Finite Group Databasebeta

← #25112139

Subgroups — #25112139

Order 11008.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D172C211yesmaximal, characteristic
2C2×#14582905C211yesmaximal, characteristic, complemented
3C22×#13063247C211yesmaximal, characteristic, complemented
4#19137524C211yesmaximal, characteristic, complemented
5#19135521C211yesmaximal, characteristic, complemented
6#19135419C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135023C211yesmaximal, characteristic, complemented
9#19134915C211yesmaximal, characteristic, complemented
10#19134910C211yesmaximal, characteristic, complemented
11#19134606C211yesmaximal, characteristic, complemented
12#19134527C211yesmaximal, characteristic, complemented
13#19134527C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C22×D4×D43—21no—
19D4×D172—24no—
20D4×D172C418yescomplemented
21C2×#13063322C2211yescharacteristic
22C2×#13063300—21no—
23C2×#13063299C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25C2×#13063295—21no—
26C2×#13063295—21no—
27C2×C4×D172C2211yescharacteristic
28C2×#13063284C2211yescharacteristic, complemented
29C22×C4⋊Dic43C2211yescharacteristic, complemented
30#14582905—24no—
31C2×#13063247—24no—
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic, complemented
39C2×#13063247C2211yescharacteristic, complemented
40C2×#13063247C2211yescharacteristic, complemented
41C2×#13063247C2211yescharacteristic, complemented
42C2×#13063247C2211yescharacteristic, complemented
43C2×#13063247C2211yescharacteristic, complemented
44#14582792—21no—
45#14582785—21no—
46#14582779—21no—
47#14582765C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic, complemented
49#14582759C2211yescharacteristic, complemented
50C4×C4⋊Dic43C2211yescharacteristic, complemented
51C22⋊C4×Dic43—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582662C2211yescharacteristic, complemented
56C22×M16×C43C2211yescharacteristic, complemented
57C23×C8×C43C2211yescharacteristic, complemented
58C2×C4×D4×C43C2211yescharacteristic
59C43×#435—24no—
60C2×C4⋊C8×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic, complemented
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C2×#97×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C24×D43—21no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—22no—
69C22×D172—22no—
70C22×D172—21no—
71C22×D172—21no—
72C22×D172—21no—
73C22×D172—22no—
74C22×D172—22no—
75C22×D172—21no—
76C22×D172—41no—
77C22×D172—41no—
78C22×D172—41no—
79C22×D172—41no—
80C22×D172C2×C414yes—
81C22×D172C2×C414yescomplemented
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C2×D4×D43—28no—
88C2×D4×D43—44no—
89C2×D4×D43—44no—
90C23×Dic43—21no—
91C22×C4×D43—21no—
92#13063322—22no—
93#13063322C2×C414yescomplemented
94#13063300—28no—
95#13063299—22no—
96#13063299—22no—
97#13063299C2×C414yes—
98#13063299C2×C414yescomplemented
99#13063295—28no—
100#13063295—28no—
101C4×D172—22no—
102C4×D172C2×C414yescomplemented
103#13063284—22no—
104#13063284—41no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43—41no—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×C4⋊Dic43C2311yescharacteristic
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121#13063247—22no—
122#13063247—22no—
123#13063247—22no—
124#13063247—22no—
125#13063247—22no—
126#13063247—22no—
127#13063247—22no—
128#13063247—41no—
129#13063247—41no—
130#13063247—41no—
131#13063247—41no—
132#13063247D414yescomplemented
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C22×D4×C43D411yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C2×M16×C43—22no—
142C2×M16×C43—22no—
143C2×M16×C43—41no—
144C22×C8×C43—22no—
145C22×C8×C43—22no—
146C22×C8×C43—41no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C22×C8×C43C2311yescharacteristic
151C4×D4×C43C2×C414yes—
152C4×D4×C43D414yes—
153C2×C4⋊C4×C43D411yescharacteristic
154C2×C22⋊C4×C43D411yescharacteristic
155C2×C22⋊C4×C43D411yescharacteristic
156C2×C42×C43C2311yescharacteristic
157C4⋊C8×C43—22no—
158C22⋊C8×C43—22no—
159C22⋊C8×C43—22no—
160#97×C43—22no—
161C24×C43C2×D411yescharacteristic
162C24×C43C2×D411yescharacteristic
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—24no—
167C23×D43—24no—
168C23×D43—42no—
169C23×D43—42no—
170C23×D43—42no—
171C23×D43—42no—
172C23×D43—42no—
173C23×D43—42no—
174C23×D43—42no—
175C23×D43—42no—
176C23×D43—81no—
177C23×D43—81no—
178C23×D43—81no—
179C23×D43—81no—
180C2×D4×C43—22no—
181C2×D4×C43—22no—
182C2×D4×C43C22⋊C414yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C22×C412yes—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D412yes—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—42no—
205C2×C22⋊D43—42no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—42no—
212C22×Dic43—42no—
213C22×Dic43—81no—
214D4×D43—432no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—24no—
219C2×D172—24no—
220C2×D172—24no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—24no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—28no—
233C2×D172—28no—
234C2×D172—42no—
235C2×D172—42no—
236C2×D172—42no—
237C2×D172—42no—
238C2×D172—44no—
239C2×D172—44no—
240C2×D172—44no—
241C2×D172—44no—
242C2×D172—44no—
243C2×D172—44no—
244C2×D172—42no—
245C2×D172—42no—
246C2×D172—81no—
247C2×D172—81no—
248C2×D172C22×C412yes—
249C2×D172C22×C412yes—
250C2×D172C22×C412yes—
251C2×D172C2×D412yes—
252C2×D172#4112yes—
253C2×C4×D43—24no—
254C2×C4×D43—42no—
255C2×C4×D43—42no—
256M16×C43—44no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—44no—
269C2×C8×C43C2×D412yescomplemented
270C4⋊C4×C43C22⋊C414yes—
271C22⋊C4×C43C22⋊C414yes—
272C22⋊C4×C43C22⋊C414yes—
273C42×C43C22×C412yes—
274C42×C43C2×D412yes—
275C22⋊Dic43—42no—
276C22⋊Dic43—42no—
277C22⋊Dic43—81no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—42no—
290C4⋊Dic43C22×C412yes—
291C4⋊Dic43C2×D412yescomplemented
292C4×Dic43—42no—
293C4×Dic43—81no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—21no—
304C23×C43C2×C22⋊C412yes—
305C23×C43C2×C22⋊C412yes—
306C23×C43AGL(1,ℤ/8)12yes—
307C23×C43AGL(1,ℤ/8)12yes—
308C23×C43C22×D411yescharacteristic
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—48no—
315C22×D43—48no—
316C22×D43—41no—
317C22×D43—41no—
318C22×D43—41no—
319C22×D43—41no—
320C22×D43—48no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—41no—
324C22×D43—41no—
325C22×D43—41no—
326C22×D43—41no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—48no—
334C22×D43—84no—
335C22×D43—84no—
336C22×D43—84no—
337C22×D43—84no—
338C22×D43—84no—
339C22×D43—84no—
340C22×D43—84no—
341C22×D43—84no—
342C22×D43—84no—
343C22×D43—84no—
344D4×C43—28no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43C2×C22⋊C412yes—
362C2×C4×C43C2×C22⋊C412yes—
363C2×C4×C43C2×C22⋊C412yes—
364C2×C4×C43C2×C22⋊C412yes—
365C2×C4×C43C23×C411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C22×D411yescharacteristic
368C2×C4×C43C2×#4111yescharacteristic
369C2×C4×C43H(5,𝔽2)11yescharacteristic
370C2×C4×C43H(5,𝔽2)11yescharacteristic
371C22⋊D43—48no—
372C22⋊D43—48no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—41no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—84no—
389D172—22no—
390D172—22no—
391D172—22no—
392D172—22no—
393D172—22no—
394D172—22no—
395D172—22no—
396D172—48no—
397D172—48no—
398D172—48no—
399D172—41no—
400D172—41no—
401D172—41no—
402D172—41no—
403D172—84no—
404D172C4×D414yes—
405C4×D43—48no—
406C8×C43—22no—
407C8×C43—41no—
408C8×C43—41no—
409C8×C43—41no—
410#22423—431nomaximal, Sylow
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43#41814yescomplemented
425C22×C43C22×C22⋊C411yescharacteristic
426C22×C43D4211yescharacteristic
427C22×C43#54611yescharacteristic
428C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C43#57611yescharacteristic
431C22×C43#57711yescharacteristic
432C2×D43—24no—
433C2×D43—42no—
434C2×D43—42no—
435C2×D43—42no—
436C2×D43—42no—
437C2×D43—42no—
438C2×D43—42no—
439C2×D43—42no—
440C2×D43—42no—
441C2×D43—42no—
442C2×D43—42no—
443C2×D43—42no—
444C2×D43—42no—
445C2×D43—816no—
446C2×D43—816no—
447C2×D43—81no—
448C2×D43—81no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43—81no—
454C2×D43—81no—
455C4×C43—22no—
456C4×C43—22no—
457C4×C43—22no—
458C4×C43—22no—
459C4×C43C2×C4×D411yescharacteristic
460C4×C43#51811yescharacteristic
461C4×C43D4211yescharacteristic
462C4×C43#54611yescharacteristic
463Dic43—42no—
464Dic43—42no—
465Dic43—81no—
466Dic43—81no—
467Dic43—81no—
468C2×D42—431no—
469C2×#435D4311yescharacteristic, complemented
470C2×#418—431no—
471C22×#102—431no—
472#2352—431no—
473#1982—431no—
474#1961—431no—
475#1895—431no—
476#1893—431no—
477#1875—431no—
478#1874—431no—
479#1804—431no—
480#1786—431no—
481#1786—431no—
482#1762—431no—
483C2×C43—24no—
484C2×C43—42no—
485C2×C43D4×C22⋊C411yescharacteristic
486C2×C43C2×#41811yescharacteristic
487C2×C43#289711yescharacteristic
488C2×C43#326411yescharacteristic
489C2×C43#326511yescharacteristic
490C2×C43#331011yescharacteristic
491C2×C43#331811yescharacteristic
492D43—44no—
493D43—82no—
494D43—82no—
495C23×D4—431no—
496C23×D4—431no—
497C23×D4—861no—
498C22×M16C2×D4311yescharacteristic, complemented
499C23×C8C2×D4311yescharacteristic, complemented
500D42—438no—
501D42—864no—
502C2×#127—431no—
503C2×#121—431no—
504C2×#121—431no—
505C2×#121—861no—
506C2×#120—861no—
507C2×#120—861no—
508C2×C4×D4—431no—
509C2×C4×D4C2×D4311yescharacteristic
510C2×#117—431no—
511C22×C4⋊C4—431no—
512#435—24no—
513C2×C4⋊C8C2×D4311yescharacteristic, complemented
514#418—864no—
515C2×#102—431no—
516C2×#102—431no—
517C2×#102—431no—
518C2×#102—431no—
519C2×#102—431no—
520C2×#102—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102—431no—
524C2×#102—431no—
525C2×#102—431no—
526C2×#102—431no—
527C2×#102—864no—
528C2×C22⋊C8C2×D4311yescharacteristic, complemented
529C2×C22⋊C8C2×D4311yescharacteristic, complemented
530C2×#97C2×D4311yescharacteristic, complemented
531#388—861no—
532#387—861no—
533#386—861no—
534#382—431no—
535#380—431no—
536#380—431no—
537C4×C4⋊C4—431no—
538C4×C22⋊C4—861no—
539#340—431no—
540#340—431no—
541#340—431no—
542#340—431no—
543C43#2242311yescharacteristic, complemented, Sylow
544C25—861no—
545C25—861no—
546C22×D4—434no—
547C22×D4—434no—
548C22×D4—431no—
549C22×D4—431no—
550C22×D4—431no—
551C22×D4—862no—
552C22×D4—862no—
553C22×D4—862no—
554C22×D4—862no—
555C22×D4—861no—
556C22×D4—861no—
557C22×D4—868no—
558C22×D4—861no—
559C22×D4—861no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—862no—
563C22×D4—862no—
564C22×D4—1721no—
565C22×D4—1721no—
566C22×D4—1721no—
567C22×D4—1721no—
568C22×D4—1724no—
569C22×D4—1724no—
570C22×D4D17211yescharacteristic
571C23×C4—861no—
572C23×C4—861no—
573C23×C4C22×D4311yescharacteristic
574C23×C4C22×D4311yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C22×D4311yescharacteristic
582C22×C8C22×D4311yescharacteristic
583C22×C8C22×D4311yescharacteristic
584C22×C8C22×D4311yescharacteristic
585#127—434no—
586#127—862no—
587#121—434no—
588#121—434no—
589#121—862no—
590#121—862no—
591#121—868no—
592#120—868no—
593#120—868no—
594C4×D4—434no—
595C4×D4—862no—
596C4×D4C4×D4314yes—
597C4×D4C22⋊D4314yes—
598#117—862no—
599#117—1721no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—431no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4—1721no—
608C2×C4⋊C4D17211yescharacteristic
609C2×C22⋊C4—861no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4D17211yescharacteristic
616C2×C22⋊C4D17211yescharacteristic
617C2×C42—861no—
618C2×C42—861no—
619C2×C42C22×D4311yescharacteristic
620C4⋊C8—22no—
621#102—434no—
622#102—862no—
623#102—862no—
624#102—862no—
625#102—862no—
626#102—862no—
627#102—862no—
628#102—862no—
629#102—1721no—
630#102—1721no—
631#102—1721no—
632#102—1721no—
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—861no—
637#95—861no—
638#95—861no—
639#95—861no—
640#95—861no—
641C24—861no—
642C24—864no—
643C24—864no—
644C24—861no—
645C24—861no—
646C24—3441no—
647C24—3441no—
648C24—3441no—
649C24—3441no—
650C24—1722no—
651C24—1722no—
652C24—1722no—
653C24—1722no—
654C24—1722no—
655C24—1722no—
656C24—1722no—
657C24—1722no—
658C24C2×D17211yescharacteristic
659C24C2×D17211yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—432no—
663C2×D4—432no—
664C2×D4—432no—
665C2×D4—432no—
666C2×D4—432no—
667C2×D4—868no—
668C2×D4—868no—
669C2×D4—864no—
670C2×D4—864no—
671C2×D4—864no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—864no—
675C2×D4—861no—
676C2×D4—861no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—861no—
682C2×D4—861no—
683C2×D4—861no—
684C2×D4—861no—
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—3441no—
689C2×D4—3441no—
690C2×D4—1724no—
691C2×D4—1724no—
692C2×D4—1724no—
693C2×D4—1724no—
694C2×D4—1724no—
695C2×D4—1724no—
696C2×D4—1722no—
697C2×D4—1722no—
698C2×D4—1722no—
699C2×D4—1722no—
700C2×D4—1722no—
701C2×D4—1722no—
702C2×D4—17232no—
703C2×D4—1722no—
704C2×D4—1722no—
705C2×D4—1722no—
706C2×D4—1722no—
707C2×D4(C2×D43)⋊C414yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—864no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—3441no—
723C22×C4—1722no—
724C22×C4—1722no—
725C22×C4—1722no—
726C22×C4—1722no—
727C22×C4C2×C4×D4312yes—
728C22×C4C2×C4×D4312yes—
729C22×C4C2×D17211yescharacteristic
730C22×C4C2×D17211yescharacteristic
731C22×C4C2×D17211yescharacteristic
732C22×C4C2×D17211yescharacteristic
733C22×C4C2×C22⋊D4312yes—
734C22×C4C2×C22⋊D4312yes—
735C22×C4C23×D4311yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8D4×D4312yescomplemented
750C4⋊C4—432no—
751C4⋊C4—432no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—1722no—
761C4⋊C4(C2×D43)⋊C414yes—
762C22⋊C4—864no—
763C22⋊C4—864no—
764C22⋊C4—864no—
765C22⋊C4—3441no—
766C22⋊C4—1722no—
767C22⋊C4—1722no—
768C22⋊C4(C2×D43)⋊C414yes—
769C22⋊C4(C2×D43)⋊C414yes—
770C42—3441no—
771C42—1722no—
772C42C2×C4×D4312yes—
773C42C2×C22⋊D4312yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—3444no—
790C23—3444no—
791C23—3444no—
792C23—3444no—
793C23—3444no—
794C23—3444no—
795C23—3444no—
796C23—3444no—
797C23—3444no—
798C23—3444no—
799C23—1728no—
800C23—1728no—
801C23—1728no—
802C23—1728no—
803C23—1721no—
804C23—1721no—
805C23—1721no—
806C23—1721no—
807C23—1721no—
808C23—1721no—
809C23—1721no—
810C23—1721no—
811C23—1721no—
812C23—1721no—
813C23—1721no—
814C23—1721no—
815C23—1721no—
816C23—1721no—
817C23—1721no—
818C23—1721no—
819C23C2×(C2×D43)⋊C412yes—
820C23C2×(C2×D43)⋊C412yes—
821C23#1306335312yes—
822C23#1306335312yes—
823C23C22×D17211yescharacteristic
824D4—28no—
825D4—434no—
826D4—862no—
827D4—862no—
828D4—862no—
829D4—862no—
830D4—862no—
831D4—862no—
832D4—862no—
833D4—3444no—
834D4—1728no—
835D4—1728no—
836D4—1728no—
837D4—1728no—
838D4—1728no—
839D4—1721no—
840D4—1721no—
841D4—1721no—
842D4—1721no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—862no—
860C2×C4—862no—
861C2×C4—3444no—
862C2×C4—1728no—
863C2×C4—1721no—
864C2×C4—1721no—
865C2×C4—1721no—
866C2×C4—1721no—
867C2×C4—1721no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4C2×(C2×D43)⋊C412yes—
877C2×C4C2×(C2×D43)⋊C412yes—
878C2×C4C2×(C2×D43)⋊C412yes—
879C2×C4C2×(C2×D43)⋊C412yes—
880C2×C4C22×C4×D4311yescharacteristic
881C2×C4C2×D4×D4311yescharacteristic
882C2×C4C22×C22⋊D4311yescharacteristic
883C2×C4#41×D4311yescharacteristic
884C2×C4#1306337011yescharacteristic
885C2×C4#1306337111yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—864no—
904C22—34416no—
905C22—34416no—
906C22—3441no—
907C22—3441no—
908C22—3441no—
909C22—3441no—
910C22—3441no—
911C22—3441no—
912C22—3441no—
913C22—3441no—
914C22—1722no—
915C22—1722no—
916C22—1722no—
917C22—1722no—
918C22—1722no—
919C22—1722no—
920C22—1722no—
921C22—1722no—
922C22—1722no—
923C22—1722no—
924C22—1722no—
925C22—1722no—
926C22#1458290514yescomplemented
927C22C22×(C2×D43)⋊C411yescharacteristic
928C22D4×D17211yescharacteristic
929C22#1458354411yescharacteristic
930C22C2×#1306335311yescharacteristic
931C22C2×#1306335311yescharacteristic
932C22#1458370411yescharacteristic
933C22#1458371111yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—3441no—
939C4—3441no—
940C4—3441no—
941C4—1722no—
942C4—1722no—
943C4C4×D4×D4311yescharacteristic
944C4#1458337111yescharacteristic
945C4D4×C22⋊D4311yescharacteristic
946C4#1458353711yescharacteristic
947C2—24no—
948C2—42no—
949C2—3442no—
950C2—3442no—
951C2—1724no—
952C2D4×(C2×D43)⋊C411yescharacteristic
953C2C2×#1458290511yescharacteristic
954C2#1914312211yescharacteristic
955C2#1914608011yescharacteristic
956C2#1914609511yescharacteristic
957C2#1914661811yescharacteristic
958C2#1914673811yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×D4×D172C2
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22423
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. C2×#14582905C2semidirect
3. C22×#13063247C2semidirect
4. #19137524C2semidirect
5. #19135521C2semidirect
6. #19135419C2semidirect
7. #19135033C2semidirect
8. #19135023C2semidirect
9. #19134915C2semidirect
10. #19134910C2semidirect
11. #19134606C2semidirect
12. #19134527C2semidirect
13. #19134527C2semidirect
14. #19134421C2semidirect
15. C2×C43×#435C2semidirect
20. D4×D172C4semidirect
28. C2×#13063284C22semidirect
29. C22×C4⋊Dic43C22semidirect
36. C2×#13063247C22semidirect
37. C2×#13063247C22semidirect
38. C2×#13063247C22semidirect
39. C2×#13063247C22semidirect
40. C2×#13063247C22semidirect
41. C2×#13063247C22semidirect
42. C2×#13063247C22semidirect
43. C2×#13063247C22semidirect
47. #14582765C22semidirect
48. #14582759C22semidirect
49. #14582759C22semidirect
50. C4×C4⋊Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582662C22semidirect
56. C22×M16×C43C22semidirect
57. C23×C8×C43C22semidirect
60. C2×C4⋊C8×C43C22semidirect
61. C2×C22⋊C8×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C2×#97×C43C22semidirect
81. C22×D172C2×C4semidirect
93. #13063322C2×C4semidirect
98. #13063299C2×C4semidirect
102. C4×D172C2×C4semidirect
132. #13063247D4semidirect
269. C2×C8×C43C2×D4semidirect
291. C4⋊Dic43C2×D4semidirect
424. C22×C43#418semidirect
469. C2×#435D43semidirect
498. C22×M16C2×D43semidirect
499. C23×C8C2×D43semidirect
513. C2×C4⋊C8C2×D43semidirect
528. C2×C22⋊C8C2×D43semidirect
529. C2×C22⋊C8C2×D43semidirect
530. C2×#97C2×D43semidirect
543. C43#22423semidirect
749. C2×C8D4×D43semidirect
926. C22#14582905semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D1722
C2×#145829052
C22×#130632472
#191375242
#191355212
#191354192
#191350332
#191350232
#191349152
#191349102
#191346062
#191345272
#191344212
C2×C43×#4352
#2242343