Finite Group Databasebeta

← C2×#20243803 #26217926

Subgroups — C2×#20243803 #26217926

Order 12032.

1870 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic, complemented
2C2×#15689634C211yesmaximal, characteristic
3C2×#15689105C211yesmaximal, characteristic, complemented
4C2×#15689087C211yesmaximal, characteristic, complemented
5#20243803C218yesmaximal, direct product factor
6C2×#15688895C211yesmaximal, characteristic, complemented
7C2×#15688894C211yesmaximal, characteristic, complemented
8C2×C47×#407C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689889—22no—
11#15689889—22no—
12#15689889—22no—
13#15689889C2214yescomplemented
14C2×#13094032—22no—
15C2×#13094030—22no—
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×M16×D47—22no—
19#15689634—22no—
20#15689634—22no—
21#15689634C414yes—
22#15689634C2214yes—
23C2×#13094007C412yes—
24C2×#13094003—21no—
25C2×#13093998—21no—
26C2×#13093993C412yes—
27C2×C4×C22⋊D47—22no—
28C2×#13093983C2211yescharacteristic
29#15689105—22no—
30#15689105C2214yescomplemented
31C2×#13093942—21no—
32C2×#13093940—21no—
33#15689087—22no—
34#15689087C2214yescomplemented
35C2×C22⋊(C47⋊C8)—22no—
36#15688895C2214yescomplemented
37#15688894C2214yescomplemented
38C24×C4×C47C2211yescharacteristic
39C22×M16×C47C2211yescharacteristic
40C22×M16×C47C2211yescharacteristic
41C47×#407—22no—
42C47×#407C2214yescomplemented
43C2×C22⋊C8×C47—22no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350C2×C412yes—
53C2×#10625350D412yes—
54C2×#10625350D412yes—
55C2×#10625350C2312yes—
56C22×Dic94D411yescharacteristic
57C22×D188D411yescharacteristic
58C22×C22⋊D47—22no—
59C22×C22⋊D47C2×C412yes—
60C22×C4×D47D412yes—
61#13094032—28no—
62#13094032—28no—
63#13094030—28no—
64#13094030—28no—
65C2×#10625329—21no—
66C2×#10625329—21no—
67C2×#10625329—21no—
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329—21no—
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625329—21no—
74C2×#10625329D412yescomplemented
75C2×#10625329C2312yes—
76C2×#10625329C2312yes—
77C2×#10625324—24no—
78M16×D47—28no—
79M16×D47—28no—
80C22×C47⋊C8—21no—
81C22×C47⋊C8D412yescomplemented
82C2×C8×D47—24no—
83#13094007—24no—
84#13094007C2×C418yes—
85#13094003—24no—
86#13094003—24no—
87#13093998—24no—
88#13093998—24no—
89#13093993—24no—
90#13093993C2×C418yes—
91C4×C22⋊D47—28no—
92C4×C22⋊D47—28no—
93#13093983—21no—
94#13093983—21no—
95#13093983C2×C412yes—
96#13093983C2312yes—
97C2×C4⋊Dic47—21no—
98C2×Dic47⋊C4—22no—
99C2×C22⋊Dic47—22no—
100C2×C22⋊Dic47C2×C412yes—
101C2×(C2×D47)⋊C4—22no—
102C2×C4×Dic47—21no—
103#13093942—24no—
104#13093940—24no—
105C22⋊(C47⋊C8)—28no—
106C25×C47C2×C411yescharacteristic
107C23×C4×C47—21no—
108C23×C4×C47—21no—
109C23×C4×C47—21no—
110C23×C4×C47—21no—
111C23×C4×C47—21no—
112C23×C4×C47—21no—
113C23×C4×C47—21no—
114C23×C4×C47—21no—
115C23×C4×C47—21no—
116C23×C4×C47—21no—
117C23×C4×C47—21no—
118C23×C4×C47—21no—
119C23×C4×C47C2×C411yescharacteristic
120C23×C4×C47C2×C412yes—
121C23×C4×C47C2312yes—
122C23×C4×C47C2311yescharacteristic
123C2×M16×C47—21no—
124C2×M16×C47—21no—
125C2×M16×C47—21no—
126C2×M16×C47—21no—
127C2×M16×C47—21no—
128C2×M16×C47—21no—
129C2×M16×C47—21no—
130C2×M16×C47—21no—
131C2×M16×C47—21no—
132C2×M16×C47D412yescomplemented
133C2×M16×C47C2312yes—
134C2×M16×C47C2312yes—
135C22×C8×C47—21no—
136C22×C8×C47D412yescomplemented
137C22⋊C8×C47—28no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47—21no—
144C24×C47—44no—
145C24×C47C22×C412yes—
146C24×C47C22×C411yescharacteristic
147C23×D47C22⋊C412yes—
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—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—41no—
167C22×C4×C47—41no—
168C22×C4×C47—41no—
169C22×C4×C47—41no—
170C22×C4×C47—41no—
171C22×C4×C47—41no—
172C22×C4×C47—41no—
173C22×C4×C47—41no—
174C22×C4×C47—41no—
175C22×C4×C47—41no—
176C22×C4×C47—41no—
177C22×C4×C47—41no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47—41no—
181C22×C4×C47—41no—
182C22×C4×C47C22×C412yes—
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47#4111yescharacteristic
193C22×C4×C47#4111yescharacteristic
194C22×C4×C47#4111yescharacteristic
195C22×C4×C47#4111yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47—22no—
198C2×C22⋊D47—22no—
199C2×C22⋊D47—22no—
200C2×C22⋊D47—22no—
201C2×C22⋊D47—28no—
202C2×C22⋊D47—48no—
203C2×C22⋊D47C22⋊C414yes—
204C2×C22⋊D47C22×C414yes—
205C22×Dic47—22no—
206C22×Dic47C22⋊C412yes—
207#10625350—22no—
208#10625350—22no—
209#10625350—22no—
210#10625350—22no—
211#10625350—22no—
212#10625350—22no—
213#10625350—22no—
214#10625350—22no—
215#10625350—22no—
216#10625350—22no—
217#10625350—22no—
218#10625350—22no—
219#10625350—22no—
220#10625350—22no—
221#10625350—22no—
222#10625350—22no—
223C2×D188—21no—
224C2×D188—21no—
225C2×D188—21no—
226C2×D188—21no—
227C2×D188C22⋊C412yes—
228C2×D188C2×D412yes—
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×C4×D47—22no—
233C2×C4×D47C22⋊C414yes—
234C2×C4×D47C2×D414yes—
235C2×Dic94—21no—
236C2×Dic94—21no—
237C2×Dic94—21no—
238C2×Dic94—21no—
239C2×Dic94C22⋊C412yes—
240C2×Dic94C2×D412yes—
241M16×C47—22no—
242M16×C47—22no—
243M16×C47—22no—
244M16×C47—22no—
245M16×C47—22no—
246M16×C47—22no—
247M16×C47—41no—
248M16×C47—41no—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47—41no—
253C2×C8×C47—41no—
254C2×C8×C47C2×D414yescomplemented
255C22⋊Dic47—22no—
256C22⋊Dic47—28no—
257C22⋊Dic47C22×C414yes—
258(C2×D47)⋊C4—28no—
259C4⋊Dic47—22no—
260C4⋊Dic47—22no—
261Dic47⋊C4—28no—
262C4×Dic47—22no—
263C4×Dic47—22no—
264#10625329—22no—
265#10625329—22no—
266#10625329—22no—
267#10625329—22no—
268#10625329—22no—
269#10625329—22no—
270#10625329—41no—
271#10625329—41no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8—22no—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—41no—
276C2×C47⋊C8—41no—
277C2×C47⋊C8C2×D414yescomplemented
278#10625324—216no—
279C8×D47—216no—
280C23×C47—24no—
281C23×C47—24no—
282C23×C47—24no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—42no—
287C23×C47—44no—
288C23×C47—42no—
289C23×C47—42no—
290C23×C47—42no—
291C23×C47—44no—
292C23×C47—44no—
293C23×C47—44no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47C2×C22⋊C411yescharacteristic
299C23×C47C2×C22⋊C411yescharacteristic
300C23×C47C4×D411yescharacteristic
301C23×C47C4×D411yescharacteristic
302C23×C47C4×D411yescharacteristic
303C23×C47C4×D411yescharacteristic
304C23×C47C23×C411yescharacteristic
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—44no—
308C22×D47C2×C22⋊C414yes—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47C2×C22⋊C411yescharacteristic
325C2×C4×C47C2×C22⋊C411yescharacteristic
326C2×C4×C47C4×D411yescharacteristic
327C2×C4×C47C4×D411yescharacteristic
328C2×C4×C47C4×D411yescharacteristic
329C2×C4×C47C4×D411yescharacteristic
330C2×C4×C47#12011yescharacteristic
331C2×C4×C47#12011yescharacteristic
332C2×C4×C47#12011yescharacteristic
333C2×C4×C47#12011yescharacteristic
334C2×C4×C47#12111yescharacteristic
335C2×C4×C47#12111yescharacteristic
336C2×C4×C47#12111yescharacteristic
337C2×C4×C47#12111yescharacteristic
338C2×C4×C47#12111yescharacteristic
339C2×C4×C47#12111yescharacteristic
340C2×C4×C47#12111yescharacteristic
341C2×C4×C47#12111yescharacteristic
342C2×C4×C47#12311yescharacteristic
343C2×C4×C47#12311yescharacteristic
344C2×C4×C47#12311yescharacteristic
345C2×C4×C47#12311yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47C2×#4111yescharacteristic
351C2×C4×C47C2×#4111yescharacteristic
352C22⋊D47—24no—
353C22⋊D47—24no—
354C22⋊D47—24no—
355C22⋊D47—24no—
356C22⋊D47—416no—
357C2×Dic47—22no—
358C2×Dic47—22no—
359C2×Dic47—24no—
360C2×Dic47—44no—
361C2×Dic47C2×C22⋊C414yes—
362D188—22no—
363D188—22no—
364D188—22no—
365D188—22no—
366C4×D47—24no—
367C4×D47—24no—
368C4×D47—24no—
369C4×D47—24no—
370Dic94—22no—
371Dic94—22no—
372Dic94—22no—
373Dic94—22no—
374C8×C47—24no—
375C8×C47—42no—
376C47⋊C8—24no—
377C47⋊C8—42no—
378C2×#1891—471nomaximal, Sylow
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—22no—
382C22×C47—24no—
383C22×C47—24no—
384C22×C47—24no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—41no—
388C22×C47—41no—
389C22×C47—42no—
390C22×C47—44no—
391C22×C47—42no—
392C22×C47—42no—
393C22×C47—44no—
394C22×C47—44no—
395C22×C47—44no—
396C22×C47—42no—
397C22×C47#38611yescharacteristic
398C22×C47#38611yescharacteristic
399C22×C47#38611yescharacteristic
400C22×C47#38611yescharacteristic
401C22×C47C22×C22⋊C411yescharacteristic
402C22×C47C2×C4×D411yescharacteristic
403C22×C47C2×C4×D411yescharacteristic
404C2×D47—24no—
405C2×D47—44no—
406C2×D47—44no—
407C2×D47—82no—
408C4×C47—42no—
409C4×C47#38611yescharacteristic
410C4×C47#38611yescharacteristic
411C4×C47#38611yescharacteristic
412C4×C47#38611yescharacteristic
413C4×C47C2×#12011yescharacteristic
414C4×C47C2×#12111yescharacteristic
415C4×C47C2×#12111yescharacteristic
416C4×C47C2×#12311yescharacteristic
417Dic47—24no—
418Dic47—44no—
419C2×#568—471no—
420C2×#525—471no—
421C2×#413—471no—
422C2×#407—471no—
423C2×#407D4711yescharacteristic, complemented
424#1891—478no—
425C2×#344—471no—
426C2×#344—471no—
427C2×C47—21no—
428C2×C47—21no—
429C2×C47—21no—
430C2×C47—21no—
431C2×C47—21no—
432C2×C47—21no—
433C2×C47—44no—
434C2×C47#189112yescomplemented
435C2×C47C2×#38611yescharacteristic
436D47—44no—
437C22×#41—471no—
438C24×C4C2×D4711yescharacteristic
439#568—474no—
440#568—942no—
441#568—942no—
442#568—942no—
443C2×#131—942no—
444C2×#131—942no—
445C22×M16—471no—
446C22×M16—471no—
447C22×M16—942no—
448C22×M16C2×D4711yescharacteristic
449C22×M16C2×D4711yescharacteristic
450#525—474no—
451#525—474no—
452#525—942no—
453#525—942no—
454C2×#123—472no—
455C2×C22⋊Q8—941no—
456C2×#121—941no—
457C2×#120—472no—
458C2×C4×D4—942no—
459C2×#117—471no—
460#413—474no—
461#413—942no—
462C2×#101—941no—
463C2×#100—941no—
464#407—22no—
465#407—474no—
466#407—942no—
467#407C2×D4714yescomplemented
468C2×C22⋊C8—22no—
469C2×C22⋊C8—942no—
470#344—474no—
471#344—474no—
472C47C2×#189111yescharacteristic, complemented, Sylow
473C25C4×D4711yescharacteristic
474C2×#41—472no—
475C2×#41—472no—
476C2×#41—472no—
477C2×#41—472no—
478C2×#41—941no—
479C2×#41—941no—
480C2×#41—941no—
481C2×#41—941no—
482C2×#41—941no—
483C2×#41—941no—
484C2×#41—941no—
485C2×#41—941no—
486C22×Q8—471no—
487C22×D4—472no—
488C22×D4—471no—
489C22×D4—942no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—472no—
503C23×C4C4×D4711yescharacteristic
504C23×C4C4×D4712yes—
505C23×C4C22×D4712yes—
506C23×C4C22×D4711yescharacteristic
507#131—948no—
508#131—948no—
509#131—948no—
510#131—948no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—472no—
521C2×M16—472no—
522C2×M16—472no—
523C2×M16—944no—
524C2×M16—948no—
525C2×M16—948no—
526C2×M16—941no—
527C2×M16—941no—
528C2×M16—941no—
529C2×M16—941no—
530C2×M16—941no—
531C2×M16—941no—
532C2×M16—941no—
533C2×M16—941no—
534C2×M16—941no—
535C2×M16C22⋊D4712yescomplemented
536C2×M16C22×D4712yes—
537C2×M16C22×D4712yes—
538C22×C8—21no—
539C22×C8—472no—
540C22×C8—944no—
541C22×C8—941no—
542C22×C8C22⋊D4712yescomplemented
543#123—478no—
544#123—944no—
545C22⋊Q8—944no—
546C22⋊Q8—944no—
547#121—944no—
548#121—944no—
549#120—478no—
550#120—944no—
551C4×D4—948no—
552C4×D4—948no—
553#117—472no—
554#117—472no—
555#117—941no—
556#117—941no—
557C2×C4⋊C4—942no—
558C2×C4⋊C4—941no—
559C2×C22⋊C4—472no—
560C2×C22⋊C4—942no—
561C2×C22⋊C4—942no—
562C2×C42—941no—
563#101—944no—
564#100—944no—
565C22⋊C8—28no—
566C22⋊C8—948no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—21no—
572C24—21no—
573C24—44no—
574C24—472no—
575C24C2×C4×D4712yes—
576C24C2×C4×D4711yescharacteristic
577#41—942no—
578#41—942no—
579#41—942no—
580#41—942no—
581#41—942no—
582#41—942no—
583#41—942no—
584#41—942no—
585#41—942no—
586#41—942no—
587#41—942no—
588#41—942no—
589#41—942no—
590#41—942no—
591#41—942no—
592#41—942no—
593C2×Q8—472no—
594C2×Q8—472no—
595C2×Q8—941no—
596C2×Q8—941no—
597C2×Q8—941no—
598C2×Q8—941no—
599C2×D4—474no—
600C2×D4—474no—
601C2×D4—472no—
602C2×D4—472no—
603C2×D4—942no—
604C2×D4—942no—
605C2×D4—942no—
606C2×D4—942no—
607C2×D4—948no—
608C2×D4—941no—
609C2×D4—941no—
610C2×D4—941no—
611C2×D4—941no—
612C2×D4—1888no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—472no—
648C22×C4—474no—
649C22×C4—474no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4C2×C4×D4712yes—
656C22×C4C2×C4×D4711yescharacteristic
657C22×C4#1062535011yescharacteristic
658C22×C4#1062535011yescharacteristic
659C22×C4D4×D4711yescharacteristic
660C22×C4D4×D4711yescharacteristic
661C22×C4D4×D4711yescharacteristic
662C22×C4D4×D4711yescharacteristic
663C22×C4D4×D4711yescharacteristic
664C22×C4D4×D4711yescharacteristic
665C22×C4#1062535211yescharacteristic
666C22×C4#1062535211yescharacteristic
667C22×C4C2×C22⋊D4711yescharacteristic
668C22×C4C2×C22⋊D4711yescharacteristic
669C22×C4C23×D4711yescharacteristic
670M16—22no—
671M16—22no—
672M16—22no—
673M16—22no—
674M16—22no—
675M16—22no—
676M16—41no—
677M16—41no—
678M16—9416no—
679M16—942no—
680M16—942no—
681M16—942no—
682M16—942no—
683M16—942no—
684M16—942no—
685M16—1881no—
686M16—1881no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—474no—
693C2×C8—9416no—
694C2×C8—942no—
695C2×C8—942no—
696C2×C8—942no—
697C2×C8—1881no—
698C2×C8—1881no—
699C2×C8C2×C22⋊D4714yescomplemented
700C4⋊C4—948no—
701C4⋊C4—942no—
702C4⋊C4—942no—
703C22⋊C4—474no—
704C22⋊C4—948no—
705C22⋊C4—948no—
706C22⋊C4—942no—
707C42—942no—
708C42—942no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—42no—
716C23—44no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—474no—
728C23—942no—
729C23—942no—
730C23—1884no—
731C23C22⋊C4×D4711yescharacteristic
732C23C22⋊C4×D4711yescharacteristic
733C23(C22⋊D47)⋊C411yescharacteristic
734C23(C22⋊D47)⋊C411yescharacteristic
735C23C4×C22⋊D4711yescharacteristic
736C23C4×C22⋊D4711yescharacteristic
737C23C22×C4×D4711yescharacteristic
738Q8—942no—
739Q8—942no—
740Q8—942no—
741Q8—942no—
742D4—944no—
743D4—944no—
744D4—944no—
745D4—944no—
746D4—942no—
747D4—942no—
748D4—942no—
749D4—942no—
750D4—18816no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—474no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—944no—
770C2×C4—944no—
771C2×C4—944no—
772C2×C4—944no—
773C2×C4—944no—
774C2×C4—1884no—
775C2×C4C22⋊C4×D4711yescharacteristic
776C2×C4C22⋊C4×D4711yescharacteristic
777C2×C4(C22⋊D47)⋊C411yescharacteristic
778C2×C4(C22⋊D47)⋊C411yescharacteristic
779C2×C4C4×C22⋊D4711yescharacteristic
780C2×C4C4×C22⋊D4711yescharacteristic
781C2×C4#1309399211yescharacteristic
782C2×C4#1309399211yescharacteristic
783C2×C4#1309399211yescharacteristic
784C2×C4#1309399211yescharacteristic
785C2×C4#1309399511yescharacteristic
786C2×C4#1309399511yescharacteristic
787C2×C4#1309399511yescharacteristic
788C2×C4#1309399511yescharacteristic
789C2×C4#1309399711yescharacteristic
790C2×C4#1309399711yescharacteristic
791C2×C4#1309399711yescharacteristic
792C2×C4#1309399711yescharacteristic
793C2×C4#1309400611yescharacteristic
794C2×C4#1309400611yescharacteristic
795C2×C4#1309400611yescharacteristic
796C2×C4#1309400611yescharacteristic
797C2×C4C2×D4×D4711yescharacteristic
798C2×C4C2×D4×D4711yescharacteristic
799C2×C4C2×D4×D4711yescharacteristic
800C2×C4C22×C22⋊D4711yescharacteristic
801C2×C4C2×#1062535211yescharacteristic
802C2×C4C2×#1062535011yescharacteristic
803C8—24no—
804C8—42no—
805C8—944no—
806C8—1882no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—42no—
824C22—44no—
825C22—944no—
826C22—3762no—
827C22—1884no—
828C22—1884no—
829C22#1568899911yescharacteristic
830C22#1568899911yescharacteristic
831C22#1568899911yescharacteristic
832C22#1568899911yescharacteristic
833C22C2×C22⋊C4×D4711yescharacteristic
834C22C2×(C22⋊D47)⋊C411yescharacteristic
835C22C2×C4×C22⋊D4711yescharacteristic
836C4—42no—
837C4—944no—
838C4—1884no—
839C4#1568899911yescharacteristic
840C4#1568899911yescharacteristic
841C4#1568899911yescharacteristic
842C4#1568899911yescharacteristic
843C4C2×#1309399211yescharacteristic
844C4C2×#1309399511yescharacteristic
845C4C2×#1309399711yescharacteristic
846C4C2×#1309400611yescharacteristic
847C2—21no—
848C2—21no—
849C2—21no—
850C2—21no—
851C2—21no—
852C2—21no—
853C2—44no—
854C2—1884no—
855C2#2024380312yesdirect product factor
856C2C2×#1568899911yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#407C2
socleC22×C47#386
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC2×#407D47
hypocenterC47C2×#1891
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#15689889C2semidirect
3. C2×#15689105C2semidirect
4. C2×#15689087C2semidirect
5. #20243803C2direct (N × H)
6. C2×#15688895C2semidirect
7. C2×#15688894C2semidirect
8. C2×C47×#407C2semidirect
13. #15689889C22semidirect
30. #15689105C22semidirect
34. #15689087C22semidirect
36. #15688895C22semidirect
37. #15688894C22semidirect
42. C47×#407C22semidirect
74. C2×#10625329D4semidirect
81. C22×C47⋊C8D4semidirect
132. C2×M16×C47D4semidirect
136. C22×C8×C47D4semidirect
254. C2×C8×C47C2×D4semidirect
277. C2×C47⋊C8C2×D4semidirect
423. C2×#407D47semidirect
434. C2×C47#1891semidirect
467. #407C2×D47semidirect
472. C47C2×#1891semidirect
535. C2×M16C22⋊D47semidirect
542. C22×C8C22⋊D47semidirect
699. C2×C8C2×C22⋊D47semidirect
855. C2#20243803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156896342
C2×#156891052
C2×#156890872
#202438032
C2×#156888952
C2×#156888942
C2×C47×#4072
C2×#189147