Finite Group Databasebeta

← #224581

Subgroups — #224581

Order 512.

944 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36605C211yesmaximal, characteristic
2#22625C211yesmaximal, characteristic, complemented
3#13819C211yesmaximal, characteristic, complemented
4#9713C211yesmaximal, characteristic
5#9713C211yesmaximal, characteristic
6#9711C211yesmaximal, characteristic, complemented
7#9681C211yesmaximal, characteristic
8#9681C211yesmaximal, characteristic
9#9679C211yesmaximal, characteristic, complemented
10#8577C211yesmaximal, characteristic
11#8576C211yesmaximal, characteristic, complemented
12#8574C211yesmaximal, characteristic, complemented
13C4×#328C211yesmaximal, characteristic, complemented
14C4×#328C211yesmaximal, characteristic, complemented
15C4×#327C211yesmaximal, characteristic
16#2857C2211yescharacteristic
17#2850C2211yescharacteristic
18#2850C2211yescharacteristic
19#2594—21no—
20#2579—21no—
21#2573—21no—
22#2570C411yescharacteristic, complemented
23#2545C411yescharacteristic, complemented
24#2525—21no—
25#2514C411yescharacteristic, complemented
26#2512C411yescharacteristic, complemented
27#2510—21no—
28#2481—21no—
29#2447C411yescharacteristic, complemented
30#2446C411yescharacteristic, complemented
31#2373—21no—
32#2367C411yescharacteristic, complemented
33#2356C411yescharacteristic, complemented
34#2353—21no—
35C4×C22⋊Q8C2211yescharacteristic
36C4×C22⋊Q8C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C2×#387—21no—
39C2×C4×C4⋊C4C2211yescharacteristic
40#1939—21no—
41#1916—21no—
42#1916—21no—
43#1797C2211yescharacteristic
44#1797C2211yescharacteristic
45#1797C2211yescharacteristic
46C8×C4⋊C4—21no—
47C4×C22⋊C8C2211yescharacteristic
48C4×C22⋊C8C2211yescharacteristic
49C4×C22⋊C8C2211yescharacteristic
50C2×#328C2211yescharacteristic
51C2×#328C2211yescharacteristic
52C2×#328C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62#1436—21no—
63#1436—21no—
64C4⋊#95C2211yescharacteristic
65#1434C2211yescharacteristic
66#1434C2211yescharacteristic
67C4×#95—21no—
68C4×#95C2211yescharacteristic
69C4×#95C2211yescharacteristic
70C4×#95C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C2×C4⋊Q8C2×C411yescharacteristic
76C2×#126—21no—
77C2×#124C2×C411yescharacteristic
78C2×#124C2×C411yescharacteristic
79C2×C22⋊Q8C2311yescharacteristic
80C2×C22⋊Q8C2311yescharacteristic
81C2×#121C2311yescharacteristic
82C2×C4×Q8C2×C411yescharacteristic
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×C42—21no—
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C22⋊C8C2311yescharacteristic
99C2×C22⋊C8C2311yescharacteristic
100C2×C22⋊C8C2311yescharacteristic
101C2×C22⋊C8C2311yescharacteristic
102C2×C4×C8—21no—
103C2×C4×C8—21no—
104C2×C4×C8—21no—
105#401—21no—
106#400—21no—
107#400—21no—
108#400—21no—
109#398—21no—
110#398—21no—
111#397—21no—
112#397—21no—
113#397—21no—
114#396—21no—
115#396—21no—
116#396—21no—
117#391C2×C411yescharacteristic
118#391C2×C411yescharacteristic
119#391C2×C411yescharacteristic
120#391C2×C411yescharacteristic
121#391C2×C411yescharacteristic
122#391C2×C411yescharacteristic
123#390C2×C411yescharacteristic
124#390C2×C411yescharacteristic
125#390C2×C411yescharacteristic
126#389—21no—
127#389—21no—
128#389C2×C411yescharacteristic
129#389C2×C411yescharacteristic
130#389C2×C411yescharacteristic
131#388—21no—
132#388—21no—
133#388—21no—
134#388—21no—
135#388—21no—
136#388—21no—
137#388—21no—
138#388—21no—
139#388—21no—
140#388—21no—
141#387—28no—
142#387—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#386—21no—
152#386—21no—
153#386—21no—
154#386—21no—
155#386—21no—
156#385—21no—
157#385—21no—
158#385—21no—
159#385—21no—
160#384C2×C411yescharacteristic
161#383—21no—
162#383—21no—
163#382C2×C411yescharacteristic
164#382C2×C411yescharacteristic
165#381—21no—
166#380—21no—
167#380—21no—
168#380C2311yescharacteristic
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4C2×C411yescharacteristic
172C4×C4⋊C4C2×C411yescharacteristic
173C4×C4⋊C4C2×C411yescharacteristic
174C4×C4⋊C4C2×C411yescharacteristic
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4D411yescharacteristic
179C4×C4⋊C4D411yescharacteristic
180C4×C4⋊C4D411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C22⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186#376—21no—
187C2×#95—21no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95—21no—
191C2×#95—21no—
192C2×#95—21no—
193C2×#95—21no—
194C2×#95—21no—
195C2×#95D411yescharacteristic
196C2×#95D411yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201#336—21no—
202#336—21no—
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#328—22no—
208#328—22no—
209#328—22no—
210#328—22no—
211#328—41no—
212#328—41no—
213#328—41no—
214#328—41no—
215#327—22no—
216#327—22no—
217#327—41no—
218#327—41no—
219C22×Q8C22×C411yescharacteristic
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—42no—
242#124—81no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251#121—21no—
252#121—21no—
253#121—21no—
254#121—21no—
255C4×Q8—42no—
256C4×Q8—81no—
257C4×D4—42no—
258C4×D4—42no—
259C4×D4—81no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
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×C22⋊C4—21no—
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×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—24no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—42no—
312C2×C42—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—81no—
317C2×C42—81no—
318C2×C42—81no—
319C2×C42—81no—
320C2×C42—81no—
321C2×C42—81no—
322C2×C42C22×C411yescharacteristic
323C2×C42C22×C411yescharacteristic
324C2×C42C22×C411yescharacteristic
325C2×C42C22×C411yescharacteristic
326C2×C42C22×C411yescharacteristic
327C2×C42C22×C411yescharacteristic
328C2×C42C2×D411yescharacteristic
329C2×C42C2×D411yescharacteristic
330C2×C42C2×D411yescharacteristic
331C2×C42C2×D411yescharacteristic
332C2×C42C2×D411yescharacteristic
333C2×C42C2×D411yescharacteristic
334C4⋊C8—42no—
335C4⋊C8—81no—
336C4⋊C8—81no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8#4112yes—
345C4×C8—42no—
346C4×C8—81no—
347C4×C8—81no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—21no—
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—42no—
383#95—42no—
384#95—42no—
385#95—81no—
386#95C22⋊C411yescharacteristic
387#95C22⋊C411yescharacteristic
388#95C22⋊C411yescharacteristic
389#95C22⋊C411yescharacteristic
390#95C22⋊C411yescharacteristic
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394#95#4112yes—
395C24—21no—
396C24C22×D411yescharacteristic
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
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—22no—
416C22×C4—22no—
417C22×C4—22no—
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—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
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—42no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4C2×C22⋊C411yescharacteristic
478C22×C4C2×C22⋊C411yescharacteristic
479C22×C4C2×C22⋊C411yescharacteristic
480C22×C4C2×C22⋊C411yescharacteristic
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×C4#13512yes—
490C22×C4#13512yes—
491C22×C4C23×C411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4H(5,𝔽2)11yescharacteristic
496C22×C42−1+411yescharacteristic
497C2×C8—22no—
498C2×C8—41no—
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—
509C4⋊C4—22no—
510C4⋊C4—22no—
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—21no—
521C4⋊C4—21no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—42no—
525C4⋊C4—41no—
526C4⋊C4—41no—
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—84no—
538C4⋊C4#10414yes—
539C22⋊C4—42no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C42—22no—
559C42—22no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C42—41no—
568C42—41no—
569C42—41no—
570C42—42no—
571C42—42no—
572C42—42no—
573C42—81no—
574C42—81no—
575C42—84no—
576C42—84no—
577C42—84no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23C22×C22⋊C411yescharacteristic
590C23#54811yescharacteristic
591C23#55011yescharacteristic
592C23C2×#13511yescharacteristic
593C23C2×#13511yescharacteristic
594C23#57711yescharacteristic
595C23#57811yescharacteristic
596Q8—81no—
597Q8—81no—
598Q8—81no—
599Q8—81no—
600D4—81no—
601D4—81no—
602D4—81no—
603D4—81no—
604D4—81no—
605D4—81no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
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—24no—
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—42no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
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—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
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—41no—
671C2×C4—41no—
672C2×C4—41no—
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—81no—
692C2×C4—81no—
693C2×C4—81no—
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—162no—
706C2×C4#41012yes—
707C2×C4#41612yes—
708C2×C4#41612yes—
709C2×C4C2×#10412yes—
710C2×C4C2×#10412yes—
711C2×C4C2×#10412yes—
712C2×C4C4×#4111yescharacteristic
713C2×C4#52011yescharacteristic
714C2×C4#54811yescharacteristic
715C2×C4#55011yescharacteristic
716C8—42no—
717C8—81no—
718C8—81no—
719C8—81no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22#234111yescharacteristic
740C22C2×#41011yescharacteristic
741C22#288311yescharacteristic
742C22C2×#41611yescharacteristic
743C22#289811yescharacteristic
744C22C22×#10411yescharacteristic
745C22#290111yescharacteristic
746C22#336011yescharacteristic
747C22#336411yescharacteristic
748C22#339311yescharacteristic
749C22#339411yescharacteristic
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—22no—
755C4—22no—
756C4—22no—
757C4—22no—
758C4—22no—
759C4—22no—
760C4—44no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—82no—
768C4—82no—
769C4—82no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—81no—
775C4—81no—
776C4—81no—
777C2—21no—
778C2—21no—
779C2—21no—
780C2—21no—
781C2—161no—
782C2#1753311yescharacteristic
783C2#1754811yescharacteristic
784C2#1760911yescharacteristic
785C2#1761511yescharacteristic
786C2#2253511yescharacteristic
787C2#2254111yescharacteristic
788C2#2255011yescharacteristic
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. #22625C2semidirect
3. #13819C2semidirect
6. #9711C2semidirect
9. #9679C2semidirect
11. #8576C2semidirect
12. #8574C2semidirect
13. C4×#328C2semidirect
14. C4×#328C2semidirect
22. #2570C4semidirect
23. #2545C4semidirect
25. #2514C4semidirect
26. #2512C4semidirect
29. #2447C4semidirect
30. #2446C4semidirect
32. #2367C4semidirect
33. #2356C4semidirect

Maximal subgroups

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

subgroupindex
#366052
#226252
#138192
#97132
#97112
#96812
#96792
#85772
#85762
#85742
C4×#3282
C4×#3272