Finite Group Databasebeta

← #556181

Subgroups — #556181

Order 512.

5282 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#537C211yesmaximal, characteristic
2C2×#2311C211yesmaximal, characteristic, complemented
3C2×#2297C211yesmaximal, characteristic, complemented
4#14702C211yesmaximal, characteristic, complemented
5#14698C211yesmaximal, characteristic, complemented
6#14449C214yesmaximal, complemented
7#14417C214yesmaximal, complemented
8#14363C214yesmaximal, complemented
9#14363C214yesmaximal, complemented
10#14258C211yesmaximal, characteristic, complemented
11#14257C211yesmaximal, characteristic, complemented
12#14139C211yesmaximal, characteristic, complemented
13#14138C211yesmaximal, characteristic, complemented
14#14137C211yesmaximal, characteristic, complemented
15#14136C211yesmaximal, characteristic, complemented
16#13937C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic, complemented
18#13924C211yesmaximal, characteristic, complemented
19#13904C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C23×#41C2211yescharacteristic
22C2×#537—28no—
23C2×#537—28no—
24C2×#537C4116yescomplemented
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2212yes—
28C22×#121C2212yes—
29C22×#121C2212yes—
30C22×#121C2212yes—
31C22×#121C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C23×C42C2211yescharacteristic
38#2311—28no—
39#2297—28no—
40C2×#391C2212yes—
41C2×#391C2212yes—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#390C2212yes—
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2214yes—
57C2×#386C2214yes—
58C2×#381C2214yes—
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67#1445C2214yes—
68#1445C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1437C2214yes—
80#1437C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C22⋊#95C2214yes—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—42no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41—42no—
102C22×#41—42no—
103C22×#41—42no—
104C22×#41—42no—
105C22×#41—42no—
106C22×#41C2×C418yes—
107C22×#41C2×C418yescomplemented
108C22×#41D418yes—
109C22×#41D418yes—
110C23×Q8C2311yescharacteristic
111C23×Q8C2311yescharacteristic
112C23×D4C2311yescharacteristic
113C23×D4C2312yes—
114C23×D4C2312yes—
115C23×D4C2312yes—
116C23×D4C2311yescharacteristic
117C23×D4C2311yescharacteristic
118C23×D4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2312yes—
123C24×C4C2312yes—
124C24×C4C2312yes—
125C24×C4C2312yes—
126#537—2128no—
127C2×C22⋊Q8—28no—
128C2×C22⋊Q8—28no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8C2×C418yescomplemented
134C2×C22⋊Q8C2×C418yescomplemented
135C2×C22⋊Q8C2×C4116yescomplemented
136C2×#121—28no—
137C2×#121—28no—
138C2×#121—28no—
139C2×#121—28no—
140C2×#121—28no—
141C2×#121—28no—
142C2×#121—24no—
143C2×#121—24no—
144C2×#121—24no—
145C2×#121—24no—
146C2×#121C2×C4116yes—
147C2×#121C2×C4116yescomplemented
148C2×#121C2×C4116yescomplemented
149C2×#121C2×C418yescomplemented
150C2×#121C2×C418yescomplemented
151C2×#117—24no—
152C2×#117—24no—
153C2×#117—42no—
154C2×#117—42no—
155C2×#117—42no—
156C2×#117—42no—
157C22×C4⋊C4—24no—
158C22×C4⋊C4—24no—
159C22×C4⋊C4—24no—
160C22×C4⋊C4—42no—
161C22×C4⋊C4—42no—
162C22×C4⋊C4C2×C418yescomplemented
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2314yes—
187C22×C22⋊C4C2314yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2314yes—
192C22×C42—24no—
193C22×C42—42no—
194C22×C42—42no—
195C22×C42C2311yescharacteristic
196C22×C42C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2312yes—
200C22×C42C2312yes—
201#391—28no—
202#391—28no—
203#391—42no—
204#391—42no—
205#391—42no—
206#391—42no—
207#390—28no—
208#390—28no—
209#390—42no—
210#390—42no—
211#390—42no—
212#390—42no—
213#386—28no—
214#386—28no—
215#386—28no—
216#386—28no—
217#386—48no—
218#386—48no—
219#381—48no—
220#380—24no—
221#380—24no—
222#380—24no—
223#380—24no—
224C4×C22⋊C4—24no—
225C4×C22⋊C4—24no—
226C4×C22⋊C4—24no—
227C4×C22⋊C4—24no—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2314yes—
242C2×#95C2314yes—
243C2×#95C2314yes—
244C2×#95C2314yes—
245C2×#95C2314yes—
246C2×#95C2314yes—
247C2×#95C2314yes—
248C25C2412yes—
249C25C2411yescharacteristic
250C25C2411yescharacteristic
251C25C2411yescharacteristic
252C2×#41—232no—
253C2×#41—416no—
254C2×#41—416no—
255C2×#41—416no—
256C2×#41—416no—
257C2×#41—416no—
258C2×#41—416no—
259C2×#41—416no—
260C2×#41—416no—
261C2×#41—416no—
262C2×#41—416no—
263C2×#41—416no—
264C2×#41—416no—
265C2×#41C22⋊C4164yescomplemented
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—41no—
273C22×Q8—41no—
274C22×Q8—41no—
275C22×Q8—41no—
276C22×Q8C22×C414yes—
277C22×Q8C22×C414yes—
278C22×Q8C2×D414yes—
279C22×Q8C2×D414yes—
280C22×D4—24no—
281C22×D4—24no—
282C22×D4—24no—
283C22×D4—24no—
284C22×D4—24no—
285C22×D4—24no—
286C22×D4—22no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—41no—
293C22×D4—41no—
294C22×D4—41no—
295C22×D4—41no—
296C22×D4—41no—
297C22×D4—41no—
298C22×D4—41no—
299C22×D4—41no—
300C22×D4—41no—
301C22×D4—41no—
302C22×D4—41no—
303C22×D4—41no—
304C22×D4—42no—
305C22×D4—42no—
306C22×D4—42no—
307C22×D4—42no—
308C22×D4—44no—
309C22×D4—44no—
310C22×D4—44no—
311C22×D4—44no—
312C22×D4C22×C414yes—
313C22×D4C22×C418yes—
314C22×D4C22×C418yes—
315C22×D4C22×C418yes—
316C22×D4C22×C414yes—
317C22×D4C22×C414yes—
318C22×D4C22×C414yes—
319C22×D4C2×D414yes—
320C22×D4C2×D414yes—
321C22×D4C2×D414yes—
322C22×D4C2×D414yes—
323C22×D4C2×D414yes—
324C22×D4C2×D414yes—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—24no—
338C23×C4—24no—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—24no—
345C23×C4—42no—
346C23×C4—42no—
347C23×C4—42no—
348C23×C4—42no—
349C23×C4—42no—
350C23×C4—42no—
351C23×C4—42no—
352C23×C4—42no—
353C23×C4—42no—
354C23×C4—42no—
355C23×C4—44no—
356C23×C4—44no—
357C23×C4—44no—
358C23×C4—44no—
359C23×C4C22×C414yes—
360C23×C4C22×C414yes—
361C23×C4C22×C414yes—
362C23×C4C22×C418yes—
363C23×C4C22×C418yes—
364C23×C4C2×D414yes—
365C23×C4C2×D414yes—
366C23×C4C2×D414yes—
367C23×C4C2×D414yes—
368C23×C4C2×D414yes—
369C23×C4C2×D414yes—
370C23×C4C2412yes—
371C23×C4C2412yes—
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2412yes—
377C23×C4C2412yes—
378C23×C4C2412yes—
379C23×C4C2412yes—
380C23×C4C2412yes—
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C22⋊Q8—264no—
386C22⋊Q8—232no—
387C22⋊Q8—232no—
388#121—264no—
389#121—264no—
390#121—264no—
391#121—232no—
392#121—232no—
393#117—416no—
394#117—416no—
395C2×C4⋊C4—232no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—416no—
425C2×C4⋊C4C22×C418yes—
426C2×C4⋊C4C22×C414yes—
427C2×C4⋊C4C22×C414yes—
428C2×C4⋊C4C22×C418yes—
429C2×C4⋊C4C22×C418yes—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—28no—
453C2×C22⋊C4—28no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—44no—
463C2×C22⋊C4—44no—
464C2×C22⋊C4—44no—
465C2×C22⋊C4—44no—
466C2×C22⋊C4—44no—
467C2×C22⋊C4—44no—
468C2×C22⋊C4—44no—
469C2×C22⋊C4—44no—
470C2×C22⋊C4—44no—
471C2×C22⋊C4—44no—
472C2×C22⋊C4—44no—
473C2×C22⋊C4—44no—
474C2×C22⋊C4—44no—
475C2×C22⋊C4—44no—
476C2×C22⋊C4C22×C418yes—
477C2×C22⋊C4C22×C418yes—
478C2×C22⋊C4C22×C418yes—
479C2×C22⋊C4C22×C418yes—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—24no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—24no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—42no—
495C2×C42—42no—
496C2×C42—42no—
497C2×C42—42no—
498C2×C42—416no—
499#95—24no—
500#95—24no—
501#95—24no—
502#95—24no—
503#95—24no—
504#95—24no—
505#95—24no—
506#95—24no—
507#95—28no—
508#95—28no—
509#95—44no—
510#95—44no—
511#95—44no—
512#95—44no—
513#95—44no—
514#95—44no—
515#95—44no—
516#95—44no—
517#95—44no—
518#95—44no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—24no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—24no—
551C24—24no—
552C24—24no—
553C24C23×C414yes—
554C24C23×C412yes—
555C24C23×C412yes—
556C24C23×C412yes—
557C24C22×D412yes—
558C24C22×D412yes—
559C24C22×D412yes—
560C24C22×D412yes—
561C24C22×D412yes—
562C24C22×D412yes—
563C24C2511yescharacteristic
564#41—4128no—
565#41—4128no—
566C2×Q8—28no—
567C2×Q8—28no—
568C2×Q8—28no—
569C2×Q8—44no—
570C2×Q8—44no—
571C2×Q8—44no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×Q8C2×C22⋊C4116yes—
580C2×D4—216no—
581C2×D4—216no—
582C2×D4—216no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—44no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4—416no—
607C2×D4—416no—
608C2×D4—48no—
609C2×D4—48no—
610C2×D4—48no—
611C2×D4—48no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—88no—
617C2×D4—88no—
618C2×D4—84no—
619C2×D4—84no—
620C2×D4—84no—
621C2×D4—84no—
622C2×D4C2×C22⋊C4116yes—
623C2×D4C2×C22⋊C4116yes—
624C2×D4C2×C22⋊C4116yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—28no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—28no—
654C22×C4—28no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—216no—
682C22×C4—216no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—22no—
710C22×C4—24no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—48no—
718C22×C4—48no—
719C22×C4—48no—
720C22×C4—416no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—48no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—48no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—88no—
733C22×C4—84no—
734C22×C4—84no—
735C22×C4—84no—
736C22×C4—84no—
737C22×C4—88no—
738C22×C4—88no—
739C22×C4C2×C22⋊C4116yes—
740C22×C4C2×C22⋊C4116yes—
741C22×C4C2×C22⋊C4116yes—
742C22×C4C23×C414yes—
743C22×C4C23×C414yes—
744C22×C4C23×C414yes—
745C22×C4C23×C412yes—
746C22×C4C23×C412yes—
747C22×C4C23×C412yes—
748C22×C4C23×C412yes—
749C22×C4C22×D412yes—
750C22×C4C22×D412yes—
751C22×C4C22×D412yes—
752C22×C4C22×D412yes—
753C22×C4C22×D412yes—
754C22×C4C22×D412yes—
755C22×C4C22×D412yes—
756C22×C4C22×D412yes—
757C22×C4H(5,𝔽2)14yes—
758C22×C4H(5,𝔽2)12yes—
759C22×C4H(5,𝔽2)12yes—
760C22×C4H(5,𝔽2)12yes—
761C22×C4H(5,𝔽2)12yes—
762C22×C42−1+414yes—
763C4⋊C4—216no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—216no—
767C4⋊C4—216no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C22⋊C4—216no—
775C22⋊C4—216no—
776C22⋊C4—216no—
777C22⋊C4—216no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—88no—
785C22⋊C4—88no—
786C22⋊C4—84no—
787C22⋊C4—84no—
788C22⋊C4—84no—
789C22⋊C4—84no—
790C22⋊C4—88no—
791C22⋊C4—88no—
792C42—48no—
793C42—48no—
794C42—44no—
795C42—44no—
796C42—44no—
797C42—44no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—28no—
844C23—28no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—44no—
874C23—44no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—44no—
880C23—44no—
881C23—44no—
882C23—44no—
883C23—44no—
884C23—44no—
885C23—44no—
886C23—44no—
887C23C22×C22⋊C414yes—
888C23C22×C22⋊C414yes—
889C23C22×C22⋊C414yes—
890C23C24×C411yescharacteristic
891C23C23×D411yescharacteristic
892C23C23×D411yescharacteristic
893C23C2×H(5,𝔽2)11yescharacteristic
894C23C2×H(5,𝔽2)11yescharacteristic
895C23C2×H(5,𝔽2)11yescharacteristic
896C23C2×H(5,𝔽2)11yescharacteristic
897C23C2×H(5,𝔽2)12yes—
898C23C2×2−1+412yes—
899C23#58512yes—
900C23#58512yes—
901Q8—416no—
902Q8—416no—
903D4—416no—
904D4—416no—
905D4—416no—
906D4—432no—
907D4—416no—
908D4—816no—
909D4—816no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—232no—
929C2×C4—232no—
930C2×C4—232no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—28no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—432no—
945C2×C4—432no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—44no—
954C2×C4—44no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—44no—
986C2×C4—42no—
987C2×C4—44no—
988C2×C4—42no—
989C2×C4—44no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—44no—
995C2×C4—42no—
996C2×C4—44no—
997C2×C4—42no—
998C2×C4—816no—
999C2×C4—816no—
1000C2×C4C22×C22⋊C414yes—
1001C2×C4C22×C22⋊C414yes—
1002C2×C4C22×C22⋊C414yes—
1003C2×C4C22×C22⋊C414yes—
1004C2×C4#51814yes—
1005C2×C4#51814yes—
1006C2×C4#53414yes—
1007C2×C4#53414yes—
1008C2×C4#53414yes—
1009C2×C4#53414yes—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—24no—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22—44no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—48no—
1044C22—48no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—82no—
1049C22—82no—
1050C22—84no—
1051C22—84no—
1052C22—82no—
1053C22—82no—
1054C22C23×C22⋊C411yescharacteristic
1055C22C2×#51811yescharacteristic
1056C22C2×#51811yescharacteristic
1057C22C4×H(5,𝔽2)12yes—
1058C22C4×2−1+412yes—
1059C22C2×#53411yescharacteristic
1060C22C2×#53411yescharacteristic
1061C22C2×#53411yescharacteristic
1062C22C2×#53411yescharacteristic
1063C22#348812yes—
1064C22#348912yes—
1065C22#349811yescharacteristic
1066C22#349911yescharacteristic
1067C22#350011yescharacteristic
1068C22#350011yescharacteristic
1069C22#353612yes—
1070C22#353912yes—
1071C22#354112yes—
1072C22#354212yes—
1073C22#354612yes—
1074C22#354712yes—
1075C22#354812yes—
1076C22#355112yes—
1077C4—24no—
1078C4—24no—
1079C4—24no—
1080C4—44no—
1081C4—44no—
1082C4—44no—
1083C4—44no—
1084C4—44no—
1085C4—82no—
1086C4—82no—
1087C4—82no—
1088C4—82no—
1089C4—82no—
1090C4—82no—
1091C4#230818yes—
1092C2—44no—
1093C2—44no—
1094C2—44no—
1095C2—84no—
1096C2C2×#230811yescharacteristic
1097C2#3425811yescharacteristic
1098C2#3425911yescharacteristic
1099C2#3441012yes—
1100C2#3441412yes—
1101C2#3726812yes—
1102C2#3727212yes—
1103C2#3729611yescharacteristic
1104C2#3730011yescharacteristic
1105C2#3738811yescharacteristic
1106C2#3741811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#537C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2311C2semidirect
3. C2×#2297C2semidirect
4. #14702C2semidirect
5. #14698C2semidirect
6. #14449C2semidirect
7. #14417C2semidirect
8. #14363C2semidirect
9. #14363C2semidirect
10. #14258C2semidirect
11. #14257C2semidirect
12. #14139C2semidirect
13. #14138C2semidirect
14. #14137C2semidirect
15. #14136C2semidirect
16. #13937C2semidirect
17. #13937C2semidirect
18. #13924C2semidirect
19. #13904C2semidirect
24. C2×#537C4semidirect
107. C22×#41C2×C4semidirect
133. C2×C22⋊Q8C2×C4semidirect
134. C2×C22⋊Q8C2×C4semidirect
135. C2×C22⋊Q8C2×C4semidirect
147. C2×#121C2×C4semidirect
148. C2×#121C2×C4semidirect
149. C2×#121C2×C4semidirect
150. C2×#121C2×C4semidirect
162. C22×C4⋊C4C2×C4semidirect
265. C2×#41C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5372
C2×#23112
C2×#22972
#147022
#146982
#144492
#144172
#143632
#142582
#142572
#141392
#141382
#141372
#141362
#139372
#139242
#139042