Finite Group Databasebeta

← #26222807

Subgroups — #26222807

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689357C211yesmaximal, characteristic
2C2×C4×#10625334C211yesmaximal, characteristic, complemented
3C2×#15689079C211yesmaximal, characteristic, complemented
4#20246081C211yesmaximal, characteristic, complemented
5#20244253C211yesmaximal, characteristic, complemented
6#20244118C211yesmaximal, characteristic, complemented
7#20244088C211yesmaximal, characteristic, complemented
8#20244084C211yesmaximal, characteristic, complemented
9#20243827C211yesmaximal, characteristic, complemented
10#20243824C211yesmaximal, characteristic, complemented
11#20243415C211yesmaximal, characteristic, complemented
12C4×#13093957C211yesmaximal, characteristic, complemented
13#20243216C211yesmaximal, characteristic, complemented
14#20243213C211yesmaximal, characteristic, complemented
15C47×#2324C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C2×#13093998C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21#15689357C418yescomplemented
22C4×#10625334—24no—
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093957C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093944C2211yescharacteristic
30C2×#13093944C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32#15689079—24no—
33C2×#13093935C2211yescharacteristic
34C2×#13093935C2211yescharacteristic
35C2×C4×C47⋊C8C2211yescharacteristic
36C2×C4×C47⋊C8C2211yescharacteristic
37#15689025C2211yescharacteristic
38#15689023—21no—
39#15689021C2211yescharacteristic
40#15689013—21no—
41#15688999—21no—
42#15688994—21no—
43#15688983C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×#121×C47C2211yescharacteristic
52C2×C4×D4×C47C2211yescharacteristic
53C2×#117×C47C2211yescharacteristic
54C47×#390—21no—
55C47×#390C2211yescharacteristic
56C47×#389C2211yescharacteristic
57C47×#388—21no—
58C47×#386—21no—
59C47×#385—21no—
60C47×#380C2211yescharacteristic
61C4×C4⋊C4×C47C2211yescharacteristic
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C22×C4×D47—21no—
65C2×#10625334—22no—
66C2×#10625334—22no—
67C2×#10625334C2×C414yes—
68C2×#10625329—22no—
69C2×#10625329—22no—
70C2×#10625329—22no—
71C22×C47⋊C8—22no—
72C22×C47⋊C8—22no—
73C22×C47⋊C8C2×C414yescomplemented
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78#13093998—22no—
79#13093998C2×C414yescomplemented
80C4×D188—22no—
81C4×D188—22no—
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×Dic47⋊C4—21no—
86C2×C22⋊Dic47—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×(C2×D47)⋊C4—21no—
91C2×C4×Dic47—21no—
92#13093957—22no—
93#13093957—22no—
94#13093957C2×C414yescomplemented
95#13093945—22no—
96#13093945—22no—
97#13093945C2×C414yescomplemented
98#13093944—22no—
99#13093944—22no—
100#13093944C2×C414yescomplemented
101#13093935—22no—
102#13093935—22no—
103C4×C47⋊C8—22no—
104C4×C47⋊C8D414yescomplemented
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C22×D4×C47—21no—
109C22×D4×C47C2311yescharacteristic
110C23×C4×C47—21no—
111C23×C4×C47C2311yescharacteristic
112#121×C47—22no—
113#121×C47C2×C414yescomplemented
114C4×D4×C47—22no—
115C4×D4×C47—22no—
116#117×C47—22no—
117#117×C47—22no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47D411yescharacteristic
120C2×C4⋊C4×C47D411yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C42×C47—21no—
132C2×C42×C47C2311yescharacteristic
133C2×C42×C47C2311yescharacteristic
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137C24×C47—21no—
138C24×C47C2×D411yescharacteristic
139C23×D47—21no—
140C2×D4×C47—24no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—81no—
147C2×D4×C47—81no—
148C2×D4×C47C22×C412yes—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—42no—
157C22×C4×C47—81no—
158C22×C4×C47—81no—
159C22×C4×C47C22×C412yes—
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47#4112yes—
166C22×C4×C47C2411yescharacteristic
167C2×C22⋊D47—24no—
168C2×C22⋊D47—81no—
169C2×C22⋊D47—81no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C2×D188—21no—
174C2×D188—21no—
175C2×D188—21no—
176C2×D188—21no—
177C2×D188—21no—
178C2×D188C22×C412yes—
179C2×C4×D47—42no—
180C2×C4×D47—81no—
181C2×C4×D47—81no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47—22no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—81no—
190C4⋊C4×C47C22×C412yes—
191C22⋊C4×C47—24no—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—22no—
194C22⋊C4×C47—42no—
195C22⋊C4×C47—81no—
196C22⋊C4×C47—81no—
197C22⋊C4×C47—81no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—81no—
201C42×C47C2×D412yes—
202C42×C47#4112yes—
203C22⋊Dic47—81no—
204#10625334—28no—
205(C2×D47)⋊C4—24no—
206(C2×D47)⋊C4—42no—
207(C2×D47)⋊C4—81no—
208(C2×D47)⋊C4—81no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47C22×C412yes—
215Dic47⋊C4—81no—
216C4×Dic47—81no—
217#10625329—28no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—28no—
225C2×C47⋊C8C22×C412yes—
226C2×C47⋊C8C22×C412yes—
227C2×C47⋊C8C2×D412yes—
228C2×C47⋊C8C2×D412yes—
229C2×C47⋊C8#4112yes—
230C2×C47⋊C8#4112yes—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—22no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47C4×D412yes—
245C23×C47C22×D411yescharacteristic
246C22×D47—22no—
247C22×D47—41no—
248C22×D47—41no—
249C22×D47—41no—
250C22×D47—41no—
251C22×D47—41no—
252C22×D47—41no—
253D4×C47—22no—
254D4×C47—22no—
255D4×C47—41no—
256D4×C47—41no—
257D4×C47—84no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—84no—
284C2×C4×C47C4×D412yes—
285C2×C4×C47#12112yes—
286C2×C4×C47#12112yes—
287C2×C4×C47C23×C411yescharacteristic
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47C2×#4111yescharacteristic
292C2×C4×C47C2×#4111yescharacteristic
293C22⋊D47—84no—
294C2×Dic47—22no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303D188—22no—
304D188—22no—
305D188—41no—
306D188—41no—
307C4×D47—84no—
308C47⋊C8—22no—
309C47⋊C8—22no—
310C47⋊C8—22no—
311C47⋊C8C4×D414yes—
312#21524—471nomaximal, Sylow
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—41no—
319C22×C47—41no—
320C22×C47—42no—
321C22×C47—42no—
322C22×C47—42no—
323C22×C47—81no—
324C22×C47—81no—
325C22×C47—81no—
326C22×C47—81no—
327C22×C47C2×C4×D411yescharacteristic
328C22×C47C2×#12111yescharacteristic
329C22×C47#53211yescharacteristic
330C22×C47#57611yescharacteristic
331C22×C47#57611yescharacteristic
332C22×C47#57611yescharacteristic
333C22×C47#57811yescharacteristic
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—81no—
338C2×D47—81no—
339C2×D47—81no—
340C2×D47—81no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—42no—
345C4×C47—41no—
346C4×C47—41no—
347C4×C47—81no—
348C4×C47—81no—
349C4×C47C2×C4×D411yescharacteristic
350C4×C47C4×#4111yescharacteristic
351C4×C47#52511yescharacteristic
352C4×C47#52911yescharacteristic
353Dic47—42no—
354Dic47—81no—
355Dic47—81no—
356C2×#466—471no—
357C2×C4×D8—471no—
358C2×#405—471no—
359#2324—471no—
360#2324D4711yescharacteristic, complemented
361#1970—471no—
362#1942—471no—
363#1936—471no—
364#1936—471no—
365#1895—471no—
366#1895—471no—
367#1808—471no—
368C4×#107—471no—
369#1762—471no—
370#1762—471no—
371C2×C47—42no—
372C2×C47—82no—
373C2×C47C4×#12111yescharacteristic
374C2×C47#294811yescharacteristic
375C2×C47#295111yescharacteristic
376C2×C47#305811yescharacteristic
377C2×C47#306111yescharacteristic
378C2×C47#317511yescharacteristic
379C2×C47#317611yescharacteristic
380D47—82no—
381C22×D8—471no—
382C22×M16—471no—
383C23×C8—471no—
384C2×#121—471no—
385C2×#121C2×D4711yescharacteristic
386C2×C4×D4—471no—
387C2×C4×D4C2×D4711yescharacteristic
388C2×#117C2×D4711yescharacteristic
389#466—478no—
390C4×D8—944no—
391C2×#107—471no—
392C2×#107—471no—
393C2×#107—471no—
394C2×#102—471no—
395C2×#102—471no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×#102—471no—
400#405—944no—
401C2×#97—471no—
402C2×#97—471no—
403C2×C4×C8—471no—
404C2×C4×C8—471no—
405#390—21no—
406#390—471no—
407#390—941no—
408#390C2×D4711yescharacteristic
409#389—471no—
410#389C2×D4711yescharacteristic
411#388—21no—
412#388—941no—
413#386—21no—
414#386—941no—
415#385—21no—
416#385—941no—
417#380—471no—
418#380C2×D4711yescharacteristic
419C4×C4⋊C4—471no—
420C4×C4⋊C4C2×D4711yescharacteristic
421#340—471no—
422#340—471no—
423#340—471no—
424#340—471no—
425#340—471no—
426#340—471no—
427C47#2152411yescharacteristic, complemented, Sylow
428C22×D4—21no—
429C22×D4—471no—
430C22×D4—941no—
431C22×D4C22×D4711yescharacteristic
432C23×C4—21no—
433C23×C4—941no—
434C23×C4C22×D4711yescharacteristic
435C2×D8—474no—
436C2×D8—942no—
437C2×D8—942no—
438C2×M16—942no—
439C2×M16—942no—
440C2×M16—942no—
441C22×C8—471no—
442C22×C8—474no—
443C22×C8—471no—
444C22×C8—471no—
445C22×C8—471no—
446C22×C8—942no—
447C22×C8—942no—
448#121—22no—
449#121—474no—
450#121—942no—
451#121C4×D4714yescomplemented
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—942no—
455C4×D4—942no—
456#117—22no—
457#117—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—941no—
463C2×C4⋊C4C22⋊D4711yescharacteristic
464C2×C4⋊C4C22⋊D4711yescharacteristic
465C2×C4⋊C4C22×D4711yescharacteristic
466C2×C4⋊C4C22×D4711yescharacteristic
467C2×C4⋊C4C22×D4711yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—941no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4—941no—
477C2×C22⋊C4—941no—
478C2×C22⋊C4C22⋊D4711yescharacteristic
479C2×C22⋊C4C22⋊D4711yescharacteristic
480C2×C42—21no—
481C2×C42—941no—
482C2×C42C22×D4711yescharacteristic
483C2×C42C22×D4711yescharacteristic
484#107—474no—
485#107—942no—
486#107—942no—
487#102—474no—
488#102—474no—
489#102—942no—
490#102—942no—
491#102—942no—
492#102—942no—
493#97—942no—
494#97—942no—
495C4×C8—474no—
496C4×C8—942no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—941no—
501#95—941no—
502#95—941no—
503C24—21no—
504C24—941no—
505C24C2×C22⋊D4711yescharacteristic
506C2×D4—24no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4—472no—
515C2×D4—944no—
516C2×D4—941no—
517C2×D4—941no—
518C2×D4—941no—
519C2×D4—941no—
520C2×D4—941no—
521C2×D4—3761no—
522C2×D4—3761no—
523C2×D4C2×C4×D4712yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—3761no—
538C22×C4—3761no—
539C22×C4—1882no—
540C22×C4C2×C4×D4712yes—
541C22×C4#1062535012yes—
542C22×C4C2×C22⋊D4711yescharacteristic
543C22×C4C2×C22⋊D4711yescharacteristic
544C22×C4C2×C22⋊D4711yescharacteristic
545C22×C4C2×C22⋊D4711yescharacteristic
546C22×C4C2×C22⋊D4711yescharacteristic
547C22×C4C23×D4711yescharacteristic
548D8—948no—
549M16—948no—
550C2×C8—472no—
551C2×C8—472no—
552C2×C8—472no—
553C2×C8—472no—
554C2×C8—472no—
555C2×C8—472no—
556C2×C8—948no—
557C2×C8—941no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8—941no—
561C2×C8—941no—
562C2×C8—941no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—81no—
571C4⋊C4—472no—
572C4⋊C4—941no—
573C4⋊C4—941no—
574C4⋊C4—941no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—3761no—
578C4⋊C4C2×C4×D4712yes—
579C22⋊C4—24no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—944no—
587C22⋊C4—3761no—
588C22⋊C4—3761no—
589C22⋊C4—3761no—
590C22⋊C4—1882no—
591C42—21no—
592C42—21no—
593C42—81no—
594C42—3761no—
595C42D4×D4712yes—
596C42#1062535212yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—942no—
611C23—1881no—
612C23—1881no—
613C23—1881no—
614C23—1881no—
615C23—1881no—
616C23—1881no—
617C23C4×C22⋊D4712yes—
618C23C22×C22⋊D4711yescharacteristic
619D4—22no—
620D4—22no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—942no—
625D4—942no—
626D4—3764no—
627D4—1881no—
628D4—1881no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—942no—
656C2×C4—3764no—
657C2×C4—1881no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1881no—
661C2×C4—1881no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4—1881no—
665C2×C4C4×C22⋊D4712yes—
666C2×C4#1309399612yes—
667C2×C4#1309399612yes—
668C2×C4C22×C4×D4711yescharacteristic
669C2×C4C2×D4×D4711yescharacteristic
670C2×C4#41×D4711yescharacteristic
671C2×C4#41×D4711yescharacteristic
672C2×C4C2×#1062535211yescharacteristic
673C2×C4C2×#1062535011yescharacteristic
674C8—474no—
675C8—942no—
676C8—942no—
677C8—942no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—3761no—
693C22—3761no—
694C22—3761no—
695C22—3761no—
696C22—1882no—
697C22—1882no—
698C22—1882no—
699C22C2×C4×C22⋊D4711yescharacteristic
700C22C2×#1309399611yescharacteristic
701C22#1568966911yescharacteristic
702C22#1568992611yescharacteristic
703C22#1568992611yescharacteristic
704C22#1568992611yescharacteristic
705C22#1568993811yescharacteristic
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—3761no—
715C4—3761no—
716C4—1882no—
717C4C4×D4×D4711yescharacteristic
718C4C4×#1062535211yescharacteristic
719C4#1568963211yescharacteristic
720C4#1568965311yescharacteristic
721C2—42no—
722C2—82no—
723C2—3762no—
724C2C4×#1309399611yescharacteristic
725C2#2025223811yescharacteristic
726C2#2025226111yescharacteristic
727C2#2025303311yescharacteristic
728C2#2025305511yescharacteristic
729C2#2025402111yescharacteristic
730C2#2025403211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2324C2
socleC23×C47C22×D4
prime radicalC2×#15689357C2
cosocleC22×C4×C47C24
hypercenter#2324D47
hypocenterC47#21524
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625334C2semidirect
3. C2×#15689079C2semidirect
4. #20246081C2semidirect
5. #20244253C2semidirect
6. #20244118C2semidirect
7. #20244088C2semidirect
8. #20244084C2semidirect
9. #20243827C2semidirect
10. #20243824C2semidirect
11. #20243415C2semidirect
12. C4×#13093957C2semidirect
13. #20243216C2semidirect
14. #20243213C2semidirect
15. C47×#2324C2semidirect
21. #15689357C4semidirect
73. C22×C47⋊C8C2×C4semidirect
79. #13093998C2×C4semidirect
94. #13093957C2×C4semidirect
97. #13093945C2×C4semidirect
100. #13093944C2×C4semidirect
104. C4×C47⋊C8D4semidirect
113. #121×C47C2×C4semidirect
360. #2324D47semidirect
427. C47#21524semidirect
451. #121C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156893572
C2×C4×#106253342
C2×#156890792
#202460812
#202442532
#202441182
#202440882
#202440842
#202438272
#202438242
#202434152
C4×#130939572
#202432162
#202432132
C47×#23242
#2152447