Finite Group Databasebeta

← #25153654

Subgroups — #25153654

Order 11008.

1206 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×#14583179C211yesmaximal, characteristic, complemented
2C22×#13063246C211yesmaximal, characteristic
3#19138297C211yesmaximal, characteristic, complemented
4#19136123C211yesmaximal, characteristic, complemented
5#19135983C211yesmaximal, characteristic, complemented
6#19135983C211yesmaximal, characteristic, complemented
7#19135731C211yesmaximal, characteristic, complemented
8#19134842C211yesmaximal, characteristic, complemented
9#19134842C211yesmaximal, characteristic, complemented
10#19134782C211yesmaximal, characteristic, complemented
11#19134775C211yesmaximal, characteristic, complemented
12#19134622C211yesmaximal, characteristic, complemented
13#19134595C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic
15D4×C22⋊C4×C43C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063325C2211yescharacteristic, complemented
18C2×#13063302—21no—
19C22×C4⋊Dic43C2211yescharacteristic
20#14583179—24no—
21C2×#13063258C2211yescharacteristic, complemented
22C2×#13063258C2211yescharacteristic, complemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063258C2211yescharacteristic, complemented
25C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
26C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
27C2×#13063246—24no—
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37#14582831—21no—
38#14582820—21no—
39#14582797C2211yescharacteristic, complemented
40#14582797C2211yescharacteristic, complemented
41#14582774—21no—
42#14582769C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C23×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C22×C22⋊C4×C43—21no—
54C43×#390C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#386—21no—
57C43×#386—21no—
58C43×#380C2211yescharacteristic
59C43×#379—21no—
60C4×C22⋊C4×C43C2211yescharacteristic
61C22×Dic86—21no—
62C23×Dic43—21no—
63C22×C43⋊C8—22no—
64C22×C43⋊C8—22no—
65C22×C43⋊C8—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063325—22no—
71#13063325—41no—
72#13063302—44no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—41no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86#13063258—22no—
87#13063258—22no—
88#13063258—41no—
89#13063258—41no—
90C4⋊(C43⋊C8)—22no—
91C4⋊(C43⋊C8)—41no—
92#13063246—22no—
93#13063246—22no—
94#13063246—22no—
95#13063246—22no—
96#13063246—22no—
97#13063246—41no—
98#13063246—41no—
99#13063246D414yes—
100C22⋊(C43⋊C8)—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C25×C43—21no—
105C22×D4×C43—22no—
106C22×D4×C43—22no—
107C22×D4×C43—21no—
108C22×D4×C43—22no—
109C22×D4×C43—41no—
110C22×D4×C43—41no—
111C22×D4×C43Q814yescomplemented
112C22×D4×C43C2311yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43—21no—
115C23×C4×C43—21no—
116C23×C4×C43C2311yescharacteristic
117C4×D4×C43—22no—
118C4×D4×C43—22no—
119C4×D4×C43—41no—
120C4×D4×C43—41no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—44no—
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#95×C43—21no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—81no—
146C24×C43—81no—
147C24×C43C2×D411yescharacteristic
148C2×D4×C43—24no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—28no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—44no—
161C2×D4×C43—44no—
162C2×D4×C43—44no—
163C2×D4×C43C2×D412yes—
164C2×D4×C43C2×Q812yes—
165C2×D4×C43C2×Q812yes—
166C2×D4×C43#4112yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—42no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43—81no—
178C22×C4×C43—81no—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×Q812yes—
185C22×C4×C43#4112yes—
186C22×C4×C43C2411yescharacteristic
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43—81no—
194C2×Dic86—42no—
195C2×Dic86—42no—
196C2×Dic86—81no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—42no—
205C22⋊C4×C43—42no—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—81no—
208C22⋊C4×C43—81no—
209C22⋊C4×C43D814yes—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C22⋊Dic43—42no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—42no—
223C4⋊Dic43—42no—
224C4⋊Dic43—42no—
225C4⋊Dic43—81no—
226C4⋊Dic43C2×D412yes—
227Dic43⋊C4—42no—
228Dic43⋊C4—42no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—44no—
241C2×C43⋊C8C2×D412yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—48no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—48no—
262C23×C43—84no—
263C23×C43—84no—
264C23×C43—84no—
265C23×C43—84no—
266C23×C43—84no—
267C23×C43C22⋊Q812yes—
268C23×C43C2×D812yes—
269C23×C43#13712yes—
270C23×C43C22×D411yescharacteristic
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—48no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43C22⋊Q814yescomplemented
280C2×C4×C43—21no—
281C2×C4×C43—21no—
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—22no—
289C2×C4×C43—22no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—84no—
303C2×C4×C43—84no—
304C2×C4×C43C22⋊Q812yes—
305C2×C4×C43C2×D812yes—
306C2×C4×C43C2×D812yes—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C22×Q811yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×Dic43—22no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—84no—
326Dic86—84no—
327C43⋊C8—22no—
328C43⋊C8—41no—
329C43⋊C8—41no—
330C43⋊C8—41no—
331#25950—431nomaximal, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—24no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—816no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43#47414yescomplemented
354C22×C43C2×C22⋊Q811yescharacteristic
355C22×C43D4211yescharacteristic
356C22×C43#54611yescharacteristic
357C22×C43C22×D811yescharacteristic
358C22×C43C2×#13711yescharacteristic
359C22×C43#57611yescharacteristic
360C22×C43#57711yescharacteristic
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43—81no—
367C4×C43—81no—
368C4×C43C2×C22⋊Q811yescharacteristic
369C4×C43#54311yescharacteristic
370C4×C43#54611yescharacteristic
371C4×C43#55111yescharacteristic
372Dic43—42no—
373Dic43—81no—
374Dic43—81no—
375Dic43—81no—
376C2×#474—431no—
377C22×#102—431no—
378#2440—431no—
379D4×C22⋊C4D4311yescharacteristic
380#2093—431no—
381#2067—431no—
382#2067—431no—
383#2023—431no—
384#1862—431no—
385#1862—431no—
386#1852—431no—
387#1850—431no—
388#1808—431no—
389#1802—431no—
390#1786—431no—
391C2×C43—24no—
392C2×C43—44no—
393C2×C43—82no—
394C2×C43#243711yescharacteristic
395C2×C43C2×#47411yescharacteristic
396C2×C43#308111yescharacteristic
397C2×C43#326611yescharacteristic
398C2×C43D4×D811yescharacteristic
399C2×C43#329411yescharacteristic
400C2×C43#331411yescharacteristic
401C23×D4C2×D4311yescharacteristic
402C23×C8—431no—
403C2×C4⋊Q8—431no—
404C2×C22⋊Q8—861no—
405C2×C4×D4C2×D4311yescharacteristic
406C2×C4×D4C2×D4311yescharacteristic
407C22×C4⋊C4—431no—
408C22×C22⋊C4—21no—
409#474—864no—
410C2×#107—431no—
411C2×#107—431no—
412C2×#107—431no—
413C2×#107—431no—
414C2×C4⋊C8—431no—
415C2×C4⋊C8—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—864no—
425C2×C22⋊C8—431no—
426#398—861no—
427#395—861no—
428#390C2×D4311yescharacteristic
429#390C2×D4311yescharacteristic
430#389—431no—
431#389—431no—
432#386—21no—
433#386—21no—
434#385—861no—
435#384—431no—
436#380—431no—
437#380C2×D4311yescharacteristic
438#379—21no—
439C4×C22⋊C4C2×D4311yescharacteristic
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#336—431no—
445#336—431no—
446C43#2595011yescharacteristic, complemented, Sylow
447C25—21no—
448C22×Q8—861no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—21no—
453C22×D4—41no—
454C22×D4—41no—
455C22×D4Dic8614yescomplemented
456C22×D4C22×D4311yescharacteristic
457C22×D4C22×D4311yescharacteristic
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—861no—
461C23×C4C22×D4311yescharacteristic
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8—431no—
466C22×C8—862no—
467C22×C8—862no—
468C22×C8—1721no—
469C4⋊Q8—862no—
470C4⋊Q8—1721no—
471C22⋊Q8—1724no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—41no—
475C4×D4—41no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—1721no—
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—44no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4C22⋊D4311yescharacteristic
500C2×C22⋊C4C22⋊D4311yescharacteristic
501C2×C42C22×D4311yescharacteristic
502C2×C42C22×D4311yescharacteristic
503#107—862no—
504#107—862no—
505#107—1721no—
506#107—1721no—
507C4⋊C8—862no—
508C4⋊C8—1721no—
509#102—434no—
510#102—862no—
511#102—862no—
512#102—862no—
513#102—862no—
514#102—862no—
515#102—1721no—
516#102—1721no—
517C22⋊C8—862no—
518#95—21no—
519#95—861no—
520#95—861no—
521#95—861no—
522#95C22⋊D4311yescharacteristic
523#95C22⋊D4311yescharacteristic
524C24—21no—
525C24—21no—
526C24—24no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—81no—
532C24—81no—
533C24C2×C22⋊D4311yescharacteristic
534C2×Q8—3441no—
535C2×Q8—1722no—
536C2×Q8—1722no—
537C2×D4—28no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4C2×Dic8612yes—
553C2×D4C2×Dic8612yes—
554C2×D4D4×D4312yes—
555C2×D4#1062190012yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—3441no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4C2×Dic8612yes—
576C22×C4#1062189812yes—
577C22×C4C2×C22⋊D4311yescharacteristic
578C22×C4C2×C22⋊D4311yescharacteristic
579C22×C4C2×C22⋊D4311yescharacteristic
580C22×C4C2×C22⋊D4311yescharacteristic
581C22×C4C2×C22⋊D4311yescharacteristic
582C22×C4C23×D4311yescharacteristic
583C2×C8—432no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—1724no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—432no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—3441no—
609C4⋊C4—1722no—
610C4⋊C4—1722no—
611C4⋊C4—1722no—
612C4⋊C4—1722no—
613C4⋊C4—1722no—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—81no—
621C22⋊C4—81no—
622C22⋊C4—1722no—
623C22⋊C4#1062188214yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—48no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#1306330412yes—
654C23C2×#1062188212yes—
655C23#1306335512yes—
656C23C22×C22⋊D4311yescharacteristic
657Q8—3444no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#1306330214yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—862no—
692C2×C4—3444no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4#1306330412yes—
705C2×C4C2×#1062188212yes—
706C2×C4C2×#1062188212yes—
707C2×C4C2×D4×D4311yescharacteristic
708C2×C4C22×Dic8611yescharacteristic
709C2×C4C2×#1062190011yescharacteristic
710C2×C4C2×#1062189811yescharacteristic
711C2×C4#1306337011yescharacteristic
712C2×C4#1306337011yescharacteristic
713C8—862no—
714C8—1721no—
715C8—1721no—
716C8—1721no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#1458317914yescomplemented
739C22C2×#1306330411yescharacteristic
740C22D4×C22⋊D4311yescharacteristic
741C22#1458354311yescharacteristic
742C22C22×#1062188211yescharacteristic
743C22C2×#1306335511yescharacteristic
744C22#1458370211yescharacteristic
745C22#1458371011yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—3441no—
754C4—3441no—
755C4—3441no—
756C4—1722no—
757C4C2×#1306330211yescharacteristic
758C4#1458352511yescharacteristic
759C4#1458353911yescharacteristic
760C4#1458357511yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#1913825611yescharacteristic
765C2C2×#1458317911yescharacteristic
766C2#1914442611yescharacteristic
767C2#1914610111yescharacteristic
768C2D4×#1062188211yescharacteristic
769C2#1914640811yescharacteristic
770C2#1914667611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterD4×C22⋊C4D43
hypocenterC43#25950
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14583179C2semidirect
3. #19138297C2semidirect
4. #19136123C2semidirect
5. #19135983C2semidirect
6. #19135983C2semidirect
7. #19135731C2semidirect
8. #19134842C2semidirect
9. #19134842C2semidirect
10. #19134782C2semidirect
11. #19134775C2semidirect
12. #19134622C2semidirect
13. #19134595C2semidirect
17. C2×#13063325C22semidirect
21. C2×#13063258C22semidirect
22. C2×#13063258C22semidirect
23. C2×#13063258C22semidirect
24. C2×#13063258C22semidirect
25. C2×C4⋊(C43⋊C8)C22semidirect
26. C2×C4⋊(C43⋊C8)C22semidirect
39. #14582797C22semidirect
40. #14582797C22semidirect
42. #14582769C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
111. C22×D4×C43Q8semidirect
279. D4×C43C22⋊Q8semidirect
353. C22×C43#474semidirect
446. C43#25950semidirect
455. C22×D4Dic86semidirect
666. D4#13063302semidirect
738. C22#14583179semidirect

Maximal subgroups

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

subgroupindex
C2×#145831792
C22×#130632462
#191382972
#191361232
#191359832
#191357312
#191348422
#191347822
#191347752
#191346222
#191345952
#191345262
D4×C22⋊C4×C432
#2595043