Finite Group Databasebeta

← #25063764

Subgroups — #25063764

Order 11008.

1108 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147887C211yesmaximal, characteristic
2C2×#14582953C211yesmaximal, characteristic, complemented
3C4×#13063281C211yesmaximal, characteristic, complemented
4#19133119C212yesmaximal, complemented
5#19133117C212yesmaximal, complemented
6#19133105C212yesmaximal, complemented
7#19133101C212yesmaximal, complemented
8#19133087C211yesmaximal, characteristic, complemented
9#19133086C211yesmaximal, characteristic, complemented
10#19133084C211yesmaximal, characteristic, complemented
11C43×#1501C211yesmaximal, characteristic, complemented
12#14583452C411yescharacteristic, complemented
13#14583451C411yescharacteristic, complemented
14#14583451C2211yescharacteristic
15#14583445C411yescharacteristic, complemented
16#14583444C411yescharacteristic, complemented
17#14583444C2211yescharacteristic
18#14583435C411yescharacteristic, complemented
19#14583435C2211yescharacteristic
20#14583430C411yescharacteristic, complemented
21#14583430C2211yescharacteristic
22#14583429—21no—
23#14583429—21no—
24#14583426—21no—
25#14583426—21no—
26#14583410C2211yescharacteristic
27#14583405—21no—
28#14583405—21no—
29#41×Dic43C411yescharacteristic, complemented
30#14583367C411yescharacteristic, complemented
31C4×#10621900—21no—
32C4×#10621900—21no—
33C2×#13063281—21no—
34C22×C4×Dic43C2211yescharacteristic
35#14582953—21no—
36#14582953—21no—
37#14582953C2212yes—
38#14582953C2212yes—
39C2×Dic43⋊C8—21no—
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×#13063235—21no—
42C4×Dic43⋊C4—21no—
43#14582750C2212yes—
44C22⋊C4×Dic43—21no—
45C4×C22⋊Dic43C2211yescharacteristic
46#14582744C2212yes—
47C42×Dic43—21no—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#525C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621898C2×C411yescharacteristic
60C2×#10621900—21no—
61C2×#10621900—21no—
62C23×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C22×C43⋊C8—21no—
65#13063324C2×C411yescharacteristic
66#13063324C2×C411yescharacteristic
67#13063323C2×C411yescharacteristic
68#13063321C2×C411yescharacteristic
69#13063320—21no—
70#13063320—21no—
71#13063318—21no—
72#13063318—21no—
73#13063316C2×C411yescharacteristic
74#13063316C2×C411yescharacteristic
75#13063315—21no—
76#13063315—21no—
77#13063314C2×C411yescharacteristic
78#13063312C2×C411yescharacteristic
79#13063311—21no—
80#13063311—21no—
81#13063309—21no—
82#13063309—21no—
83#13063308—21no—
84#13063306—21no—
85#13063306—21no—
86#13063304C2×C411yescharacteristic
87#13063304C2311yescharacteristic
88#13063302—21no—
89#13063302—21no—
90#13063302—21no—
91#13063302—21no—
92#13063299C2×C411yescharacteristic
93#13063299C2311yescharacteristic
94#13063297—21no—
95#13063297—21no—
96#13063297—21no—
97#13063297—21no—
98#13063294—21no—
99Q8×Dic43C2×C411yescharacteristic
100Q8×Dic43C2×C411yescharacteristic
101C4×Dic86—21no—
102C4×Dic86—21no—
103#13063290—21no—
104#13063290—21no—
105#13063290C2×C411yescharacteristic
106#13063290C2×C411yescharacteristic
107D4×Dic43—21no—
108D4×Dic43—21no—
109D4×Dic43—21no—
110D4×Dic43—21no—
111D4×Dic43C2×C411yescharacteristic
112D4×Dic43C2×C411yescharacteristic
113#13063287C2×C411yescharacteristic
114#13063287C2×C411yescharacteristic
115C4×C22⋊D43—21no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119(C22⋊D43)⋊C4—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125#13063284—21no—
126#13063284C2×C411yescharacteristic
127#13063283—21no—
128#13063283—21no—
129#13063282—21no—
130#13063281—28no—
131#13063281—21no—
132#13063281—21no—
133#13063281—21no—
134#13063281—21no—
135C2×Dic43⋊C4—22no—
136C2×C22⋊Dic43—21no—
137C2×C4×Dic43—22no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43—22no—
141C2×C4×Dic43C2×C411yescharacteristic
142C2×C4×Dic43C2×C411yescharacteristic
143C2×C4×Dic43C2×C411yescharacteristic
144C2×C4×Dic43C2×C411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C2×C4×Dic43D411yescharacteristic
147C2×C4×Dic43D411yescharacteristic
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43D411yescharacteristic
151C2×C4×Dic43C2311yescharacteristic
152C2×C4×Dic43C2311yescharacteristic
153C42×D43—21no—
154Dic43⋊C8—22no—
155Dic43⋊C8—22no—
156C22⋊(C43⋊C8)—21no—
157C22⋊(C43⋊C8)C2312yes—
158#13063235—22no—
159#13063235—22no—
160C43⋊#95—22no—
161C43⋊#95C2312yes—
162C2×#41×C43C2×C411yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C22×C8×C43—21no—
165#123×C43—21no—
166C22⋊Q8×C43C2×C411yescharacteristic
167C22⋊Q8×C43C2311yescharacteristic
168#121×C43C2×C411yescharacteristic
169#121×C43C2311yescharacteristic
170#120×C43—21no—
171C4×D4×C43—21no—
172C4×D4×C43—21no—
173#117×C43C2×C411yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C42×C43—21no—
176C22⋊C8×C43—21no—
177C22⋊C8×C43C2312yes—
178#95×C43C2312yes—
179C24×C43C2×D411yescharacteristic
180#41×C43—42no—
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43C22×C411yescharacteristic
186C22×C4×C43—21no—
187C22×C4×C43—22no—
188C22×C4×C43—42no—
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—21no—
196C2×C22⋊D43—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C22×Dic43—24no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—22no—
204C22×Dic43—42no—
205C22×Dic43C22⋊C411yescharacteristic
206C22×Dic43C22⋊C411yescharacteristic
207C22×Dic43C22⋊C411yescharacteristic
208C22×Dic43C22⋊C411yescharacteristic
209C22×Dic43C22⋊C411yescharacteristic
210C22×Dic43C22⋊C411yescharacteristic
211C22×Dic43C22⋊C411yescharacteristic
212C22×Dic43C22⋊C411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621900—44no—
218#10621900—44no—
219#10621898—42no—
220C2×D172C22×C411yescharacteristic
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86C22×C411yescharacteristic
227C2×C8×C43—22no—
228C2×C8×C43—42no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C22×C411yescharacteristic
232C4⋊C4×C43C22×C411yescharacteristic
233C22⋊C4×C43—24no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C42×C43—21no—
240C42×C43—42no—
241C22⋊Dic43—24no—
242C22⋊Dic43—21no—
243C22⋊Dic43—21no—
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—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—28no—
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—
271Dic43⋊C4—21no—
272C4×Dic43—28no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—44no—
279C4×Dic43—42no—
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22⋊C411yescharacteristic
288C4×Dic43C22×C411yescharacteristic
289C4×Dic43C22×C411yescharacteristic
290C4×Dic43C22×C411yescharacteristic
291C4×Dic43C22×C411yescharacteristic
292C4×Dic43C2×D411yescharacteristic
293C4×Dic43C2×D411yescharacteristic
294C4×Dic43C2×D411yescharacteristic
295C4×Dic43C2×D411yescharacteristic
296C2×C43⋊C8—22no—
297C2×C43⋊C8—42no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—21no—
301C23×C43—41no—
302C23×C43C2×C22⋊C411yescharacteristic
303C23×C43C2×C22⋊C411yescharacteristic
304C23×C43C22×D411yescharacteristic
305C22×D43—21no—
306Q8×C43—41no—
307D4×C43—41no—
308D4×C43—42no—
309D4×C43—42no—
310D4×C43—42no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—24no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43C2×C22⋊C411yescharacteristic
326C2×C4×C43C23×C411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C22⋊D43—42no—
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—42no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—24no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43#10414yes—
353C2×Dic43C2×C22⋊C411yescharacteristic
354C2×Dic43C2×C22⋊C411yescharacteristic
355C2×Dic43C2×C22⋊C411yescharacteristic
356C2×Dic43C2×C22⋊C411yescharacteristic
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361D172—41no—
362C4×D43—42no—
363C4×D43—42no—
364C4×D43—42no—
365Dic86—42no—
366Dic86—42no—
367Dic86—41no—
368C8×C43—42no—
369C43⋊C8—42no—
370#17543—431nomaximal, Sylow
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—44no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43C2×#10412yes—
383C22×C43C22×C22⋊C411yescharacteristic
384C22×C43#57512yes—
385C2×D43—41no—
386C2×D43—41no—
387C2×D43—41no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—44no—
392C4×C43—41no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43#41012yes—
396Dic43—21no—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—21no—
402Dic43—44no—
403Dic43—41no—
404Dic43—41no—
405Dic43—41no—
406Dic43C2×#10412yes—
407Dic43C2×#10412yes—
408#3444—431no—
409C2×#432—431no—
410C4×#117—431no—
411#1509—432no—
412#1509—432no—
413#1506—432no—
414#1505—432no—
415#1501—431no—
416#1501—431no—
417#1501—431no—
418#1501D4311yescharacteristic, complemented
419C2×C43—22no—
420C2×C43—22no—
421C2×C43—41no—
422C2×C43—81no—
423C2×C43C2×#41011yescharacteristic
424C2×C43#289611yescharacteristic
425C2×C43C22×#10411yescharacteristic
426D43—81no—
427#533—431no—
428#533—431no—
429#533—431no—
430#532—431no—
431#532—431no—
432#532—431no—
433#529—431no—
434#529—431no—
435#529—431no—
436#529—431no—
437#529—861no—
438#529—861no—
439#529—861no—
440#529—861no—
441#525—431no—
442#525—861no—
443#525—861no—
444#525C2×D4311yescharacteristic
445C4×#41—431no—
446C4×#41—431no—
447C4×#41—861no—
448C4×#41—861no—
449C2×#117—861no—
450C22×C42—431no—
451#432—432no—
452#432—432no—
453#432—861no—
454#432—861no—
455C2×C4⋊C8—861no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8C2×D4311yescharacteristic
458C2×#97—861no—
459C4×C4⋊C4—432no—
460C4×C4⋊C4—861no—
461C4×C22⋊C4—431no—
462C4×C22⋊C4—861no—
463C4×C22⋊C4C2×D4311yescharacteristic
464#376—432no—
465C43—861no—
466#328—432no—
467#328—432no—
468#328—432no—
469#328C2×D4312yes—
470#327—432no—
471#327—432no—
472#327—432no—
473#327C2×D4312yes—
474C43#1754311yescharacteristic, complemented, Sylow
475C2×#41—431no—
476C2×#41—861no—
477C2×#41—861no—
478C2×#41C4×D4311yescharacteristic
479C23×C4—431no—
480C23×C4—431no—
481C23×C4C22×D4311yescharacteristic
482C22×C8—21no—
483C22×C8—861no—
484C4⋊Q8—431no—
485C4⋊Q8—431no—
486C4⋊Q8—431no—
487#127—431no—
488#126—861no—
489#126—861no—
490#126—861no—
491#126—861no—
492#125—431no—
493#125—431no—
494#125—861no—
495#125—861no—
496#124—431no—
497#124—431no—
498#124—861no—
499#124—861no—
500#123—21no—
501#123—861no—
502#123—861no—
503#123—861no—
504#123—861no—
505#123—861no—
506C22⋊Q8—431no—
507C22⋊Q8—431no—
508C22⋊Q8—861no—
509C22⋊Q8—861no—
510C22⋊Q8—861no—
511C22⋊Q8—861no—
512C22⋊Q8C4×D4311yescharacteristic
513C22⋊Q8C22×D4311yescharacteristic
514#121—431no—
515#121—431no—
516#121—861no—
517#121—861no—
518#121—861no—
519#121—861no—
520#121C4×D4311yescharacteristic
521#121C22×D4311yescharacteristic
522#120—21no—
523#120—861no—
524C4×Q8—431no—
525C4×Q8—431no—
526C4×Q8—431no—
527C4×Q8—431no—
528C4×Q8—861no—
529C4×Q8—861no—
530C4×Q8—861no—
531C4×Q8—861no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—431no—
535C4×D4—431no—
536C4×D4—431no—
537C4×D4—431no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4—861no—
547C4×D4—861no—
548C4×D4—861no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
552#117—431no—
553#117—861no—
554#117—861no—
555#117—861no—
556#117—861no—
557#117—861no—
558#117—861no—
559#117—861no—
560#117—861no—
561#117—868no—
562#117C4×D4311yescharacteristic
563C2×C4⋊C4—862no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—861no—
566C2×C42—21no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—431no—
574C2×C42—431no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—861no—
580C2×C42—861no—
581C2×C42—862no—
582C2×C42—862no—
583C2×C42—861no—
584C4⋊C8—862no—
585C4⋊C8—862no—
586C22⋊C8—21no—
587C22⋊C8—432no—
588C22⋊C8—861no—
589C22⋊C8C22×D4312yes—
590#97—862no—
591#97—862no—
592#95—432no—
593#95—862no—
594#95C22×D4312yes—
595C24D4×D4311yescharacteristic
596#41—42no—
597#41—1722no—
598#41—1724no—
599#41—1724no—
600C2×Q8—431no—
601C2×Q8—861no—
602C2×Q8—861no—
603C2×Q8C2×C4×D4311yescharacteristic
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—431no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4C2×C4×D4311yescharacteristic
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—864no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—862no—
635C22×C4—861no—
636C22×C4—1722no—
637C22×C4C2×C4×D4311yescharacteristic
638C22×C4C2×C4×D4311yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4D4×D4311yescharacteristic
642C22×C4C23×D4311yescharacteristic
643C2×C8—22no—
644C2×C8—42no—
645C2×C8—862no—
646C2×C8—1722no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—431no—
650C4⋊C4—431no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—868no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4C2×C4×D4311yescharacteristic
667C4⋊C4C2×C4×D4311yescharacteristic
668C22⋊C4—24no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—864no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C22⋊C4—861no—
687C22⋊C4—861no—
688C42—21no—
689C42—42no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42—431no—
702C42—431no—
703C42—431no—
704C42—431no—
705C42—431no—
706C42—861no—
707C42—861no—
708C42—861no—
709C42—861no—
710C42—868no—
711C42—861no—
712C42—1722no—
713C42—1724no—
714C23—22no—
715C23—22no—
716C23—21no—
717C23—41no—
718C23—861no—
719C23C22⋊C4×D4311yescharacteristic
720C23C22⋊C4×D4311yescharacteristic
721C23C2×D4×D4311yescharacteristic
722Q8—41no—
723Q8—1721no—
724Q8—1722no—
725Q8—1722no—
726D4—41no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—1721no—
731D4—1722no—
732D4—1722no—
733D4—1722no—
734D4—1722no—
735D4—1722no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—431no—
750C2×C4—431no—
751C2×C4—434no—
752C2×C4—431no—
753C2×C4—431no—
754C2×C4—431no—
755C2×C4—431no—
756C2×C4—431no—
757C2×C4—431no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—864no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1722no—
777C2×C4—1722no—
778C2×C4—1722no—
779C2×C4—1722no—
780C2×C4C22⋊C4×D4311yescharacteristic
781C2×C4C22⋊C4×D4311yescharacteristic
782C2×C4C22×C4×D4311yescharacteristic
783C2×C4C2×D4×D4311yescharacteristic
784C8—42no—
785C8—1722no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—44no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—1721no—
798C22—1721no—
799C22—1721no—
800C22#104×D4312yes—
801C22C2×C22⋊C4×D4311yescharacteristic
802C22#1458369612yes—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—44no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—432no—
811C4—432no—
812C4—861no—
813C4—861no—
814C4—861no—
815C4—861no—
816C4—861no—
817C4—861no—
818C4—1724no—
819C4—1721no—
820C4—1721no—
821C4—1721no—
822C4#1458287112yes—
823C2—22no—
824C2—22no—
825C2—41no—
826C2—81no—
827C2—3441no—
828C2C2×#1458287111yescharacteristic
829C2#1914311011yescharacteristic
830C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1501C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1501D43
hypocenterC43#17543
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. C2×#14582953C2semidirect
3. C4×#13063281C2semidirect
4. #19133119C2semidirect
5. #19133117C2semidirect
6. #19133105C2semidirect
7. #19133101C2semidirect
8. #19133087C2semidirect
9. #19133086C2semidirect
10. #19133084C2semidirect
11. C43×#1501C2semidirect
12. #14583452C4semidirect
13. #14583451C4semidirect
15. #14583445C4semidirect
16. #14583444C4semidirect
18. #14583435C4semidirect
20. #14583430C4semidirect
29. #41×Dic43C4semidirect
30. #14583367C4semidirect
418. #1501D43semidirect
474. C43#17543semidirect

Maximal subgroups

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

subgroupindex
#191478872
C2×#145829532
C4×#130632812
#191331192
#191331172
#191331052
#191331012
#191330872
#191330862
#191330842
C43×#15012
#1754343