Finite Group Databasebeta

← #207284

Subgroups — #207284

Order 512.

1008 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35079C211yesmaximal, characteristic
2#21932C211yesmaximal, characteristic
3#13780C211yesmaximal, characteristic
4#9913C211yesmaximal, characteristic, complemented
5#9913C211yesmaximal, characteristic, complemented
6#9912C211yesmaximal, characteristic, complemented
7#9911C211yesmaximal, characteristic, complemented
8#9910C211yesmaximal, characteristic, complemented
9#9910C211yesmaximal, characteristic, complemented
10#9909C211yesmaximal, characteristic, complemented
11#9908C211yesmaximal, characteristic, complemented
12#8024C211yesmaximal, characteristic
13#8023C211yesmaximal, characteristic
14#8016C211yesmaximal, characteristic
15#8015C211yesmaximal, characteristic
16C2×#407C2211yescharacteristic
17C22×C22⋊C8C2211yescharacteristic
18#2857C2211yescharacteristic
19#2857C2211yescharacteristic
20#2851C2211yescharacteristic
21#2851C2211yescharacteristic
22#2667—21no—
23#2665—21no—
24#2569—21no—
25#2549—21no—
26#2442C411yescharacteristic, complemented
27#2442C411yescharacteristic, complemented
28#2441C411yescharacteristic, complemented
29#2441C411yescharacteristic, complemented
30#2440C411yescharacteristic, complemented
31#2440C411yescharacteristic, complemented
32#2439C411yescharacteristic, complemented
33#2439C411yescharacteristic, complemented
34#2437—21no—
35#2437—21no—
36#2329—21no—
37#2329—21no—
38#2280C2211yescharacteristic
39C2×#381C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43#1851—21no—
44#1851—21no—
45#1850—21no—
46#1850—21no—
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1437—21no—
52#1437—21no—
53#1436—21no—
54#1436—21no—
55#1434C2211yescharacteristic
56#1434C2211yescharacteristic
57C4×#95C2211yescharacteristic
58C4×#95C2211yescharacteristic
59#1294C2211yescharacteristic
60#1294C2211yescharacteristic
61#1294C2211yescharacteristic
62#1294C2211yescharacteristic
63#1294C2211yescharacteristic
64#1294C2211yescharacteristic
65#1294C2211yescharacteristic
66#1294C2211yescharacteristic
67#1294C2211yescharacteristic
68#1294C2211yescharacteristic
69#1294C2211yescharacteristic
70#1294C2211yescharacteristic
71#1294C2211yescharacteristic
72#1294C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75C24×C4C2311yescharacteristic
76C22×M16—21no—
77C23×C8—21no—
78C2×C4⋊Q8C2×C411yescharacteristic
79C2×C4⋊Q8C2×C411yescharacteristic
80C2×#125C2×C411yescharacteristic
81C2×#125C2×C411yescharacteristic
82C2×C22⋊Q8—21no—
83C2×C22⋊Q8—21no—
84C2×C22⋊Q8—21no—
85C2×C22⋊Q8—21no—
86C2×#117C2×C411yescharacteristic
87C2×#117C2×C411yescharacteristic
88C22×C4⋊C4—21no—
89C22×C4⋊C4C2×C411yescharacteristic
90C22×C4⋊C4C2×C411yescharacteristic
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4D411yescharacteristic
95C22×C22⋊C4D411yescharacteristic
96C22×C42—21no—
97C22×C42—21no—
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104#407—22no—
105#407—22no—
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8—21no—
109C2×C22⋊C8—21no—
110C2×C22⋊C8C2311yescharacteristic
111C2×C22⋊C8C2311yescharacteristic
112C2×C22⋊C8C2311yescharacteristic
113C2×C22⋊C8C2311yescharacteristic
114#400—21no—
115#400—21no—
116#399—21no—
117#399—21no—
118#398—21no—
119#398—21no—
120#398—21no—
121#398—21no—
122#396—21no—
123#396—21no—
124#396—21no—
125#396—21no—
126#395—21no—
127#395—21no—
128#393—21no—
129#393—21no—
130#391—21no—
131#391—21no—
132#391—21no—
133#391—21no—
134#389—21no—
135#389—21no—
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#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#387—21no—
154#385—21no—
155#385—21no—
156#385—21no—
157#385—21no—
158#385—21no—
159#385—21no—
160#385—21no—
161#385—21no—
162#384C2×C411yescharacteristic
163#384C2×C411yescharacteristic
164#382C2×C411yescharacteristic
165#382C2×C411yescharacteristic
166#381—21no—
167#381—22no—
168#381Q814yescomplemented
169#380—21no—
170#380—21no—
171#380—21no—
172#380—21no—
173#380—22no—
174#380—21no—
175#380—21no—
176#380C2×C411yescharacteristic
177#380C2×C411yescharacteristic
178#380C2×C411yescharacteristic
179#380C2×C411yescharacteristic
180#380Q814yescomplemented
181#380C2311yescharacteristic
182#380C2311yescharacteristic
183#380C2311yescharacteristic
184#380C2311yescharacteristic
185#379—21no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4—21no—
188C4×C22⋊C4C2×C411yescharacteristic
189C4×C22⋊C4C2×C411yescharacteristic
190C4×C22⋊C4C2×C411yescharacteristic
191C4×C22⋊C4C2×C411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193C4×C22⋊C4D411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95D411yescharacteristic
205C2×#95D411yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210#336—21no—
211#336—21no—
212#336—21no—
213#336—21no—
214C25C2×D411yescharacteristic
215C22×Q8—21no—
216C22×Q8—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—81no—
224C23×C4—81no—
225C23×C4C22×C411yescharacteristic
226C23×C4C22×C411yescharacteristic
227C23×C4C2×D411yescharacteristic
228C23×C4C2×D411yescharacteristic
229C23×C4C2×D411yescharacteristic
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×Q812yes—
235C23×C4C2×Q812yes—
236C23×C4#4112yes—
237C23×C4#4112yes—
238C23×C4C2411yescharacteristic
239C2×M16—42no—
240C2×M16—81no—
241C2×M16—81no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—42no—
247C22×C8—81no—
248C22×C8—81no—
249C4⋊Q8—81no—
250C4⋊Q8—81no—
251#125—81no—
252#125—81no—
253C22⋊Q8—44no—
254C22⋊Q8—44no—
255C22⋊Q8—81no—
256C22⋊Q8—81no—
257C22⋊Q8—81no—
258C22⋊Q8—81no—
259#117—81no—
260#117—81no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
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—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—81no—
283C2×C4⋊C4—81no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4C22×C411yescharacteristic
287C2×C4⋊C4C22×C411yescharacteristic
288C2×C4⋊C4C22×C411yescharacteristic
289C2×C4⋊C4C22×C411yescharacteristic
290C2×C4⋊C4C22×C411yescharacteristic
291C2×C4⋊C4C22×C411yescharacteristic
292C2×C4⋊C4C22×C411yescharacteristic
293C2×C4⋊C4C22×C411yescharacteristic
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—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—81no—
309C2×C22⋊C4—81no—
310C2×C22⋊C4—81no—
311C2×C22⋊C4—81no—
312C2×C22⋊C4—81no—
313C2×C22⋊C4—81no—
314C2×C22⋊C4C22⋊C411yescharacteristic
315C2×C22⋊C4C22⋊C411yescharacteristic
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—42no—
325C2×C42—42no—
326C2×C42—81no—
327C2×C42—81no—
328C2×C42—81no—
329C2×C42—81no—
330C2×C42—81no—
331C2×C42—81no—
332C2×C42C22×C411yescharacteristic
333C2×C42C22×C411yescharacteristic
334C2×C42C22×C411yescharacteristic
335C2×C42C22×C411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C2×C42C2×D411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C4⋊C8—81no—
341C4⋊C8—81no—
342C4⋊C8—81no—
343C4⋊C8—81no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—42no—
353C22⋊C8—42no—
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—24no—
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—42no—
380#95—42no—
381#95—81no—
382#95—81no—
383#95—81no—
384#95—81no—
385#95C22⋊C411yescharacteristic
386#95C22⋊C411yescharacteristic
387#95C22⋊C411yescharacteristic
388#95C22⋊C411yescharacteristic
389#95C22⋊C411yescharacteristic
390#95C22⋊C411yescharacteristic
391#95C22⋊C411yescharacteristic
392#95C22⋊C411yescharacteristic
393#95C2×Q812yes—
394#95C2×Q812yes—
395#95C2×Q812yes—
396#95C2×Q812yes—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—41no—
402C24—41no—
403C24—41no—
404C24—41no—
405C24C2×C22⋊C411yescharacteristic
406C24C2×C22⋊C411yescharacteristic
407C24C22⋊Q812yes—
408C24C22⋊Q812yes—
409C24C22×D411yescharacteristic
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8—81no—
413C2×Q8—81no—
414C2×Q8—81no—
415C2×Q8—81no—
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—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
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—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—82no—
483C22×C4—82no—
484C22×C4—82no—
485C22×C4—82no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×C22⋊C411yescharacteristic
497C22×C4C2×C22⋊C411yescharacteristic
498C22×C4C2×C22⋊C411yescharacteristic
499C22×C4C2×C22⋊C411yescharacteristic
500C22×C4C4×Q812yes—
501C22×C4C4×Q812yes—
502C22×C4C4×Q812yes—
503C22×C4C4×Q812yes—
504C22×C4C22⋊Q812yes—
505C22×C4C22⋊Q812yes—
506C22×C4#12412yes—
507C22×C4#12412yes—
508C22×C4C4⋊Q812yes—
509C22×C4C4⋊Q812yes—
510C22×C4C23×C411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×Q811yescharacteristic
513C22×C4C22×Q811yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516M16—84no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—84no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—81no—
545C4⋊C4—81no—
546C4⋊C4—81no—
547C4⋊C4—81no—
548C4⋊C4—81no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4—81no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4—84no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—84no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—84no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—81no—
592C42—81no—
593C42—84no—
594C42—84no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—81no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23#39112yes—
628C23#39112yes—
629C23C22×C22⋊C411yescharacteristic
630C23C2×C22⋊Q811yescharacteristic
631C23C2×C22⋊Q811yescharacteristic
632C23#57611yescharacteristic
633C23#57711yescharacteristic
634C23#57711yescharacteristic
635C23#57811yescharacteristic
636Q8—162no—
637Q8—162no—
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—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
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—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—162no—
743C2×C4—162no—
744C2×C4#39112yes—
745C2×C4#39112yes—
746C2×C4#42112yes—
747C2×C4#42112yes—
748C2×C4C2×C4×Q811yescharacteristic
749C2×C4C2×C4×Q811yescharacteristic
750C2×C4C2×#12411yescharacteristic
751C2×C4C2×C4⋊Q811yescharacteristic
752C8—81no—
753C8—81no—
754C8—81no—
755C8—81no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22C2×#39111yescharacteristic
787C22#288311yescharacteristic
788C22#288311yescharacteristic
789C22#289711yescharacteristic
790C22#289811yescharacteristic
791C22C2×#42111yescharacteristic
792C22C2×#42111yescharacteristic
793C22#308111yescharacteristic
794C22#308211yescharacteristic
795C22#308311yescharacteristic
796C22#308411yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—22no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4—81no—
821C4—81no—
822C4—81no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—42no—
828C2—42no—
829C2#1759711yescharacteristic
830C2#1759811yescharacteristic
831C2#1759911yescharacteristic
832C2#1760011yescharacteristic
833C2#2131511yescharacteristic
834C2#2132911yescharacteristic
835C2#2133311yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #9913C2semidirect
5. #9913C2semidirect
6. #9912C2semidirect
7. #9911C2semidirect
8. #9910C2semidirect
9. #9910C2semidirect
10. #9909C2semidirect
11. #9908C2semidirect
26. #2442C4semidirect
27. #2442C4semidirect
28. #2441C4semidirect
29. #2441C4semidirect
30. #2440C4semidirect
31. #2440C4semidirect
32. #2439C4semidirect
33. #2439C4semidirect
168. #381Q8semidirect
180. #380Q8semidirect

Maximal subgroups

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

subgroupindex
#350792
#219322
#137802
#99132
#99122
#99112
#99102
#99092
#99082
#80242
#80232
#80162
#80152