Finite Group Databasebeta

← #223377

Subgroups — #223377

Order 512.

1066 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#555C211yesmaximal, characteristic
2#22748C211yesmaximal, characteristic, complemented
3#21101C211yesmaximal, characteristic, complemented
4#9873C211yesmaximal, characteristic, complemented
5#9865C211yesmaximal, characteristic, complemented
6#9074C211yesmaximal, characteristic, complemented
7#9072C211yesmaximal, characteristic, complemented
8#8940C211yesmaximal, characteristic, complemented
9#8939C211yesmaximal, characteristic, complemented
10#8708C211yesmaximal, characteristic, complemented
11#8708C211yesmaximal, characteristic, complemented
12#8565C211yesmaximal, characteristic, complemented
13#8170C211yesmaximal, characteristic, complemented
14#7891C211yesmaximal, characteristic, complemented
15#7890C211yesmaximal, characteristic, complemented
16C2×#555C411yescharacteristic
17C2×#431C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21#2372—21no—
22#2372—21no—
23#2369C411yescharacteristic
24#2363—21no—
25#2363C411yescharacteristic
26#2363C411yescharacteristic
27#2354C411yescharacteristic
28#2354C411yescharacteristic
29#2346—21no—
30#2346C411yescharacteristic
31#2346C411yescharacteristic
32C4×C4⋊Q8C2211yescharacteristic
33C4×#124—21no—
34C4×#124—21no—
35C4×#121—21no—
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C42×D4C2211yescharacteristic
39C42×D4C2211yescharacteristic
40C4×#117—21no—
41C4×#117C2211yescharacteristic
42C4×#117C2211yescharacteristic
43#1923—21no—
44#1923—21no—
45#1916—21no—
46#1916—21no—
47#1869—21no—
48#1869—21no—
49#1850—21no—
50#1831C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53C4×C4⋊C8C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55C8×C22⋊C4—21no—
56C4×C22⋊C8C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1744C2211yescharacteristic
59C2×D4⋊C8C2211yescharacteristic
60C2×D4⋊C8C2211yescharacteristic
61C2×D4⋊C8C2211yescharacteristic
62C2×D4⋊C8C2211yescharacteristic
63#1279C2211yescharacteristic
64#1279C2211yescharacteristic
65#1279C2211yescharacteristic
66#1279C2211yescharacteristic
67#1279C2211yescharacteristic
68#1279C2211yescharacteristic
69#1279C2211yescharacteristic
70#1279C2211yescharacteristic
71#1279C2211yescharacteristic
72#1279C2211yescharacteristic
73#1279C2211yescharacteristic
74#1279C2211yescharacteristic
75C23×C8—21no—
76C23×C8—21no—
77#555—24no—
78#555C818yescomplemented
79C2×C4⋊Q8C2×C411yescharacteristic
80C2×#124—21no—
81C2×#124—21no—
82C2×#121—21no—
83C2×#121C2×C411yescharacteristic
84C2×#121C2×C411yescharacteristic
85C2×C4×Q8—21no—
86C2×C4×D4—21no—
87C2×C4×D4—21no—
88C2×C4×D4C2×C411yescharacteristic
89C2×C4×D4C2×C411yescharacteristic
90C2×C4×D4C2×C411yescharacteristic
91C2×C4×D4D411yescharacteristic
92C2×C4×D4D411yescharacteristic
93C2×C4×D4C2311yescharacteristic
94C2×#117—21no—
95C2×#117—21no—
96C2×#117C2×C411yescharacteristic
97C2×#117C2×C411yescharacteristic
98C2×#117C2×C411yescharacteristic
99C2×#117C2×C411yescharacteristic
100C22×C42—21no—
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103#431—22no—
104#431—22no—
105#431—41no—
106#431—41no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—41no—
112C2×C4⋊C8C2311yescharacteristic
113C2×C4⋊C8C2311yescharacteristic
114C2×C4⋊C8C2311yescharacteristic
115C2×C4⋊C8C2311yescharacteristic
116C2×C22⋊C8—21no—
117C2×C22⋊C8—21no—
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×C4×C8—22no—
123C2×C4×C8—21no—
124C2×C4×C8—21no—
125C2×C4×C8—21no—
126C2×C4×C8—41no—
127C2×C4×C8C2311yescharacteristic
128C2×C4×C8C2311yescharacteristic
129C2×C4×C8C2311yescharacteristic
130C2×C4×C8C2311yescharacteristic
131#391—21no—
132#391—21no—
133#391—21no—
134#390—21no—
135#390—21no—
136#390—21no—
137#390C2×C411yescharacteristic
138#390C2×C411yescharacteristic
139#389—21no—
140#389—21no—
141#389C2×C411yescharacteristic
142#389C2×C411yescharacteristic
143#389C2×C411yescharacteristic
144#389C2×C411yescharacteristic
145#388—21no—
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#388—21no—
155#388—21no—
156#388—21no—
157#386—21no—
158#386—21no—
159#386—21no—
160#386—21no—
161#384C2×C411yescharacteristic
162#382—21no—
163#382—21no—
164#380—21no—
165#380C2×C411yescharacteristic
166#380C2×C411yescharacteristic
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170C4×C4⋊C4C2×C411yescharacteristic
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⋊C4D411yescharacteristic
178C4×C4⋊C4D411yescharacteristic
179C4×C4⋊C4C2311yescharacteristic
180C4×C4⋊C4C2311yescharacteristic
181C4×C4⋊C4C2311yescharacteristic
182C4×C22⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4—21no—
189C4×C22⋊C4—21no—
190C4×C22⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4C2×C411yescharacteristic
194C4×C22⋊C4C2×C411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196C4×C22⋊C4D411yescharacteristic
197C4×C22⋊C4D411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199#376—21no—
200#376—21no—
201#376—21no—
202#376—21no—
203C43—21no—
204C43—21no—
205C43C2311yescharacteristic
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214#336—21no—
215#336—21no—
216D4⋊C8—22no—
217D4⋊C8—22no—
218D4⋊C8—41no—
219D4⋊C8—41no—
220C22×Q8—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4C22⋊C411yescharacteristic
224C22×D4C22×C411yescharacteristic
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4C22×C411yescharacteristic
229C23×C4C22×C411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—42no—
243C22×C8—42no—
244C22×C8—42no—
245C22×C8—42no—
246C22×C8—42no—
247C22×C8—81no—
248C4⋊Q8—22no—
249C4⋊Q8C2×C814yescomplemented
250#124—28no—
251#124—28no—
252#121—28no—
253#121—22no—
254#121—22no—
255#121C2×C814yescomplemented
256#121C2×C814yescomplemented
257C4×Q8—81no—
258C4×Q8—81no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—41no—
266C4×D4—41no—
267C4×D4—41no—
268C4×D4—42no—
269C4×D4—81no—
270C4×D4—81no—
271C4×D4—81no—
272C4×D4—81no—
273C4×D4C2×C814yes—
274C4×D4C2×C814yescomplemented
275C4×D4M1614yes—
276#117—22no—
277#117—22no—
278#117—28no—
279#117—22no—
280#117—22no—
281#117—41no—
282#117—41no—
283#117—44no—
284#117C2×C814yescomplemented
285#117C2×C814yescomplemented
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4C22⋊C411yescharacteristic
294C2×C4⋊C4C22⋊C411yescharacteristic
295C2×C4⋊C4C22⋊C411yescharacteristic
296C2×C4⋊C4C22×C411yescharacteristic
297C2×C4⋊C4C22×C411yescharacteristic
298C2×C4⋊C4C22×C411yescharacteristic
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4C22⋊C411yescharacteristic
319C2×C22⋊C4C22⋊C411yescharacteristic
320C2×C22⋊C4C22⋊C411yescharacteristic
321C2×C22⋊C4C22⋊C411yescharacteristic
322C2×C22⋊C4C22⋊C411yescharacteristic
323C2×C22⋊C4C22⋊C411yescharacteristic
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42C22×C411yescharacteristic
348C2×C42C22×C411yescharacteristic
349C2×C42C22×C411yescharacteristic
350C2×C42C22×C411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C2×C42C2×D411yescharacteristic
357C2×C42C2×D411yescharacteristic
358C2×C42C2×D411yescharacteristic
359C2×C42C2411yescharacteristic
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—42no—
368C4⋊C8—42no—
369C4⋊C8—42no—
370C4⋊C8#4112yes—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—42no—
374C22⋊C8—42no—
375C22⋊C8—42no—
376C22⋊C8—81no—
377C4×C8—21no—
378C4×C8—21no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—21no—
384C4×C8—42no—
385C4×C8—42no—
386C4×C8—81no—
387C4×C8#4112yes—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
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#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95C22⋊C411yescharacteristic
409C24—21no—
410C24C2×C22⋊C411yescharacteristic
411C24C2×C22⋊C411yescharacteristic
412C2×Q8—24no—
413C2×Q8—81no—
414C2×Q8—81no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—81no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4C22⋊C814yes—
429C2×D4C22×C812yes—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
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—24no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
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×C4C22×C812yes—
488C22×C4C22×C812yes—
489C22×C4C2×M1612yes—
490C22×C4C2×M1612yes—
491C22×C4C23×C411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C22×D411yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—48no—
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—
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—84no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—24no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—41no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4C22⋊C814yes—
540C4⋊C4C22×C812yes—
541C4⋊C4C22×C812yes—
542C4⋊C4C22×C812yes—
543C4⋊C4#13112yes—
544C22⋊C4—24no—
545C22⋊C4—24no—
546C22⋊C4—24no—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—22no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4C22⋊C814yes—
565C22⋊C4C22⋊C814yes—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—24no—
585C42—24no—
586C42—41no—
587C42—41no—
588C42—42no—
589C42—42no—
590C42—42no—
591C42—42no—
592C42—42no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—42no—
600C42—81no—
601C42—81no—
602C42C22×C812yes—
603C42C2×M1612yes—
604C42C2×#4111yescharacteristic
605C42C2×#4111yescharacteristic
606C42H(5,𝔽2)11yescharacteristic
607C422−1+411yescharacteristic
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23C2×C22⋊C812yes—
628C23C2×C22⋊C812yes—
629C23C22×C22⋊C411yescharacteristic
630Q8—84no—
631D4—22no—
632D4—22no—
633D4—44no—
634D4—41no—
635D4—41no—
636D4—84no—
637D4—84no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
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—42no—
678C2×C4—42no—
679C2×C4—48no—
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—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—84no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4C2×C22⋊C812yes—
713C2×C4C2×C22⋊C812yes—
714C2×C4C2×C22⋊C812yes—
715C2×C4C2×C22⋊C812yes—
716C2×C4#42112yes—
717C2×C4C4×#4111yescharacteristic
718C2×C4#52011yescharacteristic
719C2×C4#54611yescharacteristic
720C2×C4#54611yescharacteristic
721C2×C4#54711yescharacteristic
722C2×C4#54711yescharacteristic
723C2×C4C23×C811yescharacteristic
724C2×C4C22×M1611yescharacteristic
725C2×C4C2×#13111yescharacteristic
726C2×C4#56811yescharacteristic
727C2×C4#57511yescharacteristic
728C2×C4#57511yescharacteristic
729C2×C4#57611yescharacteristic
730C2×C4#57711yescharacteristic
731C8—42no—
732C8—42no—
733C8—42no—
734C8—81no—
735C8—81no—
736C8—81no—
737C8—81no—
738C8—81no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22#233911yescharacteristic
761C22C22×C22⋊C811yescharacteristic
762C22#288011yescharacteristic
763C22#289611yescharacteristic
764C22#289711yescharacteristic
765C22C2×#42111yescharacteristic
766C22#290111yescharacteristic
767C4—22no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—21no—
772C4—21no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—41no—
778C4—42no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C8×#4111yescharacteristic
787C4#297011yescharacteristic
788C4#298811yescharacteristic
789C4#299011yescharacteristic
790C4#331911yescharacteristic
791C4#332111yescharacteristic
792C4#334711yescharacteristic
793C4#334811yescharacteristic
794C2—42no—
795C2—42no—
796C2—82no—
797C2#1743711yescharacteristic
798C2#1743811yescharacteristic
799C2#1751311yescharacteristic
800C2#1752611yescharacteristic
801C2#2246911yescharacteristic
802C2#2249211yescharacteristic
803C2#2250611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C23×C8
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×#555C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22748C2semidirect
3. #21101C2semidirect
4. #9873C2semidirect
5. #9865C2semidirect
6. #9074C2semidirect
7. #9072C2semidirect
8. #8940C2semidirect
9. #8939C2semidirect
10. #8708C2semidirect
11. #8708C2semidirect
12. #8565C2semidirect
13. #8170C2semidirect
14. #7891C2semidirect
15. #7890C2semidirect
78. #555C8semidirect
249. C4⋊Q8C2×C8semidirect
255. #121C2×C8semidirect
256. #121C2×C8semidirect
274. C4×D4C2×C8semidirect
284. #117C2×C8semidirect
285. #117C2×C8semidirect

Maximal subgroups

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

subgroupindex
C4×#5552
#227482
#211012
#98732
#98652
#90742
#90722
#89402
#89392
#87082
#85652
#81702
#78912
#78902