Finite Group Databasebeta

← #25103274

Subgroups — #25103274

Order 11008.

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×#14583150C211yesmaximal, characteristic
2C2×C4×#10621882C211yesmaximal, characteristic, complemented
3C2×#14582855C211yesmaximal, characteristic, complemented
4#19137288C211yesmaximal, characteristic, complemented
5#19135470C211yesmaximal, characteristic, complemented
6#19135335C211yesmaximal, characteristic, complemented
7#19135281C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19135024C211yesmaximal, characteristic, complemented
10#19135021C211yesmaximal, characteristic, complemented
11#19134626C211yesmaximal, characteristic, complemented
12C4×#13063256C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C43×#2324C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583150C418yescomplemented
22C4×#10621882—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32#14582855—24no—
33C2×#13063236C2211yescharacteristic
34C2×#13063236C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582799—21no—
39#14582797C2211yescharacteristic
40#14582789—21no—
41#14582775—21no—
42#14582770—21no—
43#14582759C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C2×#121×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C43×#390—21no—
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#388—21no—
58C43×#386—21no—
59C43×#385—21no—
60C43×#380C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C4×D43—21no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882C2×C414yes—
68C2×#10621877—22no—
69C2×#10621877—22no—
70C2×#10621877C2×C414yescomplemented
71C22×C43⋊C8—22no—
72C22×C43⋊C8—22no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063299—22no—
79#13063299C2×C414yescomplemented
80C4×D172—22no—
81C4×D172—22no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92#13063258—22no—
93#13063256—22no—
94#13063256C2×C414yescomplemented
95#13063246—22no—
96#13063246—22no—
97#13063246C2×C414yescomplemented
98#13063245—22no—
99#13063245—22no—
100#13063245C2×C414yescomplemented
101#13063236—22no—
102#13063236—22no—
103C4×C43⋊C8—22no—
104C4×C43⋊C8D414yescomplemented
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×D4×C43—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C23×C4×C43C2311yescharacteristic
112#121×C43—22no—
113#121×C43C2×C414yescomplemented
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116#117×C43—22no—
117#117×C43—22no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137C24×C43—21no—
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—24no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—81no—
147C2×D4×C43—81no—
148C2×D4×C43C22×C412yes—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—81no—
158C22×C4×C43—81no—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43#4112yes—
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43—81no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172C22×C412yes—
179C2×C4×D43—42no—
180C2×C4×D43—81no—
181C2×C4×D43—81no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—81no—
190C4⋊C4×C43C22×C412yes—
191C22⋊C4×C43—24no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—81no—
196C22⋊C4×C43—81no—
197C22⋊C4×C43—81no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—81no—
201C42×C43C2×D412yes—
202C42×C43#4112yes—
203C22⋊Dic43—81no—
204#10621882—28no—
205(C2×D43)⋊C4—24no—
206(C2×D43)⋊C4—42no—
207(C2×D43)⋊C4—81no—
208(C2×D43)⋊C4—81no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C22×C412yes—
215Dic43⋊C4—81no—
216C4×Dic43—81no—
217#10621877—28no—
218C2×C43⋊C8—28no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8C22×C412yes—
226C2×C43⋊C8C22×C412yes—
227C2×C43⋊C8C2×D412yes—
228C2×C43⋊C8C2×D412yes—
229C2×C43⋊C8#4112yes—
230C2×C43⋊C8#4112yes—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—22no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43C4×D412yes—
245C23×C43C22×D411yescharacteristic
246C22×D43—22no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253D4×C43—22no—
254D4×C43—22no—
255D4×C43—41no—
256D4×C43—41no—
257D4×C43—84no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—84no—
284C2×C4×C43C4×D412yes—
285C2×C4×C43#12112yes—
286C2×C4×C43#12112yes—
287C2×C4×C43C23×C411yescharacteristic
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C22⋊D43—84no—
294C2×Dic43—22no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303D172—22no—
304D172—22no—
305D172—41no—
306D172—41no—
307C4×D43—84no—
308C43⋊C8—22no—
309C43⋊C8—22no—
310C43⋊C8—22no—
311C43⋊C8C4×D414yes—
312#21536—431nomaximal, Sylow
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43—41no—
320C22×C43—42no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43—81no—
324C22×C43—81no—
325C22×C43—81no—
326C22×C43—81no—
327C22×C43C2×C4×D411yescharacteristic
328C22×C43C2×#12111yescharacteristic
329C22×C43#53211yescharacteristic
330C22×C43#57611yescharacteristic
331C22×C43#57611yescharacteristic
332C22×C43#57711yescharacteristic
333C22×C43#57711yescharacteristic
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—81no—
338C2×D43—81no—
339C2×D43—81no—
340C2×D43—81no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—41no—
346C4×C43—41no—
347C4×C43—81no—
348C4×C43—81no—
349C4×C43C2×C4×D411yescharacteristic
350C4×C43C4×#4111yescharacteristic
351C4×C43#52511yescharacteristic
352C4×C43#52911yescharacteristic
353Dic43—42no—
354Dic43—81no—
355Dic43—81no—
356C2×#469—431no—
357C2×C4×D8—431no—
358C2×#405—431no—
359#2324—431no—
360#2324D4311yescharacteristic, complemented
361#1972—431no—
362#1944—431no—
363#1934—431no—
364#1934—431no—
365#1893—431no—
366#1893—431no—
367#1809—431no—
368C4×#106—431no—
369#1762—431no—
370#1762—431no—
371C2×C43—42no—
372C2×C43—82no—
373C2×C43C4×#12111yescharacteristic
374C2×C43#294611yescharacteristic
375C2×C43#294611yescharacteristic
376C2×C43#305811yescharacteristic
377C2×C43#306011yescharacteristic
378C2×C43#317911yescharacteristic
379C2×C43#317911yescharacteristic
380D43—82no—
381C22×D8—431no—
382C22×M16—431no—
383C23×C8—431no—
384C2×#121—431no—
385C2×#121C2×D4311yescharacteristic
386C2×C4×D4—431no—
387C2×C4×D4C2×D4311yescharacteristic
388C2×#117C2×D4311yescharacteristic
389#469—438no—
390C4×D8—864no—
391C2×#107—431no—
392C2×#106—431no—
393C2×#106—431no—
394C2×#102—431no—
395C2×#102—431no—
396C2×#102—431no—
397C2×#102—431no—
398C2×#102—431no—
399C2×#102—431no—
400#405—864no—
401C2×#97—431no—
402C2×#97—431no—
403C2×C4×C8—431no—
404C2×C4×C8—431no—
405#390—21no—
406#390—431no—
407#390—861no—
408#390C2×D4311yescharacteristic
409#389—431no—
410#389C2×D4311yescharacteristic
411#388—21no—
412#388—861no—
413#386—21no—
414#386—861no—
415#385—21no—
416#385—861no—
417#380—431no—
418#380C2×D4311yescharacteristic
419C4×C4⋊C4—431no—
420C4×C4⋊C4C2×D4311yescharacteristic
421#340—431no—
422#340—431no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427C43#2153611yescharacteristic, complemented, Sylow
428C22×D4—21no—
429C22×D4—431no—
430C22×D4—861no—
431C22×D4C22×D4311yescharacteristic
432C23×C4—21no—
433C23×C4—861no—
434C23×C4C22×D4311yescharacteristic
435C2×D8—434no—
436C2×D8—862no—
437C2×D8—862no—
438C2×M16—434no—
439C2×M16—862no—
440C2×M16—862no—
441C22×C8—431no—
442C22×C8—431no—
443C22×C8—431no—
444C22×C8—431no—
445C22×C8—862no—
446C22×C8—862no—
447C22×C8—862no—
448#121—22no—
449#121—434no—
450#121—862no—
451#121C4×D4314yescomplemented
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—862no—
455C4×D4—862no—
456#117—22no—
457#117—22no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4C22⋊D4311yescharacteristic
464C2×C4⋊C4C22⋊D4311yescharacteristic
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C4⋊C4C22×D4311yescharacteristic
467C2×C4⋊C4C22×D4311yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4C22⋊D4311yescharacteristic
479C2×C22⋊C4C22⋊D4311yescharacteristic
480C2×C42—21no—
481C2×C42—861no—
482C2×C42C22×D4311yescharacteristic
483C2×C42C22×D4311yescharacteristic
484#107—862no—
485#106—434no—
486#106—862no—
487#102—434no—
488#102—434no—
489#102—862no—
490#102—862no—
491#102—862no—
492#102—862no—
493#97—862no—
494#97—862no—
495C4×C8—434no—
496C4×C8—862no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—861no—
501#95—861no—
502#95—861no—
503C24—21no—
504C24—861no—
505C24C2×C22⋊D4311yescharacteristic
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—432no—
515C2×D4—864no—
516C2×D4—861no—
517C2×D4—861no—
518C2×D4—861no—
519C2×D4—861no—
520C2×D4—861no—
521C2×D4—3441no—
522C2×D4—3441no—
523C2×D4C2×C4×D4312yes—
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—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—3441no—
538C22×C4—3441no—
539C22×C4—1722no—
540C22×C4C2×C4×D4312yes—
541C22×C4#1062189812yes—
542C22×C4C2×C22⋊D4311yescharacteristic
543C22×C4C2×C22⋊D4311yescharacteristic
544C22×C4C2×C22⋊D4311yescharacteristic
545C22×C4C2×C22⋊D4311yescharacteristic
546C22×C4C2×C22⋊D4311yescharacteristic
547C22×C4C23×D4311yescharacteristic
548D8—868no—
549M16—868no—
550C2×C8—432no—
551C2×C8—432no—
552C2×C8—432no—
553C2×C8—432no—
554C2×C8—432no—
555C2×C8—432no—
556C2×C8—868no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
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—432no—
572C4⋊C4—861no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—3441no—
578C4⋊C4C2×C4×D4312yes—
579C22⋊C4—24no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—864no—
587C22⋊C4—3441no—
588C22⋊C4—3441no—
589C22⋊C4—3441no—
590C22⋊C4—1722no—
591C42—21no—
592C42—21no—
593C42—81no—
594C42—3441no—
595C42D4×D4312yes—
596C42#1062190012yes—
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—862no—
611C23—1721no—
612C23—1721no—
613C23—1721no—
614C23—1721no—
615C23—1721no—
616C23—1721no—
617C23C4×C22⋊D4312yes—
618C23C22×C22⋊D4311yescharacteristic
619D4—22no—
620D4—22no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—862no—
625D4—862no—
626D4—3444no—
627D4—1721no—
628D4—1721no—
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—862no—
656C2×C4—3444no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4C4×C22⋊D4312yes—
666C2×C4#1306329712yes—
667C2×C4#1306329712yes—
668C2×C4C22×C4×D4311yescharacteristic
669C2×C4C2×D4×D4311yescharacteristic
670C2×C4#41×D4311yescharacteristic
671C2×C4#41×D4311yescharacteristic
672C2×C4C2×#1062190011yescharacteristic
673C2×C4C2×#1062189811yescharacteristic
674C8—434no—
675C8—862no—
676C8—862no—
677C8—862no—
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—3441no—
693C22—3441no—
694C22—3441no—
695C22—3441no—
696C22—1722no—
697C22—1722no—
698C22—1722no—
699C22C2×C4×C22⋊D4311yescharacteristic
700C22C2×#1306329711yescharacteristic
701C22#1458344511yescharacteristic
702C22#1458370211yescharacteristic
703C22#1458370211yescharacteristic
704C22#1458370711yescharacteristic
705C22#1458371011yescharacteristic
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—41no—
711C4—41no—
712C4—81no—
713C4—81no—
714C4—3441no—
715C4—3441no—
716C4—1722no—
717C4C4×D4×D4311yescharacteristic
718C4C4×#1062190011yescharacteristic
719C4#1458340811yescharacteristic
720C4#1458342911yescharacteristic
721C2—42no—
722C2—82no—
723C2—3442no—
724C2C4×#1306329711yescharacteristic
725C2#1914342311yescharacteristic
726C2#1914342711yescharacteristic
727C2#1914424011yescharacteristic
728C2#1914425411yescharacteristic
729C2#1914527211yescharacteristic
730C2#1914528011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2324C2
socleC23×C43C22×D4
prime radicalC2×#14583150C2
cosocleC22×C4×C43C24
hypercenter#2324D43
hypocenterC43#21536
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. C2×#14582855C2semidirect
4. #19137288C2semidirect
5. #19135470C2semidirect
6. #19135335C2semidirect
7. #19135281C2semidirect
8. #19135277C2semidirect
9. #19135024C2semidirect
10. #19135021C2semidirect
11. #19134626C2semidirect
12. C4×#13063256C2semidirect
13. #19134423C2semidirect
14. #19134420C2semidirect
15. C43×#2324C2semidirect
21. #14583150C4semidirect
70. C2×#10621877C2×C4semidirect
79. #13063299C2×C4semidirect
94. #13063256C2×C4semidirect
97. #13063246C2×C4semidirect
100. #13063245C2×C4semidirect
104. C4×C43⋊C8D4semidirect
113. #121×C43C2×C4semidirect
360. #2324D43semidirect
427. C43#21536semidirect
451. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831502
C2×C4×#106218822
C2×#145828552
#191372882
#191354702
#191353352
#191352812
#191352772
#191350242
#191350212
#191346262
C4×#130632562
#191344232
#191344202
C43×#23242
#2153643