Finite Group Databasebeta

← C2×#60315 #10574475

Subgroups — C2×#60315 #10574475

Order 512.

6602 conjugacy classes of subgroups.

The subgroup lattice has 1093 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3529C211yesmaximal, characteristic
2#60315C2132yesmaximal, direct product factor
3C2×#2994C212yesmaximal, complemented
4C2×#2993C212yesmaximal, complemented
5C2×#2992C212yesmaximal, complemented
6C2×#2981C212yesmaximal, complemented
7C2×#2979C211yesmaximal, characteristic, complemented
8C2×#2978C212yesmaximal, complemented
9C2×#2978C211yesmaximal, characteristic, complemented
10C2×#2977C211yesmaximal, characteristic, complemented
11C2×#2976C212yesmaximal, complemented
12C2×#2969C212yesmaximal, complemented
13C2×#2968C212yesmaximal, complemented
14C2×#2967C212yesmaximal, complemented
15C2×#2935C212yesmaximal, complemented
16C2×#2933C212yesmaximal, complemented
17C2×#2932C211yesmaximal, characteristic, complemented
18C2×#2930C211yesmaximal, characteristic, complemented
19C2×#2929C211yesmaximal, characteristic, complemented
20C2×#2929C212yesmaximal, complemented
21C22×#131C2211yescharacteristic
22C22×#131C2212yes—
23C22×#131C2211yescharacteristic, complemented
24C23×M16C2211yescharacteristic, complemented
25C24×C8C2211yescharacteristic, complemented
26#3529C4116yes—
27#3529C22116yes—
28C2×#563C411yescharacteristic
29C2×#563C412yes—
30C2×#562C412yes—
31C2×#562C412yes—
32C2×#562C412yes—
33C2×H(3,𝔽4)C411yescharacteristic
34C2×#560C411yescharacteristic
35C2×#560C412yes—
36C2×#560C411yescharacteristic
37C2×#560C412yes—
38C2×#532C2211yescharacteristic
39C2×#532C2212yes—
40C2×#529C2212yes—
41C2×#529C2212yes—
42C2×#529C2212yes—
43C2×#525C2212yes—
44C2×#525C2211yescharacteristic
45C2×#525C2211yescharacteristic
46C2×#525C2212yes—
47#2994C22132yescomplemented
48#2993C22132yescomplemented
49#2992C22132yescomplemented
50#2981C22132yescomplemented
51#2979C22116yescomplemented
52#2978C22116yescomplemented
53#2978C22132yescomplemented
54#2977C22116yescomplemented
55#2976C22132yescomplemented
56#2969C22132yescomplemented
57#2968C22132yescomplemented
58#2967C22132yescomplemented
59C2×#446C2212yescomplemented
60C2×#446C2212yescomplemented
61C2×#446C2212yescomplemented
62C2×C8×Q8C2212yescomplemented
63#2935C22132yescomplemented
64#2933C22132yescomplemented
65#2932C22116yescomplemented
66#2930C22116yescomplemented
67#2929C22116yescomplemented
68#2929C22132yescomplemented
69C2×#436C2212yes—
70C2×#436C2212yes—
71C2×#436C2212yes—
72C2×#436C2212yescomplemented
73C2×#436C2212yescomplemented
74C2×#436C2212yescomplemented
75C2×#436C2212yescomplemented
76C2×#436C2212yescomplemented
77C2×#436C2212yescomplemented
78C2×#435C2212yes—
79C2×#435C2212yes—
80C2×#435C2212yes—
81C2×#435C2212yes—
82C2×#435C2212yes—
83C2×#435C2212yes—
84C2×#435C2212yescomplemented
85C2×#435C2212yescomplemented
86C2×#435C2212yescomplemented
87C2×#435C2212yescomplemented
88C2×#435C2212yescomplemented
89C2×#435C2212yescomplemented
90C2×#435C2212yescomplemented
91C2×#435C2212yescomplemented
92C2×#435C2212yescomplemented
93C2×#435C2212yescomplemented
94C2×#435C2212yescomplemented
95C2×#435C2212yescomplemented
96C2×C8×D4C2212yes—
97C2×C8×D4C2212yes—
98C2×C8×D4C2212yes—
99C2×C8×D4C2212yescomplemented
100C2×C8×D4C2212yescomplemented
101C2×C8×D4C2212yescomplemented
102C2×C8×D4C2212yescomplemented
103C2×C8×D4C2212yescomplemented
104C2×C8×D4C2212yescomplemented
105C2×#433C2212yescomplemented
106C2×#433C2212yescomplemented
107C2×#433C2212yescomplemented
108C2×#433C2212yescomplemented
109C2×#433C2212yescomplemented
110C2×#433C2212yescomplemented
111C2×#432C2212yescomplemented
112C2×#431C2212yescomplemented
113C2×#431C2212yescomplemented
114C2×#424C2211yescharacteristic, complemented
115C2×#424C2212yescomplemented
116C2×#424C2212yescomplemented
117C2×#424C2211yescharacteristic, complemented
118C2×#423C2211yescharacteristic, complemented
119C22×C4⋊C8C2212yescomplemented
120C2×#408C2212yes—
121C2×#408C2212yes—
122C2×#408C2211yescharacteristic
123C2×#408C2211yescharacteristic
124C2×#408C2211yescharacteristic
125C2×#408C2212yes—
126C2×#408C2212yescomplemented
127C2×#408C2211yescharacteristic, complemented
128C2×#407C2211yescharacteristic, complemented
129C2×#407C2211yescharacteristic, complemented
130C2×#407C2212yescomplemented
131C22×C22⋊C8C2212yescomplemented
132C2×#405C2211yescharacteristic, complemented
133C2×#405C2212yescomplemented
134C2×#405C2212yescomplemented
135C2×#405C2211yescharacteristic, complemented
136C2×C4×M16C2212yescomplemented
137C22×#97C2211yescharacteristic, complemented
138C22×#41C2312yes—
139C22×#41C2311yescharacteristic
140C22×#41C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C2×#131—44no—
144C2×#131—48no—
145C2×#131—44no—
146C2×#131C2318yes—
147C2×#131C23116yes—
148C2×#131C2318yescomplemented
149C22×M16—44no—
150C22×M16C2312yes—
151C22×M16C2312yes—
152C22×M16C2312yes—
153C22×M16C2311yescharacteristic
154C22×M16C2312yes—
155C22×M16C2311yescharacteristic
156C22×M16C2311yescharacteristic
157C22×M16C2312yes—
158C22×M16C2311yescharacteristic
159C22×M16C2311yescharacteristic
160C22×M16C2312yes—
161C22×M16C2311yescharacteristic
162C22×M16C2318yescomplemented
163C23×C8—44no—
164C23×C8C2311yescharacteristic
165C23×C8C2311yescharacteristic
166C23×C8C2312yes—
167C23×C8C2311yescharacteristic
168C23×C8C2311yescharacteristic
169C23×C8C2312yes—
170C23×C8C2312yes—
171C23×C8C2312yes—
172C23×C8C2311yescharacteristic
173C23×C8C2312yes—
174C23×C8C2311yescharacteristic
175C23×C8C2312yes—
176C23×C8C2318yescomplemented
177#563C2×C4132yes—
178#563C2×C4116yes—
179#562C2×C4132yes—
180#562C2×C4132yes—
181#562C2×C4132yes—
182H(3,𝔽4)C2×C4116yes—
183#560C2×C4132yes—
184#560C2×C4116yes—
185#560C2×C4132yes—
186#560C2×C4116yes—
187#532C2×C418yes—
188#532C2×C4116yes—
189#532C2318yes—
190#532C23116yes—
191C2×C4⋊Q8C2×C411yescharacteristic
192C2×C4⋊Q8C2×C412yes—
193C2×#127C2×C411yescharacteristic
194C2×#127C2×C412yes—
195#529C2×C4116yes—
196#529C2×C4116yes—
197#529C2×C4116yes—
198#529C23116yes—
199#529C23116yes—
200#529C23116yes—
201C2×#126C2×C412yes—
202C2×#126C2×C412yes—
203C2×#126C2×C412yes—
204C2×#126C2×C412yes—
205C2×#126C2×C412yes—
206C2×#126C2×C412yes—
207C2×#125C2×C412yes—
208C2×#125C2×C412yes—
209C2×#125C2×C412yes—
210C2×#124C2×C412yes—
211C2×#124C2×C412yes—
212C2×#124C2×C412yes—
213C2×#124C2×C411yescharacteristic
214C2×#124C2×C412yes—
215C2×#124C2×C411yescharacteristic
216C2×#124C2×C412yes—
217#525C2×C4116yes—
218#525C2×C418yes—
219#525C2×C418yes—
220#525C2×C4116yes—
221#525C2318yes—
222#525C23116yes—
223#525C2318yes—
224#525C23116yes—
225C2×#123C2×C412yes—
226C2×#123C2×C411yescharacteristic
227C2×#123C2×C411yescharacteristic
228C2×#123C2×C412yes—
229C2×#123C2×C412yes—
230C2×#123C2×C411yescharacteristic
231C2×#123C2×C411yescharacteristic
232C2×#123C2×C412yes—
233C2×#123C2×C412yes—
234C2×#123C2×C412yes—
235C2×#123C2×C412yes—
236C2×#123C2×C412yes—
237C2×#123C2×C412yes—
238C2×#123C2×C412yes—
239C2×C22⋊Q8C2×C412yes—
240C2×C22⋊Q8C2×C412yes—
241C2×C22⋊Q8C2×C412yes—
242C2×C22⋊Q8C2×C412yes—
243C2×C22⋊Q8C2×C412yes—
244C2×C22⋊Q8C2×C412yes—
245C2×C22⋊Q8C2×C412yes—
246C2×C22⋊Q8C2×C412yes—
247C2×C22⋊Q8C2×C412yes—
248C2×#121C2×C412yes—
249C2×#121C2×C412yes—
250C2×#121C2×C412yes—
251C2×#121C2×C412yes—
252C2×#121C2×C412yes—
253C2×#121C2×C412yes—
254C2×#121C2×C412yes—
255C2×#121C2×C412yes—
256C2×#121C2×C412yes—
257C2×#121C2×C412yes—
258C2×#121C2×C412yes—
259C2×#121C2×C412yes—
260C2×#121C2×C412yes—
261C2×#121C2×C412yes—
262C2×#121C2×C412yes—
263C2×#120C2×C412yes—
264C2×#120C2×C411yescharacteristic
265C2×#120C2×C411yescharacteristic
266C2×#120C2×C412yes—
267C2×#120C2×C412yes—
268C2×#120C2×C411yescharacteristic
269C2×#120C2×C411yescharacteristic
270C2×#120C2×C412yes—
271C2×C4×Q8C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×#117C2311yescharacteristic
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2311yescharacteristic
285C22×C42C2311yescharacteristic
286C22×C42C2312yes—
287#446C23116yescomplemented
288#446C23116yescomplemented
289#446C23116yescomplemented
290C8×Q8C23116yescomplemented
291#436C23116yes—
292#436C23116yes—
293#436C23116yes—
294#436C23116yescomplemented
295#436C23116yescomplemented
296#436C23116yescomplemented
297#436C23116yescomplemented
298#436C23116yescomplemented
299#436C23116yescomplemented
300#435C23116yes—
301#435C23116yes—
302#435C23116yes—
303#435C23116yes—
304#435C23116yes—
305#435C23116yes—
306#435C23116yescomplemented
307#435C23116yescomplemented
308#435C23116yescomplemented
309#435C23116yescomplemented
310#435C23116yescomplemented
311#435C23116yescomplemented
312#435C23116yescomplemented
313#435C23116yescomplemented
314#435C23116yescomplemented
315#435C23116yescomplemented
316#435C23116yescomplemented
317#435C23116yescomplemented
318C8×D4C23116yes—
319C8×D4C23116yes—
320C8×D4C23116yes—
321C8×D4C23116yescomplemented
322C8×D4C23116yescomplemented
323C8×D4C23116yescomplemented
324C8×D4C23116yescomplemented
325C8×D4C23116yescomplemented
326C8×D4C23116yescomplemented
327#433C23116yescomplemented
328#433C23116yescomplemented
329#433C23116yescomplemented
330#433C23116yescomplemented
331#433C23116yescomplemented
332#433C23116yescomplemented
333#432C23116yescomplemented
334#431C23116yescomplemented
335#431C23116yescomplemented
336#424C23116yescomplemented
337#424C2318yescomplemented
338#424C2318yescomplemented
339#424C23116yescomplemented
340#423C2318yescomplemented
341C2×C4⋊C8C2312yes—
342C2×C4⋊C8C2312yes—
343C2×C4⋊C8C2312yes—
344C2×C4⋊C8C2312yes—
345C2×C4⋊C8C2312yes—
346C2×C4⋊C8C2312yes—
347C2×C4⋊C8C2312yes—
348C2×C4⋊C8C2312yes—
349C2×C4⋊C8C2312yes—
350C2×C4⋊C8C2312yes—
351C2×C4⋊C8C2312yes—
352C2×C4⋊C8C2312yes—
353C2×C4⋊C8C23116yescomplemented
354#408C23116yes—
355#408C2318yes—
356#408C2318yes—
357#408C2318yes—
358#408C23116yes—
359#408C23116yes—
360#408C2318yescomplemented
361#408C23116yescomplemented
362#407C23116yescomplemented
363#407C2318yescomplemented
364#407C2318yescomplemented
365C2×C22⋊C8C2312yes—
366C2×C22⋊C8C2312yes—
367C2×C22⋊C8C2312yes—
368C2×C22⋊C8C2312yes—
369C2×C22⋊C8C2312yes—
370C2×C22⋊C8C2312yes—
371C2×C22⋊C8C2312yes—
372C2×C22⋊C8C2312yes—
373C2×C22⋊C8C2312yes—
374C2×C22⋊C8C2312yes—
375C2×C22⋊C8C2312yes—
376C2×C22⋊C8C2312yes—
377C2×C22⋊C8C2312yes—
378C2×C22⋊C8C2312yes—
379C2×C22⋊C8C2312yes—
380C2×C22⋊C8C2312yes—
381C2×C22⋊C8C2312yes—
382C2×C22⋊C8C2312yes—
383C2×C22⋊C8C23116yescomplemented
384#405C2318yescomplemented
385#405C23116yescomplemented
386#405C2318yescomplemented
387#405C23116yescomplemented
388C4×M16C23116yescomplemented
389C2×#97C2312yes—
390C2×#97C2312yes—
391C2×#97C2312yes—
392C2×#97C2312yes—
393C2×#97C2312yes—
394C2×#97C2312yes—
395C2×#97C2318yescomplemented
396C2×C4×C8C2312yes—
397C2×C4×C8C2312yes—
398C2×C4×C8C2312yes—
399C2×C4×C8C2312yes—
400C2×C4×C8C2312yes—
401C2×C4×C8C2312yes—
402C25C22×C411yescharacteristic
403C25C22×C411yescharacteristic
404C2×#41—42no—
405C2×#41—44no—
406C2×#41—42no—
407C2×#41—44no—
408C2×#41—42no—
409C2×#41—42no—
410C2×#41C22×C418yes—
411C2×#41C22×C414yes—
412C2×#41C22×C414yes—
413C2×#41C2414yes—
414C2×#41C2418yes—
415C2×#41C2414yes—
416C22×Q8C22×C412yes—
417C22×Q8C22×C412yes—
418C22×Q8C22×C411yescharacteristic
419C22×Q8C22×C411yescharacteristic
420C22×D4C22×C412yes—
421C22×D4C22×C412yes—
422C22×D4C22×C412yes—
423C22×D4C22×C412yes—
424C22×D4C22×C412yes—
425C22×D4C22×C412yes—
426C22×D4C22×C412yes—
427C22×D4C22×C412yes—
428C22×D4C22×C412yes—
429C22×D4C22×C412yes—
430C22×D4C22×C411yescharacteristic
431C22×D4C22×C412yes—
432C22×D4C22×C411yescharacteristic
433C22×D4C22×C412yes—
434C22×D4C22×C411yescharacteristic
435C22×D4C22×C412yes—
436C22×D4C22×C411yescharacteristic
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4C22×C412yes—
442C23×C4C22×C412yes—
443C23×C4C22×C412yes—
444C23×C4C22×C411yescharacteristic
445C23×C4C22×C412yes—
446C23×C4C22×C411yescharacteristic
447C23×C4C22×C412yes—
448C23×C4C22×C414yes—
449C23×C4C22×C414yes—
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2414yes—
457C23×C4C2414yes—
458#131—416no—
459#131—432no—
460#131—416no—
461C2×M16—28no—
462C2×M16—28no—
463C2×M16—44no—
464C2×M16—44no—
465C2×M16—42no—
466C2×M16—44no—
467C2×M16—42no—
468C2×M16—42no—
469C2×M16—42no—
470C2×M16—42no—
471C2×M16—44no—
472C2×M16—42no—
473C2×M16—416no—
474C2×M16C2418yes—
475C2×M16C2418yes—
476C2×M16C2418yes—
477C2×M16C2414yes—
478C2×M16C2418yes—
479C2×M16C2414yes—
480C2×M16C2414yes—
481C2×M16C2414yes—
482C2×M16C2418yes—
483C2×M16C2414yes—
484C2×M16C2418yes—
485C2×M16C2414yes—
486C22×C8—28no—
487C22×C8—24no—
488C22×C8—24no—
489C22×C8—24no—
490C22×C8—416no—
491C22×C8—42no—
492C22×C8—44no—
493C22×C8—42no—
494C22×C8—44no—
495C22×C8—42no—
496C22×C8—44no—
497C22×C8—44no—
498C22×C8—44no—
499C22×C8C2418yes—
500C22×C8C2414yes—
501C22×C8C2414yes—
502C22×C8C2414yes—
503C22×C8C2412yes—
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2412yes—
507C22×C8C2412yes—
508C22×C8C2412yes—
509C22×C8C2411yescharacteristic
510C22×C8C2412yes—
511C22×C8C2412yes—
512C22×C8C2414yes—
513C22×C8C2418yes—
514C22×C8C2414yes—
515C22×C8C2418yes—
516C22×C8C2418yes—
517C22×C8C2418yes—
518C22×C8C2414yes—
519C22×C8C2418yes—
520C22×C8C2411yescharacteristic
521C4⋊Q8C22×C418yes—
522C4⋊Q8C22×C4116yes—
523#127C22×C418yes—
524#127C22×C4116yes—
525#126C22×C4116yes—
526#126C22×C4116yes—
527#126C22×C4116yes—
528#126C22×C4116yes—
529#126C22×C4116yes—
530#126C22×C4116yes—
531#125C22×C4116yes—
532#125C22×C4116yes—
533#125C22×C4116yes—
534#124C22×C4116yes—
535#124C22×C4116yes—
536#124C22×C4116yes—
537#124C22×C418yes—
538#124C22×C4116yes—
539#124C22×C418yes—
540#124C22×C4116yes—
541#123C22×C418yes—
542#123C22×C4116yes—
543#123C22×C418yes—
544#123C22×C4116yes—
545#123C22×C418yes—
546#123C22×C4116yes—
547#123C22×C418yes—
548#123C22×C4116yes—
549#123C22×C4116yes—
550#123C22×C4116yes—
551#123C22×C4116yes—
552#123C22×C4116yes—
553#123C22×C4116yes—
554#123C22×C4116yes—
555C22⋊Q8C22×C4116yes—
556C22⋊Q8C22×C4116yes—
557C22⋊Q8C22×C4116yes—
558C22⋊Q8C22×C4116yes—
559C22⋊Q8C22×C4116yes—
560C22⋊Q8C22×C4116yes—
561C22⋊Q8C22×C4116yes—
562C22⋊Q8C22×C4116yes—
563C22⋊Q8C22×C4116yes—
564#121C22×C4116yes—
565#121C22×C4116yes—
566#121C22×C4116yes—
567#121C22×C4116yes—
568#121C22×C4116yes—
569#121C22×C4116yes—
570#121C22×C4116yes—
571#121C22×C4116yes—
572#121C22×C4116yes—
573#121C22×C4116yes—
574#121C22×C4116yes—
575#121C22×C4116yes—
576#121C22×C4116yes—
577#121C22×C4116yes—
578#121C22×C4116yes—
579#120C22×C418yes—
580#120C22×C4116yes—
581#120C22×C418yes—
582#120C22×C4116yes—
583#120C22×C418yes—
584#120C22×C4116yes—
585#120C22×C418yes—
586#120C22×C4116yes—
587C4×Q8C22×C418yes—
588C4×Q8C2418yes—
589C4×D4C22×C418yes—
590C4×D4C22×C418yes—
591C4×D4C22×C418yes—
592C4×D4C22×C418yes—
593C4×D4C22×C418yes—
594C4×D4C22×C418yes—
595C4×D4C22×C418yes—
596C4×D4C22×C418yes—
597C4×D4C22×C418yes—
598C4×D4C2418yes—
599C4×D4C2418yes—
600C4×D4C2418yes—
601C4×D4C2418yes—
602C4×D4C2418yes—
603C4×D4C2418yes—
604C4×D4C2418yes—
605C4×D4C2418yes—
606C4×D4C2418yes—
607#117C22×C414yes—
608#117C22×C418yes—
609#117C22×C418yes—
610#117C22×C414yes—
611#117C2414yes—
612#117C2418yes—
613#117C2414yes—
614#117C2418yes—
615C2×C4⋊C4C22×C412yes—
616C2×C4⋊C4C22×C412yes—
617C2×C4⋊C4C22×C412yes—
618C2×C4⋊C4C22×C412yes—
619C2×C4⋊C4C22×C412yes—
620C2×C4⋊C4C22×C412yes—
621C2×C4⋊C4C22×C412yes—
622C2×C4⋊C4C22×C412yes—
623C2×C4⋊C4C22×C412yes—
624C2×C4⋊C4C22×C412yes—
625C2×C4⋊C4C22×C412yes—
626C2×C4⋊C4C22×C412yes—
627C2×C4⋊C4C22×C412yes—
628C2×C4⋊C4C22×C412yes—
629C2×C4⋊C4C22×C412yes—
630C2×C4⋊C4C22×C412yes—
631C2×C4⋊C4C22×C412yes—
632C2×C4⋊C4C22×C412yes—
633C2×C22⋊C4C22×C411yescharacteristic
634C2×C22⋊C4C22×C412yes—
635C2×C22⋊C4C22×C412yes—
636C2×C22⋊C4C22×C411yescharacteristic
637C2×C22⋊C4C22×C411yescharacteristic
638C2×C22⋊C4C22×C412yes—
639C2×C22⋊C4C22×C412yes—
640C2×C22⋊C4C22×C411yescharacteristic
641C2×C22⋊C4C22×C412yes—
642C2×C22⋊C4C22×C412yes—
643C2×C22⋊C4C22×C412yes—
644C2×C22⋊C4C22×C412yes—
645C2×C22⋊C4C22×C412yes—
646C2×C22⋊C4C22×C412yes—
647C2×C22⋊C4C22×C412yes—
648C2×C22⋊C4C22×C412yes—
649C2×C22⋊C4C22×C412yes—
650C2×C22⋊C4C22×C412yes—
651C2×C22⋊C4C22×C412yes—
652C2×C22⋊C4C22×C412yes—
653C2×C22⋊C4C22×C412yes—
654C2×C22⋊C4C22×C412yes—
655C2×C22⋊C4C22×C412yes—
656C2×C22⋊C4C22×C412yes—
657C2×C22⋊C4C22×C412yes—
658C2×C22⋊C4C22×C412yes—
659C2×C42C22×C411yescharacteristic
660C2×C42C22×C412yes—
661C2×C42C22×C411yescharacteristic
662C2×C42C22×C412yes—
663C2×C42C22×C414yes—
664C2×C42C22×C418yes—
665C2×C42C2414yes—
666C2×C42C2418yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C4⋊C8C2418yes—
671C4⋊C8C2418yes—
672C4⋊C8C2418yes—
673C4⋊C8C2418yes—
674C4⋊C8C2418yes—
675C4⋊C8C2418yes—
676C4⋊C8C2418yes—
677C4⋊C8C2418yes—
678C4⋊C8C2418yes—
679C4⋊C8C2418yes—
680C4⋊C8C2418yes—
681C4⋊C8C2418yes—
682C22⋊C8C2418yes—
683C22⋊C8C2418yes—
684C22⋊C8C2418yes—
685C22⋊C8C2418yes—
686C22⋊C8C2418yes—
687C22⋊C8C2418yes—
688C22⋊C8C2418yes—
689C22⋊C8C2418yes—
690C22⋊C8C2418yes—
691C22⋊C8C2418yes—
692C22⋊C8C2418yes—
693C22⋊C8C2418yes—
694C22⋊C8C2418yes—
695C22⋊C8C2418yes—
696C22⋊C8C2418yes—
697C22⋊C8C2418yes—
698C22⋊C8C2418yes—
699C22⋊C8C2418yes—
700#97C2418yes—
701#97C2418yes—
702#97C2418yes—
703#97C2418yes—
704#97C2418yes—
705#97C2418yes—
706C4×C8C2418yes—
707C4×C8C2418yes—
708C4×C8C2418yes—
709C4×C8C2418yes—
710C4×C8C2418yes—
711C4×C8C2418yes—
712C24—42no—
713C24—44no—
714C24—42no—
715C24—44no—
716C24C23×C412yes—
717C24C23×C411yescharacteristic
718C24C23×C411yescharacteristic
719C24C23×C412yes—
720C24C23×C411yescharacteristic
721C24C23×C412yes—
722C24C23×C414yes—
723C24C23×C414yes—
724#41—44no—
725#41—48no—
726#41—44no—
727#41—48no—
728#41—416no—
729#41—48no—
730#41—48no—
731#41—44no—
732#41—44no—
733C2×Q8—44no—
734C2×Q8—42no—
735C2×Q8—44no—
736C2×Q8—42no—
737C2×Q8C23×C418yes—
738C2×Q8C23×C414yes—
739C2×Q8C23×C418yes—
740C2×Q8C23×C414yes—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—42no—
755C2×D4—44no—
756C2×D4—42no—
757C2×D4—44no—
758C2×D4C23×C418yes—
759C2×D4C23×C418yes—
760C2×D4C23×C418yes—
761C2×D4C23×C418yes—
762C2×D4C23×C418yes—
763C2×D4C23×C418yes—
764C2×D4C23×C418yes—
765C2×D4C23×C418yes—
766C2×D4C23×C418yes—
767C2×D4C23×C414yes—
768C2×D4C23×C418yes—
769C2×D4C23×C414yes—
770C2×D4C23×C418yes—
771C2×D4C23×C414yes—
772C2×D4C23×C418yes—
773C2×D4C23×C418yes—
774C2×D4C23×C414yes—
775C22×C4—24no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—22no—
783C22×C4—24no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—24no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—48no—
790C22×C4—48no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—42no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—42no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C23×C411yescharacteristic
801C22×C4C23×C412yes—
802C22×C4C23×C412yes—
803C22×C4C23×C414yes—
804C22×C4C23×C412yes—
805C22×C4C23×C412yes—
806C22×C4C23×C412yes—
807C22×C4C23×C412yes—
808C22×C4C23×C412yes—
809C22×C4C23×C412yes—
810C22×C4C23×C411yescharacteristic
811C22×C4C23×C412yes—
812C22×C4C23×C411yescharacteristic
813C22×C4C23×C412yes—
814C22×C4C23×C412yes—
815C22×C4C23×C414yes—
816C22×C4C23×C412yes—
817C22×C4C23×C414yes—
818C22×C4C23×C418yes—
819C22×C4C23×C418yes—
820C22×C4C23×C418yes—
821C22×C4C23×C418yes—
822C22×C4C23×C414yes—
823C22×C4C23×C418yes—
824C22×C4C23×C414yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832M16—216no—
833M16—216no—
834M16—48no—
835M16—48no—
836M16—44no—
837M16—48no—
838M16—44no—
839M16—44no—
840M16—44no—
841M16—44no—
842M16—48no—
843M16—44no—
844C2×C8—24no—
845C2×C8—22no—
846C2×C8—22no—
847C2×C8—22no—
848C2×C8—24no—
849C2×C8—24no—
850C2×C8—24no—
851C2×C8—24no—
852C2×C8—24no—
853C2×C8—216no—
854C2×C8—28no—
855C2×C8—28no—
856C2×C8—28no—
857C2×C8—44no—
858C2×C8—48no—
859C2×C8—44no—
860C2×C8—48no—
861C2×C8—44no—
862C2×C8—48no—
863C2×C8—48no—
864C2×C8—48no—
865C2×C8H(5,𝔽2)14yes—
866C2×C8C2514yes—
867C2×C8C2514yes—
868C2×C8C2514yes—
869C2×C8C2512yes—
870C2×C8C2514yes—
871C2×C8C2514yes—
872C2×C8C2514yes—
873C2×C8C2512yes—
874C2×C8C2512yes—
875C2×C8C2512yes—
876C4⋊C4C23×C418yes—
877C4⋊C4C23×C418yes—
878C4⋊C4C23×C418yes—
879C4⋊C4C23×C418yes—
880C4⋊C4C23×C418yes—
881C4⋊C4C23×C418yes—
882C4⋊C4C23×C418yes—
883C4⋊C4C23×C418yes—
884C4⋊C4C23×C418yes—
885C4⋊C4C23×C418yes—
886C4⋊C4C23×C418yes—
887C4⋊C4C23×C418yes—
888C4⋊C4C23×C418yes—
889C4⋊C4C23×C418yes—
890C4⋊C4C23×C418yes—
891C4⋊C4C23×C418yes—
892C4⋊C4C23×C418yes—
893C4⋊C4C23×C418yes—
894C22⋊C4C23×C414yes—
895C22⋊C4C23×C418yes—
896C22⋊C4C23×C414yes—
897C22⋊C4C23×C418yes—
898C22⋊C4C23×C414yes—
899C22⋊C4C23×C418yes—
900C22⋊C4C23×C414yes—
901C22⋊C4C23×C418yes—
902C22⋊C4C23×C418yes—
903C22⋊C4C23×C418yes—
904C22⋊C4C23×C418yes—
905C22⋊C4C23×C418yes—
906C22⋊C4C23×C418yes—
907C22⋊C4C23×C418yes—
908C22⋊C4C23×C418yes—
909C22⋊C4C23×C418yes—
910C22⋊C4C23×C418yes—
911C22⋊C4C23×C418yes—
912C22⋊C4C23×C418yes—
913C22⋊C4C23×C418yes—
914C22⋊C4C23×C418yes—
915C22⋊C4C23×C418yes—
916C22⋊C4C23×C418yes—
917C22⋊C4C23×C418yes—
918C22⋊C4C23×C418yes—
919C22⋊C4C23×C418yes—
920C42C23×C414yes—
921C42C23×C414yes—
922C42C23×C414yes—
923C42C23×C414yes—
924C42C23×C418yes—
925C42C23×C414yes—
926C42C23×C418yes—
927C42C2514yes—
928C42C2514yes—
929C42C2514yes—
930C23—24no—
931C23—22no—
932C23—22no—
933C23—24no—
934C23—22no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—44no—
946C23—48no—
947C23—44no—
948C23—48no—
949C23—416no—
950C23—88no—
951C23C24×C412yes—
952C23C24×C414yes—
953C23C24×C412yes—
954C23C24×C414yes—
955C23C24×C412yes—
956C23C24×C414yes—
957C23C24×C411yescharacteristic
958Q8—48no—
959Q8—44no—
960Q8—48no—
961Q8—44no—
962D4—48no—
963D4—48no—
964D4—48no—
965D4—48no—
966D4—48no—
967D4—48no—
968D4—48no—
969D4—48no—
970D4—48no—
971D4—44no—
972D4—44no—
973D4—48no—
974D4—48no—
975D4—44no—
976D4—48no—
977D4—44no—
978D4—48no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—28no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—28no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—44no—
1010C2×C4—48no—
1011C2×C4—48no—
1012C2×C4—44no—
1013C2×C4—48no—
1014C2×C4—48no—
1015C2×C4—48no—
1016C2×C4C24×C412yes—
1017C2×C4C24×C414yes—
1018C2×C4C24×C414yes—
1019C2×C4C24×C414yes—
1020C2×C4C24×C414yes—
1021C2×C4C24×C414yes—
1022C2×C4C24×C414yes—
1023C2×C4C24×C414yes—
1024C2×C4C24×C412yes—
1025C2×C4C24×C414yes—
1026C2×C4C24×C412yes—
1027C2×C4C24×C414yes—
1028C2×C4C24×C411yescharacteristic
1029C2×C4C2×H(5,𝔽2)12yes—
1030C2×C4#58512yes—
1031C2×C4C2611yescharacteristic
1032C8—24no—
1033C8—22no—
1034C8—22no—
1035C8—22no—
1036C8—24no—
1037C8—24no—
1038C8—24no—
1039C8—24no—
1040C8—24no—
1041C8C2×H(5,𝔽2)14yes—
1042C22—24no—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—24no—
1052C22—22no—
1053C22—22no—
1054C22—24no—
1055C22—22no—
1056C22—24no—
1057C22—416no—
1058C22—44no—
1059C22—48no—
1060C22—48no—
1061C22—44no—
1062C22—44no—
1063C22—48no—
1064C22—88no—
1065C22C4×H(5,𝔽2)12yes—
1066C22#357314yes—
1067C22C25×C411yescharacteristic
1068C4—24no—
1069C4—24no—
1070C4—24no—
1071C4—24no—
1072C4—24no—
1073C4—24no—
1074C4—24no—
1075C4—22no—
1076C4—22no—
1077C4—24no—
1078C4—22no—
1079C4—24no—
1080C4C4×H(5,𝔽2)12yes—
1081C4C22×H(5,𝔽2)11yescharacteristic
1082C4C2×#58511yescharacteristic
1083C2—42no—
1084C2—44no—
1085C2—42no—
1086C2—44no—
1087C2—42no—
1088C2—44no—
1089C2#6031514yesdirect product factor
1090C2C2×C4×H(5,𝔽2)11yescharacteristic
1091C2C2×#357312yes—
subgroupG/H
centerC22×C4C25
commutatorC22C25×C4
Frattini, cosocleC2×C4C26
socleC23C24×C4
prime radicalC2×#3529C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60315C2direct (N × H)
3. C2×#2994C2semidirect
4. C2×#2993C2semidirect
5. C2×#2992C2semidirect
6. C2×#2981C2semidirect
7. C2×#2979C2semidirect
8. C2×#2978C2semidirect
9. C2×#2978C2semidirect
10. C2×#2977C2semidirect
11. C2×#2976C2semidirect
12. C2×#2969C2semidirect
13. C2×#2968C2semidirect
14. C2×#2967C2semidirect
15. C2×#2935C2semidirect
16. C2×#2933C2semidirect
17. C2×#2932C2semidirect
18. C2×#2930C2semidirect
19. C2×#2929C2semidirect
20. C2×#2929C2semidirect
23. C22×#131C22semidirect
24. C23×M16C22semidirect
25. C24×C8C22semidirect
47. #2994C22semidirect
48. #2993C22semidirect
49. #2992C22semidirect
50. #2981C22semidirect
51. #2979C22semidirect
52. #2978C22semidirect
53. #2978C22semidirect
54. #2977C22semidirect
55. #2976C22semidirect
56. #2969C22semidirect
57. #2968C22semidirect
58. #2967C22semidirect
59. C2×#446C22semidirect
60. C2×#446C22semidirect
61. C2×#446C22semidirect
62. C2×C8×Q8C22semidirect
63. #2935C22semidirect
64. #2933C22semidirect
65. #2932C22semidirect
66. #2930C22semidirect
67. #2929C22semidirect
68. #2929C22semidirect
72. C2×#436C22semidirect
73. C2×#436C22semidirect
74. C2×#436C22semidirect
75. C2×#436C22semidirect
76. C2×#436C22semidirect
77. C2×#436C22semidirect
84. C2×#435C22semidirect
85. C2×#435C22semidirect
86. C2×#435C22semidirect
87. C2×#435C22semidirect
88. C2×#435C22semidirect
89. C2×#435C22semidirect
90. C2×#435C22semidirect
91. C2×#435C22semidirect
92. C2×#435C22semidirect
93. C2×#435C22semidirect
94. C2×#435C22semidirect
95. C2×#435C22semidirect
99. C2×C8×D4C22semidirect
100. C2×C8×D4C22semidirect
101. C2×C8×D4C22semidirect
102. C2×C8×D4C22semidirect
103. C2×C8×D4C22semidirect
104. C2×C8×D4C22semidirect
105. C2×#433C22semidirect
106. C2×#433C22semidirect
107. C2×#433C22semidirect
108. C2×#433C22semidirect
109. C2×#433C22semidirect
110. C2×#433C22semidirect
111. C2×#432C22semidirect
112. C2×#431C22semidirect
113. C2×#431C22semidirect
114. C2×#424C22semidirect
115. C2×#424C22semidirect
116. C2×#424C22semidirect
117. C2×#424C22semidirect
118. C2×#423C22semidirect
119. C22×C4⋊C8C22semidirect
126. C2×#408C22semidirect
127. C2×#408C22semidirect
128. C2×#407C22semidirect
129. C2×#407C22semidirect
130. C2×#407C22semidirect
131. C22×C22⋊C8C22semidirect
132. C2×#405C22semidirect
133. C2×#405C22semidirect
134. C2×#405C22semidirect
135. C2×#405C22semidirect
136. C2×C4×M16C22semidirect
137. C22×#97C22semidirect
148. C2×#131C23semidirect
162. C22×M16C23semidirect
176. C23×C8C23semidirect
287. #446C23semidirect
288. #446C23semidirect
289. #446C23semidirect
290. C8×Q8C23semidirect
294. #436C23semidirect
295. #436C23semidirect
296. #436C23semidirect
297. #436C23semidirect
298. #436C23semidirect
299. #436C23semidirect
306. #435C23semidirect
307. #435C23semidirect
308. #435C23semidirect
309. #435C23semidirect
310. #435C23semidirect
311. #435C23semidirect
312. #435C23semidirect
313. #435C23semidirect
314. #435C23semidirect
315. #435C23semidirect
316. #435C23semidirect
317. #435C23semidirect
321. C8×D4C23semidirect
322. C8×D4C23semidirect
323. C8×D4C23semidirect
324. C8×D4C23semidirect
325. C8×D4C23semidirect
326. C8×D4C23semidirect
327. #433C23semidirect
328. #433C23semidirect
329. #433C23semidirect
330. #433C23semidirect
331. #433C23semidirect
332. #433C23semidirect
333. #432C23semidirect
334. #431C23semidirect
335. #431C23semidirect
336. #424C23semidirect
337. #424C23semidirect
338. #424C23semidirect
339. #424C23semidirect
340. #423C23semidirect
353. C2×C4⋊C8C23semidirect
360. #408C23semidirect
361. #408C23semidirect
362. #407C23semidirect
363. #407C23semidirect
364. #407C23semidirect
383. C2×C22⋊C8C23semidirect
384. #405C23semidirect
385. #405C23semidirect
386. #405C23semidirect
387. #405C23semidirect
388. C4×M16C23semidirect
395. C2×#97C23semidirect
1089. C2#60315direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35292
#603152
C2×#29942
C2×#29932
C2×#29922
C2×#29812
C2×#29792
C2×#29782
C2×#29772
C2×#29762
C2×#29692
C2×#29682
C2×#29672
C2×#29352
C2×#29332
C2×#29322
C2×#29302
C2×#29292