Finite Group Databasebeta

← #25112199

Subgroups — #25112199

Order 11008.

1606 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×#14583545C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic, complemented
3C2×#14582905C211yesmaximal, characteristic, complemented
4#19137524C211yesmaximal, characteristic, complemented
5#19135525C211yesmaximal, characteristic, complemented
6#19135406C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135028C211yesmaximal, characteristic, complemented
9#19134910C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134606C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134527C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C2×C43×#436C211yesmaximal, 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×#13063284C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic, complemented
29C2×C22⋊C4×D43—21no—
30#14582905—24no—
31#14582901—24no—
32C2×#13063250C2211yescharacteristic, complemented
33C2×#13063250C2211yescharacteristic, complemented
34C2×#13063250C2211yescharacteristic, complemented
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44#14582792—21no—
45#14582785—21no—
46#14582779—21no—
47#14582765C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic
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
57C22×M16×C43C2211yescharacteristic, complemented
58C2×C4×D4×C43C2211yescharacteristic
59C43×#436—24no—
60C2×C4⋊C8×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C2×C4×C8×C43C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—41no—
69C2×#10621898—41no—
70C2×#10621898C2×C414yes—
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—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86#13063313—22no—
87#13063313C2×C414yescomplemented
88#13063310—28no—
89#13063304—22no—
90#13063304C2×C414yescomplemented
91#13063299—22no—
92#13063299C2×C414yes—
93#13063298—28no—
94#13063293—28no—
95C4×D172—22no—
96C4×D172C2×C414yescomplemented
97#13063284—22no—
98#13063284—41no—
99C2×C4⋊Dic43—22no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—41no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C22⋊C4×D43—28no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119#13063250—22no—
120#13063250—22no—
121#13063250—41no—
122#13063250—41no—
123#13063247—22no—
124#13063247—22no—
125#13063247—22no—
126#13063247—22no—
127#13063247—22no—
128#13063247—41no—
129#13063247—41no—
130#13063247D414yescomplemented
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C22×D4×C43D411yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×M16×C43—22no—
140C2×M16×C43—22no—
141C2×M16×C43—22no—
142C2×M16×C43—22no—
143C2×M16×C43—41no—
144C2×M16×C43—41no—
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C4×D4×C43C2×C414yes—
150C4×D4×C43D414yes—
151C2×C4⋊C4×C43D411yescharacteristic
152C2×C22⋊C4×C43D411yescharacteristic
153C2×C22⋊C4×C43D411yescharacteristic
154C2×C42×C43C2311yescharacteristic
155C4⋊C8×C43—22no—
156C22⋊C8×C43—22no—
157C22⋊C8×C43—22no—
158C4×C8×C43—22no—
159C24×C43C2×D411yescharacteristic
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—24no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—42no—
168C23×D43—81no—
169C23×D43—81no—
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43C22⋊C414yes—
173C22×C4×C43—21no—
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×C43C22×C412yes—
182C22×C4×C43C22×C412yes—
183C22×C4×C43C2×D412yes—
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—42no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—81no—
195C2×C22⋊D43—81no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—42no—
203C22×Dic43—42no—
204C22×Dic43—81no—
205#10621898—28no—
206#10621898—44no—
207#10621898—44no—
208#10621898—44no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—24no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—28no—
219C2×D172—42no—
220C2×D172—42no—
221C2×D172—44no—
222C2×D172—44no—
223C2×D172—44no—
224C2×D172C22×C412yes—
225C2×D172C22×C412yes—
226C2×D172C2×D412yes—
227C2×D172#4112yes—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—81no—
233C2×C4×D43—81no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240M16×C43—44no—
241M16×C43—44no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
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×C43C2×D412yes—
254C4⋊C4×C43C22⋊C414yes—
255C22⋊C4×C43C22⋊C414yes—
256C22⋊C4×C43C22⋊C414yes—
257C42×C43C22×C412yes—
258C42×C43C2×D412yes—
259C22⋊Dic43—24no—
260C22⋊Dic43—42no—
261C22⋊Dic43—42no—
262C22⋊Dic43—81no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—42no—
276C4⋊Dic43C22×C412yes—
277C4⋊Dic43C2×D412yes—
278Dic43⋊C4—24no—
279C4×Dic43—42no—
280C4×Dic43—81no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43C2×C22⋊C412yes—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—48no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—48no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43—84no—
317D4×C43—44no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43C2×C22⋊C412yes—
335C2×C4×C43C2×C22⋊C412yes—
336C2×C4×C43C2×C22⋊C412yes—
337C2×C4×C43C2×C22⋊C412yes—
338C2×C4×C43C23×C411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C22⋊D43—48no—
345C22⋊D43—84no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—41no—
350C2×Dic43—41no—
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×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—84no—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—22no—
370D172—48no—
371D172—41no—
372D172—41no—
373D172C4×D414yes—
374C4×D43—48no—
375C4×D43—84no—
376Dic86—22no—
377Dic86—22no—
378Dic86—41no—
379Dic86—41no—
380C8×C43—22no—
381C8×C43—41no—
382C8×C43—41no—
383C8×C43—41no—
384#22427—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43C22×C22⋊C411yescharacteristic
400C22×C43D4211yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43#57511yescharacteristic
403C22×C43#57511yescharacteristic
404C22×C43#57611yescharacteristic
405C22×C43#57711yescharacteristic
406C2×D43—24no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—816no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43—81no—
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—22no—
424C4×C43—22no—
425C4×C43C2×C4×D411yescharacteristic
426C4×C43#51811yescharacteristic
427C4×C43D4211yescharacteristic
428C4×C43#54611yescharacteristic
429Dic43—42no—
430Dic43—42no—
431Dic43—42no—
432Dic43—81no—
433Dic43—81no—
434Dic43—81no—
435C2×#546—431no—
436C2×#436D4311yescharacteristic, complemented
437C2×#417—431no—
438C2×#418—431no—
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1895—431no—
443#1894—431no—
444#1874—431no—
445#1873—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—42no—
451C2×C43—42no—
452C2×C43D4×C22⋊C411yescharacteristic
453C2×C43#289611yescharacteristic
454C2×C43#289711yescharacteristic
455C2×C43#327311yescharacteristic
456C2×C43#327511yescharacteristic
457C2×C43#332211yescharacteristic
458C2×C43#332311yescharacteristic
459D43—44no—
460D43—82no—
461C22×#41—431no—
462C23×D4—431no—
463C22×M16C2×D4311yescharacteristic
464C22×M16C2×D4311yescharacteristic, complemented
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—
478#436—24no—
479C2×C4⋊C8C2×D4311yescharacteristic, complemented
480#418—864no—
481#417—864no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102—431no—
493C2×#102—431no—
494C2×C22⋊C8C2×D4311yescharacteristic
495C2×C22⋊C8C2×D4311yescharacteristic, complemented
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⋊C4—431no—
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340—431no—
508#340—431no—
509C43#2242711yescharacteristic, 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—862no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4—862no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4D17211yescharacteristic
530C23×C4—861no—
531C23×C4—861no—
532C23×C4—861no—
533C23×C4C22×D4311yescharacteristic
534C23×C4C22×D4311yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8C22×D4311yescharacteristic
542C22×C8C22×D4311yescharacteristic
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—862no—
552#121—868no—
553#120—868no—
554C4×D4—434no—
555C4×D4—862no—
556C4×D4C4×D4314yes—
557C4×D4C22⋊D4314yes—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—862no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4—1721no—
569C2×C4⋊C4D17211yescharacteristic
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—868no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4D17211yescharacteristic
580C2×C22⋊C4D17211yescharacteristic
581C2×C42—861no—
582C2×C42—861no—
583C2×C42C22×D4311yescharacteristic
584C4⋊C8—22no—
585#103—862no—
586#103—862no—
587#103—1721no—
588#103—1721no—
589#102—434no—
590#102—862no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—1721no—
596#102—1721no—
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—861no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—861no—
606C24—864no—
607C24—861no—
608C24—3441no—
609C24—3441no—
610C24—1722no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24C2×D17211yescharacteristic
615C24C2×D17211yescharacteristic
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—41no—
627C2×D4—41no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—432no—
631C2×D4—432no—
632C2×D4—868no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—3441no—
645C2×D4—3441no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4—1724no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4—1722no—
653C2×D4(C2×D43)⋊C414yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—864no—
666C22×C4—864no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—3441no—
671C22×C4—3441no—
672C22×C4—3441no—
673C22×C4—1722no—
674C22×C4—1722no—
675C22×C4—1722no—
676C22×C4—1722no—
677C22×C4C2×C4×D4312yes—
678C22×C4C2×C4×D4312yes—
679C22×C4C2×D17211yescharacteristic
680C22×C4C2×D17211yescharacteristic
681C22×C4C2×D17211yescharacteristic
682C22×C4C2×D17211yescharacteristic
683C22×C4C2×C22⋊D4312yes—
684C22×C4C2×C22⋊D4312yes—
685C22×C4C23×D4311yescharacteristic
686M16—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8D4×D4312yes—
700C4⋊C4—432no—
701C4⋊C4—432no—
702C4⋊C4—864no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—1722no—
712C4⋊C4(C2×D43)⋊C414yes—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—3441no—
719C22⋊C4—1722no—
720C22⋊C4—1722no—
721C22⋊C4(C2×D43)⋊C414yes—
722C22⋊C4(C2×D43)⋊C414yes—
723C42—3441no—
724C42—1722no—
725C42C2×C4×D4312yes—
726C42C2×C22⋊D4312yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—862no—
743C23—3444no—
744C23—3444no—
745C23—3444no—
746C23—3444no—
747C23—3444no—
748C23—1728no—
749C23—1728no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23C2×(C2×D43)⋊C412yes—
761C23C2×(C2×D43)⋊C412yes—
762C23C22×D17211yescharacteristic
763Q8—862no—
764Q8—862no—
765Q8—1721no—
766Q8—1721no—
767D4—44no—
768D4—434no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—862no—
774D4—3444no—
775D4—1728no—
776D4—1728no—
777D4—1721no—
778D4—1721no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—3444no—
799C2×C4—3444no—
800C2×C4—1728no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4C2×(C2×D43)⋊C412yes—
817C2×C4C2×(C2×D43)⋊C412yes—
818C2×C4C2×(C2×D43)⋊C412yes—
819C2×C4C2×(C2×D43)⋊C412yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C22×C22⋊D4311yescharacteristic
823C2×C4#41×D4311yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337111yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—864no—
845C22—34416no—
846C22—3441no—
847C22—3441no—
848C22—3441no—
849C22—3441no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22C22×(C2×D43)⋊C411yescharacteristic
860C22D4×D17211yescharacteristic
861C22#1458354411yescharacteristic
862C22#1458369911yescharacteristic
863C22#1458369911yescharacteristic
864C22#1458370411yescharacteristic
865C22#1458371111yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—3441no—
871C4—3441no—
872C4—3441no—
873C4—1722no—
874C4—1722no—
875C4—1722no—
876C4C4×D4×D4311yescharacteristic
877C4#1458337111yescharacteristic
878C4D4×C22⋊D4311yescharacteristic
879C4#1458353711yescharacteristic
880C2—42no—
881C2—42no—
882C2—3442no—
883C2—1724no—
884C2D4×(C2×D43)⋊C411yescharacteristic
885C2#1914311511yescharacteristic
886C2#1914312211yescharacteristic
887C2#1914620711yescharacteristic
888C2#1914623111yescharacteristic
889C2#1914679811yescharacteristic
890C2#1914681311yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#436C2
socleC23×C43C22×D4
prime radicalC2×#14583545C2
cosocleC22×C4×C43C24
hypercenterC2×#436D43
hypocenterC43#22427
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#14582901C2semidirect
3. C2×#14582905C2semidirect
4. #19137524C2semidirect
5. #19135525C2semidirect
6. #19135406C2semidirect
7. #19135033C2semidirect
8. #19135028C2semidirect
9. #19134910C2semidirect
10. #19134905C2semidirect
11. #19134606C2semidirect
12. #19134536C2semidirect
13. #19134527C2semidirect
14. C4×#13063247C2semidirect
15. C2×C43×#436C2semidirect
19. #14583545C4semidirect
28. C22×C4⋊Dic43C22semidirect
32. C2×#13063250C22semidirect
33. C2×#13063250C22semidirect
34. C2×#13063250C22semidirect
35. C2×#13063250C22semidirect
47. #14582765C22semidirect
49. #14582759C22semidirect
50. C4×C4⋊Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582662C22semidirect
57. C22×M16×C43C22semidirect
60. C2×C4⋊C8×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C2×C4×C8×C43C22semidirect
78. C22×D172C2×C4semidirect
87. #13063313C2×C4semidirect
90. #13063304C2×C4semidirect
96. C4×D172C2×C4semidirect
130. #13063247D4semidirect
436. C2×#436D43semidirect
464. C22×M16C2×D43semidirect
479. C2×C4⋊C8C2×D43semidirect
495. C2×C22⋊C8C2×D43semidirect
496. C2×C4×C8C2×D43semidirect
509. C43#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#145835452
C2×#145829012
C2×#145829052
#191375242
#191355252
#191354062
#191350332
#191350282
#191349102
#191349052
#191346062
#191345362
#191345272
C4×#130632472
C2×C43×#4362
#2242743