Finite Group Databasebeta

← #25102295

Subgroups — #25102295

Order 11008.

1468 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10621900C211yesmaximal, characteristic
2C2×#14583058C211yesmaximal, characteristic
3C2×#14583004C211yesmaximal, characteristic, complemented
4C4×#13063301C211yesmaximal, characteristic, complemented
5#19134933C211yesmaximal, characteristic, complemented
6#19134931C211yesmaximal, characteristic, complemented
7#19134904C211yesmaximal, characteristic, complemented
8#19134854C211yesmaximal, characteristic, complemented
9#19134846C211yesmaximal, characteristic, complemented
10#19134791C211yesmaximal, characteristic, complemented
11#19134532C211yesmaximal, characteristic
12#19134426C211yesmaximal, characteristic, complemented
13#19134420C211yesmaximal, characteristic, complemented
14#19134358C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C4×#10621900—24no—
20C4×#10621900—24no—
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×C4×C22⋊D43—21no—
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063283C2211yescharacteristic
27C2×#13063281—21no—
28C22×C4×Dic43—21no—
29C2×C42×D43C2211yescharacteristic
30#14583058C418yescomplemented
31#14583004—24no—
32C2×#13063256C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42#14582806C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582780—21no—
45#14582770—21no—
46#14582756C2211yescharacteristic
47C4×Dic43⋊C4—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49C4×(C2×D43)⋊C4—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C43×#440—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#97×C43C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—22no—
69C2×#10621900C2×C414yes—
70C22×Dic86C2311yescharacteristic
71C22×C22⋊D43—21no—
72C23×Dic43—21no—
73C23×Dic43—21no—
74C22×C4×D43D411yescharacteristic
75C22×C4×D43D411yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621885—22no—
78C2×#10621885—22no—
79C2×#10621885C2×C414yescomplemented
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063301—22no—
83#13063301C2×C414yescomplemented
84C4×Dic86—22no—
85C4×Dic86D414yes—
86#13063290—22no—
87#13063290—22no—
88D4×Dic43—22no—
89D4×Dic43—22no—
90C4×C22⋊D43—28no—
91(C22⋊D43)⋊C4—28no—
92#13063283—22no—
93#13063283—22no—
94#13063281—28no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×C4×Dic43—28no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43D411yescharacteristic
113C2×C4×Dic43C2311yescharacteristic
114C42×D43—22no—
115C42×D43—22no—
116#13063256—22no—
117#13063250—22no—
118#13063250C2×C414yescomplemented
119#13063249—22no—
120#13063248—22no—
121#13063246—22no—
122#13063246C2×C414yescomplemented
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8C2×C414yescomplemented
125#13063236—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×Q8×C43C2311yescharacteristic
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C2×SD16×C43—22no—
135C2×SD16×C43—22no—
136C2×SD16×C43C2×C414yescomplemented
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C4×Q8×C43—22no—
140C4×Q8×C43—22no—
141C4×D4×C43—22no—
142C4×D4×C43D414yes—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#107×C43—22no—
150#103×C43—22no—
151#102×C43—22no—
152#97×C43—22no—
153C24×C43—21no—
154C23×D43C2×D411yescharacteristic
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C22×C412yes—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43C22×C412yes—
165C2×D4×C43C2×D412yes—
166C2×D4×C43#4112yes—
167C22×C4×C43—24no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—42no—
172C22×C4×C43—42no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—24no—
177C2×C22⋊D43—24no—
178C2×C22⋊D43—24no—
179C22×Dic43—24no—
180C22×Dic43—24no—
181C22×Dic43—24no—
182C22×Dic43—24no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192#10621900—28no—
193#10621900—28no—
194#10621900—28no—
195#10621900—28no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—22no—
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43—41no—
204C2×C4×D43—41no—
205C2×C4×D43—41no—
206C2×C4×D43C22×C412yes—
207C2×C4×D43#4112yes—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86C22×C412yes—
212C2×Dic86C2×D412yes—
213C2×Dic86#4112yes—
214SD16×C43—28no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43C22×C412yes—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—42no—
225C4⋊C4×C43C2×D412yes—
226C22⋊C4×C43—24no—
227C42×C43—42no—
228C42×C43C2×D412yes—
229C42×C43C2×D412yes—
230C22⋊Dic43—24no—
231#10621885—28no—
232(C2×D43)⋊C4—24no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—42no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43C22×C412yes—
240C4⋊Dic43C2×D412yes—
241Dic43⋊C4—24no—
242Dic43⋊C4—24no—
243Dic43⋊C4—24no—
244Dic43⋊C4—42no—
245C4×Dic43—24no—
246C4×Dic43—24no—
247C4×Dic43—22no—
248C4×Dic43—22no—
249C4×Dic43—24no—
250C4×Dic43—21no—
251C4×Dic43—21no—
252C4×Dic43—42no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8C22×C412yes—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43C22×D411yescharacteristic
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43C4×D412yes—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—41no—
277Q8×C43—41no—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43C4×D414yes—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—48no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43#12012yes—
297C2×C4×C43#12012yes—
298C2×C4×C43C23×C411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C22⋊D43—216no—
305C2×Dic43—216no—
306C2×Dic43—22no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—22no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—48no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43C4×D412yes—
327C2×Dic43#13712yes—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—44no—
333C4×D43—44no—
334Dic86—22no—
335Dic86—22no—
336Dic86—22no—
337Dic86C4×D414yes—
338C8×C43—22no—
339C8×C43—41no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342#21457—431nomaximal, Sylow
343C22×C43—24no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43C2×C4×D411yescharacteristic
351C22×C43C2×#12011yescharacteristic
352C22×C43#52511yescharacteristic
353C22×C43C2×#13711yescharacteristic
354C22×C43#57511yescharacteristic
355C22×C43#57511yescharacteristic
356C22×C43#57511yescharacteristic
357C2×D43—22no—
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—41no—
361C2×D43—41no—
362C2×D43—41no—
363C2×D43—41no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43—81no—
369C4×C43C2×C4×D411yescharacteristic
370C4×C43C2×C4×D411yescharacteristic
371C4×C43#52511yescharacteristic
372C4×C43#52511yescharacteristic
373Dic43—22no—
374Dic43—24no—
375Dic43—22no—
376Dic43—42no—
377Dic43—41no—
378Dic43—42no—
379Dic43—81no—
380C2×C4×#41—431no—
381C2×#452—431no—
382C2×#441—431no—
383C2×#440D4311yescharacteristic, complemented
384C4×C22⋊Q8—431no—
385#1878—431no—
386#1877—431no—
387#1873—431no—
388#1864—431no—
389#1863—431no—
390#1854—431no—
391#1788—431no—
392#1763—431no—
393#1762—431no—
394#1749—431no—
395C2×C43—44no—
396C2×C43C4×#12011yescharacteristic
397C2×C43#294311yescharacteristic
398C2×C43C4×#13711yescharacteristic
399C2×C43#300511yescharacteristic
400C2×C43#300711yescharacteristic
401C2×C43#311111yescharacteristic
402C2×C43#311611yescharacteristic
403D43—42no—
404C22×#41—431no—
405C22×Q16—431no—
406C22×SD16C2×D4311yescharacteristic
407C2×C22⋊Q8—431no—
408C4×#41—864no—
409C4×#41—864no—
410C2×C4×Q8—431no—
411C2×C4×Q8—431no—
412C2×C4×Q8C2×D4311yescharacteristic
413C2×C4×D4—431no—
414C2×C4×D4—861no—
415C2×C4×D4—861no—
416C2×C4×D4C2×D4311yescharacteristic
417C2×#117—431no—
418C2×#117—861no—
419C22×C42—431no—
420C22×C42—861no—
421#452—438no—
422#441—864no—
423#440—24no—
424C2×#107C2×D4311yescharacteristic
425C2×#106—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103C2×D4311yescharacteristic
431C2×#102—431no—
432C2×#102—431no—
433C2×#102C2×D4311yescharacteristic
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×#97—431no—
437C2×#97C2×D4311yescharacteristic
438#391—431no—
439#389—431no—
440#387—861no—
441#385—861no—
442#380—431no—
443C4×C4⋊C4—431no—
444C4×C4⋊C4—861no—
445C4×C22⋊C4—861no—
446#340—431no—
447#340—431no—
448#340—431no—
449#340—431no—
450#336—431no—
451#336—431no—
452C43#2145711yescharacteristic, complemented, Sylow
453C2×#41—434no—
454C2×#41—862no—
455C2×#41—862no—
456C2×#41—862no—
457C2×#41—862no—
458C2×#41—862no—
459C22×Q8—431no—
460C22×Q8C22×D4311yescharacteristic
461C22×D4—861no—
462C22×D4C22×D4311yescharacteristic
463C23×C4—21no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—861no—
468C23×C4—861no—
469C2×Q16—434no—
470C2×Q16—862no—
471C2×Q16—862no—
472C2×SD16—22no—
473C2×SD16—22no—
474C2×SD16C4×D4314yescomplemented
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C22⋊Q8—434no—
480C22⋊Q8—862no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—434no—
484C4×Q8—862no—
485C4×Q8—862no—
486C4×Q8—862no—
487C4×D4—22no—
488C4×D4—868no—
489C4×D4—862no—
490C4×D4—868no—
491C4×D4—862no—
492C4×D4C22⋊D4314yes—
493#117—868no—
494#117—862no—
495#117—862no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C42—21no—
512C2×C42—431no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—868no—
518C2×C42—861no—
519C2×C42—862no—
520C2×C42—862no—
521C2×C42—861no—
522C2×C42C22×D4311yescharacteristic
523#107—22no—
524#106—862no—
525#103—22no—
526#103—434no—
527#103—862no—
528#103—862no—
529#103—862no—
530#102—22no—
531#102—434no—
532#102—862no—
533C22⋊C8—434no—
534C22⋊C8—862no—
535#97—22no—
536#97—862no—
537#95—861no—
538#95—861no—
539#95—861no—
540#95—861no—
541#95—861no—
542C24—21no—
543C24—431no—
544#41—868no—
545#41—868no—
546#41—868no—
547#41—868no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—432no—
554C2×Q8—432no—
555C2×Q8—432no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8C2×C4×D4312yes—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—864no—
564C2×D4—864no—
565C2×D4—864no—
566C2×D4C2×C4×D4312yes—
567C2×D4#1062189812yes—
568C2×D4C2×C22⋊D4312yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—432no—
578C22×C4—432no—
579C22×C4—431no—
580C22×C4—862no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—864no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—861no—
595C22×C4—1721no—
596C22×C4—1721no—
597C22×C4—1721no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4D4×D4311yescharacteristic
601C22×C4D4×D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603Q16—868no—
604SD16—28no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—432no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8C2×C4×D4312yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4—432no—
622C4⋊C4—432no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—1722no—
631C4⋊C4C2×C22⋊D4312yes—
632C22⋊C4—24no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—1722no—
637C42—42no—
638C42—864no—
639C42—864no—
640C42—862no—
641C42—862no—
642C42—864no—
643C42—861no—
644C42—861no—
645C42—1722no—
646C42D4×D4312yes—
647C42C2×C22⋊D4312yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—432no—
656C23—861no—
657C23—861no—
658C23—861no—
659C23—861no—
660C23—861no—
661C23—861no—
662C23C2×D4×D4311yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667Q8—434no—
668Q8—862no—
669Q8—862no—
670Q8—862no—
671D4—22no—
672D4—22no—
673D4—22no—
674D4—8616no—
675D4C4×C22⋊D4314yes—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—48no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—432no—
691C2×C4—432no—
692C2×C4—8616no—
693C2×C4—862no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—862no—
697C2×C4—861no—
698C2×C4—862no—
699C2×C4—861no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—1724no—
710C2×C4—1724no—
711C2×C4—1728no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4#1306329312yes—
720C2×C4#1306329312yes—
721C2×C4C22×C4×D4311yescharacteristic
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C22×C22⋊D4311yescharacteristic
724C2×C4#41×D4311yescharacteristic
725C2×C4#41×D4311yescharacteristic
726C2×C4C2×#1062189811yescharacteristic
727C8—22no—
728C8—41no—
729C8—862no—
730C8—1721no—
731C22—24no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—862no—
739C22—862no—
740C22—862no—
741C22—1721no—
742C22—1721no—
743C22—1721no—
744C22—1721no—
745C22C4×D4×D4311yescharacteristic
746C22C2×#1306329311yescharacteristic
747C22#1458340811yescharacteristic
748C22#137×D4311yescharacteristic
749C22#1458369511yescharacteristic
750C22#1458369511yescharacteristic
751C22#1458369811yescharacteristic
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—81no—
757C4—862no—
758C4—864no—
759C4—862no—
760C4—3441no—
761C4—1721no—
762C4—1722no—
763C4—1722no—
764C4C4×D4×D4311yescharacteristic
765C4C2×C4×C22⋊D4311yescharacteristic
766C4#1458340611yescharacteristic
767C4#1458340811yescharacteristic
768C2—44no—
769C2—1722no—
770C2C4×#1306329311yescharacteristic
771C2#1914339011yescharacteristic
772C2#1914341711yescharacteristic
773C2#1914383411yescharacteristic
774C2#1914385111yescharacteristic
775C2#1914470811yescharacteristic
776C2#1914475311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenterC2×#440D43
hypocenterC43#21457
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
3. C2×#14583004C2semidirect
4. C4×#13063301C2semidirect
5. #19134933C2semidirect
6. #19134931C2semidirect
7. #19134904C2semidirect
8. #19134854C2semidirect
9. #19134846C2semidirect
10. #19134791C2semidirect
12. #19134426C2semidirect
13. #19134420C2semidirect
14. #19134358C2semidirect
15. C2×C43×#440C2semidirect
30. #14583058C4semidirect
79. C2×#10621885C2×C4semidirect
83. #13063301C2×C4semidirect
118. #13063250C2×C4semidirect
122. #13063246C2×C4semidirect
124. (C2×D43)⋊C8C2×C4semidirect
136. C2×SD16×C43C2×C4semidirect
383. C2×#440D43semidirect
452. C43#21457semidirect
474. C2×SD16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106219002
C2×#145830582
C2×#145830042
C4×#130633012
#191349332
#191349312
#191349042
#191348542
#191348462
#191347912
#191345322
#191344262
#191344202
#191343582
C2×C43×#4402
#2145743