Finite Group Databasebeta

← #223633

Subgroups — #223633

Order 512.

1051 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36167C211yesmaximal, characteristic
2#22554C211yesmaximal, characteristic
3#13896C211yesmaximal, characteristic
4#9913C211yesmaximal, characteristic, complemented
5#9887C211yesmaximal, characteristic, complemented
6#9152C211yesmaximal, characteristic, complemented
7#9143C211yesmaximal, characteristic
8#9116C211yesmaximal, characteristic, complemented
9#9111C211yesmaximal, characteristic
10#8714C211yesmaximal, characteristic, complemented
11#8712C211yesmaximal, characteristic
12#8578C211yesmaximal, characteristic, complemented
13#8217C211yesmaximal, characteristic, complemented
14#8017C211yesmaximal, characteristic, complemented
15C2×#1294C211yesmaximal, characteristic
16C2×#432C2211yescharacteristic
17C22×C22⋊C8C2211yescharacteristic
18#2855C2211yescharacteristic
19#2851C2211yescharacteristic
20#2848C2211yescharacteristic
21#2577—21no—
22#2530—21no—
23#2505—21no—
24#2503C411yescharacteristic, complemented
25#2495C411yescharacteristic, complemented
26#2494C411yescharacteristic, complemented
27#2493—21no—
28#2493—21no—
29#2489C411yescharacteristic, complemented
30#2483—21no—
31#2442C411yescharacteristic, complemented
32#2421C411yescharacteristic, complemented
33#2360C411yescharacteristic, complemented
34#2344C411yescharacteristic, complemented
35#2343—21no—
36#2342—21no—
37C4×C22⋊Q8C2211yescharacteristic
38C2×#385—21no—
39#2283C2211yescharacteristic
40C2×#382C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43C22×#95C2211yescharacteristic
44#1924—21no—
45#1924—21no—
46#1850—21no—
47#1817C2211yescharacteristic
48#1797C2211yescharacteristic
49#1779C2211yescharacteristic
50#1752—21no—
51#1749C2211yescharacteristic
52C2×#328C2211yescharacteristic
53C2×#328C2211yescharacteristic
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56#1442—21no—
57#1442—21no—
58C4⋊#95C2211yescharacteristic
59#1434C2211yescharacteristic
60#1434C2211yescharacteristic
61C22⋊#95—21no—
62C22⋊#95C2211yescharacteristic
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×C4—21no—
76C24×C4C2311yescharacteristic
77C23×C8—21no—
78C2×#125C2×C411yescharacteristic, complemented
79C2×C22⋊Q8C2×C411yescharacteristic
80C2×C22⋊Q8C2×C411yescharacteristic
81C2×C22⋊Q8C2311yescharacteristic
82C2×C4×Q8C2×C411yescharacteristic, complemented
83C2×#117—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4C2×C411yescharacteristic
87C22×C4⋊C4C2×C411yescharacteristic
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4D411yescharacteristic
91C22×C22⋊C4D411yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94#432—22no—
95#432—41no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C22⋊C8—22no—
99C2×C22⋊C8—21no—
100C2×C22⋊C8—21no—
101C2×C22⋊C8—21no—
102C2×C22⋊C8—41no—
103C2×C22⋊C8C2311yescharacteristic
104C2×C22⋊C8C2311yescharacteristic
105C2×C22⋊C8C2311yescharacteristic
106C2×C22⋊C8C2311yescharacteristic
107C2×#97—21no—
108C2×#97—21no—
109#401—21no—
110#400—21no—
111#400—21no—
112#400—21no—
113#400—21no—
114#400—21no—
115#400—21no—
116#398—21no—
117#397—21no—
118#397—21no—
119#397—21no—
120#397—21no—
121#391C2×C411yescharacteristic, complemented
122#391C2×C411yescharacteristic, complemented
123#391C2×C411yescharacteristic, complemented
124#389—21no—
125#389C2×C411yescharacteristic, complemented
126#389C2×C411yescharacteristic, complemented
127#389C2×C411yescharacteristic, complemented
128#389C2×C411yescharacteristic, complemented
129#389C2×C411yescharacteristic, complemented
130#388—21no—
131#388—21no—
132#388—21no—
133#388—21no—
134#387—21no—
135#387—21no—
136#387—21no—
137#387—21no—
138#387—21no—
139#387—21no—
140#387—21no—
141#387—21no—
142#387—21no—
143#387—21no—
144#385—21no—
145#385—21no—
146#385—21no—
147#385—21no—
148#385—21no—
149#385—21no—
150#385—21no—
151#385—21no—
152#385—21no—
153#385—44no—
154#383—21no—
155#383—21no—
156#382—21no—
157#382—22no—
158#382—41no—
159#382C2×C411yescharacteristic, complemented
160#382C2×C411yescharacteristic, complemented
161#382C2×C411yescharacteristic, complemented
162#381—21no—
163#381—21no—
164#381—21no—
165#381—21no—
166#381—21no—
167#380—21no—
168#380—21no—
169#380—21no—
170#380C2×C411yescharacteristic
171#380C2×C411yescharacteristic
172#380C2×C411yescharacteristic
173#380C2×C411yescharacteristic
174#380C2311yescharacteristic
175#380C2311yescharacteristic
176#380C2311yescharacteristic
177#379—21no—
178C4×C4⋊C4—21no—
179C4×C4⋊C4C2×C411yescharacteristic, complemented
180C4×C4⋊C4C2×C411yescharacteristic, complemented
181C4×C4⋊C4C2×C411yescharacteristic, complemented
182C4×C22⋊C4—21no—
183C4×C22⋊C4—21no—
184C4×C22⋊C4—21no—
185C4×C22⋊C4C2×C411yescharacteristic
186C4×C22⋊C4C2×C411yescharacteristic
187C4×C22⋊C4C2×C411yescharacteristic
188C4×C22⋊C4C2×C411yescharacteristic
189C4×C22⋊C4D411yescharacteristic
190C4×C22⋊C4D411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193#376—21no—
194C2×#95—21no—
195C2×#95—22no—
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×#95—41no—
205C2×#95D411yescharacteristic
206C2×#95D411yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211#336—21no—
212#336—21no—
213#336—21no—
214#336—21no—
215#328—22no—
216#328—22no—
217#328—41no—
218#328—41no—
219C25C2×D411yescharacteristic
220C22×Q8C22×C411yescharacteristic
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—81no—
238C23×C4—81no—
239C23×C4—81no—
240C23×C4C22×C411yescharacteristic
241C23×C4C22×C411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2411yescharacteristic
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—42no—
255C22×C8—42no—
256C22×C8—81no—
257#125—81no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C22⋊Q8—42no—
263C22⋊Q8—81no—
264C4×Q8—81no—
265#117—44no—
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—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4—81no—
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—22no—
295C2×C22⋊C4—22no—
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×C22⋊C4—21no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4C22⋊C411yescharacteristic
313C2×C22⋊C4C22⋊C411yescharacteristic
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×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—81no—
329C2×C42C22×C411yescharacteristic
330C2×C42C22×C411yescharacteristic
331C2×C42C22×C411yescharacteristic
332C2×C42C22×C411yescharacteristic
333C2×C42C2×D411yescharacteristic
334C2×C42C2×D411yescharacteristic
335C2×C42C2×D411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C4⋊C8—42no—
338C4⋊C8—81no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—42no—
347C22⋊C8—42no—
348C22⋊C8—81no—
349C22⋊C8#4112yes—
350#97—42no—
351#97—81no—
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—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—81no—
392#95—81no—
393#95—81no—
394#95C22⋊C411yescharacteristic
395#95C22⋊C411yescharacteristic
396#95C22⋊C411yescharacteristic
397#95C22⋊C411yescharacteristic
398#95C22⋊C411yescharacteristic
399#95C22⋊C411yescharacteristic
400#95C22⋊C411yescharacteristic
401#95C22⋊C411yescharacteristic
402#95#4112yes—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—22no—
409C24—41no—
410C24—41no—
411C24C2×C22⋊C411yescharacteristic
412C24C2×C22⋊C411yescharacteristic
413C24AGL(1,ℤ/8)12yes—
414C24#13712yes—
415C24C22×D411yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—41no—
419C2×Q8—41no—
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—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—22no—
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—22no—
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—48no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—82no—
502C22×C4—82no—
503C22×C4—82no—
504C22×C4—82no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—84no—
508C22×C4—84no—
509C22×C4—84no—
510C22×C4—84no—
511C22×C4—84no—
512C22×C4—84no—
513C22×C4C2×C22⋊C411yescharacteristic
514C22×C4C2×C22⋊C411yescharacteristic
515C22×C4C2×C22⋊C411yescharacteristic
516C22×C4C2×C22⋊C411yescharacteristic
517C22×C4C2×C22⋊C411yescharacteristic
518C22×C4C2×C22⋊C411yescharacteristic
519C22×C4C2×C22⋊C411yescharacteristic
520C22×C4C2×C22⋊C411yescharacteristic
521C22×C4C2×C22⋊C411yescharacteristic
522C22×C4C2×C22⋊C411yescharacteristic
523C22×C4C23×C411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4H(5,𝔽2)11yescharacteristic
528C22×C42−1+411yescharacteristic
529C2×C8—22no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—84no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4—81no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—81no—
563C4⋊C4—81no—
564C4⋊C4—84no—
565C4⋊C4—84no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C22⋊C4—84no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—42no—
602C42—42no—
603C42—81no—
604C42—81no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—22no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23#41012yes—
636C23#41712yes—
637C23#41712yes—
638C23#42112yes—
639C23C22×C22⋊C411yescharacteristic
640C23#54611yescharacteristic
641C23#54711yescharacteristic
642C23C2×AGL(1,ℤ/8)11yescharacteristic
643C23C2×#13711yescharacteristic
644C23#57711yescharacteristic
645C23#57811yescharacteristic
646Q8—81no—
647Q8—81no—
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—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—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
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—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
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—81no—
743C2×C4—816no—
744C2×C4—84no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—162no—
761C2×C4C4×#4111yescharacteristic
762C2×C4#52011yescharacteristic
763C2×C4#54611yescharacteristic
764C2×C4#54711yescharacteristic
765C8—42no—
766C8—81no—
767C8—81no—
768C8—81no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—22no—
774C22—21no—
775C22—21no—
776C22—22no—
777C22—21no—
778C22—22no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—22no—
783C22—22no—
784C22—21no—
785C22—21no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22#151214yes—
799C22#233911yescharacteristic
800C22C2×#41011yescharacteristic
801C22#288311yescharacteristic
802C22C2×#41711yescharacteristic
803C22#289811yescharacteristic
804C22C2×#42111yescharacteristic
805C22#290111yescharacteristic
806C22#331011yescharacteristic
807C22#331211yescharacteristic
808C22#334311yescharacteristic
809C22#334411yescharacteristic
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—82no—
825C4—82no—
826C4—81no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4—161no—
835C4—161no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—24no—
840C2—21no—
841C2—42no—
842C2C2×#151211yescharacteristic
843C2#1759811yescharacteristic
844C2#1760911yescharacteristic
845C2#1762211yescharacteristic
846C2#2247711yescharacteristic
847C2#2249111yescharacteristic
848C2#2250611yescharacteristic
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. #9887C2semidirect
6. #9152C2semidirect
8. #9116C2semidirect
10. #8714C2semidirect
12. #8578C2semidirect
13. #8217C2semidirect
14. #8017C2semidirect
24. #2503C4semidirect
25. #2495C4semidirect
26. #2494C4semidirect
29. #2489C4semidirect
31. #2442C4semidirect
32. #2421C4semidirect
33. #2360C4semidirect
34. #2344C4semidirect
78. C2×#125C2×C4semidirect
82. C2×C4×Q8C2×C4semidirect
121. #391C2×C4semidirect
122. #391C2×C4semidirect
123. #391C2×C4semidirect
125. #389C2×C4semidirect
126. #389C2×C4semidirect
127. #389C2×C4semidirect
128. #389C2×C4semidirect
129. #389C2×C4semidirect
159. #382C2×C4semidirect
160. #382C2×C4semidirect
161. #382C2×C4semidirect
179. C4×C4⋊C4C2×C4semidirect
180. C4×C4⋊C4C2×C4semidirect
181. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#361672
#225542
#138962
#99132
#98872
#91522
#91432
#91162
#91112
#87142
#87122
#85782
#82172
#80172
C2×#12942