Finite Group Databasebeta

← #216502

Subgroups — #216502

Order 512.

907 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35083C211yesmaximal, characteristic
2#21953C211yesmaximal, characteristic, complemented
3#13787C211yesmaximal, characteristic, complemented
4#9909C211yesmaximal, characteristic, complemented
5#9908C211yesmaximal, characteristic, complemented
6#9713C211yesmaximal, characteristic
7#9713C211yesmaximal, characteristic
8#9118C211yesmaximal, characteristic
9#9116C211yesmaximal, characteristic, complemented
10#9114C211yesmaximal, characteristic
11#9112C211yesmaximal, characteristic, complemented
12#8578C211yesmaximal, characteristic, complemented
13#8576C211yesmaximal, characteristic, complemented
14#8573C211yesmaximal, characteristic
15#8571C211yesmaximal, characteristic
16C2×#432C2211yescharacteristic
17C2×#431C2211yescharacteristic
18#2857C2211yescharacteristic
19#2855C2211yescharacteristic
20#2854C2211yescharacteristic
21#2850C2211yescharacteristic
22#2654—21no—
23#2650—21no—
24#2512C411yescharacteristic, complemented
25#2511C411yescharacteristic, complemented
26#2509C411yescharacteristic, complemented
27#2508C411yescharacteristic, complemented
28#2488—21no—
29#2481—21no—
30#2452C411yescharacteristic, complemented
31#2451C411yescharacteristic, complemented
32#2449—21no—
33#2448C411yescharacteristic, complemented
34#2447C411yescharacteristic, complemented
35#2419—21no—
36#2334—21no—
37#2332—21no—
38C4×C22⋊Q8C2211yescharacteristic
39C4×#121C2211yescharacteristic
40C2×#387—21no—
41C2×C4×C4⋊C4C2211yescharacteristic
42#1940—21no—
43#1940—21no—
44#1939—21no—
45#1939—21no—
46#1797C2211yescharacteristic
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50C2×#328C2211yescharacteristic
51C2×#328C2211yescharacteristic
52C2×#328C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57C2×#327C2211yescharacteristic
58#1436—21no—
59#1436—21no—
60C4⋊#95C2211yescharacteristic
61#1434—21no—
62#1434C2211yescharacteristic
63#1434C2211yescharacteristic
64#1434C2211yescharacteristic
65C4×#95C2211yescharacteristic
66C4×#95C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C2×C4⋊Q8C2×C411yescharacteristic
76C2×#126—21no—
77C2×#124C2×C411yescharacteristic
78C2×#123—21no—
79C2×C22⋊Q8—21no—
80C2×C22⋊Q8—21no—
81C2×C22⋊Q8C2311yescharacteristic
82C2×#121C2311yescharacteristic
83C2×C4×Q8C2×C411yescharacteristic
84C2×C4×D4—21no—
85C2×C4×D4C2×C411yescharacteristic
86C22×C4⋊C4—21no—
87C22×C4⋊C4D411yescharacteristic
88C22×C4⋊C4D411yescharacteristic
89C22×C42—21no—
90C22×C42—21no—
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94#432—41no—
95#432—41no—
96#431—41no—
97#431—41no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×C22⋊C8C2311yescharacteristic
105C2×C22⋊C8C2311yescharacteristic
106C2×C22⋊C8C2311yescharacteristic
107C2×C22⋊C8C2311yescharacteristic
108C2×#97—21no—
109C2×C4×C8—21no—
110#400—21no—
111#400—21no—
112#400—21no—
113#400—21no—
114#400—21no—
115#399—21no—
116#398—21no—
117#398—21no—
118#397—21no—
119#397—21no—
120#397—21no—
121#397—21no—
122#396—21no—
123#396—21no—
124#395—21no—
125#393—21no—
126#391—21no—
127#391—21no—
128#391C2×C411yescharacteristic
129#391C2×C411yescharacteristic
130#391C2×C411yescharacteristic
131#391C2×C411yescharacteristic
132#390C2×C411yescharacteristic
133#390C2×C411yescharacteristic
134#390C2×C411yescharacteristic
135#390C2×C411yescharacteristic
136#389—21no—
137#389—21no—
138#389C2×C411yescharacteristic
139#389C2×C411yescharacteristic
140#389C2×C411yescharacteristic
141#389C2×C411yescharacteristic
142#389C2×C411yescharacteristic
143#389C2×C411yescharacteristic
144#389C2×C411yescharacteristic
145#389C2×C411yescharacteristic
146#388—21no—
147#388—21no—
148#388—21no—
149#388—21no—
150#388—21no—
151#388—21no—
152#388—21no—
153#388—21no—
154#387—28no—
155#387—21no—
156#387—21no—
157#387—21no—
158#387—21no—
159#387—21no—
160#387—21no—
161#387—21no—
162#387—21no—
163#386—21no—
164#386—21no—
165#386—21no—
166#386—21no—
167#385—21no—
168#385—21no—
169#385—21no—
170#385—21no—
171#384C2×C411yescharacteristic
172#382—21no—
173#382C2×C411yescharacteristic
174#381—21no—
175#381—21no—
176#380—21no—
177#380C2311yescharacteristic
178#380C2311yescharacteristic
179C4×C4⋊C4—21no—
180C4×C4⋊C4C2×C411yescharacteristic
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4C2×C411yescharacteristic
186C4×C4⋊C4D411yescharacteristic
187C4×C4⋊C4D411yescharacteristic
188C4×C4⋊C4D411yescharacteristic
189C4×C4⋊C4D411yescharacteristic
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95D411yescharacteristic
202C2×#95D411yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211#328—41no—
212#328—41no—
213#328—41no—
214#328—41no—
215#327—41no—
216#327—41no—
217#327—41no—
218#327—41no—
219C22×Q8—21no—
220C22×Q8C22×C411yescharacteristic
221C22×D4—21no—
222C22×D4C22×C411yescharacteristic
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2411yescharacteristic
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C4⋊Q8—81no—
240#126—44no—
241#124—81no—
242#123—81no—
243#123—81no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—44no—
249C22⋊Q8—81no—
250C22⋊Q8—81no—
251#121—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255C4×Q8—81no—
256C4×D4—81no—
257C4×D4—81no—
258C4×D4—81no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—81no—
276C2×C4⋊C4—81no—
277C2×C4⋊C4C22⋊C411yescharacteristic
278C2×C4⋊C4C22⋊C411yescharacteristic
279C2×C4⋊C4C22⋊C411yescharacteristic
280C2×C4⋊C4C22⋊C411yescharacteristic
281C2×C4⋊C4C22⋊C411yescharacteristic
282C2×C4⋊C4C22⋊C411yescharacteristic
283C2×C4⋊C4C22⋊C411yescharacteristic
284C2×C4⋊C4C22⋊C411yescharacteristic
285C2×C4⋊C4C22×C411yescharacteristic
286C2×C4⋊C4C22×C411yescharacteristic
287C2×C4⋊C4C22×C411yescharacteristic
288C2×C4⋊C4C22×C411yescharacteristic
289C2×C4⋊C4C22×C411yescharacteristic
290C2×C4⋊C4C22×C411yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—24no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—42no—
315C2×C42—81no—
316C2×C42—81no—
317C2×C42—81no—
318C2×C42—81no—
319C2×C42—81no—
320C2×C42—81no—
321C2×C42C22×C411yescharacteristic
322C2×C42C22×C411yescharacteristic
323C2×C42C22×C411yescharacteristic
324C2×C42C22×C411yescharacteristic
325C2×C42C22×C411yescharacteristic
326C2×C42C22×C411yescharacteristic
327C2×C42C2×D411yescharacteristic
328C2×C42C2×D411yescharacteristic
329C2×C42C2×D411yescharacteristic
330C2×C42C2×D411yescharacteristic
331C2×C42C2×D411yescharacteristic
332C2×C42C2×D411yescharacteristic
333C4⋊C8—42no—
334C4⋊C8—42no—
335C4⋊C8—81no—
336C4⋊C8—81no—
337C4⋊C8—81no—
338C4⋊C8—81no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347#97—42no—
348C4×C8—42no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—42no—
384#95—81no—
385#95—81no—
386#95—81no—
387#95—81no—
388#95C22⋊C411yescharacteristic
389#95C22⋊C411yescharacteristic
390#95C22⋊C411yescharacteristic
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394#95C22⋊C411yescharacteristic
395#95C22⋊C411yescharacteristic
396C24—21no—
397C24C22×D411yescharacteristic
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—42no—
403C2×Q8—81no—
404C2×Q8—81no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4C2×C22⋊C411yescharacteristic
482C22×C4C2×C22⋊C411yescharacteristic
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C22⋊C411yescharacteristic
485C22×C4C2×C22⋊C411yescharacteristic
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C23×C411yescharacteristic
494C22×C4C22×D411yescharacteristic
495C22×C4H(5,𝔽2)11yescharacteristic
496C22×C4H(5,𝔽2)11yescharacteristic
497C22×C42−1+411yescharacteristic
498C22×C42−1+411yescharacteristic
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—42no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—81no—
533C4⋊C4—81no—
534C4⋊C4—81no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4—81no—
540C4⋊C4—84no—
541C4⋊C4#10414yes—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—41no—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C42—41no—
575C42—41no—
576C42—41no—
577C42—42no—
578C42—81no—
579C42—81no—
580C42—84no—
581C42—84no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C22×C22⋊C411yescharacteristic
594C23#53711yescharacteristic
595C23#53711yescharacteristic
596C23#57611yescharacteristic
597C23#57711yescharacteristic
598C23#57711yescharacteristic
599C23#57811yescharacteristic
600Q8—81no—
601Q8—81no—
602Q8—162no—
603D4—81no—
604D4—81no—
605D4—81no—
606D4—81no—
607D4—81no—
608D4—81no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—162no—
713C2×C4C2×#10412yes—
714C2×C4C2×#10412yes—
715C2×C4C2×#10412yes—
716C2×C4#42112yes—
717C2×C4#52011yescharacteristic
718C2×C4#52011yescharacteristic
719C2×C4#53511yescharacteristic
720C2×C4#53611yescharacteristic
721C8—81no—
722C8—81no—
723C8—81no—
724C8—81no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22#231111yescharacteristic
745C22#288311yescharacteristic
746C22#288411yescharacteristic
747C22#289711yescharacteristic
748C22#289811yescharacteristic
749C22C22×#10411yescharacteristic
750C22C2×#42111yescharacteristic
751C22#325711yescharacteristic
752C22#325811yescharacteristic
753C22#326211yescharacteristic
754C22#326311yescharacteristic
755C4—22no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—82no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—161no—
787C2#1754711yescharacteristic
788C2#1754911yescharacteristic
789C2#1759811yescharacteristic
790C2#1760211yescharacteristic
791C2#2185611yescharacteristic
792C2#2187711yescharacteristic
793C2#2189611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21953C2semidirect
3. #13787C2semidirect
4. #9909C2semidirect
5. #9908C2semidirect
9. #9116C2semidirect
11. #9112C2semidirect
12. #8578C2semidirect
13. #8576C2semidirect
24. #2512C4semidirect
25. #2511C4semidirect
26. #2509C4semidirect
27. #2508C4semidirect
30. #2452C4semidirect
31. #2451C4semidirect
33. #2448C4semidirect
34. #2447C4semidirect

Maximal subgroups

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

subgroupindex
#350832
#219532
#137872
#99092
#99082
#97132
#91182
#91162
#91142
#91122
#85782
#85762
#85732
#85712