Finite Group Databasebeta

← #208488

Subgroups — #208488

Order 512.

1043 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34914C211yesmaximal, characteristic
2#21430C211yesmaximal, characteristic, complemented
3#20431C211yesmaximal, characteristic, complemented
4#9869C211yesmaximal, characteristic, complemented
5#9865C211yesmaximal, characteristic, complemented
6#9678C211yesmaximal, characteristic, complemented
7#9674C211yesmaximal, characteristic, complemented
8#8944C211yesmaximal, characteristic, complemented
9#8944C211yesmaximal, characteristic, complemented
10#8939C211yesmaximal, characteristic, complemented
11#8939C211yesmaximal, characteristic, complemented
12#8183C211yesmaximal, characteristic, complemented
13#8177C211yesmaximal, characteristic, complemented
14#8174C211yesmaximal, characteristic, complemented
15C4×D4⋊C8C211yesmaximal, characteristic, complemented
16C2×#529—21no—
17C2×#423C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C2×#405—21no—
20#2560—21no—
21#2559—21no—
22#2558—21no—
23#2557—21no—
24#2512C411yescharacteristic
25#2506C411yescharacteristic
26#2496C411yescharacteristic
27#2491C411yescharacteristic
28#2452C411yescharacteristic
29#2445C411yescharacteristic
30#2428C411yescharacteristic
31#2422C411yescharacteristic
32#2398—21no—
33#2392—21no—
34C4×C4⋊Q8C2211yescharacteristic
35C4×#127C2211yescharacteristic
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38#2293C2211yescharacteristic
39#2290—21no—
40C42×D4C2211yescharacteristic
41C4×#117C2211yescharacteristic
42#1923—21no—
43#1923—21no—
44#1916—21no—
45#1916—21no—
46#1768—21no—
47#1768—21no—
48#1767C2211yescharacteristic
49#1767C2211yescharacteristic
50C4×C4⋊C8C2211yescharacteristic
51C4×C4⋊C8C2211yescharacteristic
52C4×C4⋊C8C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C4×C22⋊C8C2211yescharacteristic
55C4×C22⋊C8C2211yescharacteristic
56#1744C2211yescharacteristic
57#1729—21no—
58C42×C8C2211yescharacteristic
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63C2×D4⋊C8C2211yescharacteristic
64C2×D4⋊C8C2211yescharacteristic
65C2×D4⋊C8C2211yescharacteristic
66C2×D4⋊C8C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C22×M16—21no—
76C23×C8—21no—
77C2×C4⋊Q8C2×C411yescharacteristic
78C2×#127C2×C411yescharacteristic
79#529—44no—
80#529—44no—
81C2×#126—21no—
82C2×#126—21no—
83C2×#125—21no—
84C2×#124—21no—
85C2×#123—21no—
86C2×#123—21no—
87C2×C22⋊Q8—21no—
88C2×#121—21no—
89C2×#121C2×C411yescharacteristic
90C2×#121C2×C411yescharacteristic
91C2×C4×Q8—21no—
92C2×C4×D4—21no—
93C2×C4×D4—21no—
94C2×C4×D4—21no—
95C2×C4×D4—21no—
96C2×C4×D4C2×C411yescharacteristic
97C2×C4×D4C2×C411yescharacteristic
98C2×C4×D4C2311yescharacteristic
99C2×C4×D4C2311yescharacteristic
100C2×#117—21no—
101C2×#117D411yescharacteristic
102C2×#117D411yescharacteristic
103C22×C42—21no—
104C22×C42C2311yescharacteristic
105#423—22no—
106#423—22no—
107C2×C4⋊C8—21no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—22no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8C2311yescharacteristic
114C2×C4⋊C8C2311yescharacteristic
115C2×C4⋊C8C2311yescharacteristic
116C2×C4⋊C8C2311yescharacteristic
117C2×C22⋊C8—21no—
118C2×C22⋊C8—21no—
119#405—44no—
120C2×#97—21no—
121C2×#97—21no—
122C2×C4×C8—21no—
123C2×C4×C8—21no—
124C2×C4×C8—21no—
125C2×C4×C8—21no—
126C2×C4×C8C2311yescharacteristic
127C2×C4×C8C2311yescharacteristic
128C2×C4×C8C2311yescharacteristic
129C2×C4×C8C2311yescharacteristic
130#400—21no—
131#400—21no—
132#398—21no—
133#397—21no—
134#397—21no—
135#397—21no—
136#396—21no—
137#396—21no—
138#394—21no—
139#394—21no—
140#394—21no—
141#394—21no—
142#394—21no—
143#393—21no—
144#393—21no—
145#392—21no—
146#391—21no—
147#390—21no—
148#390—21no—
149#390C2×C411yescharacteristic
150#390C2×C411yescharacteristic
151#390C2×C411yescharacteristic
152#390C2×C411yescharacteristic
153#390C2×C411yescharacteristic
154#390C2×C411yescharacteristic
155#389—21no—
156#389C2×C411yescharacteristic
157#389C2×C411yescharacteristic
158#389C2×C411yescharacteristic
159#389C2×C411yescharacteristic
160#389C2×C411yescharacteristic
161#389C2×C411yescharacteristic
162#388—21no—
163#388—21no—
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#387—21no—
169#387—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#386—21no—
174#385—21no—
175#385—21no—
176#384C2×C411yescharacteristic
177#384C2×C411yescharacteristic
178#380C2×C411yescharacteristic
179#380C2×C411yescharacteristic
180C4×C4⋊C4—21no—
181C4×C4⋊C4C2×C411yescharacteristic
182C4×C4⋊C4C2×C411yescharacteristic
183C4×C4⋊C4C2×C411yescharacteristic
184C4×C4⋊C4C2×C411yescharacteristic
185C4×C4⋊C4D411yescharacteristic
186C4×C4⋊C4D411yescharacteristic
187C4×C4⋊C4C2311yescharacteristic
188C4×C4⋊C4C2311yescharacteristic
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4C2×C411yescharacteristic
196C4×C22⋊C4C2×C411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199#376D411yescharacteristic
200#376D411yescharacteristic
201C43C2311yescharacteristic
202C43C2311yescharacteristic
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211#336—21no—
212#336—21no—
213D4⋊C8—22no—
214D4⋊C8—22no—
215D4⋊C8—22no—
216D4⋊C8—22no—
217D4⋊C8—22no—
218D4⋊C8—22no—
219D4⋊C8—22no—
220D4⋊C8—22no—
221C22×Q8—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4C22×C411yescharacteristic
227C22×D4C22×C411yescharacteristic
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4C22×C411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C2×M16—24no—
236C2×M16—42no—
237C2×M16—42no—
238C22×C8—24no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—42no—
248C22×C8—42no—
249C4⋊Q8—22no—
250C4⋊Q8—41no—
251#127—22no—
252#127—41no—
253#126—44no—
254#126—44no—
255#125—44no—
256#124—44no—
257#123—44no—
258#123—44no—
259C22⋊Q8—44no—
260#121—22no—
261#121—22no—
262#121—41no—
263#121—41no—
264#121—44no—
265C4×Q8—42no—
266C4×Q8—42no—
267C4×D4—22no—
268C4×D4—22no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—41no—
278C4×D4—41no—
279C4×D4—42no—
280C4×D4—42no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4—42no—
284C4×D4—42no—
285C4×D4—42no—
286C4×D4—42no—
287#117—41no—
288#117—41no—
289#117—42no—
290#117—42no—
291#117D814yes—
292#117SD1614yes—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4C22⋊C411yescharacteristic
305C2×C4⋊C4C22⋊C411yescharacteristic
306C2×C4⋊C4C22⋊C411yescharacteristic
307C2×C4⋊C4C22⋊C411yescharacteristic
308C2×C4⋊C4C22×C411yescharacteristic
309C2×C4⋊C4C22×C411yescharacteristic
310C2×C4⋊C4C22×C411yescharacteristic
311C2×C4⋊C4C22×C411yescharacteristic
312C2×C4⋊C4C22×C411yescharacteristic
313C2×C4⋊C4C22×C411yescharacteristic
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
335C2×C22⋊C4C22⋊C411yescharacteristic
336C2×C22⋊C4C22⋊C411yescharacteristic
337C2×C22⋊C4C22⋊C411yescharacteristic
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42C22×C411yescharacteristic
349C2×C42C22×C411yescharacteristic
350C2×C42C22×C411yescharacteristic
351C2×C42C22×C411yescharacteristic
352C2×C42C22×C411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C2×C42C2×D411yescharacteristic
357C2×C42C2×D411yescharacteristic
358C2×C42C2×D411yescharacteristic
359C2×C42C2×D411yescharacteristic
360C2×C42C2×D411yescharacteristic
361C2×C42C2×D411yescharacteristic
362C2×C42C2×D411yescharacteristic
363C2×C42C2411yescharacteristic
364C4⋊C8—24no—
365C4⋊C8—24no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—42no—
371C4⋊C8—42no—
372C4⋊C8#4112yes—
373C4⋊C8#4112yes—
374C4⋊C8#4112yes—
375C4⋊C8#4112yes—
376C22⋊C8—42no—
377C22⋊C8—42no—
378#97—42no—
379#97—42no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—21no—
384C4×C8—21no—
385C4×C8—21no—
386C4×C8—21no—
387C4×C8—21no—
388C4×C8—42no—
389C4×C8—42no—
390C4×C8—42no—
391C4×C8—42no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409#95C22⋊C411yescharacteristic
410#95C22⋊C411yescharacteristic
411#95C22⋊C411yescharacteristic
412C24—21no—
413C24—21no—
414C24C2×C22⋊C411yescharacteristic
415C2×Q8—42no—
416C2×Q8—42no—
417C2×Q8—81no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—81no—
438C2×D4—81no—
439C2×D4—81no—
440C2×D4—81no—
441C2×D4#13112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—42no—
463C22×C4—42no—
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—42no—
477C22×C4—42no—
478C22×C4—81no—
479C22×C4—81no—
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×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×D812yes—
492C22×C4C2×SD1612yes—
493C22×C4C23×C411yescharacteristic
494C22×C4C22×D411yescharacteristic
495C22×C4C22×D411yescharacteristic
496M16—48no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—48no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—81no—
546C4⋊C4#10214yes—
547C4⋊C4#10214yes—
548C4⋊C4#13112yes—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4#10214yes—
574C22⋊C4#10214yes—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—42no—
602C42—42no—
603C42C2×D812yes—
604C42C2×D812yes—
605C42C2×SD1612yes—
606C42C2×SD1612yes—
607C42C2×#4111yescharacteristic
608C42C2×#4111yescharacteristic
609C42C2×#4111yescharacteristic
610C42C2×#4111yescharacteristic
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23C2×#10212yes—
632C23C22×C22⋊C411yescharacteristic
633Q8—84no—
634D4—22no—
635D4—22no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—84no—
643D4—84no—
644D4—84no—
645D4—84no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
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—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4C2×#10212yes—
715C2×C4C2×#10212yes—
716C2×C4C2×#10212yes—
717C2×C4C2×#10212yes—
718C2×C4C2×#10212yes—
719C2×C4C4×#4111yescharacteristic
720C2×C4C4×#4111yescharacteristic
721C2×C4#52511yescharacteristic
722C2×C4#52511yescharacteristic
723C2×C4#53211yescharacteristic
724C2×C4#53211yescharacteristic
725C2×C4C2×#13111yescharacteristic
726C2×C4C2×#13111yescharacteristic
727C2×C4#56811yescharacteristic
728C2×C4#56811yescharacteristic
729C2×C4C22×D811yescharacteristic
730C2×C4C22×SD1611yescharacteristic
731C2×C4#57511yescharacteristic
732C2×C4#57511yescharacteristic
733C8—42no—
734C8—42no—
735C8—42no—
736C8—42no—
737C8—42no—
738C8—42no—
739C8—81no—
740C8—81no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#229711yescharacteristic
763C22#288011yescharacteristic
764C22#288011yescharacteristic
765C22C22×#10211yescharacteristic
766C22#289611yescharacteristic
767C22#290111yescharacteristic
768C22#290111yescharacteristic
769C4—22no—
770C4—22no—
771C4—22no—
772C4—22no—
773C4—21no—
774C4—21no—
775C4—22no—
776C4—42no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4#296611yescharacteristic
789C4#296711yescharacteristic
790C4#296811yescharacteristic
791C4#296911yescharacteristic
792C4#310011yescharacteristic
793C4#310011yescharacteristic
794C4#310311yescharacteristic
795C4#310311yescharacteristic
796C2—42no—
797C2—82no—
798C2—161no—
799C2#1750711yescharacteristic
800C2#1750711yescharacteristic
801C2#1751311yescharacteristic
802C2#1751611yescharacteristic
803C2#2138111yescharacteristic
804C2#2138411yescharacteristic
805C2#2138611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radical#2428C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C4×#117 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21430C2semidirect
3. #20431C2semidirect
4. #9869C2semidirect
5. #9865C2semidirect
6. #9678C2semidirect
7. #9674C2semidirect
8. #8944C2semidirect
9. #8944C2semidirect
10. #8939C2semidirect
11. #8939C2semidirect
12. #8183C2semidirect
13. #8177C2semidirect
14. #8174C2semidirect
15. C4×D4⋊C8C2semidirect

Maximal subgroups

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

subgroupindex
#349142
#214302
#204312
#98692
#98652
#96782
#96742
#89442
#89392
#81832
#81772
#81742
C4×D4⋊C82