Finite Group Databasebeta

← #25112019

Subgroups — #25112019

Order 11008.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583544C211yesmaximal, characteristic
2C2×C8×D172C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137527C211yesmaximal, characteristic, complemented
6#19135527C211yesmaximal, characteristic, complemented
7#19135406C211yesmaximal, characteristic, complemented
8#19135022C211yesmaximal, characteristic, complemented
9#19135017C211yesmaximal, characteristic, complemented
10#19134916C211yesmaximal, characteristic, complemented
11#19134901C211yesmaximal, characteristic, complemented
12#19134605C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#19134524C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic, complemented
20#14583544—24no—
21#14583544C418yescomplemented
22C2×#13063313C2211yescharacteristic
23C2×#13063309—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063300C2211yescharacteristic
26C2×#13063299—21no—
27C2×#13063295—21no—
28C2×C4×D172C2211yescharacteristic
29C2×#13063283C2211yescharacteristic, complemented
30C2×C4⋊C4×D43C2211yescharacteristic
31C22×(C2×D43)⋊C4—21no—
32C8×D172—24no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
34#14582892—24no—
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063250C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
38C2×#13063248C2211yescharacteristic, complemented
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45#102×D43—24no—
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
48#14582790—21no—
49#14582784—21no—
50#14582777—21no—
51#14582765C2211yescharacteristic, complemented
52#14582756C2211yescharacteristic
53#14582756C2211yescharacteristic, complemented
54C4×(C2×D43)⋊C4—21no—
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic, complemented
61C4×C4⋊C4×C43C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—22no—
68C2×#10621900—41no—
69C2×#10621900—41no—
70C2×#10621900C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×D172—21no—
73C22×D172D411yescharacteristic
74C22×D172C2311yescharacteristic
75C22×C22⋊D43—21no—
76C22×C22⋊D43—21no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—22no—
80C2×D4×D43—41no—
81C2×D4×D43—41no—
82C2×D4×D43C2×C414yes—
83C23×Dic43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C2×C8×D43—22no—
90C2×C8×D43—22no—
91C2×C8×D43—22no—
92C2×C8×D43—22no—
93C2×C8×D43—41no—
94C2×C8×D43—41no—
95#13063313—22no—
96#13063313C2×C414yescomplemented
97#13063309—28no—
98#13063305—22no—
99#13063305C2×C414yes—
100#13063300—22no—
101#13063300C2×C414yescomplemented
102#13063299—28no—
103#13063295—28no—
104C4×D172C2×C414yes—
105C4×D172D414yes—
106#13063283—22no—
107#13063283—41no—
108C2×C4⋊Dic43—21no—
109C2×C4⋊Dic43D411yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
113C4⋊C4×D43—22no—
114C4⋊C4×D43—41no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—28no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4D411yescharacteristic
124C2×(C2×D43)⋊C4D411yescharacteristic
125C2×C4×Dic43—21no—
126C4⋊(C43⋊C8)—22no—
127#13063250—22no—
128#13063250—41no—
129#13063248—22no—
130#13063248—41no—
131#13063247—22no—
132#13063247—41no—
133#13063246—22no—
134#13063246—22no—
135#13063245—22no—
136#13063245—41no—
137(C2×D43)⋊C8—22no—
138(C2×D43)⋊C8—22no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C43⋊#95—21no—
142C43⋊#95—21no—
143C22×D4×C43C2311yescharacteristic
144C23×C4×C43—21no—
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C4×D4×C43—22no—
148C4×D4×C43C2×C414yescomplemented
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153C2×C42×C43—21no—
154C2×C42×C43C2311yescharacteristic
155#102×C43—22no—
156#102×C43D414yescomplemented
157C4×C8×C43—22no—
158#95×C43—21no—
159C24×C43—21no—
160C23×D43—21no—
161C23×D43—24no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—81no—
167C23×D43—81no—
168C23×D43C2×D411yescharacteristic
169C23×D43C2×D411yescharacteristic
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43C22×C412yes—
174C2×D4×C43C2×D412yes—
175C2×D4×C43#4112yes—
176C22×C4×C43—24no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—81no—
181C22×C4×C43—81no—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2411yescharacteristic
185C2×C22⋊D43—24no—
186C2×C22⋊D43—24no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C22×Dic43—24no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199#10621900—28no—
200#10621900—44no—
201#10621900—44no—
202#10621900—44no—
203D4×D43—28no—
204D4×D43—44no—
205D4×D43—44no—
206D4×D43—44no—
207C2×D172—21no—
208C2×D172—24no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—81no—
216C2×D172—81no—
217C2×D172C22⋊C414yes—
218C2×D172C22×C412yes—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—81no—
230C2×C4×D43C22×C412yes—
231C2×C4×D43C22×C412yes—
232C2×C4×D43C2×D412yes—
233C2×C4×D43C2×D412yes—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43C2×D412yes—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43C22×C412yes—
251C4⋊C4×C43C2×D412yes—
252C22⋊C4×C43—24no—
253C42×C43—81no—
254C42×C43C22×C412yes—
255C42×C43C2×D412yes—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—42no—
262(C2×D43)⋊C4—81no—
263(C2×D43)⋊C4C22⋊C414yes—
264(C2×D43)⋊C4C22⋊C414yes—
265C4⋊Dic43—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43C22⋊C414yes—
271Dic43⋊C4—42no—
272C4×Dic43—42no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C8×D43—44no—
280C8×D43—44no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43C22×D411yescharacteristic
289C22×D43—21no—
290C22×D43—21no—
291C22×D43—21no—
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—22no—
300C22×D43—48no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—48no—
308C22×D43—84no—
309C22×D43—84no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43C2×C22⋊C412yes—
314C22×D43C2×C22⋊C412yes—
315C22×D43#13512yes—
316C22×D43#13512yes—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43C4×D414yes—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—84no—
335C2×C4×C43C2×C22⋊C412yes—
336C2×C4×C43C2×C22⋊C412yes—
337C2×C4×C43C23×C411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C22⋊D43—48no—
344C22⋊D43—48no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—22no—
350C2×Dic43—48no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43C2×C22⋊C412yes—
360C2×Dic43C2×C22⋊C412yes—
361D172—28no—
362D172—22no—
363D172—22no—
364D172—41no—
365D172—41no—
366D172—84no—
367C4×D43—22no—
368C4×D43—22no—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—84no—
376Dic86—22no—
377Dic86—22no—
378Dic86—41no—
379Dic86—41no—
380C8×C43—22no—
381C8×C43—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22414—431nomaximal, Sylow
385C22×C43—24no—
386C22×C43—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43C22×C22⋊C411yescharacteristic
393C22×C43D4211yescharacteristic
394C22×C43#54611yescharacteristic
395C22×C43C2×#13511yescharacteristic
396C22×C43C2×#13511yescharacteristic
397C22×C43#57611yescharacteristic
398C22×C43#57711yescharacteristic
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—41no—
411C2×D43—41no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—816no—
416C2×D43—81no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43#41614yescomplemented
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—42no—
424C4×C43—42no—
425C4×C43—81no—
426C4×C43C2×C4×D411yescharacteristic
427C4×C43#51811yescharacteristic
428C4×C43D4211yescharacteristic
429C4×C43#54611yescharacteristic
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—81no—
434Dic43—81no—
435C2×#546—431no—
436C2×C8×D4—431no—
437C2×#416—431no—
438C22×#102—431no—
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1893—431no—
443#1892—431no—
444#1875—431no—
445#1872—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102D4311yescharacteristic, complemented
450C2×C43—44no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43C2×#41611yescharacteristic
453C2×C43#289711yescharacteristic
454C2×C43#328011yescharacteristic
455C2×C43#328211yescharacteristic
456C2×C43#329611yescharacteristic
457C2×C43#329711yescharacteristic
458D43—24no—
459D43—42no—
460D43—82no—
461C22×#41—431no—
462C23×D4—431no—
463C23×C8—431no—
464C23×C8—431no—
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×#121—431no—
471C2×#121—861no—
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4C2×D4311yescharacteristic
475C2×#117—431no—
476C22×C4⋊C4—431no—
477C22×C22⋊C4—861no—
478C8×D4—864no—
479C2×C4⋊C8—431no—
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—864no—
492C2×#102C2×D4311yescharacteristic
493C2×#102C2×D4311yescharacteristic
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C4×C8C2×D4311yescharacteristic, complemented
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380—431no—
503C4×C4⋊C4C2×D4311yescharacteristic, complemented
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340C2×D4311yescharacteristic, complemented
508#340C2×D4311yescharacteristic, complemented
509C43#2241411yescharacteristic, complemented, Sylow
510C25—861no—
511C2×#41—434no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8—431no—
518C22×D4—434no—
519C22×D4—431no—
520C22×D4—431no—
521C22×D4—861no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—862no—
525C22×D4—862no—
526C22×D4—861no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4C22×D4311yescharacteristic
530C23×C4—21no—
531C23×C4—431no—
532C23×C4—431no—
533C23×C4—861no—
534C23×C4—861no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—862no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—1721no—
542C22×C8—1721no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—434no—
549C22⋊Q8—862no—
550#121—434no—
551#121—868no—
552#121—862no—
553#120—868no—
554C4×D4—22no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4C4×D4314yescomplemented
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—862no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—1721no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—868no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C42—21no—
582C2×C42—861no—
583C2×C42C22×D4311yescharacteristic
584C4⋊C8—862no—
585#103—862no—
586#103—862no—
587#103—1721no—
588#103—1721no—
589#102—22no—
590#102—862no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—1721no—
595#102—1721no—
596#102D17214yescomplemented
597C22⋊C8—862no—
598C22⋊C8—862no—
599C4×C8—22no—
600#95—21no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—21no—
606C24—431no—
607C24—431no—
608C24—864no—
609C24—861no—
610C24—3441no—
611C24—3441no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615C24—1722no—
616#41—868no—
617#41—1724no—
618#41—1724no—
619#41—1724no—
620C2×Q8—432no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—434no—
630C2×D4—432no—
631C2×D4—862no—
632C2×D4—862no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—868no—
636C2×D4—864no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4C2×C4×D4312yes—
652C2×D4C2×D17212yes—
653C2×D4#1062189812yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—432no—
666C22×C4—864no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—3441no—
679C22×C4—1722no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4—1722no—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4311yescharacteristic
685C22×C4C23×D4311yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—1724no—
698C2×C8—1724no—
699C2×C8C2×D17212yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—434no—
705C4⋊C4—864no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—1722no—
711C4⋊C4C2×C4×D4312yes—
712C4⋊C4C2×D17212yes—
713C22⋊C4—24no—
714C22⋊C4—434no—
715C22⋊C4—434no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—3441no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—81no—
724C42—1722no—
725C42C2×C4×D4312yes—
726C42D4×D4312yes—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—432no—
735C23—432no—
736C23—432no—
737C23—432no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—861no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—861no—
748C23—862no—
749C23—3444no—
750C23—3444no—
751C23—3444no—
752C23—3444no—
753C23—3444no—
754C23—1728no—
755C23—1728no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23—1721no—
762C23C2×D4×D4311yescharacteristic
763Q8—862no—
764Q8—862no—
765Q8—1721no—
766Q8—1721no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—868no—
771D4—862no—
772D4—862no—
773D4—3444no—
774D4—1728no—
775D4—1728no—
776D4—1721no—
777D4—1721no—
778D4C4×D17214yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—84no—
793C2×C4—432no—
794C2×C4—432no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—3444no—
809C2×C4—1728no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4C22⋊C4×D4312yes—
819C2×C4C22⋊C4×D4312yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C22×D17211yescharacteristic
823C2×C4C2×#1062189811yescharacteristic
824C2×C4#1306337111yescharacteristic
825C2×C4#1306337111yescharacteristic
826C8—22no—
827C8—41no—
828C8—1721no—
829C8—1721no—
830C22—24no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—434no—
838C22—862no—
839C22—862no—
840C22—862no—
841C22—862no—
842C22—862no—
843C22—862no—
844C22—862no—
845C22—862no—
846C22—862no—
847C22—34416no—
848C22—3441no—
849C22—3441no—
850C22—3441no—
851C22—3441no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1721no—
856C22—1721no—
857C22—1721no—
858C22—1721no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22D4×D17211yescharacteristic
861C22#1458354511yescharacteristic
862C22#135×D4311yescharacteristic
863C22#135×D4311yescharacteristic
864C22#1458370011yescharacteristic
865C22#1458370511yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—862no—
872C4—862no—
873C4—3441no—
874C4—3441no—
875C4—1722no—
876C4C2×C4×D17211yescharacteristic
877C4#1458337311yescharacteristic
878C4D4×D17211yescharacteristic
879C4#1458354511yescharacteristic
880C2—44no—
881C2—864no—
882C2—3442no—
883C2—1722no—
884C2C22⋊C4×D17211yescharacteristic
885C2#416×D4311yescharacteristic
886C2#1914311611yescharacteristic
887C2#1914628111yescharacteristic
888C2#1914630411yescharacteristic
889C2#1914643511yescharacteristic
890C2#1914645011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583544C2
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43#22414
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×D172C2semidirect
3. C2×#14582892C2semidirect
4. C2×#102×D43C2semidirect
5. #19137527C2semidirect
6. #19135527C2semidirect
7. #19135406C2semidirect
8. #19135022C2semidirect
9. #19135017C2semidirect
10. #19134916C2semidirect
11. #19134901C2semidirect
12. #19134605C2semidirect
13. #19134532C2semidirect
14. #19134524C2semidirect
15. C4×#102×C43C2semidirect
19. C22×C8×D43C22semidirect
21. #14583544C4semidirect
29. C2×#13063283C22semidirect
33. C2×C4⋊(C43⋊C8)C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063248C22semidirect
38. C2×#13063248C22semidirect
47. C2×(C2×D43)⋊C8C22semidirect
51. #14582765C22semidirect
53. #14582756C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
60. C2×C4×C8×C43C22semidirect
61. C4×C4⋊C4×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
70. C2×#10621900C2×C4semidirect
96. #13063313C2×C4semidirect
101. #13063300C2×C4semidirect
148. C4×D4×C43C2×C4semidirect
156. #102×C43D4semidirect
420. C2×D43#416semidirect
449. C4×#102D43semidirect
496. C2×C4×C8C2×D43semidirect
503. C4×C4⋊C4C2×D43semidirect
507. #340C2×D43semidirect
508. #340C2×D43semidirect
509. C43#22414semidirect
557. C4×D4C4×D43semidirect
596. #102D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145835442
C2×C8×D1722
C2×#145828922
C2×#102×D432
#191375272
#191355272
#191354062
#191350222
#191350172
#191349162
#191349012
#191346052
#191345322
#191345242
C4×#102×C432
#2241443