Finite Group Databasebeta

← #123829

Subgroups — #123829

Order 512.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#343C211yesmaximal, characteristic
2C22×#343C211yesmaximal, characteristic
3C22×#341C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6C22×#340C211yesmaximal, characteristic
7C2×#1729C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C24×C8C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C2×#343—22no—
16C2×#343—22no—
17C2×#343—22no—
18C2×#343—22no—
19C2×#343—22no—
20C2×#343C414yescomplemented
21C2×#341—22no—
22C2×#341—22no—
23C2×#341C414yescomplemented
24#1736—22no—
25#1736—22no—
26#1736—22no—
27#1736C414yescomplemented
28C2×#340—22no—
29C2×#340—22no—
30C2×#340—22no—
31C2×#340—22no—
32C2×#340—22no—
33#1729—22no—
34#1729—22no—
35C2×#336—22no—
36C24×C4—21no—
37C24×C4—21no—
38C24×C4C2311yescharacteristic
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×M16—21no—
61C22×M16—21no—
62C22×M16—21no—
63C22×M16—21no—
64C22×M16—21no—
65C22×M16—21no—
66C22×M16—21no—
67C22×M16—21no—
68C22×M16—21no—
69C22×M16—21no—
70C22×M16—21no—
71C22×M16—21no—
72C22×M16C2×C412yes—
73C22×M16C2×C412yes—
74C22×M16C2×C412yes—
75C22×M16C2×C412yes—
76C22×M16C2×C412yes—
77C22×M16D412yes—
78C22×M16D412yes—
79C22×M16D412yes—
80C22×M16Q812yes—
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×C8—21no—
93C23×C8—21no—
94C23×C8—21no—
95C23×C8—21no—
96C23×C8C2×C412yes—
97C23×C8D412yes—
98C23×C8Q812yes—
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×#117C2×C412yes—
110C2×#117D412yes—
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⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4C2×C412yes—
134C22×C4⋊C4C2×C412yes—
135C22×C4⋊C4D412yes—
136C22×C4⋊C4D412yes—
137C22×C4⋊C4D412yes—
138C22×C4⋊C4D412yes—
139C22×C4⋊C4Q812yes—
140C22×C22⋊C4—21no—
141C22×C42—21no—
142#343—28no—
143#343—28no—
144#341—28no—
145#340—28no—
146#340—28no—
147#340—28no—
148#336—28no—
149C25#4111yescharacteristic
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—41no—
158C23×C4—41no—
159C23×C4—41no—
160C23×C4—41no—
161C23×C4—41no—
162C23×C4—41no—
163C23×C4—41no—
164C23×C4—41no—
165C23×C4—82no—
166C23×C4—82no—
167C23×C4—82no—
168C23×C4—82no—
169C23×C4C22×C411yescharacteristic
170C23×C4C22×C411yescharacteristic
171C23×C4C22×C411yescharacteristic
172C23×C4C2×D411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×Q811yescharacteristic
182C23×C4C2×Q811yescharacteristic
183C23×C4C2×Q811yescharacteristic
184C23×C4#4111yescharacteristic
185C23×C4#4111yescharacteristic
186C23×C4#4111yescharacteristic
187C23×C4#4111yescharacteristic
188C23×C4#4111yescharacteristic
189C23×C4#4111yescharacteristic
190C23×C4#4111yescharacteristic
191C23×C4#4111yescharacteristic
192C23×C4#4111yescharacteristic
193C23×C4#4111yescharacteristic
194C23×C4#4111yescharacteristic
195C23×C4#4111yescharacteristic
196C23×C4#4111yescharacteristic
197C23×C4#4111yescharacteristic
198C23×C4#4111yescharacteristic
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—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—41no—
245C2×M16—41no—
246C2×M16—41no—
247C2×M16—41no—
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×M16—41no—
273C2×M16—41no—
274C2×M16—41no—
275C2×M16—41no—
276C2×M16—41no—
277C2×M16—41no—
278C2×M16—41no—
279C2×M16—41no—
280C2×M16C4214yes—
281C2×M16C22⋊C414yes—
282C2×M16C4⋊C414yes—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
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×C8—41no—
330C22×C8—41no—
331C22×C8—41no—
332C22×C8—41no—
333C22×C8—41no—
334C22×C8—41no—
335C22×C8—41no—
336C22×C8—41no—
337C22×C8—41no—
338C22×C8C4⋊C414yes—
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—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
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⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—41no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—41no—
408C2×C4⋊C4—41no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4C22⋊C414yes—
415C2×C4⋊C4C22⋊C414yes—
416C2×C4⋊C4C4⋊C414yes—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—41no—
422C2×C22⋊C4—41no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—41no—
426C2×C42—41no—
427C2×C42—41no—
428C2×C42—41no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24#11711yescharacteristic
434C24C4×D411yescharacteristic
435C24C4×Q811yescharacteristic
436C24#12111yescharacteristic
437C24C22⋊Q811yescharacteristic
438C24#12311yescharacteristic
439C24#12311yescharacteristic
440C24#12311yescharacteristic
441C24#12311yescharacteristic
442C24#12411yescharacteristic
443C24#12511yescharacteristic
444C24#12611yescharacteristic
445C24#12611yescharacteristic
446C24#12611yescharacteristic
447C24#12611yescharacteristic
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
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—42no—
468C22×C4—42no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4—84no—
472C22×C4—84no—
473C22×C4—82no—
474C22×C4—82no—
475C22×C4—82no—
476C22×C4—82no—
477C22×C4—82no—
478C22×C4—82no—
479C22×C4—82no—
480C22×C4—82no—
481C22×C4—84no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4—84no—
485C22×C4—82no—
486C22×C4—82no—
487C22×C4—82no—
488C22×C4—82no—
489C22×C4C2×C4211yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C4⋊C411yescharacteristic
494C22×C4C2×C4⋊C411yescharacteristic
495C22×C4C2×C4⋊C411yescharacteristic
496C22×C4#11711yescharacteristic
497C22×C4#11711yescharacteristic
498C22×C4#11711yescharacteristic
499C22×C4#11711yescharacteristic
500C22×C4#11711yescharacteristic
501C22×C4#11711yescharacteristic
502C22×C4#11711yescharacteristic
503C22×C4#11711yescharacteristic
504C22×C4#11711yescharacteristic
505C22×C4#11711yescharacteristic
506C22×C4#11711yescharacteristic
507C22×C4C4×D411yescharacteristic
508C22×C4C4×D411yescharacteristic
509C22×C4C4×D411yescharacteristic
510C22×C4C4×D411yescharacteristic
511C22×C4C4×D411yescharacteristic
512C22×C4C4×D411yescharacteristic
513C22×C4C4×D411yescharacteristic
514C22×C4C4×D411yescharacteristic
515C22×C4C4×D411yescharacteristic
516C22×C4C4×D411yescharacteristic
517C22×C4C4×D411yescharacteristic
518C22×C4C4×D411yescharacteristic
519C22×C4C4×D411yescharacteristic
520C22×C4C4×D411yescharacteristic
521C22×C4C4×D411yescharacteristic
522C22×C4C4×D411yescharacteristic
523C22×C4C4×D411yescharacteristic
524C22×C4C4×Q811yescharacteristic
525C22×C4C4×Q811yescharacteristic
526C22×C4C4×Q811yescharacteristic
527C22×C4C4×Q811yescharacteristic
528C22×C4C4×Q811yescharacteristic
529C22×C4#12011yescharacteristic
530C22×C4#12011yescharacteristic
531C22×C4#12011yescharacteristic
532C22×C4#12011yescharacteristic
533C22×C4#12111yescharacteristic
534C22×C4#12111yescharacteristic
535C22×C4#12111yescharacteristic
536C22×C4#12111yescharacteristic
537C22×C4#12111yescharacteristic
538C22×C4#12111yescharacteristic
539C22×C4#12111yescharacteristic
540C22×C4#12111yescharacteristic
541C22×C4#12111yescharacteristic
542C22×C4#12111yescharacteristic
543C22×C4#12111yescharacteristic
544C22×C4#12111yescharacteristic
545C22×C4#12111yescharacteristic
546C22×C4#12111yescharacteristic
547C22×C4#12111yescharacteristic
548C22×C4#12111yescharacteristic
549C22×C4#12111yescharacteristic
550C22×C4C22⋊Q811yescharacteristic
551C22×C4C22⋊Q811yescharacteristic
552C22×C4C22⋊Q811yescharacteristic
553C22×C4C22⋊Q811yescharacteristic
554C22×C4C22⋊Q811yescharacteristic
555C22×C4C22⋊Q811yescharacteristic
556C22×C4C22⋊Q811yescharacteristic
557C22×C4C22⋊Q811yescharacteristic
558C22×C4C22⋊Q811yescharacteristic
559C22×C4C22⋊Q811yescharacteristic
560C22×C4C22⋊Q811yescharacteristic
561C22×C4C22⋊Q811yescharacteristic
562C22×C4C22⋊Q811yescharacteristic
563C22×C4C22⋊Q811yescharacteristic
564C22×C4C22⋊Q811yescharacteristic
565C22×C4C22⋊Q811yescharacteristic
566C22×C4C22⋊Q811yescharacteristic
567C22×C4#12311yescharacteristic
568C22×C4#12311yescharacteristic
569C22×C4#12311yescharacteristic
570C22×C4#12311yescharacteristic
571C22×C4#12311yescharacteristic
572C22×C4#12311yescharacteristic
573C22×C4#12311yescharacteristic
574C22×C4#12311yescharacteristic
575C22×C4#12311yescharacteristic
576C22×C4#12311yescharacteristic
577C22×C4#12311yescharacteristic
578C22×C4#12311yescharacteristic
579C22×C4#12311yescharacteristic
580C22×C4#12311yescharacteristic
581C22×C4#12311yescharacteristic
582C22×C4#12311yescharacteristic
583C22×C4#12311yescharacteristic
584C22×C4#12311yescharacteristic
585C22×C4#12311yescharacteristic
586C22×C4#12311yescharacteristic
587C22×C4#12411yescharacteristic
588C22×C4#12411yescharacteristic
589C22×C4#12411yescharacteristic
590C22×C4#12411yescharacteristic
591C22×C4#12411yescharacteristic
592C22×C4#12411yescharacteristic
593C22×C4#12411yescharacteristic
594C22×C4#12411yescharacteristic
595C22×C4#12411yescharacteristic
596C22×C4#12411yescharacteristic
597C22×C4#12411yescharacteristic
598C22×C4#12511yescharacteristic
599C22×C4#12511yescharacteristic
600C22×C4#12511yescharacteristic
601C22×C4#12511yescharacteristic
602C22×C4#12511yescharacteristic
603C22×C4#12511yescharacteristic
604C22×C4#12511yescharacteristic
605C22×C4#12511yescharacteristic
606C22×C4#12511yescharacteristic
607C22×C4#12511yescharacteristic
608C22×C4#12511yescharacteristic
609C22×C4#12611yescharacteristic
610C22×C4#12611yescharacteristic
611C22×C4#12611yescharacteristic
612C22×C4#12611yescharacteristic
613C22×C4#12611yescharacteristic
614C22×C4#12611yescharacteristic
615C22×C4#12611yescharacteristic
616C22×C4#12611yescharacteristic
617C22×C4#12611yescharacteristic
618C22×C4#12611yescharacteristic
619C22×C4#12611yescharacteristic
620C22×C4#12611yescharacteristic
621C22×C4#12611yescharacteristic
622C22×C4#12611yescharacteristic
623C22×C4#12611yescharacteristic
624C22×C4#12611yescharacteristic
625C22×C4#12711yescharacteristic
626C22×C4C4⋊Q811yescharacteristic
627C22×C4C4⋊Q811yescharacteristic
628C22×C4C4⋊Q811yescharacteristic
629M16—24no—
630M16—24no—
631M16—24no—
632M16—24no—
633M16—24no—
634M16—24no—
635M16—42no—
636M16—42no—
637M16—42no—
638M16—42no—
639M16—42no—
640M16—42no—
641M16—42no—
642M16—42no—
643M16—42no—
644M16—42no—
645M16—42no—
646M16—42no—
647M16—42no—
648M16—42no—
649M16—42no—
650M16—42no—
651M16—42no—
652M16—42no—
653C2×C8—24no—
654C2×C8—24no—
655C2×C8—24no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
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—
671C2×C8—42no—
672C2×C8—42no—
673C2×C8—42no—
674C2×C8—42no—
675C2×C8—42no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8—42no—
683C2×C8—42no—
684C2×C8—42no—
685C2×C8—42no—
686C2×C8—42no—
687C2×C8—42no—
688C2×C8—42no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—24no—
693C4⋊C4—24no—
694C4⋊C4—24no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—42no—
704C4⋊C4—42no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4—42no—
708C4⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C42—42no—
714C42—42no—
715C42—42no—
716C42—42no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23C4×C4⋊C411yescharacteristic
750C23#38111yescharacteristic
751C23#38311yescharacteristic
752C23#38511yescharacteristic
753C23#38611yescharacteristic
754C23#38711yescharacteristic
755C23#38711yescharacteristic
756C23#38711yescharacteristic
757C23#38711yescharacteristic
758C23#38711yescharacteristic
759C23#38711yescharacteristic
760C23#38711yescharacteristic
761C23#38811yescharacteristic
762C23#38811yescharacteristic
763C23#38811yescharacteristic
764C23#38811yescharacteristic
765C23#38811yescharacteristic
766C23#38911yescharacteristic
767C23#39111yescharacteristic
768C23#39411yescharacteristic
769C23#39411yescharacteristic
770C23#39611yescharacteristic
771C23#39711yescharacteristic
772C23#39711yescharacteristic
773C23#39711yescharacteristic
774C23#39711yescharacteristic
775C23#39711yescharacteristic
776C23#39711yescharacteristic
777C23#39811yescharacteristic
778C23#39911yescharacteristic
779C23#40011yescharacteristic
780C23#40011yescharacteristic
781C23#40011yescharacteristic
782C23#40011yescharacteristic
783C23#40111yescharacteristic
784C23#47112yes—
785C23#47112yes—
786C23#47212yes—
787C23#47312yes—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—84no—
794C2×C4—84no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4—84no—
799C2×C4—82no—
800C2×C4—84no—
801C2×C4—82no—
802C2×C4—84no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—84no—
806C2×C4—84no—
807C2×C4—82no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—82no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4#37611yescharacteristic
814C2×C4C4×C22⋊C411yescharacteristic
815C2×C4C4×C22⋊C411yescharacteristic
816C2×C4C4×C22⋊C411yescharacteristic
817C2×C4C4×C4⋊C411yescharacteristic
818C2×C4C4×C4⋊C411yescharacteristic
819C2×C4#38011yescharacteristic
820C2×C4#38011yescharacteristic
821C2×C4#38011yescharacteristic
822C2×C4#38111yescharacteristic
823C2×C4#38111yescharacteristic
824C2×C4#38211yescharacteristic
825C2×C4#38211yescharacteristic
826C2×C4#38211yescharacteristic
827C2×C4#38311yescharacteristic
828C2×C4#38311yescharacteristic
829C2×C4#38511yescharacteristic
830C2×C4#38511yescharacteristic
831C2×C4#38511yescharacteristic
832C2×C4#38511yescharacteristic
833C2×C4#38511yescharacteristic
834C2×C4#38611yescharacteristic
835C2×C4#38611yescharacteristic
836C2×C4#38611yescharacteristic
837C2×C4#38611yescharacteristic
838C2×C4#38611yescharacteristic
839C2×C4#38711yescharacteristic
840C2×C4#38711yescharacteristic
841C2×C4#38711yescharacteristic
842C2×C4#38711yescharacteristic
843C2×C4#38711yescharacteristic
844C2×C4#38711yescharacteristic
845C2×C4#38711yescharacteristic
846C2×C4#38711yescharacteristic
847C2×C4#38711yescharacteristic
848C2×C4#38711yescharacteristic
849C2×C4#38711yescharacteristic
850C2×C4#38711yescharacteristic
851C2×C4#38711yescharacteristic
852C2×C4#38711yescharacteristic
853C2×C4#38711yescharacteristic
854C2×C4#38711yescharacteristic
855C2×C4#38711yescharacteristic
856C2×C4#38811yescharacteristic
857C2×C4#38811yescharacteristic
858C2×C4#38811yescharacteristic
859C2×C4#38811yescharacteristic
860C2×C4#38811yescharacteristic
861C2×C4#38811yescharacteristic
862C2×C4#38811yescharacteristic
863C2×C4#38811yescharacteristic
864C2×C4#38811yescharacteristic
865C2×C4#38811yescharacteristic
866C2×C4#38811yescharacteristic
867C2×C4#38811yescharacteristic
868C2×C4#38811yescharacteristic
869C2×C4#38811yescharacteristic
870C2×C4#38811yescharacteristic
871C2×C4#38811yescharacteristic
872C2×C4#38811yescharacteristic
873C2×C4#38811yescharacteristic
874C2×C4#38811yescharacteristic
875C2×C4#38911yescharacteristic
876C2×C4#38911yescharacteristic
877C2×C4#38911yescharacteristic
878C2×C4#38911yescharacteristic
879C2×C4#38911yescharacteristic
880C2×C4#39011yescharacteristic
881C2×C4#39011yescharacteristic
882C2×C4#39011yescharacteristic
883C2×C4#39111yescharacteristic
884C2×C4#39111yescharacteristic
885C2×C4#39211yescharacteristic
886C2×C4#39311yescharacteristic
887C2×C4#39311yescharacteristic
888C2×C4#39311yescharacteristic
889C2×C4#39411yescharacteristic
890C2×C4#39411yescharacteristic
891C2×C4#39411yescharacteristic
892C2×C4#39411yescharacteristic
893C2×C4#39411yescharacteristic
894C2×C4#39411yescharacteristic
895C2×C4#39411yescharacteristic
896C2×C4#39511yescharacteristic
897C2×C4#39611yescharacteristic
898C2×C4#39611yescharacteristic
899C2×C4#39611yescharacteristic
900C2×C4#39611yescharacteristic
901C2×C4#39611yescharacteristic
902C2×C4#39711yescharacteristic
903C2×C4#39711yescharacteristic
904C2×C4#39711yescharacteristic
905C2×C4#39711yescharacteristic
906C2×C4#39711yescharacteristic
907C2×C4#39711yescharacteristic
908C2×C4#39711yescharacteristic
909C2×C4#39711yescharacteristic
910C2×C4#39711yescharacteristic
911C2×C4#39811yescharacteristic
912C2×C4#39811yescharacteristic
913C2×C4#39811yescharacteristic
914C2×C4#39811yescharacteristic
915C2×C4#39811yescharacteristic
916C2×C4#39811yescharacteristic
917C2×C4#39811yescharacteristic
918C2×C4#39811yescharacteristic
919C2×C4#39911yescharacteristic
920C2×C4#39911yescharacteristic
921C2×C4#40011yescharacteristic
922C2×C4#40011yescharacteristic
923C2×C4#40011yescharacteristic
924C2×C4#40011yescharacteristic
925C2×C4#40011yescharacteristic
926C2×C4#40011yescharacteristic
927C2×C4#40011yescharacteristic
928C2×C4#40011yescharacteristic
929C2×C4#40011yescharacteristic
930C2×C4#40011yescharacteristic
931C2×C4#40011yescharacteristic
932C2×C4#40111yescharacteristic
933C8—44no—
934C8—44no—
935C8—44no—
936C8—44no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—22no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22#143411yescharacteristic
978C22#143611yescharacteristic
979C22#143611yescharacteristic
980C22#143911yescharacteristic
981C22#144011yescharacteristic
982C22#144011yescharacteristic
983C22#144111yescharacteristic
984C22#144211yescharacteristic
985C22#144211yescharacteristic
986C22#144311yescharacteristic
987C22#144311yescharacteristic
988C22#144311yescharacteristic
989C22#144311yescharacteristic
990C22#144511yescharacteristic
991C22#144511yescharacteristic
992C22#190712yes—
993C22#190812yes—
994C22#193012yes—
995C22#193112yes—
996C22#195112yes—
997C22#195212yes—
998C22#204511yescharacteristic
999C22#204611yescharacteristic
1000C22#204611yescharacteristic
1001C22#204711yescharacteristic
1002C22#205112yes—
1003C22#205212yes—
1004C22#206312yes—
1005C22#206412yes—
1006C22#207812yes—
1007C22#207912yes—
1008C4—84no—
1009C4—84no—
1010C4—84no—
1011C4#143411yescharacteristic
1012C4#143411yescharacteristic
1013C4#143611yescharacteristic
1014C4#143711yescharacteristic
1015C4#143911yescharacteristic
1016C4#143911yescharacteristic
1017C4#144011yescharacteristic
1018C4#144111yescharacteristic
1019C4#144111yescharacteristic
1020C4#144211yescharacteristic
1021C4#144211yescharacteristic
1022C4#144211yescharacteristic
1023C4#144211yescharacteristic
1024C4#144311yescharacteristic
1025C4#144311yescharacteristic
1026C4#144511yescharacteristic
1027C2—21no—
1028C2—21no—
1029C2—21no—
1030C2—21no—
1031C2—21no—
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2#755611yescharacteristic
1036C2#1089612yes—
1037C2#1106111yescharacteristic
1038C2#1106211yescharacteristic
1039C2#1116311yescharacteristic
1040C2#1116411yescharacteristic
1041C2#1119212yes—
1042C2#1124912yes—
1043C2#1127011yescharacteristic
1044C2#1127111yescharacteristic
1045C2#1130312yes—
subgroupG/H
center, socleC24#121
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25#41
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
20. C2×#343C4semidirect
23. C2×#341C4semidirect
27. #1736C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3432
C22×#3412
C2×#17362
C22×#3402
C2×#17292