Finite Group Databasebeta

← #25112152

Subgroups — #25112152

Order 11008.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582971C211yesmaximal, characteristic, complemented
2C2×#14582904C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4#19137544C211yesmaximal, characteristic, complemented
5#19135528C211yesmaximal, characteristic, complemented
6#19135412C211yesmaximal, characteristic, complemented
7#19135029C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134918C211yesmaximal, characteristic, complemented
10#19134908C211yesmaximal, characteristic, complemented
11#19134595C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic, complemented
15C2×C43×#546C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic, complemented
18C2×#13063284C2211yescharacteristic
19C2×#13063284C2211yescharacteristic, complemented
20#14582971—24no—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
22#14582904—24no—
23#14582895—24no—
24C2×#13063249C2211yescharacteristic, complemented
25C2×#13063249C2211yescharacteristic, complemented
26C2×#13063249C2211yescharacteristic, complemented
27C2×#13063249C2211yescharacteristic, complemented
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
38C2×#13063236C2211yescharacteristic, complemented
39#14582802—21no—
40#14582792—21no—
41#14582792—21no—
42#14582769C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic, complemented
45C4⋊C4×Dic43—21no—
46C4×C4⋊Dic43C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51C22×#41×C43C2211yescharacteristic
52C23×D4×C43C2211yescharacteristic
53C43×#546—24no—
54C43×#546C418yescomplemented
55C2×#124×C43C2211yescharacteristic
56C2×#123×C43—21no—
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43—21no—
59C2×#121×C43C2211yescharacteristic
60C2×#120×C43—21no—
61C2×C4×D4×C43C2211yescharacteristic
62C2×C4×D4×C43C2211yescharacteristic
63C22×C22⋊C4×C43—21no—
64C2×#10621877—22no—
65C2×#10621877—22no—
66C2×#10621877—41no—
67C22×C43⋊C8—22no—
68C22×C43⋊C8—22no—
69C22×C43⋊C8—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063284—22no—
75#13063284—22no—
76#13063284—41no—
77#13063284—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C4⋊(C43⋊C8)—22no—
92#13063249—22no—
93#13063249—22no—
94#13063249—41no—
95#13063249—41no—
96#13063246—22no—
97#13063246—22no—
98#13063246—22no—
99#13063246—22no—
100#13063246—22no—
101#13063246—41no—
102#13063246—41no—
103#13063246D414yescomplemented
104C22⋊(C43⋊C8)—22no—
105C22⋊(C43⋊C8)—22no—
106#13063236—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C25×C43—21no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—22no—
114C2×#41×C43—41no—
115C2×#41×C43—41no—
116C2×#41×C43C2×C414yes—
117C22×Q8×C43C2311yescharacteristic
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—21no—
121C22×D4×C43—21no—
122C22×D4×C43—21no—
123C22×D4×C43—22no—
124C22×D4×C43—41no—
125C22×D4×C43—41no—
126C22×D4×C43C2×C414yes—
127C22×D4×C43D411yescharacteristic
128C22×D4×C43C2311yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C23×C4×C43—21no—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134#124×C43—22no—
135#124×C43C2×C414yes—
136#123×C43—28no—
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43C2×C414yes—
139#121×C43—22no—
140#121×C43—28no—
141#121×C43C2×C414yes—
142#120×C43—28no—
143C4×D4×C43—22no—
144C4×D4×C43C2×C414yes—
145C4×D4×C43C2×C414yes—
146C4×D4×C43D414yes—
147C2×C4⋊C4×C43—21no—
148C2×C4⋊C4×C43D411yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—21no—
151C2×C22⋊C4×C43—21no—
152C2×C22⋊C4×C43—21no—
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—28no—
156C2×C22⋊C4×C43D411yescharacteristic
157C2×C22⋊C4×C43D411yescharacteristic
158C2×C42×C43C2311yescharacteristic
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—24no—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43—42no—
165C24×C43—42no—
166C24×C43—81no—
167C24×C43—81no—
168C24×C43C2×D411yescharacteristic
169C24×C43C2×D411yescharacteristic
170#41×C43—28no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43C22×C412yes—
180C2×D4×C43—24no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—24no—
186C2×D4×C43—24no—
187C2×D4×C43—28no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—41no—
193C2×D4×C43—41no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—44no—
199C2×D4×C43—44no—
200C2×D4×C43—44no—
201C2×D4×C43—81no—
202C2×D4×C43—81no—
203C2×D4×C43C22⋊C414yes—
204C2×D4×C43C22×C412yes—
205C2×D4×C43C22×C412yes—
206C2×D4×C43C2×D412yes—
207C2×D4×C43#4112yes—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—24no—
217C22×C4×C43—24no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—42no—
221C22×C4×C43—42no—
222C22×C4×C43—81no—
223C22×C4×C43—81no—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C22×C412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C22⋊C414yes—
240C4⋊C4×C43C22×C412yes—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—24no—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43C22⋊C414yes—
247C22⋊C4×C43C22⋊C414yes—
248C42×C43C22×C412yes—
249C42×C43C2×D412yes—
250C22⋊Dic43—42no—
251C22⋊Dic43—42no—
252C22⋊Dic43—81no—
253C22⋊Dic43—81no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—42no—
262C4⋊Dic43—81no—
263C4⋊Dic43C2×D412yes—
264C4×Dic43—42no—
265C4×Dic43—42no—
266C4×Dic43—42no—
267#10621877—44no—
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—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—44no—
280C2×C43⋊C8C2×D412yes—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—22no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—22no—
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×C43—22no—
297C23×C43—48no—
298C23×C43—48no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—84no—
310C23×C43—84no—
311C23×C43—84no—
312C23×C43—84no—
313C23×C43—84no—
314C23×C43C2×C22⋊C412yes—
315C23×C43C2×C22⋊C412yes—
316C23×C43C22×D411yescharacteristic
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43—22no—
326D4×C43—44no—
327D4×C43—48no—
328D4×C43—48no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—84no—
332D4×C43C4×D414yes—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—48no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—84no—
357C2×C4×C43C2×C22⋊C412yes—
358C2×C4×C43C2×C22⋊C412yes—
359C2×C4×C43C2×C22⋊C412yes—
360C2×C4×C43C2×C22⋊C412yes—
361C2×C4×C43C23×C411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C2×#4111yescharacteristic
365C2×C4×C43H(5,𝔽2)11yescharacteristic
366C2×C4×C43H(5,𝔽2)11yescharacteristic
367C2×Dic43—22no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C43⋊C8—22no—
380C43⋊C8—41no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383#22424—431nomaximal, Sylow
384C22×C43—24no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—42no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—42no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—42no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43—816no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43C22×C22⋊C411yescharacteristic
414C22×C43D4211yescharacteristic
415C22×C43#54611yescharacteristic
416C22×C43#57511yescharacteristic
417C22×C43#57511yescharacteristic
418C22×C43#57611yescharacteristic
419C22×C43#57711yescharacteristic
420C4×C43—22no—
421C4×C43—22no—
422C4×C43—22no—
423C4×C43—22no—
424C4×C43—42no—
425C4×C43—42no—
426C4×C43C2×C4×D411yescharacteristic
427C4×C43#51811yescharacteristic
428C4×C43D4211yescharacteristic
429C4×C43#54611yescharacteristic
430Dic43—42no—
431Dic43—81no—
432Dic43—81no—
433Dic43—81no—
434C2×#546D4311yescharacteristic
435C2×#435—431no—
436C2×#418—431no—
437C2×#416—431no—
438#2354—431no—
439#1983—431no—
440#1959—431no—
441#1894—431no—
442#1893—431no—
443#1875—431no—
444#1873—431no—
445#1802—431no—
446#1788—431no—
447#1786—431no—
448#1762—431no—
449C2×C43—42no—
450C2×C43—42no—
451C2×C43—44no—
452C2×C43—82no—
453C2×C43D4×C22⋊C411yescharacteristic
454C2×C43#289611yescharacteristic
455C2×C43#289711yescharacteristic
456C2×C43#326711yescharacteristic
457C2×C43#326811yescharacteristic
458C2×C43#331111yescharacteristic
459C2×C43#331911yescharacteristic
460C22×#41C2×D4311yescharacteristic
461C23×D4C2×D4311yescharacteristic
462C22×M16—431no—
463C23×C8—431no—
464#546—24no—
465#546Dic4318yescomplemented
466C2×#124C2×D4311yescharacteristic
467C2×#123—21no—
468C2×C22⋊Q8C2×D4311yescharacteristic
469C2×#121—21no—
470C2×#121C2×D4311yescharacteristic
471C2×#120—21no—
472C2×C4×D4C2×D4311yescharacteristic
473C2×C4×D4C2×D4311yescharacteristic
474C2×#117—431no—
475C2×#117—431no—
476C22×C22⋊C4—21no—
477#435—864no—
478C2×C4⋊C8—431no—
479#418—864no—
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—431no—
492C2×#102—431no—
493C2×C22⋊C8—431no—
494C2×C22⋊C8—431no—
495C2×#97—431no—
496#390—861no—
497#388—861no—
498#388—861no—
499#384—431no—
500#380—431no—
501#380—431no—
502C4×C4⋊C4—431no—
503C4×C4⋊C4—861no—
504#340—431no—
505#340—431no—
506#340—431no—
507#340—431no—
508C43#2242411yescharacteristic, complemented, Sylow
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic4314yes—
516C22×Q8C22×D4311yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×Dic4314yes—
526C22×D4C22⋊D4311yescharacteristic
527C22×D4C22×D4311yescharacteristic
528C22×D4C22×D4311yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D4311yescharacteristic
532C23×C4C22×D4311yescharacteristic
533C2×M16—862no—
534C2×M16—862no—
535C2×M16—1721no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8—431no—
540C22×C8—862no—
541C22×C8—862no—
542C22×C8—1721no—
543#124—22no—
544#124C2×Dic4314yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×Dic4314yes—
548#121—22no—
549#121—28no—
550#121C2×Dic4314yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×Dic4314yes—
554C4×D4C2×Dic4314yes—
555C4×D4C22⋊D4314yes—
556#117—862no—
557#117—862no—
558#117—1721no—
559#117—1721no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22⋊D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4C22⋊D4311yescharacteristic
580C2×C22⋊C4C22⋊D4311yescharacteristic
581C2×C42—861no—
582C2×C42—861no—
583C2×C42—861no—
584C2×C42C22×D4311yescharacteristic
585C4⋊C8—862no—
586#103—862no—
587#103—862no—
588#103—1721no—
589#103—1721no—
590#102—434no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—862no—
596#102—1721no—
597#102—1721no—
598C22⋊C8—862no—
599C22⋊C8—862no—
600#97—862no—
601#95—861no—
602#95—861no—
603#95—861no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D4311yescharacteristic
614C24C2×C22⋊D4311yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic4312yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic4314yes—
649C2×D4D4×D4312yes—
650C2×D4#1062190012yes—
651C2×D4C22×Dic4312yes—
652C2×D4C22×Dic4312yes—
653C22×C4—21no—
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—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4C22×Dic4312yes—
674C22×C4C22×Dic4312yes—
675C22×C4C2×C22⋊D4311yescharacteristic
676C22×C4C2×C22⋊D4311yescharacteristic
677C22×C4C2×C22⋊D4311yescharacteristic
678C22×C4C2×C22⋊D4311yescharacteristic
679C22×C4C2×C22⋊D4312yes—
680C22×C4C2×C22⋊D4312yes—
681C22×C4C23×D4311yescharacteristic
682M16—1724no—
683C2×C8—432no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—1724no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—432no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—3441no—
707C4⋊C4—1722no—
708C4⋊C4C22⋊Dic4314yes—
709C4⋊C4C22×Dic4312yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—3441no—
716C22⋊C4—3441no—
717C22⋊C4—1722no—
718C22⋊C4—1722no—
719C22⋊C4C22⋊Dic4314yes—
720C22⋊C4C22⋊Dic4314yes—
721C42—1722no—
722C42—1722no—
723C42—1722no—
724C42C22×Dic4312yes—
725C42C2×C22⋊D4312yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic4312yes—
760C23C2×C22⋊Dic4312yes—
761C23C22×C22⋊D4311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic4314yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
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—22no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—862no—
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×C4C2×C22⋊Dic4312yes—
815C2×C4C2×C22⋊Dic4312yes—
816C2×C4C2×C22⋊Dic4312yes—
817C2×C4C2×C22⋊Dic4312yes—
818C2×C4C23×Dic4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4C22×C22⋊D4311yescharacteristic
821C2×C4C2×#1062190011yescharacteristic
822C2×C4#1306337011yescharacteristic
823C2×C4#1306337011yescharacteristic
824C8—862no—
825C8—1721no—
826C8—1721no—
827C8—1721no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊Dic4311yescharacteristic
858C22D4×C22⋊D4311yescharacteristic
859C22#1458354311yescharacteristic
860C22#1458369711yescharacteristic
861C22#1458369711yescharacteristic
862C22#1458370211yescharacteristic
863C22#1458371011yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—3441no—
871C4—3441no—
872C4—3441no—
873C4—1722no—
874C4C2×D4×Dic4311yescharacteristic
875C4#1458337411yescharacteristic
876C4D4×C22⋊D4311yescharacteristic
877C4#1458354311yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊Dic4311yescharacteristic
883C2#1914311411yescharacteristic
884C2#1914312111yescharacteristic
885C2#1914611611yescharacteristic
886C2#1914613111yescharacteristic
887C2#1914663111yescharacteristic
888C2#1914675111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#546C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#546D43
hypocenterC43#22424
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14582971C2semidirect
2. C2×#14582904C2semidirect
3. C2×#14582895C2semidirect
4. #19137544C2semidirect
5. #19135528C2semidirect
6. #19135412C2semidirect
7. #19135029C2semidirect
8. #19135024C2semidirect
9. #19134918C2semidirect
10. #19134908C2semidirect
11. #19134595C2semidirect
12. #19134535C2semidirect
13. #19134526C2semidirect
14. #19134420C2semidirect
17. C23×C43⋊C8C22semidirect
19. C2×#13063284C22semidirect
21. C2×C4⋊(C43⋊C8)C22semidirect
24. C2×#13063249C22semidirect
25. C2×#13063249C22semidirect
26. C2×#13063249C22semidirect
27. C2×#13063249C22semidirect
37. C2×C22⋊(C43⋊C8)C22semidirect
38. C2×#13063236C22semidirect
42. #14582769C22semidirect
44. #14582759C22semidirect
46. C4×C4⋊Dic43C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
54. C43×#546C4semidirect
103. #13063246D4semidirect
465. #546Dic43semidirect
508. C43#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#145829712
C2×#145829042
C2×#145828952
#191375442
#191355282
#191354122
#191350292
#191350242
#191349182
#191349082
#191345952
#191345352
#191345262
#191344202
C2×C43×#5462
#2242443