Finite Group Databasebeta

← #123665

Subgroups — #123665

Order 512.

1674 conjugacy classes of subgroups.

The subgroup lattice has 997 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#341C211yesmaximal, characteristic
2C2×#1735C211yesmaximal, characteristic
3C22×#339C211yesmaximal, characteristic
4C22×#339C211yesmaximal, characteristic
5C2×#1729C211yesmaximal, characteristic
6C2×#1729C211yesmaximal, characteristic
7C22×#336C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C24×C8C2211yescharacteristic
11C24×C8C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#341—22no—
16C2×#341—22no—
17C2×#341—22no—
18#1735—22no—
19#1735—22no—
20C2×#340C414yescomplemented
21C2×#339—22no—
22C2×#339—22no—
23C2×#339—22no—
24C2×#339—22no—
25C2×#339—22no—
26C2×#339C414yescomplemented
27#1729—22no—
28#1729—22no—
29#1729—22no—
30#1729C414yescomplemented
31C2×#336—22no—
32C2×#336—22no—
33C2×#336—22no—
34C2×#336—22no—
35C2×#336—22no—
36C24×C4—21no—
37C24×C4C2311yescharacteristic
38C22×M16—21no—
39C22×M16—21no—
40C22×M16—21no—
41C22×M16—21no—
42C22×M16—21no—
43C22×M16—21no—
44C22×M16—21no—
45C22×M16—21no—
46C22×M16—21no—
47C22×M16—21no—
48C22×M16—21no—
49C22×M16—21no—
50C22×M16—21no—
51C22×M16—21no—
52C22×M16—21no—
53C22×M16—21no—
54C22×M16—21no—
55C22×M16—21no—
56C22×M16—21no—
57C22×M16—21no—
58C22×M16—21no—
59C22×M16—21no—
60C22×M16C2×C412yes—
61C22×M16C2×C412yes—
62C22×M16D412yes—
63C22×M16D412yes—
64C22×M16D412yes—
65C22×M16Q812yes—
66C23×C8—21no—
67C23×C8—21no—
68C23×C8—21no—
69C23×C8—21no—
70C23×C8—21no—
71C23×C8—21no—
72C23×C8—21no—
73C23×C8—21no—
74C23×C8—21no—
75C23×C8—21no—
76C23×C8—21no—
77C23×C8—21no—
78C23×C8—21no—
79C23×C8—21no—
80C23×C8—21no—
81C23×C8—21no—
82C23×C8—21no—
83C23×C8—21no—
84C23×C8—21no—
85C23×C8—21no—
86C23×C8—21no—
87C23×C8—21no—
88C23×C8—21no—
89C23×C8—21no—
90C23×C8—21no—
91C23×C8—21no—
92C23×C8C2×C412yes—
93C23×C8C2×C412yes—
94C23×C8D412yes—
95C23×C8D412yes—
96C23×C8D412yes—
97C23×C8Q812yes—
98C2×#117—21no—
99C2×#117—21no—
100C2×#117—21no—
101C2×#117—21no—
102C2×#117—21no—
103C2×#117—21no—
104C2×#117—21no—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—21no—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117C2×C412yes—
119C2×#117C2×C412yes—
120C2×#117D412yes—
121C2×#117D412yes—
122C22×C4⋊C4C2×C412yes—
123C22×C4⋊C4C2×C412yes—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C42—21no—
127C22×C42—21no—
128C22×C42—21no—
129C22×C42—21no—
130C22×C42—21no—
131C22×C42—21no—
132C22×C42—21no—
133C22×C42—21no—
134C22×C42—21no—
135C22×C42—21no—
136C22×C42—21no—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42C2×C412yes—
140C22×C42D412yes—
141C22×C42Q812yes—
142#341—28no—
143#340—28no—
144#339—28no—
145#339—28no—
146#336—28no—
147#336—28no—
148#336—28no—
149C25#4111yescharacteristic
150C23×C4—28no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—44no—
157C23×C4—41no—
158C23×C4—41no—
159C23×C4—41no—
160C23×C4—41no—
161C23×C4C22×C411yescharacteristic
162C23×C4C22×C411yescharacteristic
163C23×C4C22×C411yescharacteristic
164C23×C4C2×D411yescharacteristic
165C23×C4C2×D411yescharacteristic
166C23×C4C2×D411yescharacteristic
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D411yescharacteristic
173C23×C4C2×Q811yescharacteristic
174C23×C4C2×Q811yescharacteristic
175C23×C4C2×Q811yescharacteristic
176C23×C4#4111yescharacteristic
177C23×C4#4111yescharacteristic
178C23×C4#4111yescharacteristic
179C23×C4#4111yescharacteristic
180C23×C4#4111yescharacteristic
181C23×C4#4111yescharacteristic
182C23×C4#4111yescharacteristic
183C23×C4#4111yescharacteristic
184C23×C4#4111yescharacteristic
185C23×C4#4111yescharacteristic
186C23×C4#4111yescharacteristic
187C23×C4#4111yescharacteristic
188C23×C4#4111yescharacteristic
189C23×C4#4111yescharacteristic
190C23×C4#4111yescharacteristic
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16—22no—
198C2×M16—22no—
199C2×M16—22no—
200C2×M16—22no—
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—22no—
205C2×M16—22no—
206C2×M16—22no—
207C2×M16—22no—
208C2×M16—22no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—22no—
212C2×M16—22no—
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16—22no—
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—41no—
222C2×M16—41no—
223C2×M16—41no—
224C2×M16—41no—
225C2×M16—41no—
226C2×M16—41no—
227C2×M16—41no—
228C2×M16—41no—
229C2×M16—41no—
230C2×M16—41no—
231C2×M16—41no—
232C2×M16—41no—
233C2×M16—41no—
234C2×M16—41no—
235C2×M16—41no—
236C2×M16—41no—
237C2×M16—41no—
238C2×M16—41no—
239C2×M16—41no—
240C2×M16—41no—
241C2×M16—41no—
242C2×M16—41no—
243C2×M16—41no—
244C2×M16—41no—
245C2×M16C22⋊C414yes—
246C2×M16C4⋊C414yes—
247C22×C8—22no—
248C22×C8—22no—
249C22×C8—22no—
250C22×C8—22no—
251C22×C8—22no—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8—22no—
256C22×C8—22no—
257C22×C8—22no—
258C22×C8—22no—
259C22×C8—22no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—41no—
290C22×C8—41no—
291C22×C8—41no—
292C22×C8—41no—
293C22×C8—41no—
294C22×C8—41no—
295C22×C8—41no—
296C22×C8—41no—
297C22×C8—41no—
298C22×C8—41no—
299C22×C8—41no—
300C22×C8—41no—
301C22×C8—41no—
302C22×C8—41no—
303C22×C8—41no—
304C22×C8—41no—
305C22×C8—41no—
306C22×C8—41no—
307C22×C8—41no—
308C22×C8—41no—
309C22×C8—41no—
310C22×C8—41no—
311C22×C8—41no—
312C22×C8—41no—
313C22×C8—41no—
314C22×C8—41no—
315C22×C8—41no—
316C22×C8—41no—
317C22×C8—41no—
318C22×C8—41no—
319C22×C8—41no—
320C22×C8—41no—
321C22×C8—41no—
322C22×C8—41no—
323C22×C8—41no—
324C22×C8—41no—
325C22×C8—41no—
326C22×C8—41no—
327C22×C8—41no—
328C22×C8—41no—
329C22×C8C22⋊C414yes—
330C22×C8C4⋊C414yes—
331#117—22no—
332#117—22no—
333#117—22no—
334#117—22no—
335#117—22no—
336#117—22no—
337#117—22no—
338#117—22no—
339#117—22no—
340#117—22no—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—41no—
348#117—41no—
349#117—41no—
350#117—41no—
351#117—41no—
352#117—41no—
353#117—41no—
354#117—41no—
355#117—41no—
356#117—41no—
357#117—41no—
358#117—41no—
359#117—41no—
360#117—41no—
361#117—41no—
362#117—41no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4C4214yes—
374C2×C4⋊C4C22⋊C414yes—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—41no—
407C2×C42—41no—
408C2×C42—41no—
409C2×C42—41no—
410C2×C42—41no—
411C2×C42—41no—
412C2×C42—41no—
413C2×C42—41no—
414C2×C42—41no—
415C2×C42—41no—
416C2×C42—41no—
417C2×C42—41no—
418C2×C42—41no—
419C2×C42—41no—
420C2×C42—41no—
421C2×C42—41no—
422C2×C42—41no—
423C2×C42—41no—
424C2×C42—41no—
425C2×C42—41no—
426C2×C42C4⋊C414yes—
427C24—24no—
428C24—24no—
429C24#11711yescharacteristic
430C24C4×D411yescharacteristic
431C24C4×D411yescharacteristic
432C24#12111yescharacteristic
433C24C22⋊Q811yescharacteristic
434C24#12311yescharacteristic
435C24#12311yescharacteristic
436C24#12411yescharacteristic
437C24#12411yescharacteristic
438C24#12511yescharacteristic
439C24#12511yescharacteristic
440C24#12611yescharacteristic
441C24#12611yescharacteristic
442C24#12611yescharacteristic
443C24#12611yescharacteristic
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—48no—
451C22×C4—48no—
452C22×C4—48no—
453C22×C4—48no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4C2×C4211yescharacteristic
472C22×C4C2×C22⋊C411yescharacteristic
473C22×C4C2×C22⋊C411yescharacteristic
474C22×C4C2×C22⋊C411yescharacteristic
475C22×C4C2×C4⋊C411yescharacteristic
476C22×C4C2×C4⋊C411yescharacteristic
477C22×C4C2×C4⋊C411yescharacteristic
478C22×C4#11711yescharacteristic
479C22×C4#11711yescharacteristic
480C22×C4#11711yescharacteristic
481C22×C4#11711yescharacteristic
482C22×C4#11711yescharacteristic
483C22×C4#11711yescharacteristic
484C22×C4#11711yescharacteristic
485C22×C4#11711yescharacteristic
486C22×C4#11711yescharacteristic
487C22×C4#11711yescharacteristic
488C22×C4#11711yescharacteristic
489C22×C4C4×D411yescharacteristic
490C22×C4C4×D411yescharacteristic
491C22×C4C4×D411yescharacteristic
492C22×C4C4×D411yescharacteristic
493C22×C4C4×D411yescharacteristic
494C22×C4C4×D411yescharacteristic
495C22×C4C4×D411yescharacteristic
496C22×C4C4×D411yescharacteristic
497C22×C4C4×D411yescharacteristic
498C22×C4C4×D411yescharacteristic
499C22×C4C4×D411yescharacteristic
500C22×C4C4×D411yescharacteristic
501C22×C4C4×D411yescharacteristic
502C22×C4C4×D411yescharacteristic
503C22×C4C4×D411yescharacteristic
504C22×C4C4×D411yescharacteristic
505C22×C4C4×Q811yescharacteristic
506C22×C4C4×Q811yescharacteristic
507C22×C4C4×Q811yescharacteristic
508C22×C4C4×Q811yescharacteristic
509C22×C4C4×Q811yescharacteristic
510C22×C4C4×Q811yescharacteristic
511C22×C4#12011yescharacteristic
512C22×C4#12011yescharacteristic
513C22×C4#12011yescharacteristic
514C22×C4#12011yescharacteristic
515C22×C4#12111yescharacteristic
516C22×C4#12111yescharacteristic
517C22×C4#12111yescharacteristic
518C22×C4#12111yescharacteristic
519C22×C4#12111yescharacteristic
520C22×C4#12111yescharacteristic
521C22×C4#12111yescharacteristic
522C22×C4#12111yescharacteristic
523C22×C4#12111yescharacteristic
524C22×C4#12111yescharacteristic
525C22×C4#12111yescharacteristic
526C22×C4#12111yescharacteristic
527C22×C4#12111yescharacteristic
528C22×C4#12111yescharacteristic
529C22×C4#12111yescharacteristic
530C22×C4#12111yescharacteristic
531C22×C4#12111yescharacteristic
532C22×C4C22⋊Q811yescharacteristic
533C22×C4C22⋊Q811yescharacteristic
534C22×C4C22⋊Q811yescharacteristic
535C22×C4C22⋊Q811yescharacteristic
536C22×C4C22⋊Q811yescharacteristic
537C22×C4C22⋊Q811yescharacteristic
538C22×C4C22⋊Q811yescharacteristic
539C22×C4C22⋊Q811yescharacteristic
540C22×C4C22⋊Q811yescharacteristic
541C22×C4C22⋊Q811yescharacteristic
542C22×C4C22⋊Q811yescharacteristic
543C22×C4C22⋊Q811yescharacteristic
544C22×C4C22⋊Q811yescharacteristic
545C22×C4C22⋊Q811yescharacteristic
546C22×C4C22⋊Q811yescharacteristic
547C22×C4C22⋊Q811yescharacteristic
548C22×C4C22⋊Q811yescharacteristic
549C22×C4#12311yescharacteristic
550C22×C4#12311yescharacteristic
551C22×C4#12311yescharacteristic
552C22×C4#12311yescharacteristic
553C22×C4#12311yescharacteristic
554C22×C4#12311yescharacteristic
555C22×C4#12311yescharacteristic
556C22×C4#12311yescharacteristic
557C22×C4#12311yescharacteristic
558C22×C4#12311yescharacteristic
559C22×C4#12311yescharacteristic
560C22×C4#12311yescharacteristic
561C22×C4#12311yescharacteristic
562C22×C4#12311yescharacteristic
563C22×C4#12311yescharacteristic
564C22×C4#12311yescharacteristic
565C22×C4#12311yescharacteristic
566C22×C4#12311yescharacteristic
567C22×C4#12311yescharacteristic
568C22×C4#12311yescharacteristic
569C22×C4#12311yescharacteristic
570C22×C4#12311yescharacteristic
571C22×C4#12411yescharacteristic
572C22×C4#12411yescharacteristic
573C22×C4#12411yescharacteristic
574C22×C4#12411yescharacteristic
575C22×C4#12411yescharacteristic
576C22×C4#12411yescharacteristic
577C22×C4#12411yescharacteristic
578C22×C4#12411yescharacteristic
579C22×C4#12411yescharacteristic
580C22×C4#12411yescharacteristic
581C22×C4#12511yescharacteristic
582C22×C4#12511yescharacteristic
583C22×C4#12511yescharacteristic
584C22×C4#12511yescharacteristic
585C22×C4#12511yescharacteristic
586C22×C4#12511yescharacteristic
587C22×C4#12511yescharacteristic
588C22×C4#12511yescharacteristic
589C22×C4#12511yescharacteristic
590C22×C4#12511yescharacteristic
591C22×C4#12611yescharacteristic
592C22×C4#12611yescharacteristic
593C22×C4#12611yescharacteristic
594C22×C4#12611yescharacteristic
595C22×C4#12611yescharacteristic
596C22×C4#12611yescharacteristic
597C22×C4#12611yescharacteristic
598C22×C4#12611yescharacteristic
599C22×C4#12611yescharacteristic
600C22×C4#12611yescharacteristic
601C22×C4#12611yescharacteristic
602C22×C4#12611yescharacteristic
603C22×C4#12611yescharacteristic
604C22×C4#12611yescharacteristic
605C22×C4#12611yescharacteristic
606C22×C4#12611yescharacteristic
607C22×C4#12711yescharacteristic
608C22×C4C4⋊Q811yescharacteristic
609C22×C4C4⋊Q811yescharacteristic
610C22×C4C4⋊Q811yescharacteristic
611M16—24no—
612M16—24no—
613M16—24no—
614M16—24no—
615M16—42no—
616M16—42no—
617M16—42no—
618M16—42no—
619M16—42no—
620M16—42no—
621M16—42no—
622M16—42no—
623M16—42no—
624M16—42no—
625M16—42no—
626M16—42no—
627C2×C8—24no—
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—42no—
636C2×C8—42no—
637C2×C8—42no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8—42no—
641C2×C8—42no—
642C2×C8—42no—
643C2×C8—42no—
644C2×C8—42no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8—42no—
648C2×C8—42no—
649C2×C8—42no—
650C2×C8—42no—
651C2×C8—42no—
652C2×C8—42no—
653C2×C8—42no—
654C2×C8—42no—
655C2×C8—42no—
656C2×C8—42no—
657C2×C8—42no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—42no—
661C2×C8—42no—
662C2×C8—42no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8—42no—
666C2×C8—42no—
667C2×C8—42no—
668C2×C8—42no—
669C2×C8—42no—
670C2×C8—42no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C42—24no—
688C42—24no—
689C42—42no—
690C42—42no—
691C42—42no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42—42no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42—42no—
701C42—42no—
702C42—42no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23C4×C22⋊C411yescharacteristic
724C23#38211yescharacteristic
725C23#38311yescharacteristic
726C23#38511yescharacteristic
727C23#38611yescharacteristic
728C23#38711yescharacteristic
729C23#38711yescharacteristic
730C23#38711yescharacteristic
731C23#38711yescharacteristic
732C23#38711yescharacteristic
733C23#38811yescharacteristic
734C23#38811yescharacteristic
735C23#38811yescharacteristic
736C23#38811yescharacteristic
737C23#38811yescharacteristic
738C23#38811yescharacteristic
739C23#38811yescharacteristic
740C23#38911yescharacteristic
741C23#39011yescharacteristic
742C23#39311yescharacteristic
743C23#39411yescharacteristic
744C23#39611yescharacteristic
745C23#39711yescharacteristic
746C23#39711yescharacteristic
747C23#39711yescharacteristic
748C23#39711yescharacteristic
749C23#39811yescharacteristic
750C23#39811yescharacteristic
751C23#40011yescharacteristic
752C23#40011yescharacteristic
753C23#40011yescharacteristic
754C23#40011yescharacteristic
755C23#40011yescharacteristic
756C23#40011yescharacteristic
757C23#40111yescharacteristic
758C23#44314yes—
759C23#44414yes—
760C2×C4—28no—
761C2×C4—48no—
762C2×C4—48no—
763C2×C4—44no—
764C2×C4—48no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—44no—
769C2×C4—48no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4—82no—
778C2×C4—82no—
779C2×C4#37611yescharacteristic
780C2×C4C4×C22⋊C411yescharacteristic
781C2×C4C4×C22⋊C411yescharacteristic
782C2×C4C4×C4⋊C411yescharacteristic
783C2×C4C4×C4⋊C411yescharacteristic
784C2×C4C4×C4⋊C411yescharacteristic
785C2×C4#38011yescharacteristic
786C2×C4#38011yescharacteristic
787C2×C4#38011yescharacteristic
788C2×C4#38111yescharacteristic
789C2×C4#38111yescharacteristic
790C2×C4#38111yescharacteristic
791C2×C4#38211yescharacteristic
792C2×C4#38211yescharacteristic
793C2×C4#38311yescharacteristic
794C2×C4#38311yescharacteristic
795C2×C4#38511yescharacteristic
796C2×C4#38511yescharacteristic
797C2×C4#38511yescharacteristic
798C2×C4#38511yescharacteristic
799C2×C4#38511yescharacteristic
800C2×C4#38611yescharacteristic
801C2×C4#38611yescharacteristic
802C2×C4#38611yescharacteristic
803C2×C4#38611yescharacteristic
804C2×C4#38611yescharacteristic
805C2×C4#38711yescharacteristic
806C2×C4#38711yescharacteristic
807C2×C4#38711yescharacteristic
808C2×C4#38711yescharacteristic
809C2×C4#38711yescharacteristic
810C2×C4#38711yescharacteristic
811C2×C4#38711yescharacteristic
812C2×C4#38711yescharacteristic
813C2×C4#38711yescharacteristic
814C2×C4#38711yescharacteristic
815C2×C4#38711yescharacteristic
816C2×C4#38711yescharacteristic
817C2×C4#38711yescharacteristic
818C2×C4#38711yescharacteristic
819C2×C4#38711yescharacteristic
820C2×C4#38711yescharacteristic
821C2×C4#38711yescharacteristic
822C2×C4#38711yescharacteristic
823C2×C4#38711yescharacteristic
824C2×C4#38811yescharacteristic
825C2×C4#38811yescharacteristic
826C2×C4#38811yescharacteristic
827C2×C4#38811yescharacteristic
828C2×C4#38811yescharacteristic
829C2×C4#38811yescharacteristic
830C2×C4#38811yescharacteristic
831C2×C4#38811yescharacteristic
832C2×C4#38811yescharacteristic
833C2×C4#38811yescharacteristic
834C2×C4#38811yescharacteristic
835C2×C4#38811yescharacteristic
836C2×C4#38811yescharacteristic
837C2×C4#38811yescharacteristic
838C2×C4#38811yescharacteristic
839C2×C4#38811yescharacteristic
840C2×C4#38811yescharacteristic
841C2×C4#38911yescharacteristic
842C2×C4#38911yescharacteristic
843C2×C4#38911yescharacteristic
844C2×C4#38911yescharacteristic
845C2×C4#38911yescharacteristic
846C2×C4#39011yescharacteristic
847C2×C4#39011yescharacteristic
848C2×C4#39111yescharacteristic
849C2×C4#39111yescharacteristic
850C2×C4#39111yescharacteristic
851C2×C4#39211yescharacteristic
852C2×C4#39311yescharacteristic
853C2×C4#39311yescharacteristic
854C2×C4#39411yescharacteristic
855C2×C4#39411yescharacteristic
856C2×C4#39411yescharacteristic
857C2×C4#39411yescharacteristic
858C2×C4#39411yescharacteristic
859C2×C4#39411yescharacteristic
860C2×C4#39411yescharacteristic
861C2×C4#39411yescharacteristic
862C2×C4#39511yescharacteristic
863C2×C4#39611yescharacteristic
864C2×C4#39611yescharacteristic
865C2×C4#39611yescharacteristic
866C2×C4#39611yescharacteristic
867C2×C4#39611yescharacteristic
868C2×C4#39711yescharacteristic
869C2×C4#39711yescharacteristic
870C2×C4#39711yescharacteristic
871C2×C4#39711yescharacteristic
872C2×C4#39711yescharacteristic
873C2×C4#39711yescharacteristic
874C2×C4#39711yescharacteristic
875C2×C4#39711yescharacteristic
876C2×C4#39711yescharacteristic
877C2×C4#39711yescharacteristic
878C2×C4#39711yescharacteristic
879C2×C4#39811yescharacteristic
880C2×C4#39811yescharacteristic
881C2×C4#39811yescharacteristic
882C2×C4#39811yescharacteristic
883C2×C4#39811yescharacteristic
884C2×C4#39811yescharacteristic
885C2×C4#39811yescharacteristic
886C2×C4#39911yescharacteristic
887C2×C4#39911yescharacteristic
888C2×C4#39911yescharacteristic
889C2×C4#40011yescharacteristic
890C2×C4#40011yescharacteristic
891C2×C4#40011yescharacteristic
892C2×C4#40011yescharacteristic
893C2×C4#40011yescharacteristic
894C2×C4#40011yescharacteristic
895C2×C4#40011yescharacteristic
896C2×C4#40011yescharacteristic
897C2×C4#40011yescharacteristic
898C2×C4#40111yescharacteristic
899C8—44no—
900C8—44no—
901C8—44no—
902C8—44no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—22no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22#143411yescharacteristic
936C22#143611yescharacteristic
937C22#143711yescharacteristic
938C22#143911yescharacteristic
939C22#144011yescharacteristic
940C22#144111yescharacteristic
941C22#144211yescharacteristic
942C22#144211yescharacteristic
943C22#144211yescharacteristic
944C22#144211yescharacteristic
945C22#144311yescharacteristic
946C22#144311yescharacteristic
947C22#144311yescharacteristic
948C22#144311yescharacteristic
949C22#144511yescharacteristic
950C22#176412yes—
951C22#176512yes—
952C22#187614yes—
953C22#192214yes—
954C22#192914yes—
955C22#192914yes—
956C22#193712yes—
957C22#193812yes—
958C22#194512yes—
959C22#194612yes—
960C4—48no—
961C4—84no—
962C4—84no—
963C4#143411yescharacteristic
964C4#143411yescharacteristic
965C4#143611yescharacteristic
966C4#143611yescharacteristic
967C4#143911yescharacteristic
968C4#143911yescharacteristic
969C4#144011yescharacteristic
970C4#144011yescharacteristic
971C4#144111yescharacteristic
972C4#144111yescharacteristic
973C4#144211yescharacteristic
974C4#144211yescharacteristic
975C4#144311yescharacteristic
976C4#144311yescharacteristic
977C4#144511yescharacteristic
978C4#144511yescharacteristic
979C2—21no—
980C2—21no—
981C2—21no—
982C2—21no—
983C2—21no—
984C2—21no—
985C2—21no—
986C2—21no—
987C2#755611yescharacteristic
988C2#1080912yes—
989C2#1088211yescharacteristic
990C2#1088311yescharacteristic
991C2#1093412yes—
992C2#1119112yes—
993C2#1122112yes—
994C2#1125812yes—
995C2#1131712yes—
subgroupG/H
centerC23×C4C2×D4
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC24C4×D4
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4 ◁ C24×C8 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
20. C2×#340C4semidirect
26. C2×#339C4semidirect
30. #1729C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3412
C2×#17352
C22×#3392
C2×#17292
C22×#3362