Finite Group Databasebeta

← C23×#16298 #19163924

Subgroups — C23×#16298 #19163924

Order 5888.

2830 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#399C211yesmaximal, characteristic, complemented
2C2×C23×#396C212yesmaximal, complemented
3C2×C23×#379C211yesmaximal, characteristic
4C2×C23×#379C212yesmaximal
5C23×#1439C212yesmaximal, complemented
6C23×#1439C212yesmaximal, complemented
7C23×#1439C212yesmaximal, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1439C212yesmaximal, complemented
10C26×C23C2211yescharacteristic
11C22×C4⋊C4×C23C2211yescharacteristic, complemented
12C22×C4⋊C4×C23C2212yescomplemented
13C22×C4⋊C4×C23C2212yescomplemented
14C22×C4⋊C4×C23C2211yescharacteristic, complemented
15C22×C22⋊C4×C23C2212yes—
16C22×C22⋊C4×C23C2212yes—
17C22×C22⋊C4×C23C2212yes—
18C22×C22⋊C4×C23C2212yes—
19C22×C22⋊C4×C23C2212yes—
20C22×C22⋊C4×C23C2212yes—
21C22×C22⋊C4×C23C2212yes—
22C22×C22⋊C4×C23C2211yescharacteristic
23C22×C22⋊C4×C23C2212yes—
24C22×C22⋊C4×C23C2211yescharacteristic
25C23×#399—24no—
26C23×#396—28no—
27C23×#379—28no—
28C23×#379—24no—
29C2×C23×#95C2212yescomplemented
30C2×C23×#95C2211yescharacteristic, complemented
31C2×C23×#95C2211yescharacteristic, complemented
32C2×C23×#95C2212yescomplemented
33C2×C23×#95C2212yescomplemented
34C2×C23×#95C2212yescomplemented
35C25×C23—24no—
36C25×C23—22no—
37C25×C23—22no—
38C25×C23—24no—
39C25×C23—41no—
40C25×C23—42no—
41C25×C23—42no—
42C25×C23—41no—
43C25×C23—41no—
44C25×C23—41no—
45C25×C23Q814yes—
46C25×C23C2312yes—
47C25×C23C2311yescharacteristic
48C23×C4×C23C2312yes—
49C23×C4×C23C2312yes—
50C23×C4×C23C2312yes—
51C23×C4×C23C2311yescharacteristic
52C23×C4×C23C2312yes—
53C23×C4×C23C2312yes—
54C23×C4×C23C2311yescharacteristic
55C2×C4⋊C4×C23—24no—
56C2×C4⋊C4×C23—24no—
57C2×C4⋊C4×C23—24no—
58C2×C4⋊C4×C23—24no—
59C2×C4⋊C4×C23—22no—
60C2×C4⋊C4×C23—41no—
61C2×C4⋊C4×C23—42no—
62C2×C4⋊C4×C23—42no—
63C2×C4⋊C4×C23—42no—
64C2×C4⋊C4×C23—41no—
65C2×C4⋊C4×C23—41no—
66C2×C22⋊C4×C23—24no—
67C2×C22⋊C4×C23—22no—
68C2×C22⋊C4×C23—24no—
69C2×C22⋊C4×C23—24no—
70C2×C22⋊C4×C23—24no—
71C2×C22⋊C4×C23—24no—
72C2×C22⋊C4×C23—24no—
73C2×C22⋊C4×C23—24no—
74C2×C22⋊C4×C23—24no—
75C2×C22⋊C4×C23—24no—
76C2×C22⋊C4×C23—24no—
77C2×C22⋊C4×C23—24no—
78C2×C22⋊C4×C23—24no—
79C2×C22⋊C4×C23—24no—
80C2×C22⋊C4×C23—42no—
81C2×C22⋊C4×C23—41no—
82C2×C22⋊C4×C23—42no—
83C2×C22⋊C4×C23—41no—
84C2×C22⋊C4×C23—42no—
85C2×C22⋊C4×C23—42no—
86C2×C22⋊C4×C23—42no—
87C2×C22⋊C4×C23—42no—
88C2×C22⋊C4×C23—42no—
89C2×C22⋊C4×C23—42no—
90C2×C22⋊C4×C23—41no—
91C2×C22⋊C4×C23—42no—
92C2×C22⋊C4×C23—42no—
93C2×C22⋊C4×C23—41no—
94C2×C22⋊C4×C23D418yes—
95C2×C22⋊C4×C23D414yes—
96C23×#95—24no—
97C23×#95—22no—
98C23×#95—42no—
99C23×#95—41no—
100C23×#95—42no—
101C23×#95—42no—
102C24×C23—22no—
103C24×C23—22no—
104C24×C23—22no—
105C24×C23—22no—
106C24×C23—22no—
107C24×C23—22no—
108C24×C23—22no—
109C24×C23—21no—
110C24×C23—21no—
111C24×C23—22no—
112C24×C23—21no—
113C24×C23—22no—
114C24×C23—22no—
115C24×C23—21no—
116C24×C23—22no—
117C24×C23—22no—
118C24×C23—22no—
119C24×C23—22no—
120C24×C23—22no—
121C24×C23—22no—
122C24×C23—216no—
123C24×C23—28no—
124C24×C23—44no—
125C24×C23—48no—
126C24×C23—44no—
127C24×C23—44no—
128C24×C23—48no—
129C24×C23—48no—
130C24×C23—48no—
131C24×C23—48no—
132C24×C23—48no—
133C24×C23—44no—
134C24×C23—48no—
135C24×C23—44no—
136C24×C23—48no—
137C24×C23—44no—
138C24×C23—44no—
139C24×C23—48no—
140C24×C23—44no—
141C24×C23—48no—
142C24×C23—44no—
143C24×C23—44no—
144C24×C23—48no—
145C24×C23C2×D414yes—
146C24×C23C2×D412yes—
147C24×C23C2×Q814yes—
148C24×C23C2×Q812yes—
149C24×C23#4112yes—
150C24×C23#4114yes—
151C24×C23C2411yescharacteristic
152C22×C4×C23—22no—
153C22×C4×C23—22no—
154C22×C4×C23—22no—
155C22×C4×C23—22no—
156C22×C4×C23—22no—
157C22×C4×C23—22no—
158C22×C4×C23—22no—
159C22×C4×C23—21no—
160C22×C4×C23—22no—
161C22×C4×C23—21no—
162C22×C4×C23—22no—
163C22×C4×C23—21no—
164C22×C4×C23—22no—
165C22×C4×C23—22no—
166C22×C4×C23—22no—
167C22×C4×C23—22no—
168C22×C4×C23—21no—
169C22×C4×C23—22no—
170C22×C4×C23—22no—
171C22×C4×C23—22no—
172C22×C4×C23—22no—
173C22×C4×C23—22no—
174C22×C4×C23—22no—
175C22×C4×C23—22no—
176C22×C4×C23—22no—
177C22×C4×C23—22no—
178C22×C4×C23—22no—
179C22×C4×C23—22no—
180C22×C4×C23—22no—
181C22×C4×C23—22no—
182C22×C4×C23—22no—
183C22×C4×C23—22no—
184C22×C4×C23—22no—
185C22×C4×C23—22no—
186C22×C4×C23—22no—
187C22×C4×C23—22no—
188C22×C4×C23—22no—
189C22×C4×C23—22no—
190C22×C4×C23—22no—
191C22×C4×C23—22no—
192C22×C4×C23—22no—
193C22×C4×C23C2×D414yes—
194C22×C4×C23C2×D412yes—
195C22×C4×C23C2×D412yes—
196C22×C4×C23C2×D414yes—
197C4⋊C4×C23—44no—
198C4⋊C4×C23—48no—
199C4⋊C4×C23—48no—
200C4⋊C4×C23—44no—
201C22⋊C4×C23—48no—
202C22⋊C4×C23—44no—
203C22⋊C4×C23—48no—
204C22⋊C4×C23—48no—
205C22⋊C4×C23—48no—
206C22⋊C4×C23—48no—
207C22⋊C4×C23—48no—
208C22⋊C4×C23—48no—
209C22⋊C4×C23—48no—
210C22⋊C4×C23—44no—
211#16298C2311yesmaximal, characteristic, direct product factor, Sylow
212C23×C23—24no—
213C23×C23—24no—
214C23×C23—24no—
215C23×C23—24no—
216C23×C23—22no—
217C23×C23—24no—
218C23×C23—22no—
219C23×C23—22no—
220C23×C23—24no—
221C23×C23—22no—
222C23×C23—24no—
223C23×C23—22no—
224C23×C23—24no—
225C23×C23—24no—
226C23×C23—22no—
227C23×C23—24no—
228C23×C23—24no—
229C23×C23—24no—
230C23×C23—24no—
231C23×C23—24no—
232C23×C23—24no—
233C23×C23—24no—
234C23×C23—24no—
235C23×C23—24no—
236C23×C23—24no—
237C23×C23—24no—
238C23×C23—24no—
239C23×C23—24no—
240C23×C23—24no—
241C23×C23—24no—
242C23×C23—416no—
243C23×C23—432no—
244C23×C23—432no—
245C23×C23—416no—
246C23×C23—416no—
247C23×C23—416no—
248C23×C23—416no—
249C23×C23—432no—
250C23×C23—432no—
251C23×C23—416no—
252C23×C23—416no—
253C23×C23—42no—
254C23×C23—42no—
255C23×C23—42no—
256C23×C23—42no—
257C23×C23—42no—
258C23×C23—42no—
259C23×C23—42no—
260C23×C23—42no—
261C23×C23—42no—
262C23×C23—42no—
263C23×C23—42no—
264C23×C23—42no—
265C23×C23—41no—
266C23×C23—42no—
267C23×C23—42no—
268C23×C23—42no—
269C23×C23—42no—
270C23×C23—42no—
271C23×C23—41no—
272C23×C23—42no—
273C23×C23—41no—
274C23×C23—41no—
275C23×C23—42no—
276C23×C23—42no—
277C23×C23—42no—
278C23×C23—42no—
279C23×C23C22⋊Q818yes—
280C23×C23C22⋊Q814yes—
281C23×C23C22×D412yes—
282C23×C23C22×D411yescharacteristic
283C23×C23C22×Q811yescharacteristic
284C23×C23C2×#4111yescharacteristic
285C23×C23C2×#4112yes—
286C23×C23H(5,𝔽2)11yescharacteristic
287C23×C23H(5,𝔽2)11yescharacteristic
288C23×C23H(5,𝔽2)11yescharacteristic
289C23×C23H(5,𝔽2)12yes—
290C23×C23H(5,𝔽2)12yes—
291C23×C23H(5,𝔽2)11yescharacteristic
292C2×C4×C23—24no—
293C2×C4×C23—22no—
294C2×C4×C23—24no—
295C2×C4×C23—22no—
296C2×C4×C23—24no—
297C2×C4×C23—24no—
298C2×C4×C23—24no—
299C2×C4×C23—24no—
300C2×C4×C23—24no—
301C2×C4×C23—24no—
302C2×C4×C23—42no—
303C2×C4×C23—42no—
304C2×C4×C23—42no—
305C2×C4×C23—42no—
306C2×C4×C23—42no—
307C2×C4×C23—42no—
308C2×C4×C23—41no—
309C2×C4×C23—42no—
310C2×C4×C23—42no—
311C2×C4×C23—41no—
312C2×C4×C23—42no—
313C2×C4×C23—41no—
314C2×C4×C23—42no—
315C2×C4×C23—41no—
316C2×C4×C23—42no—
317C2×C4×C23—42no—
318C2×C4×C23—42no—
319C2×C4×C23—42no—
320C2×C4×C23—42no—
321C2×C4×C23—42no—
322C2×C4×C23—42no—
323C2×C4×C23—42no—
324C2×C4×C23—42no—
325C2×C4×C23—42no—
326C2×C4×C23—42no—
327C2×C4×C23—42no—
328C2×C4×C23—42no—
329C2×C4×C23—42no—
330C2×C4×C23—42no—
331C2×C4×C23—42no—
332C2×C4×C23—42no—
333C2×C4×C23—42no—
334C2×C4×C23—42no—
335C2×C4×C23—42no—
336C2×C4×C23—42no—
337C2×#399C2×C2311yescharacteristic, complemented
338C2×#396C2×C2312yescomplemented
339C2×#379C2×C2311yescharacteristic
340C2×#379C2×C2312yes—
341#1439C2×C2312yescomplemented
342#1439C2×C2312yescomplemented
343#1439C2×C2312yescomplemented
344#1439C2×C2312yescomplemented
345#1439C2×C2311yescharacteristic, complemented
346C22×C23—28no—
347C22×C23—24no—
348C22×C23—28no—
349C22×C23—28no—
350C22×C23—28no—
351C22×C23—464no—
352C22×C23—44no—
353C22×C23—42no—
354C22×C23—44no—
355C22×C23—44no—
356C22×C23—44no—
357C22×C23—44no—
358C22×C23—42no—
359C22×C23—42no—
360C22×C23—44no—
361C22×C23—44no—
362C22×C23—44no—
363C22×C23—44no—
364C22×C23—44no—
365C22×C23—44no—
366C22×C23—44no—
367C22×C23—42no—
368C22×C23—44no—
369C22×C23—42no—
370C22×C23—44no—
371C22×C23—42no—
372C22×C23—44no—
373C22×C23C2×C22⋊Q812yes—
374C22×C23C2×C22⋊Q811yescharacteristic
375C22×C23#53412yes—
376C22×C23#53411yescharacteristic
377C22×C23#53512yes—
378C22×C23#53511yescharacteristic
379C22×C23#53811yescharacteristic
380C22×C23#53812yes—
381C22×C23#53811yescharacteristic
382C22×C23#53812yes—
383C22×C23#54311yescharacteristic
384C22×C23#54312yes—
385C22×C23#54311yescharacteristic
386C22×C23D4211yescharacteristic
387C22×C23D4212yes—
388C22×C23#54612yes—
389C22×C23#54612yes—
390C22×C23#54612yes—
391C22×C23#55112yes—
392C22×C23#55111yescharacteristic
393C22×C23#56011yescharacteristic
394C22×C23#56011yescharacteristic
395C22×C23#56012yes—
396C4×C23—44no—
397C4×C23—42no—
398C4×C23—44no—
399C4×C23—42no—
400C4×C23—82no—
401C4×C23—82no—
402C4×C23—82no—
403C26C22×C2311yescharacteristic
404C22×C4⋊C4C22×C2311yescharacteristic, complemented
405C22×C4⋊C4C22×C2312yescomplemented
406C22×C4⋊C4C22×C2312yescomplemented
407C22×C4⋊C4C22×C2311yescharacteristic, complemented
408C22×C22⋊C4C22×C2312yes—
409C22×C22⋊C4C22×C2312yes—
410C22×C22⋊C4C22×C2312yes—
411C22×C22⋊C4C22×C2312yes—
412C22×C22⋊C4C22×C2312yes—
413C22×C22⋊C4C22×C2312yes—
414C22×C22⋊C4C22×C2312yes—
415C22×C22⋊C4C22×C2311yescharacteristic
416C22×C22⋊C4C22×C2312yes—
417C22×C22⋊C4C22×C2311yescharacteristic
418#399—24no—
419#396—28no—
420#379—28no—
421#379—24no—
422C2×#95C22×C2312yescomplemented
423C2×#95C22×C2311yescharacteristic, complemented
424C2×#95C22×C2312yescomplemented
425C2×#95C22×C2312yescomplemented
426C2×#95C22×C2311yescharacteristic, complemented
427C2×#95C22×C2312yescomplemented
428C2×C23—48no—
429C2×C23—44no—
430C2×C23#243711yescharacteristic
431C2×C23#243712yes—
432C2×C23#262612yes—
433C2×C23#262611yescharacteristic
434C2×C23#266811yescharacteristic
435C2×C23#266911yescharacteristic
436C2×C23#267812yes—
437C2×C23#268512yes—
438C2×C23#269711yescharacteristic
439C2×C23#273511yescharacteristic
440C2×C23#284211yescharacteristic
441C25—24no—
442C25—22no—
443C25—22no—
444C25—24no—
445C25—41no—
446C25—42no—
447C25—42no—
448C25—41no—
449C25—41no—
450C25—41no—
451C25Q8×C2314yes—
452C25C23×C2312yes—
453C25C23×C2311yescharacteristic
454C23×C4C23×C2312yes—
455C23×C4C23×C2312yes—
456C23×C4C23×C2312yes—
457C23×C4C23×C2311yescharacteristic
458C23×C4C23×C2312yes—
459C23×C4C23×C2312yes—
460C23×C4C23×C2311yescharacteristic
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—41no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—41no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4D4×C2318yes—
501C2×C22⋊C4D4×C2314yes—
502#95—24no—
503#95—22no—
504#95—42no—
505#95—41no—
506#95—42no—
507#95—42no—
508C23#1629811yescharacteristic, direct product factor, Sylow
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—21no—
519C24—22no—
520C24—22no—
521C24—21no—
522C24—22no—
523C24—21no—
524C24—21no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—216no—
530C24—28no—
531C24—44no—
532C24—48no—
533C24—44no—
534C24—48no—
535C24—44no—
536C24—44no—
537C24—48no—
538C24—48no—
539C24—48no—
540C24—48no—
541C24—48no—
542C24—44no—
543C24—48no—
544C24—44no—
545C24—44no—
546C24—48no—
547C24—44no—
548C24—48no—
549C24—44no—
550C24—44no—
551C24—48no—
552C24C2×D4×C2314yes—
553C24C2×D4×C2312yes—
554C24C2×Q8×C2314yes—
555C24C2×Q8×C2312yes—
556C24#41×C2312yes—
557C24#41×C2314yes—
558C24C24×C2311yescharacteristic
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4C2×D4×C2312yes—
601C22×C4C2×D4×C2314yes—
602C22×C4C2×D4×C2314yes—
603C22×C4C2×D4×C2312yes—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—44no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—432no—
649C23—416no—
650C23—432no—
651C23—416no—
652C23—416no—
653C23—416no—
654C23—432no—
655C23—432no—
656C23—416no—
657C23—416no—
658C23—416no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C23×C22⋊Q818yes—
686C23C23×C22⋊Q814yes—
687C23C22×D4×C2312yes—
688C23C22×D4×C2311yescharacteristic
689C23C22×Q8×C2311yescharacteristic
690C23C2×#41×C2311yescharacteristic
691C23C2×#41×C2312yes—
692C23C23×H(5,𝔽2)11yescharacteristic
693C23C23×H(5,𝔽2)12yes—
694C23C23×H(5,𝔽2)12yes—
695C23C23×H(5,𝔽2)11yescharacteristic
696C23C23×H(5,𝔽2)11yescharacteristic
697C23C23×H(5,𝔽2)11yescharacteristic
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C22—28no—
744C22—28no—
745C22—28no—
746C22—28no—
747C22—24no—
748C22—464no—
749C22—44no—
750C22—42no—
751C22—42no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—42no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22C2×C23×C22⋊Q811yescharacteristic
771C22C2×C23×C22⋊Q812yes—
772C22C23×#53412yes—
773C22C23×#53411yescharacteristic
774C22C23×#53512yes—
775C22C23×#53511yescharacteristic
776C22C23×#53811yescharacteristic
777C22C23×#53812yes—
778C22C23×#53811yescharacteristic
779C22C23×#53812yes—
780C22C23×#54311yescharacteristic
781C22C23×#54312yes—
782C22C23×#54311yescharacteristic
783C22D42×C2311yescharacteristic
784C22D42×C2312yes—
785C22C23×#54612yes—
786C22C23×#54612yes—
787C22C23×#54612yes—
788C22C23×#55112yes—
789C22C23×#55111yescharacteristic
790C22C23×#56011yescharacteristic
791C22C23×#56011yescharacteristic
792C22C23×#56012yes—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—42no—
797C4—82no—
798C4—82no—
799C4—82no—
800C2—48no—
801C2—44no—
802C2C23×#243712yes—
803C2C23×#243711yescharacteristic
804C2C23×#262612yes—
805C2C23×#262611yescharacteristic
806C2C23×#266811yescharacteristic
807C2C23×#266911yescharacteristic
808C2C23×#267812yes—
809C2C23×#268512yes—
810C2C23×#269711yescharacteristic
811C2C23×#273511yescharacteristic
812C2C23×#284211yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutator, Frattini, cosocleC24C24×C23
prime radicalC26×C23C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C23×#399C2semidirect
2. C2×C23×#396C2semidirect
5. C23×#1439C2semidirect
6. C23×#1439C2semidirect
7. C23×#1439C2semidirect
8. C23×#1439C2semidirect
9. C23×#1439C2semidirect
11. C22×C4⋊C4×C23C22semidirect
12. C22×C4⋊C4×C23C22semidirect
13. C22×C4⋊C4×C23C22semidirect
14. C22×C4⋊C4×C23C22semidirect
29. C2×C23×#95C22semidirect
30. C2×C23×#95C22semidirect
31. C2×C23×#95C22semidirect
32. C2×C23×#95C22semidirect
33. C2×C23×#95C22semidirect
34. C2×C23×#95C22semidirect
211. #16298C23direct (N × H)
337. C2×#399C2×C23semidirect
338. C2×#396C2×C23semidirect
341. #1439C2×C23semidirect
342. #1439C2×C23semidirect
343. #1439C2×C23semidirect
344. #1439C2×C23semidirect
345. #1439C2×C23semidirect
404. C22×C4⋊C4C22×C23semidirect
405. C22×C4⋊C4C22×C23semidirect
406. C22×C4⋊C4C22×C23semidirect
407. C22×C4⋊C4C22×C23semidirect
422. C2×#95C22×C23semidirect
423. C2×#95C22×C23semidirect
424. C2×#95C22×C23semidirect
425. C2×#95C22×C23semidirect
426. C2×#95C22×C23semidirect
427. C2×#95C22×C23semidirect
508. C23#16298direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3992
C2×C23×#3962
C2×C23×#3792
C23×#14392
#1629823