Finite Group Databasebeta

← #154034

Subgroups — #154034

Order 512.

3318 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C22×#387C212yesmaximal
3C2×C4⋊#95C212yesmaximal
4#7557C212yesmaximal
5#7557C212yesmaximal
6#7557C212yesmaximal
7#7554C212yesmaximal
8#7554C211yesmaximal, characteristic
9#7554C211yesmaximal, characteristic
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2212yes—
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2212yes—
15C23×C42C2211yescharacteristic
16C2×#389—28no—
17C2×#389C418yescomplemented
18C2×#387—28no—
19C2×#387—28no—
20C2×#387C4116yescomplemented
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2212yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30C22×#95C2211yescharacteristic
31C22×#95C2211yescharacteristic
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2211yescharacteristic
35C22×#95C2211yescharacteristic
36C4⋊#95—28no—
37C24×C4C2312yes—
38C24×C4C2312yes—
39C24×C4C2312yes—
40C24×C4C2311yescharacteristic
41C24×C4C2312yes—
42C24×C4C2312yes—
43C24×C4C2311yescharacteristic
44C24×C4C2312yes—
45C24×C4C2311yescharacteristic
46C22×C4⋊C4—24no—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—24no—
53C22×C4⋊C4—24no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4—42no—
56C22×C4⋊C4—42no—
57C22×C4⋊C4—42no—
58C22×C4⋊C4—42no—
59C22×C4⋊C4—41no—
60C22×C4⋊C4—41no—
61C22×C4⋊C4—42no—
62C22×C4⋊C4C2×C418yes—
63C22×C4⋊C4C2×C418yes—
64C22×C4⋊C4C2×C414yes—
65C22×C4⋊C4C2×C418yes—
66C22×C4⋊C4C2×C414yes—
67C22×C4⋊C4D414yes—
68C22×C4⋊C4D418yes—
69C22×C4⋊C4Q814yes—
70C22×C42—24no—
71C22×C42—24no—
72C22×C42—24no—
73C22×C42—24no—
74C22×C42—24no—
75C22×C42—42no—
76C22×C42—42no—
77C22×C42—41no—
78C22×C42—41no—
79C22×C42—42no—
80C22×C42C2×C418yes—
81C22×C42C2×C414yes—
82#389—232no—
83#387—264no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—24no—
92C2×#95—24no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—24no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—22no—
102C2×#95—24no—
103C2×#95—22no—
104C2×#95—41no—
105C2×#95—41no—
106C2×#95—41no—
107C2×#95—41no—
108C2×#95—42no—
109C2×#95—42no—
110C2×#95—42no—
111C2×#95—41no—
112C2×#95—42no—
113C2×#95—42no—
114C2×#95—41no—
115C2×#95—42no—
116C2×#95—42no—
117C2×#95—41no—
118C2×#95—41no—
119C2×#95—42no—
120C2×#95—42no—
121C2×#95—42no—
122C2×#95C2×C418yes—
123C2×#95C2×C418yes—
124C2×#95C2×C418yes—
125C2×#95C2×C418yes—
126C2×#95C2×C418yes—
127C2×#95D414yes—
128C2×#95Q814yes—
129C25C2411yescharacteristic
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—22no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—21no—
162C23×C4—22no—
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—22no—
170C23×C4—21no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—22no—
181C23×C4—21no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—22no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4C22×C414yes—
227C23×C4C22×C414yes—
228C23×C4C22×C414yes—
229C23×C4C22×C412yes—
230C23×C4C22×C414yes—
231C23×C4C22×C414yes—
232C23×C4C22×C412yes—
233C23×C4C22×C414yes—
234C23×C4C22×C414yes—
235C23×C4C22×C412yes—
236C23×C4C22×C414yes—
237C23×C4C22×C414yes—
238C23×C4C2×D412yes—
239C23×C4C2×D414yes—
240C23×C4C2×D414yes—
241C23×C4C2×D414yes—
242C23×C4C2×D414yes—
243C23×C4C2×D414yes—
244C23×C4C2×D412yes—
245C23×C4C2×Q814yes—
246C23×C4C2×Q812yes—
247C23×C4C2×Q812yes—
248C23×C4C2×Q814yes—
249C23×C4#4112yes—
250C23×C4#4114yes—
251C23×C4#4114yes—
252C23×C4#4112yes—
253C2×C4⋊C4—216no—
254C2×C4⋊C4—216no—
255C2×C4⋊C4—28no—
256C2×C4⋊C4—216no—
257C2×C4⋊C4—216no—
258C2×C4⋊C4—48no—
259C2×C4⋊C4—48no—
260C2×C4⋊C4—44no—
261C2×C4⋊C4—44no—
262C2×C4⋊C4—48no—
263C2×C4⋊C4—48no—
264C2×C4⋊C4—48no—
265C2×C4⋊C4—48no—
266C2×C4⋊C4—48no—
267C2×C4⋊C4—48no—
268C2×C4⋊C4—48no—
269C2×C4⋊C4—48no—
270C2×C4⋊C4—48no—
271C2×C4⋊C4—48no—
272C2×C4⋊C4C42116yes—
273C2×C4⋊C4C22⋊C4132yes—
274C2×C4⋊C4C22⋊C4116yes—
275C2×C4⋊C4C4⋊C4132yes—
276C2×C4⋊C4C4⋊C4116yes—
277C2×C42—216no—
278C2×C42—28no—
279C2×C42—216no—
280C2×C42—48no—
281C2×C42—44no—
282C2×C42—44no—
283C2×C42—48no—
284C2×C42—48no—
285C2×C42—48no—
286C2×C42—48no—
287C2×C42—48no—
288C2×C42—48no—
289#95—216no—
290#95—216no—
291#95—216no—
292#95—216no—
293#95—216no—
294#95—44no—
295#95—44no—
296#95—48no—
297#95—48no—
298#95—48no—
299#95—48no—
300#95—44no—
301#95—48no—
302#95—44no—
303#95—48no—
304C24C23×C411yescharacteristic
305C24C23×C412yes—
306C24C22×D412yes—
307C24C22×D411yescharacteristic
308C24C22×D411yescharacteristic
309C24C22×Q811yescharacteristic
310C24C22×Q811yescharacteristic
311C24C2×#4111yescharacteristic
312C24C2×#4112yes—
313C24C2×#4112yes—
314C24C2×#4111yescharacteristic
315C24H(5,𝔽2)11yescharacteristic
316C24H(5,𝔽2)12yes—
317C24H(5,𝔽2)11yescharacteristic
318C24H(5,𝔽2)11yescharacteristic
319C24H(5,𝔽2)12yes—
320C24H(5,𝔽2)11yescharacteristic
321C242−1+412yes—
322C242−1+411yescharacteristic
323C242−1+412yes—
324C242−1+411yescharacteristic
325C242−1+411yescharacteristic
326C242−1+411yescharacteristic
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
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—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
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—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4C2×C4218yes—
591C22×C4C2×C4214yes—
592C22×C4C2×C22⋊C418yes—
593C22×C4C2×C22⋊C418yes—
594C22×C4C2×C22⋊C418yes—
595C22×C4C2×C22⋊C418yes—
596C22×C4C2×C22⋊C414yes—
597C22×C4C2×C4⋊C414yes—
598C22×C4C2×C4⋊C418yes—
599C22×C4C2×C4⋊C418yes—
600C22×C4C2×C4⋊C418yes—
601C22×C4C2×C4⋊C418yes—
602C22×C4C4×D418yes—
603C22×C4C4×D414yes—
604C22×C4C4×Q818yes—
605C22×C4C4×Q814yes—
606C4⋊C4—432no—
607C4⋊C4—432no—
608C4⋊C4—416no—
609C4⋊C4#95164yescomplemented
610C42—432no—
611C42—416no—
612C23C22×C4211yescharacteristic
613C23C22×C22⋊C411yescharacteristic
614C23C22×C22⋊C412yes—
615C23C22×C4⋊C411yescharacteristic
616C23C22×C4⋊C412yes—
617C23C2×C4×D412yes—
618C23C2×C4×D411yescharacteristic
619C23C2×C4×Q812yes—
620C23C2×C4×Q811yescharacteristic
621C23C4×#4111yescharacteristic
622C23C4×#4111yescharacteristic
623C23C4×#4112yes—
624C23C4×#4112yes—
625C23#51811yescharacteristic
626C23#51811yescharacteristic
627C23#51812yes—
628C23#51811yescharacteristic
629C23#51911yescharacteristic
630C23#51911yescharacteristic
631C23#51912yes—
632C23#51911yescharacteristic
633C23#52012yes—
634C23#52012yes—
635C23#52012yes—
636C23#52012yes—
637C23#52012yes—
638C23#52011yescharacteristic
639C23#52011yescharacteristic
640C23#52012yes—
641C23#53411yescharacteristic
642C23#53512yes—
643C23#53512yes—
644C23#53612yes—
645C23#53612yes—
646C23#53612yes—
647C23#53712yes—
648C23#53711yescharacteristic
649C23#53711yescharacteristic
650C23#53711yescharacteristic
651C23#53811yescharacteristic
652C23#53812yes—
653C23#53811yescharacteristic
654C23#53912yes—
655C23#53912yes—
656C23#53911yescharacteristic
657C23#53911yescharacteristic
658C23#53912yes—
659C23#54012yes—
660C23#54112yes—
661C23#54112yes—
662C23#54112yes—
663C23#54212yes—
664C23#54212yes—
665C23#54311yescharacteristic
666C23#54412yes—
667C23#54411yescharacteristic
668C23#54411yescharacteristic
669C23#54411yescharacteristic
670C23#54412yes—
671C23D4212yes—
672C23D4211yescharacteristic
673C23#54612yes—
674C23#54612yes—
675C23#54612yes—
676C23#54612yes—
677C23#54712yes—
678C23#54711yescharacteristic
679C23#54711yescharacteristic
680C23#54812yes—
681C23#54812yes—
682C23#54812yes—
683C23D4×Q812yes—
684C23D4×Q811yescharacteristic
685C23D4×Q811yescharacteristic
686C23D4×Q811yescharacteristic
687C23#55012yes—
688C23#55011yescharacteristic
689C23#55112yes—
690C23#55212yes—
691C23#55212yes—
692C23#55312yes—
693C23#55412yes—
694C23#55411yescharacteristic
695C23#55412yes—
696C23#55611yescharacteristic
697C23#55712yes—
698C23#55711yescharacteristic
699C23#55711yescharacteristic
700C23Q8211yescharacteristic
701C23#56012yes—
702C23#56211yescharacteristic
703C23#56212yes—
704C23#56212yes—
705C23#56312yes—
706C23#56311yescharacteristic
707C23#56312yes—
708C23#56312yes—
709C23#56311yescharacteristic
710C23#56411yescharacteristic
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—28no—
735C2×C4—28no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—82no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—82no—
815C2×C4—82no—
816C2×C4—82no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4—82no—
821C2×C4—82no—
822C2×C4—82no—
823C2×C4—82no—
824C2×C4—82no—
825C2×C4—82no—
826C2×C4—82no—
827C2×C4—82no—
828C2×C4—82no—
829C2×C4—82no—
830C2×C4—82no—
831C2×C4—82no—
832C2×C4C2×#9518yes—
833C2×C4C2×#95116yes—
834C22C22×#9511yescharacteristic
835C22C42×D411yescharacteristic
836C22C42×Q811yescharacteristic
837C22#227411yescharacteristic
838C22#227411yescharacteristic
839C22#227511yescharacteristic
840C22#227611yescharacteristic
841C22#230911yescharacteristic
842C22#231011yescharacteristic
843C22#231112yes—
844C22#231112yes—
845C22#231611yescharacteristic
846C22#231611yescharacteristic
847C22#231712yes—
848C22#231712yes—
849C22#232212yes—
850C22#232312yes—
851C22#232511yescharacteristic
852C22#232711yescharacteristic
853C22#232912yes—
854C22#232911yescharacteristic
855C22#233012yes—
856C22#233111yescharacteristic
857C22#233211yescharacteristic
858C22#233311yescharacteristic
859C22#233412yes—
860C22#233412yes—
861C22#233512yes—
862C22#233611yescharacteristic
863C22#233612yes—
864C22#233611yescharacteristic
865C22D4×C22⋊C412yes—
866C22D4×C22⋊C411yescharacteristic
867C22#233911yescharacteristic
868C22#233912yes—
869C22Q8×C22⋊C412yes—
870C22Q8×C22⋊C411yescharacteristic
871C22#234112yes—
872C22#234111yescharacteristic
873C22D4×C4⋊C412yes—
874C22D4×C4⋊C411yescharacteristic
875C22#234911yescharacteristic
876C22#234912yes—
877C22Q8×C4⋊C412yes—
878C22Q8×C4⋊C411yescharacteristic
879C22#235112yes—
880C22#235111yescharacteristic
881C22#235912yes—
882C22#236012yes—
883C22#236411yescharacteristic
884C22#236511yescharacteristic
885C22#236811yescharacteristic
886C22#237012yes—
887C22#237111yescharacteristic
888C22#237312yes—
889C22#237612yes—
890C22#237711yescharacteristic
891C22#237812yes—
892C22#237811yescharacteristic
893C22#238111yescharacteristic
894C22#238212yes—
895C22#238211yescharacteristic
896C22#238312yes—
897C22#267312yes—
898C22#267412yes—
899C22#267612yes—
900C22#267712yes—
901C22#268112yes—
902C22#268211yescharacteristic
903C22#268311yescharacteristic
904C22#269012yes—
905C22#269212yes—
906C22#269412yes—
907C22#269612yes—
908C22#270212yes—
909C22#270412yes—
910C22#270512yes—
911C22#270712yes—
912C22#271112yes—
913C22#271312yes—
914C22#271312yes—
915C22#271412yes—
916C22#271612yes—
917C22#271912yes—
918C22#272012yes—
919C22#272112yes—
920C22#272312yes—
921C22#272512yes—
922C22#272611yescharacteristic
923C22#272611yescharacteristic
924C22#272711yescharacteristic
925C22#273411yescharacteristic
926C22#275512yes—
927C22#277412yes—
928C22#279112yes—
929C22#279212yes—
930C22#280212yes—
931C22#280511yescharacteristic
932C22#280611yescharacteristic
933C4—28no—
934C4—216no—
935C4—48no—
936C4—48no—
937C4—44no—
938C4—44no—
939C4—84no—
940C4—84no—
941C4—84no—
942C2#1379011yescharacteristic
943C2#1379211yescharacteristic
944C2#1379511yescharacteristic
945C2D4×#9511yescharacteristic
946C2Q8×#9511yescharacteristic
947C2#1382511yescharacteristic
948C2#1383311yescharacteristic
949C2#1436012yes—
950C2#1436212yes—
951C2#1440412yes—
952C2#1440612yes—
953C2#1441811yescharacteristic
954C2#1442011yescharacteristic
955C2#1443911yescharacteristic
956C2#1444111yescharacteristic
957C2#1444811yescharacteristic
958C2#1445112yes—
959C2#1446511yescharacteristic
960C2#1446812yes—
961C2#1447411yescharacteristic
962C2#1448711yescharacteristic
963C2#1449312yes—
964C2#1450212yes—
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC23C22×C42
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
17. C2×#389C4semidirect
20. C2×#387C4semidirect
609. C4⋊C4#95semidirect

Maximal subgroups

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

subgroupindex
C22×#3892
C22×#3872
C2×C4⋊#952
#75572
#75542