Finite Group Databasebeta

← #18089252

Subgroups — #18089252

Order 4864.

1558 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10597393C211yesmaximal, characteristic
2C22×#10597292C211yesmaximal, characteristic, complemented
3C22×#10597278C211yesmaximal, characteristic
4C22×#10597266C211yesmaximal, characteristic
5C2×#11926298C211yesmaximal, characteristic, complemented
6#14561864C211yesmaximal, characteristic, complemented
7C22×C19×#103C211yesmaximal, characteristic, complemented
8C23×D76C2211yescharacteristic
9C23×C19⋊C8C2211yescharacteristic
10C2×#10597393—22no—
11C2×#10597393—22no—
12C2×#10597393—22no—
13C2×#10597393—22no—
14C2×#10597393—22no—
15C2×#10597393C414yescomplemented
16C22×C4⋊Dic19C2211yescharacteristic
17C22×(C2×D19)⋊C4—22no—
18C22×C4×Dic19C2211yescharacteristic
19C2×#10597292—22no—
20C2×#10597292—22no—
21C2×#10597292—22no—
22C2×#10597278—22no—
23C2×#10597278—22no—
24C2×#10597278—22no—
25C2×#10597266—22no—
26C2×#10597266—22no—
27C2×#10597266—22no—
28C2×C19⋊#95—22no—
29#11926298—22no—
30C23×Q8×C19C2211yescharacteristic
31C23×C8×C19C2211yescharacteristic
32C22×C4⋊C4×C19C2211yescharacteristic
33C2×C19×#103—22no—
34C2×C19×#103—22no—
35C2×C19×#103—22no—
36C24×D19—21no—
37C22×Q8×C19—21no—
38C22×Q8×C19—21no—
39C22×Q8×C19—21no—
40C22×Q8×C19—21no—
41C22×Q8×C19—21no—
42C22×Q8×C19—21no—
43C22×Q8×C19—21no—
44C22×Q8×C19—21no—
45C22×Q8×C19—21no—
46C22×Q8×C19—21no—
47C22×Q8×C19—21no—
48C22×Q8×C19C2×C412yes—
49C22×Q8×C19D412yes—
50C22×Q8×C19D412yes—
51C23×C4×C19—21no—
52C23×C4×C19—21no—
53C23×C4×C19C2311yescharacteristic
54C23×Dic19—21no—
55C23×Dic19D412yes—
56C22×D76—21no—
57C22×D76—21no—
58C22×D76—21no—
59C22×D76—21no—
60C22×D76—21no—
61C22×D76—21no—
62C22×D76—21no—
63C22×D76—21no—
64C22×D76—21no—
65C22×D76—21no—
66C22×D76—21no—
67C22×D76C2×C412yes—
68C22×D76D412yes—
69C22×D76D412yes—
70C22×C8×C19—21no—
71C22×C8×C19—21no—
72C22×C8×C19—21no—
73C22×C8×C19—21no—
74C22×C8×C19—21no—
75C22×C8×C19—21no—
76C22×C8×C19D412yes—
77C2×C4⋊C4×C19—21no—
78C2×C4⋊C4×C19—21no—
79C2×C4⋊C4×C19—21no—
80C2×C4⋊C4×C19—21no—
81C2×C4⋊C4×C19—21no—
82C2×C4⋊C4×C19D412yes—
83#10597393—28no—
84#10597393—28no—
85#10597393—28no—
86#10597393—28no—
87C2×(C2×D19)⋊C4—28no—
88C2×(C2×D19)⋊C4—28no—
89C2×(C2×D19)⋊C4—28no—
90C2×C4⋊Dic19—21no—
91C2×C4⋊Dic19—21no—
92C2×C4⋊Dic19—21no—
93C2×C4⋊Dic19—21no—
94C2×C4⋊Dic19—21no—
95C2×C4⋊Dic19D412yes—
96C2×C4×Dic19—21no—
97C2×C4×Dic19—21no—
98C2×C4×Dic19—21no—
99C2×C4×Dic19—21no—
100C2×C4×Dic19C2×C412yes—
101C2×C4×Dic19D412yes—
102C22×C19⋊C8—21no—
103C22×C19⋊C8—21no—
104C22×C19⋊C8—21no—
105C22×C19⋊C8—21no—
106C22×C19⋊C8—21no—
107C22×C19⋊C8—21no—
108C22×C19⋊C8D412yes—
109C19×#103—28no—
110#10597292—28no—
111C19⋊#95—44no—
112#10597278—28no—
113#10597266—28no—
114C24×C19C2×D411yescharacteristic
115C23×D19—22no—
116C23×D19—22no—
117C23×D19—22no—
118C23×D19—41no—
119C23×D19—41no—
120C23×D19—41no—
121C23×D19—41no—
122C23×D19—42no—
123C23×D19—42no—
124C23×D19—42no—
125C23×D19—42no—
126C2×Q8×C19—22no—
127C2×Q8×C19—22no—
128C2×Q8×C19—22no—
129C2×Q8×C19—22no—
130C2×Q8×C19—22no—
131C2×Q8×C19—22no—
132C2×Q8×C19—22no—
133C2×Q8×C19—22no—
134C2×Q8×C19—22no—
135C2×Q8×C19—22no—
136C2×Q8×C19—22no—
137C2×Q8×C19—22no—
138C2×Q8×C19—22no—
139C2×Q8×C19—22no—
140C2×Q8×C19—22no—
141C2×Q8×C19—41no—
142C2×Q8×C19—41no—
143C2×Q8×C19—41no—
144C2×Q8×C19—41no—
145C2×Q8×C19—41no—
146C2×Q8×C19—41no—
147C2×Q8×C19—41no—
148C2×Q8×C19—41no—
149C2×Q8×C19—41no—
150C2×Q8×C19—41no—
151C2×Q8×C19—41no—
152C2×Q8×C19—41no—
153C2×Q8×C19C22⋊C414yes—
154C22×C4×C19—22no—
155C22×C4×C19—22no—
156C22×C4×C19—22no—
157C22×C4×C19—22no—
158C22×C4×C19—41no—
159C22×C4×C19—41no—
160C22×C4×C19—41no—
161C22×C4×C19—41no—
162C22×C4×C19—41no—
163C22×C4×C19—41no—
164C22×C4×C19—42no—
165C22×C4×C19—42no—
166C22×C4×C19C22×C411yescharacteristic
167C22×C4×C19C2×D411yescharacteristic
168C22×C4×C19C2×D411yescharacteristic
169C22×C4×C19C2×D411yescharacteristic
170C22×C4×C19C2×D411yescharacteristic
171C22×C4×C19C2×D411yescharacteristic
172C22×C4×C19C2×D411yescharacteristic
173C22×C4×C19C2×D411yescharacteristic
174C22×C4×C19C2×D411yescharacteristic
175C22×C4×C19C2×D411yescharacteristic
176C22×C4×C19#4111yescharacteristic
177C22×C4×C19#4111yescharacteristic
178C22×C4×C19#4111yescharacteristic
179C22×C4×C19#4111yescharacteristic
180C22×Dic19—22no—
181C22×Dic19—22no—
182C22×Dic19—22no—
183C22×Dic19—22no—
184C22×Dic19—22no—
185C22×Dic19—22no—
186C22×Dic19—22no—
187C22×Dic19—41no—
188C22×Dic19—41no—
189C22×Dic19—42no—
190C22×Dic19—42no—
191C22×Dic19C22⋊C414yes—
192C2×D76—22no—
193C2×D76—22no—
194C2×D76—22no—
195C2×D76—22no—
196C2×D76—22no—
197C2×D76—22no—
198C2×D76—22no—
199C2×D76—22no—
200C2×D76—22no—
201C2×D76—22no—
202C2×D76—22no—
203C2×D76—22no—
204C2×D76—22no—
205C2×D76—22no—
206C2×D76—22no—
207C2×D76—41no—
208C2×D76—41no—
209C2×D76—41no—
210C2×D76—41no—
211C2×D76—41no—
212C2×D76—41no—
213C2×D76—41no—
214C2×D76—41no—
215C2×D76—41no—
216C2×D76—41no—
217C2×D76—41no—
218C2×D76—41no—
219C2×D76C22⋊C414yes—
220C2×C8×C19—22no—
221C2×C8×C19—22no—
222C2×C8×C19—22no—
223C2×C8×C19—41no—
224C2×C8×C19—41no—
225C2×C8×C19—41no—
226C2×C8×C19—41no—
227C4⋊C4×C19—22no—
228C4⋊C4×C19—22no—
229C4⋊C4×C19—41no—
230C4⋊C4×C19—41no—
231(C2×D19)⋊C4—232no—
232C4⋊Dic19—22no—
233C4⋊Dic19—22no—
234C4⋊Dic19—41no—
235C4⋊Dic19—41no—
236C4×Dic19—22no—
237C4×Dic19—22no—
238C4×Dic19—22no—
239C4×Dic19—22no—
240C2×C19⋊C8—22no—
241C2×C19⋊C8—22no—
242C2×C19⋊C8—22no—
243C2×C19⋊C8—41no—
244C2×C19⋊C8—41no—
245C2×C19⋊C8—41no—
246C2×C19⋊C8—41no—
247#11009—191nomaximal, Sylow
248C23×C19C2×C22⋊C411yescharacteristic
249C23×C19#12011yescharacteristic
250C23×C19#12011yescharacteristic
251C23×C19#12111yescharacteristic
252C23×C19#12111yescharacteristic
253C23×C19#12411yescharacteristic
254C23×C19#12711yescharacteristic
255C23×C19#13512yes—
256C23×C19#13512yes—
257C23×C19AGL(1,ℤ/8)12yes—
258C23×C19#13712yes—
259C22×D19—24no—
260C22×D19—42no—
261C22×D19—42no—
262C22×D19—42no—
263C22×D19—42no—
264C22×D19—42no—
265C22×D19—42no—
266C22×D19—44no—
267C22×D19—44no—
268C22×D19—44no—
269C22×D19—44no—
270C22×D19—44no—
271C22×D19—44no—
272C22×D19—82no—
273C22×D19—82no—
274C22×D19—82no—
275C22×D19—82no—
276C22×D19—82no—
277C22×D19—82no—
278C22×D19—81no—
279C22×D19—81no—
280C22×D19—81no—
281C22×D19—81no—
282Q8×C19—24no—
283Q8×C19—24no—
284Q8×C19—42no—
285Q8×C19—42no—
286Q8×C19—42no—
287Q8×C19—42no—
288Q8×C19—42no—
289Q8×C19—42no—
290C2×C4×C19—24no—
291C2×C4×C19—42no—
292C2×C4×C19—42no—
293C2×C4×C19—42no—
294C2×C4×C19—42no—
295C2×C4×C19—42no—
296C2×C4×C19—42no—
297C2×C4×C19—42no—
298C2×C4×C19—44no—
299C2×C4×C19—82no—
300C2×C4×C19—81no—
301C2×C4×C19—81no—
302C2×C4×C19C2×C22⋊C411yescharacteristic
303C2×C4×C19C2×C22⋊C411yescharacteristic
304C2×C4×C19C4×D411yescharacteristic
305C2×C4×C19C4×D411yescharacteristic
306C2×C4×C19C4×D411yescharacteristic
307C2×C4×C19C4×D411yescharacteristic
308C2×C4×C19#12011yescharacteristic
309C2×C4×C19#12011yescharacteristic
310C2×C4×C19#12011yescharacteristic
311C2×C4×C19#12011yescharacteristic
312C2×C4×C19#12011yescharacteristic
313C2×C4×C19#12011yescharacteristic
314C2×C4×C19#12111yescharacteristic
315C2×C4×C19#12111yescharacteristic
316C2×C4×C19#12111yescharacteristic
317C2×C4×C19#12111yescharacteristic
318C2×C4×C19#12111yescharacteristic
319C2×C4×C19#12111yescharacteristic
320C2×C4×C19#12111yescharacteristic
321C2×C4×C19#12111yescharacteristic
322C2×C4×C19#12111yescharacteristic
323C2×C4×C19#12111yescharacteristic
324C2×C4×C19#12311yescharacteristic
325C2×C4×C19#12311yescharacteristic
326C2×C4×C19#12311yescharacteristic
327C2×C4×C19#12311yescharacteristic
328C2×C4×C19#12411yescharacteristic
329C2×C4×C19#12711yescharacteristic
330C2×Dic19—24no—
331C2×Dic19—24no—
332C2×Dic19—24no—
333C2×Dic19—42no—
334C2×Dic19—42no—
335C2×Dic19—42no—
336C2×Dic19—42no—
337C2×Dic19—42no—
338C2×Dic19—44no—
339C2×Dic19—82no—
340C2×Dic19—81no—
341C2×Dic19—81no—
342D76—24no—
343D76—24no—
344D76—42no—
345D76—42no—
346D76—42no—
347D76—42no—
348D76—42no—
349D76—42no—
350C8×C19—42no—
351C19⋊C8—42no—
352C22×#124—191no—
353C22×#103—191no—
354C22×#103D1911yescharacteristic, complemented
355C22×#102—191no—
356C22×#102—191no—
357C2×#336—191no—
358C4⋊#95—191no—
359C22×C19#37911yescharacteristic
360C22×C19#39011yescharacteristic
361C22×C19#39011yescharacteristic
362C22×C19#39211yescharacteristic
363C22×C19#39211yescharacteristic
364C22×C19#39411yescharacteristic
365C22×C19#39411yescharacteristic
366C22×C19#41612yes—
367C22×C19#41712yes—
368C22×C19#44912yes—
369C22×C19#44912yes—
370C22×C19#45212yes—
371C22×C19#45212yes—
372C22×C19#46312yes—
373C22×C19#46312yes—
374C22×C19#46412yes—
375C22×C19#46412yes—
376C22×C19#48812yes—
377C22×C19#48912yes—
378C22×C19#49511yescharacteristic
379C22×C19#49511yescharacteristic
380C22×C19#49611yescharacteristic
381C22×C19#49711yescharacteristic
382C2×D19—44no—
383C2×D19—48no—
384C2×D19—82no—
385C2×D19—82no—
386C2×D19—84no—
387C2×D19—82no—
388C2×D19—82no—
389C2×D19—82no—
390C2×D19—82no—
391C2×D19—84no—
392C2×D19—84no—
393C4×C19—44no—
394C4×C19—82no—
395C4×C19#38611yescharacteristic
396C4×C19#38611yescharacteristic
397C4×C19#38611yescharacteristic
398C4×C19#38611yescharacteristic
399C4×C19#39211yescharacteristic
400C4×C19#39211yescharacteristic
401C4×C19#39411yescharacteristic
402C4×C19#39411yescharacteristic
403Dic19—44no—
404Dic19—82no—
405C23×Q8C2×D1911yescharacteristic
406C23×D4—191no—
407C23×C8—191no—
408C23×C8C2×D1911yescharacteristic
409C2×#124—194no—
410C2×#124—382no—
411C2×#124—382no—
412C2×#124—382no—
413C2×#124—382no—
414C2×#124—382no—
415C22×C4⋊C4—191no—
416C22×C4⋊C4C2×D1911yescharacteristic
417C22×C22⋊C4—382no—
418C22×C42—191no—
419C2×#103—22no—
420C2×#103—22no—
421C2×#103—22no—
422C2×#103—382no—
423C2×#103—382no—
424C2×#103—382no—
425C2×#102—382no—
426C2×#102—382no—
427C2×#102—382no—
428C2×#102—382no—
429C2×#102—382no—
430C2×#102—382no—
431C2×#95—382no—
432#336—382no—
433C2×C19#143811yescharacteristic
434C2×C19#178812yes—
435C2×C19#195811yescharacteristic
436C2×C19#195911yescharacteristic
437C2×C19#198312yes—
438C2×C19#201211yescharacteristic
439C2×C19#201211yescharacteristic
440C2×C19#201511yescharacteristic
441C2×C19#201511yescharacteristic
442C2×C19#204212yes—
443C2×C19#204212yes—
444D19—84no—
445C25—381no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—21no—
450C22×Q8—21no—
451C22×Q8—21no—
452C22×Q8—21no—
453C22×Q8—21no—
454C22×Q8—21no—
455C22×Q8—21no—
456C22×Q8—21no—
457C22×Q8C4×D1912yes—
458C22×Q8D7612yes—
459C22×Q8C22⋊D1912yes—
460C22×D4—192no—
461C22×D4—192no—
462C22×D4—192no—
463C22×D4—381no—
464C22×D4—381no—
465C22×D4—381no—
466C22×D4—381no—
467C22×D4—381no—
468C22×D4—381no—
469C22×D4—381no—
470C22×D4—381no—
471C22×D4—381no—
472C22×D4—381no—
473C22×D4—381no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—192no—
477C23×C4—381no—
478C23×C4C22×D1911yescharacteristic
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—192no—
486C22×C8—381no—
487C22×C8—381no—
488C22×C8—381no—
489C22×C8—381no—
490C22×C8—381no—
491C22×C8—381no—
492C22×C8C22⋊D1912yes—
493#124—388no—
494#124—388no—
495#124—388no—
496#124—388no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—192no—
503C2×C4⋊C4—381no—
504C2×C4⋊C4—381no—
505C2×C4⋊C4—381no—
506C2×C4⋊C4—381no—
507C2×C4⋊C4—381no—
508C2×C4⋊C4C22⋊D1912yes—
509C2×C22⋊C4—388no—
510C2×C22⋊C4—388no—
511C2×C22⋊C4—388no—
512C2×C42—192no—
513C2×C42—192no—
514C2×C42—381no—
515C2×C42—381no—
516C2×C42—381no—
517C2×C42—381no—
518#103—28no—
519#103—388no—
520#102—388no—
521#102—388no—
522#95—764no—
523C19#1100911yescharacteristic, complemented, Sylow
524C24—382no—
525C24—382no—
526C24—382no—
527C24—761no—
528C24—761no—
529C24—761no—
530C24—761no—
531C24—762no—
532C24—762no—
533C24—762no—
534C24—762no—
535C24D4×D1911yescharacteristic
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8—41no—
563C2×Q8(C2×D19)⋊C414yes—
564C2×D4—194no—
565C2×D4—382no—
566C2×D4—382no—
567C2×D4—382no—
568C2×D4—382no—
569C2×D4—382no—
570C2×D4—382no—
571C2×D4—382no—
572C2×D4—382no—
573C2×D4—382no—
574C2×D4—382no—
575C2×D4—382no—
576C2×D4—382no—
577C2×D4—382no—
578C2×D4—382no—
579C2×D4—382no—
580C2×D4—761no—
581C2×D4—761no—
582C2×D4—761no—
583C2×D4—761no—
584C2×D4—761no—
585C2×D4—761no—
586C2×D4—761no—
587C2×D4—761no—
588C2×D4—761no—
589C2×D4—761no—
590C2×D4—761no—
591C2×D4—761no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—194no—
605C22×C4—382no—
606C22×C4—382no—
607C22×C4—382no—
608C22×C4—382no—
609C22×C4—382no—
610C22×C4—382no—
611C22×C4—382no—
612C22×C4—761no—
613C22×C4—761no—
614C22×C4—762no—
615C22×C4—762no—
616C22×C4C2×C4×D1911yescharacteristic
617C22×C4C2×D7611yescharacteristic
618C22×C4#6454111yescharacteristic
619C22×C4#6454111yescharacteristic
620C22×C4D4×D1911yescharacteristic
621C22×C4D4×D1911yescharacteristic
622C22×C4D4×D1911yescharacteristic
623C22×C4D4×D1911yescharacteristic
624C22×C4D4×D1911yescharacteristic
625C22×C4#6454311yescharacteristic
626C22×C4#6454311yescharacteristic
627C22×C4C2×C22⋊D1911yescharacteristic
628C22×C4C2×C22⋊D1911yescharacteristic
629C22×C4C2×C22⋊D1911yescharacteristic
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—382no—
638C2×C8—382no—
639C2×C8—382no—
640C2×C8—761no—
641C2×C8—761no—
642C2×C8—761no—
643C2×C8—761no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—382no—
649C4⋊C4—382no—
650C4⋊C4—761no—
651C4⋊C4—761no—
652C22⋊C4—3832no—
653C42—382no—
654C42—382no—
655C42—382no—
656C42—382no—
657C23—384no—
658C23—764no—
659C23—764no—
660C23—764no—
661C23—764no—
662C23—762no—
663C23—762no—
664C23—764no—
665C23—762no—
666C23—762no—
667C23—764no—
668C23—762no—
669C23—762no—
670C23—1522no—
671C23—1522no—
672C23—1521no—
673C23—1521no—
674C23—1521no—
675C23—1521no—
676C23—1522no—
677C23—1522no—
678C23—1522no—
679C23—1522no—
680C23C22⋊C4×D1911yescharacteristic
681C23#1059732811yescharacteristic
682C23#1059733011yescharacteristic
683C23#1059733111yescharacteristic
684C23#1059736012yes—
685C23#1059736212yes—
686C23#1059736412yes—
687C23#1059736512yes—
688C23#1059738311yescharacteristic
689C23#1059738511yescharacteristic
690C23#1059738611yescharacteristic
691Q8—24no—
692Q8—24no—
693Q8—42no—
694Q8—42no—
695Q8—42no—
696Q8—42no—
697Q8—42no—
698Q8—42no—
699D4—384no—
700D4—384no—
701D4—762no—
702D4—762no—
703D4—762no—
704D4—762no—
705D4—762no—
706D4—762no—
707C2×C4—24no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—82no—
719C2×C4—384no—
720C2×C4—384no—
721C2×C4—384no—
722C2×C4—762no—
723C2×C4—762no—
724C2×C4—762no—
725C2×C4—762no—
726C2×C4—762no—
727C2×C4—764no—
728C2×C4—1521no—
729C2×C4—1521no—
730C2×C4—1522no—
731C2×C4C22⋊C4×D1911yescharacteristic
732C2×C4(C22⋊D19)⋊C411yescharacteristic
733C2×C4(C22⋊D19)⋊C411yescharacteristic
734C2×C4#1059732811yescharacteristic
735C2×C4#1059732811yescharacteristic
736C2×C4#1059732911yescharacteristic
737C2×C4#1059732911yescharacteristic
738C2×C4#1059733011yescharacteristic
739C2×C4#1059733011yescharacteristic
740C2×C4#1059733011yescharacteristic
741C2×C4#1059733111yescharacteristic
742C2×C4#1059733211yescharacteristic
743C2×C4C2×(C2×D19)⋊C411yescharacteristic
744C2×C4C4×C22⋊D1911yescharacteristic
745C2×C4C4×C22⋊D1911yescharacteristic
746C2×C4#1059737511yescharacteristic
747C2×C4#1059737611yescharacteristic
748C2×C4#1059737611yescharacteristic
749C2×C4#1059738311yescharacteristic
750C2×C4#1059738311yescharacteristic
751C2×C4#1059738311yescharacteristic
752C2×C4#1059738411yescharacteristic
753C2×C4#1059738411yescharacteristic
754C2×C4#1059738511yescharacteristic
755C2×C4#1059738511yescharacteristic
756C2×C4#1059738511yescharacteristic
757C2×C4#1059738611yescharacteristic
758C2×C4#1059739911yescharacteristic
759C8—42no—
760C8—762no—
761C22—764no—
762C22—768no—
763C22—1524no—
764C22—1524no—
765C22—1522no—
766C22—1522no—
767C22—1522no—
768C22—1522no—
769C22—1522no—
770C22—1522no—
771C22—1524no—
772C22#1192639911yescharacteristic
773C22#1192644411yescharacteristic
774C22#1192644411yescharacteristic
775C22#1192645211yescharacteristic
776C22#1192645311yescharacteristic
777C22#1192645911yescharacteristic
778C22#1192646011yescharacteristic
779C22#1192653912yes—
780C22#1192654412yes—
781C22#1192668812yes—
782C22#1192669212yes—
783C22#1192670512yes—
784C22#1192670912yes—
785C22#1192676112yes—
786C22#1192676212yes—
787C22#1192676812yes—
788C22#1192676912yes—
789C22#1192690012yes—
790C22#1192690512yes—
791C22#1192692511yescharacteristic
792C22#1192692911yescharacteristic
793C22#1192693011yescharacteristic
794C22#1192693711yescharacteristic
795C4—44no—
796C4—82no—
797C4—764no—
798C4—1522no—
799C4#1192642011yescharacteristic
800C4#1192642011yescharacteristic
801C4#1192642111yescharacteristic
802C4#1192642311yescharacteristic
803C4#1192645211yescharacteristic
804C4#1192645311yescharacteristic
805C4#1192645911yescharacteristic
806C4#1192646011yescharacteristic
807C2—1524no—
808C2#1456187411yescharacteristic
809C2#1456357412yes—
810C2#1456444311yescharacteristic
811C2#1456444811yescharacteristic
812C2#1456456412yes—
813C2#1456470911yescharacteristic
814C2#1456471311yescharacteristic
815C2#1456472611yescharacteristic
816C2#1456473011yescharacteristic
817C2#1456487212yes—
818C2#1456487312yes—
subgroupG/H
centerC24D4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC22×C19×#103C2
socleC24×C19C2×D4
prime radicalC23×D76C22
cosocleC23×C4×C19C23
hypercenterC22×#103D19
hypocenterC19#11009
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#10597292C2semidirect
5. C2×#11926298C2semidirect
6. #14561864C2semidirect
7. C22×C19×#103C2semidirect
15. C2×#10597393C4semidirect
354. C22×#103D19semidirect
523. C19#11009semidirect

Maximal subgroups

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

subgroupindex
C22×#105973932
C22×#105972922
C22×#105972782
C22×#105972662
C2×#119262982
#145618642
C22×C19×#1032
#1100919