Finite Group Databasebeta

← #25112902

Subgroups — #25112902

Order 11008.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583614C211yesmaximal, characteristic
2#19137524C211yesmaximal, characteristic, complemented
3#19135568C211yesmaximal, characteristic, complemented
4#19135546C211yesmaximal, characteristic, complemented
5#19135033C211yesmaximal, characteristic, complemented
6#19135023C211yesmaximal, characteristic, complemented
7#19134915C211yesmaximal, characteristic, complemented
8#19134910C211yesmaximal, characteristic, complemented
9#19134691C211yesmaximal, characteristic, complemented
10#19134691C211yesmaximal, characteristic, complemented
11#19134606C211yesmaximal, characteristic, complemented
12#19134421C211yesmaximal, characteristic, complemented
13#19134315C211yesmaximal, characteristic, complemented
14#19134312C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16#14583614—24no—
17#14583614C418yescomplemented
18C2×#13063325C2211yescharacteristic
19C2×#13063311—21no—
20C2×#13063311—21no—
21C2×#13063299C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×#13063296—21no—
24C2×C4×D172C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26C2×#13063284C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C2×#13063283—21no—
29C22×C4⋊Dic43C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34#14582792—21no—
35#14582785—21no—
36#14582779—21no—
37#14582765C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582759C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C22⋊C4×Dic43—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#435—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C22×Dic86—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68#13063325—22no—
69#13063325C2×C414yescomplemented
70#13063311—28no—
71#13063311—28no—
72#13063299—22no—
73#13063299—22no—
74#13063299C2×C414yes—
75#13063299C2×C414yescomplemented
76#13063296—28no—
77C4×D172—22no—
78C4×D172C2×C414yescomplemented
79#13063284—22no—
80#13063284—22no—
81#13063284—22no—
82#13063284—41no—
83#13063284C2×C414yes—
84#13063284C2×C414yescomplemented
85#13063283—28no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—41no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109#13063247—22no—
110#13063247—22no—
111#13063247—41no—
112#13063247—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C22×D4×C43D411yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C2×M16×C43—22no—
122C2×M16×C43—22no—
123C2×M16×C43—41no—
124C22×C8×C43—22no—
125C22×C8×C43—22no—
126C22×C8×C43—41no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C4×D4×C43C2×C414yes—
132C4×D4×C43D414yes—
133C2×C4⋊C4×C43D411yescharacteristic
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—22no—
138C22⋊C8×C43—22no—
139C22⋊C8×C43—22no—
140#97×C43—22no—
141C24×C43C2×D411yescharacteristic
142C24×C43C2×D411yescharacteristic
143C23×D43—21no—
144C2×D4×C43—41no—
145C2×D4×C43—41no—
146C2×D4×C43C22⋊C414yes—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C22×C412yes—
157C22×C4×C43C2×D412yes—
158C22×C4×C43C2×D412yes—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—24no—
165C2×C22⋊D43—24no—
166C2×C22⋊D43—81no—
167C2×C22⋊D43—81no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43—81no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—42no—
178C22×Dic43—42no—
179C22×Dic43—81no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172C22×C412yes—
186C2×C4×D43—24no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×Dic86—24no—
190C2×Dic86—81no—
191C2×Dic86—81no—
192M16×C43—44no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—44no—
205C2×C8×C43#4112yes—
206C4⋊C4×C43C22⋊C414yes—
207C22⋊C4×C43C22⋊C414yes—
208C22⋊C4×C43C22⋊C414yes—
209C42×C43C22×C412yes—
210C42×C43C2×D412yes—
211C22⋊Dic43—24no—
212C22⋊Dic43—24no—
213C22⋊Dic43—42no—
214C22⋊Dic43—42no—
215C22⋊Dic43—81no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—24no—
219C4⋊Dic43—24no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—42no—
231C4⋊Dic43C22×C412yes—
232C4⋊Dic43C22×C412yes—
233C4⋊Dic43C22×C412yes—
234C4⋊Dic43#4112yes—
235C4×Dic43—24no—
236C4×Dic43—24no—
237C4×Dic43—42no—
238C4×Dic43—81no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43C2×C22⋊C412yes—
252C23×C43C2×C22⋊C412yes—
253C23×C43C22×D411yescharacteristic
254C22×D43—22no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261D4×C43—44no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43C2×C22⋊C412yes—
279C2×C4×C43C2×C22⋊C412yes—
280C2×C4×C43C2×C22⋊C412yes—
281C2×C4×C43C2×C22⋊C412yes—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C22⋊D43—84no—
289C22⋊D43—84no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—84no—
312D172—22no—
313D172—22no—
314D172—41no—
315D172—41no—
316C4×D43—48no—
317Dic86—84no—
318C8×C43—22no—
319C8×C43—41no—
320C8×C43—41no—
321C8×C43—41no—
322#22492—431nomaximal, Sylow
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43C22×C22⋊C411yescharacteristic
338C22×C43#54611yescharacteristic
339C22×C43#54711yescharacteristic
340C22×C43#57511yescharacteristic
341C22×C43#57511yescharacteristic
342C22×C43#57611yescharacteristic
343C22×C43#57711yescharacteristic
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43—81no—
350C2×D43—81no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43C4×#4111yescharacteristic
356C4×C43#52011yescharacteristic
357C4×C43#54611yescharacteristic
358C4×C43#54711yescharacteristic
359Dic43—42no—
360Dic43—42no—
361Dic43—42no—
362Dic43—42no—
363Dic43—81no—
364Dic43—81no—
365Dic43—81no—
366C2×#555—431no—
367C2×#435D4311yescharacteristic, complemented
368#2352—431no—
369#1993—431no—
370#1988—431no—
371#1895—431no—
372#1893—431no—
373#1875—431no—
374#1874—431no—
375#1825—431no—
376#1825—431no—
377#1804—431no—
378#1762—431no—
379#1736—431no—
380#1735—431no—
381C2×C43—42no—
382C2×C43—42no—
383C2×C43#233911yescharacteristic
384C2×C43#289611yescharacteristic
385C2×C43#289711yescharacteristic
386C2×C43#331911yescharacteristic
387C2×C43#332111yescharacteristic
388C2×C43#334711yescharacteristic
389C2×C43#334811yescharacteristic
390D43—82no—
391C22×M16C2×D4311yescharacteristic
392C23×C8C2×D4311yescharacteristic
393#555—438no—
394#555—864no—
395C2×C4⋊Q8—431no—
396C2×#124—861no—
397C2×#124—861no—
398C2×#121—431no—
399C2×#121—431no—
400C2×#121—861no—
401C2×C4×D4—431no—
402C2×C4×D4C2×D4311yescharacteristic
403C2×#117—431no—
404C2×#117—431no—
405C2×#117—431no—
406C2×#117—861no—
407C22×C4⋊C4—431no—
408#435—24no—
409C2×C4⋊C8C2×D4311yescharacteristic
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×C22⋊C8C2×D4311yescharacteristic
415C2×C22⋊C8C2×D4311yescharacteristic
416C2×#97C2×D4311yescharacteristic
417#388—861no—
418#387—861no—
419#386—861no—
420#382—431no—
421#380—431no—
422#380—431no—
423C4×C4⋊C4—431no—
424C4×C22⋊C4—861no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437C43#2249211yescharacteristic, complemented, Sylow
438C22×Q8—861no—
439C22×D4—431no—
440C22×D4—861no—
441C22×D4—861no—
442C22×D4D17211yescharacteristic
443C23×C4—861no—
444C23×C4—861no—
445C23×C4C22×D4311yescharacteristic
446C23×C4C22×D4311yescharacteristic
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—41no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—41no—
453C22×C8C22×D4311yescharacteristic
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C4⋊Q8—434no—
458C4⋊Q8—862no—
459#124—868no—
460#124—868no—
461#121—434no—
462#121—434no—
463#121—868no—
464#121—862no—
465#121—862no—
466C4×D4—434no—
467C4×D4—862no—
468C4×D4C4×D4314yes—
469C4×D4C22⋊D4314yes—
470#117—434no—
471#117—434no—
472#117—862no—
473#117—862no—
474#117—868no—
475#117—862no—
476#117—1721no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—1721no—
488C2×C4⋊C4D17211yescharacteristic
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4D17211yescharacteristic
498C2×C22⋊C4D17211yescharacteristic
499C2×C42—861no—
500C2×C42—861no—
501C2×C42—861no—
502C2×C42—861no—
503C2×C42C22×D4311yescharacteristic
504C4⋊C8—22no—
505#102—862no—
506#102—862no—
507#102—1721no—
508#102—1721no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511#97—22no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517C24—861no—
518C24C2×D17211yescharacteristic
519C24C2×D17211yescharacteristic
520C2×Q8—864no—
521C2×Q8—3441no—
522C2×Q8—3441no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—432no—
526C2×D4—864no—
527C2×D4—864no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—3441no—
534C2×D4—3441no—
535C2×D4—3441no—
536C2×D4—3441no—
537C2×D4(C2×D43)⋊C414yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—864no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—3441no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4C2×C4×D4312yes—
560C22×C4C2×C4×D4312yes—
561C22×C4C2×D17211yescharacteristic
562C22×C4C2×D17211yescharacteristic
563C22×C4C2×D17211yescharacteristic
564C22×C4C2×D17211yescharacteristic
565C22×C4C2×C22⋊D4312yes—
566C22×C4C2×C22⋊D4312yes—
567C22×C4C23×D4311yescharacteristic
568M16—44no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—44no—
581C2×C8#1062190012yes—
582C4⋊C4—432no—
583C4⋊C4—432no—
584C4⋊C4—432no—
585C4⋊C4—432no—
586C4⋊C4—864no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—1722no—
598C4⋊C4(C2×D43)⋊C414yes—
599C22⋊C4—864no—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—864no—
604C22⋊C4—3441no—
605C22⋊C4—1722no—
606C22⋊C4—1722no—
607C22⋊C4(C2×D43)⋊C414yes—
608C22⋊C4(C2×D43)⋊C414yes—
609C42—864no—
610C42—864no—
611C42—3441no—
612C42—1722no—
613C42C2×C4×D4312yes—
614C42C2×C22⋊D4312yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—862no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23C2×(C2×D43)⋊C412yes—
635C23C2×(C2×D43)⋊C412yes—
636C23C22×D17211yescharacteristic
637Q8—3444no—
638D4—44no—
639D4—862no—
640D4—862no—
641D4—3444no—
642D4—3444no—
643D4—1721no—
644D4—1721no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—3444no—
666C2×C4—1728no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4C2×(C2×D43)⋊C412yes—
685C2×C4C2×(C2×D43)⋊C412yes—
686C2×C4C2×(C2×D43)⋊C412yes—
687C2×C4C2×(C2×D43)⋊C412yes—
688C2×C4C22×C4×D4311yescharacteristic
689C2×C4C22×C22⋊D4311yescharacteristic
690C2×C4#41×D4311yescharacteristic
691C2×C4C2×#1062190011yescharacteristic
692C2×C4#1306337011yescharacteristic
693C2×C4#1306337211yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—3441no—
713C22—3441no—
714C22—3441no—
715C22—3441no—
716C22—1722no—
717C22—1722no—
718C22—1722no—
719C22C22×(C2×D43)⋊C411yescharacteristic
720C22#1458354411yescharacteristic
721C22#1458355311yescharacteristic
722C22#1458369911yescharacteristic
723C22#1458369911yescharacteristic
724C22#1458370411yescharacteristic
725C22#1458371111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—3441no—
731C4—3441no—
732C4—3441no—
733C4—1722no—
734C4—1722no—
735C4—1722no—
736C4—1722no—
737C4C4×#1062190011yescharacteristic
738C4#1458337811yescharacteristic
739C4#1458354311yescharacteristic
740C4#1458354811yescharacteristic
741C2—42no—
742C2—42no—
743C2—3442no—
744C2#1913742011yescharacteristic
745C2#1914311511yescharacteristic
746C2#1914312211yescharacteristic
747C2#1914675311yescharacteristic
748C2#1914678311yescharacteristic
749C2#1914709711yescharacteristic
750C2#1914711211yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583614C2
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22492
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #19137524C2semidirect
3. #19135568C2semidirect
4. #19135546C2semidirect
5. #19135033C2semidirect
6. #19135023C2semidirect
7. #19134915C2semidirect
8. #19134910C2semidirect
9. #19134691C2semidirect
10. #19134691C2semidirect
11. #19134606C2semidirect
12. #19134421C2semidirect
13. #19134315C2semidirect
14. #19134312C2semidirect
15. C2×C43×#435C2semidirect
17. #14583614C4semidirect
69. #13063325C2×C4semidirect
75. #13063299C2×C4semidirect
78. C4×D172C2×C4semidirect
84. #13063284C2×C4semidirect
367. C2×#435D43semidirect
437. C43#22492semidirect

Maximal subgroups

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

subgroupindex
C2×#145836142
#191375242
#191355682
#191355462
#191350332
#191350232
#191349152
#191349102
#191346912
#191346062
#191344212
#191343152
#191343122
C2×C43×#4352
#2249243