Finite Group Databasebeta

← C2×#37493 #7633667

Subgroups — C2×#37493 #7633667

Order 512.

7808 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37493C2132yesmaximal, direct product factor
2C2×#2828C212yesmaximal, complemented
3C2×#2829C212yesmaximal, complemented
4C2×#2513C211yesmaximal, characteristic, complemented
5C2×#2490C211yesmaximal, characteristic, complemented
6C2×#2442C211yesmaximal, characteristic, complemented
7C2×#2445C211yesmaximal, characteristic, complemented
8C2×#2428C211yesmaximal, characteristic, complemented
9C2×#2433C211yesmaximal, characteristic, complemented
10C2×#2416C211yesmaximal, characteristic, complemented
11C2×#2408C211yesmaximal, characteristic, complemented
12C2×#2424C212yesmaximal, complemented
13C2×#2418C212yesmaximal, complemented
14C2×#2641C211yesmaximal, characteristic, complemented
15C2×#2644C211yesmaximal, characteristic, complemented
16C2×#2624C211yesmaximal, characteristic, complemented
17C2×#2619C211yesmaximal, characteristic, complemented
18C2×#2661C212yesmaximal, complemented
19C2×#2648C212yesmaximal, complemented
20C2×#2622C212yesmaximal, complemented
21C2×#2617C212yesmaximal, complemented
22C2×C4×#121C211yesmaximal, characteristic, complemented
23C22×#390C211yesmaximal, characteristic, complemented
24C2×#2290C211yesmaximal, characteristic, complemented
25C24×D4C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#127C2211yescharacteristic
28C22×#125C2211yescharacteristic, complemented
29C22×#123C2212yescomplemented
30C22×#121C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×#121C2212yes—
34C22×#121C2212yescomplemented
35C22×#121C2211yescharacteristic, complemented
36C22×#120C2212yes—
37C22×#120C2212yes—
38C22×#120C2212yes—
39C22×C4×D4C2211yescharacteristic
40C22×C4×D4C2212yes—
41C22×C4×D4C2211yescharacteristic, complemented
42C22×#117C2211yescharacteristic, complemented
43C23×C4⋊C4C2211yescharacteristic
44C23×C22⋊C4C2212yes—
45C23×C22⋊C4C2212yes—
46C23×C42C2211yescharacteristic
47#2829C22132yescomplemented
48#2828C22132yescomplemented
49#2661C22132yescomplemented
50#2648C22132yescomplemented
51#2644C22116yescomplemented
52#2641C22116yescomplemented
53#2624C22116yescomplemented
54#2622C22132yescomplemented
55#2619C22116yescomplemented
56#2617C22132yescomplemented
57#2513C22116yescomplemented
58#2490C22116yescomplemented
59#2445C22116yescomplemented
60#2442C22116yescomplemented
61#2433C22116yescomplemented
62#2428C22116yescomplemented
63#2424C22132yescomplemented
64#2418C22132yescomplemented
65#2416C22116yescomplemented
66#2408C22116yescomplemented
67C2×#400C2212yescomplemented
68C2×#399C2212yescomplemented
69C2×#398C2212yescomplemented
70C2×#397C2212yescomplemented
71C2×#397C2212yescomplemented
72C2×#397C2212yescomplemented
73C2×#397C2212yescomplemented
74C2×#397C2212yescomplemented
75C2×#397C2212yescomplemented
76C2×#397C2212yescomplemented
77C2×#396C2212yescomplemented
78C2×#396C2212yescomplemented
79C2×#394C2212yes—
80C2×#394C2212yescomplemented
81C2×#394C2212yescomplemented
82C2×#394C2212yescomplemented
83C2×#394C2212yescomplemented
84C2×#394C2212yescomplemented
85C2×#394C2212yescomplemented
86C2×#394C2212yescomplemented
87C2×#394C2212yescomplemented
88C2×#394C2212yescomplemented
89C2×#394C2212yescomplemented
90C2×#394C2212yescomplemented
91C2×#394C2212yescomplemented
92C2×#394C2212yescomplemented
93C2×#392C2212yes—
94C2×#392C2212yes—
95C2×#392C2212yes—
96C2×#392C2212yescomplemented
97C2×#392C2212yescomplemented
98C2×#392C2212yescomplemented
99C4×#121C22116yescomplemented
100C2×#390C2212yes—
101C2×#390C2211yescharacteristic
102C2×#390C2211yescharacteristic
103C2×#390C2211yescharacteristic
104C2×#390C2212yes—
105C2×#390C2211yescharacteristic
106C2×#390C2211yescharacteristic
107C2×#390C2211yescharacteristic
108C2×#390C2211yescharacteristic
109C2×#390C2211yescharacteristic
110C2×#390C22116yescomplemented
111C2×#390C2212yescomplemented
112C2×#390C2211yescharacteristic, complemented
113C2×#390C2211yescharacteristic, complemented
114C2×#389C2211yescharacteristic, complemented
115C2×#389C2211yescharacteristic, complemented
116C2×#389C2211yescharacteristic, complemented
117C2×#389C2211yescharacteristic, complemented
118#2290C22116yescomplemented
119C2×#388C2212yescomplemented
120C2×#388C2212yescomplemented
121C2×#388C2211yescharacteristic, complemented
122C2×#388C2212yescomplemented
123C2×#388C2212yescomplemented
124C2×#388C2211yescharacteristic, complemented
125C2×#387C2211yescharacteristic, complemented
126C2×#387C2211yescharacteristic, complemented
127C2×#386C2212yes—
128C2×#386C2211yescharacteristic
129C2×#386C2211yescharacteristic
130C2×#386C2212yes—
131C2×#386C2212yescomplemented
132C2×#386C2212yescomplemented
133C2×#385C2211yescharacteristic
134C2×#385C2212yes—
135C2×#385C2211yescharacteristic
136C2×#382C2211yescharacteristic, complemented
137C2×#380C2212yes—
138C2×#380C2211yescharacteristic
139C2×#380C2211yescharacteristic, complemented
140C2×#379C2212yes—
141C2×C4×C4⋊C4C2211yescharacteristic, complemented
142C2×C4×C4⋊C4C2211yescharacteristic, complemented
143C2×C4×C22⋊C4C2211yescharacteristic
144C2×C4×C22⋊C4C2212yescomplemented
145C2×C4×C22⋊C4C2211yescharacteristic, complemented
146C2×#376C2211yescharacteristic, complemented
147C26C2312yes—
148C23×D4—28no—
149C23×D4—44no—
150C23×D4—44no—
151C23×D4C2311yescharacteristic
152C23×D4C2311yescharacteristic
153C23×D4C2311yescharacteristic
154C23×D4C2312yes—
155C23×D4C2311yescharacteristic
156C23×D4C2312yes—
157C23×D4C2318yes—
158C23×D4C2312yes—
159C23×D4C2312yes—
160C23×D4C2312yes—
161C23×D4C2312yes—
162C23×D4C2312yes—
163C23×D4C2312yes—
164C23×D4C2312yes—
165C24×C4C2311yescharacteristic
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168C24×C4C2311yescharacteristic
169C24×C4C2312yes—
170C24×C4C2312yes—
171C2×#127—44no—
172C2×#127—44no—
173C2×#127C2318yes—
174C2×#127C2318yes—
175C2×#125—44no—
176C2×#125C2318yescomplemented
177C2×#123—48no—
178C2×#123C23116yescomplemented
179C2×#121—28no—
180C2×#121—48no—
181C2×#121—44no—
182C2×#121—44no—
183C2×#121—44no—
184C2×#121—48no—
185C2×#121C2318yes—
186C2×#121C23116yes—
187C2×#121C2318yes—
188C2×#121C2318yes—
189C2×#121C2318yescomplemented
190C2×#121C23116yescomplemented
191C2×#120—48no—
192C2×#120—48no—
193C2×#120—48no—
194C2×#120C23116yes—
195C2×#120C23116yes—
196C2×#120C23116yes—
197C2×C4×D4—28no—
198C2×C4×D4—44no—
199C2×C4×D4—48no—
200C2×C4×D4C2318yes—
201C2×C4×D4C23116yes—
202C2×C4×D4C2318yescomplemented
203C2×#117—44no—
204C2×#117C2318yescomplemented
205C22×C4⋊C4—44no—
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2318yes—
224C22×C22⋊C4—48no—
225C22×C22⋊C4—48no—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C23116yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C22⋊C4C2311yescharacteristic
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2312yes—
250C22×C22⋊C4C2312yes—
251C22×C22⋊C4C2312yes—
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C23116yes—
263C22×C42—44no—
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2318yes—
272C22×C42C2312yes—
273#400C23116yescomplemented
274#399C23116yescomplemented
275#398C23116yescomplemented
276#397C23116yescomplemented
277#397C23116yescomplemented
278#397C23116yescomplemented
279#397C23116yescomplemented
280#397C23116yescomplemented
281#397C23116yescomplemented
282#397C23116yescomplemented
283#396C23116yescomplemented
284#396C23116yescomplemented
285#394C23116yes—
286#394C23116yescomplemented
287#394C23116yescomplemented
288#394C23116yescomplemented
289#394C23116yescomplemented
290#394C23116yescomplemented
291#394C23116yescomplemented
292#394C23116yescomplemented
293#394C23116yescomplemented
294#394C23116yescomplemented
295#394C23116yescomplemented
296#394C23116yescomplemented
297#394C23116yescomplemented
298#394C23116yescomplemented
299#392C23116yes—
300#392C23116yes—
301#392C23116yes—
302#392C23116yescomplemented
303#392C23116yescomplemented
304#392C23116yescomplemented
305#390C23116yes—
306#390C2318yes—
307#390C2318yes—
308#390C2318yes—
309#390C2318yes—
310#390C2318yes—
311#390C2318yes—
312#390C23116yes—
313#390C2318yes—
314#390C2318yes—
315#390C2318yescomplemented
316#390C2318yescomplemented
317#390C23116yescomplemented
318#389C2318yescomplemented
319#389C2318yescomplemented
320#389C2318yescomplemented
321#389C2318yescomplemented
322#388C2318yescomplemented
323#388C23116yescomplemented
324#388C23116yescomplemented
325#388C23116yescomplemented
326#388C2318yescomplemented
327#388C23116yescomplemented
328#387C2318yescomplemented
329#387C2318yescomplemented
330#386C2318yes—
331#386C23116yes—
332#386C23116yes—
333#386C2318yes—
334#386C23116yescomplemented
335#386C23116yescomplemented
336#385C2318yes—
337#385C23116yes—
338#385C2318yes—
339#382C2318yescomplemented
340#380C23116yes—
341#380C2318yes—
342#380C2318yescomplemented
343#379C23116yes—
344C4×C4⋊C4C2318yescomplemented
345C4×C4⋊C4C2318yescomplemented
346C4×C22⋊C4C2318yes—
347C4×C22⋊C4C23116yescomplemented
348C4×C22⋊C4C2318yescomplemented
349#376C2318yescomplemented
350C2×#95C2311yescharacteristic
351C2×#95C2311yescharacteristic
352C2×#95C2312yes—
353C2×#95C2312yes—
354C2×#95C2312yes—
355C2×#95C2312yes—
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2312yes—
363C2×#95C2312yes—
364C2×#95C2312yes—
365C2×#95C2312yes—
366C2×#95C2312yes—
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C25—28no—
370C25—28no—
371C25—28no—
372C25—44no—
373C25—44no—
374C25—44no—
375C25—44no—
376C25C2412yes—
377C25C2412yes—
378C25C2411yescharacteristic
379C25C2412yes—
380C25C2411yescharacteristic
381C25C2418yes—
382C22×D4—24no—
383C22×D4—28no—
384C22×D4—28no—
385C22×D4—24no—
386C22×D4—28no—
387C22×D4—24no—
388C22×D4—24no—
389C22×D4—28no—
390C22×D4—232no—
391C22×D4—24no—
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—24no—
398C22×D4—24no—
399C22×D4—416no—
400C22×D4—416no—
401C22×D4—44no—
402C22×D4—44no—
403C22×D4—464no—
404C22×D4—44no—
405C22×D4—44no—
406C22×D4—44no—
407C22×D4—44no—
408C22×D4—44no—
409C22×D4—44no—
410C22×D4—44no—
411C22×D4—44no—
412C22×D4—44no—
413C22×D4—44no—
414C22×D4—44no—
415C22×D4—44no—
416C22×D4—44no—
417C22×D4—44no—
418C22×D4—44no—
419C22×D4—44no—
420C22×D4—44no—
421C22×D4—44no—
422C22×D4—44no—
423C22×D4—44no—
424C22×D4—44no—
425C22×D4C2414yes—
426C22×D4C2418yes—
427C22×D4C2414yes—
428C22×D4C2414yes—
429C22×D4C2414yes—
430C22×D4C2418yes—
431C22×D4C2418yes—
432C22×D4C2418yes—
433C22×D4C2418yes—
434C22×D4C2418yes—
435C22×D4C2418yes—
436C22×D4C2418yes—
437C22×D4C2418yes—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—24no—
441C23×C4—24no—
442C23×C4—28no—
443C23×C4—24no—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—28no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—44no—
452C23×C4—44no—
453C23×C4—44no—
454C23×C4—44no—
455C23×C4#4118yes—
456C23×C4C2414yes—
457C23×C4C2411yescharacteristic
458C23×C4C2412yes—
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2414yes—
473C23×C4C2414yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2418yes—
477C23×C4C2414yes—
478C23×C4C2418yes—
479C23×C4C2411yescharacteristic
480#127—416no—
481#127—416no—
482#125—416no—
483#123—432no—
484#121—232no—
485#121—432no—
486#121—416no—
487#121—416no—
488#121—416no—
489#121—432no—
490#120—432no—
491#120—432no—
492#120—432no—
493C4×D4—232no—
494C4×D4—416no—
495C4×D4—432no—
496#117—416no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—416no—
505C2×C4⋊C4—44no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—44no—
510C2×C4⋊C4—44no—
511C2×C4⋊C4—44no—
512C2×C4⋊C4—44no—
513C2×C4⋊C4—44no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—28no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—28no—
538C2×C22⋊C4—28no—
539C2×C22⋊C4—28no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—432no—
542C2×C22⋊C4—44no—
543C2×C22⋊C4—44no—
544C2×C22⋊C4—44no—
545C2×C22⋊C4—44no—
546C2×C22⋊C4—44no—
547C2×C22⋊C4—44no—
548C2×C22⋊C4—432no—
549C2×C22⋊C4—44no—
550C2×C22⋊C4—44no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—44no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4—44no—
557C2×C22⋊C4—44no—
558C2×C22⋊C4—44no—
559C2×C22⋊C4—44no—
560C2×C22⋊C4—44no—
561C2×C22⋊C4—44no—
562C2×C22⋊C4—44no—
563C2×C22⋊C4—44no—
564C2×C22⋊C4—44no—
565C2×C22⋊C4—44no—
566C2×C22⋊C4—44no—
567C2×C22⋊C4—44no—
568C2×C22⋊C4—44no—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C42—24no—
605C2×C42—24no—
606C2×C42—24no—
607C2×C42—24no—
608C2×C42—24no—
609C2×C42—416no—
610C2×C42—44no—
611C2×C42—42no—
612C2×C42—42no—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2414yes—
618C2×C42C2418yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2418yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—24no—
646C24—216no—
647C24—24no—
648C24—24no—
649C24—24no—
650C24—24no—
651C24—22no—
652C24—24no—
653C24—24no—
654C24—22no—
655C24—22no—
656C24—24no—
657C24—24no—
658C24—24no—
659C24—24no—
660C24—24no—
661C24—24no—
662C24—24no—
663C24—24no—
664C24—24no—
665C24—22no—
666C24—22no—
667C24—24no—
668C24—24no—
669C24—24no—
670C24—22no—
671C24—24no—
672C24—24no—
673C24—216no—
674C24—216no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—432no—
680C24—432no—
681C24—432no—
682C24—816no—
683C24—816no—
684C24—816no—
685C24—816no—
686C24C2×#4114yes—
687C24H(5,𝔽2)14yes—
688C24H(5,𝔽2)14yes—
689C24C2514yes—
690C24C2514yes—
691C24C2512yes—
692C24C2514yes—
693C24C2512yes—
694C24C2511yescharacteristic
695C2×D4—28no—
696C2×D4—216no—
697C2×D4—216no—
698C2×D4—28no—
699C2×D4—216no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—432no—
714C2×D4—4128no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—416no—
737C2×D4—432no—
738C2×D4—416no—
739C2×D4—416no—
740C2×D4—416no—
741C2×D4—816no—
742C2×D4—816no—
743C2×D4—816no—
744C2×D4—816no—
745C2×D4—816no—
746C2×D4—816no—
747C2×D4—816no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—232no—
753C22×C4—28no—
754C22×C4—28no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—28no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—24no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—22no—
795C22×C4—28no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—216no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—216no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—416no—
816C22×C4—416no—
817C22×C4—416no—
818C22×C4—816no—
819C22×C4—816no—
820C22×C4C2×#4114yes—
821C22×C4C2×#41116yes—
822C22×C4C2×#4114yes—
823C22×C4H(5,𝔽2)14yes—
824C22×C4H(5,𝔽2)14yes—
825C22×C4H(5,𝔽2)14yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C22⋊C4—28no—
862C22⋊C4—216no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—216no—
867C22⋊C4—216no—
868C22⋊C4—216no—
869C22⋊C4—28no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C42—28no—
897C42—28no—
898C42—28no—
899C42—28no—
900C42—28no—
901C42—44no—
902C42—44no—
903C42—48no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—28no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—22no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—22no—
921C23—24no—
922C23—24no—
923C23—22no—
924C23—22no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—22no—
935C23—22no—
936C23—24no—
937C23—24no—
938C23—22no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—432no—
943C23—432no—
944C23—44no—
945C23—48no—
946C23—48no—
947C23—48no—
948C23—44no—
949C23—48no—
950C23—432no—
951C23—48no—
952C23—48no—
953C23—44no—
954C23—48no—
955C23—48no—
956C23—48no—
957C23—48no—
958C23—44no—
959C23—48no—
960C23—48no—
961C23—48no—
962C23—48no—
963C23—44no—
964C23—48no—
965C23—44no—
966C23—48no—
967C23—48no—
968C23—48no—
969C23—44no—
970C23—48no—
971C23—48no—
972C23—48no—
973C23—816no—
974C23—816no—
975C23—816no—
976C23—816no—
977C23—8128no—
978C23#540116yes—
979C23C22×#4114yes—
980C23C22×#4112yes—
981C23C2×H(5,𝔽2)14yes—
982C23C2×H(5,𝔽2)14yes—
983C23C2×H(5,𝔽2)12yes—
984C23C2×H(5,𝔽2)12yes—
985C23C2×H(5,𝔽2)12yes—
986C23C2×H(5,𝔽2)12yes—
987C23C2×H(5,𝔽2)12yes—
988C23#58512yes—
989C23C2611yescharacteristic
990D4—432no—
991D4—416no—
992D4—432no—
993D4—416no—
994D4—416no—
995D4—416no—
996D4—816no—
997D4—816no—
998D4—816no—
999D4—816no—
1000D4—816no—
1001D4—816no—
1002D4—816no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—232no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—416no—
1056C2×C4—416no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—48no—
1063C2×C4—44no—
1064C2×C4—44no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—48no—
1068C2×C4—48no—
1069C2×C4—44no—
1070C2×C4—48no—
1071C2×C4—44no—
1072C2×C4—416no—
1073C2×C4—816no—
1074C2×C4—816no—
1075C2×C4#538116yes—
1076C2×C4C22×#4114yes—
1077C2×C4C22×#4114yes—
1078C2×C4C2×H(5,𝔽2)14yes—
1079C2×C4C2×H(5,𝔽2)14yes—
1080C2×C4C2×H(5,𝔽2)14yes—
1081C22—24no—
1082C22—24no—
1083C22—24no—
1084C22—232no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—44no—
1089C22—42no—
1090C22—44no—
1091C22—44no—
1092C22—42no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—42no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22—42no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—42no—
1105C22—44no—
1106C22—44no—
1107C22—44no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—42no—
1115C22—44no—
1116C22—864no—
1117C22—88no—
1118C22—816no—
1119C22—816no—
1120C22—816no—
1121C22C2×#53814yes—
1122C22C2×#54018yes—
1123C22C2×#54014yes—
1124C22#346014yes—
1125C22#353714yes—
1126C22#354214yes—
1127C22#354314yes—
1128C22#355814yes—
1129C22C23×#4111yescharacteristic
1130C22C22×H(5,𝔽2)11yescharacteristic
1131C22C22×H(5,𝔽2)11yescharacteristic
1132C22C22×H(5,𝔽2)11yescharacteristic
1133C22C22×H(5,𝔽2)11yescharacteristic
1134C22C22×H(5,𝔽2)11yescharacteristic
1135C22C2×#58511yescharacteristic
1136C4—24no—
1137C4—24no—
1138C4—42no—
1139C4—44no—
1140C4—42no—
1141C4—44no—
1142C4—42no—
1143C4—44no—
1144C4—44no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4C2×#53818yes—
1154C2—28no—
1155C2—84no—
1156C2—82no—
1157C2—84no—
1158C2—84no—
1159C2#3749318yesdirect product factor
1160C2C22×#53811yescharacteristic
1161C2C22×#54011yescharacteristic
1162C2C2×#346011yescharacteristic
1163C2C2×#354211yescharacteristic
1164C2C2×#353711yescharacteristic
1165C2C2×#355811yescharacteristic
1166C2C2×#354311yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37493C2direct (N × H)
2. C2×#2828C2semidirect
3. C2×#2829C2semidirect
4. C2×#2513C2semidirect
5. C2×#2490C2semidirect
6. C2×#2442C2semidirect
7. C2×#2445C2semidirect
8. C2×#2428C2semidirect
9. C2×#2433C2semidirect
10. C2×#2416C2semidirect
11. C2×#2408C2semidirect
12. C2×#2424C2semidirect
13. C2×#2418C2semidirect
14. C2×#2641C2semidirect
15. C2×#2644C2semidirect
16. C2×#2624C2semidirect
17. C2×#2619C2semidirect
18. C2×#2661C2semidirect
19. C2×#2648C2semidirect
20. C2×#2622C2semidirect
21. C2×#2617C2semidirect
22. C2×C4×#121C2semidirect
23. C22×#390C2semidirect
24. C2×#2290C2semidirect
28. C22×#125C22semidirect
29. C22×#123C22semidirect
34. C22×#121C22semidirect
35. C22×#121C22semidirect
41. C22×C4×D4C22semidirect
42. C22×#117C22semidirect
47. #2829C22semidirect
48. #2828C22semidirect
49. #2661C22semidirect
50. #2648C22semidirect
51. #2644C22semidirect
52. #2641C22semidirect
53. #2624C22semidirect
54. #2622C22semidirect
55. #2619C22semidirect
56. #2617C22semidirect
57. #2513C22semidirect
58. #2490C22semidirect
59. #2445C22semidirect
60. #2442C22semidirect
61. #2433C22semidirect
62. #2428C22semidirect
63. #2424C22semidirect
64. #2418C22semidirect
65. #2416C22semidirect
66. #2408C22semidirect
67. C2×#400C22semidirect
68. C2×#399C22semidirect
69. C2×#398C22semidirect
70. C2×#397C22semidirect
71. C2×#397C22semidirect
72. C2×#397C22semidirect
73. C2×#397C22semidirect
74. C2×#397C22semidirect
75. C2×#397C22semidirect
76. C2×#397C22semidirect
77. C2×#396C22semidirect
78. C2×#396C22semidirect
80. C2×#394C22semidirect
81. C2×#394C22semidirect
82. C2×#394C22semidirect
83. C2×#394C22semidirect
84. C2×#394C22semidirect
85. C2×#394C22semidirect
86. C2×#394C22semidirect
87. C2×#394C22semidirect
88. C2×#394C22semidirect
89. C2×#394C22semidirect
90. C2×#394C22semidirect
91. C2×#394C22semidirect
92. C2×#394C22semidirect
96. C2×#392C22semidirect
97. C2×#392C22semidirect
98. C2×#392C22semidirect
99. C4×#121C22semidirect
110. C2×#390C22semidirect
111. C2×#390C22semidirect
112. C2×#390C22semidirect
113. C2×#390C22semidirect
114. C2×#389C22semidirect
115. C2×#389C22semidirect
116. C2×#389C22semidirect
117. C2×#389C22semidirect
118. #2290C22semidirect
119. C2×#388C22semidirect
120. C2×#388C22semidirect
121. C2×#388C22semidirect
122. C2×#388C22semidirect
123. C2×#388C22semidirect
124. C2×#388C22semidirect
125. C2×#387C22semidirect
126. C2×#387C22semidirect
131. C2×#386C22semidirect
132. C2×#386C22semidirect
136. C2×#382C22semidirect
139. C2×#380C22semidirect
141. C2×C4×C4⋊C4C22semidirect
142. C2×C4×C4⋊C4C22semidirect
144. C2×C4×C22⋊C4C22semidirect
145. C2×C4×C22⋊C4C22semidirect
146. C2×#376C22semidirect
176. C2×#125C23semidirect
178. C2×#123C23semidirect
189. C2×#121C23semidirect
190. C2×#121C23semidirect
202. C2×C4×D4C23semidirect
204. C2×#117C23semidirect
273. #400C23semidirect
274. #399C23semidirect
275. #398C23semidirect
276. #397C23semidirect
277. #397C23semidirect
278. #397C23semidirect
279. #397C23semidirect
280. #397C23semidirect
281. #397C23semidirect
282. #397C23semidirect
283. #396C23semidirect
284. #396C23semidirect
286. #394C23semidirect
287. #394C23semidirect
288. #394C23semidirect
289. #394C23semidirect
290. #394C23semidirect
291. #394C23semidirect
292. #394C23semidirect
293. #394C23semidirect
294. #394C23semidirect
295. #394C23semidirect
296. #394C23semidirect
297. #394C23semidirect
298. #394C23semidirect
302. #392C23semidirect
303. #392C23semidirect
304. #392C23semidirect
315. #390C23semidirect
316. #390C23semidirect
317. #390C23semidirect
318. #389C23semidirect
319. #389C23semidirect
320. #389C23semidirect
321. #389C23semidirect
322. #388C23semidirect
323. #388C23semidirect
324. #388C23semidirect
325. #388C23semidirect
326. #388C23semidirect
327. #388C23semidirect
328. #387C23semidirect
329. #387C23semidirect
334. #386C23semidirect
335. #386C23semidirect
339. #382C23semidirect
342. #380C23semidirect
344. C4×C4⋊C4C23semidirect
345. C4×C4⋊C4C23semidirect
347. C4×C22⋊C4C23semidirect
348. C4×C22⋊C4C23semidirect
349. #376C23semidirect
1159. C2#37493direct (N × H)

Maximal subgroups

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

subgroupindex
#374932
C2×#28282
C2×#28292
C2×#25132
C2×#24902
C2×#24422
C2×#24452
C2×#24282
C2×#24332
C2×#24162
C2×#24082
C2×#24242
C2×#24182
C2×#26412
C2×#26442
C2×#26242
C2×#26192
C2×#26612
C2×#26482
C2×#26222
C2×#26172
C2×C4×#1212
C22×#3902
C2×#22902