Finite Group Databasebeta

← #26215882

Subgroups — #26215882

Order 12032.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094032C211yesmaximal, characteristic
2C2×#15689164C211yesmaximal, characteristic, complemented
3C2×#15689162C211yesmaximal, characteristic, complemented
4#20245977C211yesmaximal, characteristic
5#20245977C211yesmaximal, characteristic
6#20243421C211yesmaximal, characteristic, complemented
7#20243420C211yesmaximal, characteristic, complemented
8#20243420C211yesmaximal, characteristic, complemented
9#20243415C211yesmaximal, characteristic, complemented
10#20243414C211yesmaximal, characteristic, complemented
11#20243411C211yesmaximal, characteristic, complemented
12#20243410C211yesmaximal, characteristic, complemented
13#20243103C211yesmaximal, characteristic, complemented
14#340×D47C211yesmaximal, characteristic, complemented
15C47×#1809C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C2×#13094032—24no—
18C2×#13094032—24no—
19C2×#13094032C418yescomplemented
20C22×#10625324C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C23×C47⋊C8C2211yescharacteristic
23C22×C8×D47C2211yescharacteristic
24C22×C8×D47C2211yescharacteristic
25C2×#13093982C2211yescharacteristic
26C2×#13093982C2211yescharacteristic
27C2×C4⋊C4×D47C2211yescharacteristic
28C2×C4⋊C4×D47C2211yescharacteristic
29#15689164—24no—
30#15689162—24no—
31C2×#13093958C2211yescharacteristic
32C2×#13093957C2211yescharacteristic
33C2×#13093957C2211yescharacteristic
34C2×#13093956C2211yescharacteristic
35C2×#13093955C2211yescharacteristic
36C2×#13093955C2211yescharacteristic
37#15689027—21no—
38#15689027—21no—
39#15689023—21no—
40#15689023—21no—
41#15689001—21no—
42#15689001—21no—
43#15688999—21no—
44#15688999—21no—
45#15688983C2211yescharacteristic
46#15688983C2211yescharacteristic
47#15688980C2211yescharacteristic
48#15688980C2211yescharacteristic
49#15688980C2211yescharacteristic
50#15688980C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55#15688885C2211yescharacteristic
56#15688885C2211yescharacteristic
57C22×M16×C47C2211yescharacteristic
58C2×#107×C47C2211yescharacteristic
59C2×#106×C47C2211yescharacteristic
60C47×#380C2211yescharacteristic
61C47×#380C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#340C2211yescharacteristic
64C2×#10625350—22no—
65C2×#10625350—22no—
66C2×#10625350—22no—
67C2×#10625350—22no—
68C2×#10625350C2×C414yes—
69C2×#10625350Q814yes—
70C22×Dic94D411yescharacteristic
71C22×D188D411yescharacteristic
72C22×C22⋊D47D411yescharacteristic
73C22×C22⋊D47D411yescharacteristic
74C22×C4×D47—21no—
75C22×C4×D47—21no—
76C22×C4×D47C2311yescharacteristic
77C22×C4×D47C2311yescharacteristic
78#13094032—232no—
79C2×#10625324—22no—
80C2×#10625324—22no—
81C2×#10625324C2×C414yes—
82C2×#10625324C2×C414yescomplemented
83C2×#10625324D414yes—
84C2×#10625324D414yes—
85C22×C47⋊C8—22no—
86C22×C47⋊C8—22no—
87C22×C47⋊C8C2×C414yescomplemented
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C2×C8×D47—22no—
91C2×C8×D47—22no—
92C2×C8×D47—22no—
93C2×C8×D47—22no—
94C2×C8×D47C2×C414yes—
95C2×C8×D47C2×C414yescomplemented
96#13093982—22no—
97#13093982—22no—
98#13093982—22no—
99#13093982—22no—
100C2×C4⋊Dic47C2311yescharacteristic
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2311yescharacteristic
103C2×C4⋊Dic47C2311yescharacteristic
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C4⋊C4×D47—22no—
107C4⋊C4×D47—22no—
108C4⋊C4×D47—22no—
109C4⋊C4×D47—22no—
110C2×C22⋊Dic47—21no—
111C2×C22⋊Dic47—21no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×(C2×D47)⋊C4—21no—
118C2×C4×Dic47—21no—
119C2×C4×Dic47—21no—
120#13093958—22no—
121#13093957—22no—
122#13093957—22no—
123#13093956—22no—
124#13093955—22no—
125#13093955—22no—
126C47⋊#95—21no—
127C47⋊#95—21no—
128C47⋊#95—21no—
129C47⋊#95—21no—
130C47⋊#95—21no—
131C47⋊#95—21no—
132C23×C4×C47C2311yescharacteristic
133C2×M16×C47—22no—
134C2×M16×C47—22no—
135C2×M16×C47C2×C414yescomplemented
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C4⋊C4×C47C2311yescharacteristic
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—21no—
144#107×C47—22no—
145#106×C47—22no—
146#95×C47—21no—
147#95×C47—21no—
148C24×C47C2×D411yescharacteristic
149C23×D47C2×D411yescharacteristic
150C23×D47C2×D411yescharacteristic
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2×Q812yes—
162C22×C4×C47C2411yescharacteristic
163C2×C22⋊D47—22no—
164C2×C22⋊D47—22no—
165C2×C22⋊D47—22no—
166C2×C22⋊D47—22no—
167C2×C22⋊D47C4⋊C414yes—
168C2×C22⋊D47C4⋊C414yes—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47C2×D411yescharacteristic
174C22×Dic47C2×D411yescharacteristic
175#10625350—28no—
176#10625350—28no—
177#10625350—28no—
178#10625350—28no—
179C2×D188—22no—
180C2×D188—22no—
181C2×D188C4⋊C414yes—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—42no—
187C2×C4×D47—42no—
188C2×C4×D47—81no—
189C2×C4×D47—81no—
190C2×C4×D47—81no—
191C2×C4×D47—81no—
192C2×C4×D47C22×C412yes—
193C2×C4×D47C22×C412yes—
194C2×C4×D47C2×D412yes—
195C2×C4×D47C2×D412yes—
196C2×C4×D47C2×Q812yes—
197C2×C4×D47C2×Q812yes—
198C2×C4×D47#4112yes—
199C2×C4×D47#4112yes—
200C2×Dic94—22no—
201C2×Dic94—22no—
202C2×Dic94C4⋊C414yes—
203M16×C47—28no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47C22×C412yes—
207C2×C8×C47C22×C412yes—
208C2×C8×C47C2×D412yes—
209C2×C8×C47C2×D412yes—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C22⋊C4×C47—81no—
219C22⋊C4×C47—81no—
220C22⋊Dic47—81no—
221C22⋊Dic47—81no—
222(C2×D47)⋊C4—42no—
223(C2×D47)⋊C4—42no—
224(C2×D47)⋊C4—81no—
225(C2×D47)⋊C4—81no—
226(C2×D47)⋊C4—81no—
227(C2×D47)⋊C4—81no—
228C4⋊Dic47—21no—
229C4⋊Dic47—21no—
230C4⋊Dic47—21no—
231C4⋊Dic47—21no—
232C4⋊Dic47—21no—
233C4⋊Dic47—21no—
234C4⋊Dic47—21no—
235C4⋊Dic47—21no—
236Dic47⋊C4—42no—
237Dic47⋊C4—42no—
238C4×Dic47—42no—
239C4×Dic47—42no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—21no—
242C2×C47⋊C8—28no—
243C2×C47⋊C8C22×C412yes—
244C2×C47⋊C8C22×C412yes—
245C2×C47⋊C8C2×D412yes—
246C2×C47⋊C8C2×D412yes—
247#10625324—28no—
248#10625324C22⋊C4116yescomplemented
249C8×D47—28no—
250C8×D47—28no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47C2×C4⋊C412yes—
258C23×C47C22×D411yescharacteristic
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
267C22×D47—21no—
268C22×D47—21no—
269C22×D47C2×C4⋊C412yes—
270C22×D47C2×C4⋊C412yes—
271C22×D47#12112yes—
272C22×D47#12112yes—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47C2×C4⋊C412yes—
292C2×C4×C47C23×C411yescharacteristic
293C2×C4×C47C22×D411yescharacteristic
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C47C22×Q811yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C22⋊D47—28no—
299C22⋊D47—28no—
300C2×Dic47—21no—
301C2×Dic47—21no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47C2×C4⋊C412yes—
315C2×Dic47C2×C4⋊C412yes—
316C2×Dic47#12112yes—
317C2×Dic47#12112yes—
318D188—28no—
319C4×D47—22no—
320C4×D47—22no—
321C4×D47—22no—
322C4×D47—22no—
323C4×D47—84no—
324C4×D47—84no—
325C4×D47C2×C22⋊C414yes—
326C4×D47#11714yes—
327C4×D47C22⋊Q814yes—
328C4×D47C22⋊Q814yes—
329Dic94—28no—
330C8×C47—22no—
331C8×C47C2×C22⋊C414yes—
332C47⋊C8—22no—
333C47⋊C8C2×C22⋊C414yes—
334#20664—471nomaximal, Sylow
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47C22×C4⋊C411yescharacteristic
343C22×C47C2×#12111yescharacteristic
344C22×C47C2×#12111yescharacteristic
345C22×C47#57611yescharacteristic
346C22×C47#57711yescharacteristic
347C22×C47#57711yescharacteristic
348C22×C47#57811yescharacteristic
349C2×D47—22no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—22no—
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—22no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C2×D47—41no—
362C2×D47#38014yes—
363C4×C47—22no—
364C4×C47—81no—
365C4×C47—81no—
366C4×C47—81no—
367C4×C47—81no—
368C4×C47C22×C22⋊C411yescharacteristic
369C4×C47C2×#11711yescharacteristic
370C4×C47C2×C22⋊Q811yescharacteristic
371C4×C47C2×C22⋊Q811yescharacteristic
372Dic47—22no—
373Dic47—81no—
374Dic47—81no—
375Dic47—81no—
376Dic47—81no—
377Dic47#38014yes—
378C22×#131—471no—
379C2×#428—471no—
380C2×#428—471no—
381#2311—471no—
382#2311—471no—
383#1809—471no—
384#1809—471no—
385#1809—471no—
386#1809D4711yescharacteristic, complemented
387#1808—471no—
388#1808—471no—
389#1807—471no—
390#1807—471no—
391#1735—471no—
392C2×#340—471no—
393C2×C47—42no—
394C2×C47C2×#38011yescharacteristic
395C2×C47#291211yescharacteristic
396C2×C47#291311yescharacteristic
397C2×C47#306211yescharacteristic
398C2×C47#306211yescharacteristic
399C2×C47#306311yescharacteristic
400C2×C47#306311yescharacteristic
401D47—24no—
402D47—42no—
403C22×#41—471no—
404C2×#131—478no—
405C2×#131—944no—
406C2×#131—944no—
407C22×M16—471no—
408C22×M16—471no—
409C22×M16C2×D4711yescharacteristic
410C23×C8—471no—
411C23×C8—471no—
412C23×C8—471no—
413C2×#117—471no—
414C2×#117—471no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4—471no—
417#428—944no—
418#428—944no—
419C2×#107—471no—
420C2×#107—471no—
421C2×#107—471no—
422C2×#107C2×D4711yescharacteristic
423C2×#106—471no—
424C2×#106—471no—
425C2×#106—471no—
426C2×#106C2×D4711yescharacteristic
427#391—941no—
428#391—941no—
429#390—941no—
430#390—941no—
431#386—941no—
432#386—941no—
433#386—941no—
434#386—941no—
435#380—471no—
436#380—471no—
437#380—471no—
438#380—471no—
439#380—471no—
440#380—471no—
441#380C2×D4711yescharacteristic
442#380C2×D4711yescharacteristic
443#340—471no—
444#340—471no—
445#340—471no—
446#340—471no—
447#340—471no—
448#340—471no—
449#340C2×D4711yescharacteristic
450#340C2×D4711yescharacteristic
451C47#2066411yescharacteristic, complemented, Sylow
452C2×#41—474no—
453C2×#41—474no—
454C2×#41—942no—
455C2×#41—942no—
456C2×#41—942no—
457C2×#41—942no—
458C22×Q8—471no—
459C22×D4—471no—
460C22×D4—471no—
461C22×D4—471no—
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—941no—
465C23×C4—941no—
466C23×C4C22×D4711yescharacteristic
467#131—9432no—
468C2×M16—22no—
469C2×M16—22no—
470C2×M16—474no—
471C2×M16—474no—
472C2×M16—474no—
473C2×M16—474no—
474C2×M16—942no—
475C2×M16—942no—
476C2×M16C4×D4714yescomplemented
477C22×C8—471no—
478C22×C8—474no—
479C22×C8—471no—
480C22×C8—474no—
481C22×C8—474no—
482C22×C8—942no—
483C22×C8—942no—
484C22×C8—942no—
485C22×C8—942no—
486C22×C8—942no—
487C22×C8—942no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490#117—942no—
491#117—942no—
492#117—942no—
493#117—942no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—942no—
499C2×C4⋊C4—942no—
500C2×C4⋊C4—942no—
501C2×C4⋊C4—942no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4C22×D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C22⋊C4—941no—
516C2×C22⋊C4—941no—
517C2×C22⋊C4—941no—
518C2×C42—941no—
519C2×C42—941no—
520#107—22no—
521#107—942no—
522#107—942no—
523#107—942no—
524#106—22no—
525#106—942no—
526#106—942no—
527#106—942no—
528#95—21no—
529#95—21no—
530#95—941no—
531#95—941no—
532#95—941no—
533#95—941no—
534#95—941no—
535#95—941no—
536C24—471no—
537C24—471no—
538C24D4×D4711yescharacteristic
539#41—948no—
540#41—948no—
541#41—948no—
542#41—948no—
543C2×Q8—474no—
544C2×Q8—942no—
545C2×Q8—942no—
546C2×D4—474no—
547C2×D4—474no—
548C2×D4—474no—
549C2×D4—942no—
550C2×D4—942no—
551C2×D4—942no—
552C2×D4—942no—
553C2×D4—942no—
554C2×D4—942no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—471no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—472no—
567C22×C4—472no—
568C22×C4—472no—
569C22×C4—472no—
570C22×C4—471no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—3761no—
582C22×C4—3761no—
583C22×C4—3761no—
584C22×C4—3761no—
585C22×C4—1882no—
586C22×C4—1882no—
587C22×C4C2×C4×D4712yes—
588C22×C4D4×D4711yescharacteristic
589C22×C4Q8×D4712yes—
590C22×C4C23×D4711yescharacteristic
591M16—28no—
592M16—4716no—
593M16—948no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—472no—
597C2×C8—472no—
598C2×C8—472no—
599C2×C8—472no—
600C2×C8—948no—
601C2×C8—948no—
602C2×C8—941no—
603C2×C8—941no—
604C2×C8—948no—
605C2×C8C2×C4×D4712yes—
606C2×C8C2×C4×D4712yes—
607C2×C8D4×D4712yes—
608C2×C8D4×D4712yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—941no—
621C4⋊C4—941no—
622C4⋊C4—941no—
623C4⋊C4—941no—
624C4⋊C4—941no—
625C4⋊C4—1882no—
626C4⋊C4—1882no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—3761no—
630C22⋊C4—3761no—
631C22⋊C4—3761no—
632C22⋊C4—3761no—
633C22⋊C4—3761no—
634C22⋊C4—3761no—
635C22⋊C4—1882no—
636C22⋊C4—1882no—
637C42—1882no—
638C42—1882no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—472no—
646C23—472no—
647C23—472no—
648C23—472no—
649C23—941no—
650C23—941no—
651C23—941no—
652C23—941no—
653C23—941no—
654C23—941no—
655C23—941no—
656C23—941no—
657C23—941no—
658C23—941no—
659C23C4⋊C4×D4712yes—
660C23C2×D4×D4711yescharacteristic
661Q8—948no—
662D4—948no—
663D4—948no—
664D4—948no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—472no—
684C2×C4—472no—
685C2×C4—472no—
686C2×C4—474no—
687C2×C4—474no—
688C2×C4—474no—
689C2×C4—474no—
690C2×C4—472no—
691C2×C4—941no—
692C2×C4—941no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—942no—
697C2×C4—3764no—
698C2×C4—3764no—
699C2×C4—1881no—
700C2×C4—1881no—
701C2×C4—1881no—
702C2×C4—1881no—
703C2×C4—1881no—
704C2×C4—1881no—
705C2×C4—1881no—
706C2×C4—1881no—
707C2×C4—1881no—
708C2×C4—1881no—
709C2×C4—1881no—
710C2×C4—1881no—
711C2×C4C4⋊C4×D4712yes—
712C2×C4C22×C4×D4711yescharacteristic
713C2×C4C2×D4×D4711yescharacteristic
714C2×C4C2×D4×D4711yescharacteristic
715C2×C4C2×Q8×D4711yescharacteristic
716C2×C4#41×D4711yescharacteristic
717C2×C4#41×D4711yescharacteristic
718C8—22no—
719C8—474no—
720C8—942no—
721C8C22⋊C4×D4714yes—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—474no—
730C22—942no—
731C22—942no—
732C22—942no—
733C22—942no—
734C22—942no—
735C22—942no—
736C22—942no—
737C22—942no—
738C22—942no—
739C22—1881no—
740C22—1881no—
741C22—1881no—
742C22—1881no—
743C22C2×C4⋊C4×D4711yescharacteristic
744C22#121×D4711yescharacteristic
745C22#121×D4711yescharacteristic
746C22#1568992711yescharacteristic
747C22#1568993211yescharacteristic
748C22#1568993311yescharacteristic
749C22#1568993911yescharacteristic
750C4—22no—
751C4—81no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—474no—
756C4—942no—
757C4—3761no—
758C4—3761no—
759C4—3761no—
760C4—3761no—
761C4C2×C22⋊C4×D4711yescharacteristic
762C4#117×D4711yescharacteristic
763C4C22⋊Q8×D4711yescharacteristic
764C4C22⋊Q8×D4711yescharacteristic
765C2—42no—
766C2—944no—
767C2—1882no—
768C2#380×D4711yescharacteristic
769C2#2025198211yescharacteristic
770C2#2025198711yescharacteristic
771C2#2025306311yescharacteristic
772C2#2025306511yescharacteristic
773C2#2025307411yescharacteristic
774C2#2025307611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1809C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#1809D47
hypocenterC47#20664
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#15689164C2semidirect
3. C2×#15689162C2semidirect
6. #20243421C2semidirect
7. #20243420C2semidirect
8. #20243420C2semidirect
9. #20243415C2semidirect
10. #20243414C2semidirect
11. #20243411C2semidirect
12. #20243410C2semidirect
13. #20243103C2semidirect
14. #340×D47C2semidirect
15. C47×#1809C2semidirect
19. C2×#13094032C4semidirect
82. C2×#10625324C2×C4semidirect
87. C22×C47⋊C8C2×C4semidirect
95. C2×C8×D47C2×C4semidirect
135. C2×M16×C47C2×C4semidirect
248. #10625324C22⋊C4semidirect
386. #1809D47semidirect
451. C47#20664semidirect
476. C2×M16C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130940322
C2×#156891642
C2×#156891622
#202459772
#202434212
#202434202
#202434152
#202434142
#202434112
#202434102
#202431032
#340×D472
C47×#18092
#2066447