Finite Group Databasebeta

← #223464

Subgroups — #223464

Order 512.

983 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
1#34763C211yesmaximal, characteristic
2#22750C211yesmaximal, characteristic, complemented
3#21102C211yesmaximal, characteristic, complemented
4#9873C211yesmaximal, characteristic, complemented
5#9868C211yesmaximal, characteristic, complemented
6#9078C211yesmaximal, characteristic, complemented
7#9076C211yesmaximal, characteristic, complemented
8#8943C211yesmaximal, characteristic, complemented
9#8939C211yesmaximal, characteristic, complemented
10#8709C211yesmaximal, characteristic, complemented
11#8707C211yesmaximal, characteristic, complemented
12#8569C211yesmaximal, characteristic, complemented
13#8179C211yesmaximal, characteristic, complemented
14#7904C211yesmaximal, characteristic, complemented
15#7893C211yesmaximal, characteristic, complemented
16C2×#529—21no—
17C2×#432C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C2×C4×M16C2211yescharacteristic
21#2521—21no—
22#2519—21no—
23#2512C411yescharacteristic
24#2506C411yescharacteristic
25#2501C411yescharacteristic
26#2496C411yescharacteristic
27#2491C411yescharacteristic
28#2488—21no—
29#2486C411yescharacteristic
30#2440C411yescharacteristic
31#2425—21no—
32#2416C411yescharacteristic
33#2396—21no—
34#2395—21no—
35C4×C4⋊Q8C2211yescharacteristic
36C4×#123—21no—
37C4×#121C2211yescharacteristic
38C4×#121C2211yescharacteristic
39#2293C2211yescharacteristic
40#2285C2211yescharacteristic
41C42×D4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43#1924—21no—
44#1924—21no—
45#1917—21no—
46#1917—21no—
47#1870—21no—
48#1869—21no—
49#1851—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
75C22×M16—21no—
76C23×C8—21no—
77C2×C4⋊Q8C2×C411yescharacteristic
78#529—44no—
79#529—44no—
80C2×#126—21no—
81C2×#126—21no—
82C2×#125—21no—
83C2×#124—21no—
84C2×#123—21no—
85C2×#123—21no—
86C2×#123—21no—
87C2×C22⋊Q8—21no—
88C2×#121—21no—
89C2×#121C2×C411yescharacteristic
90C2×#121C2×C411yescharacteristic
91C2×C4×Q8—21no—
92C2×C4×D4—21no—
93C2×C4×D4—21no—
94C2×C4×D4C2×C411yescharacteristic
95C2×C4×D4D411yescharacteristic
96C2×C4×D4D411yescharacteristic
97C2×C4×D4C2311yescharacteristic
98C2×#117—21no—
99C2×#117—21no—
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C4⋊C4C2×C411yescharacteristic
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105#432—22no—
106#432—41no—
107#431—22no—
108#431—41no—
109C2×C4⋊C8—22no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8—41no—
114C2×C4⋊C8C2311yescharacteristic
115C2×C4⋊C8C2311yescharacteristic
116C2×C4⋊C8C2311yescharacteristic
117C2×C4⋊C8C2311yescharacteristic
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×C22⋊C8—21no—
123C2×C22⋊C8—21no—
124C4×M16—22no—
125C4×M16—41no—
126C2×#97—21no—
127C2×#97—21no—
128C2×#97—21no—
129C2×C4×C8C2311yescharacteristic
130C2×C4×C8C2311yescharacteristic
131C2×C4×C8C2311yescharacteristic
132C2×C4×C8C2311yescharacteristic
133#400—21no—
134#400—21no—
135#399—21no—
136#399—21no—
137#398—21no—
138#398—21no—
139#398—21no—
140#397—21no—
141#397—21no—
142#397—21no—
143#396—21no—
144#396—21no—
145#395—21no—
146#394—21no—
147#394—21no—
148#393—21no—
149#391—21no—
150#390C2×C411yescharacteristic
151#390C2×C411yescharacteristic
152#390C2×C411yescharacteristic
153#390C2×C411yescharacteristic
154#389—21no—
155#389C2×C411yescharacteristic
156#389C2×C411yescharacteristic
157#389C2×C411yescharacteristic
158#389C2×C411yescharacteristic
159#389C2×C411yescharacteristic
160#389C2×C411yescharacteristic
161#388—21no—
162#388—21no—
163#388—21no—
164#388—21no—
165#388—21no—
166#388—21no—
167#387—21no—
168#387—21no—
169#386—21no—
170#386—21no—
171#386—21no—
172#385—21no—
173#384C2×C411yescharacteristic
174#384C2×C411yescharacteristic
175#384C2×C411yescharacteristic
176#382—21no—
177#381—21no—
178#380—21no—
179#380C2×C411yescharacteristic
180#380C2×C411yescharacteristic
181#380C2×C411yescharacteristic
182#380C2×C411yescharacteristic
183C4×C4⋊C4—21no—
184C4×C4⋊C4—21no—
185C4×C4⋊C4—21no—
186C4×C4⋊C4—21no—
187C4×C4⋊C4C2×C411yescharacteristic
188C4×C4⋊C4C2×C411yescharacteristic
189C4×C4⋊C4C2×C411yescharacteristic
190C4×C4⋊C4D411yescharacteristic
191C4×C4⋊C4D411yescharacteristic
192C4×C4⋊C4C2311yescharacteristic
193C4×C4⋊C4C2311yescharacteristic
194C4×C4⋊C4C2311yescharacteristic
195C4×C22⋊C4—21no—
196C4×C22⋊C4—21no—
197C4×C22⋊C4—21no—
198C4×C22⋊C4C2×C411yescharacteristic
199C4×C22⋊C4C2×C411yescharacteristic
200C4×C22⋊C4D411yescharacteristic
201C4×C22⋊C4D411yescharacteristic
202C4×C22⋊C4D411yescharacteristic
203C4×C22⋊C4D411yescharacteristic
204C2×#95—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
234C2×M16—42no—
235C2×M16—42no—
236C2×M16—42no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—42no—
246C22×C8—42no—
247C22×C8—81no—
248C4⋊Q8—22no—
249C4⋊Q8—41no—
250#126—44no—
251#126—44no—
252#125—44no—
253#124—44no—
254#123—44no—
255#123—44no—
256#123—44no—
257C22⋊Q8—44no—
258#121—22no—
259#121—41no—
260#121—41no—
261#121—41no—
262#121—44no—
263C4×Q8—42no—
264C4×Q8—42no—
265C4×D4—22no—
266C4×D4—22no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—41no—
272C4×D4—41no—
273C4×D4—42no—
274C4×D4—42no—
275C4×D4—42no—
276C4×D4—42no—
277C4×D4—42no—
278#117—42no—
279#117—42no—
280#117—42no—
281#117—42no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
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⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4C22⋊C411yescharacteristic
302C2×C4⋊C4C22⋊C411yescharacteristic
303C2×C4⋊C4C22⋊C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
305C2×C4⋊C4C22×C411yescharacteristic
306C2×C4⋊C4C22×C411yescharacteristic
307C2×C4⋊C4C22×C411yescharacteristic
308C2×C4⋊C4C22×C411yescharacteristic
309C2×C4⋊C4C22×C411yescharacteristic
310C2×C4⋊C4C22×C411yescharacteristic
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—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
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×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—
377#97—42no—
378#97—42no—
379#97—81no—
380C4×C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8—21no—
384C4×C8—21no—
385C4×C8—21no—
386C4×C8—21no—
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—42no—
413C2×Q8—42no—
414C2×Q8—81no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—81no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
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—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—81no—
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×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4AGL(1,ℤ/8)12yes—
490C22×C4AGL(1,ℤ/8)12yes—
491C22×C4C23×C411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C22×D411yescharacteristic
494M16—48no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
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—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4#13112yes—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C22⋊C4—81no—
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—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—41no—
595C42—41no—
596C42—42no—
597C42—42no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
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—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23#41812yes—
628C23#42112yes—
629C23C22×C22⋊C411yescharacteristic
630Q8—84no—
631D4—44no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—84no—
637D4—84no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
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—22no—
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—42no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
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—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—84no—
711C2×C4—84no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4#41812yes—
717C2×C4C4×#4111yescharacteristic
718C2×C4#52011yescharacteristic
719C2×C4#54611yescharacteristic
720C2×C4#54611yescharacteristic
721C2×C4#54711yescharacteristic
722C2×C4#54711yescharacteristic
723C2×C4C2×#13111yescharacteristic
724C2×C4#56811yescharacteristic
725C2×C4#56811yescharacteristic
726C2×C4#56811yescharacteristic
727C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
728C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
729C2×C4#57711yescharacteristic
730C2×C4#57811yescharacteristic
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—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22#233911yescharacteristic
761C22#287911yescharacteristic
762C22#288011yescharacteristic
763C22C2×#41811yescharacteristic
764C22#289811yescharacteristic
765C22C2×#42111yescharacteristic
766C22#290111yescharacteristic
767C4—22no—
768C4—21no—
769C4—21no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4#296711yescharacteristic
787C4#296911yescharacteristic
788C4#299311yescharacteristic
789C4#299511yescharacteristic
790C4#330611yescharacteristic
791C4#330811yescharacteristic
792C4#334311yescharacteristic
793C4#334511yescharacteristic
794C2—42no—
795C2—42no—
796C2—161no—
797C2#1749511yescharacteristic
798C2#1750611yescharacteristic
799C2#1751111yescharacteristic
800C2#1752411yescharacteristic
801C2#2247211yescharacteristic
802C2#2249511yescharacteristic
803C2#2250611yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radical#2416C4
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. #21102C2semidirect
4. #9873C2semidirect
5. #9868C2semidirect
6. #9078C2semidirect
7. #9076C2semidirect
8. #8943C2semidirect
9. #8939C2semidirect
10. #8709C2semidirect
11. #8707C2semidirect
12. #8569C2semidirect
13. #8179C2semidirect
14. #7904C2semidirect
15. #7893C2semidirect

Maximal subgroups

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

subgroupindex
#347632
#227502
#211022
#98732
#98682
#90782
#90762
#89432
#89392
#87092
#87072
#85692
#81792
#79042
#78932