Finite Group Databasebeta

← #25128607

Subgroups — #25128607

Order 11008.

1270 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×#14583520C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14583044C211yesmaximal, characteristic
4#19135736C211yesmaximal, characteristic, complemented
5#19135731C211yesmaximal, characteristic, complemented
6#19135688C211yesmaximal, characteristic, complemented
7#19135671C211yesmaximal, characteristic, complemented
8#19134953C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic, complemented
10#19134939C211yesmaximal, characteristic, complemented
11#19134932C211yesmaximal, characteristic, complemented
12#19134912C211yesmaximal, characteristic, complemented
13#19134902C211yesmaximal, characteristic, complemented
14#19134666C211yesmaximal, characteristic, complemented
15C43×#2311C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20#14583520—24no—
21#14583520—24no—
22C2×#13063325C2211yescharacteristic
23C2×#13063320—21no—
24C2×#13063313C2211yescharacteristic
25C2×#13063311—21no—
26C2×#13063307—21no—
27C2×#13063304C2211yescharacteristic
28C2×#13063303—21no—
29C2×#13063299C2211yescharacteristic
30C2×C4×Dic86C2211yescharacteristic
31C2×C4×D172C2211yescharacteristic
32#14583061—24no—
33#14583044—24no—
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#386—21no—
60C43×#386—21no—
61C43×#380—21no—
62C43×#380—21no—
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C4×D43—21no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—41no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883—41no—
74C2×#10621884—22no—
75C2×#10621884—22no—
76C2×#10621884—41no—
77C2×#10621882—22no—
78C2×#10621882—22no—
79C2×#10621882—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063325—22no—
85#13063325—22no—
86#13063320—28no—
87#13063313—22no—
88#13063313—22no—
89#13063311—28no—
90#13063307—28no—
91#13063304—22no—
92#13063304D414yes—
93#13063303—28no—
94#13063299—22no—
95#13063299D414yes—
96C4×Dic86—22no—
97C4×Dic86—22no—
98C4×D172—22no—
99C4×D172—22no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×C22⋊Dic43—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×C4×Dic43—21no—
111#13063249—22no—
112#13063249—22no—
113#13063248—41no—
114#13063248—41no—
115#13063246—22no—
116#13063246—22no—
117#13063245—41no—
118#13063245—41no—
119C22⋊(C43⋊C8)—22no—
120C22⋊(C43⋊C8)—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—22no—
125C2×#41×C43—41no—
126C2×#41×C43—41no—
127C22×Q8×C43C2311yescharacteristic
128C22×D4×C43—21no—
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C23×C4×C43—21no—
132C23×C4×C43C2311yescharacteristic
133#117×C43—22no—
134#117×C43—22no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—41no—
137C2×C4⋊C4×C43—41no—
138C2×C4⋊C4×C43D411yescharacteristic
139C2×C4⋊C4×C43D411yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C22⋊C4×C43D411yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C23×D43—21no—
157#41×C43—44no—
158#41×C43—44no—
159#41×C43—44no—
160#41×C43—44no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43#4112yes—
167C2×D4×C43—24no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—42no—
174C2×D4×C43—42no—
175C2×D4×C43#4112yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—24no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43—42no—
187C22×C4×C43—81no—
188C22×C4×C43—81no—
189C22×C4×C43C2×D412yes—
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—81no—
199C2×C22⋊D43—81no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172C2×D412yes—
209C2×C4×D43—24no—
210C2×C4×D43—81no—
211C2×C4×D43—81no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—24no—
218C2×Dic86—81no—
219C2×Dic86—81no—
220C2×Dic86C2×D412yes—
221C4⋊C4×C43—22no—
222C4⋊C4×C43—22no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—42no—
228C22⋊C4×C43—22no—
229C22⋊C4×C43—22no—
230C22⋊C4×C43—81no—
231C22⋊C4×C43—81no—
232C22⋊C4×C43—81no—
233C22⋊C4×C43—81no—
234C42×C43—21no—
235C42×C43—21no—
236C42×C43—21no—
237C42×C43—21no—
238C22⋊Dic43—24no—
239#10621885—44no—
240#10621884—44no—
241#10621883—44no—
242#10621882—44no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4—24no—
247C4⋊Dic43—24no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43C2×D412yes—
251C4⋊Dic43C2×D412yes—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254C4×Dic43—24no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—22no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43—41no—
280C23×C43#12012yes—
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286C22×D43—41no—
287C22×D43—41no—
288C22×D43—41no—
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—41no—
292Q8×C43—41no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—48no—
296D4×C43—41no—
297D4×C43—41no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—48no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—84no—
327C2×C4×C43#12012yes—
328C2×C4×C43C22×D411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C22⋊D43—84no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344D172—22no—
345D172—22no—
346D172—41no—
347D172—41no—
348C4×D43—84no—
349Dic86—22no—
350Dic86—22no—
351Dic86—41no—
352Dic86—41no—
353Dic86—84no—
354C43⋊C8—41no—
355C43⋊C8—41no—
356C43⋊C8—41no—
357C43⋊C8—41no—
358#23947—431nomaximal, Sylow
359C22×C43—22no—
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43—81no—
373C22×C43C2×#12011yescharacteristic
374C22×C43#52511yescharacteristic
375C22×C43#53511yescharacteristic
376C22×C43#57611yescharacteristic
377C22×C43#57711yescharacteristic
378C22×C43#57711yescharacteristic
379C22×C43#57811yescharacteristic
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—81no—
384C2×D43—81no—
385C2×D43—81no—
386C2×D43—81no—
387C4×C43—22no—
388C4×C43—42no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43—41no—
393C4×C43—81no—
394C4×C43—81no—
395C4×C43#54611yescharacteristic
396C4×C43#54611yescharacteristic
397C4×C43#54611yescharacteristic
398C4×C43#54611yescharacteristic
399Dic43—42no—
400Dic43—42no—
401Dic43—42no—
402C2×#542—431no—
403C2×#452—431no—
404C2×#449—431no—
405#2311D4311yescharacteristic, complemented
406#2024—431no—
407#2023—431no—
408#2015—431no—
409#2012—431no—
410#1880—431no—
411#1879—431no—
412#1878—431no—
413#1877—431no—
414#1874—431no—
415#1872—431no—
416#1818—431no—
417C2×C43—42no—
418C2×C43—82no—
419C2×C43#240411yescharacteristic
420C2×C43#301211yescharacteristic
421C2×C43#301311yescharacteristic
422C2×C43#312411yescharacteristic
423C2×C43#312511yescharacteristic
424C2×C43#322411yescharacteristic
425C2×C43#322511yescharacteristic
426D43—82no—
427C22×#41C2×D4311yescharacteristic
428C22×Q16—431no—
429C22×SD16—431no—
430C22×SD16—431no—
431C22×D8—431no—
432#542—864no—
433#542—864no—
434C2×C4⋊Q8—431no—
435C2×#126—861no—
436C2×#124—431no—
437C2×#124—861no—
438C2×#123—861no—
439C2×C22⋊Q8—431no—
440C2×C22⋊Q8—861no—
441C2×#121—431no—
442C2×C4×Q8—431no—
443C2×C4×D4—431no—
444C2×#117C2×D4311yescharacteristic
445C22×C4⋊C4C2×D4311yescharacteristic
446#452—864no—
447#449—864no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458#391C2×D4311yescharacteristic
459#391C2×D4311yescharacteristic
460#390C2×D4311yescharacteristic
461#390C2×D4311yescharacteristic
462#386—21no—
463#386—21no—
464#380—21no—
465#380—21no—
466#340—431no—
467#340—431no—
468#340—431no—
469#340—431no—
470#336—431no—
471#336—431no—
472#336—431no—
473#336—431no—
474C43#2394711yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—41no—
480C2×#41—41no—
481C22×Q8—431no—
482C22×Q8—861no—
483C22×Q8C22×D4311yescharacteristic
484C22×D4—21no—
485C22×D4—431no—
486C22×D4—861no—
487C22×D4C22×D4311yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—861no—
491C23×C4C22×D4311yescharacteristic
492C2×Q16—862no—
493C2×Q16—862no—
494C2×Q16—1721no—
495C2×SD16—862no—
496C2×SD16—862no—
497C2×SD16—862no—
498C2×SD16—862no—
499C2×SD16—1721no—
500C2×SD16—1721no—
501C2×D8—862no—
502C2×D8—862no—
503C2×D8—1721no—
504C22×C8—431no—
505C22×C8—431no—
506C22×C8—431no—
507C22×C8—431no—
508C4⋊Q8—862no—
509C4⋊Q8—862no—
510#126—868no—
511#124—862no—
512#124—862no—
513#124—868no—
514#123—868no—
515C22⋊Q8—434no—
516C22⋊Q8—868no—
517C22⋊Q8—862no—
518#121—434no—
519#121—862no—
520C4×Q8—862no—
521C4×Q8—862no—
522C4×D4—862no—
523C4×D4—862no—
524#117—22no—
525#117—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—431no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4C22⋊D4311yescharacteristic
535C2×C4⋊C4C22⋊D4311yescharacteristic
536C2×C4⋊C4C22×D4311yescharacteristic
537C2×C4⋊C4C22×D4311yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4C22⋊D4311yescharacteristic
548C2×C22⋊C4C22⋊D4311yescharacteristic
549C2×C42—861no—
550C2×C42C22×D4311yescharacteristic
551C2×C42C22×D4311yescharacteristic
552#103—862no—
553#103—862no—
554#103—1721no—
555#103—1721no—
556#102—862no—
557#102—862no—
558#102—1721no—
559#102—1721no—
560C22⋊C8—862no—
561C22⋊C8—862no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566C24—21no—
567C24—861no—
568C24C2×C22⋊D4311yescharacteristic
569#41—44no—
570#41—44no—
571#41—44no—
572#41—44no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—432no—
579C2×Q8—864no—
580C2×Q8—861no—
581C2×Q8—861no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×Q8—3441no—
586C2×Q8—3441no—
587C2×Q8#1062189812yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—432no—
597C2×D4—864no—
598C2×D4—861no—
599C2×D4—861no—
600C2×D4—861no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—3441no—
604C2×D4—3441no—
605C2×D4#1062189812yes—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4—864no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—3441no—
624C22×C4—3441no—
625C22×C4D4×D4312yes—
626C22×C4D4×D4312yes—
627C22×C4C2×C22⋊D4311yescharacteristic
628C22×C4C2×C22⋊D4311yescharacteristic
629C22×C4C2×C22⋊D4311yescharacteristic
630C22×C4C2×C22⋊D4311yescharacteristic
631C22×C4C2×C22⋊D4311yescharacteristic
632C22×C4C23×D4311yescharacteristic
633Q16—1724no—
634SD16—1724no—
635SD16—1724no—
636D8—1724no—
637C2×C8—861no—
638C2×C8—861no—
639C2×C8—861no—
640C2×C8—861no—
641C2×C8—861no—
642C2×C8—861no—
643C2×C8—861no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—432no—
657C4⋊C4—432no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C22⋊C4—864no—
670C22⋊C4—864no—
671C22⋊C4—864no—
672C22⋊C4—864no—
673C22⋊C4—864no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—864no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—862no—
693C23—1721no—
694C23—1721no—
695C23—1721no—
696C23—1721no—
697C23—1721no—
698C23—1721no—
699C23#1306329312yes—
700C23C22×C22⋊D4311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—41no—
704Q8—41no—
705Q8—862no—
706Q8—862no—
707Q8—3444no—
708Q8—1721no—
709Q8—1721no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—862no—
716D4—862no—
717D4—3444no—
718D4—1721no—
719D4—1721no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—48no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—3444no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1721no—
759C2×C4#1306329312yes—
760C2×C4C2×D4×D4311yescharacteristic
761C2×C4C2×D4×D4311yescharacteristic
762C2×C4C2×#1062189811yescharacteristic
763C2×C4C2×#1062189811yescharacteristic
764C2×C4#1306337011yescharacteristic
765C2×C4#1306337011yescharacteristic
766C8—1721no—
767C8—1721no—
768C8—1721no—
769C8—1721no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—3441no—
785C22—3441no—
786C22—3441no—
787C22—3441no—
788C22—1722no—
789C22—1722no—
790C22—1722no—
791C22C2×#1306329311yescharacteristic
792C22#1458341011yescharacteristic
793C22#1458346611yescharacteristic
794C22#1458370211yescharacteristic
795C22#1458370711yescharacteristic
796C22#1458371011yescharacteristic
797C22#1458371411yescharacteristic
798C4—22no—
799C4—42no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—81no—
805C4—81no—
806C4—1722no—
807C4—1722no—
808C4—1722no—
809C4#1458353911yescharacteristic
810C4#1458353911yescharacteristic
811C4#1458353911yescharacteristic
812C4#1458353911yescharacteristic
813C2—42no—
814C2—82no—
815C2—3442no—
816C2#1913791411yescharacteristic
817C2#1914389611yescharacteristic
818C2#1914390711yescharacteristic
819C2#1914485711yescharacteristic
820C2#1914487211yescharacteristic
821C2#1914568911yescharacteristic
822C2#1914570411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2311C2
socleC23×C43C22×D4
prime radicalC2×#14583044C2
hypercenter#2311D43
hypocenterC43#23947
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
1. C2×#14583520C2semidirect
2. C2×#14583061C2semidirect
4. #19135736C2semidirect
5. #19135731C2semidirect
6. #19135688C2semidirect
7. #19135671C2semidirect
8. #19134953C2semidirect
9. #19134946C2semidirect
10. #19134939C2semidirect
11. #19134932C2semidirect
12. #19134912C2semidirect
13. #19134902C2semidirect
14. #19134666C2semidirect
15. C43×#2311C2semidirect
405. #2311D43semidirect
474. C43#23947semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145830612
C2×#145830442
#191357362
#191357312
#191356882
#191356712
#191349532
#191349462
#191349392
#191349322
#191349122
#191349022
#191346662
C43×#23112
#2394743