Finite Group Databasebeta

← C22×#42985 #72301383

Subgroups — C22×#42985 #72301383

Order 1024.

95501 conjugacy classes of subgroups.

The subgroup lattice has 1251 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#550C211yesmaximal, characteristic, complemented
2C23×#537C211yesmaximal, characteristic, complemented
3C2×#42985C2196yesmaximal, direct product factor
4C22×#2673C214yesmaximal, complemented
5C22×#2688C214yesmaximal, complemented
6C22×#2815C212yesmaximal, complemented
7C22×#2535C212yesmaximal, complemented
8C22×#2543C212yesmaximal, complemented
9C22×#2504C211yesmaximal, characteristic, complemented
10C22×#2486C211yesmaximal, characteristic, complemented
11C22×#2407C212yesmaximal, complemented
12C22×#2421C212yesmaximal, complemented
13C22×#2428C212yesmaximal, complemented
14C22×#2615C211yesmaximal, characteristic, complemented
15C22×#2639C212yesmaximal, complemented
16C22×#2638C212yesmaximal, complemented
17C22×#2388C211yesmaximal, characteristic, complemented
18C22×#2339C211yesmaximal, characteristic, complemented
19C24×#41C2211yescharacteristic
20C24×#41C2211yescharacteristic
21C24×#41C2211yescharacteristic
22C22×#550—232no—
23C22×#550C22148yescomplemented
24C22×#537—232no—
25C22×#537C22148yescomplemented
26C23×#127C2212yes—
27C23×#127C2211yescharacteristic
28C23×#123C2212yes—
29C23×C22⋊Q8C2212yes—
30C23×C22⋊Q8C2212yes—
31C23×#121C2212yes—
32C23×#121C2214yes—
33C23×#121C2211yescharacteristic
34C23×#121C2212yes—
35C23×#121C2212yes—
36C23×#121C2211yescharacteristic
37C23×#121C2212yes—
38C23×#121C2214yes—
39C23×#121C2212yes—
40C23×C4×Q8C2211yescharacteristic
41C23×C4×D4C2211yescharacteristic
42C23×C4×D4C2212yes—
43C23×C4×D4C2212yes—
44C23×C4×D4C2212yes—
45C24×C4⋊C4C2211yescharacteristic
46C2×#2688C221192yescomplemented
47C2×#2673C221192yescomplemented
48#42985C2211024yesdirect product factor
49C2×#2815C22196yescomplemented
50C2×#2535C22196yescomplemented
51C2×#2543C22196yescomplemented
52C2×#2504C22148yescomplemented
53C2×#2486C22148yescomplemented
54C2×#2407C22196yescomplemented
55C2×#2421C22196yescomplemented
56C2×#2428C22196yescomplemented
57C2×#2615C22148yescomplemented
58C2×#2639C22196yescomplemented
59C2×#2638C22196yescomplemented
60C22×#400C2214yes—
61C22×#398C2212yes—
62C22×#397C2214yes—
63C22×#397C2214yes—
64C22×#397C2212yes—
65C22×#397C2212yes—
66C22×#397C2212yes—
67C2×#2388C22148yescomplemented
68C22×#395C2211yescharacteristic
69C22×#394C2212yes—
70C22×#394C2214yes—
71C22×#394C2214yes—
72C22×#394C2211yescharacteristic
73C22×#393C2211yescharacteristic
74C22×#393C2212yes—
75C22×#392C2214yes—
76C22×#392C2214yes—
77C22×#392C2214yes—
78C22×#392C2212yes—
79C22×#392C2214yes—
80C22×#392C2211yescharacteristic
81C22×#392C2212yes—
82C2×#2339C22148yescomplemented
83C22×#391C2212yes—
84C22×#390C2212yes—
85C22×#389C2212yes—
86C22×#388C2214yes—
87C22×#387C2214yes—
88C22×#386C2214yes—
89C22×#386C2214yes—
90C22×#386C2214yes—
91C22×#386C2214yes—
92C22×#386C2214yes—
93C22×#386C2214yes—
94C22×#385C2214yes—
95C22×#382C2212yes—
96C22×#381C2212yes—
97C22×#381C2212yes—
98C22×#380C2212yes—
99C22×#380C2212yes—
100C22×#380C2211yescharacteristic
101C22×C4×C22⋊C4C2212yes—
102C22×C4×C22⋊C4C2211yescharacteristic
103C23×#95C2212yes—
104C23×#41—216no—
105C23×#41—216no—
106C23×#41—416no—
107C23×#41—416no—
108C23×#41—416no—
109C23×#41D4132yescomplemented
110C23×#41C23124yes—
111C23×#41C23124yes—
112C23×#41C23124yes—
113C24×Q8C2311yescharacteristic
114C24×Q8C2311yescharacteristic
115C24×D4C2311yescharacteristic
116C24×D4C2312yes—
117C24×D4C2311yescharacteristic
118C24×D4C2311yescharacteristic
119C24×D4C2312yes—
120C24×D4C2311yescharacteristic
121C24×D4C2312yes—
122C24×D4C2314yes—
123C24×D4C2312yes—
124C24×D4C2312yes—
125C24×D4C2312yes—
126C24×D4C2312yes—
127C24×D4C2314yes—
128C24×D4C2312yes—
129C25×C4C2311yescharacteristic
130C25×C4C2312yes—
131C25×C4C2311yescharacteristic
132C25×C4C2312yes—
133C25×C4C2312yes—
134C25×C4C2314yes—
135C25×C4C2312yes—
136C2×#550—2768no—
137C2×#550C231256yescomplemented
138C2×#537—2768no—
139C2×#537C231256yescomplemented
140C22×#127—216no—
141C22×#127—232no—
142C22×#127C23124yes—
143C22×#127C23148yes—
144C22×#123—416no—
145C22×#123C23148yes—
146C22×C22⋊Q8—232no—
147C22×C22⋊Q8—232no—
148C22×C22⋊Q8C23148yes—
149C22×C22⋊Q8C23148yes—
150C22×#121—232no—
151C22×#121—264no—
152C22×#121—216no—
153C22×#121—232no—
154C22×#121—232no—
155C22×#121—216no—
156C22×#121—232no—
157C22×#121—432no—
158C22×#121—416no—
159C22×#121C23148yes—
160C22×#121C23148yes—
161C22×#121C23124yes—
162C22×#121C23124yes—
163C22×#121C23148yes—
164C22×#121C23196yes—
165C22×#121C23148yes—
166C22×#121C23196yes—
167C22×#121C23148yes—
168C22×C4×Q8—216no—
169C22×C4×Q8C23124yes—
170C22×C4×D4—216no—
171C22×C4×D4—232no—
172C22×C4×D4—416no—
173C22×C4×D4—416no—
174C22×C4×D4C23148yes—
175C22×C4×D4C23124yes—
176C22×C4×D4C23148yes—
177C22×C4×D4C23148yes—
178C23×C4⋊C4—216no—
179C23×C4⋊C4C2312yes—
180C23×C4⋊C4C2312yes—
181C23×C4⋊C4C23124yes—
182C23×C4⋊C4C2311yescharacteristic
183C23×C4⋊C4C2312yes—
184C23×C4⋊C4C2311yescharacteristic
185C23×C4⋊C4C2312yes—
186C23×C4⋊C4C2314yes—
187C23×C4⋊C4C2314yes—
188C23×C4⋊C4C2312yes—
189C23×C22⋊C4C2311yescharacteristic
190C23×C22⋊C4C2312yes—
191C23×C22⋊C4C2311yescharacteristic
192C23×C22⋊C4C2312yes—
193C23×C22⋊C4C2314yes—
194C23×C22⋊C4C2314yes—
195C23×C22⋊C4C2312yes—
196C23×C22⋊C4C2314yes—
197C23×C22⋊C4C2312yes—
198C23×C22⋊C4C2312yes—
199C23×C22⋊C4C2314yes—
200C23×C22⋊C4C2314yes—
201C23×C22⋊C4C2312yes—
202C23×C22⋊C4C2314yes—
203C23×C22⋊C4C2312yes—
204C23×C22⋊C4C2312yes—
205C23×C22⋊C4C2314yes—
206C23×C22⋊C4C2314yes—
207C23×C42C2312yes—
208C23×C42C2311yescharacteristic
209C23×C42C2312yes—
210#2815C231512yescomplemented
211#2688C2311024yescomplemented
212#2673C2311024yescomplemented
213#2639C231512yescomplemented
214#2638C231512yescomplemented
215#2615C231256yescomplemented
216#2543C231512yescomplemented
217#2535C231512yescomplemented
218#2504C231256yescomplemented
219#2486C231256yescomplemented
220#2428C231512yescomplemented
221#2421C231512yescomplemented
222#2407C231512yescomplemented
223C2×#400C23196yes—
224C2×#398C23148yes—
225C2×#397C23148yes—
226C2×#397C23196yes—
227C2×#397C23148yes—
228C2×#397C23148yes—
229C2×#397C23196yes—
230#2388C231256yescomplemented
231C2×#395C23124yes—
232C2×#394C23196yes—
233C2×#394C23124yes—
234C2×#394C23196yes—
235C2×#394C23148yes—
236C2×#393C23148yes—
237C2×#393C23124yes—
238C2×#392C23148yes—
239C2×#392C23124yes—
240C2×#392C23196yes—
241C2×#392C23196yes—
242C2×#392C23196yes—
243C2×#392C23196yes—
244C2×#392C23148yes—
245#2339C231256yescomplemented
246C2×#391C23148yes—
247C2×#390C23148yes—
248C2×#389C23148yes—
249C2×#388C23196yes—
250C2×#387C23196yes—
251C2×#386C23196yes—
252C2×#386C23196yes—
253C2×#386C23196yes—
254C2×#386C23196yes—
255C2×#386C23196yes—
256C2×#386C23196yes—
257C2×#385C23196yes—
258C2×#382C23148yes—
259C2×#381C23148yes—
260C2×#381C23148yes—
261C2×#380C23124yes—
262C2×#380C23148yes—
263C2×#380C23148yes—
264C2×C4×C22⋊C4C23124yes—
265C2×C4×C22⋊C4C23148yes—
266C22×#95C23148yes—
267C22×#95C2311yescharacteristic
268C22×#95C2312yes—
269C22×#95C2314yes—
270C22×#95C2311yescharacteristic
271C22×#95C2312yes—
272C22×#95C2312yes—
273C22×#95C2314yes—
274C22×#95C2314yes—
275C22×#95C2314yes—
276C22×#95C2314yes—
277C22×#95C2314yes—
278C22×#95C2314yes—
279C26C2412yes—
280C26C2411yescharacteristic
281C26C2412yes—
282C26C2411yescharacteristic
283C26C2412yes—
284C22×#41—2192no—
285C22×#41—2192no—
286C22×#41—4192no—
287C22×#41—4256no—
288C22×#41—4192no—
289C22×#41—4192no—
290C22×#41—4256no—
291C22×#41—4256no—
292C22×#41C2×D41384yescomplemented
293C22×#41C24164yes—
294C22×#41C24164yes—
295C22×#41C24164yes—
296C23×Q8—28no—
297C23×Q8—216no—
298C23×Q8—48no—
299C23×Q8C2×D4116yes—
300C23×Q8C24112yes—
301C23×Q8C24112yes—
302C23×D4—216no—
303C23×D4—216no—
304C23×D4—28no—
305C23×D4—232no—
306C23×D4—216no—
307C23×D4—216no—
308C23×D4—216no—
309C23×D4—28no—
310C23×D4—216no—
311C23×D4—28no—
312C23×D4—216no—
313C23×D4—216no—
314C23×D4—216no—
315C23×D4—28no—
316C23×D4—44no—
317C23×D4—48no—
318C23×D4—48no—
319C23×D4—48no—
320C23×D4—48no—
321C23×D4—416no—
322C23×D4—416no—
323C23×D4—48no—
324C23×D4—48no—
325C23×D4—48no—
326C23×D4—416no—
327C23×D4—416no—
328C23×D4—416no—
329C23×D4—416no—
330C23×D4—416no—
331C23×D4—416no—
332C23×D4—416no—
333C23×D4—416no—
334C23×D4C2×D4116yes—
335C23×D4C2×D4132yes—
336C23×D4C24112yes—
337C23×D4C24112yes—
338C23×D4C24124yes—
339C23×D4C24112yes—
340C23×D4C24124yes—
341C23×D4C24112yes—
342C23×D4C24124yes—
343C23×D4C24148yes—
344C23×D4C24124yes—
345C23×D4C24124yes—
346C23×D4C24124yes—
347C23×D4C24124yes—
348C23×D4C24148yes—
349C23×D4C24124yes—
350C24×C4—216no—
351C24×C4—216no—
352C24×C4—216no—
353C24×C4—28no—
354C24×C4—216no—
355C24×C4—216no—
356C24×C4—216no—
357C24×C4—216no—
358C24×C4—416no—
359C24×C4—416no—
360C24×C4—416no—
361C24×C4—48no—
362C24×C4—416no—
363C24×C4—416no—
364C24×C4—48no—
365C24×C4C2×D4116yes—
366C24×C4C2×D4132yes—
367C24×C4C24112yes—
368C24×C4C24124yes—
369C24×C4C2411yescharacteristic
370C24×C4C2412yes—
371C24×C4C2412yes—
372C24×C4C2414yes—
373C24×C4C2414yes—
374C24×C4C2411yescharacteristic
375C24×C4C2412yes—
376C24×C4C2412yes—
377C24×C4C24112yes—
378C24×C4C2411yescharacteristic
379C24×C4C2412yes—
380C24×C4C2411yescharacteristic
381C24×C4C24124yes—
382C24×C4C24124yes—
383C24×C4C24148yes—
384C24×C4C24124yes—
385C24×C4C2411yescharacteristic
386#550—22048no—
387#537—22048no—
388C2×#127—2192no—
389C2×#127—2384no—
390C2×#127C241128yes—
391C2×#127C24164yes—
392C2×#123—4192no—
393C2×#123C241128yes—
394C2×C22⋊Q8—2384no—
395C2×C22⋊Q8—2384no—
396C2×C22⋊Q8C241128yes—
397C2×C22⋊Q8C241128yes—
398C2×#121—2384no—
399C2×#121—2768no—
400C2×#121—2192no—
401C2×#121—2384no—
402C2×#121—2384no—
403C2×#121—2192no—
404C2×#121—2384no—
405C2×#121—4384no—
406C2×#121—4192no—
407C2×#121C24164yes—
408C2×#121C241128yes—
409C2×#121C241256yes—
410C2×#121C241128yes—
411C2×#121C241128yes—
412C2×#121C241128yes—
413C2×#121C24164yes—
414C2×#121C241128yes—
415C2×#121C241256yes—
416C2×C4×Q8—2192no—
417C2×C4×Q8C24164yes—
418C2×C4×D4—2192no—
419C2×C4×D4—2384no—
420C2×C4×D4—4192no—
421C2×C4×D4—4192no—
422C2×C4×D4C241128yes—
423C2×C4×D4C24164yes—
424C2×C4×D4C241128yes—
425C2×C4×D4C241128yes—
426C22×C4⋊C4—216no—
427C22×C4⋊C4—216no—
428C22×C4⋊C4—2192no—
429C22×C4⋊C4—28no—
430C22×C4⋊C4—216no—
431C22×C4⋊C4—28no—
432C22×C4⋊C4—232no—
433C22×C4⋊C4—216no—
434C22×C4⋊C4—232no—
435C22×C4⋊C4—48no—
436C22×C4⋊C4C24112yes—
437C22×C4⋊C4C24148yes—
438C22×C4⋊C4C24148yes—
439C22×C4⋊C4C24124yes—
440C22×C4⋊C4C24124yes—
441C22×C4⋊C4C24124yes—
442C22×C4⋊C4C24164yes—
443C22×C4⋊C4C24124yes—
444C22×C4⋊C4C24112yes—
445C22×C4⋊C4C24124yes—
446C22×C22⋊C4—216no—
447C22×C22⋊C4—28no—
448C22×C22⋊C4—232no—
449C22×C22⋊C4—28no—
450C22×C22⋊C4—216no—
451C22×C22⋊C4—232no—
452C22×C22⋊C4—216no—
453C22×C22⋊C4—48no—
454C22×C22⋊C4—416no—
455C22×C22⋊C4—48no—
456C22×C22⋊C4—416no—
457C22×C22⋊C4—416no—
458C22×C22⋊C4—48no—
459C22×C22⋊C4—48no—
460C22×C22⋊C4—416no—
461C22×C22⋊C4—416no—
462C22×C22⋊C4—48no—
463C22×C22⋊C4—416no—
464C22×C22⋊C4C24124yes—
465C22×C22⋊C4C24112yes—
466C22×C22⋊C4C24124yes—
467C22×C22⋊C4C24148yes—
468C22×C22⋊C4C24112yes—
469C22×C22⋊C4C24148yes—
470C22×C22⋊C4C24124yes—
471C22×C22⋊C4C24124yes—
472C22×C22⋊C4C24148yes—
473C22×C22⋊C4C24148yes—
474C22×C22⋊C4C24148yes—
475C22×C22⋊C4C24148yes—
476C22×C22⋊C4C24124yes—
477C22×C22⋊C4C24124yes—
478C22×C22⋊C4C24148yes—
479C22×C22⋊C4C24124yes—
480C22×C22⋊C4C24124yes—
481C22×C22⋊C4C24148yes—
482C22×C42—216no—
483C22×C42—28no—
484C22×C42—216no—
485C22×C42C24124yes—
486C22×C42C24112yes—
487C22×C42C24124yes—
488#400C241256yes—
489#398C241128yes—
490#397C241256yes—
491#397C241128yes—
492#397C241128yes—
493#397C241128yes—
494#397C241256yes—
495#395C24164yes—
496#394C241256yes—
497#394C241256yes—
498#394C241128yes—
499#394C24164yes—
500#393C241128yes—
501#393C24164yes—
502#392C241256yes—
503#392C241128yes—
504#392C241128yes—
505#392C24164yes—
506#392C241256yes—
507#392C241256yes—
508#392C241256yes—
509#391C241128yes—
510#390C241128yes—
511#389C241128yes—
512#388C241256yes—
513#387C241256yes—
514#386C241256yes—
515#386C241256yes—
516#386C241256yes—
517#386C241256yes—
518#386C241256yes—
519#386C241256yes—
520#385C241256yes—
521#382C241128yes—
522#381C241128yes—
523#381C241128yes—
524#380C24164yes—
525#380C241128yes—
526#380C241128yes—
527C4×C22⋊C4C24164yes—
528C4×C22⋊C4C241128yes—
529C2×#95C241128yes—
530C2×#95C24124yes—
531C2×#95C24148yes—
532C2×#95C24124yes—
533C2×#95C24112yes—
534C2×#95C24148yes—
535C2×#95C24148yes—
536C2×#95C24148yes—
537C2×#95C24112yes—
538C2×#95C24124yes—
539C2×#95C24148yes—
540C2×#95C24148yes—
541C2×#95C24148yes—
542C25—24no—
543C25—216no—
544C25—28no—
545C25—28no—
546C25—28no—
547C25—24no—
548C25—216no—
549C25—28no—
550C25—28no—
551C25—28no—
552C25—24no—
553C25—28no—
554C25—24no—
555C25—28no—
556C25—28no—
557C25—28no—
558C25—216no—
559C25—28no—
560C25—28no—
561C25—28no—
562C25—24no—
563C25—28no—
564C25—28no—
565C25—216no—
566C25—28no—
567C25C22×D4116yes—
568C25C22×D418yes—
569C25C25112yes—
570C25C2516yes—
571C25C25112yes—
572C25C2516yes—
573C25C25112yes—
574C25C2511yescharacteristic
575C2×#41—2256no—
576C2×#41—2256no—
577C2×#41—4256no—
578C2×#41—41536no—
579C2×#41—4256no—
580C2×#41—4256no—
581C2×#41—41536no—
582C2×#41—41536no—
583C2×#41C22×D41512yescomplemented
584C22×Q8—2128no—
585C22×Q8—248no—
586C22×Q8—296no—
587C22×Q8—448no—
588C22×Q8—464no—
589C22×Q8C22×D4196yes—
590C22×Q8C25116yes—
591C22×Q8C25116yes—
592C22×D4—296no—
593C22×D4—248no—
594C22×D4—296no—
595C22×D4—2192no—
596C22×D4—296no—
597C22×D4—296no—
598C22×D4—296no—
599C22×D4—2128no—
600C22×D4—248no—
601C22×D4—296no—
602C22×D4—248no—
603C22×D4—296no—
604C22×D4—296no—
605C22×D4—296no—
606C22×D4—248no—
607C22×D4—448no—
608C22×D4—4128no—
609C22×D4—424no—
610C22×D4—448no—
611C22×D4—448no—
612C22×D4—448no—
613C22×D4—448no—
614C22×D4—496no—
615C22×D4—496no—
616C22×D4—448no—
617C22×D4—448no—
618C22×D4—464no—
619C22×D4—4128no—
620C22×D4—464no—
621C22×D4—4128no—
622C22×D4—496no—
623C22×D4—496no—
624C22×D4—496no—
625C22×D4—496no—
626C22×D4—496no—
627C22×D4—496no—
628C22×D4—496no—
629C22×D4—496no—
630C22×D4—4128no—
631C22×D4—4128no—
632C22×D4—464no—
633C22×D4—8128no—
634C22×D4—864no—
635C22×D4—864no—
636C22×D4—864no—
637C22×D4—8128no—
638C22×D4C22×D4196yes—
639C22×D4C22×D41192yes—
640C22×D4C25116yes—
641C22×D4C25132yes—
642C22×D4C25116yes—
643C22×D4C25116yes—
644C22×D4C25164yes—
645C22×D4C25132yes—
646C22×D4C25132yes—
647C22×D4C25132yes—
648C22×D4C25132yes—
649C22×D4C25116yes—
650C22×D4C25132yes—
651C22×D4C25132yes—
652C22×D4C25164yes—
653C22×D4C25132yes—
654C23×C4—24no—
655C23×C4—28no—
656C23×C4—216no—
657C23×C4—24no—
658C23×C4—2128no—
659C23×C4—296no—
660C23×C4—24no—
661C23×C4—216no—
662C23×C4—28no—
663C23×C4—28no—
664C23×C4—24no—
665C23×C4—28no—
666C23×C4—216no—
667C23×C4—216no—
668C23×C4—216no—
669C23×C4—28no—
670C23×C4—28no—
671C23×C4—28no—
672C23×C4—28no—
673C23×C4—28no—
674C23×C4—28no—
675C23×C4—28no—
676C23×C4—28no—
677C23×C4—216no—
678C23×C4—216no—
679C23×C4—28no—
680C23×C4—216no—
681C23×C4—296no—
682C23×C4—296no—
683C23×C4—248no—
684C23×C4—296no—
685C23×C4—296no—
686C23×C4—296no—
687C23×C4—296no—
688C23×C4—4128no—
689C23×C4—496no—
690C23×C4—496no—
691C23×C4—496no—
692C23×C4—496no—
693C23×C4—448no—
694C23×C4—496no—
695C23×C4—448no—
696C23×C4—4128no—
697C23×C4—464no—
698C23×C4—4128no—
699C23×C4—864no—
700C23×C4—8128no—
701C23×C4C22×D418yes—
702C23×C4C22×D4116yes—
703C23×C4C22×D4196yes—
704C23×C4C22×D41192yes—
705C23×C4C22×D418yes—
706C23×C4H(5,𝔽2)18yes—
707C23×C4H(5,𝔽2)116yes—
708C23×C4C25112yes—
709C23×C4C25112yes—
710C23×C4C25124yes—
711C23×C4C2516yes—
712C23×C4C25112yes—
713C23×C4C25124yes—
714C23×C4C2516yes—
715C23×C4C25112yes—
716C23×C4C25116yes—
717C23×C4C25132yes—
718C23×C4C2516yes—
719C23×C4C25112yes—
720C23×C4C25116yes—
721C23×C4C2516yes—
722C23×C4C25132yes—
723C23×C4C25132yes—
724C23×C4C25164yes—
725C23×C4C25132yes—
726C23×C4C2516yes—
727#127—2256no—
728#127—2512no—
729#123—4256no—
730C22⋊Q8—2512no—
731C22⋊Q8—2512no—
732#121—2512no—
733#121—21024no—
734#121—2256no—
735#121—2512no—
736#121—2512no—
737#121—2256no—
738#121—2512no—
739#121—4512no—
740#121—4256no—
741C4×Q8—2256no—
742C4×D4—2256no—
743C4×D4—2512no—
744C4×D4—4256no—
745C4×D4—4256no—
746C2×C4⋊C4—296no—
747C2×C4⋊C4—296no—
748C2×C4⋊C4—2256no—
749C2×C4⋊C4—248no—
750C2×C4⋊C4—296no—
751C2×C4⋊C4—248no—
752C2×C4⋊C4—2192no—
753C2×C4⋊C4—296no—
754C2×C4⋊C4—2192no—
755C2×C4⋊C4—448no—
756C2×C4⋊C4C25132yes—
757C2×C4⋊C4C25132yes—
758C2×C4⋊C4C25116yes—
759C2×C4⋊C4C25132yes—
760C2×C4⋊C4C25116yes—
761C2×C4⋊C4C25132yes—
762C2×C4⋊C4C25164yes—
763C2×C4⋊C4C25164yes—
764C2×C4⋊C4C25132yes—
765C2×C22⋊C4—296no—
766C2×C22⋊C4—248no—
767C2×C22⋊C4—2192no—
768C2×C22⋊C4—296no—
769C2×C22⋊C4—248no—
770C2×C22⋊C4—2192no—
771C2×C22⋊C4—296no—
772C2×C22⋊C4—448no—
773C2×C22⋊C4—496no—
774C2×C22⋊C4—448no—
775C2×C22⋊C4—496no—
776C2×C22⋊C4—496no—
777C2×C22⋊C4—448no—
778C2×C22⋊C4—448no—
779C2×C22⋊C4—496no—
780C2×C22⋊C4—496no—
781C2×C22⋊C4—448no—
782C2×C22⋊C4—496no—
783C2×C22⋊C4C25116yes—
784C2×C22⋊C4C25132yes—
785C2×C22⋊C4C25132yes—
786C2×C22⋊C4C25116yes—
787C2×C22⋊C4C25164yes—
788C2×C22⋊C4C25164yes—
789C2×C22⋊C4C25132yes—
790C2×C22⋊C4C25164yes—
791C2×C22⋊C4C25132yes—
792C2×C22⋊C4C25132yes—
793C2×C22⋊C4C25164yes—
794C2×C22⋊C4C25164yes—
795C2×C22⋊C4C25132yes—
796C2×C22⋊C4C25164yes—
797C2×C22⋊C4C25132yes—
798C2×C22⋊C4C25132yes—
799C2×C22⋊C4C25164yes—
800C2×C22⋊C4C25164yes—
801C2×C42—296no—
802C2×C42—248no—
803C2×C42—296no—
804C2×C42C25132yes—
805C2×C42C25116yes—
806C2×C42C25132yes—
807#95C25116yes—
808#95C25132yes—
809#95C25164yes—
810#95C25116yes—
811#95C25132yes—
812#95C25132yes—
813#95C25164yes—
814#95C25164yes—
815#95C25164yes—
816#95C25164yes—
817#95C25164yes—
818#95C25164yes—
819C24—212no—
820C24—248no—
821C24—224no—
822C24—224no—
823C24—224no—
824C24—212no—
825C24—248no—
826C24—224no—
827C24—232no—
828C24—264no—
829C24—232no—
830C24—264no—
831C24—232no—
832C24—264no—
833C24—224no—
834C24—212no—
835C24—224no—
836C24—224no—
837C24—212no—
838C24—224no—
839C24—224no—
840C24—224no—
841C24—248no—
842C24—224no—
843C24—224no—
844C24—224no—
845C24—212no—
846C24—224no—
847C24—224no—
848C24—224no—
849C24—248no—
850C24—464no—
851C24—432no—
852C24—464no—
853C24—432no—
854C24—432no—
855C24—416no—
856C24—432no—
857C24—416no—
858C24—432no—
859C24—432no—
860C24—416no—
861C24—432no—
862C24—432no—
863C24—432no—
864C24—432no—
865C24—464no—
866C24—432no—
867C24—432no—
868C24—464no—
869C24—432no—
870C24—432no—
871C24C23×D4148yes—
872C24C23×D4124yes—
873C24C23×D414yes—
874C24C2×H(5,𝔽2)18yes—
875C24C2×H(5,𝔽2)14yes—
876C24#58514yes—
877C24#58518yes—
878C24C2618yes—
879C24C2614yes—
880C24C2618yes—
881C24C2614yes—
882C24C2618yes—
883C24C2613yes—
884#41—41024no—
885#41—41024no—
886#41—41024no—
887C2×Q8—232no—
888C2×Q8—264no—
889C2×Q8—2384no—
890C2×Q8—432no—
891C2×Q8—4192no—
892C2×Q8C23×D4164yes—
893C2×D4—264no—
894C2×D4—232no—
895C2×D4—264no—
896C2×D4—2128no—
897C2×D4—264no—
898C2×D4—264no—
899C2×D4—264no—
900C2×D4—232no—
901C2×D4—264no—
902C2×D4—232no—
903C2×D4—264no—
904C2×D4—264no—
905C2×D4—264no—
906C2×D4—232no—
907C2×D4—2384no—
908C2×D4—432no—
909C2×D4—4384no—
910C2×D4—416no—
911C2×D4—432no—
912C2×D4—432no—
913C2×D4—432no—
914C2×D4—432no—
915C2×D4—464no—
916C2×D4—464no—
917C2×D4—432no—
918C2×D4—432no—
919C2×D4—4192no—
920C2×D4—4384no—
921C2×D4—4192no—
922C2×D4—4384no—
923C2×D4—464no—
924C2×D4—464no—
925C2×D4—464no—
926C2×D4—464no—
927C2×D4—464no—
928C2×D4—464no—
929C2×D4—464no—
930C2×D4—464no—
931C2×D4—4384no—
932C2×D4—4384no—
933C2×D4—4192no—
934C2×D4—8384no—
935C2×D4—8192no—
936C2×D4—8192no—
937C2×D4—8192no—
938C2×D4—8384no—
939C2×D4C23×D4164yes—
940C2×D4C23×D41128yes—
941C22×C4—212no—
942C22×C4—224no—
943C22×C4—248no—
944C22×C4—212no—
945C22×C4—232no—
946C22×C4—264no—
947C22×C4—232no—
948C22×C4—264no—
949C22×C4—2384no—
950C22×C4—224no—
951C22×C4—212no—
952C22×C4—212no—
953C22×C4—248no—
954C22×C4—224no—
955C22×C4—224no—
956C22×C4—224no—
957C22×C4—224no—
958C22×C4—248no—
959C22×C4—248no—
960C22×C4—248no—
961C22×C4—224no—
962C22×C4—224no—
963C22×C4—224no—
964C22×C4—224no—
965C22×C4—224no—
966C22×C4—224no—
967C22×C4—248no—
968C22×C4—248no—
969C22×C4—224no—
970C22×C4—248no—
971C22×C4—264no—
972C22×C4—264no—
973C22×C4—232no—
974C22×C4—264no—
975C22×C4—264no—
976C22×C4—264no—
977C22×C4—264no—
978C22×C4—4384no—
979C22×C4—464no—
980C22×C4—464no—
981C22×C4—464no—
982C22×C4—464no—
983C22×C4—432no—
984C22×C4—464no—
985C22×C4—432no—
986C22×C4—4384no—
987C22×C4—416no—
988C22×C4—432no—
989C22×C4—464no—
990C22×C4—432no—
991C22×C4—416no—
992C22×C4—432no—
993C22×C4—432no—
994C22×C4—464no—
995C22×C4—4192no—
996C22×C4—4384no—
997C22×C4—8192no—
998C22×C4—8384no—
999C22×C4#534164yes—
1000C22×C4C23×D4148yes—
1001C22×C4C23×D4124yes—
1002C22×C4C23×D4164yes—
1003C22×C4C23×D41128yes—
1004C22×C4C23×D4124yes—
1005C22×C4C2×H(5,𝔽2)124yes—
1006C22×C4C2×H(5,𝔽2)148yes—
1007C22×C4C2618yes—
1008C22×C4C2618yes—
1009C22×C4C2614yes—
1010C22×C4C2618yes—
1011C22×C4C26116yes—
1012C22×C4C26116yes—
1013C22×C4C2614yes—
1014C22×C4C2618yes—
1015C22×C4C2618yes—
1016C22×C4C2614yes—
1017C22×C4C2614yes—
1018C22×C4C2614yes—
1019C4⋊C4—264no—
1020C4⋊C4—264no—
1021C4⋊C4—232no—
1022C4⋊C4—264no—
1023C4⋊C4—232no—
1024C4⋊C4—2128no—
1025C4⋊C4—264no—
1026C4⋊C4—2128no—
1027C4⋊C4—432no—
1028C22⋊C4—264no—
1029C22⋊C4—232no—
1030C22⋊C4—2128no—
1031C22⋊C4—264no—
1032C22⋊C4—232no—
1033C22⋊C4—2128no—
1034C22⋊C4—264no—
1035C22⋊C4—432no—
1036C22⋊C4—464no—
1037C22⋊C4—432no—
1038C22⋊C4—464no—
1039C22⋊C4—464no—
1040C22⋊C4—432no—
1041C22⋊C4—432no—
1042C22⋊C4—464no—
1043C22⋊C4—464no—
1044C22⋊C4—432no—
1045C22⋊C4—464no—
1046C42—264no—
1047C42—232no—
1048C42—264no—
1049C23—248no—
1050C23—296no—
1051C23—248no—
1052C23—296no—
1053C23—24no—
1054C23—216no—
1055C23—28no—
1056C23—28no—
1057C23—28no—
1058C23—24no—
1059C23—216no—
1060C23—28no—
1061C23—248no—
1062C23—296no—
1063C23—28no—
1064C23—28no—
1065C23—24no—
1066C23—28no—
1067C23—24no—
1068C23—28no—
1069C23—28no—
1070C23—28no—
1071C23—216no—
1072C23—28no—
1073C23—28no—
1074C23—28no—
1075C23—24no—
1076C23—28no—
1077C23—28no—
1078C23—28no—
1079C23—216no—
1080C23—496no—
1081C23—448no—
1082C23—496no—
1083C23—448no—
1084C23—4128no—
1085C23—4256no—
1086C23—448no—
1087C23—448no—
1088C23—496no—
1089C23—448no—
1090C23—448no—
1091C23—496no—
1092C23—448no—
1093C23—448no—
1094C23—424no—
1095C23—448no—
1096C23—448no—
1097C23—424no—
1098C23—448no—
1099C23—448no—
1100C23—448no—
1101C23—424no—
1102C23—448no—
1103C23—864no—
1104C23—8128no—
1105C23—8128no—
1106C23C2×#534116yes—
1107C23#3488116yes—
1108C23#3500116yes—
1109C23#3539132yes—
1110C23#3546132yes—
1111C23C24×D4116yes—
1112C23C24×D418yes—
1113C23C24×D416yes—
1114C23C22×H(5,𝔽2)112yes—
1115C23C22×H(5,𝔽2)16yes—
1116C23C2×#58516yes—
1117C23C2×#585112yes—
1118C23C2711yescharacteristic
1119Q8—2128no—
1120Q8—464no—
1121D4—2128no—
1122D4—4128no—
1123D4—464no—
1124D4—4128no—
1125D4—464no—
1126D4—4128no—
1127D4—4128no—
1128D4—4128no—
1129D4—464no—
1130D4—8128no—
1131D4—864no—
1132D4—864no—
1133D4—864no—
1134D4—8128no—
1135C2×C4—248no—
1136C2×C4—24no—
1137C2×C4—28no—
1138C2×C4—216no—
1139C2×C4—24no—
1140C2×C4—248no—
1141C2×C4—296no—
1142C2×C4—2128no—
1143C2×C4—28no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—216no—
1147C2×C4—28no—
1148C2×C4—28no—
1149C2×C4—28no—
1150C2×C4—28no—
1151C2×C4—216no—
1152C2×C4—216no—
1153C2×C4—216no—
1154C2×C4—28no—
1155C2×C4—28no—
1156C2×C4—28no—
1157C2×C4—28no—
1158C2×C4—28no—
1159C2×C4—28no—
1160C2×C4—216no—
1161C2×C4—216no—
1162C2×C4—28no—
1163C2×C4—216no—
1164C2×C4—4128no—
1165C2×C4—4128no—
1166C2×C4—448no—
1167C2×C4—448no—
1168C2×C4—496no—
1169C2×C4—496no—
1170C2×C4—448no—
1171C2×C4—424no—
1172C2×C4—424no—
1173C2×C4—448no—
1174C2×C4—464no—
1175C2×C4—4128no—
1176C2×C4—864no—
1177C2×C4—8128no—
1178C2×C4C2×#534196yes—
1179C2×C4C24×D4116yes—
1180C2×C4C24×D418yes—
1181C2×C4C24×D418yes—
1182C2×C4C22×H(5,𝔽2)18yes—
1183C2×C4C22×H(5,𝔽2)116yes—
1184C22—28no—
1185C22—216no—
1186C22—28no—
1187C22—216no—
1188C22—28no—
1189C22—216no—
1190C22—416no—
1191C22—48no—
1192C22—416no—
1193C22—48no—
1194C22—496no—
1195C22—4192no—
1196C22—48no—
1197C22—48no—
1198C22—416no—
1199C22—48no—
1200C22—48no—
1201C22—416no—
1202C22—48no—
1203C22—48no—
1204C22—48no—
1205C22—44no—
1206C22—48no—
1207C22—44no—
1208C22—48no—
1209C22—48no—
1210C22—44no—
1211C22—48no—
1212C22—48no—
1213C22—848no—
1214C22—896no—
1215C22—896no—
1216C22#42985164yesdirect product factor
1217C22C22×#534112yes—
1218C22C2×#3539124yes—
1219C22C2×#3546124yes—
1220C22C2×#3488112yes—
1221C22C2×#3500112yes—
1222C22C25×D411yescharacteristic
1223C22C23×H(5,𝔽2)12yes—
1224C22C23×H(5,𝔽2)11yescharacteristic
1225C22C22×#58511yescharacteristic
1226C22C22×#58512yes—
1227C4—28no—
1228C4—216no—
1229C4—28no—
1230C4—48no—
1231C4—48no—
1232C4—416no—
1233C4—44no—
1234C4—48no—
1235C4—416no—
1236C4—48no—
1237C4—44no—
1238C4C22×#534116yes—
1239C2—48no—
1240C2—416no—
1241C2—84no—
1242C2—88no—
1243C2—88no—
1244C2C2×#42985124yesdirect product factor
1245C2C23×#53411yescharacteristic
1246C2C22×#348811yescharacteristic
1247C2C22×#350011yescharacteristic
1248C2C22×#353912yes—
1249C2C22×#354612yes—
subgroupG/H
center, socleC25C25
commutator, Frattini, cosocleC23C27
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C23×#550C2semidirect
2. C23×#537C2semidirect
3. C2×#42985C2direct (N × H)
4. C22×#2673C2semidirect
5. C22×#2688C2semidirect
6. C22×#2815C2semidirect
7. C22×#2535C2semidirect
8. C22×#2543C2semidirect
9. C22×#2504C2semidirect
10. C22×#2486C2semidirect
11. C22×#2407C2semidirect
12. C22×#2421C2semidirect
13. C22×#2428C2semidirect
14. C22×#2615C2semidirect
15. C22×#2639C2semidirect
16. C22×#2638C2semidirect
17. C22×#2388C2semidirect
18. C22×#2339C2semidirect
23. C22×#550C22semidirect
25. C22×#537C22semidirect
46. C2×#2688C22semidirect
47. C2×#2673C22semidirect
48. #42985C22direct (N × H)
49. C2×#2815C22semidirect
50. C2×#2535C22semidirect
51. C2×#2543C22semidirect
52. C2×#2504C22semidirect
53. C2×#2486C22semidirect
54. C2×#2407C22semidirect
55. C2×#2421C22semidirect
56. C2×#2428C22semidirect
57. C2×#2615C22semidirect
58. C2×#2639C22semidirect
59. C2×#2638C22semidirect
67. C2×#2388C22semidirect
82. C2×#2339C22semidirect
109. C23×#41D4semidirect
137. C2×#550C23semidirect
139. C2×#537C23semidirect
210. #2815C23semidirect
211. #2688C23semidirect
212. #2673C23semidirect
213. #2639C23semidirect
214. #2638C23semidirect
215. #2615C23semidirect
216. #2543C23semidirect
217. #2535C23semidirect
218. #2504C23semidirect
219. #2486C23semidirect
220. #2428C23semidirect
221. #2421C23semidirect
222. #2407C23semidirect
230. #2388C23semidirect
245. #2339C23semidirect
292. C22×#41C2×D4semidirect
583. C2×#41C22×D4semidirect
1216. C22#42985direct (N × H)
1244. C2C2×#42985direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5502
C23×#5372
C2×#429852
C22×#26732
C22×#26882
C22×#28152
C22×#25352
C22×#25432
C22×#25042
C22×#24862
C22×#24072
C22×#24212
C22×#24282
C22×#26152
C22×#26392
C22×#26382
C22×#23882
C22×#23392