Finite Group Databasebeta

← C2×#60316 #10574476

Subgroups — C2×#60316 #10574476

Order 512.

6738 conjugacy classes of subgroups.

The subgroup lattice has 1115 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3460C211yesmaximal, characteristic
2#60316C2132yesmaximal, direct product factor
3C2×#2995C212yesmaximal, complemented
4C2×#2992C212yesmaximal, complemented
5C2×#2990C212yesmaximal, complemented
6C2×#2981C212yesmaximal, complemented
7C2×#2980C212yesmaximal, complemented
8C2×#2977C212yesmaximal, complemented
9C2×#2976C211yesmaximal, characteristic, complemented
10C2×#2976C211yesmaximal, characteristic, complemented
11C2×#2973C211yesmaximal, characteristic, complemented
12C2×#2970C212yesmaximal, complemented
13C2×#2968C212yesmaximal, complemented
14C2×#2967C212yesmaximal, complemented
15C2×#2935C212yesmaximal, complemented
16C2×#2933C212yesmaximal, complemented
17C2×#2932C212yesmaximal, complemented
18C2×#2929C211yesmaximal, characteristic, complemented
19C2×#2929C211yesmaximal, characteristic, complemented
20C22×#435C211yesmaximal, characteristic, complemented
21C22×#131C2211yescharacteristic, complemented
22C22×#131C2211yescharacteristic, complemented
23C22×#131C2212yescomplemented
24C23×M16C2211yescharacteristic
25C24×C8C2211yescharacteristic
26#3460C4116yes—
27#3460C22116yes—
28C2×#544C411yescharacteristic
29C2×#542C412yes—
30C2×#542C412yes—
31C2×#540C412yes—
32C2×#540C412yes—
33C2×#538C412yes—
34C2×#538C411yescharacteristic
35C2×#538C411yescharacteristic
36C2×#537C411yescharacteristic
37C2×#535C412yes—
38C2×#532C2212yes—
39C2×#532C2212yes—
40C2×#529C2212yes—
41C2×#529C2212yes—
42C2×#525C2211yescharacteristic
43C2×#525C2211yescharacteristic
44C2×#525C2212yes—
45C2×C4×#41C2212yes—
46C22×C4×D4C2211yescharacteristic
47#2995C22132yescomplemented
48#2992C22132yescomplemented
49#2990C22132yescomplemented
50#2981C22132yescomplemented
51#2980C22132yescomplemented
52#2977C22132yescomplemented
53#2976C22116yescomplemented
54#2976C22116yescomplemented
55#2973C22116yescomplemented
56#2970C22132yescomplemented
57#2968C22132yescomplemented
58#2967C22132yescomplemented
59C2×#446C2212yescomplemented
60C2×#446C2212yescomplemented
61C2×#446C2212yescomplemented
62C2×#446C2212yescomplemented
63#2935C22132yescomplemented
64#2933C22132yescomplemented
65#2932C22132yescomplemented
66#2929C22116yescomplemented
67#2929C22116yescomplemented
68C2×#436C2212yescomplemented
69C2×#436C2212yescomplemented
70C2×#436C2212yescomplemented
71C2×#436C2212yescomplemented
72C2×#435C2212yes—
73C2×#435C2212yes—
74C2×#435C2212yes—
75C2×#435C2212yes—
76C2×#435C2212yes—
77C2×#435C2212yes—
78C2×#435C2212yes—
79C2×#435C2212yes—
80C2×#435C2212yes—
81C2×#435C2212yes—
82C2×#435C2212yes—
83C2×#435C2212yes—
84C2×#435C22116yescomplemented
85C2×#435C2212yescomplemented
86C2×#435C2212yescomplemented
87C2×#435C2212yescomplemented
88C2×#435C2212yescomplemented
89C2×#435C2212yescomplemented
90C2×#435C2212yescomplemented
91C2×#435C2212yescomplemented
92C2×#435C2212yescomplemented
93C2×#435C2212yescomplemented
94C2×#435C2212yescomplemented
95C2×#435C2212yescomplemented
96C2×#435C2212yescomplemented
97C2×C8×D4C2212yes—
98C2×C8×D4C2212yes—
99C2×C8×D4C2212yes—
100C2×C8×D4C2212yes—
101C2×C8×D4C2212yescomplemented
102C2×C8×D4C2212yescomplemented
103C2×C8×D4C2212yescomplemented
104C2×C8×D4C2212yescomplemented
105C2×#433C2212yescomplemented
106C2×#433C2212yescomplemented
107C2×#433C2212yescomplemented
108C2×#433C2212yescomplemented
109C2×#432C2212yes—
110C2×#432C2212yescomplemented
111C2×#432C2212yescomplemented
112C2×#432C2212yescomplemented
113C2×#431C2212yescomplemented
114C2×#424C2211yescharacteristic, complemented
115C2×#424C2212yescomplemented
116C2×#424C2211yescharacteristic, complemented
117C2×#423C2212yescomplemented
118C22×C4⋊C8C2211yescharacteristic
119C22×C4⋊C8C2212yescomplemented
120C2×#408C2212yescomplemented
121C2×#408C2212yescomplemented
122C2×#408C2212yescomplemented
123C2×#408C2212yescomplemented
124C2×#408C2211yescharacteristic, complemented
125C2×#408C2212yescomplemented
126C2×#408C2211yescharacteristic, complemented
127C2×#407C2211yescharacteristic
128C2×#407C2211yescharacteristic
129C22×C22⋊C8C2212yes—
130C22×C22⋊C8C2211yescharacteristic
131C22×C22⋊C8C2211yescharacteristic
132C2×#405C2211yescharacteristic, complemented
133C2×#405C2212yescomplemented
134C2×#405C2211yescharacteristic, complemented
135C2×C4×M16C2212yescomplemented
136C22×#97C2211yescharacteristic
137C22×#97C2212yescomplemented
138C22×#41C2×C412yes—
139C22×#41C2311yescharacteristic
140C22×#41C2311yescharacteristic
141C22×#41C2312yes—
142C23×D4C2×C411yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C2×#131—44no—
146C2×#131—44no—
147C2×#131—48no—
148C2×#131C2318yescomplemented
149C2×#131C2318yescomplemented
150C2×#131C23116yescomplemented
151C22×M16—44no—
152C22×M16C2312yes—
153C22×M16C2312yes—
154C22×M16C2312yes—
155C22×M16C2311yescharacteristic
156C22×M16C2311yescharacteristic
157C22×M16C2311yescharacteristic
158C22×M16C2311yescharacteristic
159C22×M16C2312yes—
160C22×M16C2312yes—
161C22×M16C2312yes—
162C22×M16C2318yes—
163C23×C8—44no—
164C23×C8C2311yescharacteristic
165C23×C8C2312yes—
166C23×C8C2311yescharacteristic
167C23×C8C2311yescharacteristic
168C23×C8C2311yescharacteristic
169C23×C8C2312yes—
170C23×C8C2312yes—
171C23×C8C2311yescharacteristic
172C23×C8C2311yescharacteristic
173C23×C8C2312yes—
174C23×C8C2312yes—
175C23×C8C2312yes—
176C23×C8C2311yescharacteristic
177C23×C8C2311yescharacteristic
178C23×C8C2318yes—
179#544C2×C4116yes—
180#542C2×C4132yes—
181#542C2×C4132yes—
182#540C2×C4132yes—
183#540C2×C4132yes—
184#538C2×C4132yes—
185#538C2×C4116yes—
186#538C2×C4116yes—
187#537C2×C4116yes—
188#535C2×C4132yes—
189#532C2×C4116yes—
190#532C2×C4116yes—
191#532C23116yes—
192#532C23116yes—
193C2×C4⋊Q8C2×C412yes—
194C2×C4⋊Q8C2×C412yes—
195C2×#127C2×C412yes—
196C2×#127C2×C412yes—
197#529C2×C4116yes—
198#529C2×C4116yes—
199#529C23116yes—
200#529C23116yes—
201C2×#126C2×C412yes—
202C2×#126C2×C412yes—
203C2×#126C2×C412yes—
204C2×#126C2×C412yes—
205C2×#125C2×C412yes—
206C2×#125C2×C412yes—
207C2×#124C2×C412yes—
208C2×#124C2×C412yes—
209C2×#124C2×C412yes—
210C2×#124C2×C412yes—
211C2×#124C2×C412yes—
212C2×#124C2×C412yes—
213#525C2×C418yes—
214#525C2×C418yes—
215#525C2×C4116yes—
216#525C2318yes—
217#525C2318yes—
218#525C23116yes—
219C2×#123C2×C412yes—
220C2×#123C2×C412yes—
221C2×#123C2×C412yes—
222C2×#123C2×C412yes—
223C2×#123C2×C412yes—
224C2×#123C2×C412yes—
225C2×#123C2×C412yes—
226C2×#123C2×C412yes—
227C2×C22⋊Q8C2×C411yescharacteristic
228C2×C22⋊Q8C2×C411yescharacteristic
229C2×C22⋊Q8C2×C412yes—
230C2×C22⋊Q8C2×C411yescharacteristic
231C2×C22⋊Q8C2×C411yescharacteristic
232C2×C22⋊Q8C2×C412yes—
233C2×C22⋊Q8C2×C412yes—
234C2×C22⋊Q8C2×C412yes—
235C2×#121C2×C411yescharacteristic
236C2×#121C2×C411yescharacteristic
237C2×#121C2×C412yes—
238C2×#121C2×C411yescharacteristic
239C2×#121C2×C411yescharacteristic
240C2×#121C2×C412yes—
241C2×#121C2×C412yes—
242C2×#121C2×C412yes—
243C2×#121C2×C412yes—
244C2×#121C2×C412yes—
245C2×#121C2×C412yes—
246C2×#121C2×C412yes—
247C2×#121C2×C412yes—
248C2×#121C2×C412yes—
249C2×#121C2×C412yes—
250C2×#121C2×C412yes—
251C2×#120C2×C412yes—
252C2×#120C2×C412yes—
253C2×#120C2×C412yes—
254C2×#120C2×C412yes—
255C4×#41C2×C4116yes—
256C4×#41C23116yes—
257C2×C4×Q8C2×C412yes—
258C2×C4×Q8C2312yes—
259C2×C4×D4C2×C412yes—
260C2×C4×D4C2×C412yes—
261C2×C4×D4C2×C418yes—
262C2×C4×D4C2×C412yes—
263C2×C4×D4C2×C412yes—
264C2×C4×D4C2×C412yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2318yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×#117C2×C412yes—
276C2×#117C2×C412yes—
277C2×#117C2×C412yes—
278C2×#117C2311yescharacteristic
279C2×#117C2312yes—
280C2×#117C2311yescharacteristic
281C22×C4⋊C4C2×C411yescharacteristic
282C22×C22⋊C4C2×C411yescharacteristic
283C22×C22⋊C4C2×C411yescharacteristic
284C22×C42C2311yescharacteristic
285C22×C42C2312yes—
286C22×C42C2312yes—
287#446C23116yescomplemented
288#446C23116yescomplemented
289#446C23116yescomplemented
290#446C23116yescomplemented
291#436C23116yescomplemented
292#436C23116yescomplemented
293#436C23116yescomplemented
294#436C23116yescomplemented
295#435C23116yes—
296#435C23116yes—
297#435C23116yes—
298#435C23116yes—
299#435C23116yes—
300#435C23116yes—
301#435C23116yes—
302#435C23116yes—
303#435C23116yes—
304#435C23116yes—
305#435C23116yes—
306#435C23116yes—
307#435C23116yescomplemented
308#435C23116yescomplemented
309#435C23116yescomplemented
310#435C23116yescomplemented
311#435C23116yescomplemented
312#435C23116yescomplemented
313#435C23116yescomplemented
314#435C23116yescomplemented
315#435C23116yescomplemented
316#435C23116yescomplemented
317#435C23116yescomplemented
318#435C23116yescomplemented
319C8×D4C23116yes—
320C8×D4C23116yes—
321C8×D4C23116yes—
322C8×D4C23116yes—
323C8×D4C23116yescomplemented
324C8×D4C23116yescomplemented
325C8×D4C23116yescomplemented
326C8×D4C23116yescomplemented
327#433C23116yescomplemented
328#433C23116yescomplemented
329#433C23116yescomplemented
330#433C23116yescomplemented
331#432C23116yes—
332#432C23116yescomplemented
333#432C23116yescomplemented
334#432C23116yescomplemented
335#431C23116yescomplemented
336#424C2318yescomplemented
337#424C2318yescomplemented
338#424C23116yescomplemented
339#423C23116yescomplemented
340C2×C4⋊C8C2312yes—
341C2×C4⋊C8C2312yes—
342C2×C4⋊C8C2318yes—
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#408C2318yescomplemented
355#408C2318yescomplemented
356#408C23116yescomplemented
357#408C23116yescomplemented
358#408C23116yescomplemented
359#408C23116yescomplemented
360#408C23116yescomplemented
361#407C2318yes—
362#407C2318yes—
363C2×C22⋊C8C2312yes—
364C2×C22⋊C8C2312yes—
365C2×C22⋊C8C2312yes—
366C2×C22⋊C8C2312yes—
367C2×C22⋊C8C2312yes—
368C2×C22⋊C8C2312yes—
369C2×C22⋊C8C2312yes—
370C2×C22⋊C8C2312yes—
371C2×C22⋊C8C2318yes—
372C2×C22⋊C8C2318yes—
373C2×C22⋊C8C23116yes—
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⋊C8C2312yes—
384#405C2318yescomplemented
385#405C2318yescomplemented
386#405C23116yescomplemented
387C4×M16C23116yescomplemented
388C2×#97C2312yes—
389C2×#97C2312yes—
390C2×#97C2318yes—
391C2×#97C2312yes—
392C2×#97C2312yes—
393C2×#97C2312yes—
394C2×#97C2312yes—
395C2×#97C2312yes—
396C2×#97C2312yes—
397C2×#97C23116yescomplemented
398C2×C4×C8C2312yes—
399C2×C4×C8C2312yes—
400C2×C4×C8C2312yes—
401C2×C4×C8C2312yes—
402C25C22×C411yescharacteristic
403C25C22×C411yescharacteristic
404C2×#41—42no—
405C2×#41—42no—
406C2×#41—44no—
407C2×#41—44no—
408C2×#41—42no—
409C2×#41—42no—
410C2×#41—48no—
411C2×#41C22×C4116yes—
412C2×#41C22×C414yes—
413C2×#41C22×C414yes—
414C2×#41C22×C418yes—
415C2×#41C2414yes—
416C2×#41C2414yes—
417C2×#41C2418yes—
418C22×Q8C22×C412yes—
419C22×Q8C22×C411yescharacteristic
420C22×Q8C22×C411yescharacteristic
421C22×Q8C22×C412yes—
422C22×D4—44no—
423C22×D4C22×C412yes—
424C22×D4C22×C412yes—
425C22×D4C22×C412yes—
426C22×D4C22×C412yes—
427C22×D4C22×C412yes—
428C22×D4C22×C418yes—
429C22×D4C22×C412yes—
430C22×D4C22×C412yes—
431C22×D4C22×C412yes—
432C22×D4C22×C412yes—
433C22×D4C22×C412yes—
434C22×D4C22×C412yes—
435C22×D4C22×C412yes—
436C22×D4C22×C412yes—
437C22×D4C22×C411yescharacteristic
438C22×D4C22×C411yescharacteristic
439C22×D4C22×C412yes—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4—42no—
443C23×C4—42no—
444C23×C4C22×C411yescharacteristic
445C23×C4C22×C411yescharacteristic
446C23×C4C22×C411yescharacteristic
447C23×C4C22×C411yescharacteristic
448C23×C4C22×C412yes—
449C23×C4C22×C412yes—
450C23×C4C22×C412yes—
451C23×C4C22×C412yes—
452C23×C4C22×C412yes—
453C23×C4C22×C411yescharacteristic
454C23×C4C22×C411yescharacteristic
455C23×C4C22×C414yes—
456C23×C4C22×C414yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2411yescharacteristic
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2414yes—
464C23×C4C2414yes—
465#131—416no—
466#131—416no—
467#131—432no—
468C2×M16—28no—
469C2×M16—28no—
470C2×M16—44no—
471C2×M16—42no—
472C2×M16—44no—
473C2×M16—42no—
474C2×M16—42no—
475C2×M16—44no—
476C2×M16—42no—
477C2×M16—44no—
478C2×M16—416no—
479C2×M16C2418yes—
480C2×M16C2418yes—
481C2×M16C2418yes—
482C2×M16C2414yes—
483C2×M16C2414yes—
484C2×M16C2418yes—
485C2×M16C2418yes—
486C2×M16C2418yes—
487C2×M16C2414yes—
488C2×M16C2414yes—
489C22×C8—24no—
490C22×C8—24no—
491C22×C8—24no—
492C22×C8—28no—
493C22×C8—416no—
494C22×C8—42no—
495C22×C8—42no—
496C22×C8—42no—
497C22×C8—42no—
498C22×C8—44no—
499C22×C8—44no—
500C22×C8—42no—
501C22×C8—44no—
502C22×C8—44no—
503C22×C8—44no—
504C22×C8C2414yes—
505C22×C8C2414yes—
506C22×C8C2414yes—
507C22×C8C2418yes—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2412yes—
511C22×C8C2411yescharacteristic
512C22×C8C2412yes—
513C22×C8C2412yes—
514C22×C8C2412yes—
515C22×C8C2412yes—
516C22×C8C2412yes—
517C22×C8C2414yes—
518C22×C8C2414yes—
519C22×C8C2414yes—
520C22×C8C2414yes—
521C22×C8C2418yes—
522C22×C8C2418yes—
523C22×C8C2418yes—
524C22×C8C2414yes—
525C22×C8C2418yes—
526C22×C8C2418yes—
527C22×C8C2411yescharacteristic
528C4⋊Q8C22×C4116yes—
529C4⋊Q8C22×C4116yes—
530#127C22×C4116yes—
531#127C22×C4116yes—
532#126C22×C4116yes—
533#126C22×C4116yes—
534#126C22×C4116yes—
535#126C22×C4116yes—
536#125C22×C4116yes—
537#125C22×C4116yes—
538#124C22×C4116yes—
539#124C22×C4116yes—
540#124C22×C4116yes—
541#124C22×C4116yes—
542#124C22×C4116yes—
543#124C22×C4116yes—
544#123C22×C4116yes—
545#123C22×C4116yes—
546#123C22×C4116yes—
547#123C22×C4116yes—
548#123C22×C4116yes—
549#123C22×C4116yes—
550#123C22×C4116yes—
551#123C22×C4116yes—
552C22⋊Q8C22×C418yes—
553C22⋊Q8C22×C418yes—
554C22⋊Q8C22×C4116yes—
555C22⋊Q8C22×C418yes—
556C22⋊Q8C22×C418yes—
557C22⋊Q8C22×C4116yes—
558C22⋊Q8C22×C4116yes—
559C22⋊Q8C22×C4116yes—
560#121C22×C418yes—
561#121C22×C418yes—
562#121C22×C4116yes—
563#121C22×C418yes—
564#121C22×C418yes—
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#120C22×C4116yes—
577#120C22×C4116yes—
578#120C22×C4116yes—
579#120C22×C4116yes—
580C4×Q8C22×C4116yes—
581C4×Q8C22×C418yes—
582C4×Q8C2418yes—
583C4×D4C22×C418yes—
584C4×D4C22×C418yes—
585C4×D4C22×C4116yes—
586C4×D4C22×C4116yes—
587C4×D4C22×C4116yes—
588C4×D4C22×C4116yes—
589C4×D4C22×C4116yes—
590C4×D4C22×C418yes—
591C4×D4C22×C418yes—
592C4×D4C22×C418yes—
593C4×D4C22×C418yes—
594C4×D4C22×C418yes—
595C4×D4C22×C418yes—
596C4×D4C22×C418yes—
597C4×D4C2418yes—
598C4×D4C2418yes—
599C4×D4C2418yes—
600C4×D4C2418yes—
601C4×D4C2418yes—
602C4×D4C2418yes—
603C4×D4C2418yes—
604C4×D4C2418yes—
605C4×D4C2418yes—
606#117C22×C4116yes—
607#117C22×C4116yes—
608#117C22×C4116yes—
609#117C22×C414yes—
610#117C22×C418yes—
611#117C22×C414yes—
612#117C2414yes—
613#117C2414yes—
614#117C2418yes—
615C2×C4⋊C4C22×C412yes—
616C2×C4⋊C4C22×C412yes—
617C2×C4⋊C4C22×C418yes—
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×C411yescharacteristic
625C2×C4⋊C4C22×C412yes—
626C2×C4⋊C4C22×C411yescharacteristic
627C2×C4⋊C4C22×C411yescharacteristic
628C2×C4⋊C4C22×C412yes—
629C2×C4⋊C4C22×C411yescharacteristic
630C2×C4⋊C4C22×C412yes—
631C2×C4⋊C4C22×C412yes—
632C2×C4⋊C4C22×C412yes—
633C2×C4⋊C4C22×C412yes—
634C2×C22⋊C4C22×C412yes—
635C2×C22⋊C4C22×C412yes—
636C2×C22⋊C4C22×C412yes—
637C2×C22⋊C4C22×C412yes—
638C2×C22⋊C4C22×C418yes—
639C2×C22⋊C4C22×C418yes—
640C2×C22⋊C4C22×C412yes—
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×C42C22×C412yes—
659C2×C42C22×C412yes—
660C2×C42C22×C412yes—
661C2×C42C22×C414yes—
662C2×C42C22×C412yes—
663C2×C42C22×C412yes—
664C2×C42C22×C418yes—
665C2×C42C22×C418yes—
666C2×C42C2414yes—
667C2×C42C2418yes—
668C2×C42C2418yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C4⋊C8C2418yes—
673C4⋊C8C2418yes—
674C4⋊C8C2418yes—
675C4⋊C8C2418yes—
676C4⋊C8C2418yes—
677C4⋊C8C2418yes—
678C4⋊C8C2418yes—
679C4⋊C8C2418yes—
680C4⋊C8C2418yes—
681C4⋊C8C2418yes—
682C4⋊C8C2418yes—
683C4⋊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—
700C22⋊C8C2418yes—
701C22⋊C8C2418yes—
702#97C2418yes—
703#97C2418yes—
704#97C2418yes—
705#97C2418yes—
706#97C2418yes—
707#97C2418yes—
708#97C2418yes—
709#97C2418yes—
710C4×C8C2418yes—
711C4×C8C2418yes—
712C4×C8C2418yes—
713C4×C8C2418yes—
714C24—24no—
715C24—24no—
716C24—42no—
717C24—42no—
718C24—42no—
719C24—42no—
720C24C23×C411yescharacteristic
721C24C23×C411yescharacteristic
722C24C23×C412yes—
723C24C23×C412yes—
724C24C23×C412yes—
725C24C23×C411yescharacteristic
726C24C23×C414yes—
727C24C23×C414yes—
728#41—44no—
729#41—44no—
730#41—48no—
731#41—48no—
732#41—48no—
733#41—416no—
734#41—48no—
735#41—44no—
736#41—44no—
737#41—432no—
738C2×Q8—42no—
739C2×Q8—42no—
740C2×Q8—44no—
741C2×Q8—44no—
742C2×Q8C23×C418yes—
743C2×Q8C23×C414yes—
744C2×Q8C23×C414yes—
745C2×Q8C23×C418yes—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—416no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4C23×C418yes—
764C2×D4C23×C418yes—
765C2×D4C23×C418yes—
766C2×D4C23×C418yes—
767C2×D4C23×C418yes—
768C2×D4C23×C418yes—
769C2×D4C23×C418yes—
770C2×D4C23×C418yes—
771C2×D4C23×C418yes—
772C2×D4C23×C418yes—
773C2×D4C23×C418yes—
774C2×D4C23×C418yes—
775C2×D4C23×C418yes—
776C2×D4C23×C414yes—
777C2×D4C23×C414yes—
778C2×D4C23×C418yes—
779C22×C4—24no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—22no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—24no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—44no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4C23×C412yes—
809C22×C4C23×C412yes—
810C22×C4C23×C411yescharacteristic
811C22×C4C23×C412yes—
812C22×C4C23×C412yes—
813C22×C4C23×C412yes—
814C22×C4C23×C414yes—
815C22×C4C23×C414yes—
816C22×C4C23×C412yes—
817C22×C4C23×C412yes—
818C22×C4C23×C412yes—
819C22×C4C23×C412yes—
820C22×C4C23×C414yes—
821C22×C4C23×C411yescharacteristic
822C22×C4C23×C411yescharacteristic
823C22×C4C23×C412yes—
824C22×C4C23×C412yes—
825C22×C4C23×C412yes—
826C22×C4C23×C414yes—
827C22×C4C23×C414yes—
828C22×C4C23×C418yes—
829C22×C4C23×C418yes—
830C22×C4C23×C418yes—
831C22×C4C23×C418yes—
832C22×C4C23×C414yes—
833C22×C4C23×C414yes—
834C22×C4C23×C414yes—
835C22×C4C23×C414yes—
836C22×C4C23×C418yes—
837C22×C4C2512yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2511yescharacteristic
844M16—216no—
845M16—216no—
846M16—48no—
847M16—44no—
848M16—48no—
849M16—44no—
850M16—44no—
851M16—48no—
852M16—44no—
853M16—48no—
854C2×C8—22no—
855C2×C8—22no—
856C2×C8—22no—
857C2×C8—24no—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—24no—
861C2×C8—24no—
862C2×C8—24no—
863C2×C8—28no—
864C2×C8—28no—
865C2×C8—28no—
866C2×C8—216no—
867C2×C8—44no—
868C2×C8—44no—
869C2×C8—44no—
870C2×C8—44no—
871C2×C8—48no—
872C2×C8—48no—
873C2×C8—44no—
874C2×C8—48no—
875C2×C8—48no—
876C2×C8—48no—
877C2×C8H(5,𝔽2)14yes—
878C2×C8C2514yes—
879C2×C8C2512yes—
880C2×C8C2514yes—
881C2×C8C2514yes—
882C2×C8C2514yes—
883C2×C8C2514yes—
884C2×C8C2512yes—
885C2×C8C2514yes—
886C2×C8C2512yes—
887C2×C8C2512yes—
888C4⋊C4C23×C418yes—
889C4⋊C4C23×C418yes—
890C4⋊C4C23×C418yes—
891C4⋊C4C23×C418yes—
892C4⋊C4C23×C418yes—
893C4⋊C4C23×C418yes—
894C4⋊C4C23×C418yes—
895C4⋊C4C23×C418yes—
896C4⋊C4C23×C414yes—
897C4⋊C4C23×C414yes—
898C4⋊C4C23×C418yes—
899C4⋊C4C23×C414yes—
900C4⋊C4C23×C414yes—
901C4⋊C4C23×C418yes—
902C4⋊C4C23×C418yes—
903C4⋊C4C23×C418yes—
904C4⋊C4C23×C418yes—
905C4⋊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—
920C22⋊C4C23×C418yes—
921C22⋊C4C23×C418yes—
922C22⋊C4C23×C418yes—
923C22⋊C4C23×C418yes—
924C22⋊C4C23×C418yes—
925C22⋊C4C23×C418yes—
926C22⋊C4C23×C418yes—
927C22⋊C4C23×C418yes—
928C42C23×C414yes—
929C42C23×C418yes—
930C42C23×C414yes—
931C42C23×C414yes—
932C42C23×C418yes—
933C42C23×C418yes—
934C42C23×C418yes—
935C42C23×C418yes—
936C42C2514yes—
937C42C2514yes—
938C42C2514yes—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—28no—
949C23—22no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—28no—
958C23—44no—
959C23—44no—
960C23—44no—
961C23—44no—
962C23—416no—
963C23—88no—
964C23#56814yes—
965C23C24×C412yes—
966C23C24×C412yes—
967C23C24×C414yes—
968C23C24×C414yes—
969C23C24×C414yes—
970C23C24×C412yes—
971C23C24×C411yescharacteristic
972Q8—48no—
973Q8—44no—
974Q8—44no—
975Q8—48no—
976D4—216no—
977D4—216no—
978D4—48no—
979D4—48no—
980D4—48no—
981D4—48no—
982D4—48no—
983D4—48no—
984D4—48no—
985D4—44no—
986D4—44no—
987D4—48no—
988D4—48no—
989D4—48no—
990D4—48no—
991D4—48no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—28no—
1021C2×C4—28no—
1022C2×C4—28no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—48no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—48no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—48no—
1033C2×C4C24×C414yes—
1034C2×C4C24×C414yes—
1035C2×C4C24×C412yes—
1036C2×C4C24×C414yes—
1037C2×C4C24×C414yes—
1038C2×C4C24×C414yes—
1039C2×C4C24×C414yes—
1040C2×C4C24×C414yes—
1041C2×C4C24×C414yes—
1042C2×C4C24×C412yes—
1043C2×C4C24×C412yes—
1044C2×C4C24×C414yes—
1045C2×C4C24×C411yescharacteristic
1046C2×C4C2×H(5,𝔽2)12yes—
1047C2×C4#58512yes—
1048C2×C4C2611yescharacteristic
1049C8—22no—
1050C8—22no—
1051C8—22no—
1052C8—24no—
1053C8—24no—
1054C8—24no—
1055C8—24no—
1056C8—24no—
1057C8—24no—
1058C8C2×H(5,𝔽2)14yes—
1059C22—22no—
1060C22—28no—
1061C22—22no—
1062C22—24no—
1063C22—24no—
1064C22—22no—
1065C22—22no—
1066C22—24no—
1067C22—24no—
1068C22—24no—
1069C22—22no—
1070C22—22no—
1071C22—24no—
1072C22—22no—
1073C22—22no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—416no—
1078C22—48no—
1079C22—48no—
1080C22—44no—
1081C22—44no—
1082C22—48no—
1083C22—88no—
1084C22C4×H(5,𝔽2)12yes—
1085C22C2×#56814yes—
1086C22C2×#56812yes—
1087C22#357312yes—
1088C22C25×C411yescharacteristic
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—24no—
1093C4—24no—
1094C4—24no—
1095C4—22no—
1096C4—22no—
1097C4—22no—
1098C4—24no—
1099C4—24no—
1100C4—24no—
1101C4C4×H(5,𝔽2)12yes—
1102C4C22×H(5,𝔽2)11yescharacteristic
1103C4C2×#58511yescharacteristic
1104C2—24no—
1105C2—44no—
1106C2—44no—
1107C2—42no—
1108C2—42no—
1109C2—44no—
1110C2#6031614yesdirect product factor
1111C2C2×C4×H(5,𝔽2)11yescharacteristic
1112C2C22×#56811yescharacteristic
1113C2C2×#357311yescharacteristic
subgroupG/H
centerC22×C4C25
commutatorC22C25×C4
Frattini, cosocleC2×C4C26
socleC23C24×C4
prime radicalC2×#3460C2
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. #60316C2direct (N × H)
3. C2×#2995C2semidirect
4. C2×#2992C2semidirect
5. C2×#2990C2semidirect
6. C2×#2981C2semidirect
7. C2×#2980C2semidirect
8. C2×#2977C2semidirect
9. C2×#2976C2semidirect
10. C2×#2976C2semidirect
11. C2×#2973C2semidirect
12. C2×#2970C2semidirect
13. C2×#2968C2semidirect
14. C2×#2967C2semidirect
15. C2×#2935C2semidirect
16. C2×#2933C2semidirect
17. C2×#2932C2semidirect
18. C2×#2929C2semidirect
19. C2×#2929C2semidirect
20. C22×#435C2semidirect
21. C22×#131C22semidirect
22. C22×#131C22semidirect
23. C22×#131C22semidirect
47. #2995C22semidirect
48. #2992C22semidirect
49. #2990C22semidirect
50. #2981C22semidirect
51. #2980C22semidirect
52. #2977C22semidirect
53. #2976C22semidirect
54. #2976C22semidirect
55. #2973C22semidirect
56. #2970C22semidirect
57. #2968C22semidirect
58. #2967C22semidirect
59. C2×#446C22semidirect
60. C2×#446C22semidirect
61. C2×#446C22semidirect
62. C2×#446C22semidirect
63. #2935C22semidirect
64. #2933C22semidirect
65. #2932C22semidirect
66. #2929C22semidirect
67. #2929C22semidirect
68. C2×#436C22semidirect
69. C2×#436C22semidirect
70. C2×#436C22semidirect
71. 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
96. C2×#435C22semidirect
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
110. C2×#432C22semidirect
111. C2×#432C22semidirect
112. C2×#432C22semidirect
113. C2×#431C22semidirect
114. C2×#424C22semidirect
115. C2×#424C22semidirect
116. C2×#424C22semidirect
117. C2×#423C22semidirect
119. C22×C4⋊C8C22semidirect
120. C2×#408C22semidirect
121. C2×#408C22semidirect
122. C2×#408C22semidirect
123. C2×#408C22semidirect
124. C2×#408C22semidirect
125. C2×#408C22semidirect
126. C2×#408C22semidirect
132. C2×#405C22semidirect
133. C2×#405C22semidirect
134. C2×#405C22semidirect
135. C2×C4×M16C22semidirect
137. C22×#97C22semidirect
148. C2×#131C23semidirect
149. C2×#131C23semidirect
150. C2×#131C23semidirect
287. #446C23semidirect
288. #446C23semidirect
289. #446C23semidirect
290. #446C23semidirect
291. #436C23semidirect
292. #436C23semidirect
293. #436C23semidirect
294. #436C23semidirect
307. #435C23semidirect
308. #435C23semidirect
309. #435C23semidirect
310. #435C23semidirect
311. #435C23semidirect
312. #435C23semidirect
313. #435C23semidirect
314. #435C23semidirect
315. #435C23semidirect
316. #435C23semidirect
317. #435C23semidirect
318. #435C23semidirect
323. C8×D4C23semidirect
324. C8×D4C23semidirect
325. C8×D4C23semidirect
326. C8×D4C23semidirect
327. #433C23semidirect
328. #433C23semidirect
329. #433C23semidirect
330. #433C23semidirect
332. #432C23semidirect
333. #432C23semidirect
334. #432C23semidirect
335. #431C23semidirect
336. #424C23semidirect
337. #424C23semidirect
338. #424C23semidirect
339. #423C23semidirect
353. C2×C4⋊C8C23semidirect
354. #408C23semidirect
355. #408C23semidirect
356. #408C23semidirect
357. #408C23semidirect
358. #408C23semidirect
359. #408C23semidirect
360. #408C23semidirect
384. #405C23semidirect
385. #405C23semidirect
386. #405C23semidirect
387. C4×M16C23semidirect
397. C2×#97C23semidirect
1110. C2#60316direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#34602
#603162
C2×#29952
C2×#29922
C2×#29902
C2×#29812
C2×#29802
C2×#29772
C2×#29762
C2×#29732
C2×#29702
C2×#29682
C2×#29672
C2×#29352
C2×#29332
C2×#29322
C2×#29292
C22×#4352