Finite Group Databasebeta

← #26121570

Subgroups — #26121570

Order 12032.

1326 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic
2C2×#15689086C211yesmaximal, characteristic
3C22×(C2×D47)⋊C8C211yesmaximal, characteristic
4C2×#15688888C211yesmaximal, characteristic, complemented
5C2×#15688887C211yesmaximal, characteristic, complemented
6C2×#15688887C211yesmaximal, characteristic, complemented
7C2×C47×#341C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625324—21no—
12C2×M16×D47—22no—
13C2×M16×D47—22no—
14C2×M16×D47—22no—
15C2×M16×D47—22no—
16C2×M16×D47—22no—
17C2×M16×D47C414yes—
18C23×C47⋊C8C2211yescharacteristic
19C22×C8×D47—21no—
20#15689086—22no—
21#15689086C414yes—
22C2×(C2×D47)⋊C8—22no—
23C2×(C2×D47)⋊C8—22no—
24C2×(C2×D47)⋊C8—21no—
25C2×(C2×D47)⋊C8—21no—
26C2×(C2×D47)⋊C8C412yes—
27C2×(C2×D47)⋊C8C412yes—
28#15688888—22no—
29#15688887—22no—
30#15688887—22no—
31C22×M16×C47C2211yescharacteristic
32C22×M16×C47C2211yescharacteristic
33C23×C8×C47C2211yescharacteristic
34C47×#341—22no—
35C24×D47Q811yescharacteristic
36C23×Dic47Q811yescharacteristic
37C22×C4×D47—21no—
38C22×C4×D47—21no—
39C22×C4×D47—21no—
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47C2×C411yescharacteristic
46C22×C4×D47C2×C411yescharacteristic
47C22×C4×D47C2×C412yes—
48C22×C4×D47C2×C412yes—
49C22×C4×D47D412yes—
50C22×C4×D47D411yescharacteristic
51C22×C4×D47D412yes—
52C22×C4×D47D411yescharacteristic
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329C2×C412yes—
62C2×#10625329C2×C412yes—
63C2×#10625329D412yes—
64C2×#10625329D412yes—
65C2×#10625324—24no—
66C2×#10625324—24no—
67C2×#10625324—24no—
68M16×D47—28no—
69M16×D47—28no—
70M16×D47—28no—
71M16×D47—28no—
72C22×C47⋊C8—21no—
73C22×C47⋊C8—21no—
74C22×C47⋊C8—21no—
75C22×C47⋊C8—21no—
76C22×C47⋊C8—21no—
77C22×C47⋊C8—21no—
78C22×C47⋊C8—21no—
79C22×C47⋊C8—21no—
80C22×C47⋊C8C2×C412yes—
81C2×C8×D47—24no—
82C2×C8×D47—24no—
83C2×C8×D47—24no—
84(C2×D47)⋊C8—24no—
85(C2×D47)⋊C8—24no—
86(C2×D47)⋊C8—24no—
87(C2×D47)⋊C8—24no—
88C23×C4×C47C2311yescharacteristic
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47—21no—
96C2×M16×C47—21no—
97C2×M16×C47C2×C412yes—
98C2×M16×C47C2×C412yes—
99C2×M16×C47D412yes—
100C2×M16×C47D412yes—
101C22×C8×C47—21no—
102C22×C8×C47—21no—
103C22×C8×C47—21no—
104C22×C8×C47—21no—
105C22×C8×C47—21no—
106C22×C8×C47—21no—
107C22×C8×C47—21no—
108C22×C8×C47—21no—
109C22×C8×C47C2×C412yes—
110C24×C47C2×Q811yescharacteristic
111C23×D47—21no—
112C23×D47—21no—
113C23×D47—21no—
114C23×D47—21no—
115C23×D47—24no—
116C23×D47—42no—
117C23×D47C4⋊C411yescharacteristic
118C23×D47C4⋊C412yes—
119C23×D47C4⋊C412yes—
120C23×D47C4⋊C411yescharacteristic
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47#4111yescharacteristic
132C22×C4×C47#4111yescharacteristic
133C22×C4×C47#4111yescharacteristic
134C22×C4×C47#4111yescharacteristic
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47C4⋊C412yes—
140C22×Dic47C4⋊C412yes—
141C22×Dic47C4⋊C411yescharacteristic
142C22×Dic47C4⋊C411yescharacteristic
143C2×C4×D47—22no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—21no—
148C2×C4×D47—21no—
149C2×C4×D47—22no—
150C2×C4×D47—21no—
151C2×C4×D47—21no—
152C2×C4×D47—22no—
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47—22no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—22no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—21no—
170C2×C4×D47—22no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—22no—
174C2×C4×D47—21no—
175C2×C4×D47C4212yes—
176C2×C4×D47C4212yes—
177C2×C4×D47C22⋊C412yes—
178C2×C4×D47C22⋊C412yes—
179C2×C4×D47C22⋊C412yes—
180C2×C4×D47C22⋊C412yes—
181C2×C4×D47C22⋊C412yes—
182C2×C4×D47C22⋊C412yes—
183M16×C47—22no—
184M16×C47—22no—
185M16×C47—22no—
186M16×C47—22no—
187M16×C47—22no—
188M16×C47—41no—
189M16×C47—41no—
190M16×C47C22⋊C414yes—
191C2×C8×C47—22no—
192C2×C8×C47—22no—
193C2×C8×C47—22no—
194C2×C8×C47—22no—
195C2×C8×C47—22no—
196C2×C8×C47—22no—
197C2×C8×C47—22no—
198C2×C8×C47—41no—
199C2×C8×C47—41no—
200C2×C8×C47—41no—
201C2×C8×C47—41no—
202C2×C8×C47—41no—
203C2×C8×C47—41no—
204#10625329—22no—
205#10625329—22no—
206#10625329—22no—
207#10625329—22no—
208#10625329—22no—
209#10625329—41no—
210#10625329—41no—
211#10625329C22⋊C414yes—
212C2×C47⋊C8—22no—
213C2×C47⋊C8—22no—
214C2×C47⋊C8—22no—
215C2×C47⋊C8—22no—
216C2×C47⋊C8—22no—
217C2×C47⋊C8—22no—
218C2×C47⋊C8—22no—
219C2×C47⋊C8—41no—
220C2×C47⋊C8—41no—
221C2×C47⋊C8—41no—
222C2×C47⋊C8—41no—
223C2×C47⋊C8—41no—
224C2×C47⋊C8—41no—
225#10625324—216no—
226C8×D47—216no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47C2×C4⋊C411yescharacteristic
230C23×C47C2×C4⋊C411yescharacteristic
231C23×C47C2×C4⋊C411yescharacteristic
232C23×C47C22⋊Q811yescharacteristic
233C23×C47C22⋊Q811yescharacteristic
234C23×C47C22⋊Q811yescharacteristic
235C23×C47C22⋊Q811yescharacteristic
236C22×D47—21no—
237C22×D47—21no—
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—22no—
241C22×D47—22no—
242C22×D47—21no—
243C22×D47—22no—
244C22×D47—21no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—24no—
248C22×D47—24no—
249C22×D47—42no—
250C22×D47—42no—
251C22×D47—44no—
252C22×D47—44no—
253C22×D47—44no—
254C22×D47—44no—
255C22×D47#9512yes—
256C22×D47#9512yes—
257C22×D47#10814yes—
258C2×C4×C47C2×C4211yescharacteristic
259C2×C4×C47C2×C22⋊C411yescharacteristic
260C2×C4×C47C2×C22⋊C411yescharacteristic
261C2×C4×C47C2×C22⋊C411yescharacteristic
262C2×C4×C47C2×C22⋊C411yescharacteristic
263C2×C4×C47C2×C22⋊C411yescharacteristic
264C2×C4×C47#11711yescharacteristic
265C2×C4×C47#11711yescharacteristic
266C2×C4×C47C4×D411yescharacteristic
267C2×C4×C47C4×D411yescharacteristic
268C2×C4×C47C4×D411yescharacteristic
269C2×C4×C47C4×D411yescharacteristic
270C2×C4×C47C4×D411yescharacteristic
271C2×C4×C47C4×D411yescharacteristic
272C2×C4×C47C4×D411yescharacteristic
273C2×C4×C47C4×D411yescharacteristic
274C2×C4×C47#12011yescharacteristic
275C2×C4×C47#12011yescharacteristic
276C2×C4×C47#12011yescharacteristic
277C2×C4×C47#12011yescharacteristic
278C2×C4×C47#12111yescharacteristic
279C2×C4×C47#12111yescharacteristic
280C2×C4×C47#12111yescharacteristic
281C2×C4×C47#12111yescharacteristic
282C2×C4×C47#12311yescharacteristic
283C2×C4×C47#12311yescharacteristic
284C2×C4×C47#12311yescharacteristic
285C2×C4×C47#12311yescharacteristic
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—22no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47#9512yes—
295C2×Dic47#9512yes—
296C4×D47—22no—
297C4×D47—22no—
298C4×D47—22no—
299C4×D47—22no—
300C4×D47—22no—
301C4×D47—22no—
302C4×D47—22no—
303C4×D47—22no—
304C4×D47—22no—
305C4×D47—22no—
306C4×D47—22no—
307C4×D47—22no—
308C4×D47—22no—
309C4×D47—22no—
310C4×D47—22no—
311C4×D47—22no—
312C8×C47—24no—
313C8×C47—42no—
314C8×C47—42no—
315C47⋊C8—24no—
316C47⋊C8—42no—
317C47⋊C8—42no—
318#10734—471nomaximal, Sylow
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—22no—
323C22×C47—21no—
324C22×C47—21no—
325C22×C47—21no—
326C22×C47—21no—
327C22×C47C2×#9511yescharacteristic
328C22×C47#38011yescharacteristic
329C22×C47#38011yescharacteristic
330C22×C47#38511yescharacteristic
331C22×C47#38511yescharacteristic
332C22×C47#38511yescharacteristic
333C22×C47#38511yescharacteristic
334C22×C47C2×#10812yes—
335C22×C47#43012yes—
336C2×D47—24no—
337C2×D47—24no—
338C2×D47—22no—
339C2×D47—22no—
340C2×D47—22no—
341C2×D47—22no—
342C2×D47—22no—
343C2×D47—44no—
344C2×D47—44no—
345C2×D47—44no—
346C2×D47—44no—
347C2×D47—42no—
348C2×D47—42no—
349C2×D47#34114yescomplemented
350C4×C47C4×C22⋊C411yescharacteristic
351C4×C47C4×C22⋊C411yescharacteristic
352C4×C47#37911yescharacteristic
353C4×C47#38111yescharacteristic
354C4×C47#38611yescharacteristic
355C4×C47#38611yescharacteristic
356C4×C47#38611yescharacteristic
357C4×C47#38611yescharacteristic
358Dic47—22no—
359Dic47—22no—
360C23×M16—471no—
361C2×#407—471no—
362C22×C22⋊C8—471no—
363C2×#341—471no—
364C2×#341—471no—
365C2×#341—471no—
366C2×#341D4711yescharacteristic, complemented
367C2×C47—21no—
368C2×C47—21no—
369C2×C47—21no—
370C2×C47—21no—
371C2×C47C22⋊#9511yescharacteristic
372C2×C47C2×#34111yescharacteristic
373C2×C47#173811yescharacteristic
374C2×C47#185512yes—
375C2×C47#185512yes—
376D47—24no—
377D47—42no—
378C24×C4—471no—
379C22×M16—471no—
380C22×M16—471no—
381C22×M16—474no—
382C22×M16—941no—
383C22×M16—942no—
384C22×M16—942no—
385C22×M16—942no—
386C22×M16—942no—
387C22×M16—942no—
388C22×M16C2×D4711yescharacteristic
389C22×M16C2×D4711yescharacteristic
390C23×C8—471no—
391C23×C8—941no—
392C23×C8C2×D4711yescharacteristic
393#407—474no—
394#407—942no—
395C2×C22⋊C8—472no—
396C2×C22⋊C8—472no—
397C2×C22⋊C8—942no—
398C2×C22⋊C8—942no—
399C2×C22⋊C8—941no—
400C2×C22⋊C8—941no—
401#341—22no—
402#341—942no—
403#341—942no—
404#341—942no—
405C47#1073411yescharacteristic, complemented, Sylow
406C25—471no—
407C23×C4—471no—
408C23×C4—472no—
409C23×C4—471no—
410C23×C4—471no—
411C23×C4—472no—
412C23×C4—472no—
413C23×C4—472no—
414C23×C4—471no—
415C23×C4—471no—
416C23×C4—941no—
417C23×C4—941no—
418C23×C4—941no—
419C23×C4—941no—
420C23×C4—941no—
421C23×C4—941no—
422C23×C4—941no—
423C23×C4—941no—
424C23×C4C22×D4711yescharacteristic
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—21no—
432C2×M16—21no—
433C2×M16—472no—
434C2×M16—472no—
435C2×M16—472no—
436C2×M16—472no—
437C2×M16—944no—
438C2×M16—944no—
439C2×M16—944no—
440C2×M16—948no—
441C2×M16—948no—
442C2×M16—948no—
443C2×M16—941no—
444C2×M16—941no—
445C2×M16—941no—
446C2×M16—948no—
447C2×M16—941no—
448C2×M16—941no—
449C2×M16—941no—
450C2×M16—941no—
451C2×M16—941no—
452C2×M16C4×D4712yes—
453C2×M16C4×D4712yes—
454C2×M16D18812yes—
455C2×M16C22⋊D4712yes—
456C22×C8—21no—
457C22×C8—21no—
458C22×C8—21no—
459C22×C8—21no—
460C22×C8—21no—
461C22×C8—21no—
462C22×C8—21no—
463C22×C8—21no—
464C22×C8—472no—
465C22×C8—944no—
466C22×C8—944no—
467C22×C8—944no—
468C22×C8—941no—
469C22×C8—941no—
470C22×C8—941no—
471C22×C8—941no—
472C22×C8—941no—
473C22×C8—941no—
474C22×C8—941no—
475C22×C8—941no—
476C22×C8C4×D4712yes—
477C22⋊C8—944no—
478C22⋊C8—944no—
479C22⋊C8—944no—
480C22⋊C8—944no—
481C24—471no—
482C24—471no—
483C24—472no—
484C24—472no—
485C24—944no—
486C24—941no—
487C24—941no—
488C24—941no—
489C24—941no—
490C24—1882no—
491C24Q8×D4711yescharacteristic
492C22×C4—472no—
493C22×C4—472no—
494C22×C4—471no—
495C22×C4—471no—
496C22×C4—472no—
497C22×C4—472no—
498C22×C4—472no—
499C22×C4—472no—
500C22×C4—472no—
501C22×C4—472no—
502C22×C4—472no—
503C22×C4—472no—
504C22×C4—941no—
505C22×C4—941no—
506C22×C4—941no—
507C22×C4—941no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—941no—
513C22×C4—941no—
514C22×C4—942no—
515C22×C4—941no—
516C22×C4—941no—
517C22×C4—942no—
518C22×C4—941no—
519C22×C4—941no—
520C22×C4—942no—
521C22×C4—941no—
522C22×C4—941no—
523C22×C4—942no—
524C22×C4—941no—
525C22×C4—942no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—942no—
529C22×C4—941no—
530C22×C4—942no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—942no—
534C22×C4—942no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—942no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4C2×C4×D4711yescharacteristic
541C22×C4C2×C4×D4711yescharacteristic
542C22×C4C2×C4×D4711yescharacteristic
543C22×C4C2×D18811yescharacteristic
544C22×C4#1062535011yescharacteristic
545C22×C4#1062535011yescharacteristic
546C22×C4D4×D4711yescharacteristic
547C22×C4D4×D4711yescharacteristic
548C22×C4D4×D4711yescharacteristic
549C22×C4D4×D4711yescharacteristic
550C22×C4D4×D4711yescharacteristic
551C22×C4#1062535211yescharacteristic
552C22×C4#1062535411yescharacteristic
553C22×C4C2×C22⋊D4711yescharacteristic
554M16—22no—
555M16—22no—
556M16—22no—
557M16—22no—
558M16—22no—
559M16—41no—
560M16—41no—
561M16—474no—
562M16—9416no—
563M16—942no—
564M16—942no—
565M16—942no—
566M16—942no—
567M16—942no—
568M16—1881no—
569M16—1881no—
570M16(C2×D47)⋊C414yes—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—9416no—
585C2×C8—942no—
586C2×C8—942no—
587C2×C8—942no—
588C2×C8—942no—
589C2×C8—942no—
590C2×C8—942no—
591C2×C8—942no—
592C2×C8—1881no—
593C2×C8—1881no—
594C2×C8—1881no—
595C2×C8—1881no—
596C2×C8—1881no—
597C2×C8—1881no—
598C23—22no—
599C23—22no—
600C23—472no—
601C23—474no—
602C23—472no—
603C23—944no—
604C23—944no—
605C23—941no—
606C23—941no—
607C23—942no—
608C23—942no—
609C23—942no—
610C23—942no—
611C23—941no—
612C23—942no—
613C23—941no—
614C23—942no—
615C23—942no—
616C23—1882no—
617C23—1882no—
618C23—1884no—
619C23—1884no—
620C23—1884no—
621C23—1884no—
622C23C4⋊C4×D4711yescharacteristic
623C23C4⋊C4×D4711yescharacteristic
624C23C4⋊C4×D4711yescharacteristic
625C23#1309400011yescharacteristic
626C23#1309400211yescharacteristic
627C23#1309400211yescharacteristic
628C23#1309400411yescharacteristic
629C2×C4—472no—
630C2×C4—472no—
631C2×C4—942no—
632C2×C4—942no—
633C2×C4—942no—
634C2×C4—941no—
635C2×C4—941no—
636C2×C4—942no—
637C2×C4—941no—
638C2×C4—941no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4C42×D4711yescharacteristic
656C2×C4C22⋊C4×D4711yescharacteristic
657C2×C4C22⋊C4×D4711yescharacteristic
658C2×C4C22⋊C4×D4711yescharacteristic
659C2×C4C22⋊C4×D4711yescharacteristic
660C2×C4C2×(C2×D47)⋊C411yescharacteristic
661C2×C4#1309398111yescharacteristic
662C2×C4#1309398211yescharacteristic
663C2×C4(C22⋊D47)⋊C411yescharacteristic
664C2×C4(C22⋊D47)⋊C411yescharacteristic
665C2×C4C4×C22⋊D4711yescharacteristic
666C2×C4C4×C22⋊D4711yescharacteristic
667C2×C4#1309398611yescharacteristic
668C2×C4#1309398611yescharacteristic
669C2×C4C4×D18811yescharacteristic
670C2×C4C4×D18811yescharacteristic
671C2×C4#1309399211yescharacteristic
672C2×C4#1309399211yescharacteristic
673C2×C4#1309399411yescharacteristic
674C2×C4#1309399411yescharacteristic
675C2×C4#1309399511yescharacteristic
676C2×C4#1309399711yescharacteristic
677C2×C4#1309399711yescharacteristic
678C2×C4#1309399911yescharacteristic
679C2×C4#1309400611yescharacteristic
680C2×C4#1309400611yescharacteristic
681C2×C4#1309400911yescharacteristic
682C2×C4#1309400911yescharacteristic
683C8—24no—
684C8—42no—
685C8—42no—
686C8—944no—
687C8—1882no—
688C8—1882no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—474no—
698C22—944no—
699C22—944no—
700C22—942no—
701C22—942no—
702C22—942no—
703C22—942no—
704C22—942no—
705C22—1884no—
706C22—1884no—
707C22—1884no—
708C22—1884no—
709C22—1882no—
710C22—1882no—
711C22#95×D4711yescharacteristic
712C22#1568898011yescharacteristic
713C22#1568898211yescharacteristic
714C22#1568899411yescharacteristic
715C22#1568899411yescharacteristic
716C22#1568899711yescharacteristic
717C22#1568899711yescharacteristic
718C22#108×D4712yes—
719C22#1568917012yes—
720C4—942no—
721C4—942no—
722C4#1568897011yescharacteristic
723C4C4×(C2×D47)⋊C411yescharacteristic
724C4#1568897811yescharacteristic
725C4#1568898511yescharacteristic
726C4#1568899911yescharacteristic
727C4#1568899911yescharacteristic
728C4#1568900111yescharacteristic
729C4#1568900111yescharacteristic
730C2—21no—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—944no—
735C2—1882no—
736C2(C2×D47)⋊#9511yescharacteristic
737C2#341×D4711yescharacteristic
738C2#2024311311yescharacteristic
739C2#2024359112yes—
740C2#2024359412yes—
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#341C2
socleC23×C47C2×C4⋊C4
prime radicalC24×D47Q8
cosocleC23×C4×C47C23
hypercenterC2×#341D47
hypocenterC47#10734
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
4. C2×#15688888C2semidirect
5. C2×#15688887C2semidirect
6. C2×#15688887C2semidirect
7. C2×C47×#341C2semidirect
349. C2×D47#341semidirect
366. C2×#341D47semidirect
405. C47#10734semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D472
C2×#156890862
C22×(C2×D47)⋊C82
C2×#156888882
C2×#156888872
C2×C47×#3412
#1073447