Finite Group Databasebeta

← #25112992

Subgroups — #25112992

Order 11008.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic
2#19137544C211yesmaximal, characteristic, complemented
3#19135564C211yesmaximal, characteristic, complemented
4#19135550C211yesmaximal, characteristic, complemented
5#19135033C211yesmaximal, characteristic, complemented
6#19135023C211yesmaximal, characteristic, complemented
7#19134915C211yesmaximal, characteristic, complemented
8#19134915C211yesmaximal, characteristic, complemented
9#19134691C211yesmaximal, characteristic, complemented
10#19134682C211yesmaximal, characteristic, complemented
11#19134596C211yesmaximal, characteristic, complemented
12#19134421C211yesmaximal, characteristic, complemented
13#19134315C211yesmaximal, characteristic, complemented
14#19134312C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16#14583595—24no—
17#14583595C418yescomplemented
18C2×#13063320—21no—
19C2×#13063317C2211yescharacteristic
20C2×#13063307—21no—
21C2×#13063299C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×#13063297—21no—
24C2×C4×D172C2211yescharacteristic
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063284C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34#14582802—21no—
35#14582792—21no—
36#14582792—21no—
37#14582769C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582759C2211yescharacteristic
40C4⋊C4×Dic43—21no—
41C4×C4⋊Dic43C2211yescharacteristic
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×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C23×Dic43—21no—
66C22×C4×D43—21no—
67#13063320—28no—
68#13063317—22no—
69#13063317C2×C414yes—
70#13063307—28no—
71#13063299—22no—
72#13063299—22no—
73#13063299C2×C414yes—
74#13063299C2×C414yes—
75#13063297—28no—
76C4×D172—22no—
77C4×D172C2×C414yes—
78(C22⋊D43)⋊C4—28no—
79#13063284—22no—
80#13063284—22no—
81#13063284—22no—
82#13063284—41no—
83#13063284—41no—
84#13063284C2×C414yes—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2×C414yes—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111#13063247—22no—
112#13063247—22no—
113#13063247—41no—
114#13063247—41no—
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—42no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43—81no—
170C22×Dic43—24no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—81no—
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—81no—
188C2×C4×D43—81no—
189M16×C43—44no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
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—44no—
202C2×C8×C43#4112yes—
203C4⋊C4×C43C22⋊C414yes—
204C22⋊C4×C43C22⋊C414yes—
205C22⋊C4×C43C22⋊C414yes—
206C42×C43C22×C412yes—
207C42×C43C2×D412yes—
208C22⋊Dic43—24no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213(C2×D43)⋊C4—24no—
214(C2×D43)⋊C4—24no—
215(C2×D43)⋊C4—24no—
216C4⋊Dic43—24no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—42no—
228C4⋊Dic43—81no—
229C4⋊Dic43C22×C412yes—
230C4⋊Dic43C22×C412yes—
231C4⋊Dic43C22×C412yes—
232C4⋊Dic43#4112yes—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235C4×Dic43—24no—
236C4×Dic43—42no—
237C4×Dic43—42no—
238C4×Dic43—42no—
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—48no—
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—84no—
317C8×C43—22no—
318C8×C43—41no—
319C8×C43—41no—
320C8×C43—41no—
321#22498—431nomaximal, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43C22×C22⋊C411yescharacteristic
337C22×C43#54611yescharacteristic
338C22×C43#54711yescharacteristic
339C22×C43#57511yescharacteristic
340C22×C43#57511yescharacteristic
341C22×C43#57611yescharacteristic
342C22×C43#57711yescharacteristic
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43—81no—
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—22no—
354C4×C43C4×#4111yescharacteristic
355C4×C43#52011yescharacteristic
356C4×C43#54611yescharacteristic
357C4×C43#54711yescharacteristic
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361Dic43—42no—
362Dic43—81no—
363Dic43—81no—
364Dic43—81no—
365C2×#553—431no—
366C2×#435D4311yescharacteristic, complemented
367#2354—431no—
368#1992—431no—
369#1989—431no—
370#1895—431no—
371#1893—431no—
372#1875—431no—
373#1875—431no—
374#1825—431no—
375#1823—431no—
376#1802—431no—
377#1762—431no—
378#1736—431no—
379#1735—431no—
380C2×C43—42no—
381C2×C43—42no—
382C2×C43#233911yescharacteristic
383C2×C43#289611yescharacteristic
384C2×C43#289711yescharacteristic
385C2×C43#330711yescharacteristic
386C2×C43#330911yescharacteristic
387C2×C43#334711yescharacteristic
388C2×C43#335011yescharacteristic
389D43—82no—
390C22×M16C2×D4311yescharacteristic
391C23×C8C2×D4311yescharacteristic
392#553—438no—
393#553—864no—
394C2×#126—861no—
395C2×#125—431no—
396C2×#123—861no—
397C2×#121—431no—
398C2×#121—431no—
399C2×#121—861no—
400C2×C4×D4—431no—
401C2×C4×D4—861no—
402C2×C4×D4C2×D4311yescharacteristic
403C2×#117—431no—
404C2×#117—431no—
405C2×#117—431no—
406C22×C4⋊C4—431no—
407#435—24no—
408C2×C4⋊C8C2×D4311yescharacteristic
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×C22⋊C8C2×D4311yescharacteristic
414C2×C22⋊C8C2×D4311yescharacteristic
415C2×#97C2×D4311yescharacteristic
416#390—861no—
417#388—861no—
418#388—861no—
419#384—431no—
420#380—431no—
421#380—431no—
422C4×C4⋊C4—431no—
423C4×C4⋊C4—861no—
424#340—431no—
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—
436C43#2249811yescharacteristic, complemented, Sylow
437C22×D4—431no—
438C22×D4—861no—
439C22×D4—861no—
440C22×D4D17211yescharacteristic
441C23×C4—861no—
442C23×C4—861no—
443C23×C4C22×D4311yescharacteristic
444C23×C4C22×D4311yescharacteristic
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8—22no—
449C22×C8—22no—
450C22×C8—41no—
451C22×C8C22×D4311yescharacteristic
452C22×C8C22×D4311yescharacteristic
453C22×C8C22×D4311yescharacteristic
454C22×C8C22×D4311yescharacteristic
455#126—868no—
456#125—434no—
457#125—862no—
458#123—868no—
459#121—434no—
460#121—434no—
461#121—868no—
462#121—862no—
463#121—862no—
464C4×D4—434no—
465C4×D4—868no—
466C4×D4—862no—
467C4×D4C4×D4314yes—
468C4×D4C22⋊D4314yes—
469#117—434no—
470#117—862no—
471#117—862no—
472#117—862no—
473#117—1721no—
474#117—1721no—
475C2×C4⋊C4—434no—
476C2×C4⋊C4—431no—
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—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—862no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4D17211yescharacteristic
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⋊C4—861no—
498C2×C22⋊C4D17211yescharacteristic
499C2×C22⋊C4D17211yescharacteristic
500C2×C42—861no—
501C2×C42—861no—
502C2×C42—861no—
503C2×C42—861no—
504C2×C42C22×D4311yescharacteristic
505C4⋊C8—22no—
506#102—862no—
507#102—862no—
508#102—1721no—
509#102—1721no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512#97—22no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—861no—
517C24C2×D17211yescharacteristic
518C24C2×D17211yescharacteristic
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—432no—
522C2×D4—864no—
523C2×D4—864no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—3441no—
530C2×D4—3441no—
531C2×D4—1722no—
532C2×D4—1722no—
533C2×D4(C2×D43)⋊C414yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—864no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—864no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—3441no—
552C22×C4—3441no—
553C22×C4—3441no—
554C22×C4—3441no—
555C22×C4C2×C4×D4312yes—
556C22×C4C2×C4×D4312yes—
557C22×C4C2×D17211yescharacteristic
558C22×C4C2×D17211yescharacteristic
559C22×C4C2×D17211yescharacteristic
560C22×C4C2×D17211yescharacteristic
561C22×C4C2×C22⋊D4312yes—
562C22×C4C2×C22⋊D4312yes—
563C22×C4C23×D4311yescharacteristic
564M16—44no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—44no—
577C2×C8#1062190012yes—
578C4⋊C4—432no—
579C4⋊C4—432no—
580C4⋊C4—432no—
581C4⋊C4—432no—
582C4⋊C4—864no—
583C4⋊C4—864no—
584C4⋊C4—864no—
585C4⋊C4—861no—
586C4⋊C4—861no—
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—3441no—
596C4⋊C4—1722no—
597C4⋊C4(C2×D43)⋊C414yes—
598C22⋊C4—864no—
599C22⋊C4—864no—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—3441no—
603C22⋊C4—3441no—
604C22⋊C4—1722no—
605C22⋊C4—1722no—
606C22⋊C4(C2×D43)⋊C414yes—
607C22⋊C4(C2×D43)⋊C414yes—
608C42—864no—
609C42—1722no—
610C42—1722no—
611C42—1722no—
612C42C2×C4×D4312yes—
613C42C2×C22⋊D4312yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—862no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23C2×(C2×D43)⋊C412yes—
634C23C2×(C2×D43)⋊C412yes—
635C23C22×D17211yescharacteristic
636D4—44no—
637D4—862no—
638D4—862no—
639D4—3444no—
640D4—1728no—
641D4—1721no—
642D4—1721no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—3444no—
664C2×C4—3444no—
665C2×C4—1721no—
666C2×C4—1721no—
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×C4C2×(C2×D43)⋊C412yes—
683C2×C4C2×(C2×D43)⋊C412yes—
684C2×C4C2×(C2×D43)⋊C412yes—
685C2×C4C2×(C2×D43)⋊C412yes—
686C2×C4C22×C4×D4311yescharacteristic
687C2×C4C22×C22⋊D4311yescharacteristic
688C2×C4#41×D4311yescharacteristic
689C2×C4C2×#1062190011yescharacteristic
690C2×C4#1306337011yescharacteristic
691C2×C4#1306337211yescharacteristic
692C8—22no—
693C8—41no—
694C8—41no—
695C8—41no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—3441no—
711C22—3441no—
712C22—3441no—
713C22—3441no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22C22×(C2×D43)⋊C411yescharacteristic
718C22#1458354411yescharacteristic
719C22#1458355311yescharacteristic
720C22#1458369911yescharacteristic
721C22#1458369911yescharacteristic
722C22#1458370411yescharacteristic
723C22#1458371111yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—3441no—
729C4—3441no—
730C4—3441no—
731C4—1722no—
732C4—1722no—
733C4—1722no—
734C4—1722no—
735C4C4×#1062190011yescharacteristic
736C4#1458337811yescharacteristic
737C4#1458354311yescharacteristic
738C4#1458354811yescharacteristic
739C2—42no—
740C2—42no—
741C2—3442no—
742C2#1913742011yescharacteristic
743C2#1914311511yescharacteristic
744C2#1914312211yescharacteristic
745C2#1914657311yescharacteristic
746C2#1914660311yescharacteristic
747C2#1914709711yescharacteristic
748C2#1914714211yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583595C2
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22498
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. #19137544C2semidirect
3. #19135564C2semidirect
4. #19135550C2semidirect
5. #19135033C2semidirect
6. #19135023C2semidirect
7. #19134915C2semidirect
8. #19134915C2semidirect
9. #19134691C2semidirect
10. #19134682C2semidirect
11. #19134596C2semidirect
12. #19134421C2semidirect
13. #19134315C2semidirect
14. #19134312C2semidirect
15. C2×C43×#435C2semidirect
17. #14583595C4semidirect
366. C2×#435D43semidirect
436. C43#22498semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
#191375442
#191355642
#191355502
#191350332
#191350232
#191349152
#191346912
#191346822
#191345962
#191344212
#191343152
#191343122
C2×C43×#4352
#2249843