Finite Group Databasebeta

← #18088554

Subgroups — #18088554

Order 4864.

986 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926440C211yesmaximal, characteristic
2C2×C4⋊C4×Dic19C211yesmaximal, characteristic
3C2×#11926307C211yesmaximal, characteristic
4C2×#11926306C211yesmaximal, characteristic
5C2×#11926306C211yesmaximal, characteristic
6C2×#11926298C211yesmaximal, characteristic
7C2×C19×#340C211yesmaximal, characteristic
8C23×C19⋊C8C2211yescharacteristic
9C22×C4⋊Dic19C2211yescharacteristic
10C22×C4⋊Dic19C2211yescharacteristic
11C22×Dic19⋊C4—21no—
12C22×C4×Dic19—21no—
13C22×C4×Dic19C2211yescharacteristic
14#11926440—22no—
15#11926440C414yescomplemented
16C4⋊C4×Dic19—22no—
17C4⋊C4×Dic19—22no—
18C2×C19⋊#95—21no—
19C2×C19⋊#95—21no—
20#11926307C414yescomplemented
21#11926306—22no—
22#11926306C414yescomplemented
23#11926298—22no—
24C23×C8×C19C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C22×C4⋊C4×C19C2211yescharacteristic
27C19×#340—22no—
28C23×C4×C19—21no—
29C23×C4×C19—21no—
30C23×C4×C19C2311yescharacteristic
31C23×Dic19—21no—
32C23×Dic19—21no—
33C23×Dic19D411yescharacteristic
34C23×Dic19D411yescharacteristic
35C22×C8×C19—21no—
36C22×C8×C19—21no—
37C22×C8×C19—21no—
38C22×C8×C19—21no—
39C22×C8×C19—21no—
40C22×C8×C19—21no—
41C22×C8×C19C2×C412yes—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19—21no—
50C2×C4⋊C4×C19C2×C412yes—
51C2×C4⋊C4×C19C2×C412yes—
52C2×C4⋊C4×C19D412yes—
53C2×C4⋊C4×C19Q812yes—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19—21no—
59C2×C4⋊Dic19—21no—
60C2×C4⋊Dic19C2×C412yes—
61C2×C4⋊Dic19C2×C412yes—
62C2×C4⋊Dic19C2×C412yes—
63C2×C4⋊Dic19C2×C412yes—
64C2×C4⋊Dic19D412yes—
65C2×C4⋊Dic19Q812yes—
66C2×Dic19⋊C4—24no—
67C2×Dic19⋊C4—42no—
68C2×Dic19⋊C4—42no—
69C2×C4×Dic19—21no—
70C2×C4×Dic19—21no—
71C2×C4×Dic19—21no—
72C2×C4×Dic19—21no—
73C2×C4×Dic19—24no—
74C2×C4×Dic19—42no—
75C2×C4×Dic19—42no—
76C2×C4×Dic19C2×C412yes—
77C2×C4×Dic19D412yes—
78C22×C19⋊C8—21no—
79C22×C19⋊C8—21no—
80C22×C19⋊C8—21no—
81C22×C19⋊C8—21no—
82C22×C19⋊C8—21no—
83C22×C19⋊C8—21no—
84C22×C19⋊C8C2×C412yes—
85C19⋊#95—24no—
86C19⋊#95—24no—
87C24×C19C2×D411yescharacteristic
88C22×C4×C19—22no—
89C22×C4×C19—22no—
90C22×C4×C19—22no—
91C22×C4×C19—22no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19C22×C411yescharacteristic
103C22×C4×C19C22×C411yescharacteristic
104C22×C4×C19C22×C411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×Q811yescharacteristic
109C22×C4×C19C2×Q811yescharacteristic
110C22×C4×C19#4111yescharacteristic
111C22×C4×C19#4111yescharacteristic
112C22×C4×C19#4111yescharacteristic
113C22×C4×C19#4111yescharacteristic
114C22×C4×C19#4111yescharacteristic
115C22×C4×C19#4111yescharacteristic
116C22×Dic19—21no—
117C22×Dic19—21no—
118C22×Dic19—21no—
119C22×Dic19—21no—
120C22×Dic19—22no—
121C22×Dic19—22no—
122C22×Dic19—22no—
123C22×Dic19—22no—
124C22×Dic19—22no—
125C22×Dic19—21no—
126C22×Dic19—22no—
127C22×Dic19—21no—
128C22×Dic19—21no—
129C22×Dic19—21no—
130C22×Dic19—21no—
131C22×Dic19—21no—
132C22×Dic19—41no—
133C22×Dic19—41no—
134C22×Dic19—41no—
135C22×Dic19—41no—
136C22×Dic19—41no—
137C22×Dic19—41no—
138C22×Dic19—41no—
139C22×Dic19—41no—
140C22×Dic19C22⋊C412yes—
141C22×Dic19C22⋊C412yes—
142C22×Dic19SD1612yes—
143C22×Dic19Q1612yes—
144C2×C8×C19—22no—
145C2×C8×C19—22no—
146C2×C8×C19—22no—
147C2×C8×C19—41no—
148C2×C8×C19—41no—
149C2×C8×C19—41no—
150C2×C8×C19—41no—
151C4⋊C4×C19—22no—
152C4⋊C4×C19—22no—
153C4⋊C4×C19—22no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19—22no—
156C4⋊C4×C19—41no—
157C4⋊C4×C19—41no—
158C4⋊C4×C19C4⋊C414yescomplemented
159C4⋊Dic19—22no—
160C4⋊Dic19—22no—
161C4⋊Dic19—22no—
162C4⋊Dic19—22no—
163C4⋊Dic19—22no—
164C4⋊Dic19—22no—
165C4⋊Dic19C4214yescomplemented
166C4⋊Dic19C4⋊C414yescomplemented
167Dic19⋊C4—48no—
168C4×Dic19—22no—
169C4×Dic19—22no—
170C4×Dic19—22no—
171C4×Dic19—22no—
172C4×Dic19—48no—
173C2×C19⋊C8—22no—
174C2×C19⋊C8—22no—
175C2×C19⋊C8—22no—
176C2×C19⋊C8—41no—
177C2×C19⋊C8—41no—
178C2×C19⋊C8—41no—
179C2×C19⋊C8—41no—
180#10885—191nomaximal, Sylow
181C23×C19C2×C22⋊C411yescharacteristic
182C23×C19C4×D411yescharacteristic
183C23×C19C4×D411yescharacteristic
184C23×C19#12011yescharacteristic
185C23×C19C22⋊Q811yescharacteristic
186C23×C19C22⋊Q811yescharacteristic
187C23×C19#12311yescharacteristic
188C23×C19C2×SD1611yescharacteristic
189C23×C19C2×Q1611yescharacteristic
190C23×C19#13511yescharacteristic
191C23×C19#13511yescharacteristic
192C23×C19AGL(1,ℤ/8)11yescharacteristic
193C23×C19AGL(1,ℤ/8)11yescharacteristic
194C23×C19AGL(1,ℤ/8)11yescharacteristic
195C23×C19#13711yescharacteristic
196C2×C4×C19—24no—
197C2×C4×C19—42no—
198C2×C4×C19—42no—
199C2×C4×C19—42no—
200C2×C4×C19—42no—
201C2×C4×C19—42no—
202C2×C4×C19—42no—
203C2×C4×C19—42no—
204C2×C4×C19—42no—
205C2×C4×C19—42no—
206C2×C4×C19—81no—
207C2×C4×C19—81no—
208C2×C4×C19—81no—
209C2×C4×C19—81no—
210C2×C4×C19C2×C4211yescharacteristic
211C2×C4×C19C2×C4⋊C411yescharacteristic
212C2×C4×C19C2×C4⋊C411yescharacteristic
213C2×C4×C19#11711yescharacteristic
214C2×C4×C19#11711yescharacteristic
215C2×C4×C19#11711yescharacteristic
216C2×C4×C19C4×D411yescharacteristic
217C2×C4×C19C4×D411yescharacteristic
218C2×C4×C19C4×D411yescharacteristic
219C2×C4×C19C4×D411yescharacteristic
220C2×C4×C19C4×D411yescharacteristic
221C2×C4×C19C4×D411yescharacteristic
222C2×C4×C19C4×Q811yescharacteristic
223C2×C4×C19C4×Q811yescharacteristic
224C2×C4×C19C4×Q811yescharacteristic
225C2×C4×C19C4×Q811yescharacteristic
226C2×C4×C19#12111yescharacteristic
227C2×C4×C19#12111yescharacteristic
228C2×C4×C19C22⋊Q811yescharacteristic
229C2×C4×C19C22⋊Q811yescharacteristic
230C2×C4×C19#12311yescharacteristic
231C2×C4×C19#12311yescharacteristic
232C2×C4×C19#12411yescharacteristic
233C2×C4×C19#12511yescharacteristic
234C2×C4×C19#12511yescharacteristic
235C2×C4×C19#12611yescharacteristic
236C2×C4×C19#12611yescharacteristic
237C2×C4×C19C4⋊Q811yescharacteristic
238C2×Dic19—22no—
239C2×Dic19—22no—
240C2×Dic19—22no—
241C2×Dic19—22no—
242C2×Dic19—22no—
243C2×Dic19—22no—
244C2×Dic19—24no—
245C2×Dic19—24no—
246C2×Dic19—22no—
247C2×Dic19—22no—
248C2×Dic19—22no—
249C2×Dic19—42no—
250C2×Dic19—42no—
251C2×Dic19—42no—
252C2×Dic19—42no—
253C2×Dic19—42no—
254C2×Dic19—42no—
255C2×Dic19—42no—
256C2×Dic19—42no—
257C2×Dic19—41no—
258C2×Dic19—41no—
259C2×Dic19—42no—
260C2×Dic19—42no—
261C2×Dic19—42no—
262C2×Dic19—42no—
263C2×Dic19—41no—
264C2×Dic19—41no—
265C2×Dic19#10314yes—
266C8×C19—42no—
267C19⋊C8—42no—
268C2×#389—191no—
269C2×C4×C4⋊C4—191no—
270C2×#340—191no—
271C2×#340—191no—
272C2×#340—191no—
273C2×#340D1911yescharacteristic
274C2×#336—191no—
275C22×C19C4×C22⋊C411yescharacteristic
276C22×C19#38511yescharacteristic
277C22×C19#38511yescharacteristic
278C22×C19#38611yescharacteristic
279C22×C19#38711yescharacteristic
280C22×C19#38711yescharacteristic
281C22×C19#39111yescharacteristic
282C22×C19C2×#10311yescharacteristic
283C22×C19#41611yescharacteristic
284C22×C19#41711yescharacteristic
285C22×C19#41811yescharacteristic
286C22×C19C4×SD1611yescharacteristic
287C22×C19C4×SD1611yescharacteristic
288C22×C19C4×Q1611yescharacteristic
289C22×C19C4×Q1611yescharacteristic
290C22×C19#44011yescharacteristic
291C22×C19#44011yescharacteristic
292C22×C19#44211yescharacteristic
293C22×C19#44211yescharacteristic
294C22×C19#44911yescharacteristic
295C22×C19#44911yescharacteristic
296C22×C19#45011yescharacteristic
297C22×C19#45111yescharacteristic
298C22×C19#47611yescharacteristic
299C22×C19#47611yescharacteristic
300C22×C19#47711yescharacteristic
301C22×C19#47711yescharacteristic
302C22×C19#47811yescharacteristic
303C22×C19#47811yescharacteristic
304C22×C19#47911yescharacteristic
305C22×C19#47911yescharacteristic
306C22×C19#48211yescharacteristic
307C22×C19#48211yescharacteristic
308C22×C19#48311yescharacteristic
309C22×C19#48411yescharacteristic
310C4×C19—44no—
311C4×C19—82no—
312C4×C19C4×C4⋊C411yescharacteristic
313C4×C19C4×C4⋊C411yescharacteristic
314C4×C19#38711yescharacteristic
315C4×C19#38711yescharacteristic
316C4×C19#38811yescharacteristic
317C4×C19#38811yescharacteristic
318C4×C19#38911yescharacteristic
319C4×C19#38911yescharacteristic
320Dic19—24no—
321Dic19—44no—
322Dic19—42no—
323Dic19—44no—
324C23×C8—191no—
325C23×C8C2×D1911yescharacteristic
326C22×C4⋊C4—191no—
327C22×C4⋊C4—191no—
328C22×C4⋊C4—381no—
329C22×C4⋊C4C2×D1911yescharacteristic
330C22×C4⋊C4C2×D1911yescharacteristic
331C22×C42—191no—
332C22×C42—381no—
333#389—194no—
334#389—382no—
335C4×C4⋊C4—382no—
336C4×C4⋊C4—382no—
337C2×#95—381no—
338C2×#95—381no—
339#340—22no—
340#340—194no—
341#340—194no—
342#340—382no—
343#336—382no—
344C2×C19#143611yescharacteristic
345C2×C19C4×#10311yescharacteristic
346C2×C19#176211yescharacteristic
347C2×C19#186311yescharacteristic
348C2×C19#186311yescharacteristic
349C2×C19#186411yescharacteristic
350C2×C19#186411yescharacteristic
351C2×C19#187211yescharacteristic
352C2×C19#187511yescharacteristic
353C2×C19#192011yescharacteristic
354C2×C19#192011yescharacteristic
355C2×C19#192111yescharacteristic
356C2×C19#192111yescharacteristic
357C2×C19#198711yescharacteristic
358C2×C19#198911yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—191no—
362C23×C4—191no—
363C23×C4—381no—
364C23×C4—381no—
365C23×C4C22×D1911yescharacteristic
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—192no—
373C22×C8—381no—
374C22×C8—381no—
375C22×C8—381no—
376C22×C8—381no—
377C22×C8—381no—
378C22×C8—381no—
379C22×C8C4×D1912yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—192no—
389C2×C4⋊C4—192no—
390C2×C4⋊C4—192no—
391C2×C4⋊C4—192no—
392C2×C4⋊C4—192no—
393C2×C4⋊C4—192no—
394C2×C4⋊C4—381no—
395C2×C4⋊C4—381no—
396C2×C4⋊C4—381no—
397C2×C4⋊C4—381no—
398C2×C4⋊C4—381no—
399C2×C4⋊C4—381no—
400C2×C4⋊C4—384no—
401C2×C4⋊C4—762no—
402C2×C4⋊C4—762no—
403C2×C4⋊C4Dic3812yes—
404C2×C4⋊C4C4×D1912yes—
405C2×C4⋊C4C4×D1912yes—
406C2×C4⋊C4C22⋊D1912yes—
407C2×C42—192no—
408C2×C42—192no—
409C2×C42—381no—
410C2×C42—381no—
411C2×C42—381no—
412C2×C42—381no—
413C2×C42—384no—
414C2×C42—762no—
415C2×C42—762no—
416#95—384no—
417#95—384no—
418C19#1088511yescharacteristic, complemented, Sylow
419C24D4×D1911yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—192no—
435C22×C4—192no—
436C22×C4—192no—
437C22×C4—192no—
438C22×C4—381no—
439C22×C4—381no—
440C22×C4—381no—
441C22×C4—381no—
442C22×C4—381no—
443C22×C4—382no—
444C22×C4—382no—
445C22×C4—382no—
446C22×C4—381no—
447C22×C4—382no—
448C22×C4—382no—
449C22×C4—382no—
450C22×C4—381no—
451C22×C4—381no—
452C22×C4—381no—
453C22×C4—381no—
454C22×C4—761no—
455C22×C4—761no—
456C22×C4—761no—
457C22×C4—761no—
458C22×C4—761no—
459C22×C4—761no—
460C22×C4—761no—
461C22×C4—761no—
462C22×C4C2×Dic3811yescharacteristic
463C22×C4C2×C4×D1911yescharacteristic
464C22×C4C2×C4×D1911yescharacteristic
465C22×C4C2×C4×D1911yescharacteristic
466C22×C4#6454111yescharacteristic
467C22×C4#6454111yescharacteristic
468C22×C4D4×D1911yescharacteristic
469C22×C4D4×D1911yescharacteristic
470C22×C4#6454311yescharacteristic
471C22×C4#6454311yescharacteristic
472C22×C4#6454311yescharacteristic
473C22×C4Q8×D1911yescharacteristic
474C22×C4#6454511yescharacteristic
475C22×C4C2×C22⋊D1911yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—382no—
484C2×C8—382no—
485C2×C8—382no—
486C2×C8—761no—
487C2×C8—761no—
488C2×C8—761no—
489C2×C8—761no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—194no—
498C4⋊C4—194no—
499C4⋊C4—382no—
500C4⋊C4—382no—
501C4⋊C4—382no—
502C4⋊C4—382no—
503C4⋊C4—382no—
504C4⋊C4—382no—
505C4⋊C4—768no—
506C4⋊C4Dic19⋊C414yescomplemented
507C42—382no—
508C42—382no—
509C42—382no—
510C42—382no—
511C42—768no—
512C23#1059732411yescharacteristic
513C23C22⋊C4×D1911yescharacteristic
514C23(C22⋊D19)⋊C411yescharacteristic
515C23#1059732911yescharacteristic
516C23#1059733911yescharacteristic
517C23#1059734211yescharacteristic
518C23#1059735711yescharacteristic
519C23#1059735811yescharacteristic
520C23SD16×D1911yescharacteristic
521C23#1059736011yescharacteristic
522C23#1059736011yescharacteristic
523C23#1059736211yescharacteristic
524C23Q16×D1911yescharacteristic
525C23#1059736411yescharacteristic
526C23#1059738311yescharacteristic
527C2×C4—24no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—194no—
542C2×C4—382no—
543C2×C4—382no—
544C2×C4—382no—
545C2×C4—382no—
546C2×C4—382no—
547C2×C4—382no—
548C2×C4—382no—
549C2×C4—382no—
550C2×C4—384no—
551C2×C4—384no—
552C2×C4—382no—
553C2×C4—762no—
554C2×C4—762no—
555C2×C4—762no—
556C2×C4—762no—
557C2×C4—761no—
558C2×C4—761no—
559C2×C4—762no—
560C2×C4—762no—
561C2×C4—762no—
562C2×C4—762no—
563C2×C4—762no—
564C2×C4—762no—
565C2×C4—761no—
566C2×C4—761no—
567C2×C4—762no—
568C2×C4—762no—
569C2×C4C4×Dic3811yescharacteristic
570C2×C4C4×Dic3811yescharacteristic
571C2×C4C42×D1911yescharacteristic
572C2×C4#1059731811yescharacteristic
573C2×C4#1059732311yescharacteristic
574C2×C4#1059732411yescharacteristic
575C2×C4#1059732511yescharacteristic
576C2×C4(C22⋊D19)⋊C411yescharacteristic
577C2×C4(C22⋊D19)⋊C411yescharacteristic
578C2×C4(C22⋊D19)⋊C411yescharacteristic
579C2×C4#1059733011yescharacteristic
580C2×C4#1059733111yescharacteristic
581C2×C4#1059733311yescharacteristic
582C2×C4#1059733311yescharacteristic
583C2×C4#1059733411yescharacteristic
584C2×C4#1059733511yescharacteristic
585C2×C4#1059733611yescharacteristic
586C2×C4C4⋊C4×D1911yescharacteristic
587C2×C4#1059733811yescharacteristic
588C2×C4#1059733911yescharacteristic
589C2×C4#1059734011yescharacteristic
590C2×C4#1059734411yescharacteristic
591C2×C4C2×Dic19⋊C411yescharacteristic
592C2×C4C4×C22⋊D1911yescharacteristic
593C2×C4C4×C22⋊D1911yescharacteristic
594C2×C4#1059738111yescharacteristic
595C2×C4#1059738411yescharacteristic
596C2×C4#1059739211yescharacteristic
597C8—42no—
598C8—762no—
599C22#1192639111yescharacteristic
600C22#1192641511yescharacteristic
601C22#1192641611yescharacteristic
602C22#1192642011yescharacteristic
603C22#1192642611yescharacteristic
604C22#1192642711yescharacteristic
605C22#1192644811yescharacteristic
606C22#103×D1911yescharacteristic
607C22#1192653711yescharacteristic
608C22#1192654411yescharacteristic
609C22#1192654711yescharacteristic
610C22#1192663111yescharacteristic
611C22#1192663511yescharacteristic
612C22#1192663611yescharacteristic
613C22#1192663811yescharacteristic
614C22#1192664311yescharacteristic
615C22#1192664711yescharacteristic
616C22#1192665311yescharacteristic
617C22#1192665511yescharacteristic
618C22#1192668611yescharacteristic
619C22#1192668811yescharacteristic
620C22#1192669311yescharacteristic
621C22#1192669811yescharacteristic
622C22#1192683211yescharacteristic
623C22#1192683311yescharacteristic
624C22#1192683711yescharacteristic
625C22#1192683811yescharacteristic
626C22#1192684211yescharacteristic
627C22#1192684311yescharacteristic
628C22#1192684911yescharacteristic
629C22#1192685011yescharacteristic
630C22#1192686611yescharacteristic
631C22#1192686711yescharacteristic
632C22#1192687311yescharacteristic
633C22#1192687811yescharacteristic
634C4—44no—
635C4—82no—
636C4—384no—
637C4—764no—
638C4—762no—
639C4—764no—
640C4#1192639511yescharacteristic
641C4C4×Dic19⋊C411yescharacteristic
642C4#1192642511yescharacteristic
643C4#1192643111yescharacteristic
644C4#1192643211yescharacteristic
645C4#1192643311yescharacteristic
646C4#1192644011yescharacteristic
647C4#1192644111yescharacteristic
648C2#1456186611yescharacteristic
649C2#1456345411yescharacteristic
650C2#1456345911yescharacteristic
651C2#1456388611yescharacteristic
652C2#1456388711yescharacteristic
653C2#1456389311yescharacteristic
654C2#1456389411yescharacteristic
655C2#1456393911yescharacteristic
656C2#1456395411yescharacteristic
657C2#1456421811yescharacteristic
658C2#1456421911yescharacteristic
659C2#1456422511yescharacteristic
660C2#1456422611yescharacteristic
661C2#1456458111yescharacteristic
662C2#1456459111yescharacteristic
subgroupG/H
centerC24D4×D19
commutatorC2×C4×C19C2×C42
FrattiniC23×C4C22×D19
FittingC2×C19×#340C2
socle, prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#340D19
hypocenterC19#10885
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
15. #11926440C4semidirect
20. #11926307C4semidirect
22. #11926306C4semidirect
158. C4⋊C4×C19C4⋊C4semidirect
165. C4⋊Dic19C42semidirect
166. C4⋊Dic19C4⋊C4semidirect
418. C19#10885semidirect
506. C4⋊C4Dic19⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#119264402
C2×C4⋊C4×Dic192
C2×#119263072
C2×#119263062
C2×#119262982
C2×C19×#3402
#1088519