Finite Group Databasebeta

← C23×#24404 #19172030

Subgroups — C23×#24404 #19172030

Order 5888.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3484C211yesmaximal, characteristic, complemented
2C2×C23×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×C23×#99C211yesmaximal, characteristic, complemented
4C23×#2410C212yesmaximal, complemented
5C23×#2403C211yesmaximal, characteristic, complemented
6C23×#2044C212yesmaximal, complemented
7C23×#2021C212yesmaximal, complemented
8C23×#1898C212yesmaximal, complemented
9C23×#1889C211yesmaximal, characteristic, complemented
10C23×#1867C211yesmaximal, characteristic, complemented
11C23×#1790C211yesmaximal, characteristic, complemented
12C2×C23×H(5,𝔽2)C2211yescharacteristic
13C23×D4×C23C2211yescharacteristic
14C23×D4×C23C2211yescharacteristic, complemented
15C23×#546—22no—
16C23×#546—22no—
17D42×C23—22no—
18D42×C23—22no—
19C23×#535—21no—
20C23×#534—21no—
21C23×#534C2212yes—
22C23×#525—21no—
23C2×C23×#121—22no—
24C2×C23×#120—21no—
25C2×C23×#120—21no—
26C2×C23×#120C2211yescharacteristic
27C2×C23×#120C2212yes—
28C2×C23×#120C2212yescomplemented
29C2×C23×#120C2211yescharacteristic, complemented
30C23×#518C2211yescharacteristic
31C22×C22⋊C4×C23C2212yescomplemented
32C23×B(4,𝔽2)—24no—
33C2×C23×#99—24no—
34C2×C23×#99C2211yescharacteristic
35C2×C23×#99C2211yescharacteristic
36C2×C23×#99C2212yescomplemented
37C2×C23×#99C2212yescomplemented
38C2×C23×#99C2212yescomplemented
39C23×#394—22no—
40C23×#392—21no—
41C23×#392—21no—
42C23×#392—22no—
43C23×#386—21no—
44C23×#386—22no—
45C23×#386C2211yescharacteristic
46C23×#386C2211yescharacteristic, complemented
47C23×#386C2212yescomplemented
48C23×#385C2212yescomplemented
49C23×#379C2212yescomplemented
50C23×#379C2211yescharacteristic, complemented
51C23×#342C2212yescomplemented
52C23×#342C2212yescomplemented
53C25×C23D411yescharacteristic, complemented
54C25×C23C2311yescharacteristic
55C25×C23C2311yescharacteristic
56C23×H(5,𝔽2)—22no—
57C23×H(5,𝔽2)—22no—
58C23×H(5,𝔽2)—42no—
59C2×#41×C23—21no—
60C2×#41×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23—22no—
63C22×D4×C23—21no—
64C22×D4×C23—22no—
65C22×D4×C23—21no—
66C22×D4×C23—22no—
67C22×D4×C23—21no—
68C22×D4×C23—21no—
69C22×D4×C23—22no—
70C22×D4×C23—22no—
71C22×D4×C23—21no—
72C22×D4×C23—22no—
73C22×D4×C23—21no—
74C22×D4×C23—21no—
75C22×D4×C23—22no—
76C22×D4×C23—44no—
77C22×D4×C23—42no—
78C22×D4×C23D411yescharacteristic, complemented
79C22×D4×C23D411yescharacteristic, complemented
80C22×D4×C23D412yescomplemented
81C22×D4×C23D412yescomplemented
82C22×D4×C23C2311yescharacteristic
83C22×D4×C23C2312yes—
84C22×D4×C23C2311yescharacteristic
85C23×C4×C23—22no—
86C23×C4×C23D411yescharacteristic, complemented
87C23×C4×C23C2311yescharacteristic
88C23×#127—22no—
89C23×#124—22no—
90C23×#123—22no—
91C23×#123—22no—
92C23×#123—22no—
93C23×C22⋊Q8—21no—
94C23×C22⋊Q8—21no—
95C23×#121—21no—
96C23×#121—21no—
97C23×#121—22no—
98C23×#121—22no—
99C23×#121—22no—
100C23×#121—22no—
101C23×#121—22no—
102C23×#121—22no—
103C23×#121—48no—
104C23×#120—22no—
105C23×#120—22no—
106C23×#120—22no—
107C23×#120—22no—
108C23×#120—22no—
109C23×#120—22no—
110C23×#120—22no—
111C23×#120—22no—
112C23×#120—22no—
113C23×#120—22no—
114C23×#120—22no—
115C23×#120—24no—
116C23×#120—42no—
117C23×#120—42no—
118C23×#120—44no—
119C4×D4×C23—22no—
120C4×D4×C23—22no—
121C4×D4×C23—22no—
122C4×D4×C23—22no—
123C23×#117—21no—
124C2×C4⋊C4×C23—22no—
125C2×C22⋊C4×C23—21no—
126C2×C22⋊C4×C23—21no—
127C2×C22⋊C4×C23—21no—
128C2×C22⋊C4×C23—24no—
129C2×C22⋊C4×C23—21no—
130C2×C22⋊C4×C23—21no—
131C2×C22⋊C4×C23—21no—
132C2×C22⋊C4×C23—22no—
133C2×C22⋊C4×C23—22no—
134C2×C22⋊C4×C23—22no—
135C2×C22⋊C4×C23—21no—
136C2×C22⋊C4×C23—21no—
137C2×C22⋊C4×C23—22no—
138C2×C22⋊C4×C23—21no—
139C2×C22⋊C4×C23—22no—
140C2×C22⋊C4×C23—42no—
141C2×C22⋊C4×C23D412yescomplemented
142C2×C22⋊C4×C23D412yescomplemented
143C2×C22⋊C4×C23C2311yescharacteristic
144C2×C22⋊C4×C23C2311yescharacteristic
145C2×C22⋊C4×C23C2312yes—
146C2×C22⋊C4×C23C2312yes—
147C2×C22⋊C4×C23C2312yes—
148C23×#99—22no—
149C23×#99—24no—
150C23×#99—24no—
151C23×#99—42no—
152C23×#99D414yescomplemented
153C23×#95—22no—
154C23×#95—21no—
155C23×#95—21no—
156C23×#95—22no—
157C24×C23—21no—
158C24×C23—21no—
159C24×C23—22no—
160C24×C23—21no—
161C24×C23—22no—
162C24×C23—21no—
163C24×C23—21no—
164C24×C23—21no—
165C24×C23—22no—
166C24×C23—21no—
167C24×C23—21no—
168C24×C23—22no—
169C24×C23—41no—
170C24×C23—42no—
171C24×C23—42no—
172C24×C23—42no—
173C24×C23—81no—
174C24×C23—81no—
175C24×C23—81no—
176C24×C23C2×D411yescharacteristic
177C24×C23C2×D412yes—
178C24×C23C2×D411yescharacteristic
179C24×C23C2×D412yes—
180C24×C23C2×D412yes—
181C24×C23C2×D411yescharacteristic
182C24×C23C2×D411yescharacteristic
183C24×C23C2411yescharacteristic
184#41×C23—44no—
185#41×C23—44no—
186#41×C23—42no—
187#41×C23—42no—
188C2×Q8×C23—21no—
189C2×D4×C23—22no—
190C2×D4×C23—22no—
191C2×D4×C23—22no—
192C2×D4×C23—24no—
193C2×D4×C23—21no—
194C2×D4×C23—28no—
195C2×D4×C23—22no—
196C2×D4×C23—22no—
197C2×D4×C23—22no—
198C2×D4×C23—22no—
199C2×D4×C23—22no—
200C2×D4×C23—21no—
201C2×D4×C23—22no—
202C2×D4×C23—22no—
203C2×D4×C23—22no—
204C2×D4×C23—22no—
205C2×D4×C23—21no—
206C2×D4×C23—22no—
207C2×D4×C23—22no—
208C2×D4×C23—22no—
209C2×D4×C23—22no—
210C2×D4×C23—22no—
211C2×D4×C23—22no—
212C2×D4×C23—22no—
213C2×D4×C23—22no—
214C2×D4×C23—22no—
215C2×D4×C23—41no—
216C2×D4×C23—41no—
217C2×D4×C23—42no—
218C2×D4×C23—44no—
219C2×D4×C23—44no—
220C2×D4×C23—44no—
221C2×D4×C23—44no—
222C2×D4×C23—44no—
223C2×D4×C23—44no—
224C2×D4×C23—44no—
225C2×D4×C23—44no—
226C2×D4×C23—44no—
227C2×D4×C23—42no—
228C2×D4×C23—42no—
229C2×D4×C23—44no—
230C2×D4×C23—42no—
231C2×D4×C23—41no—
232C2×D4×C23—42no—
233C2×D4×C23—41no—
234C2×D4×C23—42no—
235C2×D4×C23—44no—
236C2×D4×C23—42no—
237C2×D4×C23—42no—
238C2×D4×C23—42no—
239C2×D4×C23—44no—
240C2×D4×C23—42no—
241C2×D4×C23—82no—
242C2×D4×C23—82no—
243C2×D4×C23—81no—
244C2×D4×C23—81no—
245C2×D4×C23—82no—
246C2×D4×C23—82no—
247C2×D4×C23C2×D412yes—
248C2×D4×C23#4112yes—
249C22×C4×C23—21no—
250C22×C4×C23—22no—
251C22×C4×C23—21no—
252C22×C4×C23—21no—
253C22×C4×C23—22no—
254C22×C4×C23—21no—
255C22×C4×C23—22no—
256C22×C4×C23—21no—
257C22×C4×C23—21no—
258C22×C4×C23—22no—
259C22×C4×C23—22no—
260C22×C4×C23—21no—
261C22×C4×C23—21no—
262C22×C4×C23—42no—
263C22×C4×C23—41no—
264C22×C4×C23—44no—
265C22×C4×C23—44no—
266C22×C4×C23—82no—
267C22×C4×C23C2×D412yes—
268C22×C4×C23C2×D411yescharacteristic
269C22×C4×C23C2×D411yescharacteristic
270C22×C4×C23C2×D412yes—
271C22×C4×C23C2×D412yes—
272C4⋊C4×C23—21no—
273C4⋊C4×C23—21no—
274C4⋊C4×C23—22no—
275C4⋊C4×C23—22no—
276C4⋊C4×C23—44no—
277C22⋊C4×C23—22no—
278C22⋊C4×C23—22no—
279C22⋊C4×C23—22no—
280C22⋊C4×C23—22no—
281C22⋊C4×C23—22no—
282C22⋊C4×C23—22no—
283C22⋊C4×C23—22no—
284C22⋊C4×C23—22no—
285C22⋊C4×C23—22no—
286C22⋊C4×C23—22no—
287C22⋊C4×C23—22no—
288C22⋊C4×C23—22no—
289C22⋊C4×C23—22no—
290C22⋊C4×C23—21no—
291C22⋊C4×C23—21no—
292C22⋊C4×C23—22no—
293C22⋊C4×C23—22no—
294C22⋊C4×C23—44no—
295C22⋊C4×C23—44no—
296C22⋊C4×C23—42no—
297C22⋊C4×C23—42no—
298C22⋊C4×C23—42no—
299C22⋊C4×C23—44no—
300C22⋊C4×C23—42no—
301C22⋊C4×C23—44no—
302C22⋊C4×C23—42no—
303C22⋊C4×C23—82no—
304C22⋊C4×C23—81no—
305C22⋊C4×C23C2×D414yescomplemented
306C42×C23—22no—
307#24404C2311yesmaximal, characteristic, direct product factor, Sylow
308C23×C23—21no—
309C23×C23—21no—
310C23×C23—21no—
311C23×C23—22no—
312C23×C23—22no—
313C23×C23—22no—
314C23×C23—24no—
315C23×C23—21no—
316C23×C23—21no—
317C23×C23—21no—
318C23×C23—22no—
319C23×C23—22no—
320C23×C23—24no—
321C23×C23—22no—
322C23×C23—21no—
323C23×C23—22no—
324C23×C23—21no—
325C23×C23—21no—
326C23×C23—22no—
327C23×C23—22no—
328C23×C23—41no—
329C23×C23—42no—
330C23×C23—41no—
331C23×C23—41no—
332C23×C23—41no—
333C23×C23—42no—
334C23×C23—41no—
335C23×C23—42no—
336C23×C23—42no—
337C23×C23—42no—
338C23×C23—41no—
339C23×C23—41no—
340C23×C23—41no—
341C23×C23—41no—
342C23×C23—42no—
343C23×C23—42no—
344C23×C23—41no—
345C23×C23—42no—
346C23×C23—41no—
347C23×C23—41no—
348C23×C23—42no—
349C23×C23—42no—
350C23×C23—42no—
351C23×C23—42no—
352C23×C23—41no—
353C23×C23—41no—
354C23×C23—41no—
355C23×C23—42no—
356C23×C23—42no—
357C23×C23—42no—
358C23×C23—81no—
359C23×C23—81no—
360C23×C23—82no—
361C23×C23—82no—
362C23×C23—82no—
363C23×C23—82no—
364C23×C23—84no—
365C23×C23—84no—
366C23×C23—81no—
367C23×C23—81no—
368C23×C23—84no—
369C23×C23—84no—
370C23×C23#12011yescharacteristic
371C23×C23#12012yes—
372C23×C23#12011yescharacteristic
373C23×C23#12112yescomplemented
374C23×C23C22×D411yescharacteristic
375C23×C23C22×D412yes—
376C23×C23C22×D411yescharacteristic
377C23×C23C2×#4111yescharacteristic
378C23×C23H(5,𝔽2)12yes—
379Q8×C23—42no—
380D4×C23—24no—
381D4×C23—24no—
382D4×C23—44no—
383D4×C23—42no—
384D4×C23—44no—
385D4×C23—48no—
386D4×C23—44no—
387D4×C23—44no—
388D4×C23—44no—
389D4×C23—42no—
390D4×C23—42no—
391D4×C23—42no—
392D4×C23—42no—
393D4×C23—42no—
394D4×C23—42no—
395D4×C23—44no—
396D4×C23—44no—
397D4×C23—82no—
398D4×C23—82no—
399D4×C23—82no—
400D4×C23—82no—
401D4×C23—88no—
402D4×C23—84no—
403D4×C23—84no—
404C2×C4×C23—21no—
405C2×C4×C23—21no—
406C2×C4×C23—22no—
407C2×C4×C23—24no—
408C2×C4×C23—22no—
409C2×C4×C23—22no—
410C2×C4×C23—22no—
411C2×C4×C23—21no—
412C2×C4×C23—21no—
413C2×C4×C23—21no—
414C2×C4×C23—24no—
415C2×C4×C23—22no—
416C2×C4×C23—22no—
417C2×C4×C23—42no—
418C2×C4×C23—42no—
419C2×C4×C23—44no—
420C2×C4×C23—42no—
421C2×C4×C23—42no—
422C2×C4×C23—41no—
423C2×C4×C23—42no—
424C2×C4×C23—42no—
425C2×C4×C23—41no—
426C2×C4×C23—42no—
427C2×C4×C23—42no—
428C2×C4×C23—42no—
429C2×C4×C23—41no—
430C2×C4×C23—41no—
431C2×C4×C23—42no—
432C2×C4×C23—41no—
433C2×C4×C23—41no—
434C2×C4×C23—41no—
435C2×C4×C23—41no—
436C2×C4×C23—42no—
437C2×C4×C23—81no—
438C2×C4×C23—81no—
439C2×C4×C23—88no—
440C2×C4×C23#12112yescomplemented
441#3484C2×C2311yescharacteristic, complemented
442C2×B(4,𝔽2)C2×C2311yescharacteristic, complemented
443C22×#99C2×C2311yescharacteristic, complemented
444#2410C2×C2312yescomplemented
445#2403C2×C2311yescharacteristic, complemented
446#2044C2×C2312yescomplemented
447#2021C2×C2312yescomplemented
448#1898C2×C2312yescomplemented
449#1889C2×C2311yescharacteristic, complemented
450#1867C2×C2311yescharacteristic, complemented
451#1790C2×C2311yescharacteristic, complemented
452C22×C23—21no—
453C22×C23—22no—
454C22×C23—21no—
455C22×C23—22no—
456C22×C23—21no—
457C22×C23—21no—
458C22×C23—21no—
459C22×C23—22no—
460C22×C23—22no—
461C22×C23—22no—
462C22×C23—21no—
463C22×C23—21no—
464C22×C23—22no—
465C22×C23—41no—
466C22×C23—41no—
467C22×C23—42no—
468C22×C23—44no—
469C22×C23—44no—
470C22×C23—42no—
471C22×C23—42no—
472C22×C23—42no—
473C22×C23—44no—
474C22×C23—42no—
475C22×C23—42no—
476C22×C23—42no—
477C22×C23—44no—
478C22×C23—41no—
479C22×C23—41no—
480C22×C23—42no—
481C22×C23—41no—
482C22×C23—42no—
483C22×C23—42no—
484C22×C23—41no—
485C22×C23—42no—
486C22×C23—41no—
487C22×C23—82no—
488C22×C23—81no—
489C22×C23—81no—
490C22×C23—81no—
491C22×C23—82no—
492C22×C23—84no—
493C22×C23—82no—
494C22×C23—82no—
495C22×C23—81no—
496C22×C23—82no—
497C22×C23—81no—
498C22×C23—81no—
499C22×C23—82no—
500C22×C23—84no—
501C22×C23—81no—
502C22×C23—81no—
503C22×C23—162no—
504C22×C23B(4,𝔽2)12yescomplemented
505C22×C23C2×#12011yescharacteristic
506C22×C23C2×#12111yescharacteristic
507C22×C23#53411yescharacteristic
508C22×C23D4212yes—
509C22×C23#54612yes—
510C4×C23—22no—
511C4×C23—44no—
512C4×C23—41no—
513C4×C23—42no—
514C4×C23—42no—
515C4×C23—42no—
516C4×C23—42no—
517C4×C23—82no—
518C4×C23—81no—
519C4×C23—81no—
520C2×H(5,𝔽2)C22×C2311yescharacteristic
521C23×D4C22×C2311yescharacteristic
522C23×D4C22×C2311yescharacteristic, complemented
523#546—22no—
524#546—22no—
525D42—22no—
526D42—22no—
527#535—21no—
528#534—21no—
529#534C22×C2312yes—
530#525—21no—
531C2×#121—22no—
532C2×#120—21no—
533C2×#120—21no—
534C2×#120C22×C2311yescharacteristic
535C2×#120C22×C2312yes—
536C2×#120C22×C2312yescomplemented
537C2×#120C22×C2311yescharacteristic, complemented
538#518C22×C2311yescharacteristic
539C22×C22⋊C4C22×C2312yescomplemented
540B(4,𝔽2)—24no—
541C2×#99—24no—
542C2×#99C22×C2311yescharacteristic
543C2×#99C22×C2311yescharacteristic
544C2×#99C22×C2312yescomplemented
545C2×#99C22×C2312yescomplemented
546C2×#99C22×C2312yescomplemented
547#394—22no—
548#392—21no—
549#392—21no—
550#392—22no—
551#386—21no—
552#386—22no—
553#386C22×C2311yescharacteristic
554#386C22×C2311yescharacteristic, complemented
555#386C22×C2312yescomplemented
556#385C22×C2312yescomplemented
557#379C22×C2312yescomplemented
558#379C22×C2311yescharacteristic, complemented
559#342C22×C2312yescomplemented
560#342C22×C2312yescomplemented
561C2×C23—22no—
562C2×C23—21no—
563C2×C23—21no—
564C2×C23—22no—
565C2×C23—22no—
566C2×C23—42no—
567C2×C23—41no—
568C2×C23—42no—
569C2×C23—82no—
570C2×C23—81no—
571C2×C23—82no—
572C2×C23#241011yescharacteristic
573C2×C23C2×B(4,𝔽2)11yescharacteristic
574C2×C23#302611yescharacteristic
575C25D4×C2311yescharacteristic, complemented
576C25C23×C2311yescharacteristic
577C25C23×C2311yescharacteristic
578H(5,𝔽2)—22no—
579H(5,𝔽2)—22no—
580H(5,𝔽2)—42no—
581C2×#41—21no—
582C2×#41—22no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—22no—
598C22×D4—44no—
599C22×D4—42no—
600C22×D4D4×C2311yescharacteristic, complemented
601C22×D4D4×C2311yescharacteristic, complemented
602C22×D4D4×C2312yescomplemented
603C22×D4D4×C2312yescomplemented
604C22×D4C23×C2312yes—
605C22×D4C23×C2311yescharacteristic
606C22×D4C23×C2311yescharacteristic
607C23×C4—22no—
608C23×C4D4×C2311yescharacteristic, complemented
609C23×C4C23×C2311yescharacteristic
610#127—22no—
611#124—22no—
612#123—22no—
613#123—22no—
614#123—22no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617#121—21no—
618#121—21no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—48no—
626#120—22no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—24no—
638#120—42no—
639#120—42no—
640#120—44no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—21no—
646C2×C4⋊C4—22no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—42no—
663C2×C22⋊C4D4×C2312yescomplemented
664C2×C22⋊C4D4×C2312yescomplemented
665C2×C22⋊C4C23×C2312yes—
666C2×C22⋊C4C23×C2311yescharacteristic
667C2×C22⋊C4C23×C2311yescharacteristic
668C2×C22⋊C4C23×C2312yes—
669C2×C22⋊C4C23×C2312yes—
670#99—22no—
671#99—24no—
672#99—24no—
673#99—42no—
674#99D4×C2314yescomplemented
675#95—22no—
676#95—21no—
677#95—21no—
678#95—22no—
679C23#2440411yescharacteristic, direct product factor, Sylow
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C2311yescharacteristic
700C24C2×D4×C2312yes—
701C24C2×D4×C2311yescharacteristic
702C24C2×D4×C2312yes—
703C24C2×D4×C2312yes—
704C24C2×D4×C2311yescharacteristic
705C24C2×D4×C2311yescharacteristic
706C24C24×C2311yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C2312yes—
771C2×D4#41×C2312yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C2312yes—
791C22×C4C2×D4×C2311yescharacteristic
792C22×C4C2×D4×C2311yescharacteristic
793C22×C4C2×D4×C2312yes—
794C22×C4C2×D4×C2312yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C2314yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23C23×#12011yescharacteristic
893C23C23×#12012yes—
894C23C23×#12011yescharacteristic
895C23C23×#12112yescomplemented
896C23C22×D4×C2311yescharacteristic
897C23C22×D4×C2312yes—
898C23C22×D4×C2311yescharacteristic
899C23C2×#41×C2311yescharacteristic
900C23C23×H(5,𝔽2)12yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4C23×#12112yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C23×B(4,𝔽2)12yescomplemented
1016C22C2×C23×#12011yescharacteristic
1017C22C2×C23×#12111yescharacteristic
1018C22C23×#53411yescharacteristic
1019C22D42×C2312yes—
1020C22C23×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C23×#241011yescharacteristic
1043C2C2×C23×B(4,𝔽2)11yescharacteristic
1044C2C23×#302611yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC24C24×C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C25×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#3484C2semidirect
2. C2×C23×B(4,𝔽2)C2semidirect
3. C22×C23×#99C2semidirect
4. C23×#2410C2semidirect
5. C23×#2403C2semidirect
6. C23×#2044C2semidirect
7. C23×#2021C2semidirect
8. C23×#1898C2semidirect
9. C23×#1889C2semidirect
10. C23×#1867C2semidirect
11. C23×#1790C2semidirect
14. C23×D4×C23C22semidirect
28. C2×C23×#120C22semidirect
29. C2×C23×#120C22semidirect
31. C22×C22⋊C4×C23C22semidirect
36. C2×C23×#99C22semidirect
37. C2×C23×#99C22semidirect
38. C2×C23×#99C22semidirect
46. C23×#386C22semidirect
47. C23×#386C22semidirect
48. C23×#385C22semidirect
49. C23×#379C22semidirect
50. C23×#379C22semidirect
51. C23×#342C22semidirect
52. C23×#342C22semidirect
53. C25×C23D4semidirect
78. C22×D4×C23D4semidirect
79. C22×D4×C23D4semidirect
80. C22×D4×C23D4semidirect
81. C22×D4×C23D4semidirect
86. C23×C4×C23D4semidirect
141. C2×C22⋊C4×C23D4semidirect
142. C2×C22⋊C4×C23D4semidirect
152. C23×#99D4semidirect
305. C22⋊C4×C23C2×D4semidirect
307. #24404C23direct (N × H)
373. C23×C23#121semidirect
440. C2×C4×C23#121semidirect
441. #3484C2×C23semidirect
442. C2×B(4,𝔽2)C2×C23semidirect
443. C22×#99C2×C23semidirect
444. #2410C2×C23semidirect
445. #2403C2×C23semidirect
446. #2044C2×C23semidirect
447. #2021C2×C23semidirect
448. #1898C2×C23semidirect
449. #1889C2×C23semidirect
450. #1867C2×C23semidirect
451. #1790C2×C23semidirect
504. C22×C23B(4,𝔽2)semidirect
522. C23×D4C22×C23semidirect
536. C2×#120C22×C23semidirect
537. C2×#120C22×C23semidirect
539. C22×C22⋊C4C22×C23semidirect
544. C2×#99C22×C23semidirect
545. C2×#99C22×C23semidirect
546. C2×#99C22×C23semidirect
554. #386C22×C23semidirect
555. #386C22×C23semidirect
556. #385C22×C23semidirect
557. #379C22×C23semidirect
558. #379C22×C23semidirect
559. #342C22×C23semidirect
560. #342C22×C23semidirect
575. C25D4×C23semidirect
600. C22×D4D4×C23semidirect
601. C22×D4D4×C23semidirect
602. C22×D4D4×C23semidirect
603. C22×D4D4×C23semidirect
608. C23×C4D4×C23semidirect
663. C2×C22⋊C4D4×C23semidirect
664. C2×C22⋊C4D4×C23semidirect
674. #99D4×C23semidirect
679. C23#24404direct (N × H)
828. C22⋊C4C2×D4×C23semidirect
895. C23C23×#121semidirect
962. C2×C4C23×#121semidirect
1015. C22C23×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C23×#34842
C2×C23×B(4,𝔽2)2
C22×C23×#992
C23×#24102
C23×#24032
C23×#20442
C23×#20212
C23×#18982
C23×#18892
C23×#18672
C23×#17902
#2440423