Finite Group Databasebeta

← #6448604

Subgroups — #6448604

Order 512.

3486 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic, complemented
2C2×#3080C211yesmaximal, characteristic, complemented
3C2×C4×#137C211yesmaximal, characteristic, complemented
4#34935C211yesmaximal, characteristic
5#24139C214yesmaximal, complemented
6#24137C214yesmaximal, complemented
7#24127C214yesmaximal, complemented
8#24125C214yesmaximal, complemented
9#23481C211yesmaximal, characteristic, complemented
10#23481C211yesmaximal, characteristic, complemented
11#23392C211yesmaximal, characteristic, complemented
12#23392C211yesmaximal, characteristic, complemented
13#21325C211yesmaximal, characteristic, complemented
14#21190C211yesmaximal, characteristic, complemented
15#20910C211yesmaximal, characteristic, complemented
16#20909C211yesmaximal, characteristic, complemented
17#20845C211yesmaximal, characteristic, complemented
18#20844C211yesmaximal, characteristic, complemented
19#20647C211yesmaximal, characteristic, complemented
20C22×#137C2211yescharacteristic
21C2×#552—28no—
22C2×#552—28no—
23C2×#552—22no—
24C2×#552—22no—
25C2×#552C2214yes—
26C2×#552C2214yes—
27C22×#126—21no—
28C22×#125—21no—
29C22×#125C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C22×#123—21no—
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38C22×#117—21no—
39C22×#117C2211yescharacteristic
40C23×C4⋊C4C2211yescharacteristic
41#3080—28no—
42C2×#479C2212yescomplemented
43C2×#479C2212yescomplemented
44C2×#478C2212yescomplemented
45C2×#478C2212yescomplemented
46C4×#137—28no—
47C2×#441C2212yescomplemented
48C2×#440C2212yescomplemented
49C2×C4×Q16C2212yescomplemented
50C2×C4×SD16C2212yescomplemented
51C2×#428C2211yescharacteristic
52C2×#428C2211yescharacteristic
53C2×#428C2211yescharacteristic
54C2×#423C2211yescharacteristic
55C2×#417C2211yescharacteristic
56C2×#417C2211yescharacteristic
57C2×#417C2211yescharacteristic
58C2×#419C2211yescharacteristic
59C2×#419C2211yescharacteristic
60C2×#419C2211yescharacteristic
61C2×#407C2211yescharacteristic
62C2×#407C2211yescharacteristic
63C2×#407C2211yescharacteristic
64C2×#407C2211yescharacteristic
65C2×C4×M16C2211yescharacteristic
66#2538C2212yes—
67#2537C2212yes—
68#2536C2212yes—
69#2535C2212yes—
70#2534—21no—
71#2534—21no—
72#2486—21no—
73#2408—21no—
74#2392—22no—
75C4×#121—22no—
76#2285C2211yescharacteristic
77#2280C2211yescharacteristic
78#2280C2211yescharacteristic
79#2036C2214yescomplemented
80#2036C2214yescomplemented
81#2035C2214yescomplemented
82#2035C2214yescomplemented
83#2001C2214yescomplemented
84#2001C2214yescomplemented
85#2000C2214yescomplemented
86#2000C2214yescomplemented
87#1992C2214yescomplemented
88#1991C2214yescomplemented
89#1955C2214yes—
90#1954C2214yes—
91#1875C2214yescomplemented
92#1874C2214yescomplemented
93#1873C2214yescomplemented
94#1872C2214yescomplemented
95#1854C2214yescomplemented
96#1854C2214yescomplemented
97#1853C2214yescomplemented
98#1852C2214yescomplemented
99#1805C2214yescomplemented
100#1803C2214yescomplemented
101#1736C2211yescharacteristic
102#1736C2211yescharacteristic
103#1736C2211yescharacteristic
104#1736C2211yescharacteristic
105#1736C2211yescharacteristic
106#1736C2211yescharacteristic
107C22×#41C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C23×D4D411yescharacteristic
110C24×C4—21no—
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C2×#137—24no—
114C2×#137—24no—
115C2×#137—24no—
116C22×Q16C2312yes—
117C22×SD16C2312yes—
118C22×M16C2311yescharacteristic
119C22×M16C2311yescharacteristic
120C22×M16C2311yescharacteristic
121C22×M16C2311yescharacteristic
122#552—232no—
123#552—232no—
124#552—216no—
125#552—216no—
126#552—216no—
127#552—216no—
128C2×#126—216no—
129C2×#126—24no—
130C2×#126—24no—
131C2×#125—216no—
132C2×#125—24no—
133C2×#125—24no—
134C2×#125—21no—
135C2×#125—21no—
136C2×#125—24no—
137C2×#125D418yescomplemented
138C2×#125C2312yes—
139C2×#125C2312yes—
140#525—24no—
141#525—24no—
142#525—42no—
143#525—42no—
144C2×#123—216no—
145C2×#123—24no—
146C2×#123—24no—
147C2×#123—21no—
148C2×#123—21no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8C2314yes—
156C2×C22⋊Q8C2314yes—
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×#121—22no—
160C2×#121C2312yes—
161C2×#121C2312yes—
162C2×#120—21no—
163C2×#120—21no—
164C4×#41—24no—
165C4×#41—24no—
166C2×C4×Q8—24no—
167C2×C4×Q8—21no—
168C2×C4×Q8—21no—
169C2×C4×Q8D418yescomplemented
170C2×C4×Q8C2311yescharacteristic
171C2×C4×Q8C2311yescharacteristic
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2312yes—
174C2×C4×D4—22no—
175C2×C4×D4—22no—
176C2×C4×D4—21no—
177C2×C4×D4—21no—
178C2×C4×D4—24no—
179C2×C4×D4—24no—
180C2×C4×D4D412yes—
181C2×C4×D4D412yes—
182C2×C4×D4C2311yescharacteristic
183C2×C4×D4C2311yescharacteristic
184C2×C4×D4C2312yes—
185C2×C4×D4C2312yes—
186C2×#117—216no—
187C2×#117—22no—
188C2×#117—24no—
189C2×#117—24no—
190C2×#117—24no—
191C2×#117—24no—
192C2×#117—21no—
193C2×#117C2314yes—
194C2×#117C2311yescharacteristic
195C2×#117C2311yescharacteristic
196C2×#117C2311yescharacteristic
197C22×C4⋊C4—21no—
198C22×C4⋊C4—22no—
199C22×C4⋊C4—21no—
200C22×C4⋊C4—21no—
201C22×C4⋊C4—21no—
202C22×C4⋊C4—21no—
203C22×C4⋊C4—21no—
204C22×C4⋊C4—24no—
205C22×C4⋊C4—24no—
206C22×C4⋊C4D411yescharacteristic
207C22×C4⋊C4C2314yes—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C22⋊C4—21no—
212C22×C22⋊C4—21no—
213C22×C22⋊C4—21no—
214C22×C22⋊C4D411yescharacteristic
215C22×C22⋊C4D411yescharacteristic
216C22×C42—21no—
217C22×C42—21no—
218C22×C42—21no—
219C22×C42C2311yescharacteristic
220#479—28no—
221#479—28no—
222#478—28no—
223#478—28no—
224#441—28no—
225#440—28no—
226C4×Q16—28no—
227C4×SD16—28no—
228#428—24no—
229#428—24no—
230#428—24no—
231C2×#107C2312yes—
232C2×#107C2312yes—
233C2×#107C2312yes—
234C2×#106C2312yes—
235C2×#106C2312yes—
236C2×#106C2312yes—
237#423—24no—
238C2×C4⋊C8C2312yes—
239C2×C4⋊C8C2312yes—
240#419—24no—
241#419—42no—
242#419—42no—
243#417—24no—
244#417—24no—
245#417—24no—
246C2×#103C2312yes—
247C2×#103C2312yes—
248C2×#103C2312yes—
249C2×#103C2312yes—
250C2×#103C2312yes—
251C2×#103C2314yes—
252C2×#103C2314yes—
253C2×#102C2312yes—
254C2×#102C2312yes—
255C2×#102C2312yes—
256#407—24no—
257#407—24no—
258#407—42no—
259#407—42no—
260C2×C22⋊C8C2314yes—
261C2×C22⋊C8C2314yes—
262C2×C22⋊C8C2314yes—
263C2×C22⋊C8C2314yes—
264C4×M16—24no—
265C2×#97C2312yes—
266C2×C4×C8C2312yes—
267#398—22no—
268#397—22no—
269#396—22no—
270#396—22no—
271#394—22no—
272#394—22no—
273#394—22no—
274#392—22no—
275#390—22no—
276#389—22no—
277#388—22no—
278#388—22no—
279#386—22no—
280#386—22no—
281#384C2312yes—
282#382C2312yes—
283#381—21no—
284#381—21no—
285#380—21no—
286#380—21no—
287#380—22no—
288#380C2312yes—
289#380C2312yes—
290#380C2312yes—
291#380C2312yes—
292#379—21no—
293#379—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C22⋊C4—22no—
297C4×C22⋊C4—22no—
298#340C2314yes—
299#340C2314yes—
300#340C2314yes—
301#340C2314yes—
302#340C2314yes—
303#340C2314yes—
304C25C2×D411yescharacteristic
305C25C2×D411yescharacteristic
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41#4114yes—
312C22×Q8—22no—
313C22×Q8—21no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8C2×D414yes—
319C22×Q8C2412yes—
320C22×Q8C2411yescharacteristic
321C22×D4—21no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—24no—
325C22×D4—44no—
326C22×D4C2×D412yes—
327C22×D4C2×D412yes—
328C22×D4C2411yescharacteristic
329C23×C4—28no—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—24no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—21no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—48no—
351C23×C4C2×D411yescharacteristic
352C23×C4C2×D411yescharacteristic
353C23×C4C2×D412yes—
354C23×C4C2×D412yes—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2411yescharacteristic
360#137—232no—
361C2×Q16—24no—
362C2×Q16—24no—
363C2×Q16—24no—
364C2×SD16—24no—
365C2×SD16—24no—
366C2×SD16—24no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16#4114yes—
379C22×C8C2412yes—
380C22×C8C2412yes—
381C22×C8C2412yes—
382C22×C8C2412yes—
383#126—232no—
384#126—232no—
385#125—232no—
386#125—232no—
387#125—28no—
388#125—28no—
389#125—24no—
390#125—24no—
391#125C2×D418yes—
392#125C2×D418yes—
393#123—232no—
394#123—232no—
395#123—44no—
396#123—44no—
397C22⋊Q8—216no—
398C22⋊Q8—216no—
399C22⋊Q8—28no—
400C22⋊Q8—28no—
401C22⋊Q8—28no—
402C22⋊Q8—28no—
403C22⋊Q8—24no—
404C22⋊Q8—24no—
405C22⋊Q8—42no—
406C22⋊Q8—42no—
407#121—24no—
408#121—24no—
409#121—42no—
410#121—42no—
411#121—48no—
412#120—44no—
413#120—44no—
414C4×Q8—28no—
415C4×Q8—28no—
416C4×Q8—24no—
417C4×Q8—24no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8C2×D418yes—
423C4×Q8C2×D418yes—
424C4×D4—28no—
425C4×D4—28no—
426C4×D4—24no—
427C4×D4—24no—
428C4×D4—24no—
429C4×D4—24no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—48no—
435C4×D4—48no—
436C4×D4—44no—
437C4×D4—44no—
438#117—216no—
439#117—232no—
440#117—232no—
441#117—28no—
442#117—28no—
443#117—22no—
444#117—22no—
445#117—22no—
446#117—22no—
447#117—22no—
448#117—22no—
449#117—44no—
450C2×C4⋊C4—28no—
451C2×C4⋊C4—216no—
452C2×C4⋊C4—28no—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—28no—
455C2×C4⋊C4—28no—
456C2×C4⋊C4—28no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—28no—
474C2×C4⋊C4—28no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4C2×D412yes—
482C2×C4⋊C4C2×D412yes—
483C2×C4⋊C4C2×D414yes—
484C2×C4⋊C4C2×D414yes—
485C2×C4⋊C4C2×D414yes—
486C2×C4⋊C4C2411yescharacteristic
487C2×C4⋊C4C2411yescharacteristic
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C22⋊C4—28no—
494C2×C22⋊C4—28no—
495C2×C22⋊C4—28no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4C2×D412yes—
515C2×C22⋊C4C2×D412yes—
516C2×C22⋊C4C2×D412yes—
517C2×C22⋊C4C2×D412yes—
518C2×C42—28no—
519C2×C42—28no—
520C2×C42—24no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—44no—
529C2×C42C2×D411yescharacteristic
530C2×C42C2×D411yescharacteristic
531C2×C42C2×D414yes—
532C2×C42C2×D414yes—
533C2×C42C2411yescharacteristic
534C2×C42C2411yescharacteristic
535#107—24no—
536#107—24no—
537#107—24no—
538#106—24no—
539#106—24no—
540#106—24no—
541C4⋊C8—24no—
542C4⋊C8—24no—
543#103—24no—
544#103—24no—
545#103—24no—
546#103—24no—
547#103—24no—
548#103—44no—
549#103—44no—
550#102—24no—
551#102—24no—
552#102—24no—
553C22⋊C8—28no—
554C22⋊C8—28no—
555C22⋊C8—44no—
556C22⋊C8—44no—
557#97—24no—
558C4×C8—24no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565C24—22no—
566C24—24no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—21no—
571C24—22no—
572C24—22no—
573C24—42no—
574C24—42no—
575C24—42no—
576C24C22×D412yes—
577C24C22×D412yes—
578C24C22×D411yescharacteristic
579#41—28no—
580#41—28no—
581#41—44no—
582#41—44no—
583C2×Q8—24no—
584C2×Q8—22no—
585C2×Q8—21no—
586C2×Q8—28no—
587C2×Q8—28no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—21no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—21no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8C22×D414yes—
601C2×Q8C2×#4112yes—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—416no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—82no—
622C2×D4—82no—
623C2×D4C2×#4112yes—
624C22×C4—216no—
625C22×C4—22no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—432no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—48no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—48no—
674C22×C4—42no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—42no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—82no—
687C22×C4#12014yes—
688C22×C4#12014yes—
689C22×C4C22×D412yes—
690C22×C4C22×D412yes—
691C22×C4C22×D411yescharacteristic
692C22×C4C22×D411yescharacteristic
693C22×C4C22×D411yescharacteristic
694C22×C4C22×D411yescharacteristic
695C22×C4C22×D411yescharacteristic
696C22×C4C22×D412yes—
697C22×C4C22×D412yes—
698C22×C4C2×#4112yes—
699C22×C4C2×#4112yes—
700C22×C4H(5,𝔽2)12yes—
701C22×C42−1+412yes—
702C22×C4C2511yescharacteristic
703Q16—216no—
704SD16—216no—
705M16—28no—
706M16—44no—
707M16—44no—
708M16—44no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—22no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8C2×#4114yes—
721C4⋊C4—216no—
722C4⋊C4—216no—
723C4⋊C4—216no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—42no—
750C4⋊C4—42no—
751C4⋊C4—82no—
752C4⋊C4C22×D414yes—
753C4⋊C4C22×D414yes—
754C4⋊C4C22×D414yes—
755C22⋊C4—216no—
756C22⋊C4—216no—
757C22⋊C4—216no—
758C22⋊C4—24no—
759C22⋊C4—24no—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—44no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—44no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—82no—
774C22⋊C4—82no—
775C42—216no—
776C42—28no—
777C42—28no—
778C42—42no—
779C42—42no—
780C42—42no—
781C42—42no—
782C42—42no—
783C42#12014yes—
784C42#12014yes—
785C42C22×D412yes—
786C42C22×D412yes—
787C42C22×D412yes—
788C42C22×D412yes—
789C23—22no—
790C23—22no—
791C23—28no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—48no—
807C23—48no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—42no—
813C23—44no—
814C23—41no—
815C23—41no—
816C23—42no—
817C23—84no—
818C23—84no—
819C23C2×#12012yes—
820C23#54612yes—
821C23#54712yes—
822C23#57514yes—
823C23C23×D411yescharacteristic
824Q8—24no—
825Q8—22no—
826Q8—24no—
827Q8—22no—
828Q8—48no—
829Q8—41no—
830Q8—42no—
831Q8—42no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—48no—
836D4—48no—
837D4—48no—
838D4—41no—
839D4—41no—
840D4—88no—
841D4—88no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—48no—
860C2×C4—48no—
861C2×C4—48no—
862C2×C4—432no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—48no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—48no—
874C2×C4—48no—
875C2×C4—48no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—84no—
895C2×C4—84no—
896C2×C4C2×#12012yes—
897C2×C4C2×#12012yes—
898C2×C4C2×#12012yes—
899C2×C4C2×#12012yes—
900C2×C4C2×#12012yes—
901C2×C4#52514yes—
902C2×C4#53714yes—
903C2×C4#54612yes—
904C2×C4#54712yes—
905C2×C4#54814yes—
906C2×C4#55014yes—
907C2×C4C23×D411yescharacteristic
908C2×C4C23×D411yescharacteristic
909C2×C4C22×#4111yescharacteristic
910C2×C4C22×#4111yescharacteristic
911C2×C4C2×H(5,𝔽2)11yescharacteristic
912C2×C4C2×2−1+411yescharacteristic
913C8—24no—
914C8—42no—
915C8—42no—
916C8—42no—
917C22—24no—
918C22—22no—
919C22—22no—
920C22—24no—
921C22—24no—
922C22—24no—
923C22—24no—
924C22—416no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—44no—
937C22—42no—
938C22—88no—
939C22—82no—
940C22—81no—
941C22—81no—
942C22#240714yes—
943C22C22×#12011yescharacteristic
944C22C2×#54611yescharacteristic
945C22C2×#54711yescharacteristic
946C22C2×#57512yes—
947C22#358612yes—
948C4—22no—
949C4—22no—
950C4—22no—
951C4—22no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—44no—
956C4—44no—
957C4—44no—
958C4—44no—
959C4—81no—
960C4—81no—
961C4—82no—
962C4—82no—
963C4#240714yes—
964C4C2×#52511yescharacteristic
965C4C2×#53711yescharacteristic
966C4C2×#54811yescharacteristic
967C4C2×#55011yescharacteristic
968C2—24no—
969C2—44no—
970C2—82no—
971C2—82no—
972C2C2×#240711yescharacteristic
973C2#6035911yescharacteristic
974C2#6036811yescharacteristic
975C2#6116312yes—
976C2#6125312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34935C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#552C2semidirect
2. C2×#3080C2semidirect
3. C2×C4×#137C2semidirect
5. #24139C2semidirect
6. #24137C2semidirect
7. #24127C2semidirect
8. #24125C2semidirect
9. #23481C2semidirect
10. #23481C2semidirect
11. #23392C2semidirect
12. #23392C2semidirect
13. #21325C2semidirect
14. #21190C2semidirect
15. #20910C2semidirect
16. #20909C2semidirect
17. #20845C2semidirect
18. #20844C2semidirect
19. #20647C2semidirect
42. C2×#479C22semidirect
43. C2×#479C22semidirect
44. C2×#478C22semidirect
45. C2×#478C22semidirect
47. C2×#441C22semidirect
48. C2×#440C22semidirect
49. C2×C4×Q16C22semidirect
50. C2×C4×SD16C22semidirect
79. #2036C22semidirect
80. #2036C22semidirect
81. #2035C22semidirect
82. #2035C22semidirect
83. #2001C22semidirect
84. #2001C22semidirect
85. #2000C22semidirect
86. #2000C22semidirect
87. #1992C22semidirect
88. #1991C22semidirect
91. #1875C22semidirect
92. #1874C22semidirect
93. #1873C22semidirect
94. #1872C22semidirect
95. #1854C22semidirect
96. #1854C22semidirect
97. #1853C22semidirect
98. #1852C22semidirect
99. #1805C22semidirect
100. #1803C22semidirect
137. C2×#125D4semidirect
169. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#30802
C2×C4×#1372
#349352
#241392
#241372
#241272
#241252
#234812
#233922
#213252
#211902
#209102
#209092
#208452
#208442
#206472