Finite Group Databasebeta

← C2×C4⋊C4×#120 #72302669

Subgroups — C2×C4⋊C4×#120 #72302669

Order 1024.

79085 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×D4×C4⋊C4C213yesmaximal, complemented
3C22×C4×#120C212yesmaximal
4C22×C4×#120C211yesmaximal, characteristic
5C2×#14693C212yesmaximal, complemented
6C2×#14680C211yesmaximal, characteristic, complemented
7C4⋊C4×#120C2132yesmaximal, direct product factor
8C2×#14043C216yesmaximal, complemented
9C2×#14015C216yesmaximal, complemented
10C2×#13880C213yesmaximal, complemented
11C2×#13872C213yesmaximal, complemented
12C2×C22⋊C4×C4⋊C4C213yesmaximal, complemented
13C26×C4C2211yescharacteristic
14C26×C4C2212yes—
15C23×#120C2211yescharacteristic
16C23×C4×D4C2216yes—
17C23×C4×D4C2213yes—
18C24×C4⋊C4—248no—
19C24×C4⋊C4C2213yes—
20C24×C4⋊C4C2216yes—
21C24×C4⋊C4C2213yes—
22C24×C4⋊C4C22116yescomplemented
23C24×C4⋊C4C2211yescharacteristic, complemented
24C2×D4×C4⋊C4—248no—
25C2×D4×C4⋊C4C22148yescomplemented
26C2×C4×#120—232no—
27C2×C4×#120C4132yescomplemented
28C2×C4×#120C22132yes—
29C2×C4×#120C22116yes—
30C22×#389C2216yescomplemented
31C22×#386C2216yes—
32C22×#386C2213yes—
33C22×#385C2216yes—
34C22×#385C2216yes—
35C22×#385C2216yes—
36C22×#385C2213yes—
37C22×#385C2216yescomplemented
38C22×#384C2213yescomplemented
39C22×#380C2213yes—
40C22×#380C2213yes—
41C22×#380C2213yescomplemented
42C22×#379C2212yes—
43C22×#379C2211yescharacteristic
44C22×C4×C4⋊C4C2213yescomplemented
45C22×C4×C22⋊C4C2216yes—
46C22×C4×C22⋊C4C2213yes—
47#14693C22132yescomplemented
48#14680C22116yescomplemented
49#14043C22196yescomplemented
50#14015C22196yescomplemented
51#13880C22148yescomplemented
52#13872C22148yescomplemented
53C2×#1444C22112yescomplemented
54C2×#1441C2216yescomplemented
55C2×#1439C2216yescomplemented
56C22⋊C4×C4⋊C4C22148yescomplemented
57C2×#1436C22112yescomplemented
58C2×C4⋊#95C2216yescomplemented
59C2×C22⋊#95C2216yes—
60C2×C22⋊#95C2216yes—
61C2×C22⋊#95C2216yes—
62C27C2311yescharacteristic
63C24×D4C2313yes—
64C25×C4—224no—
65C25×C4—224no—
66C25×C4—248no—
67C25×C4—216no—
68C25×C4—424no—
69C25×C4C2×C4116yescomplemented
70C25×C4C2313yes—
71C25×C4C2318yes—
72C25×C4C2311yescharacteristic
73C25×C4C2316yes—
74C25×C4C23116yes—
75C25×C4C2312yes—
76C25×C4C2316yes—
77C25×C4C2313yes—
78C22×#120C2×C4116yes—
79C22×#120D4116yes—
80C22×#120Q8116yes—
81C22×#120C2318yes—
82C22×C4×D4—224no—
83C22×C4×D4—224no—
84C22×C4×D4—248no—
85C22×C4×D4—248no—
86C22×C4×D4—424no—
87C22×C4×D4C2×C4148yescomplemented
88C22×C4×D4C23148yes—
89C22×C4×D4C23124yes—
90C23×C4⋊C4—2512no—
91C23×C4⋊C4—248no—
92C23×C4⋊C4—224no—
93C23×C4⋊C4—248no—
94C23×C4⋊C4—296no—
95C23×C4⋊C4—248no—
96C23×C4⋊C4—2384no—
97C23×C4⋊C4—224no—
98C23×C4⋊C4D4148yescomplemented
99C23×C4⋊C4C2316yes—
100C23×C4⋊C4C23124yes—
101C23×C4⋊C4C23148yes—
102C23×C4⋊C4C2311yescharacteristic
103C23×C4⋊C4C2312yes—
104C23×C4⋊C4C2313yes—
105C23×C4⋊C4C2316yes—
106C23×C4⋊C4C2313yes—
107C23×C4⋊C4C2313yes—
108C23×C4⋊C4C2316yes—
109C23×C4⋊C4C23124yes—
110C23×C4⋊C4C2316yes—
111C23×C4⋊C4C2311yescharacteristic
112C23×C4⋊C4C2318yescomplemented
113C23×C22⋊C4C2316yes—
114C23×C22⋊C4C2316yes—
115C23×C22⋊C4C2316yes—
116C23×C22⋊C4C2313yes—
117C23×C22⋊C4C2313yes—
118C23×C22⋊C4C2313yes—
119C23×C22⋊C4C2313yes—
120C23×C42C2316yes—
121C23×C42C2313yes—
122D4×C4⋊C4—2384no—
123C4×#120—2256no—
124C4×#120C2×C41256yescomplemented
125C2×#389—248no—
126C2×#389C23148yescomplemented
127C2×#386—248no—
128C2×#386C2×C4148yescomplemented
129C2×#386C23148yes—
130C2×#386C23124yes—
131C2×#385—248no—
132C2×#385—248no—
133C2×#385—248no—
134C2×#385—424no—
135C2×#385C2×C4148yescomplemented
136C2×#385C23148yes—
137C2×#385C23148yes—
138C2×#385C23148yes—
139C2×#385C23124yes—
140C2×#385C23148yescomplemented
141C2×#384—224no—
142C2×#384C23124yescomplemented
143C2×#380—224no—
144C2×#380—224no—
145C2×#380—224no—
146C2×#380C23124yes—
147C2×#380C23124yes—
148C2×#380C23124yescomplemented
149C2×#379—216no—
150C2×#379C2×C4116yescomplemented
151C2×#379C23116yes—
152C2×#379C2318yes—
153C2×C4×C4⋊C4—224no—
154C2×C4×C4⋊C4C23124yescomplemented
155C2×C4×C22⋊C4—248no—
156C2×C4×C22⋊C4C2×C4148yescomplemented
157C2×C4×C22⋊C4C23148yes—
158C2×C4×C22⋊C4C23124yes—
159C22×#95C2316yes—
160C22×#95C2316yes—
161C22×#95C23112yes—
162C22×#95C2316yes—
163C22×#95C2316yes—
164C22×#95C23112yes—
165C22×#95C2316yes—
166#1444C23196yescomplemented
167#1441C23148yescomplemented
168#1439C23148yescomplemented
169#1436C23196yescomplemented
170C4⋊#95C23148yescomplemented
171C22⋊#95C23148yes—
172C22⋊#95C23148yes—
173C22⋊#95C23148yes—
174C26—212no—
175C26—212no—
176C26—212no—
177C26—212no—
178C26C22×C418yes—
179C26C2×D418yes—
180C26C2×Q818yes—
181C26C2414yes—
182C26C2411yescharacteristic
183C26C2413yes—
184C23×D4—212no—
185C23×D4—212no—
186C23×D4—212no—
187C23×D4—212no—
188C23×D4C22×C4124yes—
189C23×D4C2×D4124yes—
190C23×D4C2×Q8124yes—
191C23×D4C24112yes—
192C24×C4—2384no—
193C24×C4—2128no—
194C24×C4—212no—
195C24×C4—212no—
196C24×C4—2384no—
197C24×C4—224no—
198C24×C4—296no—
199C24×C4—224no—
200C24×C4—224no—
201C24×C4—296no—
202C24×C4—224no—
203C24×C4—2256no—
204C24×C4—224no—
205C24×C4—224no—
206C24×C4—224no—
207C24×C4—248no—
208C24×C4—2192no—
209C24×C4—248no—
210C24×C4—212no—
211C24×C4—212no—
212C24×C4—224no—
213C24×C4—264no—
214C24×C4—28no—
215C24×C4—224no—
216C24×C4—224no—
217C24×C4—424no—
218C24×C4—424no—
219C24×C4—496no—
220C24×C4—412no—
221C24×C4—4384no—
222C24×C4—4384no—
223C24×C4C22×C4124yes—
224C24×C4C22×C4124yes—
225C24×C4C22×C4164yescomplemented
226C24×C4C22×C418yescomplemented
227C24×C4C2×D4148yes—
228C24×C4C2×D4124yes—
229C24×C4#41124yes—
230C24×C4C2412yes—
231C24×C4C2416yes—
232C24×C4C24112yes—
233C24×C4C2411yescharacteristic
234C24×C4C2413yes—
235C24×C4C2414yes—
236C24×C4C2416yes—
237C24×C4C24124yes—
238C24×C4C2418yes—
239C24×C4C24124yes—
240C24×C4C2413yes—
241C24×C4C24112yes—
242C24×C4C2413yes—
243C24×C4C2412yes—
244C24×C4C2411yescharacteristic
245C2×#120C4⋊C41256yesdirect product factor
246C2×#120C22×C4164yes—
247C2×#120C2×D4164yes—
248C2×#120C2×Q8164yes—
249C2×C4×D4—2384no—
250C2×C4×D4—296no—
251C2×C4×D4—296no—
252C2×C4×D4—2192no—
253C2×C4×D4—2192no—
254C2×C4×D4—496no—
255C2×C4×D4—4384no—
256C2×C4×D4C22×C41192yescomplemented
257C22×C4⋊C4—2768no—
258C22×C4⋊C4—2384no—
259C22×C4⋊C4—22048no—
260C22×C4⋊C4—248no—
261C22×C4⋊C4—2192no—
262C22×C4⋊C4—224no—
263C22×C4⋊C4—296no—
264C22×C4⋊C4—248no—
265C22×C4⋊C4—224no—
266C22×C4⋊C4—212no—
267C22×C4⋊C4—212no—
268C22×C4⋊C4—2384no—
269C22×C4⋊C4—2192no—
270C22×C4⋊C4—2384no—
271C22×C4⋊C4—2192no—
272C22×C4⋊C4—212no—
273C22×C4⋊C4—224no—
274C22×C4⋊C4—224no—
275C22×C4⋊C4—224no—
276C22×C4⋊C4—212no—
277C22×C4⋊C4—224no—
278C22×C4⋊C4—224no—
279C22×C4⋊C4—296no—
280C22×C4⋊C4—412no—
281C22×C4⋊C4—464no—
282C22×C4⋊C4—424no—
283C22×C4⋊C4C22×C4124yescomplemented
284C22×C4⋊C4C2×D4124yes—
285C22×C4⋊C4C2×D4148yes—
286C22×C4⋊C4C2×D4124yes—
287C22×C4⋊C4C2×D41192yescomplemented
288C22×C4⋊C4C24124yes—
289C22×C4⋊C4C2414yes—
290C22×C4⋊C4C2418yes—
291C22×C4⋊C4C24112yes—
292C22×C4⋊C4C24124yes—
293C22×C4⋊C4C24112yes—
294C22×C4⋊C4C24112yes—
295C22×C4⋊C4C24124yes—
296C22×C4⋊C4C24124yes—
297C22×C4⋊C4C2414yes—
298C22×C22⋊C4—212no—
299C22×C22⋊C4—212no—
300C22×C22⋊C4—212no—
301C22×C22⋊C4—212no—
302C22×C22⋊C4—212no—
303C22×C22⋊C4—212no—
304C22×C22⋊C4—224no—
305C22×C22⋊C4—224no—
306C22×C22⋊C4—224no—
307C22×C22⋊C4—224no—
308C22×C22⋊C4—224no—
309C22×C22⋊C4—224no—
310C22×C22⋊C4—224no—
311C22×C22⋊C4—224no—
312C22×C22⋊C4—412no—
313C22×C22⋊C4C22×C4124yes—
314C22×C22⋊C4C22×C4124yes—
315C22×C22⋊C4C22×C4124yes—
316C22×C22⋊C4C22×C4124yescomplemented
317C22×C22⋊C4C2×D4124yes—
318C22×C22⋊C4C2×Q8124yes—
319C22×C22⋊C4C24124yes—
320C22×C22⋊C4C24124yes—
321C22×C22⋊C4C24124yes—
322C22×C22⋊C4C24112yes—
323C22×C22⋊C4C24112yes—
324C22×C22⋊C4C24112yes—
325C22×C22⋊C4C24112yes—
326C22×C42—212no—
327C22×C42—212no—
328C22×C42—224no—
329C22×C42—224no—
330C22×C42—412no—
331C22×C42C22×C4124yescomplemented
332C22×C42C24124yes—
333C22×C42C24112yes—
334#389—2192no—
335#386—2192no—
336#386C22×C41192yescomplemented
337#385—2192no—
338#385—2192no—
339#385—2192no—
340#385—496no—
341#385C22×C41192yescomplemented
342#384—296no—
343#380—296no—
344#380—296no—
345#380—296no—
346#379—264no—
347#379C22×C4164yescomplemented
348C4×C4⋊C4—296no—
349C4×C22⋊C4—2192no—
350C4×C22⋊C4C22×C41192yescomplemented
351C2×#95—248no—
352C2×#95—224no—
353C2×#95—224no—
354C2×#95—224no—
355C2×#95—224no—
356C2×#95—424no—
357C2×#95C22×C4148yescomplemented
358C2×#95C24124yes—
359C2×#95C24124yes—
360C2×#95C24124yes—
361C2×#95C24124yes—
362C2×#95C24148yes—
363C2×#95C24148yes—
364C2×#95C24124yes—
365C25—232no—
366C25—296no—
367C25—296no—
368C25—296no—
369C25—2192no—
370C25—296no—
371C25—296no—
372C25—296no—
373C25—296no—
374C25—296no—
375C25—296no—
376C25—224no—
377C25—212no—
378C25—224no—
379C25—212no—
380C25—224no—
381C25—212no—
382C25—224no—
383C25—212no—
384C25—26no—
385C25—26no—
386C25—26no—
387C25—26no—
388C25C2×C4⋊C4164yescomplemented
389C25C23×C414yes—
390C25C23×C4116yes—
391C25C23×C4112yes—
392C25C22×D414yes—
393C25C22×D4116yes—
394C25C22×D4112yes—
395C25C22×D4112yes—
396C25C22×Q8116yes—
397C25C22×Q814yes—
398C25C22×Q8112yes—
399C25C2×#41112yes—
400C25H(5,𝔽2)112yes—
401C252−1+4112yes—
402C25C2512yes—
403C25C2516yes—
404C25C2511yescharacteristic
405C22×D4—296no—
406C22×D4—296no—
407C22×D4—296no—
408C22×D4—296no—
409C22×D4—296no—
410C22×D4—296no—
411C22×D4—224no—
412C22×D4—224no—
413C22×D4—224no—
414C22×D4—224no—
415C22×D4C2×C4⋊C41192yescomplemented
416C22×D4C23×C4148yes—
417C22×D4C22×D4148yes—
418C22×D4C22×Q8148yes—
419C23×C4—296no—
420C23×C4—2256no—
421C23×C4—2192no—
422C23×C4—296no—
423C23×C4—2768no—
424C23×C4—22048no—
425C23×C4—296no—
426C23×C4—224no—
427C23×C4—212no—
428C23×C4—26no—
429C23×C4—24no—
430C23×C4—26no—
431C23×C4—224no—
432C23×C4—212no—
433C23×C4—26no—
434C23×C4—212no—
435C23×C4—26no—
436C23×C4—2192no—
437C23×C4—2192no—
438C23×C4—2768no—
439C23×C4—296no—
440C23×C4—296no—
441C23×C4—2192no—
442C23×C4—248no—
443C23×C4—248no—
444C23×C4—248no—
445C23×C4—248no—
446C23×C4—2192no—
447C23×C4—2512no—
448C23×C4—2192no—
449C23×C4—26no—
450C23×C4—26no—
451C23×C4—212no—
452C23×C4—248no—
453C23×C4—224no—
454C23×C4—248no—
455C23×C4—26no—
456C23×C4—26no—
457C23×C4—212no—
458C23×C4—212no—
459C23×C4—224no—
460C23×C4—248no—
461C23×C4—212no—
462C23×C4—296no—
463C23×C4—2192no—
464C23×C4—296no—
465C23×C4—296no—
466C23×C4—224no—
467C23×C4—224no—
468C23×C4—212no—
469C23×C4—24no—
470C23×C4—212no—
471C23×C4—212no—
472C23×C4—216no—
473C23×C4—248no—
474C23×C4—224no—
475C23×C4—212no—
476C23×C4—212no—
477C23×C4—248no—
478C23×C4—224no—
479C23×C4—248no—
480C23×C4—496no—
481C23×C4—448no—
482C23×C4—448no—
483C23×C4—424no—
484C23×C4—4192no—
485C23×C4—4192no—
486C23×C4—4192no—
487C23×C4—4768no—
488C23×C4—4192no—
489C23×C4—496no—
490C23×C4—4768no—
491C23×C4—42048no—
492C23×C4—496no—
493C23×C4—496no—
494C23×C4—416no—
495C23×C4—448no—
496C23×C4—432no—
497C23×C4—848no—
498C23×C4C4×D41192yescomplemented
499C23×C4C23×C4112yes—
500C23×C4C23×C414yes—
501C23×C4C23×C4148yes—
502C23×C4C23×C4112yes—
503C23×C4C23×C4112yes—
504C23×C4C23×C4148yes—
505C23×C4C23×C414yes—
506C23×C4C23×C4116yescomplemented
507C23×C4C22×D4124yes—
508C23×C4C22×D4196yes—
509C23×C4C22×D4112yes—
510C23×C4C22×D4112yes—
511C23×C4C22×D4148yes—
512C23×C4C22×D4124yes—
513C23×C4C22×D4112yes—
514C23×C4C22×Q8112yes—
515C23×C4C2×#41112yes—
516C23×C4C2×#41148yes—
517C23×C4C2×#41112yes—
518C23×C4C25112yes—
519C23×C4C2514yes—
520C23×C4C2516yes—
521C23×C4C2512yes—
522C23×C4C25112yes—
523C23×C4C2516yes—
524C23×C4C2516yes—
525C23×C4C2514yes—
526C23×C4C2512yes—
527#120C2×C4⋊C41512yesdirect product factor
528C4×D4—2768no—
529C4×D4—4768no—
530C2×C4⋊C4—2192no—
531C2×C4⋊C4—21536no—
532C2×C4⋊C4—2768no—
533C2×C4⋊C4—296no—
534C2×C4⋊C4—2192no—
535C2×C4⋊C4—296no—
536C2×C4⋊C4—296no—
537C2×C4⋊C4—248no—
538C2×C4⋊C4—296no—
539C2×C4⋊C4—248no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—2768no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—248no—
545C2×C4⋊C4—248no—
546C2×C4⋊C4—248no—
547C2×C4⋊C4—224no—
548C2×C4⋊C4—248no—
549C2×C4⋊C4—248no—
550C2×C4⋊C4—424no—
551C2×C4⋊C4—496no—
552C2×C4⋊C4—432no—
553C2×C4⋊C4—416no—
554C2×C4⋊C4—448no—
555C2×C4⋊C4—4128no—
556C2×C4⋊C4—448no—
557C2×C4⋊C4—848no—
558C2×C4⋊C4#120164yesdirect product factor
559C2×C4⋊C4C23×C4148yescomplemented
560C2×C4⋊C4C22×D4148yes—
561C2×C4⋊C4C22×D4196yes—
562C2×C4⋊C4C22×D4148yes—
563C2×C22⋊C4—296no—
564C2×C22⋊C4—296no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—224no—
568C2×C22⋊C4—224no—
569C2×C22⋊C4—296no—
570C2×C22⋊C4—224no—
571C2×C22⋊C4—224no—
572C2×C22⋊C4—248no—
573C2×C22⋊C4—248no—
574C2×C22⋊C4—248no—
575C2×C22⋊C4—248no—
576C2×C22⋊C4—248no—
577C2×C22⋊C4—248no—
578C2×C22⋊C4—248no—
579C2×C22⋊C4—248no—
580C2×C22⋊C4—424no—
581C2×C22⋊C4—496no—
582C2×C22⋊C4—496no—
583C2×C22⋊C4—496no—
584C2×C22⋊C4C2×C4⋊C41192yescomplemented
585C2×C22⋊C4C23×C4148yes—
586C2×C22⋊C4C23×C4148yes—
587C2×C22⋊C4C23×C4148yes—
588C2×C22⋊C4C23×C4148yescomplemented
589C2×C22⋊C4C22×D4148yes—
590C2×C22⋊C4C22×Q8148yes—
591C2×C42—296no—
592C2×C42—224no—
593C2×C42—224no—
594C2×C42—248no—
595C2×C42—248no—
596C2×C42—424no—
597C2×C42—496no—
598C2×C42C23×C4148yescomplemented
599#95—296no—
600#95—248no—
601#95—248no—
602#95—248no—
603#95—248no—
604#95—448no—
605#95C23×C4196yescomplemented
606C24—232no—
607C24—296no—
608C24—2256no—
609C24—296no—
610C24—2256no—
611C24—2768no—
612C24—2192no—
613C24—296no—
614C24—2768no—
615C24—2256no—
616C24—2768no—
617C24—212no—
618C24—212no—
619C24—212no—
620C24—212no—
621C24—2768no—
622C24—296no—
623C24—248no—
624C24—296no—
625C24—248no—
626C24—224no—
627C24—224no—
628C24—248no—
629C24—296no—
630C24—248no—
631C24—296no—
632C24—248no—
633C24—296no—
634C24—248no—
635C24—296no—
636C24—248no—
637C24—224no—
638C24—248no—
639C24—224no—
640C24—248no—
641C24—248no—
642C24—248no—
643C24—248no—
644C24—26no—
645C24—26no—
646C24—26no—
647C24—26no—
648C24—224no—
649C24—224no—
650C24—224no—
651C24—224no—
652C24—224no—
653C24—224no—
654C24—44no—
655C24—412no—
656C24—412no—
657C24—412no—
658C24—424no—
659C24C22×C4⋊C4148yes—
660C24C22×C4⋊C4164yescomplemented
661C24C22×C4⋊C4116yescomplemented
662C24C2×C4×D4148yes—
663C24#520148yes—
664C24D42148yes—
665C24#547148yes—
666C24D4×Q8148yes—
667C24#554148yes—
668C24C24×C414yes—
669C24C24×C4112yes—
670C24C24×C412yes—
671C24C23×D414yes—
672C24C23×D4112yes—
673C24C23×D4112yes—
674C24C23×D412yes—
675C24C23×D416yes—
676C24C23×Q814yes—
677C24C23×Q8112yes—
678C24C23×Q812yes—
679C24C22×#41112yes—
680C24C22×#4116yes—
681C24C2×H(5,𝔽2)112yes—
682C24C2×H(5,𝔽2)16yes—
683C24C2×2−1+4112yes—
684C24C2×2−1+416yes—
685C24C2611yescharacteristic
686C2×D4—2768no—
687C2×D4—296no—
688C2×D4—296no—
689C2×D4—296no—
690C2×D4—296no—
691C2×D4—296no—
692C2×D4—296no—
693C2×D4C22×C4⋊C41192yescomplemented
694C22×C4—296no—
695C22×C4—2192no—
696C22×C4—296no—
697C22×C4—2768no—
698C22×C4—22048no—
699C22×C4—26no—
700C22×C4—24no—
701C22×C4—212no—
702C22×C4—26no—
703C22×C4—212no—
704C22×C4—26no—
705C22×C4—212no—
706C22×C4—26no—
707C22×C4—224no—
708C22×C4—296no—
709C22×C4—248no—
710C22×C4—224no—
711C22×C4—224no—
712C22×C4—224no—
713C22×C4—248no—
714C22×C4—224no—
715C22×C4—248no—
716C22×C4—224no—
717C22×C4—224no—
718C22×C4—224no—
719C22×C4—248no—
720C22×C4—2192no—
721C22×C4—2192no—
722C22×C4—296no—
723C22×C4—296no—
724C22×C4—2192no—
725C22×C4—2768no—
726C22×C4—2192no—
727C22×C4—26no—
728C22×C4—26no—
729C22×C4—212no—
730C22×C4—224no—
731C22×C4—26no—
732C22×C4—26no—
733C22×C4—212no—
734C22×C4—224no—
735C22×C4—212no—
736C22×C4—212no—
737C22×C4—224no—
738C22×C4—224no—
739C22×C4—248no—
740C22×C4—248no—
741C22×C4—248no—
742C22×C4—2192no—
743C22×C4—248no—
744C22×C4—296no—
745C22×C4—2192no—
746C22×C4—212no—
747C22×C4—212no—
748C22×C4—212no—
749C22×C4—24no—
750C22×C4—224no—
751C22×C4—212no—
752C22×C4—212no—
753C22×C4—224no—
754C22×C4—496no—
755C22×C4—4192no—
756C22×C4—4192no—
757C22×C4—4768no—
758C22×C4—4192no—
759C22×C4—4192no—
760C22×C4—496no—
761C22×C4—42048no—
762C22×C4—496no—
763C22×C4—4768no—
764C22×C4—44no—
765C22×C4—412no—
766C22×C4—496no—
767C22×C4—448no—
768C22×C4—412no—
769C22×C4—448no—
770C22×C4—412no—
771C22×C4—424no—
772C22×C4—416no—
773C22×C4—448no—
774C22×C4—4128no—
775C22×C4—48no—
776C22×C4—424no—
777C22×C4—424no—
778C22×C4—424no—
779C22×C4—448no—
780C22×C4—424no—
781C22×C4—424no—
782C22×C4—448no—
783C22×C4—432no—
784C22×C4—848no—
785C22×C4—8128no—
786C22×C4C22×C4⋊C4148yescomplemented
787C22×C4C2×C4×D4148yes—
788C22×C4C2×C4×D4148yes—
789C22×C4C2×C4×D41192yescomplemented
790C22×C4C2×#120132yes—
791C22×C4C2×#120116yes—
792C22×C4#525148yes—
793C22×C4C24×C4112yes—
794C22×C4C24×C414yes—
795C22×C4C24×C4112yes—
796C22×C4C24×C4112yes—
797C22×C4C24×C414yes—
798C22×C4C23×D4124yes—
799C22×C4C23×D4112yes—
800C22×C4C23×D4112yes—
801C22×C4C23×D4124yes—
802C22×C4C23×D4112yes—
803C22×C4C23×Q8112yes—
804C22×C4C22×#41112yes—
805C22×C4C22×#41112yes—
806C4⋊C4—2192no—
807C4⋊C4—296no—
808C4⋊C4—2192no—
809C4⋊C4—296no—
810C4⋊C4—496no—
811C4⋊C4—432no—
812C4⋊C4—416no—
813C4⋊C4—448no—
814C4⋊C4—848no—
815C4⋊C4C2×#120164yesdirect product factor
816C22⋊C4—296no—
817C22⋊C4—296no—
818C22⋊C4—296no—
819C22⋊C4—496no—
820C22⋊C4—496no—
821C22⋊C4—496no—
822C22⋊C4C22×C4⋊C41192yescomplemented
823C42—296no—
824C42—496no—
825C23—2128no—
826C23—2128no—
827C23—2384no—
828C23—22048no—
829C23—2384no—
830C23—2128no—
831C23—2384no—
832C23—296no—
833C23—2192no—
834C23—212no—
835C23—224no—
836C23—224no—
837C23—224no—
838C23—224no—
839C23—2192no—
840C23—2384no—
841C23—212no—
842C23—224no—
843C23—296no—
844C23—2192no—
845C23—224no—
846C23—224no—
847C23—296no—
848C23—212no—
849C23—296no—
850C23—2192no—
851C23—212no—
852C23—224no—
853C23—224no—
854C23—224no—
855C23—296no—
856C23—224no—
857C23—224no—
858C23—296no—
859C23—296no—
860C23—212no—
861C23—212no—
862C23—212no—
863C23—212no—
864C23—212no—
865C23—212no—
866C23—448no—
867C23—46no—
868C23—412no—
869C23—46no—
870C23—448no—
871C23—416no—
872C23—42no—
873C23—448no—
874C23—46no—
875C23—416no—
876C23—416no—
877C23D4×C4⋊C41192yescomplemented
878C23C23×C4⋊C4124yes—
879C23C23×C4⋊C414yes—
880C23C23×C4⋊C418yescomplemented
881C23C22×C4×D4124yes—
882C23C22×C4×D4112yes—
883C23C2×#520124yes—
884C23C2×#520112yes—
885C23C22×#12014yes—
886C23C2×#525112yes—
887C23C2×D42124yes—
888C23C2×D42112yes—
889C23C2×#547124yes—
890C23C2×#547112yes—
891C23C2×D4×Q8124yes—
892C23C2×D4×Q8112yes—
893C23C2×#554124yes—
894C23C2×#554112yes—
895C23#3484112yes—
896C23#3486112yes—
897C23#3492124yes—
898C23C25×C411yescharacteristic
899C23C24×D413yes—
900C23C24×D411yescharacteristic
901C23C24×Q811yescharacteristic
902C23C23×#4113yes—
903C23C22×H(5,𝔽2)13yes—
904C23C22×2−1+413yes—
905D4—2384no—
906C2×C4—2384no—
907C2×C4—224no—
908C2×C4—296no—
909C2×C4—212no—
910C2×C4—224no—
911C2×C4—212no—
912C2×C4—212no—
913C2×C4—212no—
914C2×C4—224no—
915C2×C4—212no—
916C2×C4—224no—
917C2×C4—212no—
918C2×C4—296no—
919C2×C4—212no—
920C2×C4—212no—
921C2×C4—264no—
922C2×C4—2384no—
923C2×C4—224no—
924C2×C4—212no—
925C2×C4—212no—
926C2×C4—224no—
927C2×C4—224no—
928C2×C4—224no—
929C2×C4—4384no—
930C2×C4—4384no—
931C2×C4—46no—
932C2×C4—424no—
933C2×C4—412no—
934C2×C4—46no—
935C2×C4—448no—
936C2×C4—42no—
937C2×C4—46no—
938C2×C4—424no—
939C2×C4—416no—
940C2×C4—496no—
941C2×C4—464no—
942C2×C4—412no—
943C2×C4—424no—
944C2×C4—412no—
945C2×C4—44no—
946C2×C4—412no—
947C2×C4—412no—
948C2×C4—412no—
949C2×C4—424no—
950C2×C4—864no—
951C2×C4—848no—
952C2×C4—816no—
953C2×C4C4×#120164yescomplemented
954C2×C4C23×C4⋊C4124yescomplemented
955C2×C4C22×C4×D4124yes—
956C2×C4C22×C4×D4124yes—
957C2×C4C22×#120116yes—
958C2×C4C22×#12018yes—
959C2×C4C2×#525124yes—
960C22—2512no—
961C22—224no—
962C22—248no—
963C22—224no—
964C22—248no—
965C22—2384no—
966C22—224no—
967C22—224no—
968C22—248no—
969C22—224no—
970C22—224no—
971C22—248no—
972C22—224no—
973C22—412no—
974C22—44no—
975C22—464no—
976C22—44no—
977C22—412no—
978C22—44no—
979C22—412no—
980C22C2×C4×#12018yes—
981C22C2×D4×C4⋊C4124yes—
982C22C2×D4×C4⋊C4148yescomplemented
983C22#34200124yes—
984C22D4×#12018yes—
985C22#36103124yes—
986C22Q8×#12018yes—
987C22#36546124yes—
988C22C24×C4⋊C411yescharacteristic
989C22C23×C4×D413yes—
990C22C22×#52013yes—
991C22C23×#12011yescharacteristic
992C22C22×#52513yes—
993C22C22×D4213yes—
994C22C22×D4×Q813yes—
995C22C22×#54713yes—
996C22C22×#55413yes—
997C22C2×#348413yes—
998C22C2×#349216yes—
999C22C2×#348613yes—
1000C4—224no—
1001C4—224no—
1002C4—216no—
1003C4—412no—
1004C4—44no—
1005C4—424no—
1006C4—84no—
1007C4—812no—
1008C4C2×C4×#120116yescomplemented
1009C2—248no—
1010C2—48no—
1011C2C4⋊C4×#120116yesdirect product factor
1012C2C22×C4×#12011yescharacteristic
1013C2C22×D4×C4⋊C413yes—
1014C2C2×#3420013yes—
1015C2C2×D4×#12011yescharacteristic
1016C2C2×#3610313yes—
1017C2C2×Q8×#12011yescharacteristic
1018C2C2×#3654613yes—
subgroupG/H
center, socleC25C25
commutatorC23C25×C4
Frattini, cosocleC24C26
prime radicalC23×#120C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C25×C4⋊C4C2semidirect
2. C22×D4×C4⋊C4C2semidirect
5. C2×#14693C2semidirect
6. C2×#14680C2semidirect
7. C4⋊C4×#120C2direct (N × H)
8. C2×#14043C2semidirect
9. C2×#14015C2semidirect
10. C2×#13880C2semidirect
11. C2×#13872C2semidirect
12. C2×C22⋊C4×C4⋊C4C2semidirect
22. C24×C4⋊C4C22semidirect
23. C24×C4⋊C4C22semidirect
25. C2×D4×C4⋊C4C22semidirect
27. C2×C4×#120C4semidirect
30. C22×#389C22semidirect
37. C22×#385C22semidirect
38. C22×#384C22semidirect
41. C22×#380C22semidirect
44. C22×C4×C4⋊C4C22semidirect
47. #14693C22semidirect
48. #14680C22semidirect
49. #14043C22semidirect
50. #14015C22semidirect
51. #13880C22semidirect
52. #13872C22semidirect
53. C2×#1444C22semidirect
54. C2×#1441C22semidirect
55. C2×#1439C22semidirect
56. C22⋊C4×C4⋊C4C22semidirect
57. C2×#1436C22semidirect
58. C2×C4⋊#95C22semidirect
69. C25×C4C2×C4semidirect
87. C22×C4×D4C2×C4semidirect
98. C23×C4⋊C4D4semidirect
112. C23×C4⋊C4C23semidirect
124. C4×#120C2×C4semidirect
126. C2×#389C23semidirect
128. C2×#386C2×C4semidirect
135. C2×#385C2×C4semidirect
140. C2×#385C23semidirect
142. C2×#384C23semidirect
148. C2×#380C23semidirect
150. C2×#379C2×C4semidirect
154. C2×C4×C4⋊C4C23semidirect
156. C2×C4×C22⋊C4C2×C4semidirect
166. #1444C23semidirect
167. #1441C23semidirect
168. #1439C23semidirect
169. #1436C23semidirect
170. C4⋊#95C23semidirect
225. C24×C4C22×C4semidirect
226. C24×C4C22×C4semidirect
245. C2×#120C4⋊C4direct (N × H)
256. C2×C4×D4C22×C4semidirect
283. C22×C4⋊C4C22×C4semidirect
287. C22×C4⋊C4C2×D4semidirect
316. C22×C22⋊C4C22×C4semidirect
331. C22×C42C22×C4semidirect
336. #386C22×C4semidirect
341. #385C22×C4semidirect
347. #379C22×C4semidirect
350. C4×C22⋊C4C22×C4semidirect
357. C2×#95C22×C4semidirect
388. C25C2×C4⋊C4semidirect
415. C22×D4C2×C4⋊C4semidirect
498. C23×C4C4×D4semidirect
506. C23×C4C23×C4semidirect
527. #120C2×C4⋊C4direct (N × H)
558. C2×C4⋊C4#120direct (N × H)
559. C2×C4⋊C4C23×C4semidirect
584. C2×C22⋊C4C2×C4⋊C4semidirect
588. C2×C22⋊C4C23×C4semidirect
598. C2×C42C23×C4semidirect
605. #95C23×C4semidirect
660. C24C22×C4⋊C4semidirect
661. C24C22×C4⋊C4semidirect
693. C2×D4C22×C4⋊C4semidirect
786. C22×C4C22×C4⋊C4semidirect
789. C22×C4C2×C4×D4semidirect
815. C4⋊C4C2×#120direct (N × H)
822. C22⋊C4C22×C4⋊C4semidirect
877. C23D4×C4⋊C4semidirect
880. C23C23×C4⋊C4semidirect
953. C2×C4C4×#120semidirect
954. C2×C4C23×C4⋊C4semidirect
982. C22C2×D4×C4⋊C4semidirect
1008. C4C2×C4×#120semidirect
1011. C2C4⋊C4×#120direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C4⋊C42
C22×D4×C4⋊C42
C22×C4×#1202
C2×#146932
C2×#146802
C4⋊C4×#1202
C2×#140432
C2×#140152
C2×#138802
C2×#138722
C2×C22⋊C4×C4⋊C42