Finite Group Databasebeta

← C23×#25563 #19173189

Subgroups — C23×#25563 #19173189

Order 5888.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3490C211yesmaximal, characteristic, complemented
2C23×#2410C212yesmaximal, complemented
3C23×#2405C211yesmaximal, characteristic, complemented
4C23×#2062C211yesmaximal, characteristic, complemented
5C23×#2044C211yesmaximal, characteristic, complemented
6C23×#2029C211yesmaximal, characteristic, complemented
7C23×#2021C211yesmaximal, characteristic, complemented
8C23×#1898C212yesmaximal, complemented
9C23×#1889C212yesmaximal, complemented
10C23×#1867C212yesmaximal, complemented
11C2×C23×#342C211yesmaximal, characteristic, complemented
12C23×D4×C23C2211yescharacteristic
13C23×#551—22no—
14C23×#551—22no—
15C23×#546—22no—
16C23×#546—22no—
17C23×#543C2211yescharacteristic
18C23×#538—21no—
19C23×#538—21no—
20C23×#534C2211yescharacteristic
21C23×#525—21no—
22C23×#525—21no—
23C2×C23×#123—21no—
24C2×C23×#121—22no—
25C2×C23×#120C2212yes—
26C2×C23×#120C2212yes—
27C23×#518C2212yes—
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2212yes—
30C2×C23×#99C2212yes—
31C2×C23×#99C2212yes—
32C23×#394—21no—
33C23×#394—21no—
34C23×#394—22no—
35C23×#392—22no—
36C23×#386—21no—
37C23×#386—22no—
38C23×#386C2212yes—
39C23×#385C2211yescharacteristic
40C23×#385C2211yescharacteristic
41C23×#385C2212yes—
42C23×#379C2211yescharacteristic
43C23×#379C2212yes—
44C23×#379C2211yescharacteristic
45C23×#379C2211yescharacteristic
46C23×#342C2212yes—
47C23×#342C2212yes—
48C23×#342C2212yes—
49C23×#342C2211yescharacteristic
50C23×#342C2211yescharacteristic
51C25×C23C2311yescharacteristic
52C25×C23C2311yescharacteristic
53C2×#41×C23—21no—
54C2×#41×C23—21no—
55C22×D4×C23—22no—
56C22×D4×C23—21no—
57C22×D4×C23—22no—
58C22×D4×C23—21no—
59C22×D4×C23—22no—
60C22×D4×C23—44no—
61C22×D4×C23D412yescomplemented
62C22×D4×C23D412yescomplemented
63C22×D4×C23C2312yes—
64C23×C4×C23—22no—
65C23×C4×C23D411yescharacteristic, complemented
66C23×C4×C23D411yescharacteristic, complemented
67C23×C4×C23C2311yescharacteristic
68C23×#126—22no—
69C23×#126—22no—
70C23×#124—22no—
71C23×#124—22no—
72C23×#123—22no—
73C23×#123—22no—
74C23×#123—22no—
75C23×#123—22no—
76C23×#123—22no—
77C23×#123—44no—
78C23×C22⋊Q8—21no—
79C23×C22⋊Q8—21no—
80C23×C22⋊Q8—22no—
81C23×C22⋊Q8—22no—
82C23×C22⋊Q8—21no—
83C23×C22⋊Q8—21no—
84C23×#121—21no—
85C23×#121—21no—
86C23×#121—22no—
87C23×#121—22no—
88C23×#121—21no—
89C23×#121—21no—
90C23×#121—48no—
91C23×#120—22no—
92C23×#120—22no—
93C23×#120—22no—
94C23×#120—22no—
95C23×#120—22no—
96C23×#120—24no—
97C23×#120—42no—
98C4×D4×C23—22no—
99C4×D4×C23—22no—
100C4×D4×C23—22no—
101C4×D4×C23—22no—
102C4×D4×C23—22no—
103C4×D4×C23—22no—
104C23×#117—21no—
105C23×#117—21no—
106C23×#117—22no—
107C2×C4⋊C4×C23—22no—
108C2×C4⋊C4×C23—21no—
109C2×C4⋊C4×C23—21no—
110C2×C22⋊C4×C23—22no—
111C2×C22⋊C4×C23—22no—
112C2×C22⋊C4×C23—22no—
113C2×C22⋊C4×C23—24no—
114C2×C22⋊C4×C23—21no—
115C2×C22⋊C4×C23—22no—
116C2×C22⋊C4×C23—22no—
117C2×C22⋊C4×C23—22no—
118C2×C22⋊C4×C23—21no—
119C2×C22⋊C4×C23—21no—
120C2×C22⋊C4×C23—22no—
121C2×C22⋊C4×C23—21no—
122C2×C22⋊C4×C23—22no—
123C2×C22⋊C4×C23—21no—
124C2×C22⋊C4×C23—21no—
125C2×C22⋊C4×C23—42no—
126C2×C22⋊C4×C23D412yescomplemented
127C2×C22⋊C4×C23D412yescomplemented
128C2×C22⋊C4×C23D411yescharacteristic, complemented
129C2×C22⋊C4×C23D411yescharacteristic, complemented
130C2×C22⋊C4×C23C2312yes—
131C2×C22⋊C4×C23C2311yescharacteristic
132C2×C22⋊C4×C23C2311yescharacteristic
133C2×C22⋊C4×C23C2311yescharacteristic
134C2×C22⋊C4×C23C2311yescharacteristic
135C2×C22⋊C4×C23C2312yes—
136C2×C22⋊C4×C23C2312yes—
137C23×#99—24no—
138C23×#99—42no—
139C23×#95—22no—
140C23×#95—21no—
141C23×#95—21no—
142C23×#95—22no—
143C24×C23—22no—
144C24×C23—21no—
145C24×C23—21no—
146C24×C23—21no—
147C24×C23—22no—
148C24×C23—22no—
149C24×C23—21no—
150C24×C23—21no—
151C24×C23—42no—
152C24×C23—42no—
153C24×C23—81no—
154C24×C23—81no—
155C24×C23C2×D412yes—
156C24×C23C2×D411yescharacteristic
157C24×C23C2×D412yes—
158C24×C23C2×D412yes—
159C24×C23C2×D411yescharacteristic
160C24×C23C2411yescharacteristic
161#41×C23—82no—
162#41×C23—82no—
163C2×Q8×C23—21no—
164C2×Q8×C23—21no—
165C2×D4×C23—28no—
166C2×D4×C23—24no—
167C2×D4×C23—22no—
168C2×D4×C23—22no—
169C2×D4×C23—22no—
170C2×D4×C23—22no—
171C2×D4×C23—22no—
172C2×D4×C23—22no—
173C2×D4×C23—22no—
174C2×D4×C23—22no—
175C2×D4×C23—21no—
176C2×D4×C23—21no—
177C2×D4×C23—22no—
178C2×D4×C23—22no—
179C2×D4×C23—44no—
180C2×D4×C23—42no—
181C2×D4×C23—44no—
182C2×D4×C23—42no—
183C2×D4×C23—44no—
184C2×D4×C23—42no—
185C2×D4×C23—44no—
186C2×D4×C23—42no—
187C2×D4×C23—41no—
188C2×D4×C23—41no—
189C2×D4×C23—44no—
190C2×D4×C23—44no—
191C2×D4×C23—82no—
192C2×D4×C23—82no—
193C22×C4×C23—21no—
194C22×C4×C23—21no—
195C22×C4×C23—22no—
196C22×C4×C23—22no—
197C22×C4×C23—21no—
198C22×C4×C23—22no—
199C22×C4×C23—22no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—21no—
204C22×C4×C23—22no—
205C22×C4×C23—42no—
206C22×C4×C23—44no—
207C22×C4×C23—42no—
208C22×C4×C23—44no—
209C22×C4×C23—81no—
210C22×C4×C23—82no—
211C22×C4×C23C2×D412yes—
212C22×C4×C23C2×D411yescharacteristic
213C22×C4×C23C2×D412yes—
214C22×C4×C23C2×D411yescharacteristic
215C22×C4×C23C2×D411yescharacteristic
216C22×C4×C23C2×D412yes—
217C22×C4×C23C2×D411yescharacteristic
218C4⋊C4×C23—22no—
219C4⋊C4×C23—22no—
220C4⋊C4×C23—21no—
221C4⋊C4×C23—21no—
222C4⋊C4×C23—21no—
223C4⋊C4×C23—21no—
224C4⋊C4×C23—22no—
225C4⋊C4×C23—22no—
226C4⋊C4×C23—44no—
227C4⋊C4×C23—42no—
228C4⋊C4×C23—42no—
229C22⋊C4×C23—22no—
230C22⋊C4×C23—22no—
231C22⋊C4×C23—22no—
232C22⋊C4×C23—22no—
233C22⋊C4×C23—22no—
234C22⋊C4×C23—22no—
235C22⋊C4×C23—22no—
236C22⋊C4×C23—22no—
237C22⋊C4×C23—22no—
238C22⋊C4×C23—22no—
239C22⋊C4×C23—22no—
240C22⋊C4×C23—22no—
241C22⋊C4×C23—22no—
242C22⋊C4×C23—22no—
243C22⋊C4×C23—22no—
244C22⋊C4×C23—22no—
245C22⋊C4×C23—22no—
246C22⋊C4×C23—21no—
247C22⋊C4×C23—22no—
248C22⋊C4×C23—21no—
249C22⋊C4×C23—44no—
250C22⋊C4×C23—44no—
251C22⋊C4×C23—44no—
252C22⋊C4×C23—44no—
253C22⋊C4×C23—42no—
254C22⋊C4×C23—42no—
255C22⋊C4×C23—42no—
256C22⋊C4×C23—81no—
257C22⋊C4×C23—81no—
258C22⋊C4×C23—82no—
259C22⋊C4×C23—81no—
260C22⋊C4×C23#4114yescomplemented
261C42×C23—22no—
262C42×C23—22no—
263#25563C2311yesmaximal, characteristic, direct product factor, Sylow
264C23×C23—21no—
265C23×C23—21no—
266C23×C23—22no—
267C23×C23—22no—
268C23×C23—22no—
269C23×C23—24no—
270C23×C23—21no—
271C23×C23—21no—
272C23×C23—22no—
273C23×C23—22no—
274C23×C23—22no—
275C23×C23—24no—
276C23×C23—22no—
277C23×C23—22no—
278C23×C23—22no—
279C23×C23—41no—
280C23×C23—41no—
281C23×C23—42no—
282C23×C23—41no—
283C23×C23—41no—
284C23×C23—41no—
285C23×C23—42no—
286C23×C23—42no—
287C23×C23—41no—
288C23×C23—41no—
289C23×C23—42no—
290C23×C23—41no—
291C23×C23—42no—
292C23×C23—42no—
293C23×C23—42no—
294C23×C23—42no—
295C23×C23—41no—
296C23×C23—41no—
297C23×C23—41no—
298C23×C23—42no—
299C23×C23—42no—
300C23×C23—84no—
301C23×C23—84no—
302C23×C23—82no—
303C23×C23—82no—
304C23×C23—82no—
305C23×C23—82no—
306C23×C23#12012yes—
307C23×C23#12011yescharacteristic
308C23×C23#12011yescharacteristic
309C23×C23C22×D411yescharacteristic
310C23×C23C22×D412yes—
311C23×C23C2×#4112yes—
312C23×C23H(5,𝔽2)11yescharacteristic
313C23×C232−1+411yescharacteristic
314Q8×C23—81no—
315Q8×C23—81no—
316D4×C23—44no—
317D4×C23—48no—
318D4×C23—44no—
319D4×C23—42no—
320D4×C23—42no—
321D4×C23—42no—
322D4×C23—42no—
323D4×C23—44no—
324D4×C23—44no—
325D4×C23—82no—
326D4×C23—82no—
327D4×C23—81no—
328D4×C23—81no—
329D4×C23—88no—
330C2×C4×C23—24no—
331C2×C4×C23—22no—
332C2×C4×C23—22no—
333C2×C4×C23—21no—
334C2×C4×C23—21no—
335C2×C4×C23—22no—
336C2×C4×C23—22no—
337C2×C4×C23—21no—
338C2×C4×C23—21no—
339C2×C4×C23—24no—
340C2×C4×C23—22no—
341C2×C4×C23—22no—
342C2×C4×C23—42no—
343C2×C4×C23—41no—
344C2×C4×C23—42no—
345C2×C4×C23—42no—
346C2×C4×C23—42no—
347C2×C4×C23—41no—
348C2×C4×C23—42no—
349C2×C4×C23—41no—
350C2×C4×C23—41no—
351C2×C4×C23—42no—
352C2×C4×C23—41no—
353C2×C4×C23—41no—
354C2×C4×C23—42no—
355C2×C4×C23—41no—
356C2×C4×C23—41no—
357C2×C4×C23—42no—
358C2×C4×C23—41no—
359C2×C4×C23—41no—
360C2×C4×C23—42no—
361C2×C4×C23—41no—
362C2×C4×C23—41no—
363C2×C4×C23—42no—
364C2×C4×C23—81no—
365C2×C4×C23—81no—
366C2×C4×C23—82no—
367C2×C4×C23—82no—
368C2×C4×C23—88no—
369#3490C2×C2311yescharacteristic, complemented
370#2410C2×C2312yescomplemented
371#2405C2×C2311yescharacteristic, complemented
372#2062C2×C2311yescharacteristic, complemented
373#2044C2×C2311yescharacteristic, complemented
374#2029C2×C2311yescharacteristic, complemented
375#2021C2×C2311yescharacteristic, complemented
376#1898C2×C2312yescomplemented
377#1889C2×C2312yescomplemented
378#1867C2×C2312yescomplemented
379C2×#342C2×C2311yescharacteristic, complemented
380C22×C23—21no—
381C22×C23—21no—
382C22×C23—22no—
383C22×C23—21no—
384C22×C23—22no—
385C22×C23—21no—
386C22×C23—21no—
387C22×C23—22no—
388C22×C23—21no—
389C22×C23—22no—
390C22×C23—21no—
391C22×C23—22no—
392C22×C23—42no—
393C22×C23—41no—
394C22×C23—41no—
395C22×C23—44no—
396C22×C23—42no—
397C22×C23—42no—
398C22×C23—44no—
399C22×C23—44no—
400C22×C23—42no—
401C22×C23—42no—
402C22×C23—44no—
403C22×C23—42no—
404C22×C23—42no—
405C22×C23—42no—
406C22×C23—42no—
407C22×C23—82no—
408C22×C23—81no—
409C22×C23—81no—
410C22×C23—82no—
411C22×C23—82no—
412C22×C23—82no—
413C22×C23—82no—
414C22×C23—81no—
415C22×C23—81no—
416C22×C23—82no—
417C22×C23—81no—
418C22×C23—81no—
419C22×C23B(4,𝔽2)12yes—
420C22×C23C2×#12011yescharacteristic
421C22×C23#53211yescharacteristic
422C22×C23#53711yescharacteristic
423C22×C23#54612yes—
424C22×C23#54712yes—
425C4×C23—44no—
426C4×C23—42no—
427C4×C23—42no—
428C4×C23—41no—
429C4×C23—41no—
430C4×C23—42no—
431C4×C23—41no—
432C4×C23—41no—
433C4×C23—42no—
434C4×C23—81no—
435C4×C23—81no—
436C4×C23—82no—
437C23×D4C22×C2311yescharacteristic
438#551—22no—
439#551—22no—
440#546—22no—
441#546—22no—
442#543C22×C2311yescharacteristic
443#538—21no—
444#538—21no—
445#534C22×C2311yescharacteristic
446#525—21no—
447#525—21no—
448C2×#123—21no—
449C2×#121—22no—
450C2×#120C22×C2312yes—
451C2×#120C22×C2312yes—
452#518C22×C2312yes—
453C22×C22⋊C4C22×C2311yescharacteristic
454C22×C22⋊C4C22×C2312yes—
455C2×#99C22×C2312yes—
456C2×#99C22×C2312yes—
457#394—21no—
458#394—21no—
459#394—22no—
460#392—22no—
461#386—21no—
462#386—22no—
463#386C22×C2312yes—
464#385C22×C2312yes—
465#385C22×C2311yescharacteristic
466#385C22×C2311yescharacteristic
467#379C22×C2311yescharacteristic
468#379C22×C2312yes—
469#379C22×C2311yescharacteristic
470#379C22×C2311yescharacteristic
471#342C22×C2312yes—
472#342C22×C2311yescharacteristic
473#342C22×C2312yes—
474#342C22×C2312yes—
475#342C22×C2311yescharacteristic
476C2×C23—22no—
477C2×C23—21no—
478C2×C23—21no—
479C2×C23—22no—
480C2×C23—22no—
481C2×C23—41no—
482C2×C23—42no—
483C2×C23—82no—
484C2×C23—82no—
485C2×C23#243011yescharacteristic
486C2×C23C2×B(4,𝔽2)11yescharacteristic
487C2×C23#302611yescharacteristic
488C25C23×C2311yescharacteristic
489C25C23×C2311yescharacteristic
490C2×#41—21no—
491C2×#41—21no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—44no—
498C22×D4D4×C2312yescomplemented
499C22×D4D4×C2312yescomplemented
500C22×D4C23×C2312yes—
501C23×C4—22no—
502C23×C4D4×C2311yescharacteristic, complemented
503C23×C4D4×C2311yescharacteristic, complemented
504C23×C4C23×C2311yescharacteristic
505#126—22no—
506#126—22no—
507#124—22no—
508#124—22no—
509#123—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—44no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521#121—21no—
522#121—21no—
523#121—22no—
524#121—22no—
525#121—21no—
526#121—21no—
527#121—48no—
528#120—22no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—24no—
534#120—42no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541#117—21no—
542#117—21no—
543#117—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4D4×C2311yescharacteristic, complemented
564C2×C22⋊C4D4×C2311yescharacteristic, complemented
565C2×C22⋊C4D4×C2312yescomplemented
566C2×C22⋊C4D4×C2312yescomplemented
567C2×C22⋊C4C23×C2312yes—
568C2×C22⋊C4C23×C2311yescharacteristic
569C2×C22⋊C4C23×C2311yescharacteristic
570C2×C22⋊C4C23×C2311yescharacteristic
571C2×C22⋊C4C23×C2311yescharacteristic
572C2×C22⋊C4C23×C2312yes—
573C2×C22⋊C4C23×C2312yes—
574#99—24no—
575#99—42no—
576#95—22no—
577#95—21no—
578#95—21no—
579#95—22no—
580C23#2556311yescharacteristic, direct product factor, Sylow
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C2312yes—
594C24C2×D4×C2311yescharacteristic
595C24C2×D4×C2312yes—
596C24C2×D4×C2312yes—
597C24C2×D4×C2311yescharacteristic
598C24C24×C2311yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C2312yes—
650C22×C4C2×D4×C2311yescharacteristic
651C22×C4C2×D4×C2312yes—
652C22×C4C2×D4×C2311yescharacteristic
653C22×C4C2×D4×C2311yescharacteristic
654C22×C4C2×D4×C2312yes—
655C22×C4C2×D4×C2311yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C2314yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23C23×#12012yes—
744C23C23×#12011yescharacteristic
745C23C23×#12011yescharacteristic
746C23C22×D4×C2312yes—
747C23C22×D4×C2311yescharacteristic
748C23C2×#41×C2312yes—
749C23C23×H(5,𝔽2)11yescharacteristic
750C23C23×2−1+411yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—42no—
757D4—44no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—22no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C23×B(4,𝔽2)12yes—
846C22C2×C23×#12011yescharacteristic
847C22C23×#53211yescharacteristic
848C22C23×#53711yescharacteristic
849C22C23×#54612yes—
850C22C23×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C23×#243011yescharacteristic
873C2C2×C23×B(4,𝔽2)11yescharacteristic
874C2C23×#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×#3490C2semidirect
2. C23×#2410C2semidirect
3. C23×#2405C2semidirect
4. C23×#2062C2semidirect
5. C23×#2044C2semidirect
6. C23×#2029C2semidirect
7. C23×#2021C2semidirect
8. C23×#1898C2semidirect
9. C23×#1889C2semidirect
10. C23×#1867C2semidirect
11. C2×C23×#342C2semidirect
61. C22×D4×C23D4semidirect
62. C22×D4×C23D4semidirect
65. C23×C4×C23D4semidirect
66. C23×C4×C23D4semidirect
126. C2×C22⋊C4×C23D4semidirect
127. C2×C22⋊C4×C23D4semidirect
128. C2×C22⋊C4×C23D4semidirect
129. C2×C22⋊C4×C23D4semidirect
260. C22⋊C4×C23#41semidirect
263. #25563C23direct (N × H)
369. #3490C2×C23semidirect
370. #2410C2×C23semidirect
371. #2405C2×C23semidirect
372. #2062C2×C23semidirect
373. #2044C2×C23semidirect
374. #2029C2×C23semidirect
375. #2021C2×C23semidirect
376. #1898C2×C23semidirect
377. #1889C2×C23semidirect
378. #1867C2×C23semidirect
379. C2×#342C2×C23semidirect
498. C22×D4D4×C23semidirect
499. C22×D4D4×C23semidirect
502. C23×C4D4×C23semidirect
503. C23×C4D4×C23semidirect
563. C2×C22⋊C4D4×C23semidirect
564. C2×C22⋊C4D4×C23semidirect
565. C2×C22⋊C4D4×C23semidirect
566. C2×C22⋊C4D4×C23semidirect
580. C23#25563direct (N × H)
698. C22⋊C4#41×C23semidirect

Maximal subgroups

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

subgroupindex
C23×#34902
C23×#24102
C23×#24052
C23×#20622
C23×#20442
C23×#20292
C23×#20212
C23×#18982
C23×#18892
C23×#18672
C2×C23×#3422
#2556323