Finite Group Databasebeta

← #25112079

Subgroups — #25112079

Order 11008.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583545C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic, complemented
3C22×#13063247C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic43C211yesmaximal, characteristic, complemented
5#19135525C211yesmaximal, characteristic, complemented
6#19135411C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135018C211yesmaximal, characteristic, complemented
9#19134910C211yesmaximal, characteristic, complemented
10#19134900C211yesmaximal, characteristic, complemented
11#19134596C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134527C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×D172C2211yescharacteristic
18#14583545—24no—
19#14583545C418yescomplemented
20C2×#13063313C2211yescharacteristic
21C2×#13063310—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063298—21no—
25C2×#13063293—21no—
26C2×C4×D172C2211yescharacteristic
27C2×D4×Dic43—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic, complemented
30C2×C22⋊C4×D43—21no—
31#14582901—24no—
32C2×#13063250C2211yescharacteristic, complemented
33C2×#13063250C2211yescharacteristic, complemented
34C2×#13063250C2211yescharacteristic, complemented
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063247—24no—
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45#14582798—21no—
46#14582774—21no—
47#14582774—21no—
48#14582769C2211yescharacteristic, complemented
49#14582759C2211yescharacteristic
50#14582759C2211yescharacteristic, complemented
51C4×C4⋊Dic43C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582662C2211yescharacteristic, complemented
56C22×M16×C43C2211yescharacteristic, complemented
57C23×C8×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C43×#435—24no—
60C2×C4⋊C8×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C2×#97×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—41no—
69C2×#10621898—41no—
70C2×#10621898C2×C414yescomplemented
71C22×Dic86C2311yescharacteristic
72C22×D172—22no—
73C22×D172—22no—
74C22×D172—21no—
75C22×D172—22no—
76C22×D172—41no—
77C22×D172—41no—
78C22×D172C2×C414yescomplemented
79C22×D172C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87#13063313—22no—
88#13063313C2×C414yescomplemented
89#13063310—28no—
90#13063304—22no—
91#13063304C2×C414yescomplemented
92#13063299—22no—
93#13063299C2×C414yescomplemented
94#13063298—28no—
95#13063293—28no—
96C4×D172—22no—
97C4×D172C2×C414yescomplemented
98D4×Dic43—44no—
99C2×C4⋊Dic43—22no—
100C2×C4⋊Dic43—22no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43—41no—
106C2×C4⋊Dic43—41no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
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×(C2×D43)⋊C4—21no—
120C22⋊C4×D43—28no—
121C2×C4×Dic43—21no—
122#13063250—22no—
123#13063250—22no—
124#13063250—41no—
125#13063250—41no—
126#13063247—22no—
127#13063247—22no—
128#13063247—22no—
129#13063247—22no—
130#13063247—22no—
131#13063247—41no—
132#13063247—41no—
133#13063247D414yescomplemented
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C22×D4×C43D411yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C2×M16×C43—22no—
141C2×M16×C43—22no—
142C2×M16×C43—41no—
143C22×C8×C43—22no—
144C22×C8×C43—22no—
145C22×C8×C43—41no—
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C4×D4×C43C2×C414yes—
151C4×D4×C43D414yes—
152C2×C4⋊C4×C43D411yescharacteristic
153C2×C22⋊C4×C43D411yescharacteristic
154C2×C22⋊C4×C43D411yescharacteristic
155C2×C42×C43C2311yescharacteristic
156C4⋊C8×C43—22no—
157C22⋊C8×C43—22no—
158C22⋊C8×C43—22no—
159#97×C43—22no—
160C24×C43C2×D411yescharacteristic
161C24×C43C2×D411yescharacteristic
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—24no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—42no—
168C23×D43—42no—
169C23×D43—81no—
170C23×D43—81no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43C22⋊C414yes—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43C22×C412yes—
183C22×C4×C43C22×C412yes—
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D412yes—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—24no—
192C2×C22⋊D43—24no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—81no—
196C2×C22⋊D43—81no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43—81no—
208C22×Dic43—81no—
209#10621898—28no—
210#10621898—44no—
211#10621898—44no—
212#10621898—44no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—24no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—28no—
223C2×D172—42no—
224C2×D172—42no—
225C2×D172—44no—
226C2×D172—44no—
227C2×D172—44no—
228C2×D172C22×C412yes—
229C2×D172C22×C412yes—
230C2×D172C2×D412yes—
231C2×D172#4112yes—
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—42no—
235C2×C4×D43—42no—
236C2×C4×D43—81no—
237C2×C4×D43—81no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86C22×C412yes—
244M16×C43—44no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—44no—
257C2×C8×C43C2×D412yes—
258C4⋊C4×C43C22⋊C414yes—
259C22⋊C4×C43C22⋊C414yes—
260C22⋊C4×C43C22⋊C414yes—
261C42×C43C22×C412yes—
262C42×C43C2×D412yes—
263C22⋊Dic43—24no—
264C22⋊Dic43—42no—
265C22⋊Dic43—42no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—42no—
279C4⋊Dic43—42no—
280C4⋊Dic43—42no—
281C4⋊Dic43—81no—
282C4⋊Dic43C22×C412yes—
283C4⋊Dic43C2×D412yes—
284Dic43⋊C4—24no—
285C4×Dic43—42no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43C2×C22⋊C412yes—
297C23×C43C2×C22⋊C412yes—
298C23×C43AGL(1,ℤ/8)12yes—
299C23×C43#13712yes—
300C23×C43C22×D411yescharacteristic
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—48no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315C22×D43—41no—
316C22×D43—48no—
317C22×D43—84no—
318C22×D43—84no—
319C22×D43—84no—
320C22×D43—84no—
321C22×D43—84no—
322D4×C43—28no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43C2×C22⋊C412yes—
340C2×C4×C43C2×C22⋊C412yes—
341C2×C4×C43C2×C22⋊C412yes—
342C2×C4×C43C2×C22⋊C412yes—
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C22⋊D43—48no—
350C22⋊D43—84no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—84no—
370C2×Dic43—84no—
371D172—22no—
372D172—22no—
373D172—22no—
374D172—22no—
375D172—22no—
376D172—48no—
377D172—41no—
378D172—41no—
379D172C4×D414yescomplemented
380C4×D43—48no—
381C4×D43—84no—
382Dic86—22no—
383Dic86—22no—
384Dic86—41no—
385Dic86—41no—
386C8×C43—22no—
387C8×C43—41no—
388C8×C43—41no—
389C8×C43—41no—
390#22419—431nomaximal, Sylow
391C22×C43—22no—
392C22×C43—22no—
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43#41714yescomplemented
405C22×C43C22×C22⋊C411yescharacteristic
406C22×C43D4211yescharacteristic
407C22×C43#54611yescharacteristic
408C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C43C2×#13711yescharacteristic
410C22×C43#57611yescharacteristic
411C22×C43#57711yescharacteristic
412C2×D43—24no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—816no—
423C2×D43—81no—
424C2×D43—81no—
425C2×D43—81no—
426C2×D43—81no—
427C4×C43—22no—
428C4×C43—22no—
429C4×C43—22no—
430C4×C43—22no—
431C4×C43C2×C4×D411yescharacteristic
432C4×C43#51811yescharacteristic
433C4×C43D4211yescharacteristic
434C4×C43#54611yescharacteristic
435Dic43—42no—
436Dic43—42no—
437Dic43—42no—
438Dic43—81no—
439Dic43—81no—
440Dic43—81no—
441C2×#546—431no—
442C2×#435D4311yescharacteristic, complemented
443C2×#417—431no—
444C22×#102—431no—
445D4×C4⋊C4—431no—
446#1983—431no—
447#1959—431no—
448#1895—431no—
449#1892—431no—
450#1874—431no—
451#1872—431no—
452#1802—431no—
453#1788—431no—
454#1786—431no—
455#1762—431no—
456C2×C43—24no—
457C2×C43—42no—
458C2×C43D4×C22⋊C411yescharacteristic
459C2×C43C2×#41711yescharacteristic
460C2×C43#289711yescharacteristic
461C2×C43#326411yescharacteristic
462C2×C43#326611yescharacteristic
463C2×C43#330611yescharacteristic
464C2×C43#331411yescharacteristic
465D43—44no—
466D43—82no—
467C22×#41—431no—
468C23×D4—431no—
469C22×M16C2×D4311yescharacteristic, complemented
470C23×C8C2×D4311yescharacteristic
471#546—438no—
472#546—864no—
473C2×#124—431no—
474C2×#123—861no—
475C2×C22⋊Q8—431no—
476C2×#121—431no—
477C2×#121—861no—
478C2×#120—861no—
479C2×C4×D4—431no—
480C2×C4×D4—861no—
481C2×C4×D4C2×D4311yescharacteristic
482C22×C4⋊C4—431no—
483C22×C4⋊C4—431no—
484C22×C22⋊C4—861no—
485#435—24no—
486C2×C4⋊C8C2×D4311yescharacteristic, complemented
487#417—864no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103—431no—
491C2×#103—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—431no—
496C2×#102—431no—
497C2×#102—431no—
498C2×#102—431no—
499C2×#102—431no—
500C2×#102—864no—
501C2×C22⋊C8C2×D4311yescharacteristic
502C2×C22⋊C8C2×D4311yescharacteristic, complemented
503C2×#97C2×D4311yescharacteristic, complemented
504#389—861no—
505#385—861no—
506#385—861no—
507#384—431no—
508#380—431no—
509#380—431no—
510C4×C4⋊C4—431no—
511#340—431no—
512#340—431no—
513#340—431no—
514#340—431no—
515C43#2241911yescharacteristic, complemented, Sylow
516C25—861no—
517C2×#41—434no—
518C2×#41—862no—
519C2×#41—862no—
520C2×#41—862no—
521C2×#41—1721no—
522C2×#41—1721no—
523C22×Q8—431no—
524C22×D4—434no—
525C22×D4—431no—
526C22×D4—431no—
527C22×D4—862no—
528C22×D4—862no—
529C22×D4—861no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—862no—
533C22×D4—1721no—
534C22×D4—1721no—
535C22×D4D17211yescharacteristic
536C23×C4—861no—
537C23×C4—861no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4C22×D4311yescharacteristic
541C23×C4C22×D4311yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C22×D4311yescharacteristic
549C22×C8C22×D4311yescharacteristic
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#124—434no—
553#124—862no—
554#123—868no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557#121—434no—
558#121—862no—
559#121—868no—
560#120—868no—
561C4×D4—434no—
562C4×D4—862no—
563C4×D4—1724no—
564C4×D4C4×D4314yes—
565C4×D4C22⋊D4314yes—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—862no—
572C2×C4⋊C4—862no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—1721no—
579C2×C4⋊C4—1721no—
580C2×C4⋊C4D17211yescharacteristic
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—868no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4D17211yescharacteristic
590C2×C22⋊C4D17211yescharacteristic
591C2×C42—861no—
592C2×C42C22×D4311yescharacteristic
593C4⋊C8—22no—
594#103—862no—
595#103—862no—
596#103—1721no—
597#103—1721no—
598#102—434no—
599#102—862no—
600#102—862no—
601#102—862no—
602#102—862no—
603#102—862no—
604#102—1721no—
605#102—1721no—
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—861no—
610#95—861no—
611#95—861no—
612C24—861no—
613C24—864no—
614C24—861no—
615C24—3441no—
616C24—3441no—
617C24—1722no—
618C24—1722no—
619C24—1722no—
620C24—1722no—
621C24C2×D17211yescharacteristic
622C24C2×D17211yescharacteristic
623#41—868no—
624#41—1724no—
625#41—1724no—
626#41—1724no—
627C2×Q8—432no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8—861no—
631C2×Q8—861no—
632C2×Q8—861no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—432no—
636C2×D4—432no—
637C2×D4—432no—
638C2×D4—432no—
639C2×D4—868no—
640C2×D4—864no—
641C2×D4—864no—
642C2×D4—864no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—3441no—
652C2×D4—3441no—
653C2×D4—1724no—
654C2×D4—1724no—
655C2×D4—1724no—
656C2×D4—1722no—
657C2×D4—1722no—
658C2×D4—1722no—
659C2×D4—1722no—
660C2×D4(C2×D43)⋊C414yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—864no—
673C22×C4—864no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—3441no—
678C22×C4—3441no—
679C22×C4—3441no—
680C22×C4—3441no—
681C22×C4—1722no—
682C22×C4—1722no—
683C22×C4—1722no—
684C22×C4—1722no—
685C22×C4—1722no—
686C22×C4—1722no—
687C22×C4C2×C4×D4312yes—
688C22×C4C2×C4×D4312yes—
689C22×C4C2×D17211yescharacteristic
690C22×C4C2×D17211yescharacteristic
691C22×C4C2×D17211yescharacteristic
692C22×C4C2×D17211yescharacteristic
693C22×C4C2×C22⋊D4312yes—
694C22×C4C2×C22⋊D4312yes—
695C22×C4C23×D4311yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8D4×D4312yes—
710C4⋊C4—432no—
711C4⋊C4—432no—
712C4⋊C4—864no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—3441no—
722C4⋊C4—1722no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4(C2×D43)⋊C414yes—
726C22⋊C4—864no—
727C22⋊C4—864no—
728C22⋊C4—864no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—1722no—
732C22⋊C4—1722no—
733C22⋊C4(C2×D43)⋊C414yes—
734C22⋊C4(C2×D43)⋊C414yes—
735C42—1722no—
736C42C2×C4×D4312yes—
737C42C2×C22⋊D4312yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—862no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—3444no—
753C23—3444no—
754C23—3444no—
755C23—3444no—
756C23—3444no—
757C23—1728no—
758C23—1728no—
759C23—1721no—
760C23—1721no—
761C23—1721no—
762C23—1721no—
763C23—1721no—
764C23—1721no—
765C23—1721no—
766C23—1721no—
767C23—1721no—
768C23—1721no—
769C23C2×(C2×D43)⋊C412yes—
770C23C2×(C2×D43)⋊C412yes—
771C23#1306335312yes—
772C23#1306335812yes—
773C23C22×D17211yescharacteristic
774Q8—862no—
775Q8—862no—
776Q8—1721no—
777Q8—1721no—
778D4—28no—
779D4—434no—
780D4—862no—
781D4—862no—
782D4—862no—
783D4—862no—
784D4—862no—
785D4—3444no—
786D4—1728no—
787D4—1728no—
788D4—1721no—
789D4—1721no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—3444no—
810C2×C4—3444no—
811C2×C4—3444no—
812C2×C4—1728no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4C2×(C2×D43)⋊C412yes—
829C2×C4C2×(C2×D43)⋊C412yes—
830C2×C4C2×(C2×D43)⋊C412yes—
831C2×C4C2×(C2×D43)⋊C412yes—
832C2×C4C22×C4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C22×C22⋊D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337111yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—864no—
856C22—34416no—
857C22—3441no—
858C22—3441no—
859C22—3441no—
860C22—3441no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1722no—
865C22—1722no—
866C22—1722no—
867C22—1722no—
868C22—1722no—
869C22—1722no—
870C22#1458290114yescomplemented
871C22C22×(C2×D43)⋊C411yescharacteristic
872C22D4×D17211yescharacteristic
873C22#1458354411yescharacteristic
874C22C2×#1306335311yescharacteristic
875C22C2×#1306335811yescharacteristic
876C22#1458370411yescharacteristic
877C22#1458371111yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—3441no—
883C4—3441no—
884C4—3441no—
885C4—1722no—
886C4—1722no—
887C4—1722no—
888C4C4×D4×D4311yescharacteristic
889C4#1458337111yescharacteristic
890C4D4×C22⋊D4311yescharacteristic
891C4#1458353711yescharacteristic
892C2—24no—
893C2—42no—
894C2—3442no—
895C2—1724no—
896C2D4×(C2×D43)⋊C411yescharacteristic
897C2C2×#1458290111yescharacteristic
898C2#1914312211yescharacteristic
899C2#1914608011yescharacteristic
900C2#1914611011yescharacteristic
901C2#1914655811yescharacteristic
902C2#1914667811yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583545C2
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22419
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×#14582901C2semidirect
3. C22×#13063247C2semidirect
4. D4×C4⋊Dic43C2semidirect
5. #19135525C2semidirect
6. #19135411C2semidirect
7. #19135033C2semidirect
8. #19135018C2semidirect
9. #19134910C2semidirect
10. #19134900C2semidirect
11. #19134596C2semidirect
12. #19134536C2semidirect
13. #19134527C2semidirect
14. #19134421C2semidirect
15. C2×C43×#435C2semidirect
19. #14583545C4semidirect
29. C22×C4⋊Dic43C22semidirect
32. C2×#13063250C22semidirect
33. C2×#13063250C22semidirect
34. C2×#13063250C22semidirect
35. C2×#13063250C22semidirect
48. #14582769C22semidirect
50. #14582759C22semidirect
51. C4×C4⋊Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582662C22semidirect
56. C22×M16×C43C22semidirect
60. C2×C4⋊C8×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C2×#97×C43C22semidirect
70. C2×#10621898C2×C4semidirect
78. C22×D172C2×C4semidirect
88. #13063313C2×C4semidirect
91. #13063304C2×C4semidirect
93. #13063299C2×C4semidirect
97. C4×D172C2×C4semidirect
133. #13063247D4semidirect
379. D172C4×D4semidirect
404. C22×C43#417semidirect
442. C2×#435D43semidirect
469. C22×M16C2×D43semidirect
486. C2×C4⋊C8C2×D43semidirect
502. C2×C22⋊C8C2×D43semidirect
503. C2×#97C2×D43semidirect
515. C43#22419semidirect
870. C22#14582901semidirect

Maximal subgroups

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

subgroupindex
C2×#145835452
C2×#145829012
C22×#130632472
D4×C4⋊Dic432
#191355252
#191354112
#191350332
#191350182
#191349102
#191349002
#191345962
#191345362
#191345272
#191344212
C2×C43×#4352
#2241943