescharacteristic
336C2×C4×C13C2×#4111yescharacteristic
337C2×C4×C13C2×#4111yescharacteristic
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350Dic26—22no—
351Dic26—22no—
352Dic26—41no—
353Dic26—41no—
354#1055—22no—
355#1055—22no—
356#1055—41no—
357#1055—41no—
358C22×#41C2×D1311yescharacteristic
359C22×Q16—131no—
360C22×SD16—131no—
361C2×C22⋊Q8—131no—
362C4×#41—24no—
363C4×#41—24no—
364C2×C4×Q8—131no—
365C2×C4×Q8C2×D1311yescharacteristic
366C2×C4×Q8C2×D1311yescharacteristic
367C2×C4×D4—21no—
368C2×C4×D4—21no—
369C2×C4×D4C2×D1311yescharacteristic
370C2×C4×D4C2×D1311yescharacteristic
371C2×#117—21no—
372C2×#117C2×D1311yescharacteristic
373C22×C42—21no—
374C22×C42C2×D1311yescharacteristic
375#452—138no—
376C4×Q16—264no—
377C4×SD16—264no—
378C2×#107—131no—
379C2×#106—131no—
380C2×#103—131no—
381C2×#103—131no—
382C2×#103—131no—
383C2×#103—131no—
384C2×#103—131no—
385C2×#102—131no—
386C2×#102—131no—
387C2×#102—131no—
388C2×C22⋊C8—131no—
389C2×C22⋊C8—131no—
390C2×C4×C8—131no—
391C2×C4×C8—131no—
392#391—131no—
393#389—131no—
394#387—261no—
395#385—261no—
396#380—131no—
397C4×C4⋊C4—131no—
398C4×C4⋊C4—261no—
399C4×C22⋊C4—261no—
400#340—131no—
401#340—131no—
402#340—131no—
403#340—131no—
404#336—131no—
405#336—131no—
406C22×C13—22no—
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—24no—
410C22×C13—41no—
411C22×C13—42no—
412C22×C13—41no—
413C22×C13—42no—
414C22×C13—42no—
415C22×C13—42no—
416C22×C13—41no—
417C22×C13—42no—
418C22×C13—41no—
419C22×C13—42no—
420C22×C13C2×C4×D411yescharacteristic
421C22×C13C2×#12011yescharacteristic
422C22×C13#52511yescharacteristic
423C22×C13C2×#13511yescharacteristic
424C22×C13C2×#13511yescharacteristic
425C22×C13C2×#13711yescharacteristic
426C22×C13#57511yescharacteristic
427C4×C13—22no—
428C4×C13—22no—
429C4×C13—22no—
430C4×C13—24no—
431C4×C13—41no—
432C4×C13—42no—
433C4×C13—42no—
434C4×C13#45214yescomplemented
435C4×C13C2×C4×D411yescharacteristic
436C4×C13C2×C4×D411yescharacteristic
437C4×C13#52511yescharacteristic
438C4×C13#52511yescharacteristic
439Dic13—42no—
440Dic13—42no—
441Dic13—81no—
442Dic13—81no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41C4×D1314yes—
449C22×Q8—131no—
450C22×Q8C22×D1311yescharacteristic
451C22×D4—21no—
452C22×D4C22×D1311yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4—21no—
456C23×C4C22⋊D1311yescharacteristic
457C23×C4C22⋊D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C2×Q16—134no—
460C2×Q16—262no—
461C2×Q16—262no—
462C2×SD16—134no—
463C2×SD16—262no—
464C2×SD16—262no—
465C22×C8—131no—
466C22×C8—131no—
467C22×C8—131no—
468C22×C8—131no—
469C22⋊Q8—134no—
470C22⋊Q8—262no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—262no—
475C4×Q8—262no—
476C4×Q8C22⋊D1314yes—
477C4×D4—28no—
478C4×D4—28no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4C22⋊D1314yes—
483#117—28no—
484#117—22no—
485#117—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—131no—
491C2×C4⋊C4—261no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4C22×D1311yescharacteristic
495C2×C4⋊C4C22×D1311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—261no—
500C2×C22⋊C4—261no—
501C2×C42—28no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—22no—
506C2×C42—22no—
507C2×C42—261no—
508C2×C42—261no—
509C2×C42C22⋊D1311yescharacteristic
510C2×C42C22⋊D1311yescharacteristic
511C2×C42C22×D1311yescharacteristic
512C2×C42C22×D1311yescharacteristic
513#107—262no—
514#106—262no—
515#103—134no—
516#103—262no—
517#103—262no—
518#103—262no—
519#103—262no—
520#102—134no—
521#102—262no—
522#102—262no—
523C22⋊C8—134no—
524C22⋊C8—262no—
525C4×C8—262no—
526C4×C8—262no—
527#95—261no—
528#95—261no—
529#95—261no—
530#95—261no—
531#95—261no—
532C2×C13—42no—
533C2×C13—44no—
534C2×C13C4×#12011yescharacteristic
535C2×C13C4×#13511yescharacteristic
536C2×C13C4×#13711yescharacteristic
537C2×C13C2×#45211yescharacteristic
538C2×C13#300211yescharacteristic
539C2×C13#310211yescharacteristic
540C2×C13#310711yescharacteristic
541C24—21no—
542C24C2×C22⋊D1311yescharacteristic
543#41—28no—
544#41—28no—
545#41—28no—
546#41—28no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—132no—
551C2×Q8—261no—
552C2×Q8—261no—
553C2×Q8—261no—
554C2×Q8—261no—
555C2×Q8—261no—
556C2×Q8C2×C4×D1312yes—
557C2×Q8#612712yes—
558C2×Q8C2×C22⋊D1312yes—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4C2×C4×D1312yes—
566C2×D4#612712yes—
567C2×D4C2×C22⋊D1312yes—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—41no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4C2×C4×D1312yes—
595C22×C4#612712yes—
596C22×C4C2×C22⋊D1311yescharacteristic
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C2×C22⋊D1311yescharacteristic
599C22×C4C2×C22⋊D1311yescharacteristic
600C22×C4C2×C22⋊D1311yescharacteristic
601C22×C4C23×D1311yescharacteristic
602Q16—268no—
603SD16—268no—
604C2×C8—132no—
605C2×C8—132no—
606C2×C8—261no—
607C2×C8—261no—
608C2×C8—261no—
609C2×C8—261no—
610C2×C8—261no—
611C2×C8—261no—
612C2×C8—261no—
613C2×C8—261no—
614C2×C8—261no—
615C2×C8—261no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—132no—
621C4⋊C4—264no—
622C4⋊C4—261no—
623C4⋊C4—261no—
624C4⋊C4—261no—
625C4⋊C4—261no—
626C4⋊C4—261no—
627C4⋊C4—522no—
628C4⋊C4—522no—
629C4⋊C4C2×C22⋊D1312yes—
630C4⋊C4C2×C22⋊D1312yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—264no—
635C22⋊C4—522no—
636C42—24no—
637C42—24no—
638C42—22no—
639C42—24no—
640C42—22no—
641C42—21no—
642C42—21no—
643C42—522no—
644C42—522no—
645C42C2×C22⋊D1312yes—
646C42C2×C22⋊D1312yes—
647C13C4×#45211yescharacteristic, complemented, Sylow
648C23—22no—
649C23—21no—
650C23—22no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23C4×C22⋊D1312yes—
662C23C22×C22⋊D1311yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—262no—
667Q8—262no—
668Q8—521no—
669Q8—521no—
670Q8C4×C22⋊D1314yes—
671D4—216no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4C4×C22⋊D1314yes—
676C2×C4—216no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—44no—
702C2×C4—48no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—521no—
706C2×C4—521no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—521no—
710C2×C4—521no—
711C2×C4—521no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4C4×C22⋊D1312yes—
716C2×C4#8820412yes—
717C2×C4#8820412yes—
718C2×C4#8820512yes—
719C2×C4#8820712yes—
720C2×C4#8820712yes—
721C2×C4C22×C4×D1311yescharacteristic
722C2×C4C2×#612711yescharacteristic
723C2×C4C2×#612711yescharacteristic
724C2×C4C2×#612711yescharacteristic
725C2×C4C22×C22⋊D1311yescharacteristic
726C2×C4C22×C22⋊D1311yescharacteristic
727C8—262no—
728C8—262no—
729C8—521no—
730C8—521no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—24no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—41no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22C2×C4×C22⋊D1311yescharacteristic
746C22#1171949611yescharacteristic
747C22C2×#8820411yescharacteristic
748C22C2×#8820411yescharacteristic
749C22#1171952711yescharacteristic
750C22C2×#8820511yescharacteristic
751C22C2×#8820711yescharacteristic
752C4—22no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—41no—
757C4—42no—
758C4—42no—
759C4—522no—
760C4—522no—
761C4—1041no—
762C4—1041no—
763C4#1171890014yesdirect product factor
764C4C2×C4×C22⋊D1311yescharacteristic
765C4C2×C4×C22⋊D1311yescharacteristic
766C4#1171949611yescharacteristic
767C4#1171949611yescharacteristic
768C2—42no—
769C2—44no—
770C2C4×#8820711yescharacteristic
771C2C4×#8820411yescharacteristic
772C2C4×#8820511yescharacteristic
773C2C2×#1171890011yescharacteristic
774C2#1312405411yescharacteristic
775C2#1312485411yescharacteristic
776C2#1312490711yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C4×C13×#41C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC2×C4×#41D13
hypocenterC13C4×#452
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6107C2semidirect
3. C2×C4×#6105C2semidirect
4. C4×#88178C2semidirect
5. #13115177C2semidirect
6. #13115170C2semidirect
7. #13115148C2semidirect
8. #13115104C2semidirect
9. #13115083C2semidirect
10. #13115035C2semidirect
12. C4×#88075C2semidirect
13. C4×#88072C2semidirect
14. C4×C22⋊#1055C2semidirect
33. #11718900C4direct (N × H)
114. C2×#6107C2×C4semidirect
117. C2×#6105C2×C4semidirect
122. #88178C2×C4semidirect
136. #88075C2×C4semidirect
139. #88072C2×C4semidirect
146. C22⋊#1055C2×C4semidirect
434. C4×C13#452semidirect
647. C13C4×#452semidirect
763. C4#11718900direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117189002
C2×C4×#61072
C2×C4×#61052
C4×#881782
#131151772
#131151702
#131151482
#131151042
#131150832
#131150352
#131147762
C4×#880752
C4×#880722
C4×C22⋊#10552
C2×C4×C13×#412
C4×#45213