Finite Group Databasebeta

← #25112153

Subgroups — #25112153

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×#14583543C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4#19137545C211yesmaximal, characteristic, complemented
5#19135526C211yesmaximal, characteristic, complemented
6#19135410C211yesmaximal, characteristic, complemented
7#19135028C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19134914C211yesmaximal, characteristic, complemented
10#19134907C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C2×C43×#418C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic, complemented
18#14583543—24no—
19#14583543C418yescomplemented
20C2×#13063312C2211yescharacteristic
21C2×#13063306—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063297—21no—
24C2×#13063296C2211yescharacteristic
25C2×#13063294—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063283C2211yescharacteristic, complemented
29C22×C22⋊Dic43—21no—
30#14582968—24no—
31C2×Dic43⋊C8C2211yescharacteristic, complemented
32#14582892—24no—
33C2×#13063250C2211yescharacteristic, complemented
34C2×#13063250C2211yescharacteristic, complemented
35C2×#13063248C2211yescharacteristic, complemented
36C2×#13063248C2211yescharacteristic, complemented
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
43C2×#13063235C2211yescharacteristic, complemented
44#14582799—21no—
45#14582790—21no—
46#14582787—21no—
47#14582768C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic
49#14582756C2211yescharacteristic, complemented
50C4⋊C4×Dic43C2211yescharacteristic, complemented
51C4×Dic43⋊C4—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C23×D4×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic
58C2×#117×C43C2211yescharacteristic
59C43×#418—24no—
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—41no—
68C2×#10621900—41no—
69C2×#10621900C2×C414yes—
70C22×Dic86C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C22⋊D43D411yescharacteristic
74C23×Dic43—21no—
75C23×Dic43—21no—
76C22×C4×D43C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43—41no—
82#13063312—22no—
83#13063312C2×C414yes—
84#13063306—28no—
85#13063304—22no—
86#13063304C2×C414yes—
87#13063297—28no—
88#13063296—22no—
89#13063296C2×C414yes—
90#13063294—28no—
91D4×Dic43—22no—
92D4×Dic43C2×C414yes—
93C4×C22⋊D43C2×C414yes—
94C4×C22⋊D43D414yes—
95#13063283—22no—
96#13063283—41no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4D411yescharacteristic
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—28no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4D411yescharacteristic
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118Dic43⋊C8—22no—
119#13063250—22no—
120#13063250—41no—
121#13063248—22no—
122#13063248—41no—
123#13063246—22no—
124#13063246—22no—
125#13063246—41no—
126#13063246—41no—
127C22⋊(C43⋊C8)—22no—
128(C2×D43)⋊C8—22no—
129#13063235—22no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C25×C43—21no—
134C22×D4×C43—22no—
135C22×D4×C43—22no—
136C22×D4×C43—21no—
137C22×D4×C43—22no—
138C22×D4×C43—41no—
139C22×D4×C43—41no—
140C22×D4×C43C2×C414yes—
141C22×D4×C43C2311yescharacteristic
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C2×M16×C43—22no—
145C2×M16×C43—22no—
146C2×M16×C43—41no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149#117×C43—22no—
150#117×C43—41no—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C42×C43—21no—
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—22no—
158#102×C43D414yescomplemented
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
169C23×D43C2×D411yescharacteristic
170C2×D4×C43—24no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—28no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43—44no—
183C2×D4×C43—44no—
184C2×D4×C43—44no—
185C2×D4×C43C22×C412yes—
186C2×D4×C43C22×C412yes—
187C2×D4×C43C2×D412yes—
188C2×D4×C43#4112yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C22×C412yes—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—41no—
202C2×C22⋊D43—41no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—42no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43C22⋊C414yes—
208C22×Dic43—24no—
209C22×Dic43—24no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—42no—
215C22×Dic43—42no—
216C22×Dic43—81no—
217C22×Dic43—81no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221#10621900—28no—
222#10621900—44no—
223#10621900—44no—
224#10621900—44no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43C22×C412yes—
230C2×C4×D43C2×D412yes—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86C22×C412yes—
237M16×C43—44no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43C2×D412yes—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43C2×D412yes—
248C22⋊C4×C43—42no—
249C42×C43—42no—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—81no—
256C22⋊Dic43C22⋊C414yes—
257(C2×D43)⋊C4—42no—
258(C2×D43)⋊C4—81no—
259(C2×D43)⋊C4C22⋊C414yes—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43C22×C412yes—
266Dic43⋊C4—24no—
267Dic43⋊C4—42no—
268Dic43⋊C4—81no—
269Dic43⋊C4C22⋊C414yes—
270C4×Dic43—42no—
271C4×Dic43—42no—
272C4×Dic43C22×C412yes—
273C4×Dic43C2×D412yes—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C8×D43—44no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—22no—
291C23×C43—48no—
292C23×C43—48no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—84no—
304C23×C43—84no—
305C23×C43—84no—
306C23×C43—84no—
307C23×C43—84no—
308C23×C43C2×C22⋊C412yes—
309C23×C43C22×D411yescharacteristic
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—21no—
315C22×D43—21no—
316C22×D43C2×C22⋊C412yes—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—48no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43C4×D414yes—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43C2×C22⋊C412yes—
339C2×C4×C43C23×C411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C2×C4×C43H(5,𝔽2)11yescharacteristic
345C22⋊D43—44no—
346C22⋊D43—48no—
347C22⋊D43—84no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—48no—
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—84no—
368C2×Dic43C2×C22⋊C412yes—
369C2×Dic43C2×C22⋊C412yes—
370C2×Dic43C2×C22⋊C412yes—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—22no—
375Dic86—22no—
376Dic86—22no—
377Dic86—41no—
378Dic86—41no—
379C8×C43—22no—
380C8×C43—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—42no—
389C22×C43—42no—
390C22×C43—41no—
391C22×C43—42no—
392C22×C43—41no—
393C22×C43—42no—
394C22×C43—41no—
395C22×C43—42no—
396C22×C43—41no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—816no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43C22×C22⋊C411yescharacteristic
407C22×C43D4211yescharacteristic
408C22×C43#54611yescharacteristic
409C22×C43#57511yescharacteristic
410C22×C43#57511yescharacteristic
411C22×C43#57611yescharacteristic
412C22×C43#57711yescharacteristic
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—41no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C4×C43—22no—
421C4×C43—42no—
422C4×C43—81no—
423C4×C43C2×C4×D411yescharacteristic
424C4×C43#51811yescharacteristic
425C4×C43D4211yescharacteristic
426C4×C43#54611yescharacteristic
427Dic43—22no—
428Dic43—22no—
429Dic43—22no—
430Dic43—42no—
431Dic43—42no—
432Dic43—81no—
433Dic43—81no—
434C2×#546—431no—
435C2×#435—431no—
436C2×#418D4311yescharacteristic, complemented
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—44no—
451C2×C43—82no—
452C2×C43D4×C22⋊C411yescharacteristic
453C2×C43#289611yescharacteristic
454C2×C43#289711yescharacteristic
455C2×C43#326711yescharacteristic
456C2×C43#326811yescharacteristic
457C2×C43#331111yescharacteristic
458C2×C43#331911yescharacteristic
459D43—42no—
460C22×#41—431no—
461C23×D4C2×D4311yescharacteristic
462C22×M16C2×D4311yescharacteristic
463C23×C8—431no—
464#546—438no—
465#546—864no—
466C2×#124—431no—
467C2×#123—861no—
468C2×C22⋊Q8—431no—
469C2×#121—431no—
470C2×#121—861no—
471C2×#120—861no—
472C2×C4×D4—431no—
473C2×C4×D4—431no—
474C2×#117—431no—
475C2×#117C2×D4311yescharacteristic
476C22×C22⋊C4—861no—
477#435—864no—
478C2×C4⋊C8—431no—
479#418—24no—
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×#102C2×D4311yescharacteristic
490C2×#102C2×D4311yescharacteristic
491C2×#102C2×D4311yescharacteristic
492C2×#102C2×D4311yescharacteristic
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—434no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—1721no—
515C2×#41—1721no—
516C22×Q8—431no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—431no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4C4×D4314yes—
527C22×D4C22×D4311yescharacteristic
528C22×D4C22×D4311yescharacteristic
529C23×C4—431no—
530C23×C4—861no—
531C23×C4—861no—
532C23×C4C22×D4311yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—1721no—
541C22×C8C22×D4311yescharacteristic
542C22×C8C22×D4311yescharacteristic
543#124—434no—
544#124—862no—
545#123—868no—
546C22⋊Q8—434no—
547C22⋊Q8—862no—
548#121—434no—
549#121—868no—
550#121—862no—
551#120—868no—
552C4×D4—434no—
553C4×D4—434no—
554C4×D4—434no—
555C4×D4—862no—
556#117—22no—
557#117—41no—
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—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—868no—
573C2×C22⋊C4—861no—
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—431no—
583C2×C42—861no—
584C2×C42—861no—
585C4⋊C8—862no—
586#103—862no—
587#103—862no—
588#103—1721no—
589#103—1721no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—862no—
594#102—862no—
595#102—1721no—
596#102—1721no—
597#102C22⋊D4314yescomplemented
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—
613C24—431no—
614C24D4×D4311yescharacteristic
615#41—868no—
616#41—1724no—
617#41—1724no—
618#41—1724no—
619C2×Q8—432no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—434no—
641C2×D4—864no—
642C2×D4—864no—
643C2×D4—3441no—
644C2×D4—3441no—
645C2×D4—1721no—
646C2×D4—1721no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4C2×C4×D4312yes—
650C2×D4C2×C4×D4312yes—
651C2×D4#1062189812yes—
652C2×D4C2×C22⋊D4312yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—864no—
665C22×C4—864no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—3441no—
675C22×C4—3441no—
676C22×C4—1722no—
677C22×C4—1722no—
678C22×C4C2×C4×D4312yes—
679C22×C4D4×D4311yescharacteristic
680C22×C4D4×D4312yes—
681C22×C4C23×D4311yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—1724no—
695C2×C8C2×C22⋊D4312yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—434no—
700C4⋊C4—432no—
701C4⋊C4—864no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—3441no—
708C4⋊C4—1722no—
709C4⋊C4C2×C22⋊D4312yes—
710C22⋊C4—42no—
711C22⋊C4—434no—
712C22⋊C4—434no—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—3441no—
719C22⋊C4—3441no—
720C22⋊C4—1722no—
721C42—42no—
722C42—432no—
723C42—432no—
724C42—1722no—
725C42—1722no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—84no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—432no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23—861no—
758C23—861no—
759C23—861no—
760C23C22⋊C4×D4312yes—
761C23C2×D4×D4311yescharacteristic
762Q8—862no—
763Q8—862no—
764Q8—1721no—
765Q8—1721no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—41no—
773D4—41no—
774D4—3444no—
775D4—1724no—
776D4—1728no—
777D4C4×C22⋊D4314yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—432no—
791C2×C4—432no—
792C2×C4—432no—
793C2×C4—861no—
794C2×C4—861no—
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—3444no—
806C2×C4—1728no—
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×C4—1721no—
817C2×C4C22⋊C4×D4312yes—
818C2×C4C22×C4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4C22×C22⋊D4311yescharacteristic
821C2×C4C2×#1062189811yescharacteristic
822C2×C4#1306337011yescharacteristic
823C2×C4#1306337011yescharacteristic
824C8—22no—
825C8—41no—
826C8—1721no—
827C8—1721no—
828C22—22no—
829C22—24no—
830C22—22no—
831C22—22no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—816no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—1721no—
854C22—1721no—
855C22—1721no—
856C22—1721no—
857C22C2×C22⋊C4×D4311yescharacteristic
858C22D4×C22⋊D4311yescharacteristic
859C22#1458353911yescharacteristic
860C22#1458369511yescharacteristic
861C22#1458369511yescharacteristic
862C22#1458370311yescharacteristic
863C22#1458370911yescharacteristic
864C4—22no—
865C4—42no—
866C4—81no—
867C4—862no—
868C4—862no—
869C4—862no—
870C4—3441no—
871C4—3441no—
872C4—1722no—
873C4—1722no—
874C4C2×C4×C22⋊D4311yescharacteristic
875C4#1458337211yescharacteristic
876C4D4×C22⋊D4311yescharacteristic
877C4#1458353911yescharacteristic
878C2—42no—
879C2—44no—
880C2—82no—
881C2—1722no—
882C2C22⋊C4×C22⋊D4311yescharacteristic
883C2#1914310911yescharacteristic
884C2#1914312011yescharacteristic
885C2#1914611411yescharacteristic
886C2#1914612911yescharacteristic
887C2#1914663211yescharacteristic
888C2#1914675211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
prime radicalC2×#14583543C2
cosocleC22×C4×C43C24
hypercenterC2×#418D43
hypocenterC43#22424
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#14582968C2semidirect
3. C2×#14582892C2semidirect
4. #19137545C2semidirect
5. #19135526C2semidirect
6. #19135410C2semidirect
7. #19135028C2semidirect
8. #19135020C2semidirect
9. #19134914C2semidirect
10. #19134907C2semidirect
11. #19134593C2semidirect
12. #19134532C2semidirect
13. #19134526C2semidirect
14. #19134422C2semidirect
15. C2×C43×#418C2semidirect
17. C22×C8×D43C22semidirect
19. #14583543C4semidirect
28. C2×#13063283C22semidirect
31. C2×Dic43⋊C8C22semidirect
33. C2×#13063250C22semidirect
34. C2×#13063250C22semidirect
35. C2×#13063248C22semidirect
36. C2×#13063248C22semidirect
42. C2×(C2×D43)⋊C8C22semidirect
43. C2×#13063235C22semidirect
47. #14582768C22semidirect
49. #14582756C22semidirect
50. C4⋊C4×Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
158. #102×C43D4semidirect
436. C2×#418D43semidirect
508. C43#22424semidirect
597. #102C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835432
C2×#145829682
C2×#145828922
#191375452
#191355262
#191354102
#191350282
#191350202
#191349142
#191349072
#191345932
#191345322
#191345262
#191344222
C2×C43×#4182
#2242443