Finite Group Databasebeta

← #223419

Subgroups — #223419

Order 512.

1049 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#553C211yesmaximal, characteristic
2#22750C211yesmaximal, characteristic, complemented
3#21101C211yesmaximal, characteristic, complemented
4#9875C211yesmaximal, characteristic, complemented
5#9867C211yesmaximal, characteristic, complemented
6#9076C211yesmaximal, characteristic, complemented
7#9072C211yesmaximal, characteristic, complemented
8#8943C211yesmaximal, characteristic, complemented
9#8939C211yesmaximal, characteristic, complemented
10#8708C211yesmaximal, characteristic, complemented
11#8707C211yesmaximal, characteristic, complemented
12#8565C211yesmaximal, characteristic, complemented
13#8174C211yesmaximal, characteristic, complemented
14#7902C211yesmaximal, characteristic, complemented
15C2×#1279C211yesmaximal, characteristic, complemented
16C2×#553C411yescharacteristic
17C2×#432C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4×C8C2211yescharacteristic
21#2374—21no—
22#2373—21no—
23#2370C411yescharacteristic
24#2364—21no—
25#2363C411yescharacteristic
26#2361C411yescharacteristic
27#2357C411yescharacteristic
28#2353—21no—
29#2352C411yescharacteristic
30#2347C411yescharacteristic
31#2345C411yescharacteristic
32C4×#125C2211yescharacteristic
33C4×#126—21no—
34C4×#123—21no—
35C4×#121—21no—
36C4×#121C2211yescharacteristic
37C4×#121C2211yescharacteristic
38C42×D4—21no—
39C42×D4C2211yescharacteristic
40C42×D4C2211yescharacteristic
41C4×#117C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1924—21no—
44#1923—21no—
45#1917—21no—
46#1916—21no—
47#1869—21no—
48#1869—21no—
49#1850—21no—
50#1831C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1767C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55#1752—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#553—24no—
78#553—24no—
79C2×#126—21no—
80C2×#125C2×C411yescharacteristic
81C2×#123—21no—
82C2×#121—21no—
83C2×#121C2×C411yescharacteristic
84C2×#121C2×C411yescharacteristic
85C2×C4×D4—21no—
86C2×C4×D4—21no—
87C2×C4×D4—21no—
88C2×C4×D4—21no—
89C2×C4×D4C2×C411yescharacteristic
90C2×C4×D4C2×C411yescharacteristic
91C2×C4×D4C2×C411yescharacteristic
92C2×C4×D4D411yescharacteristic
93C2×C4×D4D411yescharacteristic
94C2×C4×D4C2311yescharacteristic
95C2×#117C2×C411yescharacteristic
96C2×#117C2×C411yescharacteristic
97C22×C4⋊C4C2×C411yescharacteristic
98C22×C4⋊C4C2×C411yescharacteristic
99C22×C42—21no—
100C22×C42—21no—
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103#432—22no—
104#432—41no—
105#431—22no—
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×#97—21no—
123C2×#97—21no—
124C2×C4×C8—22no—
125C2×C4×C8—21no—
126C2×C4×C8—41no—
127C2×C4×C8C2311yescharacteristic
128C2×C4×C8C2311yescharacteristic
129C2×C4×C8C2311yescharacteristic
130C2×C4×C8C2311yescharacteristic
131#390—21no—
132#390C2×C411yescharacteristic
133#390C2×C411yescharacteristic
134#389—21no—
135#389C2×C411yescharacteristic
136#389C2×C411yescharacteristic
137#389C2×C411yescharacteristic
138#389C2×C411yescharacteristic
139#388—21no—
140#388—21no—
141#388—21no—
142#388—21no—
143#388—21no—
144#388—21no—
145#388—21no—
146#388—21no—
147#388—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#387—21no—
154#387—21no—
155#386—21no—
156#386—21no—
157#386—21no—
158#386—21no—
159#386—21no—
160#385—21no—
161#383—21no—
162#382C2×C411yescharacteristic
163#381—21no—
164#380—21no—
165#380C2×C411yescharacteristic
166#380C2×C411yescharacteristic
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173C4×C4⋊C4C2×C411yescharacteristic
174C4×C4⋊C4C2×C411yescharacteristic
175C4×C4⋊C4C2×C411yescharacteristic
176C4×C4⋊C4C2×C411yescharacteristic
177C4×C4⋊C4C2×C411yescharacteristic
178C4×C4⋊C4C2×C411yescharacteristic
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4D411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C4⋊C4C2311yescharacteristic
183C4×C4⋊C4C2311yescharacteristic
184C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196C4×C22⋊C4C2×C411yescharacteristic
197C4×C22⋊C4C2×C411yescharacteristic
198C4×C22⋊C4D411yescharacteristic
199C4×C22⋊C4D411yescharacteristic
200C4×C22⋊C4D411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202#376—21no—
203C2×#95—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×D4—21no—
221C22×D4—21no—
222C22×D4C22⋊C411yescharacteristic
223C22×D4C22×C411yescharacteristic
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4C22×C411yescharacteristic
230C23×C4C22×C411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—42no—
244C22×C8—42no—
245C22×C8—42no—
246C22×C8—42no—
247C22×C8—42no—
248C22×C8—81no—
249#126—28no—
250#125—22no—
251#125—22no—
252#123—28no—
253#121—28no—
254#121—22no—
255#121—22no—
256#121—22no—
257#121M1614yes—
258C4×D4—28no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—22no—
264C4×D4—22no—
265C4×D4—22no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—41no—
271C4×D4—42no—
272C4×D4—44no—
273C4×D4—42no—
274C4×D4—42no—
275C4×D4—81no—
276C4×D4—81no—
277#117—22no—
278#117—22no—
279#117—22no—
280#117—41no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4C22⋊C411yescharacteristic
293C2×C4⋊C4C22⋊C411yescharacteristic
294C2×C4⋊C4C22⋊C411yescharacteristic
295C2×C4⋊C4M1614yes—
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⋊C4C22⋊C411yescharacteristic
317C2×C22⋊C4C22⋊C411yescharacteristic
318C2×C22⋊C4C22⋊C411yescharacteristic
319C2×C22⋊C4C22⋊C411yescharacteristic
320C2×C22⋊C4C22⋊C411yescharacteristic
321C2×C22⋊C4C22⋊C411yescharacteristic
322C2×C42—21no—
323C2×C42—21no—
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—81no—
342C2×C42—81no—
343C2×C42—81no—
344C2×C42—81no—
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C22×C411yescharacteristic
348C2×C42C22×C411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C2×C42C2×D411yescharacteristic
357C2×C42C2411yescharacteristic
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—42no—
366C4⋊C8—42no—
367C4⋊C8—42no—
368C4⋊C8#4112yes—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8—42no—
374C22⋊C8—81no—
375#97—42no—
376#97—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#4112yes—
386#95—21no—
387#95—21no—
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×D4—22no—
413C2×D4—24no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—24no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—81no—
425C2×D4—81no—
426C2×D4C2×M1612yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
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—22no—
440C22×C4—24no—
441C22×C4—24no—
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—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4—81no—
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×M1612yes—
491C22×C4C2×M1612yes—
492C22×C4#13512yes—
493C22×C4#13512yes—
494C22×C4C23×C411yescharacteristic
495C22×C4C22×D411yescharacteristic
496C22×C4C22×D411yescharacteristic
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—48no—
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—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—84no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—41no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4C2×M1612yes—
545C4⋊C4C2×M1612yes—
546C4⋊C4C2×M1612yes—
547C4⋊C4#13112yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—24no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—41no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C42—24no—
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—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—41no—
590C42—41no—
591C42—42no—
592C42—42no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—81no—
600C42—81no—
601C42—81no—
602C42—81no—
603C42—81no—
604C42C2×#4111yescharacteristic
605C42C2×#4111yescharacteristic
606C42H(5,𝔽2)11yescharacteristic
607C422−1+411yescharacteristic
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—22no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23#40712yes—
627C23#41612yes—
628C23#42112yes—
629C23C22×C22⋊C411yescharacteristic
630D4—22no—
631D4—22no—
632D4—44no—
633D4—48no—
634D4—41no—
635D4—41no—
636D4—84no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
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—42no—
680C2×C4—42no—
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—41no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4—84no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4#40712yes—
717C2×C4#41612yes—
718C2×C4C4×#4111yescharacteristic
719C2×C4#52011yescharacteristic
720C2×C4#54611yescharacteristic
721C2×C4#54611yescharacteristic
722C2×C4#54711yescharacteristic
723C2×C4#54711yescharacteristic
724C2×C4C22×M1611yescharacteristic
725C2×C4C22×M1611yescharacteristic
726C2×C4C2×#13111yescharacteristic
727C2×C4#56811yescharacteristic
728C2×C4C2×#13511yescharacteristic
729C2×C4C2×#13511yescharacteristic
730C2×C4#57611yescharacteristic
731C2×C4#57711yescharacteristic
732C8—42no—
733C8—42no—
734C8—42no—
735C8—81no—
736C8—81no—
737C8—81no—
738C8—81no—
739C8—81no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—41no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22#148814yes—
761C22#233911yescharacteristic
762C22C2×#40711yescharacteristic
763C22#288011yescharacteristic
764C22C2×#41611yescharacteristic
765C22#289711yescharacteristic
766C22C2×#42111yescharacteristic
767C22#290111yescharacteristic
768C4—22no—
769C4—22no—
770C4—21no—
771C4—21no—
772C4—41no—
773C4—42no—
774C4—41no—
775C4—42no—
776C4—42no—
777C4—41no—
778C4—41no—
779C4—42no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4#296511yescharacteristic
788C4#297011yescharacteristic
789C4#298911yescharacteristic
790C4#299011yescharacteristic
791C4#329711yescharacteristic
792C4#330111yescharacteristic
793C4#333711yescharacteristic
794C4#333911yescharacteristic
795C2—24no—
796C2—81no—
797C2—82no—
798C2C2×#148811yescharacteristic
799C2#1745311yescharacteristic
800C2#1751011yescharacteristic
801C2#1752111yescharacteristic
802C2#2247111yescharacteristic
803C2#2248811yescharacteristic
804C2#2250611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC2×#553C4
LCSG ▷ C22×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. #22750C2semidirect
3. #21101C2semidirect
4. #9875C2semidirect
5. #9867C2semidirect
6. #9076C2semidirect
7. #9072C2semidirect
8. #8943C2semidirect
9. #8939C2semidirect
10. #8708C2semidirect
11. #8707C2semidirect
12. #8565C2semidirect
13. #8174C2semidirect
14. #7902C2semidirect
15. C2×#1279C2semidirect

Maximal subgroups

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

subgroupindex
C4×#5532
#227502
#211012
#98752
#98672
#90762
#90722
#89432
#89392
#87082
#87072
#85652
#81742
#79022
C2×#12792