Finite Group Databasebeta

← C2×#20243884 #26218170

Subgroups — C2×#20243884 #26218170

Order 12032.

1678 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689601C211yesmaximal, characteristic, complemented
2C2×#15689140C211yesmaximal, characteristic
3C2×#15689132C211yesmaximal, characteristic, complemented
4C2×#15689097C211yesmaximal, characteristic
5#20243884C218yesmaximal, direct product factor
6C2×#15688894C211yesmaximal, characteristic, complemented
7C2×#15688880C211yesmaximal, characteristic, complemented
8C22×#137×C47C211yesmaximal, characteristic
9C22×#10625329C2211yescharacteristic
10#15689601—22no—
11#15689601—22no—
12#15689601—22no—
13#15689601C2214yescomplemented
14C2×Q8×Dic47—22no—
15C2×Q8×Dic47—22no—
16C2×#13093983—22no—
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20#15689140—22no—
21#15689140C2214yes—
22C2×#13093951—22no—
23#15689132—22no—
24#15689132C2214yescomplemented
25C2×#13093948—22no—
26#15689097—22no—
27#15689097C2214yes—
28C2×#13093939—22no—
29#15688894C2214yescomplemented
30#15688880C2214yescomplemented
31C22×#41×C47C2211yescharacteristic
32C23×Q8×C47C2211yescharacteristic
33C2×#137×C47—22no—
34C2×#137×C47—22no—
35C2×#137×C47—22no—
36C2×#137×C47—22no—
37C2×#137×C47C414yescomplemented
38C2×#137×C47C2214yes—
39C22×Q16×C47C412yescomplemented
40C22×SD16×C47C412yescomplemented
41C22×M16×C47C2211yescharacteristic
42C2×#10625329—21no—
43C2×#10625329—21no—
44C2×#10625329—21no—
45C2×#10625329—21no—
46C2×#10625329—21no—
47C2×#10625329C2312yes—
48C22×C47⋊C8—21no—
49Q8×Dic47—28no—
50Q8×Dic47—28no—
51Q8×Dic47—28no—
52Q8×Dic47—28no—
53#13093983—28no—
54#13093983—21no—
55#13093983—21no—
56#13093983—21no—
57#13093983—21no—
58#13093983—28no—
59#13093983—21no—
60#13093983—21no—
61#13093983—21no—
62#13093983D412yes—
63#13093983D412yes—
64#13093983C2312yes—
65#13093983C2312yes—
66#13093983C2312yes—
67C2×C4⋊Dic47—24no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—21no—
71C2×C22⋊Dic47—21no—
72C2×C22⋊Dic47—21no—
73C2×C22⋊Dic47D412yes—
74C2×C4×Dic47—24no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47D412yes—
78#13093951—28no—
79#13093948—28no—
80#13093939—28no—
81C2×#41×C47—21no—
82C2×#41×C47—21no—
83C2×#41×C47—21no—
84C2×#41×C47—21no—
85C2×#41×C47—21no—
86C2×#41×C47—21no—
87C2×#41×C47—21no—
88C2×#41×C47—21no—
89C2×#41×C47—21no—
90C2×#41×C47—21no—
91C2×#41×C47C2×C412yes—
92C2×#41×C47C2312yes—
93C22×Q8×C47—21no—
94C22×Q8×C47—21no—
95C22×Q8×C47—21no—
96C22×Q8×C47—21no—
97C22×Q8×C47—21no—
98C22×Q8×C47—21no—
99C22×Q8×C47—21no—
100C22×Q8×C47C2×C411yescharacteristic
101C22×Q8×C47C2×C412yes—
102C22×Q8×C47C2×C412yes—
103C22×Q8×C47D412yes—
104C22×Q8×C47D412yes—
105C22×Q8×C47D412yes—
106C22×Q8×C47D412yes—
107C22×Q8×C47C2312yes—
108C22×D4×C47—21no—
109C22×D4×C47C2×C411yescharacteristic
110C23×C4×C47—21no—
111C23×C4×C47—21no—
112C23×C4×C47C2311yescharacteristic
113#137×C47—28no—
114#137×C47—28no—
115#137×C47—28no—
116#137×C47—28no—
117C2×Q16×C47—24no—
118C2×Q16×C47—24no—
119C2×Q16×C47C2×C418yescomplemented
120C2×SD16×C47—24no—
121C2×SD16×C47—24no—
122C2×SD16×C47C2×C418yescomplemented
123C2×M16×C47—21no—
124C2×M16×C47—21no—
125C2×M16×C47—21no—
126C2×M16×C47—21no—
127C2×M16×C47C2×C412yes—
128C2×M16×C47C2312yes—
129C22×C8×C47C2×C412yes—
130C24×C47—21no—
131C24×C47C2×D411yescharacteristic
132#41×C47—22no—
133#41×C47—22no—
134#41×C47—22no—
135#41×C47—22no—
136#41×C47—22no—
137#41×C47—22no—
138#41×C47—22no—
139#41×C47—22no—
140#41×C47—41no—
141#41×C47—41no—
142#41×C47—41no—
143#41×C47—41no—
144#41×C47—41no—
145#41×C47—41no—
146#41×C47—41no—
147#41×C47—41no—
148C2×Q8×C47—22no—
149C2×Q8×C47—22no—
150C2×Q8×C47—22no—
151C2×Q8×C47—22no—
152C2×Q8×C47—22no—
153C2×Q8×C47—22no—
154C2×Q8×C47—21no—
155C2×Q8×C47—22no—
156C2×Q8×C47—22no—
157C2×Q8×C47—22no—
158C2×Q8×C47—22no—
159C2×Q8×C47—22no—
160C2×Q8×C47—22no—
161C2×Q8×C47—22no—
162C2×Q8×C47—22no—
163C2×Q8×C47—22no—
164C2×Q8×C47—22no—
165C2×Q8×C47—22no—
166C2×Q8×C47—22no—
167C2×Q8×C47—22no—
168C2×Q8×C47—22no—
169C2×Q8×C47—22no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47—21no—
173C2×Q8×C47—21no—
174C2×Q8×C47C22⋊C414yes—
175C2×Q8×C47C22⋊C414yes—
176C2×Q8×C47C22⋊C414yes—
177C2×Q8×C47C22⋊C414yes—
178C2×Q8×C47C22×C412yes—
179C2×Q8×C47C22×C414yes—
180C2×Q8×C47C2×D414yes—
181C2×Q8×C47C2×D414yes—
182C2×D4×C47—22no—
183C2×D4×C47—22no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—41no—
190C2×D4×C47—41no—
191C2×D4×C47—41no—
192C2×D4×C47—41no—
193C2×D4×C47C22×C412yes—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—21no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—41no—
205C22×C4×C47—41no—
206C22×C4×C47—41no—
207C22×C4×C47—41no—
208C22×C4×C47C22×C411yescharacteristic
209C22×C4×C47C22×C411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47#4111yescharacteristic
218C22×C4×C47#4111yescharacteristic
219C22×C4×C47#4111yescharacteristic
220C22×C4×C47#4111yescharacteristic
221C22×C4×C47C2411yescharacteristic
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—41no—
225Q16×C47—216no—
226SD16×C47—216no—
227M16×C47—22no—
228M16×C47—22no—
229M16×C47—22no—
230M16×C47—22no—
231C2×C8×C47—22no—
232C2×C8×C47—22no—
233C2×C8×C47C22×C414yes—
234C22⋊Dic47—22no—
235C22⋊Dic47—22no—
236C22⋊Dic47—22no—
237C22⋊Dic47—22no—
238C22⋊Dic47—41no—
239C22⋊Dic47C2×D414yes—
240C4⋊Dic47—216no—
241C4⋊Dic47—22no—
242C4⋊Dic47—22no—
243C4⋊Dic47—22no—
244C4⋊Dic47—22no—
245C4⋊Dic47—22no—
246C4⋊Dic47—41no—
247C4×Dic47—216no—
248C4×Dic47—22no—
249C4×Dic47—22no—
250C4×Dic47—22no—
251C4×Dic47—22no—
252C4×Dic47—41no—
253C4×Dic47C2×D414yes—
254#10625329—22no—
255#10625329—22no—
256#10625329—41no—
257#10625329—41no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—41no—
260C2×C47⋊C8—41no—
261C23×C47—22no—
262C23×C47—42no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—82no—
266C23×C47C4×D411yescharacteristic
267C23×C47C4×D411yescharacteristic
268C23×C47#12011yescharacteristic
269C23×C47#12011yescharacteristic
270C23×C47#12111yescharacteristic
271C23×C47#12111yescharacteristic
272C23×C47C22×D411yescharacteristic
273Q8×C47—24no—
274Q8×C47—24no—
275Q8×C47—24no—
276Q8×C47—24no—
277Q8×C47—24no—
278Q8×C47—24no—
279Q8×C47—24no—
280Q8×C47—22no—
281Q8×C47—22no—
282Q8×C47—41no—
283Q8×C47—41no—
284Q8×C47C2×C22⋊C418yes—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—42no—
288D4×C47—42no—
289D4×C47—42no—
290D4×C47—42no—
291D4×C47—41no—
292D4×C47—41no—
293C2×C4×C47—24no—
294C2×C4×C47—24no—
295C2×C4×C47—24no—
296C2×C4×C47—24no—
297C2×C4×C47—24no—
298C2×C4×C47—24no—
299C2×C4×C47—24no—
300C2×C4×C47—22no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47C2×C22⋊C411yescharacteristic
308C2×C4×C47C2×C22⋊C411yescharacteristic
309C2×C4×C47C2×C22⋊C411yescharacteristic
310C2×C4×C47C2×C22⋊C411yescharacteristic
311C2×C4×C47C4×D411yescharacteristic
312C2×C4×C47C4×D411yescharacteristic
313C2×C4×C47C4×D411yescharacteristic
314C2×C4×C47C4×D411yescharacteristic
315C2×C4×C47C4×D411yescharacteristic
316C2×C4×C47C4×D411yescharacteristic
317C2×C4×C47#12011yescharacteristic
318C2×C4×C47#12011yescharacteristic
319C2×C4×C47#12111yescharacteristic
320C2×C4×C47#12111yescharacteristic
321C2×C4×C47#12111yescharacteristic
322C2×C4×C47#12111yescharacteristic
323C2×C4×C47#12111yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47#12311yescharacteristic
326C2×C4×C47#12311yescharacteristic
327C2×C4×C47#12311yescharacteristic
328C2×C4×C47#12311yescharacteristic
329C2×C4×C47C23×C411yescharacteristic
330C2×C4×C47C22×D411yescharacteristic
331C2×C4×C47C22×D411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C2×#4111yescharacteristic
334C2×C4×C47C2×#4111yescharacteristic
335C2×Dic47—24no—
336C2×Dic47—24no—
337C2×Dic47—44no—
338C2×Dic47—44no—
339C2×Dic47—42no—
340C2×Dic47—82no—
341C8×C47—24no—
342C47⋊C8—42no—
343C2×#1905—471nomaximal, Sylow
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—42no—
352C22×C47—82no—
353C22×C47—82no—
354C22×C47—82no—
355C22×C47#38611yescharacteristic
356C22×C47#38611yescharacteristic
357C22×C47#38611yescharacteristic
358C22×C47#38611yescharacteristic
359C22×C47C2×C4×D411yescharacteristic
360C22×C47C2×#12011yescharacteristic
361C22×C47C2×#12111yescharacteristic
362C4×C47—28no—
363C4×C47—42no—
364C4×C47#38611yescharacteristic
365C4×C47#38611yescharacteristic
366C4×C47#38611yescharacteristic
367C4×C47#38611yescharacteristic
368C4×C47C22×C22⋊C411yescharacteristic
369C4×C47C2×C4×D411yescharacteristic
370C4×C47C2×#12111yescharacteristic
371C4×C47C2×#12311yescharacteristic
372Dic47—44no—
373Dic47—44no—
374Dic47—82no—
375C22×#137D4711yescharacteristic
376C2×#519—471no—
377C2×#421—471no—
378C2×#419—471no—
379C2×#410—471no—
380#1905—478no—
381C2×#344—471no—
382C2×H(3,ℤ/4)—471no—
383C2×C47—21no—
384C2×C47—21no—
385C2×C47—21no—
386C2×C47—21no—
387C2×C47—21no—
388C2×C47—21no—
389C2×C47—82no—
390C2×C47#190512yescomplemented
391C2×C47C2×#38611yescharacteristic
392C22×#41C2×D4711yescharacteristic
393C23×Q8C2×D4711yescharacteristic
394C2×#137—22no—
395C2×#137—22no—
396C2×#137—22no—
397C2×#137—22no—
398C2×#137Dic4714yescomplemented
399C2×#137C2×D4714yes—
400C22×Q16Dic4712yescomplemented
401C22×SD16Dic4712yescomplemented
402C22×M16—471no—
403C22×M16C2×D4711yescharacteristic
404#519—474no—
405#519—942no—
406#519—942no—
407#519—942no—
408C2×C4×Q8—942no—
409C2×C4×Q8—942no—
410C2×#117—471no—
411C2×#117—471no—
412C2×#117—471no—
413C2×#117—942no—
414#421—474no—
415#421—942no—
416C2×#104—942no—
417#419—474no—
418#419—942no—
419C2×#103—942no—
420#410—474no—
421#410—942no—
422C2×#99—942no—
423#344—474no—
424H(3,ℤ/4)—474no—
425C47C2×#190511yescharacteristic, complemented, Sylow
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41C2×Dic4712yes—
437C2×#41C22×D4712yes—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8C2×Dic4711yescharacteristic
446C22×Q8C2×Dic4712yes—
447C22×Q8C2×Dic4712yes—
448C22×Q8C22⋊D4712yes—
449C22×Q8C22⋊D4712yes—
450C22×Q8C22⋊D4712yes—
451C22×Q8C22⋊D4712yes—
452C22×Q8C22×D4712yes—
453C22×D4—21no—
454C22×D4C2×Dic4711yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4C22×D4711yescharacteristic
458#137—28no—
459#137—28no—
460#137—28no—
461#137—28no—
462C2×Q16—24no—
463C2×Q16—24no—
464C2×Q16C2×Dic4718yescomplemented
465C2×SD16—24no—
466C2×SD16—24no—
467C2×SD16C2×Dic4718yescomplemented
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—472no—
473C2×M16—941no—
474C2×M16—941no—
475C2×M16—941no—
476C2×M16—941no—
477C2×M16—941no—
478C2×M16C2×Dic4712yes—
479C2×M16C22×D4712yes—
480C22×C8—941no—
481C22×C8C2×Dic4712yes—
482C4×Q8—948no—
483C4×Q8—948no—
484C4×Q8—948no—
485C4×Q8—948no—
486#117—472no—
487#117—472no—
488#117—472no—
489#117—472no—
490#117—472no—
491#117—948no—
492#117—948no—
493#117—941no—
494#117—941no—
495#117—941no—
496#117—941no—
497#117—941no—
498#117—941no—
499#117—941no—
500C2×C4⋊C4—944no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C22⋊C4—472no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C42—472no—
508C2×C42—944no—
509C2×C42—941no—
510C2×C42—941no—
511#104—948no—
512#103—948no—
513#99—948no—
514C24—21no—
515C24D4×D4711yescharacteristic
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8C22⋊Dic4714yes—
559C2×Q8C22⋊Dic4714yes—
560C2×Q8C22⋊Dic4714yes—
561C2×Q8C22⋊Dic4714yes—
562C2×Q8C22×Dic4712yes—
563C2×Q8C22×Dic4714yes—
564C2×Q8C2×C22⋊D4714yes—
565C2×Q8C2×C22⋊D4714yes—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4C22×Dic4712yes—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—1881no—
595C22×C4D4×D4711yescharacteristic
596C22×C4D4×D4711yescharacteristic
597C22×C4D4×D4711yescharacteristic
598C22×C4#1062535211yescharacteristic
599C22×C4#1062535211yescharacteristic
600C22×C4#1062535211yescharacteristic
601C22×C4#1062535211yescharacteristic
602C22×C4C22×Dic4711yescharacteristic
603C22×C4C22×Dic4711yescharacteristic
604C22×C4C2×C22⋊D4711yescharacteristic
605C22×C4C2×C22⋊D4711yescharacteristic
606C22×C4C2×C22⋊D4711yescharacteristic
607C22×C4C2×C22⋊D4711yescharacteristic
608C22×C4C23×D4711yescharacteristic
609Q16—216no—
610SD16—216no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615M16—942no—
616M16—942no—
617M16—1881no—
618M16—1881no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—942no—
622C2×C8—1881no—
623C2×C8—1881no—
624C2×C8C22×Dic4714yes—
625C4⋊C4—9416no—
626C4⋊C4—942no—
627C4⋊C4—942no—
628C4⋊C4—942no—
629C4⋊C4—942no—
630C4⋊C4—942no—
631C4⋊C4—1881no—
632C22⋊C4—474no—
633C22⋊C4—942no—
634C22⋊C4—942no—
635C22⋊C4—942no—
636C22⋊C4—942no—
637C22⋊C4—1881no—
638C42—474no—
639C42—9416no—
640C42—942no—
641C42—942no—
642C42—942no—
643C42—942no—
644C42—1881no—
645C23—22no—
646C23—42no—
647C23—41no—
648C23—41no—
649C23—82no—
650C23D4×Dic4711yescharacteristic
651C23D4×Dic4711yescharacteristic
652C23#1309399211yescharacteristic
653C23#1309399211yescharacteristic
654C23#1309399611yescharacteristic
655C23#1309399611yescharacteristic
656C23C2×D4×D4711yescharacteristic
657Q8—24no—
658Q8—24no—
659Q8—24no—
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—24no—
664Q8—22no—
665Q8—22no—
666Q8—41no—
667Q8—41no—
668Q8C2×C22⋊Dic4718yes—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—41no—
676D4—41no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—944no—
692C2×C4—944no—
693C2×C4—3762no—
694C2×C4—1882no—
695C2×C4—1884no—
696C2×C4—1884no—
697C2×C4C2×C22⋊Dic4711yescharacteristic
698C2×C4C2×C22⋊Dic4711yescharacteristic
699C2×C4C2×C22⋊Dic4711yescharacteristic
700C2×C4C2×C22⋊Dic4711yescharacteristic
701C2×C4D4×Dic4711yescharacteristic
702C2×C4D4×Dic4711yescharacteristic
703C2×C4D4×Dic4711yescharacteristic
704C2×C4D4×Dic4711yescharacteristic
705C2×C4D4×Dic4711yescharacteristic
706C2×C4D4×Dic4711yescharacteristic
707C2×C4#1309399211yescharacteristic
708C2×C4#1309399211yescharacteristic
709C2×C4#1309399611yescharacteristic
710C2×C4#1309399611yescharacteristic
711C2×C4#1309399611yescharacteristic
712C2×C4#1309399611yescharacteristic
713C2×C4#1309399611yescharacteristic
714C2×C4#1309399611yescharacteristic
715C2×C4#1309400511yescharacteristic
716C2×C4#1309400511yescharacteristic
717C2×C4#1309400511yescharacteristic
718C2×C4#1309400511yescharacteristic
719C2×C4C23×Dic4711yescharacteristic
720C2×C4C2×D4×D4711yescharacteristic
721C2×C4C22×C22⋊D4711yescharacteristic
722C2×C4C22×C22⋊D4711yescharacteristic
723C2×C4C2×#1062535211yescharacteristic
724C2×C4C2×#1062535211yescharacteristic
725C8—24no—
726C8—1882no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22#1568900311yescharacteristic
739C22#1568900311yescharacteristic
740C22#1568900311yescharacteristic
741C22#1568900311yescharacteristic
742C22C2×D4×Dic4711yescharacteristic
743C22C2×#1309399211yescharacteristic
744C22C2×#1309399611yescharacteristic
745C4—28no—
746C4—42no—
747C4—3762no—
748C4—1884no—
749C4—1884no—
750C4#1568900311yescharacteristic
751C4#1568900311yescharacteristic
752C4#1568900311yescharacteristic
753C4#1568900311yescharacteristic
754C4C22×C22⋊Dic4711yescharacteristic
755C4C2×D4×Dic4711yescharacteristic
756C4C2×#1309399611yescharacteristic
757C4C2×#1309400511yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—82no—
765C2#2024388412yesdirect product factor
766C2C2×#1568900311yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#137×C47C2
socleC22×C47#386
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC22×#137D47
hypocenterC47C2×#1905
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C2×#15689601C2semidirect
3. C2×#15689132C2semidirect
5. #20243884C2direct (N × H)
6. C2×#15688894C2semidirect
7. C2×#15688880C2semidirect
13. #15689601C22semidirect
24. #15689132C22semidirect
29. #15688894C22semidirect
30. #15688880C22semidirect
37. C2×#137×C47C4semidirect
39. C22×Q16×C47C4semidirect
40. C22×SD16×C47C4semidirect
119. C2×Q16×C47C2×C4semidirect
122. C2×SD16×C47C2×C4semidirect
390. C2×C47#1905semidirect
398. C2×#137Dic47semidirect
400. C22×Q16Dic47semidirect
401. C22×SD16Dic47semidirect
425. C47C2×#1905semidirect
464. C2×Q16C2×Dic47semidirect
467. C2×SD16C2×Dic47semidirect
765. C2#20243884direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896012
C2×#156891402
C2×#156891322
C2×#156890972
#202438842
C2×#156888942
C2×#156888802
C22×#137×C472
C2×#190547