Finite Group Databasebeta

← #25102422

Subgroups — #25102422

Order 11008.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583382C211yesmaximal, characteristic
2C2×#14583000C211yesmaximal, characteristic, complemented
3C2×Q16×Dic43C211yesmaximal, characteristic, complemented
4#19137279C211yesmaximal, characteristic, complemented
5#19134938C211yesmaximal, characteristic, complemented
6#19134931C211yesmaximal, characteristic, complemented
7#19134903C211yesmaximal, characteristic, complemented
8#19134851C211yesmaximal, characteristic, complemented
9#19134844C211yesmaximal, characteristic, complemented
10#19134785C211yesmaximal, characteristic, complemented
11#19134535C211yesmaximal, characteristic
12#19134427C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C2×C43×#452C211yesmaximal, characteristic
16#14583382—24no—
17#14583382—24no—
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×D4×Dic43—21no—
22C2×D4×Dic43—21no—
23C2×D4×Dic43C2211yescharacteristic
24C2×D4×Dic43C2211yescharacteristic
25C2×#13063284—21no—
26C2×#13063284C2211yescharacteristic
27C22×C4⋊Dic43—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29#14583000—24no—
30Q16×Dic43—24no—
31C2×#13063259C2211yescharacteristic
32C2×#13063259C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582806C2211yescharacteristic
43#14582798—21no—
44#14582798C2211yescharacteristic
45#14582792—21no—
46#14582792—21no—
47#14582785—21no—
48#14582759C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×#41×C43C2211yescharacteristic
57C22×Q16×C43C2211yescharacteristic
58C22×SD16×C43C2211yescharacteristic
59C2×C22⋊Q8×C43C2211yescharacteristic
60C43×#452C418yescomplemented
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C23×Dic43—21no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69Q8×Dic43—22no—
70Q8×Dic43—22no—
71Q8×Dic43—22no—
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74Q8×Dic43D414yes—
75D4×Dic43—28no—
76D4×Dic43—28no—
77D4×Dic43—22no—
78D4×Dic43—22no—
79D4×Dic43—22no—
80D4×Dic43D414yes—
81#13063284—28no—
82#13063284—22no—
83#13063284—22no—
84C2×C4⋊Dic43—28no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43D411yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43D411yescharacteristic
102C2×C22⋊Dic43D411yescharacteristic
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109#13063259—22no—
110#13063259—22no—
111#13063249—22no—
112#13063249—22no—
113#13063249—22no—
114#13063249—22no—
115#13063246—22no—
116#13063246—22no—
117C22⋊(C43⋊C8)—22no—
118#13063235—22no—
119C8×Dic43—22no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C2×#41×C43—22no—
126C2×#41×C43—22no—
127C2×#41×C43—22no—
128C2×#41×C43—22no—
129C2×#41×C43—22no—
130C2×#41×C43C2×C414yes—
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133C22×D4×C43—21no—
134C22×D4×C43C2311yescharacteristic
135C23×C4×C43—21no—
136C23×C4×C43C2311yescharacteristic
137C2×Q16×C43—22no—
138C2×Q16×C43—22no—
139C2×Q16×C43C2×C414yescomplemented
140C2×SD16×C43—22no—
141C2×SD16×C43—22no—
142C2×SD16×C43C2×C414yescomplemented
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43C2×C414yescomplemented
147C2×C4⋊C4×C43—21no—
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150#103×C43C2×C414yescomplemented
151#102×C43C2×C414yescomplemented
152C22⋊C8×C43C2×C414yescomplemented
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155#41×C43—28no—
156#41×C43—28no—
157#41×C43—28no—
158#41×C43—28no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C22×C412yes—
168C2×Q8×C43C22×C412yes—
169C2×Q8×C43C2×D412yes—
170C2×Q8×C43#4112yes—
171C2×D4×C43—24no—
172C2×D4×C43—24no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—24no—
177C2×D4×C43C22×C412yes—
178C2×D4×C43C2×D412yes—
179C2×D4×C43#4112yes—
180C22×C4×C43—24no—
181C22×C4×C43—24no—
182C22×C4×C43—24no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C22×C412yes—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43#4112yes—
193C22×C4×C43C2411yescharacteristic
194C22×Dic43—24no—
195C22×Dic43—24no—
196C22×Dic43—24no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—81no—
202C22×Dic43—81no—
203C22×Dic43—81no—
204C22×Dic43—81no—
205C22×Dic43—81no—
206C22×Dic43—81no—
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211Q16×C43—28no—
212SD16×C43—28no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43C22×C412yes—
218C2×C8×C43C22×C412yes—
219C4⋊C4×C43—24no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43C22×C412yes—
222C22⋊C4×C43—24no—
223C22⋊Dic43—24no—
224C22⋊Dic43—24no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—81no—
228C4⋊Dic43—24no—
229C4⋊Dic43—24no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—22no—
233C4⋊Dic43—24no—
234C4⋊Dic43—22no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—42no—
240C4⋊Dic43—81no—
241C4⋊Dic43C2×D412yes—
242C4⋊Dic43C2×D412yes—
243C4×Dic43—24no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—24no—
247C4×Dic43—42no—
248C4×Dic43—81no—
249C4×Dic43C2×D412yes—
250C4×Dic43C2×D412yes—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C23×C43—22no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—21no—
261C23×C43—22no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C4×D412yes—
271C23×C43C22×D411yescharacteristic
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43—41no—
278Q8×C43—41no—
279Q8×C43C4×D414yes—
280D4×C43—216no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43C4×D414yes—
285C2×C4×C43—216no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43C4×D412yes—
302C2×C4×C43C23×C411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—84no—
331C2×Dic43—84no—
332C2×Dic43—84no—
333C2×Dic43#12012yes—
334C2×Dic43#12012yes—
335C8×C43—22no—
336C8×C43—22no—
337C43⋊C8—41no—
338C43⋊C8—41no—
339#21465—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—24no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—42no—
354C22×C43C2×C4×D411yescharacteristic
355C22×C43C2×#12011yescharacteristic
356C22×C43#52511yescharacteristic
357C22×C43#57611yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57811yescharacteristic
360C22×C43#57811yescharacteristic
361C4×C43—22no—
362C4×C43—24no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43C2×C4×D411yescharacteristic
366C4×C43C2×C4×D411yescharacteristic
367C4×C43#52511yescharacteristic
368C4×C43#52511yescharacteristic
369Dic43—22no—
370Dic43—22no—
371Dic43—41no—
372Dic43—41no—
373Dic43—42no—
374Dic43—42no—
375Dic43—81no—
376Dic43—81no—
377C2×#520—431no—
378C2×#452D4311yescharacteristic
379C2×#440—431no—
380C2×C4×Q16—431no—
381#2323—431no—
382#1878—431no—
383#1877—431no—
384#1872—431no—
385#1863—431no—
386#1862—431no—
387#1852—431no—
388#1788—431no—
389#1763—431no—
390C4×#102—431no—
391#1750—431no—
392C2×C43—42no—
393C2×C43—44no—
394C2×C43C4×#12011yescharacteristic
395C2×C43#294711yescharacteristic
396C2×C43#295111yescharacteristic
397C2×C43#301111yescharacteristic
398C2×C43#301211yescharacteristic
399C2×C43#312011yescharacteristic
400C2×C43#312411yescharacteristic
401C22×#41C2×D4311yescharacteristic
402C22×Q16C2×D4311yescharacteristic
403C22×SD16C2×D4311yescharacteristic
404C2×C22⋊Q8C2×D4311yescharacteristic
405#520—864no—
406#520—864no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×D4—431no—
411C2×C4×D4—431no—
412C2×C4×D4—861no—
413C2×C4×D4—861no—
414C2×#117—431no—
415C2×#117—861no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—861no—
418#452Dic4318yescomplemented
419#440—864no—
420C4×Q16—864no—
421C2×#107—431no—
422C2×#107—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103C2×D4311yescharacteristic
428C2×#102—431no—
429C2×#102—431no—
430C2×#102C2×D4311yescharacteristic
431C2×C22⋊C8—431no—
432C2×C22⋊C8C2×D4311yescharacteristic
433C2×#97—431no—
434C2×C4×C8—431no—
435#391—431no—
436#389—431no—
437#389—861no—
438#388—861no—
439#388—861no—
440#387—861no—
441#380—431no—
442C4×C4⋊C4—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#336—431no—
448#336—431no—
449C43#2146511yescharacteristic, complemented, Sylow
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C2×Dic4314yes—
456C22×Q8C22×D4311yescharacteristic
457C22×Q8C22×D4311yescharacteristic
458C22×D4—21no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16C2×Dic4314yescomplemented
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16C2×Dic4314yescomplemented
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C22⋊Q8—22no—
476C22⋊Q8C2×Dic4314yescomplemented
477C4×Q8—434no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×D4—434no—
484C4×D4—862no—
485C4×D4—862no—
486C4×D4—868no—
487C4×D4—868no—
488C4×D4—862no—
489#117—862no—
490#117—862no—
491#117—868no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—868no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C42—431no—
515C2×C42—431no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520#107—862no—
521#107—862no—
522#103—862no—
523#103—862no—
524#103—862no—
525#103—862no—
526#103C2×Dic4314yescomplemented
527#102—862no—
528#102—862no—
529#102C2×Dic4314yescomplemented
530C22⋊C8—862no—
531C22⋊C8C2×Dic4314yescomplemented
532#97—862no—
533C4×C8—862no—
534#95—861no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24D4×D4311yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8D4×D4312yes—
554C2×Q8#1062190012yes—
555C2×Q8C22×Dic4312yes—
556C2×Q8C22×Dic4312yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4D4×D4312yes—
564C2×D4#1062190012yes—
565C2×D4C22×Dic4312yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—864no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4—3441no—
590C22×C4—3441no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4D4×D4311yescharacteristic
594C22×C4#1062190012yes—
595C22×C4C22×Dic4312yes—
596C22×C4C23×D4311yescharacteristic
597Q16—28no—
598SD16—28no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8C22×Dic4312yes—
610C2×C8C22×Dic4312yes—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—432no—
614C4⋊C4—432no—
615C4⋊C4—862no—
616C4⋊C4—862no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—3441no—
627C4⋊C4—1722no—
628C4⋊C4C22×Dic4312yes—
629C22⋊C4—24no—
630C22⋊C4—862no—
631C22⋊C4—862no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—3441no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42—861no—
640C42—861no—
641C42—3441no—
642C42—1722no—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23D4×Dic4312yes—
657C23C2×D4×D4311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665Q8D4×Dic4314yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4D4×Dic4314yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—3444no—
702C2×C4—3444no—
703C2×C4—3444no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4D4×Dic4312yes—
715C2×C4C23×Dic4311yescharacteristic
716C2×C4C2×D4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4C2×#1062190011yescharacteristic
719C2×C4C2×#1062190011yescharacteristic
720C2×C4C2×#1062190011yescharacteristic
721C8—22no—
722C8—22no—
723C8—1721no—
724C8—1721no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×D4×Dic4311yescharacteristic
740C22#120×D4311yescharacteristic
741C22#1458340511yescharacteristic
742C22#1458370111yescharacteristic
743C22#1458370811yescharacteristic
744C22#1458371311yescharacteristic
745C22#1458371511yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—862no—
751C4—862no—
752C4—3441no—
753C4—3441no—
754C4—1721no—
755C4—1721no—
756C4—1722no—
757C4—1722no—
758C4C2×D4×Dic4311yescharacteristic
759C4C2×D4×Dic4311yescharacteristic
760C4#1458340511yescharacteristic
761C4#1458340511yescharacteristic
762C2—42no—
763C2—44no—
764C2#120×Dic4311yescharacteristic
765C2#1914343911yescharacteristic
766C2#1914347111yescharacteristic
767C2#1914388711yescharacteristic
768C2#1914390311yescharacteristic
769C2#1914481011yescharacteristic
770C2#1914485811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#452D43
hypocenterC43#21465
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#14583000C2semidirect
3. C2×Q16×Dic43C2semidirect
4. #19137279C2semidirect
5. #19134938C2semidirect
6. #19134931C2semidirect
7. #19134903C2semidirect
8. #19134851C2semidirect
9. #19134844C2semidirect
10. #19134785C2semidirect
12. #19134427C2semidirect
13. #102×Dic43C2semidirect
14. #19134363C2semidirect
60. C43×#452C4semidirect
139. C2×Q16×C43C2×C4semidirect
142. C2×SD16×C43C2×C4semidirect
146. C22⋊Q8×C43C2×C4semidirect
150. #103×C43C2×C4semidirect
151. #102×C43C2×C4semidirect
152. C22⋊C8×C43C2×C4semidirect
418. #452Dic43semidirect
449. C43#21465semidirect
467. C2×Q16C2×Dic43semidirect
470. C2×SD16C2×Dic43semidirect
476. C22⋊Q8C2×Dic43semidirect
526. #103C2×Dic43semidirect
529. #102C2×Dic43semidirect
531. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833822
C2×#145830002
C2×Q16×Dic432
#191372792
#191349382
#191349312
#191349032
#191348512
#191348442
#191347852
#191345352
#191344272
#102×Dic432
#191343632
C2×C43×#4522
#2146543