Finite Group Databasebeta

← #25102377

Subgroups — #25102377

Order 11008.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583377C211yesmaximal, characteristic, complemented
2C2×#14583000C211yesmaximal, characteristic, complemented
3C2×SD16×Dic43C211yesmaximal, characteristic, complemented
4#19137290C211yesmaximal, characteristic
5#19134952C211yesmaximal, characteristic, complemented
6#19134952C211yesmaximal, characteristic, complemented
7#19134918C211yesmaximal, characteristic
8#19134865C211yesmaximal, characteristic, complemented
9#19134851C211yesmaximal, characteristic, complemented
10#19134796C211yesmaximal, characteristic, complemented
11#19134530C211yesmaximal, characteristic, complemented
12#19134427C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C2×C43×#448C211yesmaximal, characteristic
16#14583377—24no—
17#14583377—24no—
18C2×Q8×Dic43—21no—
19C2×Q8×Dic43—21no—
20C2×Q8×Dic43C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×Q8×Dic43C2211yescharacteristic
23C2×Q8×Dic43C2211yescharacteristic
24C2×D4×Dic43C2211yescharacteristic
25C2×#13063284—21no—
26C2×#13063284—21no—
27C2×#13063284C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29#14583000—24no—
30SD16×Dic43—24no—
31C2×#13063259C2211yescharacteristic
32C2×#13063257C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582802—21no—
43#14582802C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582792—21no—
46#14582779—21no—
47#14582774—21no—
48#14582759C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C23×Q8×C43C2211yescharacteristic
57C22×SD16×C43C2211yescharacteristic
58C22×SD16×C43C2211yescharacteristic
59C2×#121×C43C2211yescharacteristic
60C43×#448C418yescomplemented
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic
64C23×Dic43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67Q8×Dic43—28no—
68Q8×Dic43—28no—
69Q8×Dic43—22no—
70Q8×Dic43—22no—
71Q8×Dic43—22no—
72Q8×Dic43—22no—
73Q8×Dic43—22no—
74Q8×Dic43—22no—
75Q8×Dic43D414yescomplemented
76Q8×Dic43D414yescomplemented
77D4×Dic43—22no—
78D4×Dic43—22no—
79#13063284—28no—
80#13063284—28no—
81#13063284—22no—
82#13063284—22no—
83#13063284—22no—
84#13063284—22no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43D411yescharacteristic
91C2×C4⋊Dic43D411yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
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×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111#13063259—22no—
112#13063257—22no—
113#13063249—22no—
114#13063249—22no—
115#13063249—22no—
116#13063249—22no—
117#13063246—22no—
118#13063246—22no—
119C22⋊(C43⋊C8)—22no—
120#13063235—22no—
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×Q8×C43—22no—
126C22×Q8×C43—22no—
127C22×Q8×C43—22no—
128C22×Q8×C43—22no—
129C22×Q8×C43—21no—
130C22×Q8×C43—22no—
131C22×Q8×C43C2×C414yescomplemented
132C22×Q8×C43C2311yescharacteristic
133C22×Q8×C43C2311yescharacteristic
134C22×D4×C43—21no—
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C23×C4×C43C2311yescharacteristic
138C2×SD16×C43—22no—
139C2×SD16×C43—22no—
140C2×SD16×C43—22no—
141C2×SD16×C43—22no—
142C2×SD16×C43C2×C414yes—
143C2×SD16×C43C2×C414yes—
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146#121×C43—22no—
147#121×C43C2×C414yes—
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150#103×C43C2×C414yescomplemented
151#103×C43C2×C414yescomplemented
152C22⋊C8×C43C2×C414yescomplemented
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C2×Q8×C43—28no—
156C2×Q8×C43—28no—
157C2×Q8×C43—24no—
158C2×Q8×C43—24no—
159C2×Q8×C43—28no—
160C2×Q8×C43—28no—
161C2×Q8×C43—24no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43C22×C412yes—
169C2×Q8×C43C22×C412yes—
170C2×Q8×C43C2×D412yes—
171C2×Q8×C43C2×D412yes—
172C2×Q8×C43#4112yes—
173C2×Q8×C43#4112yes—
174C2×D4×C43—21no—
175C2×D4×C43—24no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—81no—
181C2×D4×C43—81no—
182C2×D4×C43C22×C412yes—
183C22×C4×C43—24no—
184C22×C4×C43—24no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—24no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43#4112yes—
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—42no—
202C22×Dic43—81no—
203C22×Dic43—81no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208SD16×C43—28no—
209SD16×C43—28no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43C22×C412yes—
215C2×C8×C43C22×C412yes—
216C4⋊C4×C43—21no—
217C4⋊C4×C43C22×C412yes—
218C22⋊C4×C43—24no—
219C22⋊Dic43—24no—
220C22⋊Dic43—22no—
221C22⋊Dic43—22no—
222C22⋊Dic43—42no—
223C22⋊Dic43—81no—
224C22⋊Dic43—81no—
225C22⋊Dic43—81no—
226C4⋊Dic43—24no—
227C4⋊Dic43—24no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—24no—
231C4⋊Dic43—24no—
232C4⋊Dic43—22no—
233C4⋊Dic43—22no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—81no—
239C4⋊Dic43C2×D412yes—
240C4⋊Dic43C2×D412yes—
241C4×Dic43—24no—
242C4×Dic43—24no—
243C4×Dic43—24no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—24no—
247C4×Dic43—24no—
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—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—22no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C4×D412yes—
271C23×C43C22×D411yescharacteristic
272Q8×C43—216no—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43C4×D414yes—
280Q8×C43C4×D414yes—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—84no—
286C2×C4×C43—216no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—21no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43C4×D412yes—
303C2×C4×C43C23×C411yescharacteristic
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
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—41no—
331C2×Dic43—84no—
332C2×Dic43#12012yes—
333C2×Dic43#12012yes—
334C8×C43—22no—
335C8×C43—22no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338#21462—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43C2×C4×D411yescharacteristic
354C22×C43C2×#12011yescharacteristic
355C22×C43#52511yescharacteristic
356C22×C43#57711yescharacteristic
357C22×C43#57711yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57811yescharacteristic
360C4×C43—24no—
361C4×C43—24no—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43C2×C4×D411yescharacteristic
365C4×C43C2×C4×D411yescharacteristic
366C4×C43#52511yescharacteristic
367C4×C43#52511yescharacteristic
368Dic43—22no—
369Dic43—22no—
370Dic43—41no—
371Dic43—42no—
372Dic43—41no—
373Dic43—42no—
374Dic43—81no—
375Dic43—81no—
376C2×#519—431no—
377C2×#448D4311yescharacteristic
378C2×#440—431no—
379C2×C4×SD16—431no—
380#2324—431no—
381#1880—431no—
382#1880—431no—
383#1875—431no—
384#1865—431no—
385#1863—431no—
386#1854—431no—
387#1787—431no—
388#1763—431no—
389C4×#103—431no—
390#1750—431no—
391C2×C43—42no—
392C2×C43—82no—
393C2×C43C4×#12011yescharacteristic
394C2×C43#294711yescharacteristic
395C2×C43#294911yescharacteristic
396C2×C43#301011yescharacteristic
397C2×C43#301311yescharacteristic
398C2×C43#312111yescharacteristic
399C2×C43#312611yescharacteristic
400C23×Q8C2×D4311yescharacteristic
401C22×SD16C2×D4311yescharacteristic
402C22×SD16C2×D4311yescharacteristic
403C2×#121C2×D4311yescharacteristic
404#519—864no—
405#519—864no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—861no—
411C2×C4×Q8—861no—
412C2×C4×D4—431no—
413C2×#117—431no—
414C2×#117—431no—
415C2×#117—861no—
416C2×#117—861no—
417#448Dic4318yescomplemented
418#440—864no—
419C4×SD16—864no—
420C2×#107—431no—
421C2×#106—431no—
422C2×#103—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103C2×D4311yescharacteristic
427C2×#103C2×D4311yescharacteristic
428C2×#102—431no—
429C2×#102—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8C2×D4311yescharacteristic
432C2×#97—431no—
433C2×C4×C8—431no—
434#390—431no—
435#390—861no—
436#389—431no—
437#388—861no—
438#386—861no—
439#385—861no—
440#380—431no—
441C4×C4⋊C4—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#336—431no—
447#336—431no—
448C43#2146211yescharacteristic, complemented, Sylow
449C22×Q8—22no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—21no—
454C22×Q8—22no—
455C22×Q8C2×Dic4314yescomplemented
456C22×Q8C22×D4311yescharacteristic
457C22×Q8C22×D4311yescharacteristic
458C22×D4—21no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16C2×Dic4314yes—
468C2×SD16C2×Dic4314yes—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473#121—22no—
474#121C2×Dic4314yes—
475C4×Q8—434no—
476C4×Q8—434no—
477C4×Q8—862no—
478C4×Q8—862no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—868no—
482C4×Q8—868no—
483C4×Q8—862no—
484C4×Q8—862no—
485C4×D4—862no—
486C4×D4—862no—
487#117—862no—
488#117—862no—
489#117—862no—
490#117—862no—
491#117—868no—
492#117—868no—
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—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42—861no—
521#107—862no—
522#106—862no—
523#103—862no—
524#103—862no—
525#103—862no—
526#103—862no—
527#103C2×Dic4314yescomplemented
528#103C2×Dic4314yescomplemented
529#102—862no—
530#102—862no—
531C22⋊C8—862no—
532C22⋊C8C2×Dic4314yescomplemented
533#97—862no—
534C4×C8—862no—
535#95—861no—
536#95—861no—
537#95—861no—
538C24—21no—
539C24D4×D4311yescharacteristic
540C2×Q8—24no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—24no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—24no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8D4×D4312yes—
554C2×Q8D4×D4312yes—
555C2×Q8#1062190012yes—
556C2×Q8#1062190012yes—
557C2×Q8C22×Dic4312yes—
558C2×Q8C22×Dic4312yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4C22×Dic4312yes—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—3441no—
587C22×C4—3441no—
588C22×C4—1722no—
589C22×C4D4×D4311yescharacteristic
590C22×C4#1062190012yes—
591C22×C4C22×Dic4312yes—
592C22×C4C23×D4311yescharacteristic
593SD16—28no—
594SD16—28no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8C22×Dic4312yes—
606C2×C8C22×Dic4312yes—
607C4⋊C4—21no—
608C4⋊C4—432no—
609C4⋊C4—432no—
610C4⋊C4—862no—
611C4⋊C4—862no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—3441no—
623C4⋊C4C22×Dic4312yes—
624C22⋊C4—24no—
625C22⋊C4—862no—
626C22⋊C4—862no—
627C22⋊C4—864no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—1722no—
632C42—432no—
633C42—432no—
634C42—864no—
635C42—864no—
636C42—864no—
637C42—864no—
638C42—864no—
639C42—861no—
640C42—861no—
641C42—3441no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23D4×Dic4312yes—
656C23C2×D4×D4311yescharacteristic
657Q8—216no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8D4×Dic4314yes—
665Q8D4×Dic4314yes—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
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—862no—
694C2×C4—862no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—3444no—
702C2×C4—1721no—
703C2×C4—1721no—
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×C4D4×Dic4312yes—
713C2×C4C23×Dic4311yescharacteristic
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4C2×#1062190011yescharacteristic
717C2×C4C2×#1062190011yescharacteristic
718C2×C4C2×#1062190011yescharacteristic
719C8—22no—
720C8—22no—
721C8—1721no—
722C8—1721no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22C2×D4×Dic4311yescharacteristic
738C22#120×D4311yescharacteristic
739C22#1458340511yescharacteristic
740C22#1458370511yescharacteristic
741C22#1458370511yescharacteristic
742C22#1458370811yescharacteristic
743C22#1458371511yescharacteristic
744C4—24no—
745C4—24no—
746C4—22no—
747C4—42no—
748C4—862no—
749C4—862no—
750C4—3441no—
751C4—3441no—
752C4—1721no—
753C4—1722no—
754C4—1721no—
755C4—1722no—
756C4C2×D4×Dic4311yescharacteristic
757C4C2×D4×Dic4311yescharacteristic
758C4#1458340511yescharacteristic
759C4#1458340511yescharacteristic
760C2—42no—
761C2—82no—
762C2#120×Dic4311yescharacteristic
763C2#1914343911yescharacteristic
764C2#1914345511yescharacteristic
765C2#1914387611yescharacteristic
766C2#1914390511yescharacteristic
767C2#1914481711yescharacteristic
768C2#1914488011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#448C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#448D43
hypocenterC43#21462
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#14583377C2semidirect
2. C2×#14583000C2semidirect
3. C2×SD16×Dic43C2semidirect
5. #19134952C2semidirect
6. #19134952C2semidirect
8. #19134865C2semidirect
9. #19134851C2semidirect
10. #19134796C2semidirect
11. #19134530C2semidirect
12. #19134427C2semidirect
13. #103×Dic43C2semidirect
14. #19134363C2semidirect
60. C43×#448C4semidirect
75. Q8×Dic43D4semidirect
76. Q8×Dic43D4semidirect
131. C22×Q8×C43C2×C4semidirect
150. #103×C43C2×C4semidirect
151. #103×C43C2×C4semidirect
152. C22⋊C8×C43C2×C4semidirect
417. #448Dic43semidirect
448. C43#21462semidirect
455. C22×Q8C2×Dic43semidirect
527. #103C2×Dic43semidirect
528. #103C2×Dic43semidirect
532. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833772
C2×#145830002
C2×SD16×Dic432
#191372902
#191349522
#191349182
#191348652
#191348512
#191347962
#191345302
#191344272
#103×Dic432
#191343632
C2×C43×#4482
#2146243