Finite Group Databasebeta

← #482890

Subgroups — #482890

Order 512.

927 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41409C211yesmaximal, characteristic
2#22477C211yesmaximal, characteristic, complemented
3#17412C211yesmaximal, characteristic, complemented
4#11899C211yesmaximal, characteristic, complemented
5#11843C211yesmaximal, characteristic, complemented
6#11840C211yesmaximal, characteristic, complemented
7#11824C211yesmaximal, characteristic, complemented
8#11813C211yesmaximal, characteristic, complemented
9#11809C211yesmaximal, characteristic, complemented
10#11786C211yesmaximal, characteristic, complemented
11#11757C211yesmaximal, characteristic, complemented
12#11754C211yesmaximal, characteristic, complemented
13#11729C211yesmaximal, characteristic, complemented
14#11718C211yesmaximal, characteristic, complemented
15C2×#1352C211yesmaximal, characteristic, complemented
16C2×#551C2211yescharacteristic
17C2×#547C411yescharacteristic, complemented
18#2924—21no—
19#2821C411yescharacteristic, complemented
20#2813C411yescharacteristic, complemented
21#2723—21no—
22#2710—21no—
23#2706—21no—
24#2692—21no—
25#2639C411yescharacteristic, complemented
26#2636C411yescharacteristic, complemented
27#2635C2211yescharacteristic
28#2628C2211yescharacteristic
29#2623C411yescharacteristic, complemented
30#2598C2211yescharacteristic
31#2539C2211yescharacteristic
32#2503C411yescharacteristic, complemented
33#2487C2211yescharacteristic
34#2413—21no—
35#2412—21no—
36#2406—21no—
37#2404—21no—
38C2×#399C2211yescharacteristic
39#2342—21no—
40#2318C411yescharacteristic, complemented
41#1996—21no—
42#1899—21no—
43#1898—21no—
44#1820C2211yescharacteristic
45#1819C2211yescharacteristic
46#1799C2211yescharacteristic
47C4×#99C2211yescharacteristic
48#1740C2211yescharacteristic
49C2×#342C2211yescharacteristic
50#1473—21no—
51#1469—21no—
52#1468—21no—
53#1466C2211yescharacteristic
54#1464C2211yescharacteristic
55#1462C2211yescharacteristic
56#1460C2211yescharacteristic
57#1458C2211yescharacteristic
58C2×#323C2211yescharacteristic
59#1352C2211yescharacteristic
60#1352C2211yescharacteristic
61#1352C2211yescharacteristic
62#1352C2211yescharacteristic
63#1352C2211yescharacteristic
64#1352C2211yescharacteristic
65#1352C2211yescharacteristic
66#1352C2211yescharacteristic
67#1352C2211yescharacteristic
68#1352C2211yescharacteristic
69#1352C2211yescharacteristic
70#1352C2211yescharacteristic
71#1343C2211yescharacteristic
72#1343C2211yescharacteristic
73#1343C2211yescharacteristic
74#1343C2211yescharacteristic
75C22×#41—21no—
76#551—41no—
77#551—41no—
78#551—41no—
79#551—41no—
80#547—41no—
81#547—41no—
82#547—41no—
83#547—41no—
84C2×C4⋊Q8C2×C411yescharacteristic, complemented
85C2×#126C2×C411yescharacteristic
86C2×#126D411yescharacteristic
87C2×#124D411yescharacteristic
88C2×#123—21no—
89C2×#123—21no—
90C2×#123—21no—
91C2×#123C2×C411yescharacteristic
92C2×#123D411yescharacteristic
93C2×#123D411yescharacteristic
94C2×C22⋊Q8—21no—
95C2×C22⋊Q8C2×C411yescharacteristic
96C2×C22⋊Q8D411yescharacteristic
97C2×#121C2×C411yescharacteristic
98C2×#121C2×C411yescharacteristic, complemented
99C2×#120—21no—
100C2×#120D411yescharacteristic
101C2×C4×D4C2×C411yescharacteristic
102C2×C4×D4C2×C411yescharacteristic, complemented
103C2×C4×D4C2311yescharacteristic
104C2×#117—21no—
105C2×#117D411yescharacteristic
106C2×#117C2311yescharacteristic
107C22×C4⋊C4—21no—
108C22×C4⋊C4C2×C411yescharacteristic
109C22×C4⋊C4C2×C411yescharacteristic, complemented
110C22×C22⋊C4—21no—
111C22×C22⋊C4—21no—
112C22×C22⋊C4D411yescharacteristic
113C22×C22⋊C4C2311yescharacteristic
114#433—41no—
115#433—41no—
116#432—21no—
117#432—21no—
118#431—21no—
119#431—21no—
120#424—41no—
121C2×#99—21no—
122C2×#99—21no—
123#407—21no—
124C2×C22⋊C8—21no—
125#405—41no—
126#400C2×C411yescharacteristic, complemented
127#400C2×C411yescharacteristic, complemented
128#400C2×C411yescharacteristic, complemented
129#400C2×C411yescharacteristic, complemented
130#400C2×C411yescharacteristic, complemented
131#400C2×C411yescharacteristic, complemented
132#399—21no—
133#399—21no—
134#399C2×C411yescharacteristic
135#399C2×C411yescharacteristic
136#399C2×C411yescharacteristic
137#399C2311yescharacteristic
138#399C2311yescharacteristic
139#399C2311yescharacteristic
140#398—21no—
141#398—21no—
142#397—21no—
143#397—21no—
144#397—21no—
145#396—21no—
146#396—21no—
147#395—21no—
148#395—21no—
149#394—21no—
150#394—21no—
151#394—21no—
152#394—21no—
153#394C2×C411yescharacteristic, complemented
154#394C2×C411yescharacteristic, complemented
155#393—21no—
156#393—21no—
157#393—21no—
158#392—21no—
159#392—21no—
160#392C2×C411yescharacteristic
161#392C2311yescharacteristic
162#391—21no—
163#390—21no—
164#390—21no—
165#389—21no—
166#389—21no—
167#388—21no—
168#388—21no—
169#388—21no—
170#388—41no—
171#388—41no—
172#387—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#386—21no—
178#386—21no—
179#386—21no—
180#386—21no—
181#386—21no—
182#385—21no—
183#385—21no—
184#385—21no—
185#385—21no—
186#385—21no—
187#385—41no—
188#383C2×C411yescharacteristic, complemented
189#382—21no—
190#382C2×C411yescharacteristic, complemented
191#381—21no—
192#381—21no—
193#381—21no—
194#381C2×C411yescharacteristic, complemented
195#380—21no—
196#380—21no—
197#380—21no—
198#380C2×C411yescharacteristic, complemented
199#379—21no—
200C4×C22⋊C4—21no—
201C4×C22⋊C4—41no—
202C4×C22⋊C4C2×C411yescharacteristic
203C2×#95C2×C411yescharacteristic
204#342—21no—
205#342—21no—
206#342—21no—
207#342—21no—
208#342C2311yescharacteristic
209#342C2311yescharacteristic
210#342C2311yescharacteristic
211#342C2311yescharacteristic
212#324—21no—
213#324—21no—
214#323—21no—
215#323—21no—
216#323—21no—
217#323—21no—
218#323C2311yescharacteristic
219#323C2311yescharacteristic
220#323C2311yescharacteristic
221#323C2311yescharacteristic
222C25C2×D411yescharacteristic
223C2×#41—42no—
224C2×#41—42no—
225C2×#41—82no—
226C2×#41—82no—
227C22×Q8—21no—
228C22×Q8C22⋊C411yescharacteristic
229C22×D4—21no—
230C22×D4—21no—
231C22×D4—21no—
232C22×D4—21no—
233C22×D4C22⋊C411yescharacteristic
234C22×D4C22⋊C411yescharacteristic
235C22×D4C22×C411yescharacteristic
236C22×D4C2×D411yescharacteristic
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—41no—
242C23×C4C22×C411yescharacteristic
243C23×C4C22×C411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C2×M16—41no—
248C22×C8—41no—
249C4⋊Q8—41no—
250C4⋊Q8—41no—
251#126—41no—
252#126—41no—
253#126—41no—
254#126—41no—
255#124—41no—
256#124—41no—
257#123—41no—
258#123—41no—
259#123—41no—
260#123—41no—
261#123—41no—
262#123—41no—
263#123—42no—
264#123—42no—
265#123—41no—
266#123—41no—
267#123—41no—
268#123—41no—
269#123—82no—
270C22⋊Q8—41no—
271C22⋊Q8—41no—
272C22⋊Q8—41no—
273C22⋊Q8—41no—
274C22⋊Q8—42no—
275C22⋊Q8—42no—
276#121—41no—
277#121—41no—
278#121—41no—
279#121—41no—
280#120—41no—
281#120—41no—
282#120—82no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—41no—
288C4×D4—41no—
289C4×D4—41no—
290C4×D4—41no—
291#117—21no—
292#117—21no—
293#117—21no—
294#117—21no—
295#117—41no—
296#117—41no—
297#117—42no—
298#117—81no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—82no—
317C2×C4⋊C4C22⋊C411yescharacteristic
318C2×C4⋊C4C22⋊C411yescharacteristic
319C2×C4⋊C4C22⋊C411yescharacteristic
320C2×C4⋊C4C22⋊C411yescharacteristic
321C2×C4⋊C4C22⋊C411yescharacteristic
322C2×C4⋊C4C22×C411yescharacteristic
323C2×C4⋊C4C22×C411yescharacteristic
324C2×C4⋊C4C22×C411yescharacteristic
325C2×C4⋊C4C22×C411yescharacteristic
326C2×C4⋊C4C22×C411yescharacteristic
327C2×C4⋊C4C2×D411yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—81no—
361C2×C22⋊C4—82no—
362C2×C22⋊C4C22⋊C411yescharacteristic
363C2×C22⋊C4C22⋊C411yescharacteristic
364C2×C22⋊C4C22⋊C411yescharacteristic
365C2×C22⋊C4C22⋊C411yescharacteristic
366C2×C22⋊C4C22⋊C411yescharacteristic
367C2×C22⋊C4C22⋊C411yescharacteristic
368C2×C22⋊C4C22⋊C411yescharacteristic
369C2×C22⋊C4C22⋊C411yescharacteristic
370C2×C22⋊C4C22×C411yescharacteristic
371C2×C22⋊C4C2×D411yescharacteristic
372C2×C22⋊C4C2×D411yescharacteristic
373C2×C22⋊C4C2×D411yescharacteristic
374C2×C22⋊C4C2×D411yescharacteristic
375C2×C22⋊C4C2411yescharacteristic
376C2×C42—21no—
377C2×C42—41no—
378C2×C42—41no—
379C2×C42C22×C411yescharacteristic
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C4⋊C8—41no—
383C4⋊C8—41no—
384C4⋊C8—41no—
385C4⋊C8—41no—
386#99—42no—
387#99—81no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—41no—
393C22⋊C8—41no—
394#97—41no—
395#97—41no—
396C4×C8—41no—
397C4×C8—41no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—41no—
416#95—41no—
417#95—41no—
418#95—41no—
419#95C22×C411yescharacteristic
420#95C22×C411yescharacteristic
421#95C22×C411yescharacteristic
422#95C22×C411yescharacteristic
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—41no—
429C24—42no—
430C24—81no—
431C24C2×C22⋊C411yescharacteristic
432C24C2×C22⋊C411yescharacteristic
433C24C2×C22⋊C411yescharacteristic
434C24C22×D411yescharacteristic
435#41—88no—
436#41—88no—
437C2×Q8—41no—
438C2×Q8—42no—
439C2×Q8—81no—
440C2×Q8—81no—
441C2×Q8—81no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—81no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4—81no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—82no—
509C22×C4—82no—
510C22×C4—161no—
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C2×C22⋊C411yescharacteristic
514C22×C4C2×C22⋊C411yescharacteristic
515C22×C4C2×C22⋊C411yescharacteristic
516C22×C4C2×C22⋊C411yescharacteristic
517C22×C4C2×C22⋊C411yescharacteristic
518C22×C4C2×C22⋊C411yescharacteristic
519C22×C4C2×C22⋊C411yescharacteristic
520C22×C4C23×C411yescharacteristic
521C22×C4C22×D411yescharacteristic
522M16—82no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—82no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—42no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—81no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4—82no—
556C4⋊C4—161no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—81no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—82no—
604C22⋊C4—82no—
605C22⋊C4—161no—
606C22⋊C4#9911yescharacteristic
607C22⋊C4#9911yescharacteristic
608C22⋊C4#9911yescharacteristic
609C22⋊C4#9911yescharacteristic
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—81no—
617C42—82no—
618C42—161no—
619C23—21no—
620C23—22no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—81no—
652C23—82no—
653C23—82no—
654C23—162no—
655C23C2×#9911yescharacteristic
656C23C2×#9911yescharacteristic
657C23C22×C22⋊C411yescharacteristic
658C23#57711yescharacteristic
659C23#57811yescharacteristic
660Q8—84no—
661Q8—161no—
662D4—42no—
663D4—42no—
664D4—81no—
665D4—81no—
666D4—82no—
667D4—82no—
668D4—84no—
669D4—82no—
670D4—161no—
671D4—161no—
672D4—161no—
673D4—162no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4—82no—
733C2×C4—81no—
734C2×C4—84no—
735C2×C4—81no—
736C2×C4—84no—
737C2×C4—82no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—164no—
748C2×C4C2×#9911yescharacteristic
749C2×C4C2×#9911yescharacteristic
750C2×C4C2×#9911yescharacteristic
751C2×C4C2×#9911yescharacteristic
752C8—81no—
753C8—81no—
754C8—81no—
755C8—81no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—81no—
778C22—82no—
779C22—82no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—161no—
792C22—161no—
793C22#212812yes—
794C22C22×#9911yescharacteristic
795C22#289811yescharacteristic
796C22#290111yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—82no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4—161no—
819C4—161no—
820C4—161no—
821C2—21no—
822C2—21no—
823C2—22no—
824C2—41no—
825C2—41no—
826C2—41no—
827C2—81no—
828C2—81no—
829C2—161no—
830C2#1760811yescharacteristic
831C2#3335011yescharacteristic
832C2C2×#212811yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radical#41409C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#551 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22477C2semidirect
3. #17412C2semidirect
4. #11899C2semidirect
5. #11843C2semidirect
6. #11840C2semidirect
7. #11824C2semidirect
8. #11813C2semidirect
9. #11809C2semidirect
10. #11786C2semidirect
11. #11757C2semidirect
12. #11754C2semidirect
13. #11729C2semidirect
14. #11718C2semidirect
15. C2×#1352C2semidirect
17. C2×#547C4semidirect
19. #2821C4semidirect
20. #2813C4semidirect
25. #2639C4semidirect
26. #2636C4semidirect
29. #2623C4semidirect
32. #2503C4semidirect
40. #2318C4semidirect
84. C2×C4⋊Q8C2×C4semidirect
98. C2×#121C2×C4semidirect
102. C2×C4×D4C2×C4semidirect
109. C22×C4⋊C4C2×C4semidirect
126. #400C2×C4semidirect
127. #400C2×C4semidirect
128. #400C2×C4semidirect
129. #400C2×C4semidirect
130. #400C2×C4semidirect
131. #400C2×C4semidirect
153. #394C2×C4semidirect
154. #394C2×C4semidirect
188. #383C2×C4semidirect
190. #382C2×C4semidirect
194. #381C2×C4semidirect
198. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
#414092
#224772
#174122
#118992
#118432
#118402
#118242
#118132
#118092
#117862
#117572
#117542
#117292
#117182
C2×#13522