Finite Group Databasebeta

← #25144090

Subgroups — #25144090

Order 11008.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583104C211yesmaximal, characteristic, complemented
2C2×#14583050C211yesmaximal, characteristic
3C2×#14583050C211yesmaximal, characteristic
4C2×C4×#10621883C211yesmaximal, characteristic, complemented
5#19138194C211yesmaximal, characteristic, complemented
6#19135969C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic, complemented
8#19135791C211yesmaximal, characteristic, complemented
9#19135677C211yesmaximal, characteristic, complemented
10#19135448C211yesmaximal, characteristic, complemented
11#19135203C211yesmaximal, characteristic, complemented
12#19134953C211yesmaximal, characteristic, complemented
13#19134929C211yesmaximal, characteristic, complemented
14#19134856C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C2×#13063325C2211yescharacteristic, complemented
21C2×#13063304C2211yescharacteristic
22C2×#13063304C2211yescharacteristic
23C2×C4×Dic86C2211yescharacteristic, complemented
24#14583104—24no—
25#14583050—24no—
26#14583050—24no—
27C4×#10621883—24no—
28C2×#13063256C2211yescharacteristic, complemented
29C2×#13063256C2211yescharacteristic, complemented
30C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
31C2×#13063248C2211yescharacteristic, complemented
32C2×#13063248C2211yescharacteristic, complemented
33C2×#13063248C2211yescharacteristic, complemented
34C2×#13063248C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic, complemented
42#14582833—21no—
43#14582822—21no—
44#14582805C2211yescharacteristic, complemented
45#14582797C2211yescharacteristic, complemented
46#14582796—21no—
47#14582792—21no—
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52C23×D4×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C22×C22⋊C4×C43—21no—
56C43×#390C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#386—21no—
59C43×#386—21no—
60C43×#380C2211yescharacteristic
61C43×#379—21no—
62C4×C22⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883—41no—
75C2×#10621883—41no—
76C2×#10621883D414yes—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063325—22no—
82#13063325—41no—
83#13063304—22no—
84#13063304—22no—
85#13063304—41no—
86#13063304—41no—
87C4×Dic86—22no—
88C4×Dic86—41no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C4×Dic43—21no—
100#13063256—22no—
101#13063256—41no—
102C4⋊(C43⋊C8)—22no—
103#13063248—22no—
104#13063248—22no—
105#13063248—22no—
106#13063248—41no—
107#13063246—22no—
108#13063246—22no—
109#13063246—22no—
110#13063246D414yes—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C4×C43⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—22no—
121C22×D4×C43—22no—
122C22×D4×C43—21no—
123C22×D4×C43—41no—
124C22×D4×C43—41no—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43—21no—
128C23×C4×C43—21no—
129C23×C4×C43C2311yescharacteristic
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C4×D4×C43—41no—
133C4×D4×C43—41no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—44no—
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C42×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148#95×C43—21no—
149#95×C43D411yescharacteristic
150#95×C43D411yescharacteristic
151C24×C43—21no—
152C24×C43—24no—
153C24×C43—21no—
154C24×C43—42no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—81no—
159C24×C43—81no—
160C24×C43C2×D411yescharacteristic
161C2×D4×C43—24no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—42no—
171C2×D4×C43—42no—
172C2×D4×C43—44no—
173C2×D4×C43—44no—
174C2×D4×C43—44no—
175C2×D4×C43—44no—
176C2×D4×C43C2×D412yes—
177C2×D4×C43C2×D412yes—
178C2×D4×C43#4112yes—
179C2×D4×C43#4112yes—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—42no—
189C22×C4×C43—42no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43—81no—
193C22×C4×C43—81no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2411yescharacteristic
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86C2×D412yes—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C22⋊C4×C43—41no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—81no—
227C22⋊C4×C43—81no—
228C22⋊C4×C43SD1614yescomplemented
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—21no—
232C42×C43—21no—
233C22⋊Dic43—42no—
234C22⋊Dic43—42no—
235#10621883—28no—
236#10621883—44no—
237#10621883—44no—
238#10621883—44no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—42no—
243C4⋊Dic43—42no—
244C4⋊Dic43C2×D412yes—
245Dic43⋊C4—42no—
246Dic43⋊C4—42no—
247Dic43⋊C4—42no—
248Dic43⋊C4—42no—
249C4×Dic43—42no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8C2×D412yes—
261C2×C43⋊C8C2×D412yes—
262C23×C43—21no—
263C23×C43—22no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—22no—
272C23×C43—48no—
273C23×C43—48no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—84no—
285C23×C43—84no—
286C23×C43—84no—
287C23×C43—84no—
288C23×C43—84no—
289C23×C43C2×SD1612yes—
290C23×C43C22×D411yescharacteristic
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—48no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43#12114yes—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—84no—
324C2×C4×C43—84no—
325C2×C4×C43C2×SD1612yes—
326C2×C4×C43C2×SD1612yes—
327C2×C4×C43C22×D411yescharacteristic
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345Dic86—22no—
346Dic86—22no—
347Dic86—41no—
348Dic86—41no—
349Dic86—41no—
350Dic86—41no—
351Dic86—41no—
352Dic86—41no—
353C43⋊C8—22no—
354C43⋊C8—22no—
355C43⋊C8—41no—
356C43⋊C8—41no—
357#25156—431nomaximal, Sylow
358C22×C43—22no—
359C22×C43—24no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—42no—
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—42no—
368C22×C43—41no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—816no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43—81no—
380C22×C43#52511yescharacteristic
381C22×C43D4211yescharacteristic
382C22×C43D4211yescharacteristic
383C22×C43C22×SD1611yescharacteristic
384C22×C43#57511yescharacteristic
385C22×C43#57711yescharacteristic
386C22×C43#57711yescharacteristic
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43—81no—
393C4×C43—81no—
394C4×C43C2×#12111yescharacteristic
395C4×C43#53811yescharacteristic
396C4×C43#54611yescharacteristic
397C4×C43#54611yescharacteristic
398Dic43—42no—
399Dic43—42no—
400Dic43—81no—
401Dic43—81no—
402C2×#461—431no—
403C2×#450—431no—
404C2×#450—431no—
405C2×C4×SD16—431no—
406#2429—431no—
407D4×C22⋊C4D4311yescharacteristic
408#2065—431no—
409#2035—431no—
410#2035—431no—
411#2013—431no—
412#1968—431no—
413#1923—431no—
414#1880—431no—
415#1877—431no—
416#1864—431no—
417C2×C43—42no—
418C2×C43—44no—
419C2×C43—82no—
420C2×C43#242411yescharacteristic
421C2×C43#310111yescharacteristic
422C2×C43#312311yescharacteristic
423C2×C43#326711yescharacteristic
424C2×C43#327511yescharacteristic
425C2×C43D4×SD1611yescharacteristic
426C2×C43D4×SD1611yescharacteristic
427C23×D4C2×D4311yescharacteristic
428C22×SD16—431no—
429C22×SD16—431no—
430C22×SD16—431no—
431C22×SD16—431no—
432C2×C4⋊Q8—431no—
433C2×C22⋊Q8—431no—
434C2×C22⋊Q8—431no—
435C2×C4×Q8—431no—
436C2×C4×D4C2×D4311yescharacteristic
437C2×C4×D4C2×D4311yescharacteristic
438C22×C22⋊C4—21no—
439#461—864no—
440#450—864no—
441#450—864no—
442C4×SD16—864no—
443C2×#106—431no—
444C2×#106—431no—
445C2×C4⋊C8—431no—
446C2×#103—431no—
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×C22⋊C8—431no—
455C2×C22⋊C8—431no—
456C2×C4×C8—431no—
457#398—861no—
458#396—861no—
459#391—431no—
460#390C2×D4311yescharacteristic
461#390C2×D4311yescharacteristic
462#389—431no—
463#389—861no—
464#388—861no—
465#386—21no—
466#386—21no—
467#380C2×D4311yescharacteristic
468#379—21no—
469C4×C22⋊C4C2×D4311yescharacteristic
470#340—431no—
471#340—431no—
472#336—431no—
473#336—431no—
474C43#2515611yescharacteristic, complemented, Sylow
475C25—21no—
476C22×Q8—431no—
477C22×Q8—431no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4C22×D4311yescharacteristic
486C22×D4C22×D4311yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C22×D4311yescharacteristic
490C2×SD16—434no—
491C2×SD16—862no—
492C2×SD16—862no—
493C2×SD16—862no—
494C2×SD16—862no—
495C2×SD16—862no—
496C2×SD16—862no—
497C2×SD16—862no—
498C2×SD16—862no—
499C2×SD16—862no—
500C2×SD16—1721no—
501C2×SD16—1721no—
502C22×C8—431no—
503C22×C8—431no—
504C22×C8—431no—
505C22×C8—431no—
506C4⋊Q8—862no—
507C4⋊Q8—1721no—
508C22⋊Q8—862no—
509C22⋊Q8—862no—
510C22⋊Q8—1721no—
511C22⋊Q8—1721no—
512C4×Q8—862no—
513C4×Q8—1721no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22×D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—44no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4C22⋊D4311yescharacteristic
539C2×C22⋊C4C22⋊D4311yescharacteristic
540C2×C42—861no—
541C2×C42C22×D4311yescharacteristic
542C2×C42C22×D4311yescharacteristic
543#106—862no—
544#106—1721no—
545C4⋊C8—862no—
546#103—862no—
547#103—862no—
548#103—862no—
549#103—1721no—
550#102—434no—
551#102—862no—
552#102—862no—
553#102—862no—
554C22⋊C8—862no—
555C22⋊C8—862no—
556C4×C8—862no—
557#95—21no—
558#95—861no—
559#95—861no—
560#95—861no—
561#95C22⋊D4311yescharacteristic
562#95C22⋊D4311yescharacteristic
563C24—21no—
564C24—24no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24C2×C22⋊D4311yescharacteristic
573C2×Q8—432no—
574C2×Q8—861no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—861no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×Q8—861no—
581C2×Q8—861no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4#1062189812yes—
601C2×D4#1062189812yes—
602C2×D4D4×D4312yes—
603C2×D4D4×D4312yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4C2×C22⋊D4311yescharacteristic
623C22×C4C2×C22⋊D4311yescharacteristic
624C22×C4C2×C22⋊D4311yescharacteristic
625C22×C4C2×C22⋊D4311yescharacteristic
626C22×C4C2×C22⋊D4311yescharacteristic
627C22×C4C23×D4311yescharacteristic
628SD16—868no—
629SD16—1724no—
630SD16—1724no—
631SD16—1724no—
632C2×C8—432no—
633C2×C8—432no—
634C2×C8—861no—
635C2×C8—861no—
636C2×C8—861no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—432no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—1722no—
653C4⋊C4—1722no—
654C4⋊C4—1722no—
655C4⋊C4—1722no—
656C4⋊C4—1722no—
657C4⋊C4—1722no—
658C22⋊C4—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—1722no—
667C22⋊C4—1722no—
668C22⋊C4#1062188314yescomplemented
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—1722no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—22no—
680C23—22no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C2×#1062188312yes—
702C23C22×C22⋊D4311yescharacteristic
703Q8—862no—
704Q8—862no—
705Q8—1721no—
706Q8—1721no—
707Q8—1721no—
708Q8—1721no—
709Q8—1721no—
710Q8—1721no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4#1306329814yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4C2×#1062188312yes—
758C2×C4C2×#1062188312yes—
759C2×C4C2×D4×D4311yescharacteristic
760C2×C4C2×D4×D4311yescharacteristic
761C2×C4C2×#1062189811yescharacteristic
762C2×C4C2×#1062189811yescharacteristic
763C2×C4#1306337011yescharacteristic
764C2×C4#1306337011yescharacteristic
765C8—862no—
766C8—862no—
767C8—1721no—
768C8—1721no—
769C22—22no—
770C22—22no—
771C22—24no—
772C22—22no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22#1458341011yescharacteristic
792C22D4×C22⋊D4311yescharacteristic
793C22D4×C22⋊D4311yescharacteristic
794C22C22×#1062188311yescharacteristic
795C22#1458369711yescharacteristic
796C22#1458371011yescharacteristic
797C22#1458371011yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—3441no—
806C4—3441no—
807C4—1722no—
808C4—1722no—
809C4C2×#1306329811yescharacteristic
810C4#1458348711yescharacteristic
811C4#1458353911yescharacteristic
812C4#1458353911yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2#1913813111yescharacteristic
817C2#1914460311yescharacteristic
818C2#1914484711yescharacteristic
819C2#1914611611yescharacteristic
820C2#1914622211yescharacteristic
821C2D4×#1062188311yescharacteristic
822C2D4×#1062188311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterD4×C22⋊C4D43
hypocenterC43#25156
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14583104C2semidirect
4. C2×C4×#10621883C2semidirect
5. #19138194C2semidirect
6. #19135969C2semidirect
7. #19135791C2semidirect
8. #19135791C2semidirect
9. #19135677C2semidirect
10. #19135448C2semidirect
11. #19135203C2semidirect
12. #19134953C2semidirect
13. #19134929C2semidirect
14. #19134856C2semidirect
20. C2×#13063325C22semidirect
23. C2×C4×Dic86C22semidirect
28. C2×#13063256C22semidirect
29. C2×#13063256C22semidirect
30. C2×C4⋊(C43⋊C8)C22semidirect
31. C2×#13063248C22semidirect
32. C2×#13063248C22semidirect
33. C2×#13063248C22semidirect
34. C2×#13063248C22semidirect
41. C2×C4×C43⋊C8C22semidirect
44. #14582805C22semidirect
45. #14582797C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
228. C22⋊C4×C43SD16semidirect
474. C43#25156semidirect
668. C22⋊C4#10621883semidirect

Maximal subgroups

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

subgroupindex
C2×#145831042
C2×#145830502
C2×C4×#106218832
#191381942
#191359692
#191357912
#191356772
#191354482
#191352032
#191349532
#191349292
#191348562
D4×C22⋊C4×C432
#2515643