Finite Group Databasebeta

← #25102379

Subgroups — #25102379

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×#14583375C211yesmaximal, characteristic, complemented
2C2×#14583036C211yesmaximal, characteristic
3C2×#14582996C211yesmaximal, characteristic, complemented
4C2×SD16×Dic43C211yesmaximal, characteristic, complemented
5#19137291C211yesmaximal, characteristic
6#19134953C211yesmaximal, characteristic, complemented
7#19134914C211yesmaximal, characteristic
8#19134866C211yesmaximal, characteristic, complemented
9#19134849C211yesmaximal, characteristic, complemented
10#19134795C211yesmaximal, characteristic, complemented
11#19134528C211yesmaximal, characteristic, complemented
12#19134427C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#19134360C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19#14583375—24no—
20#14583375—24no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×C4×Dic86—21no—
23C2×C4×Dic86C2211yescharacteristic
24C2×#13063290—21no—
25C2×#13063290C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C2×#13063283—21no—
28C2×#13063283C2211yescharacteristic
29C2×#13063282—21no—
30C2×#13063282C2211yescharacteristic
31#14583036C418yescomplemented
32#14582996—24no—
33SD16×Dic43—24no—
34C2×#13063258C2211yescharacteristic
35C2×#13063257C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582799—21no—
47#14582797C2211yescharacteristic
48#14582787—21no—
49#14582776—21no—
50#14582771—21no—
51#14582756C2211yescharacteristic
52C4⋊C4×Dic43C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582654C2211yescharacteristic
57C22×SD16×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#390C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43C2×C414yescomplemented
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43C2311yescharacteristic
76C2×#10621883—22no—
77C2×#10621883—22no—
78C2×#10621883C2×C414yes—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063296—22no—
82#13063296C2×C414yes—
83Q8×Dic43—22no—
84Q8×Dic43D414yescomplemented
85C4×Dic86—28no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88#13063290—28no—
89#13063290—22no—
90#13063290D414yescomplemented
91D4×Dic43—22no—
92D4×Dic43—22no—
93#13063283—28no—
94#13063283—22no—
95#13063283—22no—
96#13063282—28no—
97#13063282—22no—
98#13063282—22no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4D411yescharacteristic
107C2×Dic43⋊C4D411yescharacteristic
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43C2311yescharacteristic
120#13063258—22no—
121#13063257—22no—
122#13063250—22no—
123#13063250C2×C414yescomplemented
124#13063249—22no—
125#13063249C2×C414yescomplemented
126#13063248—22no—
127#13063246—22no—
128(C2×D43)⋊C8—22no—
129(C2×D43)⋊C8C2×C414yescomplemented
130#13063235—22no—
131C8×Dic43—22no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×Q8×C43C2311yescharacteristic
136C22×D4×C43C2311yescharacteristic
137C2×SD16×C43—22no—
138C2×SD16×C43—22no—
139C2×SD16×C43C2×C414yes—
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C4×Q8×C43—22no—
143C4×Q8×C43—22no—
144C2×C4⋊C4×C43—21no—
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C42×C43—21no—
150C2×C42×C43C2311yescharacteristic
151#103×C43—22no—
152#102×C43—22no—
153C24×C43—21no—
154C23×D43C2×D411yescharacteristic
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43C22×C412yes—
159C2×Q8×C43C2×D412yes—
160C2×Q8×C43#4112yes—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43C22×C412yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—24no—
174C2×C22⋊D43—81no—
175C2×C22⋊D43—81no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—42no—
181C22×Dic43—81no—
182C22×Dic43—81no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186Q8×D43—28no—
187Q8×D43—28no—
188Q8×D43—28no—
189Q8×D43—28no—
190C2×C4×D43—24no—
191C2×C4×D43—24no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—24no—
197C2×C4×D43C22×C412yes—
198C2×C4×D43#4112yes—
199C2×Dic86—24no—
200C2×Dic86—24no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—24no—
205C2×Dic86C22×C412yes—
206C2×Dic86C2×D412yes—
207C2×Dic86#4112yes—
208SD16×C43—28no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43C22×C412yes—
215C4⋊C4×C43—24no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—81no—
221C22⋊C4×C43—81no—
222C42×C43—24no—
223C42×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—24no—
226C22⋊Dic43—42no—
227#10621883—28no—
228(C2×D43)⋊C4—24no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—81no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—24no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43C22×C412yes—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—22no—
242Dic43⋊C4—22no—
243Dic43⋊C4—81no—
244C4×Dic43—24no—
245C4×Dic43—24no—
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⋊C8C22×C412yes—
257C23×C43—22no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43C22×D411yescharacteristic
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43C4×D412yes—
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43C4×D414yes—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—41no—
279D4×C43—41no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43C23×C411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C22⋊D43—84no—
302C2×Dic43—22no—
303C2×Dic43—21no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—22no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—84no—
321C2×Dic43C4×D412yes—
322C2×Dic43#12012yes—
323C2×Dic43#12012yes—
324C4×D43—216no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329Dic86—216no—
330Dic86—22no—
331Dic86—22no—
332Dic86—22no—
333Dic86C4×D414yes—
334C8×C43—22no—
335C8×C43—41no—
336C43⋊C8—22no—
337C43⋊C8—41no—
338#21462—431nomaximal, Sylow
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43C2×C4×D411yescharacteristic
347C22×C43C2×#12011yescharacteristic
348C22×C43#52511yescharacteristic
349C22×C43#57711yescharacteristic
350C22×C43#57711yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57811yescharacteristic
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C4×C43—24no—
361C4×C43—41no—
362C4×C43—42no—
363C4×C43—41no—
364C4×C43—81no—
365C4×C43C2×C4×D411yescharacteristic
366C4×C43C2×C4×D411yescharacteristic
367C4×C43#52511yescharacteristic
368C4×C43#52511yescharacteristic
369Dic43—22no—
370Dic43—22no—
371Dic43—22no—
372Dic43—24no—
373Dic43—42no—
374Dic43—42no—
375Dic43—81no—
376C2×#519—431no—
377C2×#448—431no—
378C2×#440—431no—
379C2×C4×SD16—431no—
380#2324—431no—
381#1880—431no—
382#1880D4311yescharacteristic, complemented
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—82no—
392C2×C43C4×#12011yescharacteristic
393C2×C43#294711yescharacteristic
394C2×C43#294911yescharacteristic
395C2×C43#301011yescharacteristic
396C2×C43#301311yescharacteristic
397C2×C43#312111yescharacteristic
398C2×C43#312611yescharacteristic
399D43—42no—
400C23×Q8—431no—
401C22×SD16—431no—
402C22×SD16C2×D4311yescharacteristic
403C2×#121—431no—
404#519—864no—
405#519—864no—
406C2×C4×Q8—431no—
407C2×C4×Q8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—861no—
410C2×C4×Q8—861no—
411C2×C4×Q8C2×D4311yescharacteristic
412C2×C4×D4—431no—
413C2×#117—431no—
414C2×#117—431no—
415C2×#117—861no—
416C2×#117—861no—
417#448—438no—
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×#103—431no—
427C2×#103C2×D4311yescharacteristic
428C2×#102—431no—
429C2×#102C2×D4311yescharacteristic
430C2×C22⋊C8—431no—
431C2×C22⋊C8—431no—
432C2×#97—431no—
433C2×C4×C8—431no—
434#390—861no—
435#390C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic
446#336—431no—
447#336C2×D4311yescharacteristic
448C43#2146211yescharacteristic, complemented, Sylow
449C22×Q8—434no—
450C22×Q8—431no—
451C22×Q8—861no—
452C22×Q8—862no—
453C22×Q8—862no—
454C22×Q8—862no—
455C22×Q8—862no—
456C22×Q8—862no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—861no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—431no—
461C23×C4—861no—
462C23×C4—861no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—434no—
466C2×SD16—862no—
467C2×SD16—862no—
468C2×SD16C4×D4314yes—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473#121—434no—
474#121—862no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—434no—
478C4×Q8—434no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—868no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×Q8—868no—
485C4×D4—862no—
486C4×D4—862no—
487#117—862no—
488#117—862no—
489#117—868no—
490#117—862no—
491#117—868no—
492#117—862no—
493C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C42—21no—
514C2×C42—431no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42C22×D4311yescharacteristic
521#107—862no—
522#106—862no—
523#103—22no—
524#103—434no—
525#103—434no—
526#103—862no—
527#103—862no—
528#103—862no—
529#102—22no—
530#102—862no—
531C22⋊C8—434no—
532C22⋊C8—862no—
533#97—862no—
534C4×C8—862no—
535#95—861no—
536#95—861no—
537#95—861no—
538C24—21no—
539C24—431no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—432no—
544C2×Q8—432no—
545C2×Q8—432no—
546C2×Q8—864no—
547C2×Q8—864no—
548C2×Q8—864no—
549C2×Q8—868no—
550C2×Q8—868no—
551C2×Q8—868no—
552C2×Q8—868no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8C2×C4×D4312yes—
557C2×Q8D4×D4312yes—
558C2×Q8#1062190012yes—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—864no—
565C2×D4—3441no—
566C2×D4—3441no—
567C2×D4C2×C4×D4312yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—432no—
575C22×C4—432no—
576C22×C4—864no—
577C22×C4—864no—
578C22×C4—864no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—3441no—
588C22×C4—3441no—
589C22×C4—1722no—
590C22×C4D4×D4311yescharacteristic
591C22×C4D4×D4311yescharacteristic
592C22×C4C23×D4311yescharacteristic
593SD16—28no—
594SD16—868no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—432no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8C2×C4×D4312yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—432no—
612C4⋊C4—432no—
613C4⋊C4—862no—
614C4⋊C4—862no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—3441no—
623C4⋊C4D4×D4312yes—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—862no—
627C22⋊C4—862no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4—3441no—
631C22⋊C4—1722no—
632C42—24no—
633C42—21no—
634C42—21no—
635C42—432no—
636C42—432no—
637C42—864no—
638C42—864no—
639C42—864no—
640C42—864no—
641C42—3441no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—432no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23C2×D4×D4311yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—434no—
661Q8—8616no—
662Q8—862no—
663Q8—862no—
664Q8—862no—
665Q8(C22⋊D43)⋊C414yes—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—3444no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—432no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—8616no—
690C2×C4—862no—
691C2×C4—861no—
692C2×C4—862no—
693C2×C4—861no—
694C2×C4—862no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—3444no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4C22×C4×D4311yescharacteristic
714C2×C4C2×D4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4#41×D4311yescharacteristic
718C2×C4C2×#1062190011yescharacteristic
719C8—22no—
720C8—41no—
721C8—862no—
722C8—1721no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22C4×D4×D4311yescharacteristic
738C22#120×D4311yescharacteristic
739C22#1458340911yescharacteristic
740C22#1458370511yescharacteristic
741C22#1458370611yescharacteristic
742C22#1458370911yescharacteristic
743C22#1458371511yescharacteristic
744C4—24no—
745C4—41no—
746C4—42no—
747C4—41no—
748C4—81no—
749C4—862no—
750C4—864no—
751C4—862no—
752C4—862no—
753C4—3441no—
754C4—1722no—
755C4—1722no—
756C4C4×D4×D4311yescharacteristic
757C4C2×(C22⋊D43)⋊C411yescharacteristic
758C4#1458340711yescharacteristic
759C4#1458340911yescharacteristic
760C2—82no—
761C2—1722no—
762C2#1913710011yescharacteristic
763C2#1914343511yescharacteristic
764C2#1914344911yescharacteristic
765C2#1914387811yescharacteristic
766C2#1914390511yescharacteristic
767C2#1914482111yescharacteristic
768C2#1914488411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#21462
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#14583375C2semidirect
3. C2×#14582996C2semidirect
4. C2×SD16×Dic43C2semidirect
6. #19134953C2semidirect
8. #19134866C2semidirect
9. #19134849C2semidirect
10. #19134795C2semidirect
11. #19134528C2semidirect
12. #19134427C2semidirect
13. #19134414C2semidirect
14. #19134360C2semidirect
15. C43×#1880C2semidirect
31. #14583036C4semidirect
71. C2×Q8×D43C2×C4semidirect
84. Q8×Dic43D4semidirect
90. #13063290D4semidirect
123. #13063250C2×C4semidirect
125. #13063249C2×C4semidirect
129. (C2×D43)⋊C8C2×C4semidirect
382. #1880D43semidirect
448. C43#21462semidirect

Maximal subgroups

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

subgroupindex
C2×#145833752
C2×#145830362
C2×#145829962
C2×SD16×Dic432
#191372912
#191349532
#191349142
#191348662
#191348492
#191347952
#191345282
#191344272
#191344142
#191343602
C43×#18802
#2146243