Finite Group Databasebeta

← #25065531

Subgroups — #25065531

Order 11008.

1112 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148375C211yesmaximal, characteristic
2#19143722C211yesmaximal, characteristic, complemented
3#19143717C211yesmaximal, characteristic, complemented
4#19133327C211yesmaximal, characteristic, complemented
5#19133320C211yesmaximal, characteristic, complemented
6#19133319C211yesmaximal, characteristic, complemented
7#19133290C211yesmaximal, characteristic, complemented
8#19133287C211yesmaximal, characteristic, complemented
9#19133287C211yesmaximal, characteristic, complemented
10#19133274C211yesmaximal, characteristic, complemented
11#19133274C211yesmaximal, characteristic, complemented
12#19133254C211yesmaximal, characteristic, complemented
13C2×#14582647C211yesmaximal, characteristic, complemented
14#333×D43C211yesmaximal, characteristic, complemented
15C43×#1551C211yesmaximal, characteristic, complemented
16C2×#13063372C412yes—
17D4×Dic86—21no—
18D4×Dic86—21no—
19#14583554—21no—
20#14583554—21no—
21#14583549—21no—
22#14583549—21no—
23#14583549—21no—
24#14583549—21no—
25#14583470C412yes—
26#14583469C412yes—
27#14583469C412yes—
28#14583447C2211yescharacteristic
29#14583447C2211yescharacteristic
30C2×#13063325C2211yescharacteristic
31C4⋊Q8×D43C2211yescharacteristic
32C4⋊Q8×D43C2211yescharacteristic
33C4×#10621898C2211yescharacteristic
34#14583028—21no—
35#14583027—21no—
36#14582972—21no—
37#14582970—21no—
38#14582969—21no—
39#14582967—21no—
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582956C2211yescharacteristic
43#14582955C2211yescharacteristic
44#14582955C2211yescharacteristic
45#14582951C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582921C2211yescharacteristic
48#14582921C2211yescharacteristic
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50C4⋊C8×D43C2211yescharacteristic
51C4⋊C8×D43C2211yescharacteristic
52#14582648C2211yescharacteristic
53#14582648C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582647C2211yescharacteristic
59#14582647C2211yescharacteristic
60#14582647C2211yescharacteristic
61#14582647C2211yescharacteristic
62#14582643C2211yescharacteristic
63#14582643C2211yescharacteristic
64C43×#532C2211yescharacteristic
65C43×#432C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C43×#333C2211yescharacteristic
68C43×#333C2211yescharacteristic
69C43×#331C2211yescharacteristic
70C43×#331C2211yescharacteristic
71#13063372—48no—
72C2×#10621898—22no—
73C2×#10621898C2×C411yescharacteristic
74C2×#10621900—22no—
75C2×#10621900—22no—
76C2×#10621900C2×C412yes—
77C2×#10621900C2×C412yes—
78C22×Dic86—22no—
79C22×Dic86C2×C412yes—
80C2×Q8×D43C2×C412yes—
81C2×Q8×D43C2×C412yes—
82C2×#10621872—21no—
83C2×#10621872—21no—
84C22×C43⋊C8—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063325—21no—
88#13063325—21no—
89#13063325C2×C412yes—
90#13063325C2311yescharacteristic
91#13063325C2311yescharacteristic
92#13063324—21no—
93#13063324—21no—
94#13063324—21no—
95#13063324—21no—
96#13063323C2×C412yes—
97#13063323C2×C412yes—
98#13063312C2×C412yes—
99#13063312C2×C412yes—
100#13063307—22no—
101#13063307—22no—
102#13063307—22no—
103#13063307—22no—
104#13063306—22no—
105#13063306—22no—
106#13063304—22no—
107#13063304—22no—
108#13063302—22no—
109#13063302—22no—
110#13063302—22no—
111#13063302—22no—
112#13063296—21no—
113#13063296—21no—
114#13063296—21no—
115#13063296—21no—
116C4×Dic86D411yescharacteristic
117C4×Dic86D411yescharacteristic
118C4×D172D411yescharacteristic
119C4×D172D411yescharacteristic
120D4×Dic43—21no—
121D4×Dic43—21no—
122D4×Dic43—21no—
123D4×Dic43—21no—
124C4×C22⋊D43D411yescharacteristic
125C4×C22⋊D43D411yescharacteristic
126C4×C22⋊D43D411yescharacteristic
127C4×C22⋊D43D411yescharacteristic
128#13063284C2×C411yescharacteristic
129#13063282C2×C411yescharacteristic
130#13063282C2×C411yescharacteristic
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—21no—
133C4⋊C4×D43—21no—
134C4⋊C4×D43—21no—
135C4⋊C4×D43—21no—
136C4⋊C4×D43—21no—
137C42×D43C2311yescharacteristic
138C42×D43C2311yescharacteristic
139C4⋊(C43⋊C8)—21no—
140C4⋊(C43⋊C8)C2311yescharacteristic
141C4⋊(C43⋊C8)C2311yescharacteristic
142C4⋊(C43⋊C8)C2311yescharacteristic
143C4⋊(C43⋊C8)C2311yescharacteristic
144Dic43⋊C8—21no—
145Dic43⋊C8—21no—
146Dic43⋊C8—21no—
147Dic43⋊C8—21no—
148C22⋊(C43⋊C8)—21no—
149(C2×D43)⋊C8—21no—
150(C2×D43)⋊C8—21no—
151(C2×D43)⋊C8—21no—
152(C2×D43)⋊C8—21no—
153#13063236—21no—
154#13063235—21no—
155#13063235—21no—
156C8×Dic43—21no—
157C8×Dic43—21no—
158C2×#41×C43C2×C412yes—
159C22×C8×C43—21no—
160C4⋊Q8×C43C2311yescharacteristic
161#127×C43C2311yescharacteristic
162#124×C43C2×C412yes—
163#121×C43—21no—
164#121×C43—21no—
165C4×D4×C43—21no—
166C4×D4×C43—21no—
167C2×C42×C43C2311yescharacteristic
168C4⋊C8×C43—21no—
169C4⋊C8×C43C2311yescharacteristic
170C4⋊C8×C43C2311yescharacteristic
171C4⋊C8×C43C2311yescharacteristic
172C4⋊C8×C43C2311yescharacteristic
173C22⋊C8×C43—21no—
174#97×C43—21no—
175#41×C43—44no—
176C2×Q8×C43C22×C412yes—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—22no—
180C2×D4×C43C22×C412yes—
181C22×C4×C43—22no—
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C2×C22⋊D43—22no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43C22⋊C411yescharacteristic
188C2×C22⋊D43C22⋊C411yescharacteristic
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192Q8×D43—44no—
193Q8×D43—44no—
194#10621900—44no—
195#10621900—44no—
196#10621900—48no—
197#10621900—48no—
198#10621898—24no—
199#10621898—48no—
200C2×D172C22⋊C411yescharacteristic
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43C22×C411yescharacteristic
204C2×C4×D43C22×C411yescharacteristic
205C2×C4×D43C2×D411yescharacteristic
206C2×C4×D43C2×D411yescharacteristic
207C2×C4×D43C2×D411yescharacteristic
208C2×C4×D43C2×D411yescharacteristic
209C2×Dic86—22no—
210C2×Dic86—22no—
211C2×Dic86—22no—
212C2×Dic86—48no—
213C2×Dic86—44no—
214C2×Dic86C22⋊C411yescharacteristic
215C2×Dic86C22×C412yes—
216C2×Dic86C22×C412yes—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—81no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—22no—
226C42×C43C22×C411yescharacteristic
227C42×C43C2×D411yescharacteristic
228C42×C43C2×D411yescharacteristic
229C42×C43C2411yescharacteristic
230C22⋊Dic43—22no—
231C22⋊Dic43—22no—
232C22⋊Dic43—22no—
233C22⋊Dic43—22no—
234C22⋊Dic43C22⋊C411yescharacteristic
235C22⋊Dic43C22⋊C411yescharacteristic
236(C2×D43)⋊C4C22⋊C411yescharacteristic
237(C2×D43)⋊C4C22⋊C411yescharacteristic
238(C2×D43)⋊C4C22⋊C411yescharacteristic
239(C2×D43)⋊C4C22⋊C411yescharacteristic
240C4⋊Dic43—22no—
241C4⋊Dic43—22no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43C22⋊C411yescharacteristic
247C4⋊Dic43C22⋊C411yescharacteristic
248Dic43⋊C4—22no—
249Dic43⋊C4—22no—
250Dic43⋊C4—22no—
251Dic43⋊C4—22no—
252Dic43⋊C4C22⋊C411yescharacteristic
253Dic43⋊C4C22⋊C411yescharacteristic
254Dic43⋊C4C22⋊C411yescharacteristic
255Dic43⋊C4C22⋊C411yescharacteristic
256C4×Dic43C22×C411yescharacteristic
257C4×Dic43C22×C411yescharacteristic
258C4×Dic43C2×D411yescharacteristic
259C4×Dic43C2×D411yescharacteristic
260C4×Dic43C2×D411yescharacteristic
261C4×Dic43C2×D411yescharacteristic
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—81no—
267#10621872—81no—
268#10621872—81no—
269C8×D43—81no—
270C8×D43—81no—
271C23×C43—22no—
272C23×C43C2×C22⋊C411yescharacteristic
273C22×D43C2×C22⋊C411yescharacteristic
274C22×D43C2×C22⋊C411yescharacteristic
275Q8×C43—42no—
276D4×C43—42no—
277D4×C43—44no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—41no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
288C2×C4×C43—44no—
289C2×C4×C43C2×C22⋊C411yescharacteristic
290C2×C4×C43C2×C22⋊C411yescharacteristic
291C2×C4×C43C2×C22⋊C411yescharacteristic
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C22⋊D43—22no—
296C22⋊D43—44no—
297C22⋊D43—44no—
298C22⋊D43#10014yes—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—44no—
302C2×Dic43—44no—
303C2×Dic43—44no—
304C2×Dic43C2×C22⋊C411yescharacteristic
305C2×Dic43C2×C22⋊C411yescharacteristic
306C2×Dic43C2×C22⋊C411yescharacteristic
307C2×Dic43C2×C22⋊C411yescharacteristic
308C2×Dic43C2×C22⋊C411yescharacteristic
309C2×Dic43C2×C22⋊C411yescharacteristic
310D172—22no—
311C4×D43—22no—
312C4×D43—21no—
313C4×D43—21no—
314C4×D43—21no—
315C4×D43—21no—
316C4×D43—21no—
317C4×D43—21no—
318C4×D43—21no—
319C4×D43—21no—
320C4×D43—22no—
321C4×D43—44no—
322C4×D43—44no—
323Dic86—22no—
324Dic86—44no—
325Dic86—44no—
326Dic86—44no—
327Dic86—42no—
328Dic86—42no—
329C8×C43—41no—
330C8×C43—41no—
331C8×C43—41no—
332C8×C43—41no—
333C43⋊C8—41no—
334C43⋊C8—41no—
335C43⋊C8—41no—
336C43⋊C8—41no—
337#17779—431nomaximal, Sylow
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43C2×#10012yes—
344C22×C43C22×C22⋊C411yescharacteristic
345C2×D43—21no—
346C2×D43—21no—
347C2×D43—21no—
348C2×D43—21no—
349C2×D43—21no—
350C2×D43C2×#10012yes—
351C4×C43—21no—
352C4×C43—21no—
353C4×C43—21no—
354C4×C43—21no—
355C4×C43—42no—
356C4×C43#57711yescharacteristic
357C4×C43#57711yescharacteristic
358C4×C43#57811yescharacteristic
359C4×C43#57811yescharacteristic
360Dic43—21no—
361Dic43—21no—
362Dic43—21no—
363Dic43—21no—
364Dic43—21no—
365Dic43—42no—
366Dic43—42no—
367Dic43C2×#10012yes—
368#3499—431no—
369#2990—431no—
370#2990—431no—
371#1560—431no—
372#1558—431no—
373#1558—431no—
374#1551—431no—
375#1551—431no—
376#1551—431no—
377#1551D4311yescharacteristic, complemented
378#1548—431no—
379#1548—431no—
380#1543—431no—
381C2×#333—431no—
382C2×#333—431no—
383C2×C43—22no—
384C2×C43—82no—
385C2×C43C22×#10011yescharacteristic
386C2×C43#289811yescharacteristic
387C2×C43#289811yescharacteristic
388D43—22no—
389D43—41no—
390C2×2−1+4—432no—
391D4×Q8—861no—
392D4×Q8—861no—
393#547—861no—
394#547—861no—
395#547—861no—
396#547—861no—
397#547—861no—
398#547—861no—
399#536—432no—
400#536—432no—
401#536—432no—
402#532—431no—
403#532—431no—
404#532C2×D4311yescharacteristic
405C2×C4⋊Q8—431no—
406C2×C4⋊Q8—431no—
407C2×C4⋊Q8—431no—
408C4×#41—431no—
409#446—861no—
410#446—861no—
411#435—861no—
412#435—861no—
413#435—861no—
414#435—861no—
415C8×D4—861no—
416C8×D4—861no—
417#432—431no—
418#432—431no—
419#432—431no—
420#432C2×D4311yescharacteristic
421#431—431no—
422#431—431no—
423#423—431no—
424#423—431no—
425C2×C4⋊C8—431no—
426C2×C4⋊C8—431no—
427C2×C4⋊C8—431no—
428C2×C4⋊C8C2×D4311yescharacteristic
429#333—431no—
430#333—431no—
431#333—431no—
432#333—431no—
433#333—431no—
434#333—431no—
435#333—431no—
436#333—431no—
437#333—431no—
438#333—431no—
439#333C2×D4311yescharacteristic
440#333C2×D4311yescharacteristic
441#331—431no—
442#331—431no—
443#331C2×D4311yescharacteristic
444#331C2×D4311yescharacteristic
445C43#1777911yescharacteristic, complemented, Sylow
4462−1+4—1728no—
447C2×#41—431no—
448C2×#41—432no—
449C2×#41—432no—
450C2×#41—862no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41C4×D4312yes—
454C22×Q8—432no—
455C22×Q8—432no—
456C22×Q8—432no—
457C22×Q8—862no—
458C2×M16—861no—
459C2×M16—861no—
460C22×C8—21no—
461C22×C8—861no—
462C22×C8—861no—
463C22×C8—861no—
464C4⋊Q8—432no—
465C4⋊Q8—432no—
466C4⋊Q8—432no—
467C4⋊Q8—431no—
468C4⋊Q8—431no—
469C4⋊Q8—861no—
470C4⋊Q8—861no—
471C4⋊Q8—861no—
472C4⋊Q8—861no—
473C4⋊Q8—861no—
474C4⋊Q8—861no—
475C4⋊Q8C22×D4311yescharacteristic
476#127C22×D4311yescharacteristic
477#124—432no—
478#124—432no—
479#124C4×D4312yes—
480#123—862no—
481#123—862no—
482#123—862no—
483#123—862no—
484#123—862no—
485#123—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—862no—
490C22⋊Q8—862no—
491C22⋊Q8—862no—
492#121—21no—
493#121—21no—
494#121—861no—
495#121—861no—
496#121—861no—
497#121—861no—
498C4×Q8—431no—
499C4×Q8—431no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—431no—
503C4×D4—431no—
504C4×D4—431no—
505C4×D4—431no—
506C4×D4—431no—
507C4×D4—431no—
508C4×D4—861no—
509C4×D4—861no—
510C4×D4—861no—
511C4×D4—861no—
512#117—431no—
513#117—431no—
514#117—431no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4—861no—
521C2×C42—431no—
522C2×C42—431no—
523C2×C42C22×D4311yescharacteristic
524C4⋊C8—21no—
525C4⋊C8—431no—
526C4⋊C8—431no—
527C4⋊C8—431no—
528C4⋊C8—431no—
529C4⋊C8—861no—
530C4⋊C8—861no—
531C4⋊C8—861no—
532C4⋊C8—861no—
533C4⋊C8—861no—
534C4⋊C8C22×D4311yescharacteristic
535C4⋊C8C22×D4311yescharacteristic
536C4⋊C8C22×D4311yescharacteristic
537C4⋊C8C22×D4311yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—861no—
540C22⋊C8—861no—
541C22⋊C8—861no—
542C22⋊C8—861no—
543C22⋊C8—861no—
544#97—21no—
545#97—861no—
546#97—861no—
547#97—861no—
548C4×C8—861no—
549C4×C8—861no—
550#41—44no—
551#41—864no—
552#41—1728no—
553#41—1724no—
554#41—1724no—
555#41—1728no—
556#41—1728no—
557C2×Q8—431no—
558C2×Q8—432no—
559C2×Q8—432no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8—862no—
563C2×Q8—1724no—
564C2×Q8—1728no—
565C2×Q8—1724no—
566C2×Q8—1724no—
567C2×Q8C2×C4×D4312yes—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—431no—
572C2×D4—431no—
573C2×D4—431no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4C2×C4×D4312yes—
577C22×C4—22no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4C2×C4×D4311yescharacteristic
590C22×C4D4×D4311yescharacteristic
591C22×C4D4×D4311yescharacteristic
592M16—3441no—
593M16—3441no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—81no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—3441no—
604C2×C8—3441no—
605C2×C8—3441no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—431no—
609C4⋊C4—431no—
610C4⋊C4—431no—
611C4⋊C4—431no—
612C4⋊C4—431no—
613C4⋊C4—431no—
614C4⋊C4—862no—
615C4⋊C4—862no—
616C4⋊C4—862no—
617C4⋊C4—862no—
618C4⋊C4—862no—
619C4⋊C4—862no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—431no—
627C22⋊C4—431no—
628C22⋊C4—431no—
629C22⋊C4—431no—
630C22⋊C4—431no—
631C22⋊C4—431no—
632C22⋊C4—862no—
633C22⋊C4—862no—
634C22⋊C4—862no—
635C22⋊C4—862no—
636C42—431no—
637C42—431no—
638C42—431no—
639C42—431no—
640C42—431no—
641C42—431no—
642C42C2×C4×D4311yescharacteristic
643C42D4×D4311yescharacteristic
644C42D4×D4311yescharacteristic
645C42C23×D4311yescharacteristic
646C23—22no—
647C23—431no—
648C23—431no—
649C23C22⋊C4×D4311yescharacteristic
650Q8—42no—
651Q8—862no—
652Q8—1722no—
653Q8—1722no—
654Q8—1724no—
655Q8—1724no—
656Q8—1724no—
657D4—42no—
658D4—44no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—434no—
664D4—862no—
665D4—862no—
666D4—1724no—
667D4—1724no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—44no—
675C2×C4—431no—
676C2×C4—431no—
677C2×C4—431no—
678C2×C4—431no—
679C2×C4—431no—
680C2×C4—431no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—1724no—
694C2×C4—1724no—
695C2×C4—1724no—
696C2×C4—1724no—
697C2×C4—1724no—
698C2×C4C22⋊C4×D4311yescharacteristic
699C2×C4C22⋊C4×D4311yescharacteristic
700C2×C4C22⋊C4×D4311yescharacteristic
701C2×C4C22×C4×D4311yescharacteristic
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4C2×D4×D4311yescharacteristic
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—1721no—
709C8—1721no—
710C8—1721no—
711C8—1721no—
712C22—21no—
713C22—21no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—432no—
718C22—861no—
719C22—861no—
720C22—861no—
721C22—861no—
722C22—861no—
723C22#100×D4312yes—
724C22C2×C22⋊C4×D4311yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—42no—
730C4—432no—
731C4—861no—
732C4—861no—
733C4—861no—
734C4—861no—
735C4—861no—
736C4—1722no—
737C4—1722no—
738C4#1458370611yescharacteristic
739C4#1458370911yescharacteristic
740C4#1458371311yescharacteristic
741C4#1458371511yescharacteristic
742C2—22no—
743C2—82no—
744C2—862no—
745C2—1721no—
746C2C2×#100×D4311yescharacteristic
747C2#1914312411yescharacteristic
748C2#1914312611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1551C2
socleC22×C43C22×C22⋊C4
prime radical#19148375C2
cosocleC42×C43C24
hypercenter#1551D43
hypocenterC43#17779
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
2. #19143722C2semidirect
3. #19143717C2semidirect
4. #19133327C2semidirect
5. #19133320C2semidirect
6. #19133319C2semidirect
7. #19133290C2semidirect
8. #19133287C2semidirect
9. #19133287C2semidirect
10. #19133274C2semidirect
11. #19133274C2semidirect
12. #19133254C2semidirect
13. C2×#14582647C2semidirect
14. #333×D43C2semidirect
15. C43×#1551C2semidirect
377. #1551D43semidirect
445. C43#17779semidirect

Maximal subgroups

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

subgroupindex
#191483752
#191437222
#191437172
#191333272
#191333202
#191333192
#191332902
#191332872
#191332742
#191332542
C2×#145826472
#333×D432
C43×#15512
#1777943