Finite Group Databasebeta

← #123796

Subgroups — #123796

Order 512.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#343C211yesmaximal, characteristic
2C2×#1736C211yesmaximal, characteristic
3C2×#1736C211yesmaximal, characteristic
4C22×#339C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6#13795C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C22×#117C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C22×#95—22no—
16C2×#343—22no—
17C2×#343—22no—
18C2×#343C414yescomplemented
19#1736—22no—
20#1736—22no—
21#1736—22no—
22#1736C414yescomplemented
23C2×#340—22no—
24C2×#340—21no—
25C2×#340—21no—
26C2×#339—22no—
27C2×#339—22no—
28C2×#339—22no—
29C2×#339—22no—
30C2×#339—22no—
31C2×#339C414yescomplemented
32C4⋊#95—22no—
33C4⋊#95—22no—
34C4⋊#95—22no—
35C4⋊#95—21no—
36C4⋊#95—21no—
37C22⋊#95—22no—
38C24×C4—21no—
39C24×C4—21no—
40C24×C4D412yes—
41C24×C4C2311yescharacteristic
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×M16—21no—
61C22×M16—21no—
62C22×M16—21no—
63C22×M16—21no—
64C22×M16C2×C412yes—
65C22×M16C2×C412yes—
66C22×M16C2×C412yes—
67C22×M16C2×C412yes—
68C22×M16D412yes—
69C22×M16D412yes—
70C23×C8—21no—
71C23×C8—21no—
72C2×#117—21no—
73C2×#117—21no—
74C2×#117—21no—
75C2×#117—21no—
76C2×#117—21no—
77C2×#117—21no—
78C2×#117—21no—
79C2×#117—21no—
80C2×#117—21no—
81C2×#117—21no—
82C2×#117—21no—
83C2×#117—21no—
84C2×#117—21no—
85C2×#117—21no—
86C2×#117—21no—
87C2×#117—21no—
88C2×#117—21no—
89C2×#117—21no—
90C2×#117—21no—
91C2×#117—21no—
92C2×#117C2×C412yes—
93C2×#117C2×C412yes—
94C2×#117D412yes—
95C2×#117Q812yes—
96C22×C4⋊C4—21no—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4C2×C412yes—
120C22×C4⋊C4C2×C412yes—
121C22×C4⋊C4D412yes—
122C22×C4⋊C4D412yes—
123C22×C4⋊C4D411yescharacteristic
124C22×C4⋊C4D411yescharacteristic
125C22×C4⋊C4Q812yes—
126C22×C4⋊C4Q812yes—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—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×C42—21no—
140C22×C42—21no—
141C22×C42—21no—
142C22×C42C2×C412yes—
143C22×C42D412yes—
144C22×C42D412yes—
145C2×#95—28no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—48no—
149#343—28no—
150#340—24no—
151#340—24no—
152#340—28no—
153#339—28no—
154#339—28no—
155C25C2×D411yescharacteristic
156C23×C4—24no—
157C23×C4—24no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—42no—
174C23×C4—42no—
175C23×C4—41no—
176C23×C4—41no—
177C23×C4—41no—
178C23×C4—41no—
179C23×C4—44no—
180C23×C4—44no—
181C23×C4—44no—
182C23×C4—44no—
183C23×C4—41no—
184C23×C4—41no—
185C23×C4—41no—
186C23×C4—41no—
187C23×C4C4⋊C414yes—
188C23×C4C22×C411yescharacteristic
189C23×C4C22×C411yescharacteristic
190C23×C4C22×C411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×Q811yescharacteristic
200C23×C4C2×Q811yescharacteristic
201C23×C4C2×Q811yescharacteristic
202C23×C4#4111yescharacteristic
203C23×C4#4111yescharacteristic
204C23×C4#4111yescharacteristic
205C23×C4#4111yescharacteristic
206C23×C4#4111yescharacteristic
207C23×C4#4111yescharacteristic
208C23×C4#4111yescharacteristic
209C23×C4#4111yescharacteristic
210C23×C4#4111yescharacteristic
211C23×C4#4111yescharacteristic
212C23×C4#4111yescharacteristic
213C23×C4#4111yescharacteristic
214C23×C4#4111yescharacteristic
215C23×C4#4111yescharacteristic
216C23×C4#4111yescharacteristic
217C23×C4#4111yescharacteristic
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—22no—
224C2×M16—22no—
225C2×M16—22no—
226C2×M16—22no—
227C2×M16—22no—
228C2×M16—22no—
229C2×M16—22no—
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16—22no—
240C2×M16—22no—
241C2×M16—22no—
242C2×M16—22no—
243C2×M16—22no—
244C2×M16—22no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—41no—
249C2×M16—41no—
250C2×M16—41no—
251C2×M16—41no—
252C2×M16—41no—
253C2×M16—41no—
254C2×M16—41no—
255C2×M16—41no—
256C2×M16—41no—
257C2×M16—41no—
258C2×M16—41no—
259C2×M16—41no—
260C2×M16—41no—
261C2×M16—41no—
262C2×M16—41no—
263C2×M16—41no—
264C2×M16—41no—
265C2×M16—41no—
266C2×M16—41no—
267C2×M16—41no—
268C2×M16—41no—
269C2×M16—41no—
270C2×M16—41no—
271C2×M16—41no—
272C2×M16C4214yes—
273C2×M16C22⋊C414yes—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—41no—
281C22×C8—41no—
282C22×C8—41no—
283C22×C8—41no—
284C22×C8—41no—
285C22×C8—41no—
286C22×C8—41no—
287C22×C8—41no—
288#117—22no—
289#117—22no—
290#117—22no—
291#117—22no—
292#117—22no—
293#117—22no—
294#117—22no—
295#117—22no—
296#117—22no—
297#117—22no—
298#117—22no—
299#117—22no—
300#117—22no—
301#117—22no—
302#117—22no—
303#117—22no—
304#117—41no—
305#117—41no—
306#117—41no—
307#117—41no—
308#117—41no—
309#117—41no—
310#117—41no—
311#117—41no—
312#117—41no—
313#117—41no—
314#117—41no—
315#117—41no—
316#117—41no—
317#117—41no—
318#117—41no—
319#117—41no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4—41no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4C22⋊C414yes—
391C2×C4⋊C4C4⋊C414yes—
392C2×C4⋊C4C4⋊C412yes—
393C2×C4⋊C4C4⋊C412yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4—41no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—41no—
426C2×C42—41no—
427C2×C42—41no—
428C2×C42—41no—
429C2×C42—41no—
430C2×C42—41no—
431C2×C42—41no—
432C2×C42—41no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42—41no—
436C2×C42—41no—
437C2×C42—41no—
438C2×C42—41no—
439C2×C42—41no—
440C2×C42—41no—
441C2×C42—41no—
442C2×C42—41no—
443C2×C42—41no—
444C2×C42—41no—
445C2×C42C22⋊C414yes—
446#95—416no—
447#95—84no—
448#95—84no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24C2×C4⋊C411yescharacteristic
454C24C4×D411yescharacteristic
455C24C4×D411yescharacteristic
456C24#12011yescharacteristic
457C24#12011yescharacteristic
458C24#12111yescharacteristic
459C24#12111yescharacteristic
460C24#12111yescharacteristic
461C24#12111yescharacteristic
462C24C22⋊Q811yescharacteristic
463C24C22⋊Q811yescharacteristic
464C24#12311yescharacteristic
465C24#12311yescharacteristic
466C24#12411yescharacteristic
467C24#12411yescharacteristic
468C22×C4—24no—
469C22×C4—28no—
470C22×C4—24no—
471C22×C4—28no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—48no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—48no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—44no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—84no—
533C22×C4—84no—
534C22×C4—82no—
535C22×C4—82no—
536C22×C4—84no—
537C22×C4—82no—
538C22×C4—82no—
539C22×C4—82no—
540C22×C4—82no—
541C22×C4—84no—
542C22×C4C2×C4211yescharacteristic
543C22×C4C2×C22⋊C411yescharacteristic
544C22×C4C2×C22⋊C411yescharacteristic
545C22×C4C2×C22⋊C411yescharacteristic
546C22×C4C2×C4⋊C411yescharacteristic
547C22×C4C2×C4⋊C411yescharacteristic
548C22×C4#11711yescharacteristic
549C22×C4#11711yescharacteristic
550C22×C4#11711yescharacteristic
551C22×C4#11711yescharacteristic
552C22×C4#11711yescharacteristic
553C22×C4#11711yescharacteristic
554C22×C4#11711yescharacteristic
555C22×C4#11711yescharacteristic
556C22×C4#11711yescharacteristic
557C22×C4#11711yescharacteristic
558C22×C4#11711yescharacteristic
559C22×C4#11711yescharacteristic
560C22×C4C4×D411yescharacteristic
561C22×C4C4×D411yescharacteristic
562C22×C4C4×D411yescharacteristic
563C22×C4C4×D411yescharacteristic
564C22×C4C4×D411yescharacteristic
565C22×C4C4×D411yescharacteristic
566C22×C4C4×D411yescharacteristic
567C22×C4C4×D411yescharacteristic
568C22×C4C4×D411yescharacteristic
569C22×C4C4×D411yescharacteristic
570C22×C4C4×D411yescharacteristic
571C22×C4C4×D411yescharacteristic
572C22×C4C4×D411yescharacteristic
573C22×C4C4×D411yescharacteristic
574C22×C4C4×D411yescharacteristic
575C22×C4C4×D411yescharacteristic
576C22×C4C4×Q811yescharacteristic
577C22×C4C4×Q811yescharacteristic
578C22×C4C4×Q811yescharacteristic
579C22×C4C4×Q811yescharacteristic
580C22×C4C4×Q811yescharacteristic
581C22×C4C4×Q811yescharacteristic
582C22×C4#12011yescharacteristic
583C22×C4#12011yescharacteristic
584C22×C4#12111yescharacteristic
585C22×C4#12111yescharacteristic
586C22×C4#12111yescharacteristic
587C22×C4#12111yescharacteristic
588C22×C4#12111yescharacteristic
589C22×C4#12111yescharacteristic
590C22×C4#12111yescharacteristic
591C22×C4#12111yescharacteristic
592C22×C4#12111yescharacteristic
593C22×C4#12111yescharacteristic
594C22×C4#12111yescharacteristic
595C22×C4#12111yescharacteristic
596C22×C4#12111yescharacteristic
597C22×C4#12111yescharacteristic
598C22×C4C22⋊Q811yescharacteristic
599C22×C4C22⋊Q811yescharacteristic
600C22×C4C22⋊Q811yescharacteristic
601C22×C4C22⋊Q811yescharacteristic
602C22×C4C22⋊Q811yescharacteristic
603C22×C4C22⋊Q811yescharacteristic
604C22×C4C22⋊Q811yescharacteristic
605C22×C4C22⋊Q811yescharacteristic
606C22×C4C22⋊Q811yescharacteristic
607C22×C4C22⋊Q811yescharacteristic
608C22×C4C22⋊Q811yescharacteristic
609C22×C4C22⋊Q811yescharacteristic
610C22×C4C22⋊Q811yescharacteristic
611C22×C4C22⋊Q811yescharacteristic
612C22×C4C22⋊Q811yescharacteristic
613C22×C4C22⋊Q811yescharacteristic
614C22×C4#12311yescharacteristic
615C22×C4#12311yescharacteristic
616C22×C4#12311yescharacteristic
617C22×C4#12311yescharacteristic
618C22×C4#12311yescharacteristic
619C22×C4#12311yescharacteristic
620C22×C4#12311yescharacteristic
621C22×C4#12311yescharacteristic
622C22×C4#12311yescharacteristic
623C22×C4#12311yescharacteristic
624C22×C4#12311yescharacteristic
625C22×C4#12311yescharacteristic
626C22×C4#12311yescharacteristic
627C22×C4#12311yescharacteristic
628C22×C4#12311yescharacteristic
629C22×C4#12311yescharacteristic
630C22×C4#12311yescharacteristic
631C22×C4#12311yescharacteristic
632C22×C4#12311yescharacteristic
633C22×C4#12311yescharacteristic
634C22×C4#12311yescharacteristic
635C22×C4#12311yescharacteristic
636C22×C4#12411yescharacteristic
637C22×C4#12411yescharacteristic
638C22×C4#12411yescharacteristic
639C22×C4#12411yescharacteristic
640C22×C4#12411yescharacteristic
641C22×C4#12411yescharacteristic
642C22×C4#12411yescharacteristic
643C22×C4#12411yescharacteristic
644C22×C4#12411yescharacteristic
645C22×C4#12411yescharacteristic
646C22×C4#12511yescharacteristic
647C22×C4#12511yescharacteristic
648C22×C4#12511yescharacteristic
649C22×C4#12511yescharacteristic
650C22×C4#12511yescharacteristic
651C22×C4#12511yescharacteristic
652C22×C4#12511yescharacteristic
653C22×C4#12511yescharacteristic
654C22×C4#12511yescharacteristic
655C22×C4#12511yescharacteristic
656C22×C4#12511yescharacteristic
657C22×C4#12511yescharacteristic
658C22×C4#12611yescharacteristic
659C22×C4#12611yescharacteristic
660C22×C4#12611yescharacteristic
661C22×C4#12611yescharacteristic
662C22×C4#12611yescharacteristic
663C22×C4#12611yescharacteristic
664C22×C4#12611yescharacteristic
665C22×C4#12611yescharacteristic
666C22×C4#12611yescharacteristic
667C22×C4#12611yescharacteristic
668C22×C4#12611yescharacteristic
669C22×C4#12611yescharacteristic
670C22×C4#12611yescharacteristic
671C22×C4#12611yescharacteristic
672C22×C4#12611yescharacteristic
673C22×C4#12611yescharacteristic
674C22×C4#12611yescharacteristic
675C22×C4#12611yescharacteristic
676C22×C4#12611yescharacteristic
677C22×C4#12611yescharacteristic
678C22×C4#12711yescharacteristic
679C22×C4C4⋊Q811yescharacteristic
680C22×C4C4⋊Q811yescharacteristic
681C22×C4C4⋊Q811yescharacteristic
682M16—24no—
683M16—24no—
684M16—24no—
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16—42no—
694M16—42no—
695M16—42no—
696M16—42no—
697M16—42no—
698C2×C8—24no—
699C2×C8—24no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8—42no—
705C2×C8—42no—
706C2×C8—42no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8—42no—
711C2×C8—42no—
712C4⋊C4—24no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—24no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—42no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—41no—
729C4⋊C4—41no—
730C4⋊C4—42no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—41no—
735C4⋊C4—41no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C42—24no—
749C42—24no—
750C42—42no—
751C42—42no—
752C42—42no—
753C42—42no—
754C42—42no—
755C42—42no—
756C42—42no—
757C42—42no—
758C42—42no—
759C42—42no—
760C42—42no—
761C42—42no—
762C42—42no—
763C42—42no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23C4×C4⋊C411yescharacteristic
797C23#38011yescharacteristic
798C23#38211yescharacteristic
799C23#38511yescharacteristic
800C23#38511yescharacteristic
801C23#38511yescharacteristic
802C23#38511yescharacteristic
803C23#38611yescharacteristic
804C23#38611yescharacteristic
805C23#38711yescharacteristic
806C23#38711yescharacteristic
807C23#38811yescharacteristic
808C23#38811yescharacteristic
809C23#38811yescharacteristic
810C23#38811yescharacteristic
811C23#38811yescharacteristic
812C23#38811yescharacteristic
813C23#38911yescharacteristic
814C23#38911yescharacteristic
815C23#39211yescharacteristic
816C23#39311yescharacteristic
817C23#39311yescharacteristic
818C23#39411yescharacteristic
819C23#39411yescharacteristic
820C23#39411yescharacteristic
821C23#39411yescharacteristic
822C23#39411yescharacteristic
823C23#39611yescharacteristic
824C23#39611yescharacteristic
825C23#39711yescharacteristic
826C23#39711yescharacteristic
827C23#39711yescharacteristic
828C23#39811yescharacteristic
829C23#40011yescharacteristic
830C23#40011yescharacteristic
831C23#45312yes—
832C23#45412yes—
833C23#45512yes—
834C23#45612yes—
835C2×C4—28no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—48no—
844C2×C4—48no—
845C2×C4—44no—
846C2×C4—48no—
847C2×C4—48no—
848C2×C4—48no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—84no—
859C2×C4—84no—
860C2×C4—84no—
861C2×C4—84no—
862C2×C4—84no—
863C2×C4—84no—
864C2×C4—81no—
865C2×C4—82no—
866C2×C4—82no—
867C2×C4—81no—
868C2×C4—82no—
869C2×C4—81no—
870C2×C4—82no—
871C2×C4—81no—
872C2×C4—84no—
873C2×C4—82no—
874C2×C4—84no—
875C2×C4—82no—
876C2×C4—82no—
877C2×C4—82no—
878C2×C4—82no—
879C2×C4—82no—
880C2×C4—84no—
881C2×C4#37611yescharacteristic
882C2×C4C4×C22⋊C411yescharacteristic
883C2×C4C4×C22⋊C411yescharacteristic
884C2×C4C4×C22⋊C411yescharacteristic
885C2×C4C4×C4⋊C411yescharacteristic
886C2×C4C4×C4⋊C411yescharacteristic
887C2×C4#38011yescharacteristic
888C2×C4#38011yescharacteristic
889C2×C4#38111yescharacteristic
890C2×C4#38111yescharacteristic
891C2×C4#38111yescharacteristic
892C2×C4#38211yescharacteristic
893C2×C4#38211yescharacteristic
894C2×C4#38311yescharacteristic
895C2×C4#38311yescharacteristic
896C2×C4#38311yescharacteristic
897C2×C4#38511yescharacteristic
898C2×C4#38511yescharacteristic
899C2×C4#38611yescharacteristic
900C2×C4#38611yescharacteristic
901C2×C4#38611yescharacteristic
902C2×C4#38611yescharacteristic
903C2×C4#38711yescharacteristic
904C2×C4#38711yescharacteristic
905C2×C4#38711yescharacteristic
906C2×C4#38711yescharacteristic
907C2×C4#38711yescharacteristic
908C2×C4#38711yescharacteristic
909C2×C4#38711yescharacteristic
910C2×C4#38711yescharacteristic
911C2×C4#38711yescharacteristic
912C2×C4#38711yescharacteristic
913C2×C4#38711yescharacteristic
914C2×C4#38711yescharacteristic
915C2×C4#38711yescharacteristic
916C2×C4#38711yescharacteristic
917C2×C4#38711yescharacteristic
918C2×C4#38711yescharacteristic
919C2×C4#38711yescharacteristic
920C2×C4#38711yescharacteristic
921C2×C4#38711yescharacteristic
922C2×C4#38711yescharacteristic
923C2×C4#38711yescharacteristic
924C2×C4#38711yescharacteristic
925C2×C4#38811yescharacteristic
926C2×C4#38811yescharacteristic
927C2×C4#38811yescharacteristic
928C2×C4#38811yescharacteristic
929C2×C4#38811yescharacteristic
930C2×C4#38811yescharacteristic
931C2×C4#38811yescharacteristic
932C2×C4#38811yescharacteristic
933C2×C4#38811yescharacteristic
934C2×C4#38811yescharacteristic
935C2×C4#38811yescharacteristic
936C2×C4#38811yescharacteristic
937C2×C4#38811yescharacteristic
938C2×C4#38811yescharacteristic
939C2×C4#38811yescharacteristic
940C2×C4#38811yescharacteristic
941C2×C4#38811yescharacteristic
942C2×C4#38811yescharacteristic
943C2×C4#38911yescharacteristic
944C2×C4#38911yescharacteristic
945C2×C4#38911yescharacteristic
946C2×C4#38911yescharacteristic
947C2×C4#39011yescharacteristic
948C2×C4#39011yescharacteristic
949C2×C4#39011yescharacteristic
950C2×C4#39111yescharacteristic
951C2×C4#39111yescharacteristic
952C2×C4#39111yescharacteristic
953C2×C4#39311yescharacteristic
954C2×C4#39411yescharacteristic
955C2×C4#39411yescharacteristic
956C2×C4#39411yescharacteristic
957C2×C4#39411yescharacteristic
958C2×C4#39511yescharacteristic
959C2×C4#39611yescharacteristic
960C2×C4#39611yescharacteristic
961C2×C4#39611yescharacteristic
962C2×C4#39611yescharacteristic
963C2×C4#39711yescharacteristic
964C2×C4#39711yescharacteristic
965C2×C4#39711yescharacteristic
966C2×C4#39711yescharacteristic
967C2×C4#39711yescharacteristic
968C2×C4#39711yescharacteristic
969C2×C4#39711yescharacteristic
970C2×C4#39711yescharacteristic
971C2×C4#39711yescharacteristic
972C2×C4#39711yescharacteristic
973C2×C4#39711yescharacteristic
974C2×C4#39711yescharacteristic
975C2×C4#39811yescharacteristic
976C2×C4#39811yescharacteristic
977C2×C4#39811yescharacteristic
978C2×C4#39811yescharacteristic
979C2×C4#39811yescharacteristic
980C2×C4#39811yescharacteristic
981C2×C4#39811yescharacteristic
982C2×C4#39811yescharacteristic
983C2×C4#39911yescharacteristic
984C2×C4#39911yescharacteristic
985C2×C4#39911yescharacteristic
986C2×C4#40011yescharacteristic
987C2×C4#40011yescharacteristic
988C2×C4#40011yescharacteristic
989C2×C4#40011yescharacteristic
990C2×C4#40011yescharacteristic
991C2×C4#40011yescharacteristic
992C2×C4#40011yescharacteristic
993C2×C4#40011yescharacteristic
994C2×C4#40011yescharacteristic
995C2×C4#40011yescharacteristic
996C2×C4#40011yescharacteristic
997C2×C4#40011yescharacteristic
998C2×C4#40011yescharacteristic
999C2×C4#40111yescharacteristic
1000C2×C4#40111yescharacteristic
1001C8—44no—
1002C8—44no—
1003C22—22no—
1004C22—22no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22#143411yescharacteristic
1044C22#143611yescharacteristic
1045C22#143611yescharacteristic
1046C22#143911yescharacteristic
1047C22#143911yescharacteristic
1048C22#143911yescharacteristic
1049C22#144011yescharacteristic
1050C22#144011yescharacteristic
1051C22#144111yescharacteristic
1052C22#144211yescharacteristic
1053C22#144211yescharacteristic
1054C22#144211yescharacteristic
1055C22#144211yescharacteristic
1056C22#144311yescharacteristic
1057C22#144311yescharacteristic
1058C22#185612yes—
1059C22#185712yes—
1060C22#185912yes—
1061C22#186012yes—
1062C22#188212yes—
1063C22#188312yes—
1064C22#200211yescharacteristic
1065C22#200311yescharacteristic
1066C22#200411yescharacteristic
1067C22#200511yescharacteristic
1068C22#202712yes—
1069C22#202812yes—
1070C22#203712yes—
1071C22#203812yes—
1072C22#203912yes—
1073C22#204012yes—
1074C4—48no—
1075C4—84no—
1076C4—82no—
1077C4—82no—
1078C4—84no—
1079C4—84no—
1080C4#143411yescharacteristic
1081C4#143411yescharacteristic
1082C4#143611yescharacteristic
1083C4#143711yescharacteristic
1084C4#144011yescharacteristic
1085C4#144111yescharacteristic
1086C4#144111yescharacteristic
1087C4#144211yescharacteristic
1088C4#144211yescharacteristic
1089C4#144311yescharacteristic
1090C4#144311yescharacteristic
1091C4#144311yescharacteristic
1092C4#144311yescharacteristic
1093C4#144511yescharacteristic
1094C4#144511yescharacteristic
1095C4#144511yescharacteristic
1096C2—21no—
1097C2—21no—
1098C2—21no—
1099C2—21no—
1100C2—21no—
1101C2—21no—
1102C2—21no—
1103C2—21no—
1104C2#755611yescharacteristic
1105C2#1089912yes—
1106C2#1106311yescharacteristic
1107C2#1106411yescharacteristic
1108C2#1107811yescharacteristic
1109C2#1107911yescharacteristic
1110C2#1113511yescharacteristic
1111C2#1113611yescharacteristic
1112C2#1119512yes—
1113C2#1127612yes—
1114C2#1129612yes—
subgroupG/H
center, socleC24#120
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
18. C2×#343C4semidirect
22. #1736C4semidirect
31. C2×#339C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3432
C2×#17362
C22×#3392
#137952
C2×C4⋊#952