Finite Group Databasebeta

← #123947

Subgroups — #123947

Order 512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#423C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C2×#1738C211yesmaximal, characteristic
4C2×#1733C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C22×#339C211yesmaximal, characteristic
7#20335C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C42C2211yescharacteristic
15C2×#423—22no—
16C2×#423—22no—
17C2×#423—22no—
18C2×#423—22no—
19C2×#423—22no—
20C2×#423C414yescomplemented
21C22×C4⋊C8—22no—
22C2×#344—22no—
23C2×#344—22no—
24C2×#344—22no—
25#1738—22no—
26#1738—22no—
27C2×#341—22no—
28#1733—22no—
29#1733—22no—
30C2×#339—22no—
31C2×#339—22no—
32C2×#339—22no—
33C2×#339—22no—
34C2×#339—22no—
35C2×#339C414yescomplemented
36C2×#339C412yescomplemented
37C2×#339C412yescomplemented
38#1729—22no—
39#1729—22no—
40#1728—22no—
41C24×C4—21no—
42C24×C4C2311yescharacteristic
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×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16—21no—
82C22×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16C2×C412yes—
89C22×M16C2×C412yes—
90C22×M16C2×C412yes—
91C22×M16C2×C412yes—
92C22×M16D412yes—
93C22×M16D412yes—
94C22×M16D412yes—
95C22×M16D412yes—
96C22×M16D412yes—
97C22×M16Q812yes—
98C22×M16Q812yes—
99C23×C8—21no—
100C23×C8—21no—
101C23×C8—21no—
102C23×C8D412yes—
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×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117C2×C412yes—
123C2×#117C2×C412yes—
124C2×#117D412yes—
125C2×#117D412yes—
126C2×#117Q812yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4Q812yes—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—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×C42C2×C412yes—
141C22×C42C2×C411yescharacteristic
142C22×C42C2×C412yes—
143C22×C42C2×C411yescharacteristic
144C22×C42D412yes—
145C22×C42D412yes—
146C22×C42D412yes—
147C22×C42Q812yes—
148#423—28no—
149#423—28no—
150#423—28no—
151#423—28no—
152C2×C4⋊C8—28no—
153C2×C4⋊C8—28no—
154C2×C4⋊C8—28no—
155#344—28no—
156#341—28no—
157#339—28no—
158#339—24no—
159#339—28no—
160#339—24no—
161#336—28no—
162C25#4111yescharacteristic
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—21no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—48no—
173C23×C4—41no—
174C23×C4C22×C411yescharacteristic
175C23×C4C22×C411yescharacteristic
176C23×C4C22×C411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×Q811yescharacteristic
189C23×C4C2×Q811yescharacteristic
190C23×C4C2×Q811yescharacteristic
191C23×C4C2×Q811yescharacteristic
192C23×C4C2×Q811yescharacteristic
193C23×C4#4111yescharacteristic
194C23×C4#4111yescharacteristic
195C23×C4#4111yescharacteristic
196C23×C4#4111yescharacteristic
197C23×C4#4111yescharacteristic
198C23×C4#4111yescharacteristic
199C23×C4#4111yescharacteristic
200C23×C4#4111yescharacteristic
201C23×C4#4111yescharacteristic
202C23×C4#4111yescharacteristic
203C23×C4#4111yescharacteristic
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—22no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16—22no—
250C2×M16—22no—
251C2×M16—22no—
252C2×M16—22no—
253C2×M16—22no—
254C2×M16—22no—
255C2×M16—22no—
256C2×M16—22no—
257C2×M16—22no—
258C2×M16—22no—
259C2×M16—22no—
260C2×M16—22no—
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×M16—41no—
281C2×M16—41no—
282C2×M16—41no—
283C2×M16—41no—
284C2×M16—41no—
285C2×M16—41no—
286C2×M16—41no—
287C2×M16—41no—
288C2×M16—41no—
289C2×M16—41no—
290C2×M16—41no—
291C2×M16—41no—
292C2×M16—41no—
293C2×M16—41no—
294C2×M16—41no—
295C2×M16—41no—
296C2×M16—41no—
297C2×M16—41no—
298C2×M16—41no—
299C2×M16—41no—
300C2×M16—41no—
301C2×M16—41no—
302C2×M16—41no—
303C2×M16—41no—
304C2×M16—41no—
305C2×M16—41no—
306C2×M16—41no—
307C2×M16—41no—
308C2×M16—41no—
309C2×M16—41no—
310C2×M16—41no—
311C2×M16—41no—
312C2×M16—41no—
313C2×M16C22⋊C414yes—
314C2×M16C4⋊C414yes—
315C2×M16C4⋊C414yes—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—41no—
332C22×C8—41no—
333C22×C8—41no—
334C22×C8—41no—
335C22×C8—41no—
336C22×C8—41no—
337C22×C8—41no—
338C22×C8—41no—
339C22×C8—41no—
340C22×C8—41no—
341C22×C8—41no—
342C22×C8—41no—
343C22×C8C22⋊C414yes—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—41no—
362#117—41no—
363#117—41no—
364#117—41no—
365#117—41no—
366#117—41no—
367#117—41no—
368#117—41no—
369#117—41no—
370#117—41no—
371#117—41no—
372#117—41no—
373#117—41no—
374#117—41no—
375#117C4⋊C414yes—
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—41no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4C4⋊C414yes—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—21no—
404C2×C42—22no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—22no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—22no—
411C2×C42—21no—
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—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—41no—
430C2×C42—41no—
431C2×C42—41no—
432C2×C42—41no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42—41no—
436C2×C42C4212yes—
437C2×C42C4212yes—
438C2×C42C22⋊C412yes—
439C2×C42C22⋊C414yes—
440C2×C42C22⋊C412yes—
441C2×C42C22⋊C414yes—
442C2×C42C4⋊C414yes—
443C2×C42C4⋊C412yes—
444C2×C42C4⋊C414yes—
445C2×C42C4⋊C412yes—
446C4⋊C8—232no—
447C24—44no—
448C24#11711yescharacteristic
449C24C4×D411yescharacteristic
450C24C4×D411yescharacteristic
451C24#12111yescharacteristic
452C24C22⋊Q811yescharacteristic
453C24C22⋊Q811yescharacteristic
454C24C22⋊Q811yescharacteristic
455C24#12311yescharacteristic
456C24#12311yescharacteristic
457C24#12311yescharacteristic
458C24#12311yescharacteristic
459C24#12511yescharacteristic
460C24#12511yescharacteristic
461C24#12611yescharacteristic
462C24#12611yescharacteristic
463C22×C4—28no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—48no—
476C22×C4—48no—
477C22×C4—48no—
478C22×C4—48no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—44no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—84no—
488C22×C4—84no—
489C22×C4C2×C4211yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C4⋊C411yescharacteristic
496C22×C4C2×C4⋊C411yescharacteristic
497C22×C4C2×C4⋊C411yescharacteristic
498C22×C4C2×C4⋊C411yescharacteristic
499C22×C4C2×C4⋊C411yescharacteristic
500C22×C4C2×C4⋊C411yescharacteristic
501C22×C4C2×C4⋊C411yescharacteristic
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×Q811yescharacteristic
522C22×C4C4×Q811yescharacteristic
523C22×C4C4×Q811yescharacteristic
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#12011yescharacteristic
534C22×C4#12011yescharacteristic
535C22×C4#12011yescharacteristic
536C22×C4#12011yescharacteristic
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×C4#12111yescharacteristic
551C22×C4#12111yescharacteristic
552C22×C4#12111yescharacteristic
553C22×C4#12111yescharacteristic
554C22×C4#12111yescharacteristic
555C22×C4#12111yescharacteristic
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×C4C22⋊Q811yescharacteristic
568C22×C4C22⋊Q811yescharacteristic
569C22×C4C22⋊Q811yescharacteristic
570C22×C4C22⋊Q811yescharacteristic
571C22×C4C22⋊Q811yescharacteristic
572C22×C4C22⋊Q811yescharacteristic
573C22×C4C22⋊Q811yescharacteristic
574C22×C4C22⋊Q811yescharacteristic
575C22×C4C22⋊Q811yescharacteristic
576C22×C4C22⋊Q811yescharacteristic
577C22×C4C22⋊Q811yescharacteristic
578C22×C4C22⋊Q811yescharacteristic
579C22×C4C22⋊Q811yescharacteristic
580C22×C4C22⋊Q811yescharacteristic
581C22×C4#12311yescharacteristic
582C22×C4#12311yescharacteristic
583C22×C4#12311yescharacteristic
584C22×C4#12311yescharacteristic
585C22×C4#12311yescharacteristic
586C22×C4#12311yescharacteristic
587C22×C4#12311yescharacteristic
588C22×C4#12311yescharacteristic
589C22×C4#12311yescharacteristic
590C22×C4#12311yescharacteristic
591C22×C4#12311yescharacteristic
592C22×C4#12311yescharacteristic
593C22×C4#12411yescharacteristic
594C22×C4#12411yescharacteristic
595C22×C4#12411yescharacteristic
596C22×C4#12411yescharacteristic
597C22×C4#12411yescharacteristic
598C22×C4#12411yescharacteristic
599C22×C4#12411yescharacteristic
600C22×C4#12411yescharacteristic
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#12511yescharacteristic
610C22×C4#12511yescharacteristic
611C22×C4#12611yescharacteristic
612C22×C4#12611yescharacteristic
613C22×C4#12611yescharacteristic
614C22×C4#12611yescharacteristic
615C22×C4#12611yescharacteristic
616C22×C4#12611yescharacteristic
617C22×C4#12711yescharacteristic
618C22×C4#12711yescharacteristic
619C22×C4C4⋊Q811yescharacteristic
620C22×C4C4⋊Q811yescharacteristic
621C22×C4C4⋊Q811yescharacteristic
622C22×C4C4⋊Q811yescharacteristic
623C22×C4C4⋊Q811yescharacteristic
624C22×C4C4⋊Q811yescharacteristic
625C22×C4C4⋊Q811yescharacteristic
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—
653M16—42no—
654M16—42no—
655M16—42no—
656M16—42no—
657M16—42no—
658M16—42no—
659M16—42no—
660M16—42no—
661C2×C8—24no—
662C2×C8—24no—
663C2×C8—24no—
664C2×C8—24no—
665C2×C8—24no—
666C2×C8—24no—
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—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C22⋊C4—24no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C42—22no—
706C42—22no—
707C42—24no—
708C42—24no—
709C42—22no—
710C42—24no—
711C42—22no—
712C42—22no—
713C42—24no—
714C42—22no—
715C42—24no—
716C42—42no—
717C42—42no—
718C42—42no—
719C42—42no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42#9514yes—
724C42#9514yes—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23C4×C22⋊C411yescharacteristic
741C23#38011yescharacteristic
742C23#38111yescharacteristic
743C23#38511yescharacteristic
744C23#38511yescharacteristic
745C23#38511yescharacteristic
746C23#38511yescharacteristic
747C23#38611yescharacteristic
748C23#38611yescharacteristic
749C23#38711yescharacteristic
750C23#38711yescharacteristic
751C23#38711yescharacteristic
752C23#38711yescharacteristic
753C23#38711yescharacteristic
754C23#38711yescharacteristic
755C23#38811yescharacteristic
756C23#38811yescharacteristic
757C23#38911yescharacteristic
758C23#38911yescharacteristic
759C23#39411yescharacteristic
760C23#39511yescharacteristic
761C23#39611yescharacteristic
762C23#39611yescharacteristic
763C23#39711yescharacteristic
764C23#39711yescharacteristic
765C23#39811yescharacteristic
766C23#39811yescharacteristic
767C23#39811yescharacteristic
768C23#39811yescharacteristic
769C23#39811yescharacteristic
770C23#39911yescharacteristic
771C23#39911yescharacteristic
772C23#40011yescharacteristic
773C23#40011yescharacteristic
774C23#40011yescharacteristic
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—48no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—48no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—84no—
791C2×C4—84no—
792C2×C4—84no—
793C2×C4—84no—
794C2×C4—84no—
795C2×C4C2×#9511yescharacteristic
796C2×C4C4×C22⋊C411yescharacteristic
797C2×C4C4×C4⋊C411yescharacteristic
798C2×C4C4×C4⋊C411yescharacteristic
799C2×C4C4×C4⋊C411yescharacteristic
800C2×C4C4×C4⋊C411yescharacteristic
801C2×C4#37911yescharacteristic
802C2×C4#38011yescharacteristic
803C2×C4#38011yescharacteristic
804C2×C4#38011yescharacteristic
805C2×C4#38011yescharacteristic
806C2×C4#38011yescharacteristic
807C2×C4#38211yescharacteristic
808C2×C4#38211yescharacteristic
809C2×C4#38411yescharacteristic
810C2×C4#38411yescharacteristic
811C2×C4#38511yescharacteristic
812C2×C4#38511yescharacteristic
813C2×C4#38511yescharacteristic
814C2×C4#38511yescharacteristic
815C2×C4#38511yescharacteristic
816C2×C4#38511yescharacteristic
817C2×C4#38511yescharacteristic
818C2×C4#38511yescharacteristic
819C2×C4#38611yescharacteristic
820C2×C4#38611yescharacteristic
821C2×C4#38611yescharacteristic
822C2×C4#38611yescharacteristic
823C2×C4#38611yescharacteristic
824C2×C4#38611yescharacteristic
825C2×C4#38711yescharacteristic
826C2×C4#38711yescharacteristic
827C2×C4#38711yescharacteristic
828C2×C4#38711yescharacteristic
829C2×C4#38711yescharacteristic
830C2×C4#38711yescharacteristic
831C2×C4#38711yescharacteristic
832C2×C4#38711yescharacteristic
833C2×C4#38711yescharacteristic
834C2×C4#38711yescharacteristic
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#38911yescharacteristic
847C2×C4#38911yescharacteristic
848C2×C4#38911yescharacteristic
849C2×C4#38911yescharacteristic
850C2×C4#38911yescharacteristic
851C2×C4#38911yescharacteristic
852C2×C4#38911yescharacteristic
853C2×C4#38911yescharacteristic
854C2×C4#38911yescharacteristic
855C2×C4#39011yescharacteristic
856C2×C4#39011yescharacteristic
857C2×C4#39011yescharacteristic
858C2×C4#39011yescharacteristic
859C2×C4#39111yescharacteristic
860C2×C4#39111yescharacteristic
861C2×C4#39111yescharacteristic
862C2×C4#39111yescharacteristic
863C2×C4#39111yescharacteristic
864C2×C4#39111yescharacteristic
865C2×C4#39111yescharacteristic
866C2×C4#39111yescharacteristic
867C2×C4#39211yescharacteristic
868C2×C4#39211yescharacteristic
869C2×C4#39211yescharacteristic
870C2×C4#39211yescharacteristic
871C2×C4#39311yescharacteristic
872C2×C4#39311yescharacteristic
873C2×C4#39311yescharacteristic
874C2×C4#39311yescharacteristic
875C2×C4#39411yescharacteristic
876C2×C4#39411yescharacteristic
877C2×C4#39411yescharacteristic
878C2×C4#39411yescharacteristic
879C2×C4#39411yescharacteristic
880C2×C4#39411yescharacteristic
881C2×C4#39411yescharacteristic
882C2×C4#39511yescharacteristic
883C2×C4#39511yescharacteristic
884C2×C4#39511yescharacteristic
885C2×C4#39511yescharacteristic
886C2×C4#39511yescharacteristic
887C2×C4#39511yescharacteristic
888C2×C4#39511yescharacteristic
889C2×C4#39611yescharacteristic
890C2×C4#39611yescharacteristic
891C2×C4#39611yescharacteristic
892C2×C4#39611yescharacteristic
893C2×C4#39611yescharacteristic
894C2×C4#39611yescharacteristic
895C2×C4#39711yescharacteristic
896C2×C4#39711yescharacteristic
897C2×C4#39811yescharacteristic
898C2×C4#39811yescharacteristic
899C2×C4#39811yescharacteristic
900C2×C4#39811yescharacteristic
901C2×C4#39811yescharacteristic
902C2×C4#39811yescharacteristic
903C2×C4#39811yescharacteristic
904C2×C4#39811yescharacteristic
905C2×C4#39811yescharacteristic
906C2×C4#39811yescharacteristic
907C2×C4#39811yescharacteristic
908C2×C4#39911yescharacteristic
909C2×C4#39911yescharacteristic
910C2×C4#40011yescharacteristic
911C2×C4#40011yescharacteristic
912C2×C4#40011yescharacteristic
913C2×C4#40011yescharacteristic
914C2×C4#40011yescharacteristic
915C8—44no—
916C8—44no—
917C8—44no—
918C8—44no—
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—22no—
936C22—22no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22C22⋊#9511yescharacteristic
954C22#143611yescharacteristic
955C22#143611yescharacteristic
956C22#143911yescharacteristic
957C22#143911yescharacteristic
958C22#144111yescharacteristic
959C22#144111yescharacteristic
960C22#144111yescharacteristic
961C22#144111yescharacteristic
962C22#144211yescharacteristic
963C22#144211yescharacteristic
964C22#144411yescharacteristic
965C22#144411yescharacteristic
966C22#144511yescharacteristic
967C22#144511yescharacteristic
968C22#186114yes—
969C4—28no—
970C4—44no—
971C4—84no—
972C4—84no—
973C4C4⋊#9511yescharacteristic
974C4C4⋊#9511yescharacteristic
975C4#143611yescharacteristic
976C4#143611yescharacteristic
977C4#143811yescharacteristic
978C4#143911yescharacteristic
979C4#143911yescharacteristic
980C4#144111yescharacteristic
981C4#144111yescharacteristic
982C4#144111yescharacteristic
983C4#144111yescharacteristic
984C4#144211yescharacteristic
985C4#144211yescharacteristic
986C4#144411yescharacteristic
987C4#144411yescharacteristic
988C4#144611yescharacteristic
989C2—21no—
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—21no—
997C2—21no—
998C2—21no—
999C2—21no—
1000C2—21no—
1001C2#755711yescharacteristic
1002C2#1089412yes—
1003C2#1108012yes—
1004C2#1134112yes—
subgroupG/H
centerC22×C4#120
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC23#385
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
20. C2×#423C4semidirect
35. C2×#339C4semidirect
36. C2×#339C4semidirect
37. C2×#339C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4232
C22×#3442
C2×#17382
C2×#17332
C22×#3392
#203352