Finite Group Databasebeta

← #25063311

Subgroups — #25063311

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic, complemented
3#431×D43C211yesmaximal, characteristic, complemented
4#19133054C212yesmaximal, complemented
5#19133052C212yesmaximal, complemented
6#19133030C211yesmaximal, characteristic, complemented
7#19133029C211yesmaximal, characteristic, complemented
8#19133027C211yesmaximal, characteristic, complemented
9#19132996C212yesmaximal, complemented
10#19132992C212yesmaximal, complemented
11C43×#1488C211yesmaximal, characteristic, complemented
12#14583453C411yescharacteristic
13#14583453C2211yescharacteristic
14#14583452C411yescharacteristic
15#14583446C411yescharacteristic
16#14583446C2211yescharacteristic
17#14583445C411yescharacteristic
18#14583436C411yescharacteristic
19#14583436C2211yescharacteristic
20#14583431C411yescharacteristic
21#14583431C2211yescharacteristic
22#14583429—21no—
23#14583429—21no—
24#14583427—21no—
25#14583427—21no—
26#14583411C411yescharacteristic
27#14583408—21no—
28#14583408—21no—
29#14583406C411yescharacteristic
30C4×#10621898—21no—
31C4×#10621898—21no—
32C4×#10621898C2211yescharacteristic
33C2×C42×D43C2211yescharacteristic
34#14582956C2211yescharacteristic
35#14582955C2212yes—
36#14582954—21no—
37#14582953—21no—
38#14582952C2211yescharacteristic
39#14582951—21no—
40#14582950C2212yes—
41#14582949—21no—
42C4⋊C8×D43—21no—
43C4⋊C8×D43C2212yes—
44C22⋊C8×D43—21no—
45C22⋊C8×D43—21no—
46#97×D43—21no—
47C4×C8×D43C2212yes—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C4×#41×C43C2211yescharacteristic
55C43×#432C2211yescharacteristic
56C43×#431C2211yescharacteristic
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2×C411yescharacteristic
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C2×C8×D43—22no—
66C2×C8×D43—22no—
67#13063324C2×C411yescharacteristic
68#13063324C2×C411yescharacteristic
69#13063323C2×C411yescharacteristic
70#13063321C2×C411yescharacteristic
71#13063320—21no—
72#13063320—21no—
73#13063318—21no—
74#13063318—21no—
75#13063316C2×C411yescharacteristic
76#13063316C2×C411yescharacteristic
77#13063315—21no—
78#13063315—21no—
79#13063314C2×C411yescharacteristic
80#13063312C2×C411yescharacteristic
81#13063311—21no—
82#13063311—21no—
83#13063310—21no—
84#13063310—21no—
85#13063309—21no—
86#13063307—21no—
87#13063307—21no—
88#13063306—21no—
89#13063305C2×C411yescharacteristic
90#13063305C2×C411yescharacteristic
91#13063303—21no—
92#13063303—21no—
93#13063302—21no—
94#13063302—21no—
95#13063301C2×C411yescharacteristic
96#13063301C2×C411yescharacteristic
97#13063300C2×C411yescharacteristic
98#13063300C2×C411yescharacteristic
99#13063298—21no—
100#13063298—21no—
101#13063297—21no—
102#13063297—21no—
103#13063296C2×C411yescharacteristic
104#13063296C2×C411yescharacteristic
105#13063295—21no—
106#13063293—21no—
107C4×Dic86—21no—
108C4×Dic86—21no—
109C4×Dic86—21no—
110C4×Dic86—21no—
111C4×Dic86C2×C411yescharacteristic
112C4×Dic86C2311yescharacteristic
113C4×D172—21no—
114C4×D172—21no—
115C4×D172—21no—
116C4×D172—21no—
117C4×D172C2×C411yescharacteristic
118C4×D172C2311yescharacteristic
119C4×C22⋊D43—21no—
120C4×C22⋊D43—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129#13063284—21no—
130#13063284—21no—
131#13063284C2×C411yescharacteristic
132#13063282—21no—
133#13063282—21no—
134#13063282—21no—
135#13063282—21no—
136#13063282—21no—
137C2×C4×Dic43C2×C411yescharacteristic
138C2×C4×Dic43D411yescharacteristic
139C2×C4×Dic43D411yescharacteristic
140C42×D43—21no—
141C42×D43C2×C411yescharacteristic
142C42×D43C2×C411yescharacteristic
143C42×D43D411yescharacteristic
144C42×D43D411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43C2311yescharacteristic
148C42×D43C2311yescharacteristic
149C4⋊(C43⋊C8)—21no—
150C4⋊(C43⋊C8)C2312yes—
151Dic43⋊C8—22no—
152Dic43⋊C8—22no—
153C22⋊(C43⋊C8)—21no—
154C22⋊(C43⋊C8)—21no—
155(C2×D43)⋊C8—22no—
156(C2×D43)⋊C8—22no—
157#13063236—21no—
158#13063235—22no—
159C4×C43⋊C8C2312yes—
160C8×Dic43—22no—
161C2×#41×C43C2×C411yescharacteristic
162C4×Q8×C43C2×C411yescharacteristic
163C4×Q8×C43C2311yescharacteristic
164C4×D4×C43—21no—
165C4×D4×C43—21no—
166C4×D4×C43C2×C411yescharacteristic
167C4×D4×C43C2311yescharacteristic
168#117×C43—21no—
169#117×C43C2×C411yescharacteristic
170C2×C42×C43—21no—
171C2×C42×C43C2311yescharacteristic
172C4⋊C8×C43—21no—
173C4⋊C8×C43C2312yes—
174C22⋊C8×C43—21no—
175C22⋊C8×C43—21no—
176#97×C43—21no—
177C4×C8×C43C2312yes—
178C23×D43C22⋊C411yescharacteristic
179#41×C43—42no—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194C22×Dic43C22⋊C411yescharacteristic
195C22×Dic43C22⋊C411yescharacteristic
196C22×Dic43C22⋊C411yescharacteristic
197#10621898—42no—
198#10621898—44no—
199#10621898—44no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172C22×C411yescharacteristic
203C2×C4×D43—24no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—42no—
208C2×C4×D43—42no—
209C2×C4×D43C22⋊C411yescharacteristic
210C2×C4×D43C22⋊C411yescharacteristic
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22×C411yescharacteristic
216C2×C4×D43C22×C411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86C22×C411yescharacteristic
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43C22×C411yescharacteristic
229C4⋊C4×C43C22×C411yescharacteristic
230C22⋊C4×C43—21no—
231C22⋊C4×C43—21no—
232C22⋊C4×C43—21no—
233C42×C43—21no—
234C42×C43—21no—
235C42×C43—21no—
236C42×C43C22×C411yescharacteristic
237C42×C43C2×D411yescharacteristic
238C42×C43C2×D411yescharacteristic
239C42×C43C2411yescharacteristic
240C22⋊Dic43—21no—
241C22⋊Dic43—21no—
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245(C2×D43)⋊C4—21no—
246(C2×D43)⋊C4—21no—
247(C2×D43)⋊C4—21no—
248(C2×D43)⋊C4—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43C22×C411yescharacteristic
260C4⋊Dic43C22×C411yescharacteristic
261Dic43⋊C4—21no—
262Dic43⋊C4—21no—
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271C4×Dic43—21no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43C22⋊C411yescharacteristic
275C4×Dic43C22⋊C411yescharacteristic
276C4×Dic43C22⋊C411yescharacteristic
277C4×Dic43C22⋊C411yescharacteristic
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22×C411yescharacteristic
281C4×Dic43C22×C411yescharacteristic
282C4×Dic43C2×D411yescharacteristic
283C4×Dic43C2×D411yescharacteristic
284C4×Dic43C2×D411yescharacteristic
285C4×Dic43C2×D411yescharacteristic
286C2×C43⋊C8—22no—
287C2×C43⋊C8—22no—
288C8×D43—44no—
289C8×D43—44no—
290C23×C43—21no—
291C23×C43C2×C22⋊C411yescharacteristic
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—21no—
295C22×D43—41no—
296C22×D43C2×C22⋊C411yescharacteristic
297C22×D43C2×C22⋊C411yescharacteristic
298Q8×C43—22no—
299D4×C43—22no—
300D4×C43—42no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—41no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43C2×C22⋊C411yescharacteristic
311C2×C4×C43C2×C22⋊C411yescharacteristic
312C2×C4×C43C2×C22⋊C411yescharacteristic
313C2×C4×C43C23×C411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C22⋊D43—42no—
317C22⋊D43—42no—
318C22⋊D43—42no—
319C22⋊D43—42no—
320C22⋊D43—42no—
321C2×Dic43—22no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43C2×C22⋊C411yescharacteristic
328C2×Dic43C2×C22⋊C411yescharacteristic
329C2×Dic43C2×C22⋊C411yescharacteristic
330C2×Dic43C2×C22⋊C411yescharacteristic
331C2×Dic43C2×C22⋊C411yescharacteristic
332C2×Dic43C2×C22⋊C411yescharacteristic
333D172—22no—
334D172—42no—
335D172—42no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—41no—
344C4×D43—41no—
345C4×D43—41no—
346C4×D43—41no—
347C4×D43—42no—
348C4×D43—42no—
349C4×D43—42no—
350C4×D43#13514yes—
351Dic86—22no—
352Dic86—42no—
353Dic86—42no—
354C8×C43—42no—
355C8×C43—42no—
356C43⋊C8—42no—
357C43⋊C8—42no—
358#17488—431nomaximal, Sylow
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43C22×C22⋊C411yescharacteristic
366C2×D43—21no—
367C2×D43—21no—
368C2×D43—21no—
369C2×D43—21no—
370C2×D43—44no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43#41612yes—
375C2×D43#42112yes—
376C4×C43—21no—
377C4×C43—21no—
378C4×C43—21no—
379C4×C43—21no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43—41no—
383C4×C43#56812yes—
384C4×C43C2×#13512yes—
385Dic43—21no—
386Dic43—21no—
387Dic43—21no—
388Dic43—21no—
389Dic43—21no—
390Dic43—41no—
391Dic43—41no—
392Dic43—41no—
393Dic43#41612yes—
394#3444—431no—
395C2×#432—431no—
396C2×#431—431no—
397#1494—432no—
398#1494—432no—
399#1488—431no—
400#1488—431no—
401#1488—431no—
402#1488D4311yescharacteristic, complemented
403#1481—432no—
404#1480—432no—
405C2×C43—41no—
406C2×C43—81no—
407C2×C43#287911yescharacteristic
408C2×C43C2×#41611yescharacteristic
409C2×C43C2×#42111yescharacteristic
410D43—22no—
411D43—22no—
412D43—81no—
413#533—431no—
414#533—431no—
415#533—431no—
416#532—431no—
417#532—431no—
418#532—431no—
419#529—431no—
420#529—431no—
421#529—431no—
422#529—431no—
423#529—861no—
424#529—861no—
425#529—861no—
426#529—861no—
427#525—431no—
428#525—431no—
429#525—861no—
430#525—861no—
431C4×#41—431no—
432C4×#41—861no—
433C4×#41—861no—
434C4×#41C2×D4311yescharacteristic
435C22×C42—431no—
436#432—431no—
437#432—432no—
438#432—861no—
439#432—861no—
440#432C2×D4311yescharacteristic
441#431—431no—
442#431—432no—
443#431—861no—
444#431—861no—
445#431C2×D4311yescharacteristic
446C2×C4⋊C8—432no—
447C2×C4⋊C8—861no—
448C2×C22⋊C8—861no—
449C2×C22⋊C8—861no—
450C2×#97—861no—
451C2×C4×C8—432no—
452Q8⋊C8—432no—
453Q8⋊C8—432no—
454Q8⋊C8—432no—
455Q8⋊C8C2×D4312yescomplemented
456D4⋊C8—432no—
457D4⋊C8—432no—
458D4⋊C8—432no—
459D4⋊C8C2×D4312yescomplemented
460C43#1748811yescharacteristic, complemented, Sylow
461C2×#41—431no—
462C2×#41—861no—
463C2×#41—861no—
464C2×#41C4×D4311yescharacteristic
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C22×C8—862no—
469C22×C8—862no—
470C4⋊Q8—431no—
471C4⋊Q8—431no—
472C4⋊Q8—431no—
473#127—431no—
474#126—861no—
475#126—861no—
476#126—861no—
477#126—861no—
478#125—431no—
479#125—431no—
480#125—861no—
481#125—861no—
482#124—431no—
483#124—431no—
484#124—861no—
485#124—861no—
486#123—861no—
487#123—861no—
488#123—861no—
489#123—861no—
490#123—861no—
491#123—861no—
492C22⋊Q8—431no—
493C22⋊Q8—431no—
494C22⋊Q8—431no—
495C22⋊Q8—431no—
496C22⋊Q8—861no—
497C22⋊Q8—861no—
498C22⋊Q8—861no—
499C22⋊Q8—861no—
500#121—431no—
501#121—431no—
502#121—431no—
503#121—431no—
504#121—861no—
505#121—861no—
506#121—861no—
507#121—861no—
508#120—861no—
509#120—861no—
510C4×Q8—431no—
511C4×Q8—431no—
512C4×Q8—861no—
513C4×Q8—861no—
514C4×Q8—861no—
515C4×Q8—861no—
516C4×Q8C4×D4311yescharacteristic
517C4×Q8C22×D4311yescharacteristic
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—431no—
521C4×D4—431no—
522C4×D4—861no—
523C4×D4—861no—
524C4×D4—861no—
525C4×D4—861no—
526C4×D4—861no—
527C4×D4—861no—
528C4×D4—861no—
529C4×D4—861no—
530C4×D4—861no—
531C4×D4—861no—
532C4×D4—861no—
533C4×D4—861no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4C4×D4311yescharacteristic
537C4×D4C22×D4311yescharacteristic
538#117—21no—
539#117—431no—
540#117—861no—
541#117—861no—
542#117—861no—
543#117—861no—
544#117—861no—
545#117—861no—
546#117—861no—
547#117C4×D4311yescharacteristic
548C2×C42—21no—
549C2×C42—431no—
550C2×C42—431no—
551C2×C42—431no—
552C2×C42—431no—
553C2×C42—431no—
554C2×C42—431no—
555C2×C42—431no—
556C2×C42—431no—
557C2×C42—431no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562C4⋊C8—21no—
563C4⋊C8—432no—
564C4⋊C8—862no—
565C4⋊C8—862no—
566C4⋊C8—861no—
567C4⋊C8C22×D4312yes—
568C22⋊C8—21no—
569C22⋊C8—21no—
570C22⋊C8—862no—
571C22⋊C8—862no—
572C22⋊C8—861no—
573C22⋊C8—861no—
574#97—21no—
575#97—862no—
576#97—861no—
577C4×C8—432no—
578C4×C8—862no—
579C4×C8C22×D4312yes—
580C24—431no—
581#41—42no—
582#41—1722no—
583#41—1724no—
584#41—1724no—
585C2×Q8—431no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8C2×C4×D4311yescharacteristic
589C2×D4—21no—
590C2×D4—431no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4C2×C4×D4311yescharacteristic
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—431no—
605C22×C4—431no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—864no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—1722no—
622C22×C4—1722no—
623C22×C4C2×C4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4D4×D4311yescharacteristic
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—862no—
629C2×C8—862no—
630C2×C8—1724no—
631C2×C8—1724no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—431no—
635C4⋊C4—431no—
636C4⋊C4—861no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—861no—
650C4⋊C4C2×C4×D4311yescharacteristic
651C4⋊C4C2×C4×D4311yescharacteristic
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—861no—
656C22⋊C4—861no—
657C22⋊C4—861no—
658C22⋊C4—861no—
659C22⋊C4—861no—
660C22⋊C4—861no—
661C22⋊C4—861no—
662C22⋊C4—861no—
663C22⋊C4—861no—
664C22⋊C4—861no—
665C22⋊C4—861no—
666C22⋊C4—861no—
667C22⋊C4—861no—
668C22⋊C4—861no—
669C22⋊C4—861no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—431no—
674C42—431no—
675C42—431no—
676C42—431no—
677C42—431no—
678C42—431no—
679C42—431no—
680C42—431no—
681C42—431no—
682C42—431no—
683C42—431no—
684C42—431no—
685C42—861no—
686C42—861no—
687C42—861no—
688C42C2×C4×D4311yescharacteristic
689C42D4×D4311yescharacteristic
690C42D4×D4311yescharacteristic
691C42C23×D4311yescharacteristic
692C23—21no—
693C23—431no—
694C23—431no—
695C23—862no—
696C23—862no—
697C23—861no—
698C23—1721no—
699C23C22⋊C4×D4311yescharacteristic
700Q8—22no—
701Q8—862no—
702Q8—1722no—
703Q8—1722no—
704D4—22no—
705D4—42no—
706D4—862no—
707D4—1722no—
708D4—1722no—
709D4—1722no—
710D4—1722no—
711D4—1722no—
712D4—1722no—
713D4—1722no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—431no—
724C2×C4—434no—
725C2×C4—431no—
726C2×C4—431no—
727C2×C4—431no—
728C2×C4—431no—
729C2×C4—431no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1722no—
750C2×C4C22⋊C4×D4311yescharacteristic
751C2×C4C22⋊C4×D4311yescharacteristic
752C2×C4C22⋊C4×D4311yescharacteristic
753C2×C4C22×C4×D4311yescharacteristic
754C2×C4C2×D4×D4311yescharacteristic
755C2×C4C2×D4×D4311yescharacteristic
756C8—42no—
757C8—42no—
758C8—1722no—
759C8—1722no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—432no—
767C22—432no—
768C22—861no—
769C22—861no—
770C22—861no—
771C22—861no—
772C22—1724no—
773C22—1721no—
774C22—1721no—
775C22—1721no—
776C22C2×C22⋊C4×D4311yescharacteristic
777C4—21no—
778C4—21no—
779C4—21no—
780C4—21no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—432no—
785C4—861no—
786C4—861no—
787C4—861no—
788C4—861no—
789C4—861no—
790C4—1721no—
791C4—1721no—
792C4—1721no—
793C4#1458366512yes—
794C4#135×D4312yes—
795C2—41no—
796C2—81no—
797C2—862no—
798C2—862no—
799C2—3441no—
800C2#1914303811yescharacteristic
801C2#416×D4311yescharacteristic
802C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1488C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC42×C43C24
hypercenter#1488D43
hypocenterC43#17488
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #432×D43C2semidirect
3. #431×D43C2semidirect
4. #19133054C2semidirect
5. #19133052C2semidirect
6. #19133030C2semidirect
7. #19133029C2semidirect
8. #19133027C2semidirect
9. #19132996C2semidirect
10. #19132992C2semidirect
11. C43×#1488C2semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
402. #1488D43semidirect
455. Q8⋊C8C2×D43semidirect
459. D4⋊C8C2×D43semidirect
460. C43#17488semidirect

Maximal subgroups

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

subgroupindex
#191478882
#432×D432
#431×D432
#191330542
#191330522
#191330302
#191330292
#191330272
#191329962
#191329922
C43×#14882
#1748843