Finite Group Databasebeta

← #25095831

Subgroups — #25095831

Order 11008.

3666 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063372C211yesmaximal, characteristic
2C2×#14582897C211yesmaximal, characteristic, complemented
3C2×#14582906C211yesmaximal, characteristic, complemented
4C2×#14582892C211yesmaximal, characteristic, complemented
5C2×#103×D43C211yesmaximal, characteristic, complemented
6C2×#14582864C211yesmaximal, characteristic, complemented
7#19137184C211yesmaximal, characteristic, complemented
8#19134535C211yesmaximal, characteristic, complemented
9#19134532C211yesmaximal, characteristic, complemented
10#19134532C211yesmaximal, characteristic, complemented
11#19134531C211yesmaximal, characteristic, complemented
12#19134529C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#19134528C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C2×#13063372—24no—
17C2×#13063372—24no—
18C2×#13063372—24no—
19C2×#13063372—24no—
20C2×#13063372—24no—
21C2×#13063372C418yescomplemented
22C22×#10621898—21no—
23C22×#10621898C2211yescharacteristic
24C22×#10621900—21no—
25C22×#10621900—21no—
26C22×#10621900C2211yescharacteristic
27C22×#10621900C2211yescharacteristic
28C23×Dic86—21no—
29C23×Dic86C2211yescharacteristic
30C22×Q8×D43C2211yescharacteristic
31C22×Q8×D43C2211yescharacteristic
32C22×#10621872C2211yescharacteristic
33C22×C8×D43C2211yescharacteristic
34C2×#13063283C2211yescharacteristic
35C2×C4⋊C4×D43C2211yescharacteristic
36#14582906—24no—
37#14582897—24no—
38#14582892—24no—
39C2×#13063250C2211yescharacteristic
40C2×#13063250C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43C2×#13063249C2211yescharacteristic
44C2×#13063249C2211yescharacteristic
45C2×#13063248C2211yescharacteristic
46C2×#13063248C2211yescharacteristic
47C2×#13063248C2211yescharacteristic
48C2×#13063248C2211yescharacteristic
49#103×D43—24no—
50C2×#13063246C2211yescharacteristic
51C2×#13063246C2211yescharacteristic
52#14582864—24no—
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C2×(C2×D43)⋊C8C2211yescharacteristic
55C2×(C2×D43)⋊C8C2211yescharacteristic
56#14582803—21no—
57#14582799—21no—
58#14582777—21no—
59#14582775—21no—
60#14582759C2211yescharacteristic
61#14582756C2211yescharacteristic
62#14582756C2211yescharacteristic
63C22×#41×C43C2211yescharacteristic
64C2×#103×C43C2211yescharacteristic
65C2×#103×C43C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67C2×#102×C43C2211yescharacteristic
68C2×C22⋊C8×C43C2211yescharacteristic
69C43×#380C2211yescharacteristic
70#13063372—232no—
71#13063372—232no—
72#13063372—232no—
73#13063372—232no—
74C2×#10621898—28no—
75C2×#10621898—28no—
76C2×#10621898—28no—
77C2×#10621898—22no—
78C2×#10621898—22no—
79C2×#10621898—22no—
80C2×#10621898—22no—
81C2×#10621898C2×C414yes—
82C2×#10621898D414yes—
83C2×#10621900—28no—
84C2×#10621900—28no—
85C2×#10621900—28no—
86C2×#10621900—28no—
87C2×#10621900—22no—
88C2×#10621900—22no—
89C2×#10621900—28no—
90C2×#10621900—28no—
91C2×#10621900—22no—
92C2×#10621900—22no—
93C2×#10621900—22no—
94C2×#10621900—22no—
95C2×#10621900—22no—
96C2×#10621900—22no—
97C2×#10621900C2×C414yes—
98C2×#10621900C2×C414yescomplemented
99C2×#10621900D414yes—
100C2×#10621900D414yes—
101C22×Dic86—28no—
102C22×Dic86—28no—
103C22×Dic86—21no—
104C22×Dic86—22no—
105C22×Dic86—21no—
106C22×Dic86—21no—
107C22×Dic86—28no—
108C22×Dic86—22no—
109C22×Dic86—22no—
110C22×Dic86—22no—
111C22×Dic86—22no—
112C22×Dic86C2×C414yescomplemented
113C22×Dic86D411yescharacteristic
114C22×Dic86C2311yescharacteristic
115C22×Dic86C2311yescharacteristic
116C2×Q8×D43—22no—
117C2×Q8×D43—22no—
118C2×Q8×D43—22no—
119C2×Q8×D43—22no—
120C2×Q8×D43—22no—
121C2×Q8×D43—22no—
122C2×Q8×D43—22no—
123C2×Q8×D43—22no—
124C2×Q8×D43C2×C414yes—
125C2×Q8×D43C2×C414yescomplemented
126C2×Q8×D43D414yes—
127C2×Q8×D43D414yes—
128C22×D172D411yescharacteristic
129C22×C22⋊D43—21no—
130C22×C22⋊D43—21no—
131C22×C22⋊D43D411yescharacteristic
132C22×C22⋊D43D411yescharacteristic
133C23×Dic43—21no—
134C23×Dic43—21no—
135C23×Dic43—21no—
136C22×C4×D43—21no—
137C22×C4×D43—21no—
138C22×C4×D43—21no—
139C22×C4×D43C2311yescharacteristic
140C22×C4×D43C2311yescharacteristic
141C2×#10621872—22no—
142C2×#10621872—22no—
143C2×#10621872—22no—
144C22×C43⋊C8C2311yescharacteristic
145C22×C43⋊C8C2311yescharacteristic
146C2×C8×D43—22no—
147C2×C8×D43—22no—
148C2×C8×D43—22no—
149#13063283—22no—
150#13063283—22no—
151C2×C4⋊Dic43C2311yescharacteristic
152C2×C4⋊Dic43C2311yescharacteristic
153C2×Dic43⋊C4—21no—
154C4⋊C4×D43—22no—
155C4⋊C4×D43—22no—
156C2×C22⋊Dic43—21no—
157C2×(C2×D43)⋊C4—21no—
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×C4×Dic43—21no—
161#13063250—22no—
162#13063250—22no—
163#13063250—22no—
164#13063250—22no—
165#13063249—22no—
166#13063249—22no—
167#13063248—22no—
168#13063248—22no—
169#13063248—22no—
170#13063248—22no—
171#13063246—22no—
172#13063246—22no—
173C22⋊(C43⋊C8)—22no—
174(C2×D43)⋊C8—22no—
175(C2×D43)⋊C8—22no—
176C43⋊#95—21no—
177C43⋊#95—21no—
178C43⋊#95—21no—
179C2×#41×C43—22no—
180C2×#41×C43—22no—
181C2×#41×C43—22no—
182C2×#41×C43—22no—
183C2×#41×C43—22no—
184C2×#41×C43C2×C414yescomplemented
185C22×Q8×C43C2311yescharacteristic
186C22×D4×C43—21no—
187C22×D4×C43C2311yescharacteristic
188C23×C4×C43—21no—
189C23×C4×C43C2311yescharacteristic
190C22×C8×C43C2311yescharacteristic
191C22×C8×C43C2311yescharacteristic
192C2×C4⋊C4×C43C2311yescharacteristic
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43—21no—
195#103×C43—22no—
196#103×C43—22no—
197#102×C43—22no—
198#102×C43—22no—
199C22⋊C8×C43—22no—
200#95×C43—21no—
201C24×C43—21no—
202C24×C43C2×D411yescharacteristic
203C23×D43C2×D411yescharacteristic
204C23×D43C2×D411yescharacteristic
205#41×C43—28no—
206#41×C43—28no—
207#41×C43—28no—
208#41×C43—28no—
209C2×Q8×C43—21no—
210C2×Q8×C43—21no—
211C2×Q8×C43—21no—
212C2×Q8×C43C22×C412yes—
213C2×Q8×C43C2×D412yes—
214C2×Q8×C43C2×D412yes—
215C2×D4×C43—24no—
216C2×D4×C43—24no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—24no—
221C2×D4×C43C22×C412yes—
222C2×D4×C43C2×D412yes—
223C2×D4×C43C2×D412yes—
224C22×C4×C43—24no—
225C22×C4×C43—24no—
226C22×C4×C43—24no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43C22×C412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2411yescharacteristic
238C2×C22⋊D43—24no—
239C2×C22⋊D43—24no—
240C2×C22⋊D43—22no—
241C2×C22⋊D43—22no—
242C2×C22⋊D43—24no—
243C2×C22⋊D43—24no—
244C2×C22⋊D43—24no—
245C2×C22⋊D43—24no—
246C2×C22⋊D43—22no—
247C2×C22⋊D43—22no—
248C2×C22⋊D43C22⋊C414yes—
249C2×C22⋊D43C22⋊C414yes—
250C22×Dic43—24no—
251C22×Dic43—24no—
252C22×Dic43—24no—
253C22×Dic43—24no—
254C22×Dic43—24no—
255C22×Dic43—24no—
256C22×Dic43—24no—
257C22×Dic43—24no—
258C22×Dic43—24no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43C2×D411yescharacteristic
264C22×Dic43C2×D411yescharacteristic
265Q8×D43—28no—
266Q8×D43—28no—
267Q8×D43—28no—
268Q8×D43—28no—
269Q8×D43—28no—
270Q8×D43—28no—
271Q8×D43—28no—
272Q8×D43C22⋊C4116yescomplemented
273#10621900—264no—
274#10621900—28no—
275#10621900—28no—
276#10621900—264no—
277#10621900—28no—
278#10621900—28no—
279#10621900—28no—
280#10621900—28no—
281#10621900—28no—
282#10621900C22⋊C4116yescomplemented
283#10621898—264no—
284#10621898—28no—
285#10621898—28no—
286#10621898—28no—
287#10621898—28no—
288C2×D172—22no—
289C2×D172—22no—
290C2×D172C22⋊C414yes—
291C2×C4×D43—24no—
292C2×C4×D43—24no—
293C2×C4×D43—21no—
294C2×C4×D43—21no—
295C2×C4×D43—21no—
296C2×C4×D43—21no—
297C2×C4×D43—24no—
298C2×C4×D43—24no—
299C2×C4×D43—24no—
300C2×C4×D43—24no—
301C2×C4×D43—42no—
302C2×C4×D43—81no—
303C2×C4×D43—81no—
304C2×C4×D43C22×C412yes—
305C2×C4×D43C22×C412yes—
306C2×C4×D43C2×D412yes—
307C2×C4×D43C2×D412yes—
308C2×C4×D43C2×D412yes—
309C2×C4×D43C2×D412yes—
310C2×C4×D43C2×D412yes—
311C2×C4×D43C2×D412yes—
312C2×Dic86—24no—
313C2×Dic86—24no—
314C2×Dic86—24no—
315C2×Dic86—24no—
316C2×Dic86—28no—
317C2×Dic86—28no—
318C2×Dic86—264no—
319C2×Dic86—24no—
320C2×Dic86—21no—
321C2×Dic86—21no—
322C2×Dic86—21no—
323C2×Dic86—21no—
324C2×Dic86—21no—
325C2×Dic86—21no—
326C2×Dic86—24no—
327C2×Dic86—24no—
328C2×Dic86—24no—
329C2×Dic86—24no—
330C2×Dic86—22no—
331C2×Dic86—22no—
332C2×Dic86—28no—
333C2×Dic86—28no—
334C2×Dic86C22⋊C414yes—
335C2×Dic86C22×C412yes—
336C2×Dic86C22×C412yes—
337C2×Dic86C2×D412yes—
338C2×Dic86C2×D412yes—
339C2×Dic86C2×D412yes—
340C2×Dic86C2×D412yes—
341C2×C8×C43—21no—
342C2×C8×C43—21no—
343C2×C8×C43—21no—
344C2×C8×C43—21no—
345C2×C8×C43—21no—
346C2×C8×C43—21no—
347C4⋊C4×C43—21no—
348C4⋊C4×C43—21no—
349C4⋊C4×C43—21no—
350C4⋊C4×C43—21no—
351C22⋊C4×C43—81no—
352C22⋊Dic43—81no—
353(C2×D43)⋊C4—42no—
354(C2×D43)⋊C4—81no—
355(C2×D43)⋊C4—81no—
356C4⋊Dic43—21no—
357C4⋊Dic43—21no—
358C4⋊Dic43—21no—
359C4⋊Dic43—21no—
360Dic43⋊C4—42no—
361C4×Dic43—42no—
362C2×C43⋊C8—21no—
363C2×C43⋊C8—21no—
364C2×C43⋊C8—21no—
365C2×C43⋊C8—21no—
366C2×C43⋊C8—21no—
367C2×C43⋊C8—21no—
368#10621872—44no—
369C8×D43—44no—
370C23×C43—22no—
371C23×C43—21no—
372C23×C43—21no—
373C23×C43—22no—
374C23×C43—22no—
375C23×C43—21no—
376C23×C43—21no—
377C23×C43—21no—
378C23×C43—21no—
379C23×C43—41no—
380C23×C43—41no—
381C23×C43—41no—
382C23×C43—41no—
383C23×C43C2×C22⋊C412yes—
384C23×C43C22×D411yescharacteristic
385C22×D43—21no—
386C22×D43—21no—
387C22×D43—21no—
388C22×D43—21no—
389C22×D43—21no—
390C22×D43—21no—
391C22×D43—21no—
392C22×D43—21no—
393C22×D43—21no—
394C22×D43—21no—
395C22×D43C2×C22⋊C412yes—
396C22×D43C2×C22⋊C412yes—
397C22×D43#12012yes—
398C22×D43#12012yes—
399Q8×C43—22no—
400Q8×C43—22no—
401Q8×C43—22no—
402Q8×C43C2×C22⋊C414yes—
403D4×C43—216no—
404D4×C43—22no—
405D4×C43—22no—
406D4×C43—22no—
407D4×C43C2×C22⋊C414yes—
408C2×C4×C43—216no—
409C2×C4×C43—22no—
410C2×C4×C43—21no—
411C2×C4×C43—21no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43C2×C22⋊C412yes—
425C2×C4×C43C23×C411yescharacteristic
426C2×C4×C43C22×D411yescharacteristic
427C2×C4×C43C22×D411yescharacteristic
428C2×C4×C43C22×D411yescharacteristic
429C2×C4×C43C22×D411yescharacteristic
430C2×C4×C43C22×D411yescharacteristic
431C22⋊D43—216no—
432C22⋊D43—28no—
433C22⋊D43—216no—
434C22⋊D43—28no—
435C2×Dic43—216no—
436C2×Dic43—216no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—21no—
440C2×Dic43—21no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—216no—
446C2×Dic43—41no—
447C2×Dic43—41no—
448C2×Dic43—41no—
449C2×Dic43—41no—
450C2×Dic43—41no—
451C2×Dic43—41no—
452C2×Dic43C2×C22⋊C412yes—
453C2×Dic43C2×C22⋊C412yes—
454C2×Dic43#12012yes—
455C2×Dic43#12012yes—
456D172—28no—
457C4×D43—216no—
458C4×D43—216no—
459C4×D43—22no—
460C4×D43—22no—
461C4×D43—22no—
462C4×D43—22no—
463C4×D43—84no—
464C4×D43C2×C22⋊C414yes—
465C4×D43C2×C22⋊C414yes—
466C4×D43#12014yes—
467C4×D43#12014yes—
468Dic86—216no—
469Dic86—216no—
470Dic86—22no—
471Dic86—22no—
472Dic86—22no—
473Dic86—22no—
474Dic86—22no—
475Dic86—22no—
476Dic86—28no—
477Dic86—216no—
478Dic86C2×C22⋊C414yes—
479Dic86C2×C22⋊C414yes—
480C8×C43—41no—
481C8×C43—41no—
482C43⋊C8—41no—
483C43⋊C8—41no—
484#20603—431nomaximal, Sylow
485C22×C43—22no—
486C22×C43—22no—
487C22×C43—24no—
488C22×C43—22no—
489C22×C43—42no—
490C22×C43—42no—
491C22×C43—41no—
492C22×C43—42no—
493C22×C43—41no—
494C22×C43—42no—
495C22×C43—41no—
496C22×C43—41no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43C22×C22⋊C411yescharacteristic
500C22×C43C2×#12011yescharacteristic
501C22×C43C2×#12011yescharacteristic
502C22×C43#57711yescharacteristic
503C22×C43#57711yescharacteristic
504C22×C43#57811yescharacteristic
505C22×C43#57811yescharacteristic
506C2×D43—22no—
507C2×D43—22no—
508C2×D43—22no—
509C2×D43—22no—
510C2×D43—22no—
511C2×D43—22no—
512C2×D43—22no—
513C2×D43—22no—
514C2×D43—22no—
515C2×D43—41no—
516C2×D43—41no—
517C2×D43—41no—
518C2×D43—41no—
519C2×D43#37914yes—
520C4×C43—22no—
521C4×C43—24no—
522C4×C43—81no—
523C4×C43—81no—
524C4×C43C22×C22⋊C411yescharacteristic
525C4×C43C22×C22⋊C411yescharacteristic
526C4×C43C2×#12011yescharacteristic
527C4×C43C2×#12011yescharacteristic
528Dic43—22no—
529Dic43—24no—
530Dic43—24no—
531Dic43—81no—
532Dic43—81no—
533Dic43#37914yes—
534C22×2−1+4—431no—
535C2×#417—431no—
536C2×#419—431no—
537C2×#416—431no—
538C22×#103—431no—
539C2×#408—431no—
540#2311—431no—
541#1788—431no—
542#1788—431no—
543#1788—431no—
544#1788D4311yescharacteristic, complemented
545#1787—431no—
546#1787—431no—
547#1787—431no—
548#1787—431no—
549C2×C43—42no—
550C2×C43—44no—
551C2×C43C2×#37911yescharacteristic
552C2×C43#289811yescharacteristic
553C2×C43#289811yescharacteristic
554C2×C43#301011yescharacteristic
555C2×C43#301111yescharacteristic
556C2×C43#301311yescharacteristic
557C2×C43#301311yescharacteristic
558D43—24no—
559D43—42no—
560C2×2−1+4—438no—
561C2×2−1+4—864no—
562C2×2−1+4—864no—
563C2×2−1+4—864no—
564C2×2−1+4—864no—
565C2×2−1+4—864no—
566C22×#41—431no—
567C22×#41—431no—
568C22×#41—431no—
569C22×#41—861no—
570C22×#41—861no—
571C22×#41—861no—
572C22×#41C2×D4311yescharacteristic
573C23×Q8—431no—
574C23×Q8—431no—
575C23×Q8—431no—
576C23×Q8—861no—
577C22×M16—431no—
578C23×C8—431no—
579C2×#117—431no—
580C22×C4⋊C4—431no—
581#419—864no—
582#417—864no—
583#416—864no—
584C2×#103—431no—
585C2×#103—431no—
586C2×#103—431no—
587C2×#103—431no—
588C2×#103—431no—
589C2×#103—431no—
590C2×#103—431no—
591C2×#103—431no—
592C2×#103—431no—
593C2×#103—431no—
594C2×#103—864no—
595C2×#103C2×D4311yescharacteristic
596C2×#103C2×D4311yescharacteristic
597C2×#102—431no—
598C2×#102—431no—
599C2×#102C2×D4311yescharacteristic
600C2×#102C2×D4311yescharacteristic
601#408—864no—
602C2×C22⋊C8—431no—
603C2×C22⋊C8—431no—
604C2×C22⋊C8—431no—
605C2×C22⋊C8C2×D4311yescharacteristic
606#391—861no—
607#390—861no—
608#386—861no—
609#386—861no—
610#380—431no—
611#380—431no—
612#380—431no—
613#380C2×D4311yescharacteristic
614C43#2060311yescharacteristic, complemented, Sylow
6152−1+4—8632no—
6162−1+4—8632no—
6172−1+4—8632no—
6182−1+4—8632no—
619C2×#41—22no—
620C2×#41—22no—
621C2×#41—22no—
622C2×#41—22no—
623C2×#41—22no—
624C2×#41—434no—
625C2×#41—434no—
626C2×#41—434no—
627C2×#41—434no—
628C2×#41—434no—
629C2×#41—434no—
630C2×#41—862no—
631C2×#41—862no—
632C2×#41—862no—
633C2×#41—862no—
634C2×#41—868no—
635C2×#41—868no—
636C2×#41—868no—
637C2×#41—862no—
638C2×#41—862no—
639C2×#41—862no—
640C2×#41—862no—
641C2×#41—868no—
642C2×#41—868no—
643C2×#41—862no—
644C2×#41—862no—
645C2×#41—868no—
646C2×#41—868no—
647C2×#41—868no—
648C2×#41—868no—
649C2×#41—862no—
650C2×#41—862no—
651C2×#41C4×D4314yescomplemented
652C22×Q8—431no—
653C22×Q8—434no—
654C22×Q8—434no—
655C22×Q8—434no—
656C22×Q8—434no—
657C22×Q8—434no—
658C22×Q8—431no—
659C22×Q8—431no—
660C22×Q8—861no—
661C22×Q8—861no—
662C22×Q8—862no—
663C22×Q8—862no—
664C22×Q8—862no—
665C22×Q8—862no—
666C22×Q8—868no—
667C22×Q8—868no—
668C22×Q8—868no—
669C22×Q8—862no—
670C22×Q8—862no—
671C22×Q8—862no—
672C22×Q8—862no—
673C22×Q8—862no—
674C22×Q8—862no—
675C22×Q8—862no—
676C22×Q8—862no—
677C22×Q8—861no—
678C22×Q8—862no—
679C22×Q8C22×D4311yescharacteristic
680C22×D4—21no—
681C22×D4—431no—
682C22×D4—431no—
683C22×D4—431no—
684C22×D4—861no—
685C22×D4—861no—
686C22×D4C22×D4311yescharacteristic
687C23×C4—21no—
688C23×C4—431no—
689C23×C4—431no—
690C23×C4—861no—
691C23×C4—861no—
692C23×C4—861no—
693C23×C4—861no—
694C23×C4—861no—
695C23×C4—861no—
696C23×C4C22×D4311yescharacteristic
697C2×M16—862no—
698C2×M16—862no—
699C2×M16—862no—
700C22×C8—431no—
701C22×C8—431no—
702C22×C8—862no—
703C22×C8—862no—
704C22×C8—862no—
705C22×C8C22×D4311yescharacteristic
706C22×C8C22×D4311yescharacteristic
707#117—862no—
708#117—862no—
709C2×C4⋊C4—431no—
710C2×C4⋊C4—431no—
711C2×C4⋊C4—862no—
712C2×C4⋊C4—862no—
713C2×C4⋊C4—861no—
714C2×C4⋊C4C22×D4311yescharacteristic
715C2×C4⋊C4C22×D4311yescharacteristic
716C2×C22⋊C4—21no—
717C2×C22⋊C4—861no—
718C2×C22⋊C4—861no—
719C2×C22⋊C4—861no—
720C2×C22⋊C4—861no—
721C2×C42—861no—
722#103—22no—
723#103—22no—
724#103—862no—
725#103—862no—
726#103—862no—
727#103—862no—
728#103—862no—
729#103—862no—
730#103—862no—
731#103—862no—
732#103—862no—
733#103—862no—
734#102—22no—
735#102—22no—
736#102—862no—
737#102—862no—
738C22⋊C8—22no—
739C22⋊C8—862no—
740C22⋊C8—862no—
741C22⋊C8—862no—
742#95—21no—
743#95—861no—
744#95—861no—
745#95—861no—
746C24—21no—
747C24—431no—
748C24—431no—
749C24D4×D4311yescharacteristic
750#41—28no—
751#41—28no—
752#41—28no—
753#41—28no—
754#41—4316no—
755#41—868no—
756#41—868no—
757#41—868no—
758#41—868no—
759#41—8664no—
760#41—868no—
761#41—868no—
762#41—868no—
763#41—868no—
764#41—8664no—
765#41—8664no—
766#41—868no—
767#41—868no—
768#41—868no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—434no—
773C2×Q8—4316no—
774C2×Q8—432no—
775C2×Q8—432no—
776C2×Q8—432no—
777C2×Q8—432no—
778C2×Q8—432no—
779C2×Q8—432no—
780C2×Q8—864no—
781C2×Q8—864no—
782C2×Q8—862no—
783C2×Q8—862no—
784C2×Q8—864no—
785C2×Q8—864no—
786C2×Q8—868no—
787C2×Q8—868no—
788C2×Q8—864no—
789C2×Q8—864no—
790C2×Q8—864no—
791C2×Q8—864no—
792C2×Q8—8664no—
793C2×Q8—868no—
794C2×Q8—868no—
795C2×Q8—868no—
796C2×Q8—868no—
797C2×Q8—868no—
798C2×Q8—868no—
799C2×Q8—868no—
800C2×Q8—868no—
801C2×Q8—868no—
802C2×Q8—864no—
803C2×Q8—861no—
804C2×Q8—861no—
805C2×Q8—861no—
806C2×Q8—861no—
807C2×Q8—861no—
808C2×Q8—861no—
809C2×Q8C2×C4×D4312yes—
810C2×Q8D4×D4312yes—
811C2×Q8D4×D4312yes—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—434no—
819C2×D4—434no—
820C2×D4—434no—
821C2×D4—862no—
822C2×D4—862no—
823C2×D4—862no—
824C2×D4—862no—
825C2×D4—862no—
826C2×D4—862no—
827C2×D4—864no—
828C2×D4—864no—
829C2×D4—864no—
830C2×D4—864no—
831C2×D4—864no—
832C2×D4—864no—
833C2×D4C2×C4×D4312yes—
834C2×D4D4×D4312yes—
835C2×D4D4×D4312yes—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—21no—
839C22×C4—24no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—431no—
847C22×C4—432no—
848C22×C4—432no—
849C22×C4—432no—
850C22×C4—432no—
851C22×C4—432no—
852C22×C4—432no—
853C22×C4—431no—
854C22×C4—432no—
855C22×C4—432no—
856C22×C4—864no—
857C22×C4—864no—
858C22×C4—864no—
859C22×C4—864no—
860C22×C4—864no—
861C22×C4—864no—
862C22×C4—864no—
863C22×C4—864no—
864C22×C4—864no—
865C22×C4—864no—
866C22×C4—864no—
867C22×C4—864no—
868C22×C4—864no—
869C22×C4—864no—
870C22×C4—864no—
871C22×C4—861no—
872C22×C4—861no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—3441no—
880C22×C4—3441no—
881C22×C4—1722no—
882C22×C4C2×C4×D4312yes—
883C22×C4D4×D4311yescharacteristic
884C22×C4D4×D4312yes—
885C22×C4C23×D4311yescharacteristic
886M16—1724no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—861no—
894C2×C8—861no—
895C2×C8—861no—
896C2×C8—861no—
897C2×C8—861no—
898C2×C8—861no—
899C2×C8—1724no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—861no—
905C4⋊C4—861no—
906C4⋊C4—861no—
907C4⋊C4—861no—
908C4⋊C4—1722no—
909C22⋊C4—81no—
910C22⋊C4—3441no—
911C22⋊C4—3441no—
912C22⋊C4—3441no—
913C22⋊C4—1722no—
914C42—1722no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—432no—
929C23—432no—
930C23—432no—
931C23—432no—
932C23—861no—
933C23—861no—
934C23—861no—
935C23—861no—
936C23—861no—
937C23—861no—
938C23—861no—
939C23—861no—
940C23—861no—
941C23—861no—
942C23C22⋊C4×D4312yes—
943C23C2×D4×D4311yescharacteristic
944Q8—22no—
945Q8—22no—
946Q8—22no—
947Q8—434no—
948Q8—434no—
949Q8—868no—
950Q8—8616no—
951Q8—8616no—
952Q8—8616no—
953Q8—862no—
954Q8—862no—
955Q8—862no—
956Q8—862no—
957Q8—862no—
958Q8—862no—
959Q8C22⋊C4×D4314yes—
960D4—216no—
961D4—22no—
962D4—22no—
963D4—22no—
964D4—868no—
965D4—868no—
966D4—868no—
967D4—8616no—
968D4—8616no—
969D4C22⋊C4×D4314yes—
970C2×C4—216no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—432no—
987C2×C4—432no—
988C2×C4—432no—
989C2×C4—434no—
990C2×C4—434no—
991C2×C4—434no—
992C2×C4—434no—
993C2×C4—432no—
994C2×C4—8616no—
995C2×C4—8616no—
996C2×C4—8616no—
997C2×C4—8616no—
998C2×C4—8616no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—861no—
1002C2×C4—861no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—862no—
1011C2×C4—3444no—
1012C2×C4—1721no—
1013C2×C4—1721no—
1014C2×C4—1721no—
1015C2×C4—1721no—
1016C2×C4—1721no—
1017C2×C4—1721no—
1018C2×C4C22⋊C4×D4312yes—
1019C2×C4C22×C4×D4311yescharacteristic
1020C2×C4C2×D4×D4311yescharacteristic
1021C2×C4C2×D4×D4311yescharacteristic
1022C2×C4C2×D4×D4311yescharacteristic
1023C2×C4C2×D4×D4311yescharacteristic
1024C2×C4C2×D4×D4311yescharacteristic
1025C8—41no—
1026C8—41no—
1027C8—1721no—
1028C8—1721no—
1029C22—22no—
1030C22—24no—
1031C22—22no—
1032C22—22no—
1033C22—41no—
1034C22—42no—
1035C22—41no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—41no—
1040C22—42no—
1041C22—41no—
1042C22—42no—
1043C22—434no—
1044C22—862no—
1045C22—862no—
1046C22—862no—
1047C22—862no—
1048C22—862no—
1049C22—862no—
1050C22—862no—
1051C22—862no—
1052C22—862no—
1053C22—1721no—
1054C22—1721no—
1055C22—1721no—
1056C22—1721no—
1057C22C2×C22⋊C4×D4311yescharacteristic
1058C22#120×D4311yescharacteristic
1059C22#120×D4311yescharacteristic
1060C22#1458370611yescharacteristic
1061C22#1458370911yescharacteristic
1062C22#1458371311yescharacteristic
1063C22#1458371511yescharacteristic
1064C4—22no—
1065C4—24no—
1066C4—81no—
1067C4—81no—
1068C4—434no—
1069C4—862no—
1070C4—864no—
1071C4—864no—
1072C4—3441no—
1073C4—3441no—
1074C4C2×C22⋊C4×D4311yescharacteristic
1075C4C2×C22⋊C4×D4311yescharacteristic
1076C4#120×D4311yescharacteristic
1077C4#120×D4311yescharacteristic
1078C2—42no—
1079C2—44no—
1080C2—864no—
1081C2—1722no—
1082C2#379×D4311yescharacteristic
1083C2#1914312411yescharacteristic
1084C2#1914312611yescharacteristic
1085C2#1914387811yescharacteristic
1086C2#1914388711yescharacteristic
1087C2#1914390811yescharacteristic
1088C2#1914391411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC22×#13063372C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#20603
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582897C2semidirect
3. C2×#14582906C2semidirect
4. C2×#14582892C2semidirect
5. C2×#103×D43C2semidirect
6. C2×#14582864C2semidirect
7. #19137184C2semidirect
8. #19134535C2semidirect
9. #19134532C2semidirect
10. #19134532C2semidirect
11. #19134531C2semidirect
12. #19134529C2semidirect
13. #19134528C2semidirect
14. #19134528C2semidirect
15. C43×#1788C2semidirect
21. C2×#13063372C4semidirect
98. C2×#10621900C2×C4semidirect
112. C22×Dic86C2×C4semidirect
125. C2×Q8×D43C2×C4semidirect
184. C2×#41×C43C2×C4semidirect
272. Q8×D43C22⋊C4semidirect
282. #10621900C22⋊C4semidirect
544. #1788D43semidirect
614. C43#20603semidirect
651. C2×#41C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633722
C2×#145828972
C2×#145829062
C2×#145828922
C2×#103×D432
C2×#145828642
#191371842
#191345352
#191345322
#191345312
#191345292
#191345282
C43×#17882
#2060343