Finite Group Databasebeta

← #25003224

Subgroups — #25003224

Order 11008.

1494 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2#19143114C211yesmaximal, characteristic, complemented
3C2×#14582862C211yesmaximal, characteristic, complemented
4#19136974C211yesmaximal, characteristic, complemented
5#19134306C211yesmaximal, characteristic, complemented
6C2×#14582655C211yesmaximal, characteristic, complemented
7C2×C43×#421C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583406—22no—
11#14583406—22no—
12#14583406—22no—
13#14583406C414yescomplemented
14C2×#13063306—21no—
15C2×#13063301—21no—
16C2×#13063296—21no—
17C2×#13063293—21no—
18C2×C4×C22⋊D43—22no—
19C2×#13063284C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21#14582908—21no—
22#14582904—21no—
23#14582900—22no—
24#14582895—22no—
25#14582862—22no—
26#14582862—22no—
27C2×(C2×D43)⋊C8—22no—
28#14582760—21no—
29#14582756—22no—
30#14582754—21no—
31C4×(C2×D43)⋊C4—22no—
32#14582660—22no—
33#14582655—22no—
34C22×#41×C43C2211yescharacteristic
35C22×M16×C43C2211yescharacteristic
36C2×#117×C43C2211yescharacteristic
37C43×#421—22no—
38C43×#421—22no—
39C2×#104×C43—22no—
40C24×D43D411yescharacteristic
41C22×C22⋊D43—22no—
42C23×Dic43D411yescharacteristic
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43—21no—
46C22×C4×D43—21no—
47C22×C4×D43—21no—
48C22×C4×D43—21no—
49C22×C4×D43—21no—
50C22×C4×D43—21no—
51C22×C4×D43—21no—
52C22×C4×D43—21no—
53C22×C4×D43—21no—
54C22×C4×D43—21no—
55C22×C4×D43C2×C412yes—
56C22×C4×D43D412yes—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877—21no—
62C2×#10621877—21no—
63C22×C43⋊C8D412yescomplemented
64#13063306—24no—
65#13063306—24no—
66#13063301—24no—
67#13063301—24no—
68#13063296—24no—
69#13063296—24no—
70#13063293—24no—
71#13063293—24no—
72C4×C22⋊D43—28no—
73C4×C22⋊D43—28no—
74#13063284—21no—
75#13063284—21no—
76#13063284—21no—
77#13063284—21no—
78#13063284—21no—
79#13063284—21no—
80#13063284C2×C412yes—
81#13063284D412yes—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43D412yescomplemented
84C2×Dic43⋊C4—22no—
85C2×C22⋊Dic43—22no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—24no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43D412yes—
92#13063249—24no—
93#13063246—24no—
94(C2×D43)⋊C8—28no—
95C43⋊#95—24no—
96C2×#41×C43—21no—
97C2×#41×C43—21no—
98C2×#41×C43—21no—
99C2×#41×C43—21no—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
102C2×#41×C43—21no—
103C2×#41×C43—21no—
104C2×#41×C43—21no—
105C2×#41×C43—21no—
106C2×#41×C43C2×C412yes—
107C2×#41×C43D412yes—
108C22×Q8×C43D411yescharacteristic
109C22×D4×C43—21no—
110C22×D4×C43D411yescharacteristic
111C23×C4×C43—21no—
112C23×C4×C43C2311yescharacteristic
113C2×M16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43D412yescomplemented
119C22×C8×C43—21no—
120#117×C43—21no—
121#117×C43—21no—
122#117×C43—21no—
123#117×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43D412yescomplemented
127#104×C43—28no—
128C24×C43—21no—
129C24×C43C2×D411yescharacteristic
130C23×D43—21no—
131C23×D43—21no—
132C23×D43—21no—
133C23×D43—21no—
134C23×D43—21no—
135C23×D43—21no—
136C23×D43—44no—
137C23×D43C22⋊C412yes—
138#41×C43—22no—
139#41×C43—22no—
140#41×C43—22no—
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—22no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—41no—
147#41×C43—41no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C22⋊C412yescomplemented
160C2×D4×C43—21no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—41no—
168C2×D4×C43—41no—
169C2×D4×C43—41no—
170C2×D4×C43—41no—
171C2×D4×C43C22⋊C412yescomplemented
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—21no—
175C22×C4×C43—22no—
176C22×C4×C43—41no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43C22×C411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43#4111yescharacteristic
191C22×C4×C43#4111yescharacteristic
192C22×C4×C43#4111yescharacteristic
193C22×C4×C43#4111yescharacteristic
194C2×C22⋊D43—28no—
195C2×C22⋊D43—48no—
196C22×Dic43—21no—
197C22×Dic43—22no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—22no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43C22⋊C412yes—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—22no—
213C2×C4×D43—22no—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—41no—
218C2×C4×D43—41no—
219C2×C4×D43—41no—
220C2×C4×D43—41no—
221C2×C4×D43—41no—
222C2×C4×D43—41no—
223C2×C4×D43—41no—
224C2×C4×D43—41no—
225C2×C4×D43—41no—
226C2×C4×D43—41no—
227C2×C4×D43—41no—
228C2×C4×D43—41no—
229C2×C4×D43—41no—
230C2×C4×D43—41no—
231C2×C4×D43—41no—
232C2×C4×D43—41no—
233M16×C43—22no—
234M16×C43—22no—
235M16×C43—41no—
236M16×C43—41no—
237C2×C8×C43—22no—
238C2×C8×C43—41no—
239C2×C8×C43—41no—
240C4⋊C4×C43—41no—
241C4⋊C4×C43—41no—
242C22⋊C4×C43—41no—
243C22⋊C4×C43—41no—
244C42×C43—22no—
245C42×C43—22no—
246C22⋊Dic43—28no—
247C22⋊Dic43—22no—
248C22⋊Dic43—22no—
249C22⋊Dic43—41no—
250C22⋊Dic43—41no—
251(C2×D43)⋊C4—28no—
252(C2×D43)⋊C4—48no—
253C4⋊Dic43—22no—
254C4⋊Dic43—22no—
255C4⋊Dic43—22no—
256C4⋊Dic43—22no—
257Dic43⋊C4—28no—
258C4×Dic43—22no—
259C4×Dic43—41no—
260C4×Dic43—41no—
261C4×Dic43C22⋊C414yescomplemented
262#10621877—41no—
263#10621877—41no—
264#10621877—41no—
265#10621877—41no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—22no—
269C23×C43—22no—
270C23×C43—42no—
271C23×C43—44no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43C2×C22⋊C411yescharacteristic
275C23×C43#12011yescharacteristic
276C23×C43#12011yescharacteristic
277C23×C43#12011yescharacteristic
278C23×C43#12111yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12311yescharacteristic
281C22×D43—24no—
282C22×D43—24no—
283C22×D43—24no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43—44no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298Q8×C43—22no—
299Q8×C43—22no—
300Q8×C43—41no—
301Q8×C43—41no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43—42no—
305D4×C43—42no—
306D4×C43—42no—
307D4×C43—42no—
308D4×C43—41no—
309D4×C43—41no—
310C2×C4×C43—22no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—44no—
318C2×C4×C43—42no—
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C4×D411yescharacteristic
322C2×C4×C43C4×D411yescharacteristic
323C2×C4×C43C4×D411yescharacteristic
324C2×C4×C43C4×D411yescharacteristic
325C2×C4×C43#12011yescharacteristic
326C2×C4×C43#12011yescharacteristic
327C2×C4×C43#12011yescharacteristic
328C2×C4×C43#12011yescharacteristic
329C2×C4×C43#12011yescharacteristic
330C2×C4×C43#12111yescharacteristic
331C2×C4×C43#12111yescharacteristic
332C2×C4×C43#12111yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12111yescharacteristic
338C2×C4×C43#12111yescharacteristic
339C2×C4×C43#12111yescharacteristic
340C2×C4×C43#12311yescharacteristic
341C2×C4×C43#12311yescharacteristic
342C2×C4×C43#12311yescharacteristic
343C2×C4×C43#12411yescharacteristic
344C2×C4×C43#12411yescharacteristic
345C2×C4×C43#12711yescharacteristic
346C2×C4×C43#12711yescharacteristic
347C22⋊D43—416no—
348C2×Dic43—24no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—44no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—44no—
358C2×Dic43—42no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—42no—
362C4×D43—42no—
363C4×D43—42no—
364C4×D43—42no—
365C4×D43—42no—
366C4×D43—42no—
367C8×C43—42no—
368C43⋊C8—42no—
369#10994—431nomaximal, Sylow
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—44no—
378C22×C43—42no—
379C22×C43—82no—
380C22×C43—82no—
381C22×C43#37911yescharacteristic
382C22×C43#38611yescharacteristic
383C22×C43#38611yescharacteristic
384C22×C43#39211yescharacteristic
385C22×C43#39211yescharacteristic
386C22×C43#39411yescharacteristic
387C22×C43#39411yescharacteristic
388C2×D43—24no—
389C2×D43—24no—
390C2×D43—24no—
391C2×D43—42no—
392C2×D43—44no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—44no—
396C2×D43—44no—
397C2×D43—42no—
398C2×D43—44no—
399C4×C43—42no—
400C4×C43—82no—
401C4×C43#38611yescharacteristic
402C4×C43#38611yescharacteristic
403C4×C43#39011yescharacteristic
404C4×C43#39011yescharacteristic
405C4×C43#39211yescharacteristic
406C4×C43#39211yescharacteristic
407C4×C43#39411yescharacteristic
408C4×C43#39411yescharacteristic
409Dic43—44no—
410Dic43—42no—
411Dic43—82no—
412C2×#525—431no—
413C2×#421D4311yescharacteristic, complemented
414#2896—431no—
415C2×#407—431no—
416#2280—431no—
417#1733—431no—
418C2×H(3,ℤ/4)—431no—
419C2×C43—21no—
420C2×C43—21no—
421C2×C43—21no—
422C2×C43—21no—
423C2×C43—21no—
424C2×C43—21no—
425C2×C43—82no—
426C2×C43#143811yescharacteristic
427C2×C43#201012yes—
428D43—44no—
429C22×#41C2×D4311yescharacteristic
430C24×C4—431no—
431C22×M16—431no—
432C22×M16C2×D4311yescharacteristic
433#525—434no—
434#525—862no—
435#525—862no—
436#525—862no—
437C2×#123—861no—
438C2×C22⋊Q8—861no—
439C2×#121—861no—
440C2×#120—861no—
441C2×C4×D4—862no—
442C2×#117—431no—
443C2×#117—431no—
444C2×#117C2×D4311yescharacteristic
445#421—22no—
446#421—22no—
447C2×#104—22no—
448#419—861no—
449#418—861no—
450#417—862no—
451#416—862no—
452#407—862no—
453#407—862no—
454C2×C22⋊C8—862no—
455#381—861no—
456#380—862no—
457#379—861no—
458C4×C22⋊C4—862no—
459#339—862no—
460H(3,ℤ/4)—862no—
461C43#1099411yescharacteristic, complemented, Sylow
462C25—431no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41C4×D4312yes—
474C2×#41C22⋊D4312yes—
475C22×Q8D17211yescharacteristic
476C22×D4—21no—
477C22×D4—862no—
478C22×D4D17211yescharacteristic
479C23×C4—21no—
480C23×C4—431no—
481C23×C4—432no—
482C23×C4—432no—
483C23×C4—861no—
484C23×C4—861no—
485C23×C4—861no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491C23×C4—861no—
492C23×C4—861no—
493C23×C4—861no—
494C23×C4—861no—
495C23×C4C22×D4311yescharacteristic
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—861no—
502C2×M16—861no—
503C2×M16—861no—
504C2×M16—861no—
505C2×M16—861no—
506C2×M16—861no—
507C2×M16C22⋊D4312yescomplemented
508C22×C8—21no—
509C22×C8—432no—
510#123—864no—
511#123—864no—
512C22⋊Q8—864no—
513C22⋊Q8—864no—
514#121—864no—
515#121—864no—
516#120—864no—
517#120—864no—
518C4×D4—868no—
519C4×D4—868no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—21no—
524#117—432no—
525#117—432no—
526#117—861no—
527#117—861no—
528#117—861no—
529#117—861no—
530#117—861no—
531#117—861no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—432no—
534C2×C4⋊C4—862no—
535C2×C4⋊C4—861no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—862no—
538C2×C22⋊C4—862no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—864no—
541C2×C22⋊C4—861no—
542C2×C42—432no—
543C2×C42—861no—
544C2×C42C22⋊D4312yescomplemented
545#104—28no—
546#103—864no—
547#102—864no—
548C22⋊C8—868no—
549#95—864no—
550C24—21no—
551C24—432no—
552C24—861no—
553C24—861no—
554C24—861no—
555C24—861no—
556C24—861no—
557C24—861no—
558C24—1724no—
559C24D4×D4311yescharacteristic
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8(C2×D43)⋊C412yescomplemented
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—868no—
594C2×D4—1728no—
595C2×D4(C2×D43)⋊C412yescomplemented
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—432no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—862no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—1721no—
626C22×C4—1721no—
627C22×C4—1721no—
628C22×C4—1721no—
629C22×C4—1721no—
630C22×C4—1721no—
631C22×C4—1721no—
632C22×C4—1721no—
633C22×C4—1721no—
634C22×C4—1721no—
635C22×C4—1721no—
636C22×C4—1721no—
637C22×C4—1721no—
638C22×C4—1721no—
639C22×C4—1721no—
640C22×C4—1721no—
641C22×C4C2×C4×D4311yescharacteristic
642C22×C4C2×D17211yescharacteristic
643C22×C4#1062189811yescharacteristic
644C22×C4#1062189811yescharacteristic
645C22×C4D4×D4311yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4D4×D4311yescharacteristic
650C22×C4#1062190011yescharacteristic
651C22×C4#1062190011yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C2×C22⋊D4311yescharacteristic
654C22×C4C2×C22⋊D4311yescharacteristic
655M16—22no—
656M16—22no—
657M16—41no—
658M16—41no—
659M16—1721no—
660M16—1721no—
661M16—1721no—
662M16—1721no—
663C2×C8—22no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—862no—
667C2×C8—862no—
668C2×C8—862no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—868no—
672C4⋊C4—862no—
673C4⋊C4—862no—
674C4⋊C4—862no—
675C4⋊C4—862no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—868no—
679C22⋊C4—868no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C22⋊C4—1728no—
683C22⋊C4—1721no—
684C22⋊C4—1721no—
685C42—22no—
686C42—22no—
687C42—434no—
688C42—862no—
689C42—1721no—
690C42—1721no—
691C23—22no—
692C23—42no—
693C23—44no—
694C23—41no—
695C23—41no—
696C23—864no—
697C23—864no—
698C23—864no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—1722no—
703C23—1722no—
704C23—1722no—
705C23—1724no—
706C23—1724no—
707C23—1724no—
708C23—1724no—
709C23—1721no—
710C23—1721no—
711C23—1721no—
712C23—1721no—
713C23C22⋊C4×D4311yescharacteristic
714C23#1306329311yescharacteristic
715C23#1306329311yescharacteristic
716C23#1306329511yescharacteristic
717C23#1306329611yescharacteristic
718C23#1306329811yescharacteristic
719C23#1306330711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—42no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—41no—
731D4—41no—
732D4—17216no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—864no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—1724no—
747C2×C4—1722no—
748C2×C4—1724no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4C22⋊C4×D4311yescharacteristic
762C2×C4C2×(C2×D43)⋊C411yescharacteristic
763C2×C4(C22⋊D43)⋊C411yescharacteristic
764C2×C4(C22⋊D43)⋊C411yescharacteristic
765C2×C4C4×C22⋊D4311yescharacteristic
766C2×C4C4×C22⋊D4311yescharacteristic
767C2×C4#1306329311yescharacteristic
768C2×C4#1306329311yescharacteristic
769C2×C4#1306329411yescharacteristic
770C2×C4#1306329511yescharacteristic
771C2×C4#1306329511yescharacteristic
772C2×C4#1306329611yescharacteristic
773C2×C4#1306329711yescharacteristic
774C2×C4#1306329711yescharacteristic
775C2×C4#1306329711yescharacteristic
776C2×C4#1306329711yescharacteristic
777C2×C4#1306329811yescharacteristic
778C2×C4#1306329811yescharacteristic
779C2×C4#1306329811yescharacteristic
780C2×C4#1306329911yescharacteristic
781C2×C4#1306329911yescharacteristic
782C2×C4#1306330711yescharacteristic
783C2×C4#1306330811yescharacteristic
784C2×C4#1306330911yescharacteristic
785C2×C4#1306331111yescharacteristic
786C2×C4#1306331111yescharacteristic
787C2×C4#1306332111yescharacteristic
788C2×C4#1306332111yescharacteristic
789C8—42no—
790C8—1722no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—44no—
799C22—42no—
800C22—82no—
801C22—82no—
802C22—864no—
803C22—864no—
804C22—864no—
805C22—1724no—
806C22—1722no—
807C22—1724no—
808C22—1722no—
809C22—1722no—
810C22—1724no—
811C22—1722no—
812C22—1724no—
813C22#1458275411yescharacteristic
814C22#1458277511yescharacteristic
815C22#1458277511yescharacteristic
816C22#1458280711yescharacteristic
817C22#1458280811yescharacteristic
818C22#1458281411yescharacteristic
819C22#1458281511yescharacteristic
820C4—42no—
821C4—82no—
822C4—3442no—
823C4—1724no—
824C4—1722no—
825C4#1458277611yescharacteristic
826C4#1458277811yescharacteristic
827C4#1458279911yescharacteristic
828C4#1458279911yescharacteristic
829C4#1458280711yescharacteristic
830C4#1458280811yescharacteristic
831C4#1458281411yescharacteristic
832C4#1458281511yescharacteristic
833C2—21no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—82no—
840C2—1724no—
841C2#1913283411yescharacteristic
842C2#1913566112yes—
subgroupG/H
centerC2×C4#13063321
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#421C2
socleC22×C43#392
prime radicalC2×#14583406C2
cosocleC23×C4×C43C23
hypercenterC2×#421D43
hypocenterC43#10994
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #19143114C2semidirect
3. C2×#14582862C2semidirect
4. #19136974C2semidirect
5. #19134306C2semidirect
6. C2×#14582655C2semidirect
7. C2×C43×#421C2semidirect
13. #14583406C4semidirect
63. C22×C43⋊C8D4semidirect
83. C2×C4⋊Dic43D4semidirect
118. C2×M16×C43D4semidirect
126. C2×C42×C43D4semidirect
159. C2×Q8×C43C22⋊C4semidirect
171. C2×D4×C43C22⋊C4semidirect
261. C4×Dic43C22⋊C4semidirect
413. C2×#421D43semidirect
461. C43#10994semidirect
507. C2×M16C22⋊D43semidirect
544. C2×C42C22⋊D43semidirect
581. C2×Q8(C2×D43)⋊C4semidirect
595. C2×D4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
#191431142
C2×#145828622
#191369742
#191343062
C2×#145826552
C2×C43×#4212
#1099443