Finite Group Databasebeta

← #223637

Subgroups — #223637

Order 512.

1094 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36168C211yesmaximal, characteristic
2#22554C211yesmaximal, characteristic, complemented
3#13896C211yesmaximal, characteristic, complemented
4#9913C211yesmaximal, characteristic, complemented
5#9887C211yesmaximal, characteristic, complemented
6#9156C211yesmaximal, characteristic, complemented
7#9147C211yesmaximal, characteristic
8#9118C211yesmaximal, characteristic, complemented
9#9113C211yesmaximal, characteristic
10#8714C211yesmaximal, characteristic, complemented
11#8713C211yesmaximal, characteristic, complemented
12#8577C211yesmaximal, characteristic, complemented
13#8216C211yesmaximal, characteristic, complemented
14#8017C211yesmaximal, characteristic, complemented
15C2×#1294C211yesmaximal, characteristic, complemented
16C2×#432C2211yescharacteristic
17C22×C22⋊C8C2211yescharacteristic
18#2854C2211yescharacteristic
19#2851C2211yescharacteristic
20#2847C2211yescharacteristic
21#2578—21no—
22#2531—21no—
23#2510—21no—
24#2510—21no—
25#2504C411yescharacteristic, complemented
26#2495C411yescharacteristic, complemented
27#2494C411yescharacteristic, complemented
28#2490C411yescharacteristic, complemented
29#2442C411yescharacteristic, complemented
30#2420C411yescharacteristic, complemented
31#2419—21no—
32#2412—21no—
33#2361C411yescharacteristic, complemented
34#2358—21no—
35#2353—21no—
36#2345C411yescharacteristic, complemented
37C4×#121C2211yescharacteristic
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×#327C2211yescharacteristic
53C2×#327C2211yescharacteristic
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
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×#123—21no—
80C2×#121C2×C411yescharacteristic
81C2×#121C2×C411yescharacteristic
82C2×#121C2311yescharacteristic
83C2×#120—21no—
84C2×C4×D4—21no—
85C2×C4×D4—21no—
86C2×C4×D4C2×C411yescharacteristic, complemented
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4C2×C411yescharacteristic
90C22×C4⋊C4C2×C411yescharacteristic
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4D411yescharacteristic
94C22×C22⋊C4D411yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97#432—22no—
98#432—41no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C22⋊C8—22no—
102C2×C22⋊C8—21no—
103C2×C22⋊C8—21no—
104C2×C22⋊C8—21no—
105C2×C22⋊C8—41no—
106C2×C22⋊C8C2311yescharacteristic
107C2×C22⋊C8C2311yescharacteristic
108C2×C22⋊C8C2311yescharacteristic
109C2×C22⋊C8C2311yescharacteristic
110C2×#97—21no—
111C2×#97—21no—
112#401—21no—
113#400—21no—
114#400—21no—
115#398—21no—
116#397—21no—
117#397—21no—
118#397—21no—
119#397—21no—
120#397—21no—
121#397—21no—
122#394—21no—
123#394—21no—
124#390—21no—
125#390C2×C411yescharacteristic, complemented
126#390C2×C411yescharacteristic, complemented
127#390C2×C411yescharacteristic, complemented
128#389C2×C411yescharacteristic, complemented
129#389C2×C411yescharacteristic, complemented
130#389C2×C411yescharacteristic, complemented
131#389C2×C411yescharacteristic, complemented
132#389C2×C411yescharacteristic, complemented
133#388—21no—
134#388—21no—
135#388—21no—
136#388—21no—
137#388—21no—
138#388—21no—
139#388—21no—
140#387—21no—
141#387—21no—
142#387—21no—
143#387—21no—
144#387—21no—
145#386—21no—
146#386—21no—
147#386—21no—
148#386—21no—
149#386—21no—
150#386—21no—
151#386—21no—
152#386—21no—
153#386—21no—
154#385—21no—
155#385—21no—
156#385—21no—
157#385—21no—
158#385—44no—
159#383—21no—
160#383—21no—
161#382—22no—
162#382—41no—
163#382C2×C411yescharacteristic, complemented
164#382C2×C411yescharacteristic, complemented
165#382C2×C411yescharacteristic, complemented
166#381—21no—
167#381—21no—
168#380—21no—
169#380—21no—
170#380—21no—
171#380—21no—
172#380C2×C411yescharacteristic
173#380C2×C411yescharacteristic
174#380C2×C411yescharacteristic
175#380C2×C411yescharacteristic
176#380C2311yescharacteristic
177#380C2311yescharacteristic
178#380C2311yescharacteristic
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#327—22no—
216#327—22no—
217#327—41no—
218#327—41no—
219C25C2×D411yescharacteristic
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4C22×C411yescharacteristic
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—81no—
242C23×C4—81no—
243C23×C4—81no—
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2411yescharacteristic
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—42no—
259C22×C8—42no—
260C22×C8—81no—
261#125—81no—
262#123—81no—
263#123—81no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268#121—42no—
269#121—81no—
270#120—42no—
271#120—42no—
272C4×D4—44no—
273C4×D4—81no—
274C4×D4—81no—
275C4×D4—81no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—81no—
291C2×C4⋊C4—81no—
292C2×C4⋊C4—81no—
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×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—21no—
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⋊C4—21no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—81no—
324C2×C22⋊C4—81no—
325C2×C22⋊C4C22⋊C411yescharacteristic
326C2×C22⋊C4C22⋊C411yescharacteristic
327C2×C22⋊C4C22⋊C411yescharacteristic
328C2×C22⋊C4C22⋊C411yescharacteristic
329C2×C22⋊C4C22⋊C411yescharacteristic
330C2×C22⋊C4C22⋊C411yescharacteristic
331C2×C22⋊C4C22⋊C411yescharacteristic
332C2×C22⋊C4C22⋊C411yescharacteristic
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—81no—
341C2×C42C22×C411yescharacteristic
342C2×C42C22×C411yescharacteristic
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C4⋊C8—42no—
350C4⋊C8—81no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—42no—
359C22⋊C8—42no—
360C22⋊C8—81no—
361C22⋊C8#4112yes—
362#97—42no—
363#97—81no—
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—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—81no—
398#95—81no—
399#95—81no—
400#95C22⋊C411yescharacteristic
401#95C22⋊C411yescharacteristic
402#95C22⋊C411yescharacteristic
403#95C22⋊C411yescharacteristic
404#95C22⋊C411yescharacteristic
405#95C22⋊C411yescharacteristic
406#95C22⋊C411yescharacteristic
407#95C22⋊C411yescharacteristic
408#95#4112yes—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—41no—
417C24—41no—
418C24C2×C22⋊C411yescharacteristic
419C24C2×C22⋊C411yescharacteristic
420C24AGL(1,ℤ/8)12yes—
421C24#13712yes—
422C24C22×D411yescharacteristic
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—81no—
438C2×D4—81no—
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—22no—
448C22×C4—22no—
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—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
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—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—48no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—82no—
521C22×C4—82no—
522C22×C4—82no—
523C22×C4—82no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×C22⋊C411yescharacteristic
538C22×C4C2×C22⋊C411yescharacteristic
539C22×C4C2×C22⋊C411yescharacteristic
540C22×C4C2×C22⋊C411yescharacteristic
541C22×C4C2×C22⋊C411yescharacteristic
542C22×C4C2×C22⋊C411yescharacteristic
543C22×C4C2×C22⋊C411yescharacteristic
544C22×C4C23×C411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C2×#4111yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4H(5,𝔽2)11yescharacteristic
549C22×C42−1+411yescharacteristic
550C2×C8—22no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—84no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—81no—
574C4⋊C4—81no—
575C4⋊C4—81no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4—84no—
581C4⋊C4—84no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—84no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—42no—
625C42—81no—
626C42—81no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23#41012yes—
665C23#41712yes—
666C23#41712yes—
667C23#42112yes—
668C23C22×C22⋊C411yescharacteristic
669C23#54611yescharacteristic
670C23#54711yescharacteristic
671C23C2×AGL(1,ℤ/8)11yescharacteristic
672C23C2×#13711yescharacteristic
673C23#57611yescharacteristic
674C23#57711yescharacteristic
675D4—81no—
676D4—81no—
677D4—81no—
678D4—81no—
679D4—84no—
680D4—81no—
681D4—81no—
682D4—162no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—816no—
776C2×C4—81no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—81no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—162no—
792C2×C4—162no—
793C2×C4—162no—
794C2×C4C4×#4111yescharacteristic
795C2×C4#52011yescharacteristic
796C2×C4#54611yescharacteristic
797C2×C4#54711yescharacteristic
798C8—42no—
799C8—81no—
800C8—81no—
801C8—81no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—22no—
807C22—21no—
808C22—21no—
809C22—22no—
810C22—21no—
811C22—22no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22#151214yes—
839C22#233911yescharacteristic
840C22C2×#41011yescharacteristic
841C22#288311yescharacteristic
842C22C2×#41711yescharacteristic
843C22#289711yescharacteristic
844C22C2×#42111yescharacteristic
845C22#290111yescharacteristic
846C22#331811yescharacteristic
847C22#332011yescharacteristic
848C22#334511yescharacteristic
849C22#334611yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—82no—
865C4—82no—
866C4—81no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—161no—
874C4—161no—
875C2—21no—
876C2—21no—
877C2—21no—
878C2—24no—
879C2—21no—
880C2—42no—
881C2—161no—
882C2C2×#151211yescharacteristic
883C2#1759711yescharacteristic
884C2#1760411yescharacteristic
885C2#1762211yescharacteristic
886C2#2247711yescharacteristic
887C2#2249311yescharacteristic
888C2#2250611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#2847C22
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
2. #22554C2semidirect
3. #13896C2semidirect
4. #9913C2semidirect
5. #9887C2semidirect
6. #9156C2semidirect
8. #9118C2semidirect
10. #8714C2semidirect
11. #8713C2semidirect
12. #8577C2semidirect
13. #8216C2semidirect
14. #8017C2semidirect
15. C2×#1294C2semidirect
25. #2504C4semidirect
26. #2495C4semidirect
27. #2494C4semidirect
28. #2490C4semidirect
29. #2442C4semidirect
30. #2420C4semidirect
33. #2361C4semidirect
36. #2345C4semidirect
78. C2×#125C2×C4semidirect
86. C2×C4×D4C2×C4semidirect
125. #390C2×C4semidirect
126. #390C2×C4semidirect
127. #390C2×C4semidirect
128. #389C2×C4semidirect
129. #389C2×C4semidirect
130. #389C2×C4semidirect
131. #389C2×C4semidirect
132. #389C2×C4semidirect
163. #382C2×C4semidirect
164. #382C2×C4semidirect
165. #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
#361682
#225542
#138962
#99132
#98872
#91562
#91472
#91182
#91132
#87142
#87132
#85772
#82162
#80172
C2×#12942