Finite Group Databasebeta

← #25105714

Subgroups — #25105714

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582866C211yesmaximal, characteristic, complemented
2#19137187C211yesmaximal, characteristic, complemented
3#19135034C211yesmaximal, characteristic, complemented
4#19135029C211yesmaximal, characteristic, complemented
5#19135024C211yesmaximal, characteristic, complemented
6#19135019C211yesmaximal, characteristic, complemented
7#19134918C211yesmaximal, characteristic, complemented
8#19134913C211yesmaximal, characteristic, complemented
9#19134908C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134685C211yesmaximal, characteristic, complemented
12#19134681C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#537C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28#14582866—24no—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33#14582806—21no—
34#14582802—21no—
35#14582779—21no—
36#14582779—21no—
37#14582759C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49C22×#41×C43C2211yescharacteristic
50C22×#41×C43C2211yescharacteristic
51C43×#537—24no—
52C43×#537C418yescomplemented
53C2×C22⋊Q8×C43—21no—
54C2×C22⋊Q8×C43C2211yescharacteristic
55C2×C22⋊Q8×C43C2211yescharacteristic
56C2×#121×C43—21no—
57C2×#121×C43—21no—
58C2×#121×C43—21no—
59C2×#121×C43C2211yescharacteristic
60C2×#121×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C23×Dic43—21no—
63C2×#10621877—22no—
64C2×#10621877—41no—
65C2×#10621877—41no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8—41no—
68C22×C43⋊C8—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063284—41no—
74#13063284—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—41no—
77C2×C4⋊Dic43—41no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43—21no—
88#13063249—41no—
89#13063249—41no—
90#13063249—41no—
91#13063249—41no—
92#13063246—41no—
93#13063246—41no—
94#13063246—41no—
95#13063246—41no—
96C22⋊(C43⋊C8)—22no—
97C22⋊(C43⋊C8)—22no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C2×#41×C43—22no—
105C2×#41×C43—41no—
106C2×#41×C43—41no—
107C2×#41×C43—41no—
108C2×#41×C43—41no—
109C2×#41×C43—41no—
110C2×#41×C43—41no—
111C2×#41×C43—41no—
112C2×#41×C43—41no—
113C2×#41×C43C2×C414yes—
114C2×#41×C43C2×C414yescomplemented
115C2×#41×C43D414yes—
116C22×Q8×C43D411yescharacteristic
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43—21no—
119C22×D4×C43—21no—
120C22×D4×C43—21no—
121C22×D4×C43D411yescharacteristic
122C22×D4×C43D411yescharacteristic
123C22×D4×C43D411yescharacteristic
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43—21no—
126C23×C4×C43—21no—
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C22⋊Q8×C43—28no—
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43—22no—
133C22⋊Q8×C43C2×C414yes—
134C22⋊Q8×C43C2×C414yescomplemented
135#121×C43—28no—
136#121×C43—28no—
137#121×C43—28no—
138#121×C43—22no—
139#121×C43—22no—
140#121×C43C2×C414yes—
141#121×C43C2×C414yescomplemented
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43—21no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43C2×C414yescomplemented
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43—21no—
152C2×C22⋊C4×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157#41×C43—44no—
158#41×C43—44no—
159#41×C43—44no—
160#41×C43—44no—
161#41×C43—44no—
162#41×C43—44no—
163#41×C43—44no—
164#41×C43—44no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—41no—
171C2×Q8×C43—41no—
172C2×Q8×C43C22⋊C414yes—
173C2×Q8×C43C22×C412yes—
174C2×D4×C43—21no—
175C2×D4×C43—24no—
176C2×D4×C43—24no—
177C2×D4×C43—24no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—41no—
183C2×D4×C43—41no—
184C2×D4×C43—41no—
185C2×D4×C43—41no—
186C2×D4×C43—41no—
187C2×D4×C43—41no—
188C2×D4×C43—42no—
189C2×D4×C43—42no—
190C2×D4×C43—81no—
191C2×D4×C43—81no—
192C2×D4×C43—81no—
193C2×D4×C43—81no—
194C2×D4×C43C22⋊C414yes—
195C2×D4×C43C22⋊C414yes—
196C2×D4×C43C22⋊C414yes—
197C2×D4×C43C22×C412yes—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—24no—
211C22×C4×C43—24no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—42no—
216C22×C4×C43—42no—
217C22×C4×C43—81no—
218C22×C4×C43—81no—
219C22×C4×C43C22×C412yes—
220C22×C4×C43C22×C412yes—
221C22×C4×C43C22×C412yes—
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2×D412yes—
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—42no—
234C22×Dic43—81no—
235C22×Dic43—81no—
236C4⋊C4×C43—24no—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43C22×C412yes—
242C4⋊C4×C43C22×C412yes—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C22⋊Dic43—42no—
248C22⋊Dic43—81no—
249C22⋊Dic43—81no—
250C22⋊Dic43—81no—
251C22⋊Dic43—81no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—42no—
261C4×Dic43—42no—
262#10621877—44no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—44no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
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×C43—21no—
294C23×C43—22no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43C2×C22⋊C412yes—
302C23×C43C2×C22⋊C412yes—
303C23×C43C2×C22⋊C412yes—
304C23×C43C22×D411yescharacteristic
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—44no—
308Q8×C43—41no—
309Q8×C43—41no—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43—44no—
313D4×C43—44no—
314D4×C43—44no—
315D4×C43—48no—
316D4×C43—41no—
317D4×C43—41no—
318D4×C43—84no—
319D4×C43—84no—
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×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—48no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—84no—
349C2×C4×C43C2×C22⋊C412yes—
350C2×C4×C43C2×C22⋊C412yes—
351C2×C4×C43C2×C22⋊C412yes—
352C2×C4×C43C23×C411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C2×C4×C43H(5,𝔽2)11yescharacteristic
357C2×C4×C43H(5,𝔽2)11yescharacteristic
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—41no—
370C2×Dic43—84no—
371C43⋊C8—41no—
372C43⋊C8—41no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375#21772—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43C22×C22⋊C411yescharacteristic
405C22×C43#53411yescharacteristic
406C22×C43#53411yescharacteristic
407C22×C43#57611yescharacteristic
408C22×C43#57711yescharacteristic
409C22×C43#57711yescharacteristic
410C22×C43#57811yescharacteristic
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—22no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43—42no—
417C4×C43#51811yescharacteristic
418C4×C43#51811yescharacteristic
419C4×C43#53411yescharacteristic
420C4×C43#53411yescharacteristic
421Dic43—81no—
422Dic43—81no—
423Dic43—81no—
424Dic43—81no—
425C2×#537D4311yescharacteristic
426C2×#408—431no—
427#2311—431no—
428#1895—431no—
429#1894—431no—
430#1893—431no—
431#1892—431no—
432#1875—431no—
433#1874—431no—
434#1873—431no—
435#1872—431no—
436#1824—431no—
437#1823—431no—
438#1788—431no—
439#1788—431no—
440C2×C43—42no—
441C2×C43—42no—
442C2×C43—42no—
443C2×C43—82no—
444C2×C43#230811yescharacteristic
445C2×C43#289711yescharacteristic
446C2×C43#289811yescharacteristic
447C2×C43#319811yescharacteristic
448C2×C43#320111yescharacteristic
449C2×C43#320311yescharacteristic
450C2×C43#320411yescharacteristic
451C22×#41C2×D4311yescharacteristic
452C22×#41C2×D4311yescharacteristic
453C22×M16—431no—
454C23×C8—431no—
455#537—24no—
456#537Dic4318yescomplemented
457C2×C22⋊Q8—21no—
458C2×C22⋊Q8C2×D4311yescharacteristic
459C2×C22⋊Q8C2×D4311yescharacteristic
460C2×#121—21no—
461C2×#121—21no—
462C2×#121—21no—
463C2×#121C2×D4311yescharacteristic
464C2×#121C2×D4311yescharacteristic
465C2×#117—431no—
466C22×C4⋊C4—431no—
467C22×C4⋊C4C2×D4311yescharacteristic
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476#408—864no—
477C2×C22⋊C8—431no—
478C2×C22⋊C8—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481#391—861no—
482#390—861no—
483#386—861no—
484#386—861no—
485#380—431no—
486#380—431no—
487#380—431no—
488#380—431no—
489#340—431no—
490#340—431no—
491#340—431no—
492#340—431no—
493#340—431no—
494#340—431no—
495#340—431no—
496#340—431no—
497C43#2177211yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×Dic4314yes—
508C2×#41C2×Dic4314yescomplemented
509C2×#41C22⋊D4314yes—
510C22×Q8C22⋊D4311yescharacteristic
511C22×Q8C22×D4311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D4311yescharacteristic
516C22×D4C22⋊D4311yescharacteristic
517C22×D4C22⋊D4311yescharacteristic
518C22×D4C22×D4311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—861no—
522C23×C4C22×D4311yescharacteristic
523C23×C4C22×D4311yescharacteristic
524C23×C4C22×D4311yescharacteristic
525C2×M16—862no—
526C2×M16—1721no—
527C2×M16—1721no—
528C22×C8—431no—
529C22×C8—431no—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—862no—
533C22×C8—1721no—
534C22×C8—1721no—
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×Dic4314yes—
539C22⋊Q8C2×Dic4314yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×Dic4314yes—
546#121C2×Dic4314yescomplemented
547#117—1721no—
548#117—1721no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—431no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—1721no—
559C2×C4⋊C4—1721no—
560C2×C4⋊C4C2×Dic4314yescomplemented
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C42—861no—
573#103—1721no—
574#103—1721no—
575#103—1721no—
576#103—1721no—
577#102—1721no—
578#102—1721no—
579#102—1721no—
580#102—1721no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—862no—
584C22⋊C8—862no—
585#95—861no—
586#95—861no—
587#95—861no—
588#95—861no—
589C24—21no—
590C24C2×C22⋊D4311yescharacteristic
591C24C2×C22⋊D4311yescharacteristic
592C24C2×C22⋊D4311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊Dic4314yes—
609C2×Q8C22×Dic4312yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊Dic4314yes—
631C2×D4C22⋊Dic4314yes—
632C2×D4C22⋊Dic4314yes—
633C2×D4C22×Dic4312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—3441no—
660C22×C4—3441no—
661C22×C4—1722no—
662C22×C4C22×Dic4312yes—
663C22×C4C22×Dic4312yes—
664C22×C4C22×Dic4312yes—
665C22×C4C2×C22⋊D4311yescharacteristic
666C22×C4C2×C22⋊D4311yescharacteristic
667C22×C4C2×C22⋊D4311yescharacteristic
668C22×C4C2×C22⋊D4312yes—
669C22×C4C2×C22⋊D4312yes—
670C22×C4C2×C22⋊D4312yes—
671C22×C4C23×D4311yescharacteristic
672M16—1724no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—1724no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—1722no—
700C4⋊C4C22×Dic4312yes—
701C4⋊C4C22×Dic4312yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—3441no—
707C22⋊C4—3441no—
708C22⋊C4—3441no—
709C22⋊C4—3441no—
710C22⋊C4—1722no—
711C42—1722no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊Dic4312yes—
738C23C2×C22⋊Dic4312yes—
739C23C2×C22⋊Dic4312yes—
740C23C22×C22⋊D4311yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—3444no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4C2×C22⋊Dic4312yes—
799C2×C4C2×C22⋊Dic4312yes—
800C2×C4C2×C22⋊Dic4312yes—
801C2×C4C23×Dic4311yescharacteristic
802C2×C4C22×C22⋊D4311yescharacteristic
803C2×C4#1306337011yescharacteristic
804C2×C4#1306337011yescharacteristic
805C2×C4#1306337011yescharacteristic
806C2×C4#1306337011yescharacteristic
807C8—1721no—
808C8—1721no—
809C8—1721no—
810C8—1721no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊Dic4311yescharacteristic
840C22#1458345811yescharacteristic
841C22#1458345811yescharacteristic
842C22#1458370211yescharacteristic
843C22#1458370711yescharacteristic
844C22#1458371011yescharacteristic
845C22#1458371411yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—3441no—
853C4—3441no—
854C4—3441no—
855C4—3441no—
856C4#1458337411yescharacteristic
857C4#1458337411yescharacteristic
858C4#1458345811yescharacteristic
859C4#1458345811yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#1913717311yescharacteristic
865C2#1914312111yescharacteristic
866C2#1914312811yescharacteristic
867C2#1914544111yescharacteristic
868C2#1914547111yescharacteristic
869C2#1914549211yescharacteristic
870C2#1914550111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#537C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#537D43
hypocenterC43#21772
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#14582866C2semidirect
2. #19137187C2semidirect
3. #19135034C2semidirect
4. #19135029C2semidirect
5. #19135024C2semidirect
6. #19135019C2semidirect
7. #19134918C2semidirect
8. #19134913C2semidirect
9. #19134908C2semidirect
10. #19134903C2semidirect
11. #19134685C2semidirect
12. #19134681C2semidirect
13. #19134535C2semidirect
14. #19134535C2semidirect
52. C43×#537C4semidirect
114. C2×#41×C43C2×C4semidirect
134. C22⋊Q8×C43C2×C4semidirect
141. #121×C43C2×C4semidirect
146. C2×C4⋊C4×C43C2×C4semidirect
456. #537Dic43semidirect
497. C43#21772semidirect
508. C2×#41C2×Dic43semidirect
539. C22⋊Q8C2×Dic43semidirect
546. #121C2×Dic43semidirect
560. C2×C4⋊C4C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828662
#191371872
#191350342
#191350292
#191350242
#191350192
#191349182
#191349132
#191349082
#191349032
#191346852
#191346812
#191345352
C2×C43×#5372
#2177243