Finite Group Databasebeta

← #6445395

Subgroups — #6445395

Order 512.

3042 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic
2C2×#3078C211yesmaximal, characteristic, complemented
3C22×#479C211yesmaximal, characteristic, complemented
4C4×#536C211yesmaximal, characteristic
5#24311C214yesmaximal, complemented
6#24310C214yesmaximal, complemented
7#24307C214yesmaximal, complemented
8#24306C214yesmaximal, complemented
9#23556C211yesmaximal, characteristic, complemented
10#23555C211yesmaximal, characteristic, complemented
11#23457C211yesmaximal, characteristic, complemented
12#23457C211yesmaximal, characteristic, complemented
13#21314C211yesmaximal, characteristic, complemented
14#21311C211yesmaximal, characteristic, complemented
15#20913C211yesmaximal, characteristic
16#20913C211yesmaximal, characteristic
17#20848C211yesmaximal, characteristic
18#20847C211yesmaximal, characteristic
19#20629C211yesmaximal, characteristic
20#3504—28no—
21#3504—28no—
22C2×#557—21no—
23C2×#557—21no—
24C2×#554—22no—
25C2×#554—21no—
26C2×#554—22no—
27C2×#554—21no—
28C2×#544C2211yescharacteristic
29C2×#544C2211yescharacteristic
30C2×#544C2212yes—
31C2×#544C2212yes—
32C2×#536C2211yescharacteristic
33C2×#533C2212yes—
34C2×#533C2211yescharacteristic
35C22×#125C2212yes—
36C22×#125C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#3078—28no—
42C2×#479—28no—
43C2×#479C2214yes—
44C2×#479C2214yes—
45C2×#479C2212yes—
46C2×#479C2212yes—
47C2×#477C2212yes—
48C2×#475C2212yes—
49C2×#428C2211yescharacteristic
50C2×#428C2211yescharacteristic
51C22×#107C2211yescharacteristic
52C22×#106C2211yescharacteristic
53C2×#423C2211yescharacteristic
54C22×C4⋊C8C2211yescharacteristic
55C2×#419C2211yescharacteristic
56C2×#419C2211yescharacteristic
57C22×#103C2211yescharacteristic
58C22×#103C2211yescharacteristic
59C2×#408C2211yescharacteristic
60C2×#408C2211yescharacteristic
61#2327—21no—
62#2326—21no—
63#2323C2214yes—
64#2322—22no—
65#2317C2211yescharacteristic
66#2311C2211yescharacteristic
67#2310C2211yescharacteristic
68C4×C4⋊Q8—21no—
69C4×#124—21no—
70C4×C22⋊Q8C2214yes—
71C4×#123—22no—
72C4×#117C2211yescharacteristic
73#2059C2214yes—
74#2059C2214yes—
75#2058C2214yes—
76#2057C2214yes—
77#2026C2214yes—
78#2026C2214yes—
79#2024C2214yes—
80#2024C2214yes—
81#1989C2212yes—
82#1989C2212yes—
83#1989C2214yes—
84#1989C2214yes—
85#1988C2212yes—
86#1987C2212yes—
87#1873C2214yes—
88#1873C2214yes—
89#1872C2214yes—
90#1872C2214yes—
91#1854C2214yes—
92#1854C2214yes—
93#1853C2214yes—
94#1852C2214yes—
95#1798C2214yes—
96#1797C2214yes—
97#1736C2211yescharacteristic
98#1736C2211yescharacteristic
99#1736C2211yescharacteristic
100#1736C2211yescharacteristic
101#1735C2211yescharacteristic
102#1735C2211yescharacteristic
103#1735C2211yescharacteristic
104#1735C2211yescharacteristic
105#1729C2211yescharacteristic
106#1729C2211yescharacteristic
107C22×#41C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C22×M16C2311yescharacteristic
110C22×M16C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C23×C8C2311yescharacteristic
113#557—216no—
114#557—216no—
115#554—216no—
116#554—216no—
117#554—232no—
118#554—232no—
119#544—28no—
120#544—28no—
121#544—28no—
122#544—28no—
123#544—24no—
124#544—24no—
125#544—24no—
126#544—24no—
127#536—24no—
128#536Q818yescomplemented
129#533—28no—
130#533—28no—
131#533—24no—
132#533D418yes—
133C2×C4⋊Q8—21no—
134C2×C4⋊Q8—21no—
135C2×C4⋊Q8—21no—
136C2×C4⋊Q8—22no—
137C2×C4⋊Q8—22no—
138C2×C4⋊Q8C2312yes—
139C2×C4⋊Q8C2312yes—
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2311yescharacteristic
142C2×#125—28no—
143C2×#125—28no—
144C2×#125—21no—
145C2×#125—21no—
146C2×#125—22no—
147C2×#125—22no—
148C2×#125—22no—
149C2×#125—22no—
150C2×#125—21no—
151C2×#125—21no—
152C2×#125—24no—
153C2×#125D418yes—
154C2×#125C2312yes—
155C2×#125C2312yes—
156C2×#125C2311yescharacteristic
157C2×#125C2312yes—
158C2×#125C2312yes—
159C2×#125C2311yescharacteristic
160C2×#124—21no—
161C2×#123—22no—
162C2×C22⋊Q8—22no—
163C2×C22⋊Q8—22no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—21no—
166C2×C22⋊Q8—22no—
167C2×C22⋊Q8—22no—
168C2×C22⋊Q8—22no—
169C2×C22⋊Q8—22no—
170C2×C22⋊Q8—22no—
171C2×C22⋊Q8—22no—
172C2×C22⋊Q8C2314yes—
173#520—24no—
174#520—24no—
175#520—24no—
176#520—24no—
177C4×#41—24no—
178C4×#41—24no—
179C2×C4×Q8—21no—
180C2×C4×Q8—21no—
181C2×C4×Q8—22no—
182C2×C4×Q8—22no—
183C2×C4×Q8—21no—
184C2×C4×Q8—21no—
185C2×C4×Q8—21no—
186C2×C4×Q8—21no—
187C2×C4×Q8—24no—
188C2×C4×Q8—24no—
189C2×C4×Q8D411yescharacteristic
190C2×C4×Q8D411yescharacteristic
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×D4—22no—
194C2×C4×D4—22no—
195C2×C4×D4—21no—
196C2×C4×D4—21no—
197C2×C4×D4D412yes—
198C2×C4×D4D411yescharacteristic
199C2×C4×D4D412yes—
200C2×C4×D4D411yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2311yescharacteristic
205C2×#117C2311yescharacteristic
206C2×#117C2311yescharacteristic
207C2×#117C2312yes—
208C2×#117C2311yescharacteristic
209C22×C4⋊C4—22no—
210C22×C4⋊C4—22no—
211C22×C4⋊C4—21no—
212C22×C4⋊C4—21no—
213C22×C4⋊C4—21no—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C42—21no—
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222#479—216no—
223#479—216no—
224#479—28no—
225#479—28no—
226#477—28no—
227#475—28no—
228#428—24no—
229#428—24no—
230C2×#107—24no—
231C2×#107C2312yes—
232C2×#107C2312yes—
233C2×#107C2314yes—
234C2×#106—24no—
235C2×#106C2312yes—
236C2×#106C2312yes—
237C2×#106C2314yes—
238#423—24no—
239C2×C4⋊C8—24no—
240C2×C4⋊C8C2312yes—
241C2×C4⋊C8C2312yes—
242C2×C4⋊C8C2312yes—
243C2×C4⋊C8C2312yes—
244#419—24no—
245#419—24no—
246C2×#103—24no—
247C2×#103—24no—
248C2×#103C2312yes—
249C2×#103C2312yes—
250C2×#103C2312yes—
251C2×#103C2312yes—
252C2×#103C2314yes—
253C2×#103C2314yes—
254#408—24no—
255#408—24no—
256C2×C22⋊C8C2314yes—
257C2×C22⋊C8C2314yes—
258#391—21no—
259#391—21no—
260#391—21no—
261#391C2314yes—
262#390—21no—
263#389—24no—
264#389C2314yes—
265#388—24no—
266#388—24no—
267#387—24no—
268#387—24no—
269#386—22no—
270#385—24no—
271#385—22no—
272#384—21no—
273#382—21no—
274#381—22no—
275#380C2314yes—
276C4×C4⋊C4—24no—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2312yes—
279C4×C22⋊C4—21no—
280C4×C22⋊C4—21no—
281C4×C22⋊C4—24no—
282#376—21no—
283C43—21no—
284#340C2312yes—
285#340C2314yes—
286#340C2312yes—
287#340C2314yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2314yes—
292#340C2312yes—
293#340C2314yes—
294#340C2312yes—
295#340C2312yes—
296#336C2314yes—
297#336C2314yes—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41C2×Q814yes—
303C2×#41#4114yes—
304C22×Q8—21no—
305C22×Q8—22no—
306C22×Q8—22no—
307C22×Q8—21no—
308C22×Q8—21no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8C2×D411yescharacteristic
315C22×Q8C2×Q814yes—
316C22×Q8C2412yes—
317C22×D4C2×D412yes—
318C22×D4C2×D411yescharacteristic
319C23×C4—21no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—21no—
325C23×C4C2×D412yes—
326C23×C4C2×D412yes—
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2412yes—
330C23×C4C2411yescharacteristic
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—22no—
335C2×M16—22no—
336C2×M16—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8C2412yes—
344C22×C8C2412yes—
345C22×C8C2412yes—
346C22×C8C2412yes—
347C4⋊Q8—216no—
348C4⋊Q8—216no—
349C4⋊Q8—28no—
350C4⋊Q8—28no—
351C4⋊Q8—28no—
352C4⋊Q8—24no—
353C4⋊Q8—24no—
354C4⋊Q8—24no—
355C4⋊Q8—24no—
356C4⋊Q8—22no—
357C4⋊Q8—22no—
358C4⋊Q8C2×D414yes—
359C4⋊Q8C2×D414yes—
360#125—216no—
361#125—216no—
362#125—216no—
363#125—216no—
364#125—28no—
365#125—28no—
366#125—24no—
367#125—24no—
368#125—24no—
369#125—24no—
370#125—28no—
371#125—28no—
372#125—22no—
373#125—24no—
374#125—24no—
375#125—22no—
376#125C2×D414yes—
377#125C2×D418yes—
378#125C2×D418yes—
379#125C2×D414yes—
380#124—28no—
381#123—216no—
382C22⋊Q8—216no—
383C22⋊Q8—216no—
384C22⋊Q8—216no—
385C22⋊Q8—216no—
386C22⋊Q8—216no—
387C22⋊Q8—216no—
388C22⋊Q8—216no—
389C22⋊Q8—216no—
390C22⋊Q8—28no—
391C22⋊Q8—28no—
392C22⋊Q8—28no—
393C22⋊Q8C2×Q8116yes—
394C4×Q8—28no—
395C4×Q8—28no—
396C4×Q8—216no—
397C4×Q8—216no—
398C4×Q8—28no—
399C4×Q8—28no—
400C4×Q8—24no—
401C4×Q8—24no—
402C4×Q8—24no—
403C4×Q8—24no—
404C4×Q8—24no—
405C4×Q8—24no—
406C4×Q8—44no—
407C4×Q8—44no—
408C4×D4—216no—
409C4×D4—216no—
410C4×D4—28no—
411C4×D4—28no—
412C4×D4—28no—
413C4×D4—28no—
414C4×D4—24no—
415C4×D4—24no—
416#117—22no—
417#117—22no—
418#117—22no—
419#117—22no—
420#117—22no—
421#117—24no—
422#117—24no—
423#117—24no—
424#117—24no—
425#117—24no—
426#117—24no—
427#117—22no—
428#117—22no—
429#117C2×D414yes—
430#117C2×D414yes—
431#117C2×Q814yes—
432C2×C4⋊C4—216no—
433C2×C4⋊C4—216no—
434C2×C4⋊C4—28no—
435C2×C4⋊C4—28no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—44no—
470C2×C4⋊C4C2×D411yescharacteristic
471C2×C4⋊C4C2×D411yescharacteristic
472C2×C4⋊C4C2×D412yes—
473C2×C4⋊C4C2×D412yes—
474C2×C4⋊C4C2×D414yes—
475C2×C4⋊C4C2×D414yes—
476C2×C4⋊C4C2412yes—
477C2×C4⋊C4C2412yes—
478C2×C4⋊C4C2411yescharacteristic
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2411yescharacteristic
481C2×C4⋊C4C2412yes—
482C2×C4⋊C4C2411yescharacteristic
483C2×C4⋊C4C2411yescharacteristic
484C2×C4⋊C4C2412yes—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4C2×D412yes—
494C2×C22⋊C4C2×D412yes—
495C2×C22⋊C4C2×D412yes—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—24no—
502C2×C42—24no—
503C2×C42—21no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—44no—
509C2×C42C2×D412yes—
510C2×C42C2×D412yes—
511C2×C42C2×D411yescharacteristic
512C2×C42C2×D411yescharacteristic
513C2×C42C2×D414yes—
514C2×C42C2×D414yes—
515C2×C42C2412yes—
516C2×C42C2411yescharacteristic
517C2×C42C2411yescharacteristic
518#107—28no—
519#107—24no—
520#107—24no—
521#106—28no—
522#106—24no—
523#106—24no—
524C4⋊C8—24no—
525C4⋊C8—24no—
526C4⋊C8—24no—
527C4⋊C8—24no—
528#103—28no—
529#103—28no—
530#103—24no—
531#103—24no—
532#103—24no—
533#103—24no—
534C22⋊C8—28no—
535C22⋊C8—28no—
536#95—22no—
537#95—22no—
538#95—24no—
539#95—24no—
540#95—24no—
541#95—24no—
542C24C22×D412yes—
543C24C22×D411yescharacteristic
544#41—28no—
545#41—28no—
546#41—28no—
547#41—28no—
548C2×Q8—28no—
549C2×Q8—28no—
550C2×Q8—22no—
551C2×Q8—24no—
552C2×Q8—24no—
553C2×Q8—24no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—28no—
557C2×Q8—28no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—82no—
567C2×Q8—82no—
568C2×Q8—84no—
569C2×Q8—84no—
570C2×Q8C22⋊Q814yes—
571C2×Q8C22×Q814yes—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4C22⋊Q818yes—
577C2×D4C22⋊Q814yes—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—82no—
607C22×C4—84no—
608C22×C4—82no—
609C22×C4—84no—
610C22×C4—82no—
611C22×C4#12014yes—
612C22×C4#12014yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×Q814yes—
624C22×C4C22×Q812yes—
625C22×C4C2×#4114yes—
626C22×C4C2×#4112yes—
627C22×C42−1+412yes—
628C22×C42−1+412yes—
629C22×C4C2511yescharacteristic
630M16—44no—
631M16—44no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—44no—
645C2×C8—44no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—24no—
655C4⋊C4—28no—
656C4⋊C4—24no—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—216no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—42no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—84no—
686C4⋊C4C22×D412yes—
687C4⋊C4C22×D414yes—
688C4⋊C4C22×D412yes—
689C4⋊C4C22×D412yes—
690C4⋊C4C22×D414yes—
691C4⋊C4C22×D412yes—
692C4⋊C4C22×Q814yes—
693C22⋊C4—28no—
694C22⋊C4—28no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—216no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—42no—
703C22⋊C4—84no—
704C42—28no—
705C42—28no—
706C42—24no—
707C42—24no—
708C42—24no—
709C42—24no—
710C42—24no—
711C42—22no—
712C42—22no—
713C42—44no—
714C42—44no—
715C42—44no—
716C42—42no—
717C42—82no—
718C42#12014yes—
719C42#12014yes—
720C42C22×D412yes—
721C42C22×D412yes—
722C42C22×D412yes—
723C42C22×D412yes—
724C23—22no—
725C23—22no—
726C23—24no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23C2×#12012yes—
731C23C2×C22⋊Q814yes—
732C23C2×C22⋊Q812yes—
733C23#53612yes—
734C23C23×D411yescharacteristic
735Q8—28no—
736Q8—24no—
737Q8—24no—
738Q8—48no—
739Q8—42no—
740Q8—42no—
741Q8—84no—
742Q8—84no—
743Q8—88no—
744Q8—88no—
745D4—216no—
746D4—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—48no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—84no—
788C2×C4—84no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—88no—
792C2×C4—88no—
793C2×C4—84no—
794C2×C4C2×#12012yes—
795C2×C4C2×#12012yes—
796C2×C4C2×#12012yes—
797C2×C4C2×#12012yes—
798C2×C4C2×#12012yes—
799C2×C4C2×C22⋊Q814yes—
800C2×C4C2×C22⋊Q812yes—
801C2×C4#53612yes—
802C2×C4#54814yes—
803C2×C4#54814yes—
804C2×C4D4×Q814yes—
805C2×C4D4×Q814yes—
806C2×C4C23×D411yescharacteristic
807C2×C4C23×D411yescharacteristic
808C2×C4C23×Q811yescharacteristic
809C2×C4C22×#4111yescharacteristic
810C2×C4C2×2−1+411yescharacteristic
811C2×C4C2×2−1+411yescharacteristic
812C8—42no—
813C8—42no—
814C8—42no—
815C8—42no—
816C22—24no—
817C22—22no—
818C22—22no—
819C22—24no—
820C22—28no—
821C22—24no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22#240914yes—
826C22C22×#12011yescharacteristic
827C22C22×C22⋊Q811yescharacteristic
828C22C2×#53611yescharacteristic
829C22#358412yes—
830C22#358612yes—
831C4—24no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—44no—
837C4—44no—
838C4—42no—
839C4—44no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—44no—
844C4—42no—
845C4—42no—
846C4—82no—
847C4—82no—
848C4#240914yes—
849C4C2×#54811yescharacteristic
850C4C2×#54811yescharacteristic
851C4C2×D4×Q811yescharacteristic
852C4C2×D4×Q811yescharacteristic
853C2—24no—
854C2—44no—
855C2C2×#240911yescharacteristic
856C2#6036611yescharacteristic
857C2#6037011yescharacteristic
858C2#6049912yes—
859C2#6089112yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3078C2semidirect
3. C22×#479C2semidirect
5. #24311C2semidirect
6. #24310C2semidirect
7. #24307C2semidirect
8. #24306C2semidirect
9. #23556C2semidirect
10. #23555C2semidirect
11. #23457C2semidirect
12. #23457C2semidirect
13. #21314C2semidirect
14. #21311C2semidirect
128. #536Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#30782
C22×#4792
C4×#5362
#243112
#243102
#243072
#243062
#235562
#235552
#234572
#213142
#213112
#209132
#208482
#208472
#206292