Finite Group Databasebeta

← #25106907

Subgroups — #25106907

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582864C211yesmaximal, characteristic
2#19137188C211yesmaximal, characteristic
3#19137184C211yesmaximal, characteristic
4#19134797C211yesmaximal, characteristic, complemented
5#19134796C211yesmaximal, characteristic, complemented
6#19134795C211yesmaximal, characteristic, complemented
7#19134792C211yesmaximal, characteristic, complemented
8#19134783C211yesmaximal, characteristic, complemented
9#19134781C211yesmaximal, characteristic, complemented
10#19134781C211yesmaximal, characteristic, complemented
11#19134629C211yesmaximal, characteristic, complemented
12#19134627C211yesmaximal, characteristic, complemented
13#19134623C211yesmaximal, characteristic, complemented
14#19134621C211yesmaximal, characteristic, complemented
15C43×#1852C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28#14582864C418yescomplemented
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32#14582804—21no—
33#14582803—21no—
34#14582800—21no—
35#14582799—21no—
36#14582778—21no—
37#14582778—21no—
38#14582777—21no—
39#14582775—21no—
40#14582759C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#107×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C2×#10621898—41no—
61C2×#10621898—41no—
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898C2×C414yes—
65C2×#10621898Q814yes—
66C22×Dic86D411yescharacteristic
67C22×D172D411yescharacteristic
68C22×C22⋊D43D411yescharacteristic
69C22×C22⋊D43D411yescharacteristic
70C22×C4×D43—21no—
71C22×C4×D43C2311yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—41no—
74C2×#10621872—41no—
75C2×#10621872C2×C414yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—41no—
79C2×C8×D43—41no—
80C2×C8×D43C2×C414yescomplemented
81#13063284—41no—
82#13063284—41no—
83#13063283—41no—
84#13063283—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C4⋊C4×D43—41no—
91C4⋊C4×D43—41no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103#13063259—41no—
104#13063258—41no—
105#13063258—41no—
106#13063258—41no—
107#13063257—41no—
108#13063256—41no—
109C22⋊(C43⋊C8)C2×C414yescomplemented
110(C2×D43)⋊C8C2×C414yescomplemented
111(C2×D43)⋊C8C2×C414yescomplemented
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43—21no—
120C23×C4×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—41no—
125C2×C4⋊C4×C43—41no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131#107×C43—41no—
132#107×C43—41no—
133C22⋊C8×C43C2×C414yescomplemented
134#95×C43—21no—
135C24×C43C2×D411yescharacteristic
136C23×D43C2×D411yescharacteristic
137C23×D43C2×D411yescharacteristic
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—42no—
147C22×C4×C43—81no—
148C22×C4×C43—81no—
149C22×C4×C43C22×C412yes—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×Q812yes—
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43C4⋊C414yes—
158C2×C22⋊D43C4⋊C414yes—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165#10621898—44no—
166#10621898—44no—
167#10621898—44no—
168#10621898—44no—
169C2×D172—41no—
170C2×D172—41no—
171C2×D172C4⋊C414yes—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—42no—
181C2×C4×D43—81no—
182C2×C4×D43—81no—
183C2×C4×D43C22×C412yes—
184C2×C4×D43C22×C412yes—
185C2×C4×D43C2×Q812yes—
186C2×C4×D43C2×Q812yes—
187C2×Dic86—41no—
188C2×Dic86—41no—
189C2×Dic86C4⋊C414yes—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43C22×C412yes—
195C2×C8×C43C22×C412yes—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—42no—
205C22⋊C4×C43—81no—
206C22⋊Dic43—42no—
207C22⋊Dic43—81no—
208(C2×D43)⋊C4—42no—
209(C2×D43)⋊C4—81no—
210(C2×D43)⋊C4—81no—
211(C2×D43)⋊C4—81no—
212(C2×D43)⋊C4—81no—
213(C2×D43)⋊C4—81no—
214(C2×D43)⋊C4—81no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223Dic43⋊C4—42no—
224C4×Dic43—42no—
225C4×Dic43—42no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C22×C412yes—
231C2×C43⋊C8C22×C412yes—
232#10621872—44no—
233C8×D43—44no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43C2×C4⋊C412yes—
241C23×C43C22×D411yescharacteristic
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43C2×C4⋊C412yes—
255C22×D43C2×C4⋊C412yes—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—84no—
275C2×C4×C43C2×C4⋊C412yes—
276C2×C4×C43C23×C411yescharacteristic
277C2×C4×C43C22×Q811yescharacteristic
278C2×C4×C43H(5,𝔽2)11yescharacteristic
279C2×C4×C43H(5,𝔽2)11yescharacteristic
280C2×C4×C43H(5,𝔽2)11yescharacteristic
281C2×C4×C43H(5,𝔽2)11yescharacteristic
282C22⋊D43—44no—
283C22⋊D43—44no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43C2×C4⋊C412yes—
301C2×Dic43C2×C4⋊C412yes—
302D172—44no—
303C4×D43—22no—
304C4×D43—22no—
305C4×D43—22no—
306C4×D43—22no—
307C4×D43—22no—
308C4×D43—22no—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—84no—
312Dic86—44no—
313C8×C43—22no—
314C8×C43—22no—
315C43⋊C8—22no—
316C43⋊C8—22no—
317#21947—431nomaximal, Sylow
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43C22×C4⋊C411yescharacteristic
326C22×C43#53411yescharacteristic
327C22×C43#53411yescharacteristic
328C22×C43#57611yescharacteristic
329C22×C43#57611yescharacteristic
330C22×C43#57811yescharacteristic
331C22×C43#57811yescharacteristic
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—22no—
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—41no—
339C2×D43—41no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C4×C43—22no—
347C4×C43—81no—
348C4×C43—81no—
349C4×C43—81no—
350C4×C43—81no—
351C4×C43#51811yescharacteristic
352C4×C43#51811yescharacteristic
353C4×C43#54311yescharacteristic
354C4×C43#54311yescharacteristic
355Dic43—22no—
356Dic43—22no—
357Dic43—81no—
358Dic43—81no—
359Dic43—81no—
360Dic43—81no—
361C2×#408—431no—
362#2311—431no—
363#2311—431no—
364#1854—431no—
365#1854—431no—
366#1854—431no—
367#1854—431no—
368#1852—431no—
369#1852—431no—
370#1852—431no—
371#1852D4311yescharacteristic, complemented
372#1809—431no—
373#1809—431no—
374#1808—431no—
375#1808—431no—
376C2×C43—42no—
377C2×C43#231511yescharacteristic
378C2×C43#291311yescharacteristic
379C2×C43#291311yescharacteristic
380C2×C43#319911yescharacteristic
381C2×C43#320211yescharacteristic
382C2×C43#320311yescharacteristic
383C2×C43#320311yescharacteristic
384D43—42no—
385D43—42no—
386C22×#41—431no—
387C22×M16—431no—
388C23×C8—431no—
389C2×#117—431no—
390C2×#117—431no—
391C22×C4⋊C4—431no—
392C22×C4⋊C4C2×D4311yescharacteristic
393C2×#107—431no—
394C2×#107—431no—
395C2×#107—431no—
396C2×#107—431no—
397C2×#107C2×D4311yescharacteristic
398C2×#107C2×D4311yescharacteristic
399C2×#106—431no—
400C2×#106—431no—
401#408—438no—
402C2×C22⋊C8—431no—
403C2×C22⋊C8—431no—
404C2×C22⋊C8—431no—
405C2×C22⋊C8C2×D4311yescharacteristic
406#391—861no—
407#391—861no—
408#390—861no—
409#390—861no—
410#386—861no—
411#386—861no—
412#386—861no—
413#386—861no—
414#380—431no—
415#380—431no—
416#380—431no—
417#380—431no—
418#380—431no—
419#380—431no—
420#380—431no—
421#380C2×D4311yescharacteristic
422#340—431no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340C2×D4311yescharacteristic
429#340C2×D4311yescharacteristic
430C43#2194711yescharacteristic, complemented, Sylow
431C2×#41—434no—
432C2×#41—434no—
433C2×#41—1721no—
434C2×#41—1721no—
435C2×#41—1721no—
436C2×#41—1721no—
437C22×Q8—431no—
438C22×D4—431no—
439C22×D4—431no—
440C22×D4—431no—
441C23×C4—21no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—861no—
445C23×C4C22×D4311yescharacteristic
446C2×M16—434no—
447C2×M16—1721no—
448C2×M16—1721no—
449C22×C8—431no—
450C22×C8—431no—
451C22×C8—434no—
452C22×C8—1721no—
453C22×C8—1721no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456#117—1721no—
457#117—1721no—
458#117—1721no—
459#117—1721no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4—1721no—
469C2×C4⋊C4—1721no—
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C4⋊C4C22×D4311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C42—861no—
485C2×C42—861no—
486#107—41no—
487#107—41no—
488#107—1721no—
489#107—1721no—
490#107—1721no—
491#107—1721no—
492#106—1721no—
493#106—1721no—
494C22⋊C8—434no—
495C22⋊C8—434no—
496C22⋊C8—434no—
497C22⋊C8C4×D4314yescomplemented
498#95—21no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95—861no—
503#95—861no—
504#95—861no—
505#95—861no—
506C24—431no—
507C24—431no—
508C24D4×D4311yescharacteristic
509#41—1724no—
510#41—1724no—
511#41—1724no—
512#41—1724no—
513C2×Q8—434no—
514C2×Q8—1721no—
515C2×Q8—1721no—
516C2×D4—434no—
517C2×D4—434no—
518C2×D4—434no—
519C2×D4—1721no—
520C2×D4—1721no—
521C2×D4—1721no—
522C2×D4—1721no—
523C2×D4—1721no—
524C2×D4—1721no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4—431no—
537C22×C4—431no—
538C22×C4—432no—
539C22×C4—432no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—3441no—
555C22×C4—3441no—
556C22×C4—1722no—
557C22×C4C2×C4×D4312yes—
558C22×C4D4×D4311yescharacteristic
559C22×C4Q8×D4312yes—
560C22×C4C23×D4311yescharacteristic
561M16—1724no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—432no—
567C2×C8—432no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—1724no—
573C2×C8C2×C4×D4312yes—
574C2×C8C2×C4×D4312yes—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—1722no—
593C22⋊C4—81no—
594C22⋊C4—3441no—
595C22⋊C4—3441no—
596C22⋊C4—3441no—
597C22⋊C4—3441no—
598C22⋊C4—3441no—
599C22⋊C4—3441no—
600C22⋊C4—3441no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—1722no—
604C42—1722no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—432no—
612C23—432no—
613C23—861no—
614C23—861no—
615C23—861no—
616C23—861no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23C4⋊C4×D4312yes—
626C23C2×D4×D4311yescharacteristic
627Q8—1724no—
628D4—1724no—
629D4—1724no—
630D4—1724no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—432no—
651C2×C4—432no—
652C2×C4—861no—
653C2×C4—861no—
654C2×C4—861no—
655C2×C4—861no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—3444no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4C4⋊C4×D4312yes—
678C2×C4C22×C4×D4311yescharacteristic
679C2×C4C2×Q8×D4311yescharacteristic
680C2×C4#1306337011yescharacteristic
681C2×C4#1306337011yescharacteristic
682C2×C4#1306337111yescharacteristic
683C2×C4#1306337111yescharacteristic
684C8—22no—
685C8—22no—
686C8—862no—
687C8—862no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—862no—
696C22—862no—
697C22—862no—
698C22—862no—
699C22—862no—
700C22—862no—
701C22—1721no—
702C22—1721no—
703C22—1721no—
704C22—1721no—
705C22—1721no—
706C22—1721no—
707C22—1721no—
708C22—1721no—
709C22C2×C4⋊C4×D4311yescharacteristic
710C22#1458345911yescharacteristic
711C22#1458346011yescharacteristic
712C22#1458370011yescharacteristic
713C22#1458370311yescharacteristic
714C22#1458371211yescharacteristic
715C22#1458371511yescharacteristic
716C4—22no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4—862no—
722C4—862no—
723C4—3441no—
724C4—3441no—
725C4—3441no—
726C4—3441no—
727C4#1458337111yescharacteristic
728C4#1458337111yescharacteristic
729C4#1458352411yescharacteristic
730C4#1458352411yescharacteristic
731C2—42no—
732C2—1722no—
733C2—1722no—
734C2#1913720611yescharacteristic
735C2#1914319111yescharacteristic
736C2#1914319411yescharacteristic
737C2#1914545811yescharacteristic
738C2#1914548811yescharacteristic
739C2#1914549511yescharacteristic
740C2#1914549911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1852C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1852D43
hypocenterC43#21947
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
4. #19134797C2semidirect
5. #19134796C2semidirect
6. #19134795C2semidirect
7. #19134792C2semidirect
8. #19134783C2semidirect
9. #19134781C2semidirect
10. #19134781C2semidirect
11. #19134629C2semidirect
12. #19134627C2semidirect
13. #19134623C2semidirect
14. #19134621C2semidirect
15. C43×#1852C2semidirect
28. #14582864C4semidirect
75. C2×#10621872C2×C4semidirect
80. C2×C8×D43C2×C4semidirect
109. C22⋊(C43⋊C8)C2×C4semidirect
110. (C2×D43)⋊C8C2×C4semidirect
111. (C2×D43)⋊C8C2×C4semidirect
133. C22⋊C8×C43C2×C4semidirect
371. #1852D43semidirect
430. C43#21947semidirect
497. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828642
#191371882
#191371842
#191347972
#191347962
#191347952
#191347922
#191347832
#191347812
#191346292
#191346272
#191346232
#191346212
C43×#18522
#2194743