Finite Group Databasebeta

← C2×#7613824 #72307283

Subgroups — C2×#7613824 #72307283

Order 1024.

15377 conjugacy classes of subgroups.

The subgroup lattice has 1161 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3335C212yesmaximal, complemented
2C2×#45356C212yesmaximal, complemented
3#7613824C2132yesmaximal, direct product factor
4C2×#31204C212yesmaximal, complemented
5C2×#31203C212yesmaximal, complemented
6C2×#28289C212yesmaximal, complemented
7C2×#28483C212yesmaximal, complemented
8C2×#28224C212yesmaximal, complemented
9C2×#24134C212yesmaximal, complemented
10C2×#24128C212yesmaximal, complemented
11C2×#26242C214yesmaximal, complemented
12C2×#24776C214yesmaximal, complemented
13C2×D4×#106C212yesmaximal, complemented
14C2×#21724C211yesmaximal, characteristic, complemented
15C2×#21694C211yesmaximal, characteristic, complemented
16C2×#21683C211yesmaximal, characteristic, complemented
17C22×#554C2212yes—
18C22×#547C2212yes—
19C2×#3335—232no—
20C2×#3335C22132yescomplemented
21C22×#498C2211yescharacteristic
22C22×#495C2211yescharacteristic
23C22×#481C2214yes—
24C22×#483C2214yes—
25C22×#475C2212yes—
26C22×#476C2212yes—
27C22×#465C2214yes—
28C22×#465C2214yes—
29C22×#442C2211yescharacteristic
30C22×#441C2211yescharacteristic
31C22×C4×SD16C2212yes—
32C22×C8×D4C2212yes—
33C22×C8×D4C2212yes—
34C22×C8×D4C2212yes—
35C23×#106C2214yes—
36C2×#2732—24no—
37C2×#2694—24no—
38#45356—216no—
39#45356C22132yescomplemented
40C2×#2536C2212yes—
41C2×#2540C2214yes—
42C2×#2535C2212yes—
43C2×#2407—24no—
44C2×#2417C2214yes—
45C2×#2416C2214yes—
46C2×#2456—24no—
47C2×#2397C2211yescharacteristic
48C2×D4×C4⋊C4C2214yes—
49C2×#2331C2212yes—
50C2×#2326C2212yes—
51#31204C22132yescomplemented
52#31203C22132yescomplemented
53#28483C22132yescomplemented
54#28289C22132yescomplemented
55#28224C22132yescomplemented
56#26242C22164yescomplemented
57#24776C22164yescomplemented
58#24134C22132yescomplemented
59#24128C22132yescomplemented
60C2×#2066C2214yes—
61C2×#2065C2214yes—
62C2×#2036C2214yes—
63C2×#2034C2214yes—
64C2×#2035C2214yes—
65C2×#2033C2214yes—
66C2×#2001C2214yes—
67C2×#1999C2214yes—
68D4×#106C22132yescomplemented
69#21724C22116yescomplemented
70#21694C22116yescomplemented
71#21683C22116yescomplemented
72C2×#1993C2212yes—
73C2×#1983C2214yes—
74C2×#1972C2211yescharacteristic
75C2×#1971C2211yescharacteristic
76C2×#1968C2212yes—
77C2×#1959C2212yes—
78C2×#1955C2212yes—
79C2×#1955C2212yes—
80C2×#1955C2212yes—
81C2×#1948C2214yes—
82C2×#1944C2212yes—
83C2×#1941C2212yes—
84C2×#1874C2214yes—
85C2×#1872C2214yes—
86C2×#1853C2214yes—
87C2×#1853C2214yes—
88C2×#1846C2211yescharacteristic
89C2×#1844C2211yescharacteristic
90C2×#1843C2211yescharacteristic
91C2×#1807C2214yes—
92C2×#1805C2212yes—
93C2×#1804C2212yes—
94C2×#1776C2212yes—
95C2×C4×#106C2212yes—
96C2×#1726C2211yescharacteristic
97C23×#41—22no—
98C23×Q16C2311yescharacteristic
99C23×SD16C2312yes—
100C23×D8C2311yescharacteristic
101C24×C8C2314yes—
102C2×#554—28no—
103C2×#554—216no—
104C2×#554—48no—
105C2×#554C23116yes—
106C2×#547—216no—
107C2×#547—28no—
108C2×#547—48no—
109C2×#547C23116yes—
110C22×C4⋊Q8C2312yes—
111C22×#125—22no—
112C22×#124C2312yes—
113C22×#123—24no—
114C22×C22⋊Q8—22no—
115C22×C22⋊Q8—24no—
116C22×C22⋊Q8C2314yes—
117C22×C22⋊Q8C2314yes—
118C22×#121—24no—
119C22×#121C2314yes—
120C22×#121C2314yes—
121C22×C4×Q8C2312yes—
122C22×C4×D4—22no—
123C22×C4×D4—24no—
124C22×C4×D4C2312yes—
125C22×C4×D4C2312yes—
126C22×C4×D4C2312yes—
127C22×C4×D4C2312yes—
128C23×C4⋊C4C2314yes—
129C23×C4⋊C4C2314yes—
130#3335—2256no—
131C2×#498D4116yescomplemented
132C2×#498C2318yes—
133C2×#495—28no—
134C2×#495C2318yes—
135C2×#481—232no—
136C2×#481C23132yes—
137C2×#483—232no—
138C2×#483C23132yes—
139C2×#475—216no—
140C2×#475C23116yes—
141C2×#476—216no—
142C2×#476C23116yes—
143C2×#465—232no—
144C2×#465—416no—
145C2×#465C23132yes—
146C2×#465C23132yes—
147C2×#442—44no—
148C2×#442C2318yes—
149C2×#441—44no—
150C2×#441C2318yes—
151C2×C4×SD16—216no—
152C2×C4×SD16C23116yes—
153C2×C8×D4—216no—
154C2×C8×D4—216no—
155C2×C8×D4—48no—
156C2×C8×D4C23116yes—
157C2×C8×D4C23116yes—
158C2×C8×D4C23116yes—
159C22×#107C2312yes—
160C22×#106—232no—
161C22×#106C2312yes—
162C22×#106C23132yes—
163C22×#106C2314yes—
164C22×#106C2314yes—
165C22×#106C2312yes—
166C22×#106C2311yescharacteristic
167C22×#106C2311yescharacteristic
168C22×#106C2312yes—
169C22×#106C2312yes—
170C22×C4⋊C8C2312yes—
171C22×C4⋊C8C2312yes—
172C22×C4⋊C8C2312yes—
173C22×#103C2314yes—
174C22×#103C2312yes—
175C22×#103C2314yes—
176C22×#103C2312yes—
177C22×#102C2314yes—
178C22×#102C2312yes—
179C22×#102C2314yes—
180C22×#102C2312yes—
181C22×C22⋊C8C2314yes—
182C22×C22⋊C8C2314yes—
183C22×C22⋊C8C2314yes—
184C22×#97C2311yescharacteristic
185C22×#97C2311yescharacteristic
186C22×#97C2311yescharacteristic
187C22×C4×C8C2311yescharacteristic
188C22×C4×C8C2311yescharacteristic
189C22×C4×C8C2311yescharacteristic
190#2732—264no—
191#2694—264no—
192#2540—216no—
193#2540C23132yes—
194#2536—28no—
195#2536C23116yes—
196#2535—28no—
197#2535C23116yes—
198#2456—264no—
199#2417—216no—
200#2417C23132yes—
201#2416—216no—
202#2416C23132yes—
203#2407—264no—
204#2397D418yes—
205#2397C2318yes—
206C2×#399—24no—
207C2×#399D414yes—
208C2×#398—22no—
209C2×#398—24no—
210C2×#397—22no—
211C2×#396—24no—
212C2×#396—24no—
213C2×#394—22no—
214C2×#394—24no—
215C2×#392—22no—
216C2×#392—24no—
217C2×#392D414yes—
218D4×C4⋊C4—216no—
219D4×C4⋊C4C23132yes—
220#2331—28no—
221#2331C23116yes—
222#2326—28no—
223#2326C23116yes—
224C2×#391—24no—
225C2×#391C2312yes—
226C2×#390—24no—
227C2×#390—24no—
228C2×#390C2312yes—
229C2×#389—24no—
230C2×#389C2314yes—
231C2×#388—24no—
232C2×#388—24no—
233C2×#387—24no—
234C2×#386—24no—
235C2×#386—24no—
236C2×#386—24no—
237C2×#385—24no—
238C2×#385—24no—
239C2×#385—24no—
240C2×#384C2312yes—
241C2×#382C2312yes—
242C2×#380—24no—
243C2×#380C2314yes—
244C2×#380C2314yes—
245C2×C4×C4⋊C4C2314yes—
246C2×#376C2311yescharacteristic
247#2066C23132yes—
248#2065C23132yes—
249#2036C23132yes—
250#2035C23132yes—
251#2034C23132yes—
252#2033C23132yes—
253#2001C23132yes—
254#1999C23132yes—
255#1993C23116yes—
256#1983C23132yes—
257#1972C2318yes—
258#1971C2318yes—
259#1968C23116yes—
260#1959C23116yes—
261#1955C23116yes—
262#1955C23116yes—
263#1955C23116yes—
264#1948C23132yes—
265#1944C23116yes—
266#1941C23116yes—
267#1874C23132yes—
268#1872C23132yes—
269#1853C23132yes—
270#1853C23132yes—
271#1846C2318yes—
272#1844C2318yes—
273#1843C2318yes—
274#1807C23132yes—
275#1805C23116yes—
276#1804C23116yes—
277#1776C23116yes—
278C4×#106C23116yes—
279C2×#340C2314yes—
280C2×#340C2314yes—
281C2×#340C2314yes—
282C2×#340C2314yes—
283#1726C2318yes—
284C22×#41—216no—
285C22×#41—416no—
286C22×#41—816no—
287C23×Q8—22no—
288C23×Q8C2412yes—
289C23×D4—24no—
290C23×D4—24no—
291C23×D4C2×D412yes—
292C23×D4C2×D412yes—
293C23×D4C2×D412yes—
294C23×D4C2412yes—
295C24×C4—24no—
296C24×C4—24no—
297C24×C4—22no—
298C24×C4C2414yes—
299C22×Q16—24no—
300C22×Q16—42no—
301C22×Q16—42no—
302C22×Q16C2414yes—
303C22×SD16—28no—
304C22×SD16—28no—
305C22×SD16—28no—
306C22×SD16C2418yes—
307C22×D8—24no—
308C22×D8—42no—
309C22×D8—42no—
310C22×D8C2414yes—
311C23×C8—216no—
312C23×C8—216no—
313C23×C8—216no—
314C23×C8C24116yes—
315C23×C8C2411yescharacteristic
316C23×C8C2414yes—
317C23×C8C2411yescharacteristic
318C23×C8C2411yescharacteristic
319C23×C8C2411yescharacteristic
320#554—264no—
321#554—432no—
322#554—464no—
323#547—264no—
324#547—432no—
325#547—464no—
326C2×C4⋊Q8—24no—
327C2×C4⋊Q8—28no—
328C2×C4⋊Q8C2×D4116yes—
329C2×C4⋊Q8C2418yes—
330C2×#125—216no—
331C2×#125—416no—
332C2×#124—24no—
333C2×#124—28no—
334C2×#124—28no—
335C2×#124C2418yes—
336C2×#123—232no—
337C2×#123—432no—
338C2×C22⋊Q8—28no—
339C2×C22⋊Q8—28no—
340C2×C22⋊Q8—216no—
341C2×C22⋊Q8—232no—
342C2×C22⋊Q8—216no—
343C2×C22⋊Q8—432no—
344C2×C22⋊Q8—48no—
345C2×C22⋊Q8—416no—
346C2×C22⋊Q8—48no—
347C2×C22⋊Q8—48no—
348C2×C22⋊Q8C24116yes—
349C2×C22⋊Q8C24116yes—
350C2×#121—28no—
351C2×#121—232no—
352C2×#121—28no—
353C2×#121—216no—
354C2×#121—48no—
355C2×#121—48no—
356C2×#121—48no—
357C2×#121—816no—
358C2×#121C24116yes—
359C2×#121C24116yes—
360C2×C4×Q8—24no—
361C2×C4×Q8—28no—
362C2×C4×Q8—28no—
363C2×C4×Q8C2418yes—
364C2×C4×D4—216no—
365C2×C4×D4—232no—
366C2×C4×D4—28no—
367C2×C4×D4—24no—
368C2×C4×D4—28no—
369C2×C4×D4—28no—
370C2×C4×D4—28no—
371C2×C4×D4—28no—
372C2×C4×D4—28no—
373C2×C4×D4—44no—
374C2×C4×D4—44no—
375C2×C4×D4—416no—
376C2×C4×D4—816no—
377C2×C4×D4C2×D418yes—
378C2×C4×D4C2×D418yes—
379C2×C4×D4C2×D418yes—
380C2×C4×D4C2418yes—
381C2×C4×D4C2418yes—
382C2×C4×D4C2418yes—
383C2×C4×D4C2418yes—
384C22×C4⋊C4—22no—
385C22×C4⋊C4—216no—
386C22×C4⋊C4—216no—
387C22×C4⋊C4—28no—
388C22×C4⋊C4—28no—
389C22×C4⋊C4—24no—
390C22×C4⋊C4—22no—
391C22×C4⋊C4—24no—
392C22×C4⋊C4—24no—
393C22×C4⋊C4—24no—
394C22×C4⋊C4—24no—
395C22×C4⋊C4—24no—
396C22×C4⋊C4—48no—
397C22×C4⋊C4—48no—
398C22×C4⋊C4C2×D412yes—
399C22×C4⋊C4C2×D412yes—
400C22×C4⋊C4C2×D412yes—
401C22×C4⋊C4C2412yes—
402C22×C4⋊C4C2412yes—
403C22×C4⋊C4C2414yes—
404C22×C4⋊C4C24116yes—
405C22×C4⋊C4C24116yes—
406C22×C4⋊C4C2414yes—
407C22×C22⋊C4—24no—
408C22×C22⋊C4—24no—
409C22×C22⋊C4—22no—
410C22×C22⋊C4—24no—
411C22×C22⋊C4—24no—
412C22×C22⋊C4—24no—
413C22×C22⋊C4—24no—
414C22×C22⋊C4—24no—
415C22×C22⋊C4—24no—
416C22×C22⋊C4C2×D414yes—
417C22×C22⋊C4C2×D414yes—
418C22×C22⋊C4C2×D414yes—
419C22×C42—22no—
420C22×C42—24no—
421C22×C42C2411yescharacteristic
422C22×C42C2411yescharacteristic
423C22×C42C2411yescharacteristic
424#498C2×D4164yescomplemented
425#495—232no—
426#483—2128no—
427#481—2128no—
428#476—264no—
429#475—264no—
430#465—2128no—
431#465—464no—
432#442—416no—
433#441—416no—
434C4×SD16—264no—
435C8×D4—264no—
436C8×D4—264no—
437C8×D4—432no—
438C2×#107—44no—
439C2×#107C2418yes—
440C2×#106—28no—
441C2×#106—28no—
442C2×#106—216no—
443C2×#106—216no—
444C2×#106—2128no—
445C2×#106—42no—
446C2×#106—42no—
447C2×#106C2×D4116yes—
448C2×#106C2×D4116yes—
449C2×#106C24116yes—
450C2×#106C24116yes—
451C2×#106C2418yes—
452C2×#106C2418yes—
453C2×#106C2414yes—
454C2×#106C2414yes—
455C2×#106C2418yes—
456C2×#106C2418yes—
457C2×C4⋊C8—28no—
458C2×C4⋊C8—28no—
459C2×C4⋊C8—44no—
460C2×C4⋊C8C2418yes—
461C2×C4⋊C8C2418yes—
462C2×C4⋊C8C2418yes—
463C2×#103—28no—
464C2×#103—216no—
465C2×#103—44no—
466C2×#103—48no—
467C2×#103C24116yes—
468C2×#103C2418yes—
469C2×#103C24116yes—
470C2×#103C2418yes—
471C2×#102—28no—
472C2×#102—216no—
473C2×#102—44no—
474C2×#102—48no—
475C2×#102C24116yes—
476C2×#102C2418yes—
477C2×#102C24116yes—
478C2×#102C2418yes—
479C2×C22⋊C8—216no—
480C2×C22⋊C8—216no—
481C2×C22⋊C8—48no—
482C2×C22⋊C8C24116yes—
483C2×C22⋊C8C24116yes—
484C2×C22⋊C8C24116yes—
485C2×#97—24no—
486C2×#97—24no—
487C2×#97—42no—
488C2×#97C2414yes—
489C2×#97C2414yes—
490C2×#97C2414yes—
491C2×C4×C8—24no—
492C2×C4×C8C2×D418yes—
493C2×C4×C8#4118yescomplemented
494C2×C4×C8C2414yes—
495C2×C4×C8C2414yes—
496C2×C4×C8C2414yes—
497#399—232no—
498#399C2×D4132yes—
499#398—232no—
500#398—216no—
501#397—216no—
502#396—232no—
503#396—232no—
504#394—216no—
505#394—232no—
506#392—232no—
507#392—216no—
508#392C2×D4132yes—
509#391—24no—
510#391—232no—
511#391C2418yes—
512#390—232no—
513#390—232no—
514#390—24no—
515#390C2418yes—
516#389—232no—
517#389—28no—
518#389C24116yes—
519#388—232no—
520#388—232no—
521#387—232no—
522#386—232no—
523#386—232no—
524#386—232no—
525#385—232no—
526#385—232no—
527#385—232no—
528#384—24no—
529#384C2418yes—
530#382—24no—
531#382C2418yes—
532#380—28no—
533#380—28no—
534#380—232no—
535#380C24116yes—
536#380C24116yes—
537C4×C4⋊C4—28no—
538C4×C4⋊C4C24116yes—
539#376C2×D414yes—
540#376C2414yes—
541C2×#95—22no—
542C2×#95—24no—
543C2×#95—22no—
544C2×#95—24no—
545C2×#95—24no—
546C2×#95—24no—
547C2×#95—24no—
548C2×#95C2×D414yes—
549#340C24116yes—
550#340C24116yes—
551#340C24116yes—
552#340C24116yes—
553C25—22no—
554C25C22×D414yes—
555C2×#41—464no—
556C2×#41—864no—
557C2×#41—8128no—
558C22×Q8—216no—
559C22×Q8—28no—
560C22×Q8—22no—
561C22×Q8—24no—
562C22×Q8—24no—
563C22×Q8—24no—
564C22×Q8—24no—
565C22×Q8—24no—
566C22×Q8—24no—
567C22×Q8—88no—
568C22×Q8C2514yes—
569C22×D4—216no—
570C22×D4—216no—
571C22×D4—216no—
572C22×D4—216no—
573C22×D4—216no—
574C22×D4—28no—
575C22×D4—28no—
576C22×D4—24no—
577C22×D4—22no—
578C22×D4—24no—
579C22×D4—24no—
580C22×D4—24no—
581C22×D4—24no—
582C22×D4—24no—
583C22×D4—44no—
584C22×D4—416no—
585C22×D4—416no—
586C22×D4—416no—
587C22×D4—88no—
588C22×D4—88no—
589C22×D4—88no—
590C22×D4C22×D418yes—
591C22×D4C22×D418yes—
592C22×D4C22×D418yes—
593C22×D4C2514yes—
594C23×C4—24no—
595C23×C4—28no—
596C23×C4—28no—
597C23×C4—28no—
598C23×C4—28no—
599C23×C4—28no—
600C23×C4—28no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—24no—
604C23×C4—22no—
605C23×C4—216no—
606C23×C4—216no—
607C23×C4—28no—
608C23×C4—416no—
609C23×C4—416no—
610C23×C4—416no—
611C23×C4—48no—
612C23×C4—88no—
613C23×C4—88no—
614C23×C4—88no—
615C23×C4—88no—
616C23×C4C22×D418yes—
617C23×C4C22×D414yes—
618C23×C4C22×D412yes—
619C23×C4C22×D412yes—
620C23×C4C22×D412yes—
621C23×C4C2518yes—
622C23×C4C2511yescharacteristic
623C2×Q16—28no—
624C2×Q16—44no—
625C2×Q16—44no—
626C2×Q16—416no—
627C2×SD16—216no—
628C2×SD16—216no—
629C2×SD16—216no—
630C2×SD16—432no—
631C2×D8—28no—
632C2×D8—44no—
633C2×D8—44no—
634C2×D8—416no—
635C22×C8—22no—
636C22×C8—22no—
637C22×C8—22no—
638C22×C8—22no—
639C22×C8—28no—
640C22×C8—28no—
641C22×C8—28no—
642C22×C8—22no—
643C22×C8—22no—
644C22×C8—22no—
645C22×C8—232no—
646C22×C8—232no—
647C22×C8—232no—
648C22×C8—464no—
649C22×C8C22×D414yes—
650C22×C8C22×D414yes—
651C22×C8C2×#4114yes—
652C22×C8C2×#4114yes—
653C22×C8H(5,𝔽2)14yes—
654C22×C8C2518yes—
655C22×C8C2512yes—
656C22×C8C2512yes—
657C22×C8C2512yes—
658C22×C8C2512yes—
659C4⋊Q8—232no—
660C4⋊Q8—216no—
661C4⋊Q8C22×D4132yes—
662#125—464no—
663#124—216no—
664#124—216no—
665#124—416no—
666#123—4128no—
667C22⋊Q8—232no—
668C22⋊Q8—4128no—
669C22⋊Q8—416no—
670C22⋊Q8—432no—
671C22⋊Q8—464no—
672C22⋊Q8—416no—
673C22⋊Q8—416no—
674C22⋊Q8—816no—
675#121—232no—
676#121—416no—
677#121—432no—
678#121—416no—
679#121—416no—
680#121—864no—
681#121—816no—
682C4×Q8—216no—
683C4×Q8—216no—
684C4×Q8—416no—
685C4×D4—232no—
686C4×D4—232no—
687C4×D4—216no—
688C4×D4—216no—
689C4×D4—216no—
690C4×D4—216no—
691C4×D4—216no—
692C4×D4—216no—
693C4×D4—416no—
694C4×D4—48no—
695C4×D4—48no—
696C4×D4—464no—
697C4×D4—416no—
698C4×D4—864no—
699C2×C4⋊C4—216no—
700C2×C4⋊C4—28no—
701C2×C4⋊C4—28no—
702C2×C4⋊C4—24no—
703C2×C4⋊C4—28no—
704C2×C4⋊C4—28no—
705C2×C4⋊C4—24no—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—24no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—232no—
712C2×C4⋊C4—232no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—216no—
716C2×C4⋊C4—216no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—216no—
719C2×C4⋊C4—24no—
720C2×C4⋊C4—216no—
721C2×C4⋊C4—216no—
722C2×C4⋊C4—216no—
723C2×C4⋊C4—416no—
724C2×C4⋊C4—416no—
725C2×C4⋊C4—432no—
726C2×C4⋊C4—432no—
727C2×C4⋊C4—44no—
728C2×C4⋊C4—416no—
729C2×C4⋊C4—416no—
730C2×C4⋊C4—416no—
731C2×C4⋊C4—48no—
732C2×C4⋊C4—88no—
733C2×C4⋊C4—88no—
734C2×C4⋊C4—88no—
735C2×C4⋊C4C22×D418yes—
736C2×C4⋊C4C22×D418yes—
737C2×C4⋊C4C22×D4116yes—
738C2×C4⋊C4C22×D418yes—
739C2×C4⋊C4C2514yes—
740C2×C4⋊C4C2514yes—
741C2×C4⋊C4C2518yes—
742C2×C4⋊C4C2518yes—
743C2×C22⋊C4—216no—
744C2×C22⋊C4—216no—
745C2×C22⋊C4—216no—
746C2×C22⋊C4—216no—
747C2×C22⋊C4—28no—
748C2×C22⋊C4—216no—
749C2×C22⋊C4—216no—
750C2×C22⋊C4—216no—
751C2×C22⋊C4—216no—
752C2×C22⋊C4—216no—
753C2×C22⋊C4—216no—
754C2×C22⋊C4—48no—
755C2×C22⋊C4—416no—
756C2×C22⋊C4—416no—
757C2×C22⋊C4—416no—
758C2×C22⋊C4—48no—
759C2×C22⋊C4—416no—
760C2×C22⋊C4—88no—
761C2×C22⋊C4—88no—
762C2×C22⋊C4—88no—
763C2×C22⋊C4—88no—
764C2×C22⋊C4C22×D4116yes—
765C2×C22⋊C4C22×D4116yes—
766C2×C22⋊C4C22×D4116yes—
767C2×C42—22no—
768C2×C42—22no—
769C2×C42—28no—
770C2×C42—216no—
771C2×C42—48no—
772C2×C42—88no—
773C2×C42C22×D412yes—
774C2×C42C22×D412yes—
775C2×C42C22×D414yes—
776C2×C42C22×D412yes—
777C2×C42C2×#4114yes—
778C2×C42H(5,𝔽2)14yes—
779C2×C422−1+414yes—
780C2×C42C2512yes—
781C2×C42C2512yes—
782C2×C42C2512yes—
783#107—48no—
784#106—216no—
785#106—216no—
786#106—232no—
787#106—232no—
788#106—44no—
789#106—44no—
790#106C22×D4132yes—
791#106C22×D4132yes—
792C4⋊C8—216no—
793C4⋊C8—216no—
794C4⋊C8—48no—
795#103—216no—
796#103—232no—
797#103—48no—
798#103—416no—
799#102—216no—
800#102—232no—
801#102—48no—
802#102—416no—
803C22⋊C8—232no—
804C22⋊C8—232no—
805C22⋊C8—416no—
806#97—28no—
807#97—28no—
808#97—44no—
809C4×C8—28no—
810C4×C8C22×D4116yes—
811C4×C8C2×#41116yescomplemented
812#95—216no—
813#95—216no—
814#95—216no—
815#95—216no—
816#95—28no—
817#95—28no—
818#95—216no—
819#95C22×D4116yes—
820C24—28no—
821C24—28no—
822C24—28no—
823C24—28no—
824C24—28no—
825C24—28no—
826C24—24no—
827C24—44no—
828C24—44no—
829C24—44no—
830C24—48no—
831C24—48no—
832C24#577116yes—
833C24C23×D418yes—
834C24C23×D411yescharacteristic
835#41—8256no—
836C2×Q8—232no—
837C2×Q8—24no—
838C2×Q8—24no—
839C2×Q8—24no—
840C2×Q8—24no—
841C2×Q8—24no—
842C2×Q8—24no—
843C2×Q8—44no—
844C2×Q8—44no—
845C2×Q8—44no—
846C2×Q8—48no—
847C2×Q8—48no—
848C2×Q8—48no—
849C2×Q8—48no—
850C2×Q8—816no—
851C2×Q8—832no—
852C2×D4—264no—
853C2×D4—264no—
854C2×D4—232no—
855C2×D4—232no—
856C2×D4—232no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—216no—
864C2×D4—216no—
865C2×D4—48no—
866C2×D4—432no—
867C2×D4—432no—
868C2×D4—432no—
869C2×D4—432no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—48no—
873C2×D4—44no—
874C2×D4—48no—
875C2×D4—48no—
876C2×D4—48no—
877C2×D4—816no—
878C2×D4—864no—
879C2×D4—816no—
880C2×D4—816no—
881C2×D4—1632no—
882C22×C4—28no—
883C22×C4—28no—
884C22×C4—28no—
885C22×C4—28no—
886C22×C4—216no—
887C22×C4—28no—
888C22×C4—24no—
889C22×C4—28no—
890C22×C4—28no—
891C22×C4—28no—
892C22×C4—28no—
893C22×C4—28no—
894C22×C4—28no—
895C22×C4—28no—
896C22×C4—28no—
897C22×C4—216no—
898C22×C4—216no—
899C22×C4—216no—
900C22×C4—28no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—432no—
905C22×C4—432no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—416no—
909C22×C4—416no—
910C22×C4—416no—
911C22×C4—416no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—48no—
917C22×C4—44no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—48no—
921C22×C4—432no—
922C22×C4—48no—
923C22×C4—416no—
924C22×C4—816no—
925C22×C4—832no—
926C22×C4—816no—
927C22×C4—816no—
928C22×C4—816no—
929C22×C4—864no—
930C22×C4—1632no—
931C22×C4D4218yes—
932C22×C4#54718yes—
933C22×C4C23×D414yes—
934C22×C4C23×D418yes—
935C22×C4C23×D414yes—
936C22×C4C23×D414yes—
937C22×C4C23×D412yes—
938C22×C4C23×D411yescharacteristic
939C22×C4C22×#4112yes—
940C22×C4C2×H(5,𝔽2)12yes—
941C22×C4C2×H(5,𝔽2)12yes—
942C22×C4C2×2−1+412yes—
943C22×C4#58512yes—
944C22×C4C2611yescharacteristic
945Q16—416no—
946SD16—432no—
947D8—416no—
948C2×C8—22no—
949C2×C8—22no—
950C2×C8—22no—
951C2×C8—22no—
952C2×C8—28no—
953C2×C8—28no—
954C2×C8—28no—
955C2×C8—28no—
956C2×C8—22no—
957C2×C8—22no—
958C2×C8—28no—
959C2×C8—22no—
960C2×C8—416no—
961C2×C8—44no—
962C2×C8—464no—
963C2×C8#550116yes—
964C2×C8C23×D414yes—
965C2×C8C23×D414yes—
966C2×C8C22×#4114yes—
967C2×C8C22×#4114yes—
968C2×C8C2×H(5,𝔽2)14yes—
969C4⋊C4—28no—
970C4⋊C4—232no—
971C4⋊C4—216no—
972C4⋊C4—216no—
973C4⋊C4—216no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—28no—
980C4⋊C4—48no—
981C4⋊C4—432no—
982C4⋊C4—432no—
983C4⋊C4—432no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—416no—
987C4⋊C4—48no—
988C4⋊C4—816no—
989C4⋊C4—816no—
990C4⋊C4—816no—
991C4⋊C4C23×D4116yes—
992C22⋊C4—232no—
993C22⋊C4—232no—
994C22⋊C4—416no—
995C22⋊C4—432no—
996C22⋊C4—432no—
997C22⋊C4—432no—
998C22⋊C4—416no—
999C22⋊C4—432no—
1000C22⋊C4—816no—
1001C22⋊C4—816no—
1002C22⋊C4—816no—
1003C22⋊C4—816no—
1004C42—22no—
1005C42—22no—
1006C42—24no—
1007C42—416no—
1008C42—816no—
1009C42D4218yes—
1010C42#54718yes—
1011C42C23×D414yes—
1012C42C22×#4114yes—
1013C42C2×H(5,𝔽2)14yes—
1014C42C2×2−1+414yes—
1015C23—28no—
1016C23—232no—
1017C23—232no—
1018C23—28no—
1019C23—28no—
1020C23—28no—
1021C23—232no—
1022C23—28no—
1023C23—28no—
1024C23—416no—
1025C23—416no—
1026C23—416no—
1027C23—416no—
1028C23—44no—
1029C23—48no—
1030C23—48no—
1031C23—44no—
1032C23—44no—
1033C23—816no—
1034C23—816no—
1035C23—88no—
1036C23—88no—
1037C23—88no—
1038C23C2×D4212yes—
1039C23C2×#54712yes—
1040C23#349612yes—
1041C23C2×#577116yes—
1042C23C2×#57718yes—
1043C23C24×D411yescharacteristic
1044Q8—44no—
1045Q8—44no—
1046Q8—44no—
1047Q8—44no—
1048Q8—832no—
1049Q8—88no—
1050D4—264no—
1051D4—264no—
1052D4—432no—
1053D4—44no—
1054D4—44no—
1055D4—44no—
1056D4—44no—
1057D4—864no—
1058D4—88no—
1059D4—1632no—
1060C2×C4—216no—
1061C2×C4—28no—
1062C2×C4—28no—
1063C2×C4—216no—
1064C2×C4—24no—
1065C2×C4—28no—
1066C2×C4—28no—
1067C2×C4—28no—
1068C2×C4—216no—
1069C2×C4—28no—
1070C2×C4—48no—
1071C2×C4—48no—
1072C2×C4—48no—
1073C2×C4—432no—
1074C2×C4—416no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—432no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—44no—
1082C2×C4—48no—
1083C2×C4—48no—
1084C2×C4—48no—
1085C2×C4—48no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—44no—
1090C2×C4—832no—
1091C2×C4—864no—
1092C2×C4—816no—
1093C2×C4—88no—
1094C2×C4—88no—
1095C2×C4—88no—
1096C2×C4—1632no—
1097C2×C4C2×D4218yes—
1098C2×C4C2×D4212yes—
1099C2×C4C2×#54718yes—
1100C2×C4C2×#54712yes—
1101C2×C4C2×#55014yes—
1102C2×C4#349612yes—
1103C2×C4#349714yes—
1104C2×C4#350614yes—
1105C2×C4#354814yes—
1106C2×C4C24×D411yescharacteristic
1107C2×C4C23×#4111yescharacteristic
1108C2×C4C22×H(5,𝔽2)11yescharacteristic
1109C2×C4C22×H(5,𝔽2)11yescharacteristic
1110C2×C4C22×2−1+411yescharacteristic
1111C2×C4C2×#58511yescharacteristic
1112C8—24no—
1113C8—24no—
1114C8—42no—
1115C8—48no—
1116C8C2×#55018yes—
1117C22—216no—
1118C22—216no—
1119C22—216no—
1120C22—48no—
1121C22—464no—
1122C22—48no—
1123C22—48no—
1124C22—48no—
1125C22—84no—
1126C22—88no—
1127C22—84no—
1128C22—84no—
1129C22—88no—
1130C22—1616no—
1131C22#5981514yes—
1132C22#6105018yes—
1133C22#6125918yes—
1134C22#6226918yes—
1135C22C22×D4211yescharacteristic
1136C22C22×#54711yescharacteristic
1137C22C2×#349611yescharacteristic
1138C22C22×#57714yes—
1139C4—28no—
1140C4—28no—
1141C4—48no—
1142C4—44no—
1143C4—416no—
1144C4—84no—
1145C4—88no—
1146C4—84no—
1147C4—84no—
1148C4#5981514yes—
1149C4C22×#55011yescharacteristic
1150C4C2×#354811yescharacteristic
1151C4C2×#350611yescharacteristic
1152C4C2×#349711yescharacteristic
1153C2—416no—
1154C2—164no—
1155C2#761382418yesdirect product factor
1156C2C2×#5981511yescharacteristic
1157C2C2×#6105012yes—
1158C2C2×#6125912yes—
1159C2C2×#6226912yes—
subgroupG/H
center, socleC24C23×D4
commutator, Frattini, cosocleC22×C4C26
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#2397 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#3335C2semidirect
2. C2×#45356C2semidirect
3. #7613824C2direct (N × H)
4. C2×#31204C2semidirect
5. C2×#31203C2semidirect
6. C2×#28289C2semidirect
7. C2×#28483C2semidirect
8. C2×#28224C2semidirect
9. C2×#24134C2semidirect
10. C2×#24128C2semidirect
11. C2×#26242C2semidirect
12. C2×#24776C2semidirect
13. C2×D4×#106C2semidirect
14. C2×#21724C2semidirect
15. C2×#21694C2semidirect
16. C2×#21683C2semidirect
20. C2×#3335C22semidirect
39. #45356C22semidirect
51. #31204C22semidirect
52. #31203C22semidirect
53. #28483C22semidirect
54. #28289C22semidirect
55. #28224C22semidirect
56. #26242C22semidirect
57. #24776C22semidirect
58. #24134C22semidirect
59. #24128C22semidirect
68. D4×#106C22semidirect
69. #21724C22semidirect
70. #21694C22semidirect
71. #21683C22semidirect
131. C2×#498D4semidirect
424. #498C2×D4semidirect
493. C2×C4×C8#41semidirect
811. C4×C8C2×#41semidirect
1155. C2#7613824direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#33352
C2×#453562
#76138242
C2×#312042
C2×#312032
C2×#282892
C2×#284832
C2×#282242
C2×#241342
C2×#241282
C2×#262422
C2×#247762
C2×D4×#1062
C2×#217242
C2×#216942
C2×#216832