Finite Group Databasebeta

← #26122609

Subgroups — #26122609

Order 12032.

1234 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093939C211yesmaximal, characteristic
2#20245966C211yesmaximal, characteristic
3#20245741C211yesmaximal, characteristic, complemented
4C2×#15688890C211yesmaximal, characteristic, complemented
5C2×#15688889C211yesmaximal, characteristic, complemented
6C2×#15688889C211yesmaximal, characteristic, complemented
7C22×#99×C47C211yesmaximal, characteristic
8C22×C22⋊Dic47C2211yescharacteristic
9C22×C22⋊Dic47C2211yescharacteristic
10C22×C22⋊Dic47C2211yescharacteristic
11C22×C22⋊Dic47C2211yescharacteristic
12C2×#13093939—22no—
13C2×#13093939—22no—
14C2×#13093939C414yescomplemented
15#15689003—22no—
16#15689003—22no—
17#15688986C412yescomplemented
18#15688979C412yescomplemented
19C22⋊C4×Dic47—22no—
20C22⋊C4×Dic47—22no—
21C4×C22⋊Dic47—22no—
22#15688890—22no—
23#15688889—22no—
24#15688889—22no—
25C23×D4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2211yescharacteristic
28C2×#99×C47—22no—
29C2×#99×C47—22no—
30C2×#99×C47C414yescomplemented
31C23×Dic47—21no—
32C23×Dic47—21no—
33C23×Dic47—21no—
34C23×Dic47D412yes—
35C2×C22⋊Dic47—21no—
36C2×C22⋊Dic47—21no—
37C2×C22⋊Dic47—21no—
38C2×C22⋊Dic47—21no—
39C2×C22⋊Dic47—21no—
40C2×C22⋊Dic47—21no—
41C2×C22⋊Dic47—21no—
42C2×C22⋊Dic47—21no—
43C2×C22⋊Dic47—21no—
44C2×C22⋊Dic47—21no—
45C2×C22⋊Dic47—21no—
46C2×C22⋊Dic47—21no—
47C2×C22⋊Dic47—21no—
48C2×C22⋊Dic47—21no—
49C2×C22⋊Dic47—21no—
50C2×C22⋊Dic47—21no—
51C2×C22⋊Dic47—21no—
52C2×C22⋊Dic47—24no—
53C2×C22⋊Dic47C2×C412yes—
54C2×C22⋊Dic47C2×C412yes—
55C2×C22⋊Dic47C2×C412yes—
56C2×C22⋊Dic47C2×C412yes—
57C2×C22⋊Dic47D412yes—
58C2×C22⋊Dic47D412yes—
59C2×C22⋊Dic47D412yes—
60C2×C4×Dic47—24no—
61#13093939—28no—
62C47⋊#95—24no—
63C47⋊#95—24no—
64C25×C47C2×C411yescharacteristic
65C25×C47C2311yescharacteristic
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47C2×C412yes—
79C22×D4×C47C2×C412yes—
80C23×C4×C47—21no—
81C23×C4×C47—21no—
82C23×C4×C47C2×C411yescharacteristic
83C2×C22⋊C4×C47—21no—
84C2×C22⋊C4×C47—21no—
85C2×C22⋊C4×C47—21no—
86C2×C22⋊C4×C47—21no—
87C2×C22⋊C4×C47—21no—
88C2×C22⋊C4×C47—21no—
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47C2×C412yes—
92C2×C22⋊C4×C47C2×C412yes—
93C2×C22⋊C4×C47D412yes—
94C2×C22⋊C4×C47D412yes—
95#99×C47—28no—
96C24×C47—21no—
97C24×C47—21no—
98C24×C47—21no—
99C24×C47—21no—
100C24×C47—21no—
101C24×C47—21no—
102C24×C47—82no—
103C24×C47—82no—
104C24×C47C4212yescomplemented
105C24×C47C22×C411yescharacteristic
106C24×C47C22×C411yescharacteristic
107C24×C47C22×C411yescharacteristic
108C24×C47C2×D411yescharacteristic
109C24×C47C2×D411yescharacteristic
110C24×C47C2×D411yescharacteristic
111C24×C47C2×D411yescharacteristic
112C24×C47C2×D411yescharacteristic
113C24×C47C2×D411yescharacteristic
114C24×C47#4111yescharacteristic
115C24×C47#4111yescharacteristic
116C24×C47#4111yescharacteristic
117C24×C47#4111yescharacteristic
118C24×C47#4111yescharacteristic
119C24×C47#4111yescharacteristic
120C2×D4×C47—22no—
121C2×D4×C47—22no—
122C2×D4×C47—22no—
123C2×D4×C47—22no—
124C2×D4×C47—22no—
125C2×D4×C47—22no—
126C2×D4×C47—22no—
127C2×D4×C47—22no—
128C2×D4×C47—22no—
129C2×D4×C47—22no—
130C2×D4×C47—22no—
131C2×D4×C47—22no—
132C2×D4×C47—41no—
133C2×D4×C47—41no—
134C2×D4×C47—41no—
135C2×D4×C47—41no—
136C2×D4×C47—41no—
137C2×D4×C47—41no—
138C2×D4×C47—41no—
139C2×D4×C47—41no—
140C2×D4×C47—41no—
141C2×D4×C47—41no—
142C2×D4×C47—41no—
143C2×D4×C47—41no—
144C2×D4×C47—41no—
145C2×D4×C47—41no—
146C2×D4×C47—41no—
147C2×D4×C47—41no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—41no—
159C22×C4×C47—41no—
160C22×C4×C47—82no—
161C22×C4×C47—82no—
162C22×C4×C47C4212yescomplemented
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—41no—
171C22×Dic47—41no—
172C22×Dic47—41no—
173C22×Dic47—41no—
174C22×Dic47—82no—
175C22×Dic47—82no—
176C22×Dic47—82no—
177C22×Dic47—82no—
178C22×Dic47C22⋊C414yes—
179C22⋊C4×C47—22no—
180C22⋊C4×C47—22no—
181C22⋊C4×C47—22no—
182C22⋊C4×C47—22no—
183C22⋊C4×C47—22no—
184C22⋊C4×C47—41no—
185C22⋊C4×C47—41no—
186C22⋊C4×C47C22⋊C414yescomplemented
187C22⋊Dic47—22no—
188C22⋊Dic47—22no—
189C22⋊Dic47—22no—
190C22⋊Dic47—22no—
191C22⋊Dic47—22no—
192C22⋊Dic47—22no—
193C22⋊Dic47—22no—
194C22⋊Dic47—22no—
195C22⋊Dic47—22no—
196C22⋊Dic47—22no—
197C22⋊Dic47—22no—
198C22⋊Dic47—41no—
199C22⋊Dic47—41no—
200C22⋊Dic47—41no—
201C22⋊Dic47—41no—
202C22⋊Dic47—84no—
203C22⋊Dic47C22⋊C414yescomplemented
204C4×Dic47—84no—
205C23×C47—22no—
206C23×C47—22no—
207C23×C47—22no—
208C23×C47—42no—
209C23×C47—42no—
210C23×C47—42no—
211C23×C47—42no—
212C23×C47—42no—
213C23×C47—42no—
214C23×C47—42no—
215C23×C47—44no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47—41no—
219C23×C47—41no—
220C23×C47—82no—
221C23×C47—82no—
222C23×C47—81no—
223C23×C47—81no—
224C23×C47—81no—
225C23×C47—81no—
226C23×C47—81no—
227C23×C47—81no—
228C23×C47—81no—
229C23×C47—81no—
230C23×C47—82no—
231C23×C47—82no—
232C23×C47—82no—
233C23×C47—82no—
234C23×C47C2×C4211yescharacteristic
235C23×C47C2×C22⋊C411yescharacteristic
236C23×C47C2×C22⋊C411yescharacteristic
237C23×C47C2×C22⋊C411yescharacteristic
238C23×C47#11711yescharacteristic
239C23×C47#11711yescharacteristic
240C23×C47#11711yescharacteristic
241C23×C47C4×D411yescharacteristic
242C23×C47C4×D411yescharacteristic
243C23×C47C4×D411yescharacteristic
244C23×C47C4×D411yescharacteristic
245C23×C47C4×D411yescharacteristic
246C23×C47C4×D411yescharacteristic
247C23×C47C4×D411yescharacteristic
248C23×C47C4×D411yescharacteristic
249C23×C47C4×D411yescharacteristic
250C23×C47C4×D411yescharacteristic
251C23×C47C4×D411yescharacteristic
252C23×C47C4×D411yescharacteristic
253C23×C47#12011yescharacteristic
254C23×C47#12111yescharacteristic
255C23×C47#12111yescharacteristic
256C23×C47#12111yescharacteristic
257C23×C47#12111yescharacteristic
258C23×C47#12111yescharacteristic
259C23×C47#12111yescharacteristic
260C23×C47#12311yescharacteristic
261C23×C47#12311yescharacteristic
262C23×C47#12311yescharacteristic
263C23×C47#12411yescharacteristic
264C23×C47#12411yescharacteristic
265C23×C47#12411yescharacteristic
266C23×C47#12611yescharacteristic
267C23×C47#12611yescharacteristic
268C23×C47#12711yescharacteristic
269D4×C47—42no—
270D4×C47—42no—
271D4×C47—42no—
272D4×C47—42no—
273D4×C47—42no—
274D4×C47—42no—
275D4×C47—42no—
276D4×C47—42no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—24no—
281C2×C4×C47—44no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—42no—
287C2×C4×C47—82no—
288C2×C4×C47—82no—
289C2×C4×C47—82no—
290C2×C4×C47—82no—
291C2×C4×C47—82no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—44no—
295C2×Dic47—44no—
296C2×Dic47—44no—
297C2×Dic47—44no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—82no—
301C2×Dic47—82no—
302C2×Dic47—82no—
303C2×Dic47—82no—
304C2×Dic47—82no—
305C2×Dic47—82no—
306C2×Dic47—82no—
307C2×Dic47—82no—
308#10938—471nomaximal, Sylow
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—41no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—44no—
345C22×C47—42no—
346C22×C47—82no—
347C22×C47—82no—
348C22×C47—82no—
349C22×C47—82no—
350C22×C47—82no—
351C22×C47—82no—
352C22×C47C4×C22⋊C411yescharacteristic
353C22×C47C4×C22⋊C411yescharacteristic
354C22×C47C4×C22⋊C411yescharacteristic
355C22×C47#38611yescharacteristic
356C22×C47#38611yescharacteristic
357C22×C47#38611yescharacteristic
358C22×C47#38811yescharacteristic
359C22×C47#38811yescharacteristic
360C22×C47#38811yescharacteristic
361C22×C47#38811yescharacteristic
362C22×C47#38811yescharacteristic
363C22×C47#38811yescharacteristic
364C22×C47#39011yescharacteristic
365C22×C47#39011yescharacteristic
366C22×C47#39011yescharacteristic
367C4×C47—44no—
368C4×C47—42no—
369C4×C47—82no—
370Dic47—44no—
371Dic47—44no—
372Dic47—82no—
373Dic47—82no—
374C22×#99—471no—
375C22×#99D4711yescharacteristic
376#2308—471no—
377#2273—471no—
378C2×#342—471no—
379C2×#342—471no—
380C2×#342—471no—
381C2×C47—21no—
382C2×C47—21no—
383C2×C47—21no—
384C2×C47—21no—
385C2×C47—21no—
386C2×C47—21no—
387C2×C47—21no—
388C2×C47—21no—
389C2×C47—21no—
390C2×C47—21no—
391C2×C47—21no—
392C2×C47—21no—
393C2×C47—21no—
394C2×C47—21no—
395C2×C47—82no—
396C2×C47#143711yescharacteristic
397C2×C47#191312yes—
398C23×D4C2×D4711yescharacteristic
399C22×C22⋊C4—471no—
400C22×C22⋊C4—471no—
401C22×C22⋊C4—471no—
402C22×C22⋊C4—471no—
403C22×C22⋊C4C2×D4711yescharacteristic
404C22×C22⋊C4C2×D4711yescharacteristic
405C2×#99—22no—
406C2×#99—22no—
407C2×#99—474no—
408C2×#99—942no—
409C2×#99—942no—
410C2×#99Dic4714yescomplemented
411#386—942no—
412#386—942no—
413#381—472no—
414#379—472no—
415C4×C22⋊C4—942no—
416C4×C22⋊C4—942no—
417C4×C22⋊C4—942no—
418#342—942no—
419#342—942no—
420#342—942no—
421C47#1093811yescharacteristic, complemented, Sylow
422C25C4×D4711yescharacteristic
423C25C22×D4711yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4C4×D4712yes—
437C22×D4C2×Dic4712yes—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—472no—
441C23×C4—941no—
442C23×C4—941no—
443C23×C4—941no—
444C23×C4C4×D4711yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—472no—
454C2×C22⋊C4—472no—
455C2×C22⋊C4—472no—
456C2×C22⋊C4—472no—
457C2×C22⋊C4—472no—
458C2×C22⋊C4—472no—
459C2×C22⋊C4—472no—
460C2×C22⋊C4—941no—
461C2×C22⋊C4—941no—
462C2×C22⋊C4—941no—
463C2×C22⋊C4—941no—
464C2×C22⋊C4—941no—
465C2×C22⋊C4—941no—
466C2×C22⋊C4—941no—
467C2×C22⋊C4—941no—
468C2×C22⋊C4—941no—
469C2×C22⋊C4—941no—
470C2×C22⋊C4—941no—
471C2×C22⋊C4—941no—
472C2×C22⋊C4—941no—
473C2×C22⋊C4—941no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—944no—
476C2×C22⋊C4—941no—
477C2×C22⋊C4—941no—
478C2×C22⋊C4C2×Dic4712yes—
479C2×C22⋊C4C2×Dic4712yes—
480C2×C22⋊C4C22⋊D4712yes—
481C2×C22⋊C4C22⋊D4712yes—
482C2×C42—944no—
483#99—28no—
484#99—948no—
485#95—944no—
486#95—944no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—82no—
494C24—82no—
495C24C4×Dic4712yescomplemented
496C24C2×C4×D4711yescharacteristic
497C24C2×C4×D4711yescharacteristic
498C24#1062535011yescharacteristic
499C24#1062535011yescharacteristic
500C24D4×D4711yescharacteristic
501C24D4×D4711yescharacteristic
502C24D4×D4711yescharacteristic
503C24D4×D4711yescharacteristic
504C24#1062535211yescharacteristic
505C24#1062535211yescharacteristic
506C24#1062535211yescharacteristic
507C24#1062535211yescharacteristic
508C24C22×Dic4711yescharacteristic
509C24C2×C22⋊D4711yescharacteristic
510C24C2×C22⋊D4711yescharacteristic
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—474no—
554C22×C4—942no—
555C22×C4—942no—
556C22×C4—942no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—3762no—
562C22×C4—3762no—
563C22×C4—3762no—
564C22×C4—3762no—
565C22×C4—1881no—
566C22×C4—1881no—
567C22×C4—1881no—
568C22×C4—1881no—
569C22×C4C4×Dic4712yescomplemented
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—474no—
578C22⋊C4—942no—
579C22⋊C4—942no—
580C22⋊C4—942no—
581C22⋊C4—942no—
582C22⋊C4—942no—
583C22⋊C4—942no—
584C22⋊C4—942no—
585C22⋊C4—942no—
586C22⋊C4—942no—
587C22⋊C4—942no—
588C22⋊C4—942no—
589C22⋊C4—3764no—
590C22⋊C4—1881no—
591C22⋊C4—1881no—
592C22⋊C4—1881no—
593C22⋊C4—1881no—
594C22⋊C4C22⋊Dic4714yescomplemented
595C42—3764no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—44no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—82no—
612C23—82no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23—81no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23—82no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23C2×C4×Dic4711yescharacteristic
626C23C22⋊C4×D4711yescharacteristic
627C23C22⋊C4×D4711yescharacteristic
628C23C2×C22⋊Dic4711yescharacteristic
629C23#1309398011yescharacteristic
630C23#1309398011yescharacteristic
631C23#1309398311yescharacteristic
632C23(C22⋊D47)⋊C411yescharacteristic
633C23(C22⋊D47)⋊C411yescharacteristic
634C23(C22⋊D47)⋊C411yescharacteristic
635C23(C22⋊D47)⋊C411yescharacteristic
636C23C4×C22⋊D4711yescharacteristic
637C23C4×C22⋊D4711yescharacteristic
638C23C4×C22⋊D4711yescharacteristic
639C23C4×C22⋊D4711yescharacteristic
640C23D4×Dic4711yescharacteristic
641C23D4×Dic4711yescharacteristic
642C23D4×Dic4711yescharacteristic
643C23D4×Dic4711yescharacteristic
644C23#1309399211yescharacteristic
645C23#1309399511yescharacteristic
646C23#1309399511yescharacteristic
647C23#1309399611yescharacteristic
648C23#1309399611yescharacteristic
649C23#1309399711yescharacteristic
650C23#1309399711yescharacteristic
651C23#1309400511yescharacteristic
652C23#1309400611yescharacteristic
653C23#1309400611yescharacteristic
654C23#1309401011yescharacteristic
655C23#1309401011yescharacteristic
656C23#1309401111yescharacteristic
657C23#1309401711yescharacteristic
658C23#1309401711yescharacteristic
659C23#1309402011yescharacteristic
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—44no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—944no—
684C2×C4—944no—
685C2×C4—3762no—
686C2×C4—3762no—
687C2×C4—3762no—
688C2×C4—3762no—
689C2×C4—3762no—
690C2×C4—3762no—
691C2×C4—3762no—
692C2×C4—3762no—
693C2×C4—1884no—
694C2×C4—1882no—
695C2×C4—1882no—
696C2×C4—1884no—
697C2×C4—1884no—
698C2×C4—1884no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—44no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22C4×C22⋊Dic4711yescharacteristic
743C22C22⋊C4×Dic4711yescharacteristic
744C22C22⋊C4×Dic4711yescharacteristic
745C22#1568899911yescharacteristic
746C22#1568899911yescharacteristic
747C22#1568900311yescharacteristic
748C22#1568901111yescharacteristic
749C22#1568901111yescharacteristic
750C22#1568901611yescharacteristic
751C22#1568901611yescharacteristic
752C22#1568901711yescharacteristic
753C22#1568901711yescharacteristic
754C22#1568902311yescharacteristic
755C22#1568902311yescharacteristic
756C22#1568902611yescharacteristic
757C4—44no—
758C4—42no—
759C4—82no—
760C4—3762no—
761C4—3762no—
762C4—1884no—
763C4—1884no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—82no—
779C2#2024162511yescharacteristic
780C2#2024392712yes—
subgroupG/H
centerC22#15688999
commutatorC23×C47C2×C42
FrattiniC25C22×D47
FittingC22×#99×C47C2
socleC22×C47#386
prime radicalC23×D4×C47C22
cosocleC25×C47C23
hypercenterC22×#99D47
hypocenterC47#10938
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. #20245741C2semidirect
4. C2×#15688890C2semidirect
5. C2×#15688889C2semidirect
6. C2×#15688889C2semidirect
14. C2×#13093939C4semidirect
17. #15688986C4semidirect
18. #15688979C4semidirect
30. C2×#99×C47C4semidirect
104. C24×C47C42semidirect
162. C22×C4×C47C42semidirect
186. C22⋊C4×C47C22⋊C4semidirect
203. C22⋊Dic47C22⋊C4semidirect
410. C2×#99Dic47semidirect
421. C47#10938semidirect
495. C24C4×Dic47semidirect
569. C22×C4C4×Dic47semidirect
594. C22⋊C4C22⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939392
#202459662
#202457412
C2×#156888902
C2×#156888892
C22×#99×C472
#1093847