Finite Group Databasebeta

← #25112062

Subgroups — #25112062

Order 11008.

1542 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583568C211yesmaximal, characteristic
2C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582894C211yesmaximal, characteristic, complemented
4#19137545C211yesmaximal, characteristic, complemented
5#19135520C211yesmaximal, characteristic, complemented
6#19135399C211yesmaximal, characteristic, complemented
7#19135023C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134914C211yesmaximal, characteristic, complemented
11#19134598C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134534C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#416C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583568—24no—
19#14583568C418yescomplemented
20C2×#13063321—21no—
21C2×#13063321C2211yescharacteristic
22C2×#13063299—21no—
23C2×#13063299C2211yescharacteristic
24C2×#13063296—21no—
25C2×#13063296C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C8×C22⋊D43—24no—
31C2×Dic43⋊C8C2211yescharacteristic
32#14582894—24no—
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582799—21no—
45#14582790—21no—
46#14582787—21no—
47#14582768C2211yescharacteristic
48#14582759C2211yescharacteristic
49#14582756C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51C4×Dic43⋊C4—21no—
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×#41×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic
58C2×#117×C43C2211yescharacteristic
59C43×#416—24no—
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—41no—
68C2×#10621902—41no—
69C2×#10621902C2×C414yes—
70C22×D172—21no—
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43—21no—
76C22×C22⋊D43D411yescharacteristic
77C22×C4×D43—21no—
78C22×C4×D43C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C2×C8×D43—22no—
82C2×C8×D43—22no—
83C2×C8×D43—41no—
84#13063321—28no—
85#13063321—22no—
86#13063321C2×C414yes—
87#13063299—22no—
88#13063299—28no—
89#13063299C2×C414yes—
90#13063296—22no—
91#13063296—28no—
92#13063296C2×C414yes—
93Q8×Dic43—22no—
94Q8×Dic43C2×C414yes—
95C4×C22⋊D43—28no—
96C4×C22⋊D43C2×C414yes—
97C4×C22⋊D43D414yes—
98#13063283—22no—
99#13063283—41no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4D411yescharacteristic
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43D411yescharacteristic
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118Dic43⋊C8—22no—
119#13063249—22no—
120#13063249—22no—
121#13063247—22no—
122#13063247—41no—
123#13063246—41no—
124#13063246—41no—
125#13063245—22no—
126#13063245—41no—
127C22⋊(C43⋊C8)—22no—
128(C2×D43)⋊C8—22no—
129C8×Dic43—22no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—41no—
137C2×#41×C43—41no—
138C2×#41×C43C2×C414yes—
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43—21no—
141C22×D4×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43—22no—
145C22×C8×C43—22no—
146C22×C8×C43—41no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149#117×C43—22no—
150#117×C43—41no—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C42×C43—21no—
155#103×C43—22no—
156#103×C43D414yescomplemented
157#102×C43—22no—
158#102×C43—22no—
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43C2×D411yescharacteristic
163#41×C43—28no—
164#41×C43—44no—
165#41×C43—44no—
166#41×C43—44no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43C22×C412yes—
171C2×Q8×C43C2×D412yes—
172C2×Q8×C43#4112yes—
173C2×D4×C43—21no—
174C2×D4×C43—24no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43C22×C412yes—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—81no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43C22⋊C414yes—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C22×Dic43C2×D411yescharacteristic
217#10621902—28no—
218#10621902—44no—
219#10621902—44no—
220#10621902—44no—
221C2×D172—21no—
222C2×D172—24no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—42no—
228C2×D172—42no—
229C2×D172C22×C412yes—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—24no—
235C2×C4×D43—42no—
236C2×C4×D43—42no—
237C2×C4×D43C22×C412yes—
238C2×C4×D43C2×D412yes—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—44no—
245C2×C8×C43C2×D412yes—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C2×D412yes—
250C22⋊C4×C43—42no—
251C42×C43—42no—
252C22⋊Dic43—24no—
253C22⋊Dic43—81no—
254C22⋊Dic43C22⋊C414yes—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—42no—
257(C2×D43)⋊C4—81no—
258(C2×D43)⋊C4C22⋊C414yes—
259C4⋊Dic43—21no—
260C4⋊Dic43—24no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43C22×C412yes—
266Dic43⋊C4—42no—
267Dic43⋊C4—81no—
268Dic43⋊C4C22⋊C414yes—
269C4×Dic43—24no—
270C4×Dic43—42no—
271C4×Dic43—42no—
272C4×Dic43C22×C412yes—
273C4×Dic43C2×D412yes—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C8×D43—44no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—22no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—22no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43C2×C22⋊C412yes—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43C4×D414yes—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—48no—
317D4×C43—41no—
318D4×C43—41no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—48no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43C2×C22⋊C412yes—
336C2×C4×C43C23×C411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43H(5,𝔽2)11yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C22⋊D43—28no—
343C22⋊D43—48no—
344C22⋊D43—84no—
345C22⋊D43—84no—
346C22⋊D43—84no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—22no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43C2×C22⋊C412yes—
361C2×Dic43C2×C22⋊C412yes—
362C2×Dic43C2×C22⋊C412yes—
363C2×Dic43#13512yes—
364C2×Dic43#13512yes—
365D172—22no—
366D172—22no—
367D172—48no—
368D172—41no—
369D172—41no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—48no—
375C8×C43—22no—
376C8×C43—41no—
377C43⋊C8—41no—
378C43⋊C8—41no—
379#22418—431nomaximal, Sylow
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43C22×C22⋊C411yescharacteristic
395C22×C43D4211yescharacteristic
396C22×C43#54611yescharacteristic
397C22×C43C2×#13511yescharacteristic
398C22×C43C2×#13511yescharacteristic
399C22×C43#57611yescharacteristic
400C22×C43#57711yescharacteristic
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—81no—
412C2×D43—81no—
413C2×D43—81no—
414C2×D43—81no—
415C4×C43—24no—
416C4×C43—22no—
417C4×C43—42no—
418C4×C43—81no—
419C4×C43C2×C4×D411yescharacteristic
420C4×C43#51811yescharacteristic
421C4×C43D4211yescharacteristic
422C4×C43#54611yescharacteristic
423Dic43—22no—
424Dic43—22no—
425Dic43—42no—
426Dic43—81no—
427Dic43—81no—
428Dic43#41614yescomplemented
429C2×#550—431no—
430C2×C8×D4—431no—
431C2×#416—431no—
432C2×#416D4311yescharacteristic, complemented
433#2354—431no—
434#1982—431no—
435#1957—431no—
436#1893—431no—
437#1893—431no—
438#1875—431no—
439#1875—431no—
440#1803—431no—
441#1788—431no—
442#1788—431no—
443C4×#103—431no—
444C2×C43—42no—
445C2×C43—82no—
446C2×C43D4×C22⋊C411yescharacteristic
447C2×C43C2×#41611yescharacteristic
448C2×C43#289711yescharacteristic
449C2×C43#328411yescharacteristic
450C2×C43#328711yescharacteristic
451C2×C43#330411yescharacteristic
452C2×C43#330511yescharacteristic
453D43—42no—
454D43—82no—
455C22×#41—431no—
456C22×#41C2×D4311yescharacteristic
457C23×C8—431no—
458C23×C8C2×D4311yescharacteristic
459#550—438no—
460#550—864no—
461C2×#127—431no—
462C2×#127—861no—
463C2×#121—431no—
464C2×#121—431no—
465C2×#121—861no—
466C2×#121—861no—
467C2×C4×Q8—431no—
468C2×C4×D4—431no—
469C2×C4×D4—861no—
470C2×#117—431no—
471C2×#117C2×D4311yescharacteristic
472C8×D4—864no—
473C2×C4⋊C8—431no—
474#416—24no—
475#416—864no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103C2×D4311yescharacteristic
479C2×#103C2×D4311yescharacteristic
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×#102C2×D4311yescharacteristic
487C2×#102C2×D4311yescharacteristic
488C2×C22⋊C8—431no—
489C2×C22⋊C8—431no—
490C2×C4×C8—431no—
491#390—861no—
492#388—861no—
493#388—861no—
494#384—431no—
495#380—431no—
496#380—431no—
497C4×C4⋊C4—431no—
498C4×C4⋊C4—861no—
499#340—431no—
500#340—431no—
501#340—431no—
502#340—431no—
503C43#2241811yescharacteristic, complemented, Sylow
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—434no—
510C2×#41—862no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—1721no—
514C2×#41—1721no—
515C2×#41C4×D4314yes—
516C22×Q8C22×D4311yescharacteristic
517C22×D4—21no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—861no—
521C22×D4—861no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4C22×D4311yescharacteristic
526C23×C4—21no—
527C23×C4—431no—
528C23×C4—861no—
529C23×C4C22×D4311yescharacteristic
530C22×C8—22no—
531C22×C8—22no—
532C22×C8—41no—
533C22×C8—431no—
534C22×C8—431no—
535C22×C8—862no—
536C22×C8—862no—
537C22×C8—1721no—
538C22×C8C22×D4311yescharacteristic
539C22×C8C22×D4311yescharacteristic
540#127—434no—
541#127—862no—
542#127—868no—
543#121—434no—
544#121—434no—
545#121—868no—
546#121—868no—
547#121—862no—
548#121—862no—
549C4×Q8—434no—
550C4×Q8—862no—
551C4×D4—434no—
552C4×D4—434no—
553C4×D4—868no—
554#117—22no—
555#117—41no—
556#117—862no—
557#117—1721no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—861no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4C22×D4311yescharacteristic
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—431no—
569C2×C22⋊C4—431no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—21no—
576C2×C42—431no—
577C2×C42—861no—
578C2×C42—861no—
579C2×C42—861no—
580C4⋊C8—862no—
581#103—22no—
582#103—862no—
583#103—862no—
584#103C22⋊D4314yescomplemented
585#102—22no—
586#102—22no—
587#102—862no—
588#102—862no—
589#102—1721no—
590#102—1721no—
591#102—1721no—
592#102—1721no—
593C22⋊C8—862no—
594C22⋊C8—862no—
595C4×C8—862no—
596#95—861no—
597#95—861no—
598#95—861no—
599C24—21no—
600C24—431no—
601C24—861no—
602C24D4×D4311yescharacteristic
603#41—28no—
604#41—44no—
605#41—44no—
606#41—44no—
607#41—868no—
608#41—1724no—
609#41—1724no—
610#41—1724no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×C4×D4312yes—
615C2×Q8#1062189812yes—
616C2×Q8C2×C22⋊D4312yes—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—434no—
626C2×D4—432no—
627C2×D4—864no—
628C2×D4—862no—
629C2×D4—862no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—3441no—
640C2×D4—3441no—
641C2×D4—3441no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—3441no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4C2×C4×D4312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—864no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—1722no—
674C22×C4—1722no—
675C22×C4C2×C4×D4312yes—
676C22×C4D4×D4311yescharacteristic
677C22×C4D4×D4312yes—
678C22×C4C23×D4311yescharacteristic
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—44no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—1724no—
692C2×C8C2×C22⋊D4312yes—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—434no—
697C4⋊C4—432no—
698C4⋊C4—864no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—3441no—
705C4⋊C4—1722no—
706C4⋊C4C2×C22⋊D4312yes—
707C22⋊C4—42no—
708C22⋊C4—434no—
709C22⋊C4—434no—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C22⋊C4—3441no—
713C22⋊C4—3441no—
714C22⋊C4—1722no—
715C42—42no—
716C42—432no—
717C42—432no—
718C42—864no—
719C42—1722no—
720C42—1722no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—432no—
735C23—861no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—862no—
742C23—1721no—
743C23—1721no—
744C23—1721no—
745C23—1721no—
746C23—1721no—
747C23—1721no—
748C23C22⋊C4×D4312yes—
749C23C2×D4×D4311yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8C4×C22⋊D4314yes—
754D4—22no—
755D4—22no—
756D4—48no—
757D4—41no—
758D4—41no—
759D4—868no—
760D4—862no—
761D4—862no—
762D4—3444no—
763D4—3444no—
764D4—3444no—
765D4—1728no—
766D4—1728no—
767D4—1721no—
768D4—1721no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—432no—
786C2×C4—432no—
787C2×C4—432no—
788C2×C4—432no—
789C2×C4—432no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—1728no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4C22⋊C4×D4312yes—
809C2×C4C22×C4×D4311yescharacteristic
810C2×C4C2×D4×D4311yescharacteristic
811C2×C4C22×C22⋊D4311yescharacteristic
812C2×C4C2×#1062189811yescharacteristic
813C2×C4#1306337011yescharacteristic
814C2×C4#1306337011yescharacteristic
815C8—22no—
816C8—41no—
817C8—1721no—
818C8—1721no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—3441no—
837C22—3441no—
838C22—3441no—
839C22—3441no—
840C22—1722no—
841C22—1722no—
842C22—1722no—
843C22—1721no—
844C22—1721no—
845C22—1721no—
846C22—1721no—
847C22C2×C22⋊C4×D4311yescharacteristic
848C22D4×C22⋊D4311yescharacteristic
849C22#1458353911yescharacteristic
850C22#135×D4311yescharacteristic
851C22#135×D4311yescharacteristic
852C22#1458370111yescharacteristic
853C22#1458370611yescharacteristic
854C4—22no—
855C4—24no—
856C4—42no—
857C4—81no—
858C4—434no—
859C4—862no—
860C4—862no—
861C4—3441no—
862C4—3441no—
863C4—1722no—
864C4C2×C4×C22⋊D4311yescharacteristic
865C4#1458337211yescharacteristic
866C4D4×C22⋊D4311yescharacteristic
867C4#1458353911yescharacteristic
868C2—42no—
869C2—82no—
870C2—3442no—
871C2—1722no—
872C2C22⋊C4×C22⋊D4311yescharacteristic
873C2#416×D4311yescharacteristic
874C2#1914311711yescharacteristic
875C2#1914631911yescharacteristic
876C2#1914634911yescharacteristic
877C2#1914653011yescharacteristic
878C2#1914654111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#416C2
socleC23×C43C22×D4
prime radicalC2×#14583568C2
cosocleC22×C4×C43C24
hypercenterC2×#416D43
hypocenterC43#22418
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D43C2semidirect
3. C2×#14582894C2semidirect
4. #19137545C2semidirect
5. #19135520C2semidirect
6. #19135399C2semidirect
7. #19135023C2semidirect
8. #19135020C2semidirect
9. #19134917C2semidirect
10. #19134914C2semidirect
11. #19134598C2semidirect
12. #19134535C2semidirect
13. #19134534C2semidirect
14. #103×Dic43C2semidirect
15. C2×C43×#416C2semidirect
19. #14583568C4semidirect
156. #103×C43D4semidirect
428. Dic43#416semidirect
432. C2×#416D43semidirect
503. C43#22418semidirect
584. #103C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835682
C2×C8×C22⋊D432
C2×#145828942
#191375452
#191355202
#191353992
#191350232
#191350202
#191349172
#191349142
#191345982
#191345352
#191345342
#103×Dic432
C2×C43×#4162
#2241843