Finite Group Databasebeta

← #7502446

Subgroups — #7502446

Order 512.

1898 conjugacy classes of subgroups.

The subgroup lattice has 999 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3165C211yesmaximal, characteristic
2C2×#3078C211yesmaximal, characteristic
3#34938C211yesmaximal, characteristic
4C2×#2451C211yesmaximal, characteristic
5#30977C212yesmaximal, complemented
6#30976C212yesmaximal, complemented
7#30969C212yesmaximal, complemented
8#30968C212yesmaximal, complemented
9#30957C212yesmaximal, complemented
10#30956C212yesmaximal, complemented
11#30949C212yesmaximal, complemented
12#30948C212yesmaximal, complemented
13#23732C211yesmaximal, characteristic
14#23670C211yesmaximal, characteristic
15#23657C211yesmaximal, characteristic
16#23554C211yesmaximal, characteristic
17#23552C211yesmaximal, characteristic
18#23455C211yesmaximal, characteristic
19#21094C211yesmaximal, characteristic
20#21061C211yesmaximal, characteristic
21#21034C211yesmaximal, characteristic
22#21023C211yesmaximal, characteristic
23#20874C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28#3165—28no—
29C2×#501C2212yes—
30C2×#501C2212yes—
31C2×#500C2212yes—
32C2×#498C2212yes—
33#3078—28no—
34C2×#479C2212yes—
35C2×#479C2212yes—
36C2×#477C2212yes—
37C2×#475C2212yes—
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#428C2211yescharacteristic
44C2×#423C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C2×#419C2211yescharacteristic
47C2×#419C2211yescharacteristic
48C2×#419C2211yescharacteristic
49C2×C4×M16C2211yescharacteristic
50#2552C2211yescharacteristic
51#2552C2211yescharacteristic
52#2551C2211yescharacteristic
53#2551C2211yescharacteristic
54#2550C2211yescharacteristic
55#2550C2211yescharacteristic
56#2550C2211yescharacteristic
57#2550C2211yescharacteristic
58#2549—21no—
59#2549—21no—
60#2451—21no—
61#2451—21no—
62#2451—21no—
63#2451—21no—
64#2451C2212yes—
65#2451C2212yes—
66#2451C2212yes—
67#2451C2212yes—
68#2440—21no—
69#2440—21no—
70#2399—21no—
71#2399—21no—
72C2×#398—21no—
73C2×#395—21no—
74C4×C4⋊Q8—21no—
75C4×C4⋊Q8—21no—
76#2296C2211yescharacteristic
77#2296C2211yescharacteristic
78C2×#391—21no—
79C2×#391C2211yescharacteristic
80C2×#391C2211yescharacteristic
81C2×#389C2211yescharacteristic
82C2×#389C2211yescharacteristic
83C2×#387—21no—
84#2285C2211yescharacteristic
85C4×#117C2211yescharacteristic
86C2×C4×C4⋊C4C2211yescharacteristic
87#2097C2212yes—
88#2097C2212yes—
89#2096C2212yes—
90#2095C2212yes—
91#2088C2212yes—
92#2088C2212yes—
93#2087C2212yes—
94#2086C2212yes—
95#2085C2212yes—
96#2085C2212yes—
97#2084C2212yes—
98#2083C2212yes—
99#2059C2212yes—
100#2059C2212yes—
101#2058C2212yes—
102#2058C2212yes—
103#2058C2212yes—
104#2057C2212yes—
105#2057C2212yes—
106#2057C2212yes—
107#2026C2212yes—
108#2026C2212yes—
109#2024C2212yes—
110#2024C2212yes—
111#1935C2212yes—
112#1935C2212yes—
113#1933C2212yes—
114#1933C2212yes—
115#1928C2212yes—
116#1928C2212yes—
117#1927C2212yes—
118#1927C2212yes—
119#1921C2212yes—
120#1920C2212yes—
121#1919C2212yes—
122#1918C2212yes—
123#1917C2212yes—
124#1917C2212yes—
125#1916C2212yes—
126#1916C2212yes—
127#1865C2212yes—
128#1865C2212yes—
129#1863C2212yes—
130#1863C2212yes—
131#1736C2211yescharacteristic
132#1736C2211yescharacteristic
133#1736C2211yescharacteristic
134#1736C2211yescharacteristic
135#1736C2211yescharacteristic
136#1736C2211yescharacteristic
137#1728C2211yescharacteristic
138#1728C2211yescharacteristic
139#1728C2211yescharacteristic
140#1728C2211yescharacteristic
141C23×Q8—21no—
142C23×Q8C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C22×M16C2311yescharacteristic
145C22×M16C2311yescharacteristic
146C22×M16C2311yescharacteristic
147#533—24no—
148#533—24no—
149#533—42no—
150#533—42no—
151C2×C4⋊Q8—21no—
152C2×C4⋊Q8—21no—
153C2×C4⋊Q8—24no—
154C2×C4⋊Q8—21no—
155C2×C4⋊Q8—21no—
156C2×C4⋊Q8—42no—
157C2×C4⋊Q8C2311yescharacteristic
158C2×C4⋊Q8C2311yescharacteristic
159C2×C4⋊Q8C2312yes—
160C2×C4⋊Q8C2312yes—
161C2×C4⋊Q8C2311yescharacteristic
162C2×C4⋊Q8C2311yescharacteristic
163C2×#125C2311yescharacteristic
164C2×#125C2311yescharacteristic
165C2×#125C2311yescharacteristic
166C2×#125C2311yescharacteristic
167C2×C22⋊Q8—21no—
168C2×C22⋊Q8—21no—
169C2×C22⋊Q8—21no—
170C2×C22⋊Q8—21no—
171C2×C4×Q8—21no—
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174C2×C4×Q8—21no—
175C2×C4×Q8—21no—
176C2×C4×Q8—21no—
177C2×C4×Q8—24no—
178C2×C4×Q8—42no—
179C2×C4×Q8C2312yes—
180C2×C4×Q8C2312yes—
181C2×#117C2311yescharacteristic
182C2×#117C2311yescharacteristic
183C2×#117C2311yescharacteristic
184C2×#117C2311yescharacteristic
185C22×C4⋊C4—21no—
186C22×C4⋊C4—21no—
187C22×C4⋊C4—21no—
188C22×C4⋊C4—21no—
189C22×C4⋊C4D411yescharacteristic
190C22×C4⋊C4D411yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C42—21no—
195C22×C42C2311yescharacteristic
196C22×C42C2311yescharacteristic
197C22×C42C2311yescharacteristic
198#501—28no—
199#501—28no—
200#500—28no—
201#498—28no—
202#479—28no—
203#479—28no—
204#477—28no—
205#475—28no—
206#428—24no—
207#428—24no—
208#428—24no—
209#428—24no—
210#428—42no—
211#428D418yes—
212C2×#107C2312yes—
213C2×#107C2312yes—
214C2×#107C2312yes—
215C2×#107C2312yes—
216C2×#107C2312yes—
217C2×#107C2312yes—
218C2×#106C2312yes—
219C2×#106C2312yes—
220C2×#106C2312yes—
221C2×#106C2312yes—
222C2×#106C2312yes—
223C2×#106C2312yes—
224#423—24no—
225C2×C4⋊C8C2312yes—
226C2×C4⋊C8C2312yes—
227#419—24no—
228#419—24no—
229#419—42no—
230#419Q818yescomplemented
231C2×#103C2312yes—
232C2×#103C2312yes—
233C2×#103C2312yes—
234C2×#103C2312yes—
235C2×#103C2312yes—
236C2×#103C2312yes—
237C2×#103C2312yes—
238C2×#103C2312yes—
239C4×M16—24no—
240C2×#97C2312yes—
241C2×C4×C8C2312yes—
242#398—21no—
243#398—21no—
244#398—21no—
245#398—21no—
246#398—22no—
247#398—22no—
248#398—22no—
249#398—22no—
250#398—21no—
251#398—21no—
252#398—21no—
253#398—21no—
254#395—22no—
255#395—22no—
256#395—22no—
257#395—22no—
258#395—21no—
259#395—21no—
260#395—21no—
261#395—21no—
262#395—21no—
263#395—21no—
264#395—21no—
265#395—21no—
266#391—21no—
267#391—21no—
268#391—21no—
269#391—21no—
270#391—21no—
271#391—21no—
272#391—21no—
273#391—21no—
274#391—22no—
275#391—22no—
276#391—22no—
277#391—22no—
278#391C2312yes—
279#391C2312yes—
280#391C2312yes—
281#391C2312yes—
282#389—21no—
283#389—21no—
284#389—21no—
285#389—21no—
286#389—21no—
287#389—21no—
288#389—21no—
289#389—21no—
290#389—21no—
291#389—21no—
292#389—21no—
293#389—21no—
294#389C2311yescharacteristic
295#389C2311yescharacteristic
296#389C2312yes—
297#389C2311yescharacteristic
298#389C2311yescharacteristic
299#389C2312yes—
300#389C2312yes—
301#389C2312yes—
302#389C2311yescharacteristic
303#389C2311yescharacteristic
304#389C2311yescharacteristic
305#389C2311yescharacteristic
306#387—22no—
307#387—22no—
308#387—22no—
309#387—22no—
310#385—21no—
311#385—21no—
312#385—21no—
313#385—21no—
314#384—21no—
315#384—21no—
316#384C2311yescharacteristic
317#384C2311yescharacteristic
318#382C2311yescharacteristic
319#382C2311yescharacteristic
320#380—21no—
321#380—21no—
322C4×C4⋊C4—21no—
323C4×C4⋊C4—21no—
324C4×C4⋊C4—21no—
325C4×C4⋊C4—21no—
326C4×C4⋊C4—21no—
327C4×C4⋊C4—21no—
328C4×C4⋊C4D411yescharacteristic
329C4×C4⋊C4D411yescharacteristic
330C4×C4⋊C4D411yescharacteristic
331C4×C4⋊C4D411yescharacteristic
332C4×C4⋊C4C2311yescharacteristic
333C4×C4⋊C4C2311yescharacteristic
334C4×C4⋊C4C2311yescharacteristic
335C4×C4⋊C4C2311yescharacteristic
336C4×C4⋊C4C2311yescharacteristic
337C4×C4⋊C4C2311yescharacteristic
338C4×C4⋊C4C2311yescharacteristic
339C4×C4⋊C4C2311yescharacteristic
340C4×C22⋊C4—21no—
341C4×C22⋊C4—21no—
342#376—21no—
343C2×#95—21no—
344C2×#95—21no—
345C2×#95—21no—
346C2×#95—21no—
347C2×#95—21no—
348C2×#95—21no—
349C2×#95D411yescharacteristic
350C2×#95D411yescharacteristic
351C43—21no—
352#340C2312yes—
353#340C2312yes—
354#340C2312yes—
355#340C2312yes—
356#340C2312yes—
357#340C2312yes—
358#340C2312yes—
359#340C2312yes—
360#340C2312yes—
361#340C2312yes—
362#340C2312yes—
363#340C2312yes—
364#336C2312yes—
365#336C2312yes—
366#336C2312yes—
367#336C2312yes—
368#336C2312yes—
369#336C2312yes—
370#336C2312yes—
371#336C2312yes—
372C22×Q8—21no—
373C22×Q8—21no—
374C22×Q8—21no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—22no—
384C22×Q8—44no—
385C22×Q8—44no—
386C22×Q8—82no—
387C22×Q8C2×Q814yes—
388C22×Q8C2412yes—
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—21no—
393C23×C4C2×D411yescharacteristic
394C23×C4C2×D411yescharacteristic
395C23×C4C2×D411yescharacteristic
396C23×C4C2×D411yescharacteristic
397C23×C4C2×D411yescharacteristic
398C23×C4C2×D411yescharacteristic
399C23×C4C2411yescharacteristic
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C2×M16C2×D414yes—
411C2×M16C2×Q814yes—
412C22×C8C2412yes—
413C22×C8C2412yes—
414C22×C8C2412yes—
415C22×C8C2412yes—
416C4⋊Q8—24no—
417C4⋊Q8—24no—
418C4⋊Q8—22no—
419C4⋊Q8—22no—
420C4⋊Q8—22no—
421C4⋊Q8—22no—
422C4⋊Q8—42no—
423C4⋊Q8—42no—
424C4⋊Q8—41no—
425C4⋊Q8—41no—
426C4⋊Q8—41no—
427C4⋊Q8—41no—
428C4⋊Q8—44no—
429C4⋊Q8—44no—
430C4⋊Q8—44no—
431C4⋊Q8—44no—
432#125—22no—
433#125—22no—
434#125—22no—
435#125—22no—
436#125—41no—
437#125—41no—
438#125—41no—
439#125—41no—
440C22⋊Q8—44no—
441C22⋊Q8—44no—
442C22⋊Q8—44no—
443C22⋊Q8—44no—
444C4×Q8—24no—
445C4×Q8—24no—
446C4×Q8—44no—
447C4×Q8—44no—
448C4×Q8—44no—
449C4×Q8—44no—
450C4×Q8—42no—
451C4×Q8—42no—
452C4×Q8—44no—
453C4×Q8—44no—
454#117—22no—
455#117—22no—
456#117—22no—
457#117—22no—
458#117—22no—
459#117—22no—
460#117C2×D414yes—
461#117C2×Q814yes—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—42no—
504C2×C4⋊C4—44no—
505C2×C4⋊C4—44no—
506C2×C4⋊C4—82no—
507C2×C4⋊C4—82no—
508C2×C4⋊C4C2×D411yescharacteristic
509C2×C4⋊C4C2×D411yescharacteristic
510C2×C4⋊C4C2×D411yescharacteristic
511C2×C4⋊C4C2×D411yescharacteristic
512C2×C4⋊C4C2×D411yescharacteristic
513C2×C4⋊C4C2×D414yes—
514C2×C4⋊C4C2×D411yescharacteristic
515C2×C4⋊C4C2×D411yescharacteristic
516C2×C4⋊C4C2×D411yescharacteristic
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2411yescharacteristic
520C2×C4⋊C4C2411yescharacteristic
521C2×C4⋊C4C2411yescharacteristic
522C2×C4⋊C4C2411yescharacteristic
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2411yescharacteristic
526C2×C4⋊C4C2411yescharacteristic
527C2×C4⋊C4C2411yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C42—21no—
533C2×C42—21no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—21no—
541C2×C42—21no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42—21no—
547C2×C42—21no—
548C2×C42—44no—
549C2×C42C2×D411yescharacteristic
550C2×C42C2×D411yescharacteristic
551C2×C42C2×D411yescharacteristic
552C2×C42C2×D411yescharacteristic
553C2×C42C2×D411yescharacteristic
554C2×C42C2×D411yescharacteristic
555C2×C42C2411yescharacteristic
556C2×C42C2411yescharacteristic
557C2×C42C2411yescharacteristic
558C2×C42C2411yescharacteristic
559C2×C42C2411yescharacteristic
560C2×C42C2411yescharacteristic
561#107—24no—
562#107—24no—
563#107—24no—
564#107—24no—
565#107—42no—
566#107C2×D418yes—
567#106—24no—
568#106—24no—
569#106—24no—
570#106—24no—
571#106—42no—
572#106C2×D418yes—
573C4⋊C8—24no—
574C4⋊C8—24no—
575#103—24no—
576#103—24no—
577#103—24no—
578#103—24no—
579#103—42no—
580#103—42no—
581#103C2×Q818yescomplemented
582#103C2×Q818yescomplemented
583#97—24no—
584C4×C8—24no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—21no—
598#95—21no—
599#95—21no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605#95—21no—
606#95—21no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95—21no—
613#95C2×D411yescharacteristic
614#95C2×D411yescharacteristic
615#95C2×D411yescharacteristic
616#95C2×D411yescharacteristic
617#95C2×D411yescharacteristic
618#95C2×D411yescharacteristic
619#95C2×D411yescharacteristic
620#95C2×D411yescharacteristic
621C24C22×D411yescharacteristic
622C2×Q8—24no—
623C2×Q8—22no—
624C2×Q8—28no—
625C2×Q8—28no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—42no—
631C2×Q8—42no—
632C2×Q8—42no—
633C2×Q8—42no—
634C2×Q8—44no—
635C2×Q8—44no—
636C2×Q8—42no—
637C2×Q8—44no—
638C2×Q8—44no—
639C2×Q8—42no—
640C2×Q8—42no—
641C2×Q8—44no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—42no—
645C2×Q8—44no—
646C2×Q8—81no—
647C2×Q8—81no—
648C2×Q8—81no—
649C2×Q8—81no—
650C2×Q8—82no—
651C2×Q8—82no—
652C2×Q8—816no—
653C2×Q8C22×Q814yes—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
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—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—41no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4C22×D411yescharacteristic
697C22×C4C22×D411yescharacteristic
698C22×C4C22×D411yescharacteristic
699C22×C4C22×D411yescharacteristic
700C22×C4C22×D411yescharacteristic
701C22×C4C22×D411yescharacteristic
702C22×C4C22×D411yescharacteristic
703C22×C4C22×D411yescharacteristic
704C22×C4C22×D411yescharacteristic
705C22×C4C22×D411yescharacteristic
706C22×C4C22×D411yescharacteristic
707C22×C4C22×D411yescharacteristic
708C22×C4C22×D411yescharacteristic
709C22×C4C22×D412yes—
710C22×C4C22×Q812yes—
711C22×C4H(5,𝔽2)12yes—
712C22×C42−1+412yes—
713C22×C42−1+412yes—
714C22×C42−1+412yes—
715C22×C4C2511yescharacteristic
716M16—28no—
717M16—28no—
718M16—44no—
719M16—44no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—22no—
729C2×C8—22no—
730C2×C8C22×D414yes—
731C2×C8C22×Q814yes—
732C4⋊C4—24no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—22no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—22no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—22no—
752C4⋊C4—21no—
753C4⋊C4—22no—
754C4⋊C4—22no—
755C4⋊C4—41no—
756C4⋊C4—41no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—42no—
762C4⋊C4—42no—
763C4⋊C4—42no—
764C4⋊C4—42no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4—42no—
771C4⋊C4—42no—
772C4⋊C4—42no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C4⋊C4—42no—
777C4⋊C4—42no—
778C4⋊C4—42no—
779C4⋊C4—42no—
780C4⋊C4—42no—
781C4⋊C4—81no—
782C4⋊C4—81no—
783C4⋊C4—81no—
784C4⋊C4—81no—
785C4⋊C4—81no—
786C4⋊C4—81no—
787C4⋊C4—82no—
788C4⋊C4—82no—
789C4⋊C4—82no—
790C4⋊C4—82no—
791C4⋊C4#13714yes—
792C4⋊C4C22×D412yes—
793C4⋊C4C22×D412yes—
794C4⋊C4C22×D414yes—
795C4⋊C4C22×Q812yes—
796C4⋊C4C22×Q812yes—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—42no—
800C22⋊C4—42no—
801C42—22no—
802C42—22no—
803C42—22no—
804C42—22no—
805C42—22no—
806C42—22no—
807C42—24no—
808C42—24no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—21no—
818C42—21no—
819C42—21no—
820C42—21no—
821C42—44no—
822C42—44no—
823C42—42no—
824C42—42no—
825C42—42no—
826C42—42no—
827C42—81no—
828C42—81no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23#53612yes—
834C23D4212yes—
835C23D4×Q812yes—
836C23C23×D411yescharacteristic
837Q8—24no—
838Q8—24no—
839Q8—48no—
840Q8—42no—
841Q8—42no—
842Q8—84no—
843Q8—84no—
844Q8—84no—
845Q8—88no—
846Q8—84no—
847Q8—88no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—42no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—48no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—42no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—82no—
923C2×C4—82no—
924C2×C4—84no—
925C2×C4—84no—
926C2×C4#53612yes—
927C2×C4#53614yes—
928C2×C4#54414yes—
929C2×C4D4212yes—
930C2×C4D4×Q812yes—
931C2×C4D4×Q814yes—
932C2×C4#56314yes—
933C2×C4C2×#13712yes—
934C2×C4C2×#13712yes—
935C2×C4C2×#13712yes—
936C2×C4#57512yes—
937C2×C4C23×D411yescharacteristic
938C2×C4C23×Q811yescharacteristic
939C2×C4C2×H(5,𝔽2)11yescharacteristic
940C2×C4C2×2−1+411yescharacteristic
941C2×C4C2×2−1+411yescharacteristic
942C2×C4C2×2−1+411yescharacteristic
943C8—24no—
944C8—24no—
945C8—42no—
946C8—42no—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—22no—
952C22—22no—
953C22#267714yes—
954C22C2×#53611yescharacteristic
955C22C2×D4211yescharacteristic
956C22C2×D4×Q811yescharacteristic
957C22C22×#13711yescharacteristic
958C22C2×#57511yescharacteristic
959C22#358511yescharacteristic
960C22#358611yescharacteristic
961C4—22no—
962C4—22no—
963C4—22no—
964C4—22no—
965C4—44no—
966C4—41no—
967C4—41no—
968C4—41no—
969C4—44no—
970C4—42no—
971C4—41no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—41no—
977C4—41no—
978C4—41no—
979C4—82no—
980C4—81no—
981C4—81no—
982C4—81no—
983C4—81no—
984C4—82no—
985C4#267714yes—
986C4C2×#53611yescharacteristic
987C4C2×#54411yescharacteristic
988C4C2×D4×Q811yescharacteristic
989C4C2×#56311yescharacteristic
990C2—24no—
991C2C2×#267711yescharacteristic
992C2#6086511yescharacteristic
993C2#6087011yescharacteristic
994C2#6106611yescharacteristic
995C2D4×#13711yescharacteristic
996C2Q8×#13711yescharacteristic
997C2#6136911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #30977C2semidirect
6. #30976C2semidirect
7. #30969C2semidirect
8. #30968C2semidirect
9. #30957C2semidirect
10. #30956C2semidirect
11. #30949C2semidirect
12. #30948C2semidirect
230. #419Q8semidirect
581. #103C2×Q8semidirect
582. #103C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#31652
C2×#30782
#349382
C2×#24512
#309772
#309762
#309692
#309682
#309572
#309562
#309492
#309482
#237322
#236702
#236572
#235542
#235522
#234552
#210942
#210612
#210342
#210232
#208742