Finite Group Databasebeta

← #18089345

Subgroups — #18089345

Order 4864.

1606 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#64526C211yesmaximal, characteristic
2C22×#10597273C211yesmaximal, characteristic, complemented
3C2×#11926449C211yesmaximal, characteristic, complemented
4C2×#11926447C211yesmaximal, characteristic
5C2×#11926306C211yesmaximal, characteristic, complemented
6C2×#11926298C211yesmaximal, characteristic, complemented
7C22×C19×#102C211yesmaximal, characteristic
8C23×Dic38C2211yescharacteristic
9C22×#64526—22no—
10C22×#64526—22no—
11C22×#64526—22no—
12C22×#64526—22no—
13C22×#64526—22no—
14C22×#64526—22no—
15C22×#64526C414yescomplemented
16C23×C19⋊C8C2211yescharacteristic
17C22×C4⋊Dic19C2211yescharacteristic
18C22×C22⋊Dic19—22no—
19C22×C4×Dic19C2211yescharacteristic
20C2×#10597273—22no—
21C2×#10597273—22no—
22C2×#10597273—22no—
23#11926449—22no—
24#11926449—22no—
25#11926447—22no—
26#11926447—22no—
27C2×C19⋊#95—22no—
28#11926306—22no—
29#11926298—22no—
30C23×D4×C19C2211yescharacteristic
31C23×C8×C19C2211yescharacteristic
32C22×C4⋊C4×C19C2211yescharacteristic
33C2×C19×#102—22no—
34C2×C19×#102—22no—
35C2×C19×#102—22no—
36C25×C19—21no—
37C22×D4×C19—21no—
38C22×D4×C19—21no—
39C22×D4×C19—21no—
40C22×D4×C19—21no—
41C22×D4×C19—21no—
42C22×D4×C19—21no—
43C22×D4×C19—21no—
44C22×D4×C19—21no—
45C22×D4×C19—21no—
46C22×D4×C19—21no—
47C22×D4×C19—21no—
48C22×D4×C19C2×C412yes—
49C22×D4×C19D412yes—
50C22×D4×C19D412yes—
51C23×C4×C19—21no—
52C23×C4×C19C2311yescharacteristic
53C23×Dic19—21no—
54C23×Dic19—21no—
55C23×Dic19D412yes—
56C22×Dic38—21no—
57C22×Dic38—21no—
58C22×Dic38—21no—
59C22×Dic38—21no—
60C22×Dic38—21no—
61C22×Dic38—21no—
62C22×Dic38—21no—
63C22×Dic38—21no—
64C22×Dic38—21no—
65C22×Dic38—21no—
66C22×Dic38—21no—
67C22×Dic38C2×C412yes—
68C22×Dic38D412yes—
69C22×Dic38D412yes—
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—
83C2×C22⋊Dic19—28no—
84C2×C22⋊Dic19—44no—
85C2×C22⋊Dic19—44no—
86C2×#64526—28no—
87C2×#64526—28no—
88C2×#64526—28no—
89C2×#64526—28no—
90C2×#64526—28no—
91C2×#64526—28no—
92C2×#64526—28no—
93C2×C4⋊Dic19—21no—
94C2×C4⋊Dic19—21no—
95C2×C4⋊Dic19—21no—
96C2×C4⋊Dic19—21no—
97C2×C4⋊Dic19—21no—
98C2×C4⋊Dic19D412yes—
99C2×C4×Dic19—21no—
100C2×C4×Dic19—21no—
101C2×C4×Dic19—21no—
102C2×C4×Dic19—21no—
103C2×C4×Dic19—21no—
104C2×C4×Dic19—21no—
105C22×C19⋊C8—21no—
106C22×C19⋊C8—21no—
107C22×C19⋊C8—21no—
108C22×C19⋊C8—21no—
109C22×C19⋊C8C2×C412yes—
110C22×C19⋊C8D412yes—
111C22×C19⋊C8D412yes—
112C19×#102—28no—
113C19⋊#95—28no—
114#10597273—28no—
115C24×C19—22no—
116C24×C19—22no—
117C24×C19—22no—
118C24×C19—41no—
119C24×C19—41no—
120C24×C19—41no—
121C24×C19—41no—
122C24×C19—42no—
123C24×C19—42no—
124C24×C19—42no—
125C24×C19—42no—
126C24×C19C2×D411yescharacteristic
127C2×D4×C19—22no—
128C2×D4×C19—22no—
129C2×D4×C19—22no—
130C2×D4×C19—22no—
131C2×D4×C19—22no—
132C2×D4×C19—22no—
133C2×D4×C19—22no—
134C2×D4×C19—22no—
135C2×D4×C19—22no—
136C2×D4×C19—22no—
137C2×D4×C19—22no—
138C2×D4×C19—22no—
139C2×D4×C19—22no—
140C2×D4×C19—22no—
141C2×D4×C19—22no—
142C2×D4×C19—41no—
143C2×D4×C19—41no—
144C2×D4×C19—41no—
145C2×D4×C19—41no—
146C2×D4×C19—41no—
147C2×D4×C19—41no—
148C2×D4×C19—41no—
149C2×D4×C19—41no—
150C2×D4×C19—41no—
151C2×D4×C19—41no—
152C2×D4×C19—41no—
153C2×D4×C19—41no—
154C2×D4×C19C22⋊C414yes—
155C22×C4×C19—22no—
156C22×C4×C19—41no—
157C22×C4×C19—41no—
158C22×C4×C19—42no—
159C22×C4×C19—42no—
160C22×C4×C19C22×C411yescharacteristic
161C22×C4×C19C2×D411yescharacteristic
162C22×C4×C19C2×D411yescharacteristic
163C22×C4×C19C2×D411yescharacteristic
164C22×C4×C19C2×D411yescharacteristic
165C22×C4×C19C2×D411yescharacteristic
166C22×C4×C19C2×D411yescharacteristic
167C22×C4×C19C2×D411yescharacteristic
168C22×C4×C19C2×D411yescharacteristic
169C22×C4×C19C2×D411yescharacteristic
170C22×C4×C19#4111yescharacteristic
171C22×C4×C19#4111yescharacteristic
172C22×C4×C19#4111yescharacteristic
173C22×C4×C19#4111yescharacteristic
174C22×Dic19—22no—
175C22×Dic19—22no—
176C22×Dic19—22no—
177C22×Dic19—22no—
178C22×Dic19—22no—
179C22×Dic19—22no—
180C22×Dic19—22no—
181C22×Dic19—22no—
182C22×Dic19—22no—
183C22×Dic19—22no—
184C22×Dic19—41no—
185C22×Dic19—41no—
186C22×Dic19—41no—
187C22×Dic19—41no—
188C22×Dic19—41no—
189C22×Dic19—41no—
190C22×Dic19—42no—
191C22×Dic19—42no—
192C22×Dic19SD1614yescomplemented
193C2×Dic38—22no—
194C2×Dic38—22no—
195C2×Dic38—22no—
196C2×Dic38—22no—
197C2×Dic38—22no—
198C2×Dic38—22no—
199C2×Dic38—22no—
200C2×Dic38—22no—
201C2×Dic38—22no—
202C2×Dic38—22no—
203C2×Dic38—22no—
204C2×Dic38—22no—
205C2×Dic38—22no—
206C2×Dic38—22no—
207C2×Dic38—22no—
208C2×Dic38—41no—
209C2×Dic38—41no—
210C2×Dic38—41no—
211C2×Dic38—41no—
212C2×Dic38—41no—
213C2×Dic38—41no—
214C2×Dic38—41no—
215C2×Dic38—41no—
216C2×Dic38—41no—
217C2×Dic38—41no—
218C2×Dic38—41no—
219C2×Dic38—41no—
220C2×Dic38C22⋊C414yescomplemented
221C2×C8×C19—22no—
222C2×C8×C19—22no—
223C2×C8×C19—22no—
224C2×C8×C19—41no—
225C2×C8×C19—41no—
226C2×C8×C19—41no—
227C2×C8×C19—41no—
228C4⋊C4×C19—22no—
229C4⋊C4×C19—22no—
230C4⋊C4×C19—41no—
231C4⋊C4×C19—41no—
232C22⋊Dic19—416no—
233#64526—232no—
234C4⋊Dic19—22no—
235C4⋊Dic19—22no—
236C4⋊Dic19—41no—
237C4⋊Dic19—41no—
238C4×Dic19—41no—
239C4×Dic19—41no—
240C4×Dic19—41no—
241C4×Dic19—41no—
242C2×C19⋊C8—22no—
243C2×C19⋊C8—22no—
244C2×C19⋊C8—22no—
245C2×C19⋊C8—22no—
246C2×C19⋊C8—22no—
247C2×C19⋊C8—22no—
248C2×C19⋊C8C22⋊C414yescomplemented
249#11023—191nomaximal, Sylow
250C23×C19—24no—
251C23×C19—42no—
252C23×C19—42no—
253C23×C19—42no—
254C23×C19—42no—
255C23×C19—42no—
256C23×C19—42no—
257C23×C19—44no—
258C23×C19—44no—
259C23×C19—44no—
260C23×C19—44no—
261C23×C19—44no—
262C23×C19—44no—
263C23×C19—82no—
264C23×C19—82no—
265C23×C19—82no—
266C23×C19—82no—
267C23×C19—82no—
268C23×C19—82no—
269C23×C19—81no—
270C23×C19—81no—
271C23×C19—81no—
272C23×C19—81no—
273C23×C19C4×D411yescharacteristic
274C23×C19#12011yescharacteristic
275C23×C19#12011yescharacteristic
276C23×C19#12111yescharacteristic
277C23×C19#12111yescharacteristic
278C23×C19#12111yescharacteristic
279C23×C19#12711yescharacteristic
280C23×C19C2×SD1612yes—
281C23×C19#13512yes—
282C23×C19AGL(1,ℤ/8)12yes—
283C23×C19#13712yes—
284D4×C19—24no—
285D4×C19—24no—
286D4×C19—42no—
287D4×C19—42no—
288D4×C19—42no—
289D4×C19—42no—
290D4×C19—42no—
291D4×C19—42no—
292C2×C4×C19—42no—
293C2×C4×C19—44no—
294C2×C4×C19—82no—
295C2×C4×C19—81no—
296C2×C4×C19—81no—
297C2×C4×C19C2×C22⋊C411yescharacteristic
298C2×C4×C19C2×C22⋊C411yescharacteristic
299C2×C4×C19C2×C22⋊C411yescharacteristic
300C2×C4×C19C4×D411yescharacteristic
301C2×C4×C19C4×D411yescharacteristic
302C2×C4×C19C4×D411yescharacteristic
303C2×C4×C19#12011yescharacteristic
304C2×C4×C19#12011yescharacteristic
305C2×C4×C19#12011yescharacteristic
306C2×C4×C19#12011yescharacteristic
307C2×C4×C19#12011yescharacteristic
308C2×C4×C19#12011yescharacteristic
309C2×C4×C19#12111yescharacteristic
310C2×C4×C19#12111yescharacteristic
311C2×C4×C19#12111yescharacteristic
312C2×C4×C19#12111yescharacteristic
313C2×C4×C19#12111yescharacteristic
314C2×C4×C19#12111yescharacteristic
315C2×C4×C19#12111yescharacteristic
316C2×C4×C19#12111yescharacteristic
317C2×C4×C19#12111yescharacteristic
318C2×C4×C19#12311yescharacteristic
319C2×C4×C19#12311yescharacteristic
320C2×C4×C19#12311yescharacteristic
321C2×C4×C19#12311yescharacteristic
322C2×C4×C19#12411yescharacteristic
323C2×C4×C19#12411yescharacteristic
324C2×C4×C19#12711yescharacteristic
325C2×Dic19—24no—
326C2×Dic19—24no—
327C2×Dic19—24no—
328C2×Dic19—24no—
329C2×Dic19—42no—
330C2×Dic19—42no—
331C2×Dic19—42no—
332C2×Dic19—42no—
333C2×Dic19—42no—
334C2×Dic19—42no—
335C2×Dic19—42no—
336C2×Dic19—42no—
337C2×Dic19—42no—
338C2×Dic19—42no—
339C2×Dic19—42no—
340C2×Dic19—44no—
341C2×Dic19—82no—
342C2×Dic19—81no—
343C2×Dic19—81no—
344Dic38—24no—
345Dic38—24no—
346Dic38—42no—
347Dic38—42no—
348Dic38—42no—
349Dic38—42no—
350Dic38—42no—
351Dic38—42no—
352C8×C19—42no—
353C19⋊C8—24no—
354C23×SD16—191no—
355C22×#103—191no—
356C22×#102D1911yescharacteristic
357C2×#391—191no—
358C2×#390—191no—
359C2×#340—191no—
360C2×#336—191no—
361C22×C19—48no—
362C22×C19—44no—
363C22×C19—84no—
364C22×C19—84no—
365C22×C19—82no—
366C22×C19—82no—
367C22×C19—84no—
368C22×C19—82no—
369C22×C19—82no—
370C22×C19—82no—
371C22×C19—82no—
372C22×C19#38611yescharacteristic
373C22×C19#38611yescharacteristic
374C22×C19#39011yescharacteristic
375C22×C19#39211yescharacteristic
376C22×C19#39211yescharacteristic
377C22×C19#39211yescharacteristic
378C22×C19#39411yescharacteristic
379C22×C19C4×SD1612yes—
380C22×C19#44012yes—
381C22×C19#44812yes—
382C22×C19#44912yes—
383C22×C19#45012yes—
384C22×C19#45212yes—
385C22×C19#46012yes—
386C22×C19#46112yes—
387C22×C19#46312yes—
388C22×C19#46412yes—
389C22×C19#46512yes—
390C22×C19#46812yes—
391C22×C19#49211yescharacteristic
392C22×C19#49511yescharacteristic
393C22×C19#49611yescharacteristic
394C22×C19#49711yescharacteristic
395C4×C19—82no—
396C4×C19#37911yescharacteristic
397C4×C19#38611yescharacteristic
398C4×C19#38611yescharacteristic
399C4×C19#39011yescharacteristic
400C4×C19#39211yescharacteristic
401C4×C19#39411yescharacteristic
402C4×C19#39411yescharacteristic
403C4×C19#39411yescharacteristic
404Dic19—44no—
405Dic19—44no—
406Dic19—82no—
407C23×Q8—191no—
408C23×D4C2×D1911yescharacteristic
409C22×SD16—194no—
410C22×SD16—382no—
411C22×SD16—382no—
412C22×SD16—382no—
413C22×SD16—382no—
414C22×SD16—382no—
415C22×SD16—382no—
416C23×C8—191no—
417C23×C8C2×D1911yescharacteristic
418C22×C4⋊C4—191no—
419C22×C4⋊C4C2×D1911yescharacteristic
420C22×C22⋊C4—382no—
421C22×C42—191no—
422C2×#103—382no—
423C2×#103—382no—
424C2×#103—382no—
425C2×#102—22no—
426C2×#102—22no—
427C2×#102—22no—
428#391—382no—
429#391—382no—
430#390—382no—
431#390—382no—
432C2×#95—382no—
433#340—382no—
434#336—382no—
435C2×C19—84no—
436C2×C19#143811yescharacteristic
437C2×C19#187712yes—
438C2×C19#188012yes—
439C2×C19#196811yescharacteristic
440C2×C19#197311yescharacteristic
441C2×C19#200012yes—
442C2×C19#201211yescharacteristic
443C2×C19#201311yescharacteristic
444C2×C19#201411yescharacteristic
445C2×C19#201511yescharacteristic
446C2×C19#205512yes—
447C25—21no—
448C22×Q8—192no—
449C22×Q8—192no—
450C22×Q8—192no—
451C22×Q8—381no—
452C22×Q8—381no—
453C22×Q8—381no—
454C22×Q8—381no—
455C22×Q8—381no—
456C22×Q8—381no—
457C22×Q8—381no—
458C22×Q8—381no—
459C22×Q8—381no—
460C22×Q8—381no—
461C22×Q8—381no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4C4×D1912yes—
474C22×D4D7612yes—
475C22×D4C22⋊D1912yes—
476C23×C4—21no—
477C23×C4—192no—
478C23×C4—381no—
479C23×C4—381no—
480C23×C4C22×D1911yescharacteristic
481C2×SD16—388no—
482C2×SD16—388no—
483C2×SD16—388no—
484C2×SD16—388no—
485C2×SD16—388no—
486C2×SD16—388no—
487C2×SD16—388no—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8—21no—
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—21no—
494C22×C8—192no—
495C22×C8—192no—
496C22×C8—192no—
497C22×C8—381no—
498C22×C8—381no—
499C22×C8—381no—
500C22×C8—381no—
501C22×C8C22⋊D1912yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—192no—
508C2×C4⋊C4—381no—
509C2×C4⋊C4—381no—
510C2×C4⋊C4—381no—
511C2×C4⋊C4—381no—
512C2×C4⋊C4—381no—
513C2×C4⋊C4C22⋊D1912yes—
514C2×C22⋊C4—388no—
515C2×C22⋊C4—764no—
516C2×C22⋊C4—764no—
517C2×C42—381no—
518C2×C42—381no—
519C2×C42—381no—
520C2×C42—381no—
521C2×C42—381no—
522C2×C42—381no—
523#103—388no—
524#102—28no—
525#95—388no—
526C19#1102311yescharacteristic, complemented, Sylow
527C24—22no—
528C24—22no—
529C24—22no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24—41no—
534C24—42no—
535C24—42no—
536C24—42no—
537C24—42no—
538C24D4×D1911yescharacteristic
539C2×Q8—194no—
540C2×Q8—382no—
541C2×Q8—382no—
542C2×Q8—382no—
543C2×Q8—382no—
544C2×Q8—382no—
545C2×Q8—382no—
546C2×Q8—382no—
547C2×Q8—382no—
548C2×Q8—382no—
549C2×Q8—382no—
550C2×Q8—382no—
551C2×Q8—382no—
552C2×Q8—382no—
553C2×Q8—382no—
554C2×Q8—382no—
555C2×Q8—761no—
556C2×Q8—761no—
557C2×Q8—761no—
558C2×Q8—761no—
559C2×Q8—761no—
560C2×Q8—761no—
561C2×Q8—761no—
562C2×Q8—761no—
563C2×Q8—761no—
564C2×Q8—761no—
565C2×Q8—761no—
566C2×Q8—761no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4(C2×D19)⋊C414yes—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—194no—
601C22×C4—382no—
602C22×C4—382no—
603C22×C4—382no—
604C22×C4—382no—
605C22×C4—382no—
606C22×C4—382no—
607C22×C4—382no—
608C22×C4—382no—
609C22×C4—382no—
610C22×C4—382no—
611C22×C4—761no—
612C22×C4—761no—
613C22×C4—761no—
614C22×C4—761no—
615C22×C4—761no—
616C22×C4—761no—
617C22×C4—762no—
618C22×C4—762no—
619C22×C4C2×C4×D1911yescharacteristic
620C22×C4C2×D7611yescharacteristic
621C22×C4#6454111yescharacteristic
622C22×C4#6454111yescharacteristic
623C22×C4D4×D1911yescharacteristic
624C22×C4D4×D1911yescharacteristic
625C22×C4D4×D1911yescharacteristic
626C22×C4D4×D1911yescharacteristic
627C22×C4D4×D1911yescharacteristic
628C22×C4#6454311yescharacteristic
629C22×C4#6454311yescharacteristic
630C22×C4C2×C22⋊D1911yescharacteristic
631C22×C4C2×C22⋊D1911yescharacteristic
632C22×C4C2×C22⋊D1911yescharacteristic
633SD16—3832no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—194no—
642C2×C8—382no—
643C2×C8—382no—
644C2×C8—382no—
645C2×C8—382no—
646C2×C8—382no—
647C2×C8—382no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C4⋊C4—382no—
653C4⋊C4—382no—
654C4⋊C4—761no—
655C4⋊C4—761no—
656C22⋊C4—7616no—
657C42—761no—
658C42—761no—
659C42—761no—
660C42—761no—
661C23—24no—
662C23—44no—
663C23—44no—
664C23—42no—
665C23—44no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—44no—
674C23—82no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23—82no—
680C23—82no—
681C23—82no—
682C23—82no—
683C23—82no—
684C23(C22⋊D19)⋊C411yescharacteristic
685C23#1059732811yescharacteristic
686C23#1059733011yescharacteristic
687C23#1059733011yescharacteristic
688C23#1059735712yes—
689C23#1059735812yes—
690C23SD16×D1912yes—
691C23#1059736112yes—
692C23#1059738311yescharacteristic
693C23#1059738511yescharacteristic
694C23#1059738611yescharacteristic
695Q8—384no—
696Q8—384no—
697Q8—762no—
698Q8—762no—
699Q8—762no—
700Q8—762no—
701Q8—762no—
702Q8—762no—
703D4—24no—
704D4—24no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—82no—
716C2×C4—384no—
717C2×C4—384no—
718C2×C4—384no—
719C2×C4—384no—
720C2×C4—762no—
721C2×C4—762no—
722C2×C4—762no—
723C2×C4—762no—
724C2×C4—762no—
725C2×C4—762no—
726C2×C4—762no—
727C2×C4—762no—
728C2×C4—762no—
729C2×C4—762no—
730C2×C4—764no—
731C2×C4—762no—
732C2×C4—1521no—
733C2×C4—1521no—
734C2×C4—1522no—
735C2×C4C22⋊C4×D1911yescharacteristic
736C2×C4C22⋊C4×D1911yescharacteristic
737C2×C4(C22⋊D19)⋊C411yescharacteristic
738C2×C4#1059732811yescharacteristic
739C2×C4#1059732811yescharacteristic
740C2×C4#1059732911yescharacteristic
741C2×C4#1059732911yescharacteristic
742C2×C4#1059733011yescharacteristic
743C2×C4#1059733011yescharacteristic
744C2×C4#1059733111yescharacteristic
745C2×C4#1059733111yescharacteristic
746C2×C4#1059733211yescharacteristic
747C2×C4C2×(C2×D19)⋊C411yescharacteristic
748C2×C4C4×C22⋊D1911yescharacteristic
749C2×C4C4×C22⋊D1911yescharacteristic
750C2×C4#1059737511yescharacteristic
751C2×C4#1059737611yescharacteristic
752C2×C4#1059737611yescharacteristic
753C2×C4#1059738311yescharacteristic
754C2×C4#1059738311yescharacteristic
755C2×C4#1059738311yescharacteristic
756C2×C4#1059738411yescharacteristic
757C2×C4#1059738411yescharacteristic
758C2×C4#1059738511yescharacteristic
759C2×C4#1059738511yescharacteristic
760C2×C4#1059738511yescharacteristic
761C2×C4#1059738611yescharacteristic
762C2×C4#1059739911yescharacteristic
763C8—42no—
764C8—384no—
765C22—44no—
766C22—48no—
767C22—84no—
768C22—84no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—84no—
775C22—82no—
776C22#1192642011yescharacteristic
777C22#1192642111yescharacteristic
778C22#1192644411yescharacteristic
779C22#1192645211yescharacteristic
780C22#1192645311yescharacteristic
781C22#1192645311yescharacteristic
782C22#1192645911yescharacteristic
783C22#1192663512yes—
784C22#1192664112yes—
785C22#1192668112yes—
786C22#1192668612yes—
787C22#1192669612yes—
788C22#1192670712yes—
789C22#1192674312yes—
790C22#1192674712yes—
791C22#1192675712yes—
792C22#1192676512yes—
793C22#1192677212yes—
794C22#1192678912yes—
795C22#1192691511yescharacteristic
796C22#1192692711yescharacteristic
797C22#1192693211yescharacteristic
798C22#1192693511yescharacteristic
799C4—82no—
800C4—764no—
801C4—764no—
802C4—1522no—
803C4#1192639911yescharacteristic
804C4#1192642011yescharacteristic
805C4#1192642311yescharacteristic
806C4#1192644411yescharacteristic
807C4#1192645211yescharacteristic
808C4#1192645911yescharacteristic
809C4#1192646011yescharacteristic
810C4#1192646011yescharacteristic
811C2—84no—
812C2#1456187411yescharacteristic
813C2#1456396712yes—
814C2#1456398712yes—
815C2#1456449011yescharacteristic
816C2#1456451711yescharacteristic
817C2#1456463912yes—
818C2#1456471011yescharacteristic
819C2#1456471611yescharacteristic
820C2#1456472411yescharacteristic
821C2#1456473111yescharacteristic
822C2#1456495112yes—
subgroupG/H
centerC24D4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC22×C19×#102C2
socleC24×C19C2×D4
prime radicalC23×D4×C19C22
cosocleC23×C4×C19C23
hypercenterC22×#102D19
hypocenterC19#11023
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#10597273C2semidirect
3. C2×#11926449C2semidirect
5. C2×#11926306C2semidirect
6. C2×#11926298C2semidirect
15. C22×#64526C4semidirect
192. C22×Dic19SD16semidirect
220. C2×Dic38C22⋊C4semidirect
248. C2×C19⋊C8C22⋊C4semidirect
526. C19#11023semidirect

Maximal subgroups

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

subgroupindex
C23×#645262
C22×#105972732
C2×#119264492
C2×#119264472
C2×#119263062
C2×#119262982
C22×C19×#1022
#1102319