Finite Group Databasebeta

← #370567

Subgroups — #370567

Order 512.

1686 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2440C211yesmaximal, characteristic
2C2×#1996C212yesmaximal
3#13907C211yesmaximal, characteristic
4C22⋊C4×C4⋊C4C211yesmaximal, characteristic
5#11381C212yesmaximal
6#11203C212yesmaximal
7#10912C212yesmaximal
8#10854C211yesmaximal, characteristic
9#10854C211yesmaximal, characteristic
10#10846C211yesmaximal, characteristic
11C4×#342C211yesmaximal, characteristic
12C22×C4⋊Q8C411yescharacteristic, complemented
13C22×C22⋊Q8C2212yes—
14C23×C4⋊C4C2211yescharacteristic
15#2440—21no—
16#2440—21no—
17#2440—21no—
18#2440—21no—
19#2440—22no—
20#2440—22no—
21C2×#398C412yescomplemented
22C2×#395C412yescomplemented
23C2×#389—21no—
24C2×#389C411yescharacteristic, complemented
25C2×#389C411yescharacteristic, complemented
26C2×#385C2212yes—
27C2×#384C411yescharacteristic, complemented
28C2×#380C2211yescharacteristic
29C2×#380C2212yes—
30C2×#380C2211yescharacteristic
31C2×#380C2211yescharacteristic
32C2×C4×C4⋊C4—21no—
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2212yes—
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37#1996—28no—
38C2×#342C2212yes—
39C2×#342C2212yes—
40C2×#342C2212yes—
41C2×#342C2212yes—
42C2×#342C2211yescharacteristic
43C2×#342C2211yescharacteristic
44C2×#342C2212yes—
45C2×#342C2212yes—
46C2×#342C2211yescharacteristic
47C2×#342C2211yescharacteristic
48#1441—22no—
49#1436—22no—
50C4⋊#95—21no—
51C4⋊#95—21no—
52C22⋊#95C2212yes—
53C22⋊#95C2212yes—
54C23×Q8C2×C412yes—
55C24×C4C2312yes—
56C24×C4C2311yescharacteristic
57C2×C4⋊Q8—22no—
58C2×C4⋊Q8—21no—
59C2×C4⋊Q8—21no—
60C2×C4⋊Q8—44no—
61C2×C22⋊Q8—22no—
62C2×C22⋊Q8—22no—
63C2×C22⋊Q8—22no—
64C2×C22⋊Q8—22no—
65C2×C22⋊Q8—24no—
66C2×C22⋊Q8—24no—
67C2×C22⋊Q8—42no—
68C2×C22⋊Q8—42no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—22no—
72C22×C4⋊C4—44no—
73C22×C4⋊C4C2×C412yes—
74C22×C4⋊C4C2×C412yes—
75C22×C4⋊C4C2×C412yes—
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C4⋊C4C2×C412yes—
78C22×C4⋊C4C2×C411yescharacteristic
79C22×C4⋊C4C2×C411yescharacteristic
80C22×C4⋊C4C2×C412yes—
81C22×C4⋊C4C2×C412yes—
82C22×C4⋊C4C2×C411yescharacteristic
83C22×C4⋊C4D411yescharacteristic
84C22×C4⋊C4D411yescharacteristic
85C22×C4⋊C4D411yescharacteristic
86C22×C4⋊C4D411yescharacteristic
87C22×C4⋊C4D412yes—
88C22×C4⋊C4D412yes—
89C22×C22⋊C4C2312yes—
90C22×C22⋊C4C2312yes—
91C22×C22⋊C4C2311yescharacteristic
92C22×C22⋊C4C2311yescharacteristic
93C22×C22⋊C4C2311yescharacteristic
94C22×C22⋊C4C2312yes—
95C22×C22⋊C4C2311yescharacteristic
96C22×C22⋊C4C2311yescharacteristic
97C22×C22⋊C4C2311yescharacteristic
98C22×C42—21no—
99C22×C42—21no—
100C22×C42—22no—
101C22×C42C2×C411yescharacteristic
102C22×C42C2×C411yescharacteristic
103#398—22no—
104#398—22no—
105#398—22no—
106#398—22no—
107#395—22no—
108#395—22no—
109#395—22no—
110#395—22no—
111#389—21no—
112#389—22no—
113#389—21no—
114#389—21no—
115#389—21no—
116#389—22no—
117#389—44no—
118#385—22no—
119#385—22no—
120#385—22no—
121#385—22no—
122#384—21no—
123#384—21no—
124#384—22no—
125#380—21no—
126#380—21no—
127#380—21no—
128#380—21no—
129#380—22no—
130#380—22no—
131#380—22no—
132#380—24no—
133#380—42no—
134#380Q814yescomplemented
135C4×C4⋊C4—44no—
136C4×C22⋊C4—21no—
137C4×C22⋊C4—21no—
138C4×C22⋊C4—21no—
139C4×C22⋊C4—21no—
140C4×C22⋊C4—22no—
141C4×C22⋊C4—22no—
142C4×C22⋊C4—22no—
143C4×C22⋊C4—24no—
144C4×C22⋊C4—42no—
145C4×C22⋊C4Q814yescomplemented
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—22no—
149C2×#95—22no—
150C2×#95—22no—
151C2×#95—22no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—22no—
155C2×#95—22no—
156C2×#95C2×C411yescharacteristic
157C2×#95C2×C412yes—
158C2×#95C2×C412yes—
159C2×#95C2×C411yescharacteristic
160C2×#95C2×C412yes—
161#342—24no—
162#342—24no—
163#342—24no—
164#342—22no—
165#342—22no—
166#342—24no—
167#342—42no—
168#342—42no—
169#342D414yes—
170#342Q814yescomplemented
171C25C2411yescharacteristic
172C22×Q8—22no—
173C22×Q8—22no—
174C22×Q8—24no—
175C22×Q8—42no—
176C22×Q8—44no—
177C22×Q8—82no—
178C23×C4—21no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—21no—
184C23×C4—22no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—22no—
188C23×C4—42no—
189C23×C4—42no—
190C23×C4—44no—
191C23×C4—82no—
192C23×C4C22×C412yes—
193C23×C4C22×C411yescharacteristic
194C23×C4C22×C412yes—
195C23×C4C22×C412yes—
196C23×C4C22×C412yes—
197C23×C4C22×C411yescharacteristic
198C23×C4C22×C411yescharacteristic
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C411yescharacteristic
202C23×C4C2×D412yes—
203C23×C4C2×D412yes—
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D412yes—
207C23×C4C2×D412yes—
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2×Q812yes—
211C23×C4C2×Q812yes—
212C23×C4#4112yes—
213C23×C4#4112yes—
214C4⋊Q8—48no—
215C4⋊Q8—44no—
216C4⋊Q8—44no—
217C22⋊Q8—44no—
218C22⋊Q8—44no—
219C22⋊Q8—44no—
220C22⋊Q8—44no—
221C22⋊Q8—44no—
222C22⋊Q8—44no—
223C22⋊Q8—44no—
224C22⋊Q8—44no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4—44no—
252C2×C4⋊C4—42no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—44no—
260C2×C4⋊C4—44no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—82no—
266C2×C4⋊C4—82no—
267C2×C4⋊C4C22⋊C411yescharacteristic
268C2×C4⋊C4C22⋊C412yes—
269C2×C4⋊C4C22⋊C411yescharacteristic
270C2×C4⋊C4C22⋊C411yescharacteristic
271C2×C4⋊C4C22⋊C412yes—
272C2×C4⋊C4C22⋊C412yes—
273C2×C4⋊C4C22⋊C412yes—
274C2×C4⋊C4C22⋊C412yes—
275C2×C4⋊C4C22⋊C412yes—
276C2×C4⋊C4C22⋊C411yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—22no—
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—22no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4C2×D412yes—
321C2×C22⋊C4C2×D412yes—
322C2×C22⋊C4C2×D412yes—
323C2×C22⋊C4C2×Q812yes—
324C2×C22⋊C4C2×Q812yes—
325C2×C22⋊C4C2×Q814yes—
326C2×C22⋊C4C2×Q812yes—
327C2×C22⋊C4C2×Q812yes—
328C2×C22⋊C4C2×Q812yes—
329C2×C22⋊C4#4112yes—
330C2×C22⋊C4#4112yes—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—24no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—44no—
341C2×C42—44no—
342C2×C42—42no—
343C2×C42—42no—
344C2×C42—42no—
345C2×C42—82no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—22no—
351#95—22no—
352#95—22no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—24no—
357#95—24no—
358#95—44no—
359#95—44no—
360#95—44no—
361#95—44no—
362#95—42no—
363#95—42no—
364#95—82no—
365#95—82no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24C23×C411yescharacteristic
371C24C22×D411yescharacteristic
372C24C22×D411yescharacteristic
373C24C22×D411yescharacteristic
374C24C22×Q811yescharacteristic
375C24C22×Q811yescharacteristic
376C24C22×Q811yescharacteristic
377C24C2×#4111yescharacteristic
378C24C2×#4111yescharacteristic
379C24C2×#4111yescharacteristic
380C24C2×#4111yescharacteristic
381C24H(5,𝔽2)11yescharacteristic
382C24H(5,𝔽2)11yescharacteristic
383C242−1+411yescharacteristic
384C242−1+411yescharacteristic
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8—44no—
388C2×Q8—44no—
389C2×Q8—82no—
390C2×Q8—82no—
391C2×Q8—88no—
392C2×Q8—88no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—42no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
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—42no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—42no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—42no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—84no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4—84no—
505C22×C4C2×C22⋊C412yes—
506C22×C4C2×C22⋊C412yes—
507C22×C4C2×C22⋊C412yes—
508C22×C4C2×C22⋊C411yescharacteristic
509C22×C4C2×C22⋊C411yescharacteristic
510C22×C4C2×C22⋊C411yescharacteristic
511C22×C4C2×C22⋊C412yes—
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C4×D412yes—
514C22×C4C4×D412yes—
515C22×C4C4×Q812yes—
516C22×C4C4×Q812yes—
517C22×C4C4×Q812yes—
518C22×C4C4×Q812yes—
519C22×C4C4×Q812yes—
520C22×C4C4×Q812yes—
521C22×C4C22⋊Q812yes—
522C22×C4C22⋊Q812yes—
523C22×C4C22⋊Q812yes—
524C22×C4C22⋊Q812yes—
525C22×C4#12412yes—
526C22×C4#12412yes—
527C22×C4C4⋊Q812yes—
528C22×C4C4⋊Q812yes—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—24no—
534C4⋊C4—22no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—44no—
539C4⋊C4—44no—
540C4⋊C4—44no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C4⋊C4—42no—
545C4⋊C4—48no—
546C4⋊C4—42no—
547C4⋊C4—44no—
548C4⋊C4—44no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—82no—
552C4⋊C4—82no—
553C4⋊C4—84no—
554C4⋊C4—88no—
555C4⋊C4#9914yes—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—22no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—41no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4C4⋊Q814yescomplemented
592C42—42no—
593C42—48no—
594C42—42no—
595C42—42no—
596C42—42no—
597C42—84no—
598C42—88no—
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—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23C22×C22⋊C411yescharacteristic
636C23C2×C4×D411yescharacteristic
637C23C2×C4×Q811yescharacteristic
638C23C2×C4×Q811yescharacteristic
639C23C2×C4×Q811yescharacteristic
640C23#51811yescharacteristic
641C23#51911yescharacteristic
642C23C2×C22⋊Q811yescharacteristic
643C23C2×C22⋊Q811yescharacteristic
644C23C2×#12411yescharacteristic
645C23C2×C4⋊Q811yescharacteristic
646C23C2×C4⋊Q811yescharacteristic
647C23#53211yescharacteristic
648C23#53311yescharacteristic
649C23#53311yescharacteristic
650C23#54211yescharacteristic
651C23#54211yescharacteristic
652C23#54411yescharacteristic
653C23#54411yescharacteristic
654C23D4211yescharacteristic
655C23D4211yescharacteristic
656C23#54611yescharacteristic
657C23#54611yescharacteristic
658C23#54711yescharacteristic
659C23#54811yescharacteristic
660C23#54811yescharacteristic
661C23D4×Q811yescharacteristic
662C23D4×Q811yescharacteristic
663C23D4×Q811yescharacteristic
664C23#55411yescharacteristic
665C23#55411yescharacteristic
666C23#55511yescharacteristic
667C23#55611yescharacteristic
668C23#55711yescharacteristic
669C23Q8211yescharacteristic
670Q8—88no—
671Q8—88no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—82no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—82no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—82no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—82no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4—82no—
778C2×C4—82no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4—82no—
784C2×C4—82no—
785C2×C4#39112yes—
786C2×C4#39112yes—
787C2×C4#39112yes—
788C2×C4#39112yes—
789C2×C4C2×#9914yes—
790C2×C4C2×#9912yes—
791C2×C4#41012yes—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22C2×#39111yescharacteristic
845C22C4×C4⋊Q811yescharacteristic
846C22#233111yescharacteristic
847C22D4×C22⋊C411yescharacteristic
848C22Q8×C22⋊C411yescharacteristic
849C22#236511yescharacteristic
850C22#236911yescharacteristic
851C22#243911yescharacteristic
852C22#244011yescharacteristic
853C22#245111yescharacteristic
854C22#245211yescharacteristic
855C22#249111yescharacteristic
856C22#249211yescharacteristic
857C22#255011yescharacteristic
858C22#255111yescharacteristic
859C22C22×#9911yescharacteristic
860C22C2×#41011yescharacteristic
861C22#288311yescharacteristic
862C22#288411yescharacteristic
863C4—22no—
864C4—22no—
865C4—22no—
866C4—24no—
867C4—44no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—84no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—162no—
882C4#199614yescomplemented
883C2—21no—
884C2—21no—
885C2—21no—
886C2—21no—
887C2—21no—
888C2—21no—
889C2—21no—
890C2—21no—
891C2—21no—
892C2—21no—
893C2—21no—
894C2—21no—
895C2#1405311yescharacteristic
896C2C2×#199611yescharacteristic
897C2#2133411yescharacteristic
898C2D4×#9911yescharacteristic
899C2#2240611yescharacteristic
900C2Q8×#9911yescharacteristic
901C2#2251311yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, prime radical, cosocleC25C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
12. C22×C4⋊Q8C4semidirect
21. C2×#398C4semidirect
22. C2×#395C4semidirect
24. C2×#389C4semidirect
25. C2×#389C4semidirect
27. C2×#384C4semidirect
134. #380Q8semidirect
145. C4×C22⋊C4Q8semidirect
170. #342Q8semidirect
591. C22⋊C4C4⋊Q8semidirect
882. C4#1996semidirect

Maximal subgroups

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

subgroupindex
C2×#24402
C2×#19962
#139072
C22⋊C4×C4⋊C42
#113812
#112032
#109122
#108542
#108462
C4×#3422