Finite Group Databasebeta

← #26124093

Subgroups — #26124093

Order 12032.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093946C211yesmaximal, characteristic
2C22×#13093944C211yesmaximal, characteristic
3C2×#15689024C211yesmaximal, characteristic
4C2×#15688885C211yesmaximal, characteristic, complemented
5C2×#15688877C211yesmaximal, characteristic, complemented
6#20241617C211yesmaximal, characteristic, complemented
7C2×C47×#340C211yesmaximal, characteristic, complemented
8C23×D188C2211yescharacteristic
9C23×C47⋊C8C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×(C2×D47)⋊C4—21no—
12C22×(C2×D47)⋊C4—21no—
13C22×C4×Dic47C2211yescharacteristic
14C2×#13093946—22no—
15C2×#13093946—22no—
16C2×#13093946—22no—
17C2×#13093944—22no—
18C2×#13093944—22no—
19C2×#13093944C414yescomplemented
20#15689024—22no—
21#15689024—22no—
22C2×C47⋊#95—21no—
23C2×C47⋊#95—21no—
24#15688885—22no—
25#15688877—22no—
26C23×C8×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C22×C4⋊C4×C47C2211yescharacteristic
29C47×#340—22no—
30C24×D47—21no—
31C22×D188—21no—
32C22×D188—21no—
33C22×D188—21no—
34C22×D188—21no—
35C22×D188—21no—
36C22×D188—21no—
37C22×D188—21no—
38C22×D188—21no—
39C22×D188—21no—
40C22×D188—21no—
41C22×D188—21no—
42C22×D188C2×C412yes—
43C22×D188D412yes—
44C22×D188D412yes—
45C23×Dic47—21no—
46C23×Dic47D411yescharacteristic
47C23×Dic47D411yescharacteristic
48C22×C47⋊C8—21no—
49C22×C47⋊C8—21no—
50C22×C47⋊C8—21no—
51C22×C47⋊C8—21no—
52C22×C47⋊C8—21no—
53C22×C47⋊C8—21no—
54C22×C47⋊C8C2×C412yes—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47—21no—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—21no—
60C2×C4⋊Dic47D412yes—
61C2×(C2×D47)⋊C4—24no—
62C2×(C2×D47)⋊C4—24no—
63C2×(C2×D47)⋊C4—42no—
64C2×(C2×D47)⋊C4—42no—
65C2×(C2×D47)⋊C4—42no—
66C2×(C2×D47)⋊C4—42no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47—21no—
69C2×C4×Dic47—21no—
70C2×C4×Dic47—21no—
71C2×C4×Dic47—21no—
72C2×C4×Dic47—21no—
73#13093946—28no—
74#13093944—28no—
75C47⋊#95—42no—
76C47⋊#95—42no—
77C23×C4×C47—21no—
78C23×C4×C47—21no—
79C23×C4×C47C2311yescharacteristic
80C22×C8×C47—21no—
81C22×C8×C47—21no—
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47—21no—
85C22×C8×C47—21no—
86C22×C8×C47D412yes—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47C2×C412yes—
98C2×C4⋊C4×C47D412yes—
99C24×C47C2×D411yescharacteristic
100C23×D47—22no—
101C23×D47—22no—
102C23×D47—22no—
103C23×D47—41no—
104C23×D47—41no—
105C23×D47—41no—
106C23×D47—41no—
107C23×D47—41no—
108C23×D47—41no—
109C23×D47—41no—
110C23×D47—41no—
111C23×D47—41no—
112C23×D47—41no—
113C23×D47—41no—
114C23×D47—41no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—41no—
118C22×C4×C47—41no—
119C22×C4×C47—41no—
120C22×C4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47—41no—
127C22×C4×C47—41no—
128C22×C4×C47—41no—
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47#4111yescharacteristic
136C22×C4×C47#4111yescharacteristic
137C22×C4×C47#4111yescharacteristic
138C22×C4×C47#4111yescharacteristic
139C22×C4×C47#4111yescharacteristic
140C22×C4×C47#4111yescharacteristic
141C22×C4×C47#4111yescharacteristic
142C22×C4×C47#4111yescharacteristic
143C22×Dic47—21no—
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—22no—
156C22×Dic47—41no—
157C22×Dic47—41no—
158C22×Dic47—41no—
159C22×Dic47—41no—
160C22×Dic47—41no—
161C22×Dic47—41no—
162C22×Dic47D812yes—
163C22×Dic47SD1612yes—
164C2×D188—22no—
165C2×D188—22no—
166C2×D188—22no—
167C2×D188—22no—
168C2×D188—22no—
169C2×D188—22no—
170C2×D188—22no—
171C2×D188—22no—
172C2×D188—22no—
173C2×D188—22no—
174C2×D188—22no—
175C2×D188—22no—
176C2×D188—22no—
177C2×D188—22no—
178C2×D188—22no—
179C2×D188—41no—
180C2×D188—41no—
181C2×D188—41no—
182C2×D188—41no—
183C2×D188—41no—
184C2×D188—41no—
185C2×D188—41no—
186C2×D188—41no—
187C2×D188—41no—
188C2×D188—41no—
189C2×D188—41no—
190C2×D188—41no—
191C2×D188C22⋊C414yes—
192C2×C8×C47—22no—
193C2×C8×C47—22no—
194C2×C8×C47—22no—
195C2×C8×C47—41no—
196C2×C8×C47—41no—
197C2×C8×C47—41no—
198C2×C8×C47—41no—
199C4⋊C4×C47—22no—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—22no—
202C4⋊C4×C47—22no—
203C4⋊C4×C47—41no—
204C4⋊C4×C47—41no—
205C4⋊C4×C47—41no—
206C4⋊C4×C47—41no—
207(C2×D47)⋊C4—48no—
208(C2×D47)⋊C4—48no—
209C4⋊Dic47—22no—
210C4⋊Dic47—22no—
211C4⋊Dic47—41no—
212C4⋊Dic47—41no—
213C4×Dic47—41no—
214C4×Dic47—41no—
215C4×Dic47—41no—
216C4×Dic47—41no—
217C2×C47⋊C8—22no—
218C2×C47⋊C8—22no—
219C2×C47⋊C8—22no—
220C2×C47⋊C8—41no—
221C2×C47⋊C8—41no—
222C2×C47⋊C8—41no—
223C2×C47⋊C8—41no—
224C23×C47C4×D411yescharacteristic
225C23×C47#12011yescharacteristic
226C23×C47#12111yescharacteristic
227C23×C47#12111yescharacteristic
228C23×C47#12111yescharacteristic
229C23×C47#12311yescharacteristic
230C23×C47#12411yescharacteristic
231C23×C47C2×D811yescharacteristic
232C23×C47C2×SD1611yescharacteristic
233C23×C47#13511yescharacteristic
234C23×C47#13511yescharacteristic
235C23×C47AGL(1,ℤ/8)11yescharacteristic
236C23×C47AGL(1,ℤ/8)11yescharacteristic
237C23×C47AGL(1,ℤ/8)11yescharacteristic
238C23×C47#13711yescharacteristic
239C22×D47—24no—
240C22×D47—42no—
241C22×D47—42no—
242C22×D47—42no—
243C22×D47—42no—
244C22×D47—42no—
245C22×D47—42no—
246C22×D47—42no—
247C22×D47—42no—
248C22×D47—42no—
249C22×D47—42no—
250C22×D47—42no—
251C22×D47—42no—
252C22×D47—42no—
253C22×D47—42no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47—81no—
259C22×D47—81no—
260C22×D47—81no—
261C22×D47—81no—
262C22×D47—81no—
263C22×D47—81no—
264C22×D47—81no—
265C22×D47—81no—
266C22×D47—81no—
267C22×D47—81no—
268C22×D47—81no—
269C22×D47—81no—
270C22×D47—81no—
271C22×D47—81no—
272C22×D47—81no—
273C22×D47—81no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—81no—
281C2×C4×C47—81no—
282C2×C4×C47—81no—
283C2×C4×C47—81no—
284C2×C4×C47—81no—
285C2×C4×C47—81no—
286C2×C4×C47—81no—
287C2×C4×C47—81no—
288C2×C4×C47C2×C22⋊C411yescharacteristic
289C2×C4×C47#11711yescharacteristic
290C2×C4×C47#11711yescharacteristic
291C2×C4×C47C4×D411yescharacteristic
292C2×C4×C47C4×D411yescharacteristic
293C2×C4×C47C4×D411yescharacteristic
294C2×C4×C47#12011yescharacteristic
295C2×C4×C47#12111yescharacteristic
296C2×C4×C47#12111yescharacteristic
297C2×C4×C47#12111yescharacteristic
298C2×C4×C47#12111yescharacteristic
299C2×C4×C47#12111yescharacteristic
300C2×C4×C47#12311yescharacteristic
301C2×C4×C47#12311yescharacteristic
302C2×C4×C47#12311yescharacteristic
303C2×C4×C47#12311yescharacteristic
304C2×C4×C47#12311yescharacteristic
305C2×C4×C47#12311yescharacteristic
306C2×C4×C47#12311yescharacteristic
307C2×C4×C47#12311yescharacteristic
308C2×C4×C47#12311yescharacteristic
309C2×C4×C47#12411yescharacteristic
310C2×C4×C47#12411yescharacteristic
311C2×C4×C47#12411yescharacteristic
312C2×C4×C47#12611yescharacteristic
313C2×C4×C47#12611yescharacteristic
314C2×C4×C47#12611yescharacteristic
315C2×C4×C47#12611yescharacteristic
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—81no—
334C2×Dic47—81no—
335C2×Dic47—81no—
336C2×Dic47—81no—
337D188—24no—
338D188—24no—
339D188—42no—
340D188—42no—
341D188—42no—
342D188—42no—
343D188—42no—
344D188—42no—
345C8×C47—42no—
346C47⋊C8—42no—
347#11189—471nomaximal, Sylow
348C22×C47#38611yescharacteristic
349C22×C47#38811yescharacteristic
350C22×C47#38811yescharacteristic
351C22×C47#39411yescharacteristic
352C22×C47#39411yescharacteristic
353C22×C47#39411yescharacteristic
354C22×C47#39711yescharacteristic
355C22×C47C4×D811yescharacteristic
356C22×C47C4×SD1611yescharacteristic
357C22×C47#44011yescharacteristic
358C22×C47#44211yescharacteristic
359C22×C47#44711yescharacteristic
360C22×C47#44911yescharacteristic
361C22×C47#45011yescharacteristic
362C22×C47#45211yescharacteristic
363C22×C47#45911yescharacteristic
364C22×C47#45911yescharacteristic
365C22×C47#46011yescharacteristic
366C22×C47#46111yescharacteristic
367C22×C47#46311yescharacteristic
368C22×C47#46311yescharacteristic
369C22×C47#46311yescharacteristic
370C22×C47#46411yescharacteristic
371C22×C47#46511yescharacteristic
372C22×C47#46611yescharacteristic
373C22×C47#46811yescharacteristic
374C22×C47#46911yescharacteristic
375C22×C47#48011yescharacteristic
376C22×C47#48111yescharacteristic
377C22×C47#48211yescharacteristic
378C22×C47#48211yescharacteristic
379C22×C47#48611yescharacteristic
380C22×C47#48811yescharacteristic
381C22×C47#48911yescharacteristic
382C22×C47#49011yescharacteristic
383C2×D47—44no—
384C2×D47—44no—
385C2×D47—44no—
386C2×D47—82no—
387C2×D47—82no—
388C2×D47—82no—
389C2×D47—82no—
390C2×D47—82no—
391C2×D47—82no—
392C2×D47—82no—
393C2×D47—82no—
394C2×D47—82no—
395C2×D47—82no—
396C2×D47—82no—
397C2×D47—82no—
398C4×C47—82no—
399C4×C47—82no—
400C4×C47#38111yescharacteristic
401C4×C47#38611yescharacteristic
402C4×C47#38811yescharacteristic
403C4×C47#38811yescharacteristic
404C4×C47#39411yescharacteristic
405C4×C47#39711yescharacteristic
406C4×C47#39711yescharacteristic
407C4×C47#39711yescharacteristic
408Dic47—42no—
409Dic47—42no—
410Dic47—82no—
411C22×#102—471no—
412C22×#102—471no—
413C2×#390—471no—
414C2×#340—471no—
415C2×#340D4711yescharacteristic, complemented
416C2×#336—471no—
417C4⋊#95—471no—
418C2×C47#144011yescharacteristic
419C2×C47#187711yescharacteristic
420C2×C47#187911yescharacteristic
421C2×C47#192511yescharacteristic
422C2×C47#192611yescharacteristic
423C2×C47#193411yescharacteristic
424C2×C47#193611yescharacteristic
425C2×C47#203311yescharacteristic
426C2×C47#203411yescharacteristic
427C2×C47#204111yescharacteristic
428C2×C47#204211yescharacteristic
429C2×C47#205411yescharacteristic
430C2×C47#205511yescharacteristic
431C2×C47#207111yescharacteristic
432C2×C47#207311yescharacteristic
433D47—84no—
434C23×D4—471no—
435C23×C8—471no—
436C23×C8C2×D4711yescharacteristic
437C22×C4⋊C4—471no—
438C22×C4⋊C4C2×D4711yescharacteristic
439C22×C4⋊C4C2×D4711yescharacteristic
440C22×C22⋊C4—941no—
441C22×C22⋊C4—941no—
442C22×C42—471no—
443C2×#102—474no—
444C2×#102—942no—
445C2×#102—942no—
446C2×#102—942no—
447C2×#102—942no—
448C2×#102—942no—
449#390—942no—
450#390—942no—
451C2×#95—941no—
452C2×#95—941no—
453#340—22no—
454#340—942no—
455#336—942no—
456C47#1118911yescharacteristic, complemented, Sylow
457C25—941no—
458C22×D4—472no—
459C22×D4—472no—
460C22×D4—472no—
461C22×D4—941no—
462C22×D4—941no—
463C22×D4—941no—
464C22×D4—941no—
465C22×D4—941no—
466C22×D4—941no—
467C22×D4—941no—
468C22×D4—941no—
469C22×D4—941no—
470C22×D4—941no—
471C22×D4—941no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—471no—
475C23×C4—471no—
476C23×C4—941no—
477C23×C4C22×D4711yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—472no—
485C22×C8—941no—
486C22×C8—941no—
487C22×C8—941no—
488C22×C8—941no—
489C22×C8—941no—
490C22×C8—941no—
491C22×C8D18812yes—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—472no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4C4×D4712yes—
509C2×C4⋊C4C22⋊D4712yes—
510C2×C22⋊C4—944no—
511C2×C22⋊C4—944no—
512C2×C22⋊C4—1882no—
513C2×C22⋊C4—1882no—
514C2×C22⋊C4—1882no—
515C2×C22⋊C4—1882no—
516C2×C42—941no—
517C2×C42—941no—
518C2×C42—941no—
519C2×C42—941no—
520C2×C42—941no—
521C2×C42—941no—
522#102—948no—
523#102—948no—
524#95—1882no—
525#95—1882no—
526C24—942no—
527C24—942no—
528C24—942no—
529C24—1881no—
530C24—1881no—
531C24—1881no—
532C24—1881no—
533C24—1881no—
534C24—1881no—
535C24—1881no—
536C24—1881no—
537C24—1881no—
538C24—1881no—
539C24—1881no—
540C24—1881no—
541C24D4×D4711yescharacteristic
542C2×D4—474no—
543C2×D4—942no—
544C2×D4—942no—
545C2×D4—942no—
546C2×D4—942no—
547C2×D4—942no—
548C2×D4—942no—
549C2×D4—942no—
550C2×D4—942no—
551C2×D4—942no—
552C2×D4—942no—
553C2×D4—942no—
554C2×D4—942no—
555C2×D4—942no—
556C2×D4—942no—
557C2×D4—942no—
558C2×D4—1881no—
559C2×D4—1881no—
560C2×D4—1881no—
561C2×D4—1881no—
562C2×D4—1881no—
563C2×D4—1881no—
564C2×D4—1881no—
565C2×D4—1881no—
566C2×D4—1881no—
567C2×D4—1881no—
568C2×D4—1881no—
569C2×D4—1881no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—472no—
585C22×C4—472no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—942no—
599C22×C4—1881no—
600C22×C4—1881no—
601C22×C4—1881no—
602C22×C4—1881no—
603C22×C4—1881no—
604C22×C4—1881no—
605C22×C4C2×C4×D4711yescharacteristic
606C22×C4C2×D18811yescharacteristic
607C22×C4#1062535011yescharacteristic
608C22×C4#1062535011yescharacteristic
609C22×C4#1062535011yescharacteristic
610C22×C4#1062535011yescharacteristic
611C22×C4D4×D4711yescharacteristic
612C22×C4D4×D4711yescharacteristic
613C22×C4D4×D4711yescharacteristic
614C22×C4#1062535211yescharacteristic
615C22×C4#1062535211yescharacteristic
616C22×C4#1062535411yescharacteristic
617C22×C4#1062535411yescharacteristic
618C22×C4C2×C22⋊D4711yescharacteristic
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—942no—
627C2×C8—942no—
628C2×C8—942no—
629C2×C8—1881no—
630C2×C8—1881no—
631C2×C8—1881no—
632C2×C8—1881no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—942no—
642C4⋊C4—942no—
643C4⋊C4—1881no—
644C4⋊C4—1881no—
645C22⋊C4—1888no—
646C22⋊C4—1888no—
647C42—1881no—
648C42—1881no—
649C42—1881no—
650C42—1881no—
651C23—944no—
652C23—3761no—
653C23—3761no—
654C23—3761no—
655C23—3761no—
656C23—3761no—
657C23—3761no—
658C23—3761no—
659C23—3761no—
660C23—3761no—
661C23—3761no—
662C23—3761no—
663C23—3761no—
664C23—3761no—
665C23—3761no—
666C23—3761no—
667C23—3761no—
668C23—1882no—
669C23—1882no—
670C23—1882no—
671C23—1882no—
672C23—1882no—
673C23—1882no—
674C23—1882no—
675C23—1882no—
676C23—1882no—
677C23—1882no—
678C23—1882no—
679C23—1882no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23(C22⋊D47)⋊C411yescharacteristic
687C23#1309399211yescharacteristic
688C23#1309399711yescharacteristic
689C23#1309399711yescharacteristic
690C23#1309399911yescharacteristic
691C23#1309400911yescharacteristic
692C23#1309401011yescharacteristic
693C23D8×D4711yescharacteristic
694C23SD16×D4711yescharacteristic
695C23#1309404511yescharacteristic
696C23#1309404711yescharacteristic
697C23#1309404811yescharacteristic
698C23#1309405111yescharacteristic
699C23#1309405111yescharacteristic
700C23#1309405611yescharacteristic
701D4—944no—
702D4—944no—
703D4—1882no—
704D4—1882no—
705D4—1882no—
706D4—1882no—
707D4—1882no—
708D4—1882no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—3761no—
730C2×C4—3761no—
731C2×C4—3761no—
732C2×C4—3761no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1881no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1881no—
741C2×C4—1881no—
742C2×C4—1881no—
743C2×C4—1881no—
744C2×C4C22⋊C4×D4711yescharacteristic
745C2×C4#1309398111yescharacteristic
746C2×C4#1309398211yescharacteristic
747C2×C4C4×C22⋊D4711yescharacteristic
748C2×C4#1309398611yescharacteristic
749C2×C4C4×D18811yescharacteristic
750C2×C4#1309399411yescharacteristic
751C2×C4#1309399511yescharacteristic
752C2×C4#1309399611yescharacteristic
753C2×C4#1309399711yescharacteristic
754C2×C4#1309399811yescharacteristic
755C2×C4#1309399911yescharacteristic
756C2×C4#1309400611yescharacteristic
757C2×C4#1309400611yescharacteristic
758C2×C4#1309400611yescharacteristic
759C2×C4#1309400711yescharacteristic
760C2×C4#1309400811yescharacteristic
761C2×C4#1309400911yescharacteristic
762C2×C4#1309400911yescharacteristic
763C2×C4#1309400911yescharacteristic
764C2×C4#1309400911yescharacteristic
765C2×C4#1309401011yescharacteristic
766C2×C4#1309401211yescharacteristic
767C2×C4#1309401311yescharacteristic
768C2×C4#1309401811yescharacteristic
769C2×C4#1309401911yescharacteristic
770C2×C4#1309401911yescharacteristic
771C2×C4#1309401911yescharacteristic
772C8—42no—
773C8—1882no—
774C22—3762no—
775C22—3762no—
776C22—3762no—
777C22—3762no—
778C22—3762no—
779C22—3762no—
780C22—3762no—
781C22—3762no—
782C22—3762no—
783C22—3762no—
784C22—3762no—
785C22—3762no—
786C22—1884no—
787C22—1884no—
788C22—1884no—
789C22#1568899911yescharacteristic
790C22#1568901211yescharacteristic
791C22#1568901511yescharacteristic
792C22#1568903811yescharacteristic
793C22#1568904011yescharacteristic
794C22#1568904111yescharacteristic
795C22#1568905211yescharacteristic
796C22#1568920311yescharacteristic
797C22#1568920811yescharacteristic
798C22#1568922611yescharacteristic
799C22#1568923211yescharacteristic
800C22#1568925511yescharacteristic
801C22#1568926711yescharacteristic
802C22#1568927211yescharacteristic
803C22#1568928411yescharacteristic
804C22#1568931711yescharacteristic
805C22#1568931711yescharacteristic
806C22#1568932211yescharacteristic
807C22#1568932711yescharacteristic
808C22#1568933711yescharacteristic
809C22#1568934111yescharacteristic
810C22#1568934111yescharacteristic
811C22#1568934811yescharacteristic
812C22#1568935311yescharacteristic
813C22#1568936011yescharacteristic
814C22#1568937011yescharacteristic
815C22#1568937711yescharacteristic
816C22#1568943811yescharacteristic
817C22#1568944311yescharacteristic
818C22#1568944911yescharacteristic
819C22#1568945011yescharacteristic
820C22#1568946811yescharacteristic
821C22#1568947911yescharacteristic
822C22#1568948411yescharacteristic
823C22#1568948611yescharacteristic
824C4—82no—
825C4—82no—
826C4—3762no—
827C4—1882no—
828C4—1882no—
829C4#1568898511yescharacteristic
830C4#1568900111yescharacteristic
831C4#1568901311yescharacteristic
832C4#1568901411yescharacteristic
833C4#1568903911yescharacteristic
834C4#1568904911yescharacteristic
835C4#1568905011yescharacteristic
836C4#1568905211yescharacteristic
837C2—3764no—
838C2#2024163611yescharacteristic
839C2#2024371911yescharacteristic
840C2#2024373311yescharacteristic
841C2#2024400611yescharacteristic
842C2#2024401311yescharacteristic
843C2#2024407211yescharacteristic
844C2#2024408611yescharacteristic
845C2#2024457211yescharacteristic
846C2#2024457911yescharacteristic
847C2#2024462011yescharacteristic
848C2#2024462511yescharacteristic
849C2#2024470011yescharacteristic
850C2#2024470711yescharacteristic
851C2#2024479511yescharacteristic
852C2#2024480511yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socleC24×C47C2×D4
prime radicalC23×D188C22
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#11189
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#15688885C2semidirect
5. C2×#15688877C2semidirect
6. #20241617C2semidirect
7. C2×C47×#340C2semidirect
19. C2×#13093944C4semidirect
415. C2×#340D47semidirect
456. C47#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#130939462
C22×#130939442
C2×#156890242
C2×#156888852
C2×#156888772
#202416172
C2×C47×#3402
#1118947