Finite Group Databasebeta

← C23×#24388 #19172014

Subgroups — C23×#24388 #19172014

Order 5888.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#525C211yesmaximal, characteristic, complemented
2C2×C23×#469C211yesmaximal, characteristic, complemented
3C2×C23×#468C211yesmaximal, characteristic, complemented
4C2×C23×#449C211yesmaximal, characteristic, complemented
5C2×C23×#407C211yesmaximal, characteristic, complemented
6C23×#2847C211yesmaximal, characteristic, complemented
7C23×#2035C211yesmaximal, characteristic, complemented
8C23×#2033C211yesmaximal, characteristic, complemented
9C23×#2000C211yesmaximal, characteristic, complemented
10C23×#1999C211yesmaximal, characteristic, complemented
11C23×#1895C211yesmaximal, characteristic, complemented
12C23×#1894C211yesmaximal, characteristic, complemented
13C23×#1875C211yesmaximal, characteristic, complemented
14C23×#1854C211yesmaximal, characteristic, complemented
15C23×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C22×SD16×C23C2211yescharacteristic, complemented
19C22×D8×C23C2211yescharacteristic, complemented
20C22×M16×C23C2211yescharacteristic
21C22×M16×C23C2211yescharacteristic
22C23×#525—24no—
23C23×#525—24no—
24C2×C23×#123—21no—
25C2×C23×C22⋊Q8C2211yescharacteristic
26C2×C23×C22⋊Q8C2211yescharacteristic
27C2×C23×#121C2211yescharacteristic
28C2×C23×#121C2211yescharacteristic
29C2×C23×#121C2211yescharacteristic
30C2×C23×#121C2211yescharacteristic
31C2×C23×#121C2211yescharacteristic
32C2×C23×#120—21no—
33C2×C23×#120—21no—
34C2×C4×D4×C23—21no—
35C2×C4×D4×C23—21no—
36C2×C23×#117C2211yescharacteristic
37C23×#469—24no—
38C23×#468—24no—
39C23×#449—24no—
40C2×C23×#107C2211yescharacteristic, complemented
41C2×C23×#106C2211yescharacteristic, complemented
42C2×C23×#103C2211yescharacteristic, complemented
43C2×C23×#103C2211yescharacteristic, complemented
44C2×C23×#103C2211yescharacteristic, complemented
45C2×C23×#102C2211yescharacteristic, complemented
46C2×C23×#102C2211yescharacteristic, complemented
47C2×C23×#102C2211yescharacteristic, complemented
48C2×C23×#102C2211yescharacteristic, complemented
49C2×C23×#102C2211yescharacteristic, complemented
50C23×#407—24no—
51C2×C23×C22⋊C8C2211yescharacteristic
52C2×C23×C22⋊C8C2211yescharacteristic
53C2×C23×C22⋊C8C2211yescharacteristic
54C2×C23×C22⋊C8C2211yescharacteristic
55C23×#386—21no—
56C23×#386—21no—
57C23×#386—21no—
58C23×#380C2211yescharacteristic
59C23×#380C2211yescharacteristic
60C23×#380C2211yescharacteristic
61C23×#340C2211yescharacteristic, complemented
62C23×#340C2211yescharacteristic, complemented
63C23×#340C2211yescharacteristic, complemented
64C23×#340C2211yescharacteristic, complemented
65C25×C23D411yescharacteristic
66C2×#41×C23—22no—
67C2×#41×C23—22no—
68C2×#41×C23—22no—
69C2×#41×C23—22no—
70C2×#41×C23—41no—
71C2×#41×C23—41no—
72C22×Q8×C23C2311yescharacteristic
73C22×D4×C23—21no—
74C22×D4×C23—21no—
75C22×D4×C23—21no—
76C22×D4×C23—21no—
77C22×D4×C23—21no—
78C22×D4×C23—21no—
79C22×D4×C23C2311yescharacteristic
80C22×D4×C23C2311yescharacteristic
81C23×C4×C23—22no—
82C23×C4×C23—22no—
83C23×C4×C23—22no—
84C23×C4×C23—21no—
85C23×C4×C23—22no—
86C23×C4×C23—41no—
87C23×C4×C23—41no—
88C23×C4×C23D411yescharacteristic
89C23×C4×C23D411yescharacteristic
90C23×C4×C23D411yescharacteristic
91C23×C4×C23C2311yescharacteristic
92C23×C4×C23C2311yescharacteristic
93C23×C4×C23C2311yescharacteristic
94C2×SD16×C23—22no—
95C2×SD16×C23—22no—
96C2×SD16×C23—41no—
97C2×D8×C23—22no—
98C2×D8×C23—22no—
99C2×D8×C23—41no—
100C2×M16×C23—22no—
101C2×M16×C23—22no—
102C2×M16×C23—22no—
103C2×M16×C23—22no—
104C2×M16×C23—41no—
105C2×M16×C23—41no—
106C22×C8×C23C2311yescharacteristic
107C22×C8×C23C2311yescharacteristic
108C22×C8×C23C2311yescharacteristic
109C22×C8×C23C2311yescharacteristic
110C23×#123—28no—
111C23×C22⋊Q8—22no—
112C23×C22⋊Q8—22no—
113C23×C22⋊Q8—22no—
114C23×C22⋊Q8D414yescomplemented
115C23×#121—22no—
116C23×#121—22no—
117C23×#121—22no—
118C23×#121—22no—
119C23×#121—22no—
120C23×#121—22no—
121C23×#121—22no—
122C23×#121—41no—
123C23×#121—41no—
124C23×#121D414yescomplemented
125C23×#120—28no—
126C23×#120—44no—
127C4×D4×C23—28no—
128C4×D4×C23—28no—
129C23×#117—22no—
130C23×#117—22no—
131C2×C4⋊C4×C23—21no—
132C2×C4⋊C4×C23—21no—
133C2×C4⋊C4×C23C2311yescharacteristic
134C2×C4⋊C4×C23C2311yescharacteristic
135C2×C4⋊C4×C23C2311yescharacteristic
136C2×C4⋊C4×C23C2311yescharacteristic
137C2×C4⋊C4×C23C2311yescharacteristic
138C2×C22⋊C4×C23—21no—
139C2×C22⋊C4×C23—21no—
140C2×C22⋊C4×C23—21no—
141C2×C22⋊C4×C23—21no—
142C2×C22⋊C4×C23—21no—
143C2×C22⋊C4×C23—21no—
144C2×C22⋊C4×C23—21no—
145C2×C22⋊C4×C23—21no—
146C2×C22⋊C4×C23—21no—
147C2×C22⋊C4×C23—21no—
148C2×C22⋊C4×C23—21no—
149C2×C42×C23—21no—
150C23×#107—22no—
151C23×#106—22no—
152C23×#103—22no—
153C23×#103—22no—
154C23×#103—41no—
155C23×#102—22no—
156C23×#102—22no—
157C23×#102—22no—
158C23×#102—22no—
159C23×#102—41no—
160C23×C22⋊C8—22no—
161C23×C22⋊C8—22no—
162C23×C22⋊C8—22no—
163C23×C22⋊C8D414yescomplemented
164C23×#95—21no—
165C23×#95—21no—
166C23×#95—21no—
167C24×C23—22no—
168C24×C23—22no—
169C24×C23—22no—
170C24×C23—21no—
171C24×C23—21no—
172C24×C23—41no—
173C24×C23—41no—
174C24×C23—41no—
175C24×C23—41no—
176C24×C23C2×D411yescharacteristic
177C24×C23C2×D411yescharacteristic
178C24×C23C2×D411yescharacteristic
179#41×C23—44no—
180#41×C23—44no—
181#41×C23—44no—
182#41×C23—44no—
183C2×Q8×C23—21no—
184C2×Q8×C23—21no—
185C2×Q8×C23—21no—
186C2×Q8×C23—21no—
187C2×Q8×C23—21no—
188C2×Q8×C23C2×D412yes—
189C2×D4×C23—24no—
190C2×D4×C23—24no—
191C2×D4×C23—24no—
192C2×D4×C23—21no—
193C2×D4×C23—21no—
194C2×D4×C23—21no—
195C2×D4×C23—21no—
196C2×D4×C23—21no—
197C2×D4×C23—21no—
198C2×D4×C23—21no—
199C2×D4×C23—21no—
200C2×D4×C23—21no—
201C2×D4×C23—21no—
202C2×D4×C23—21no—
203C2×D4×C23—42no—
204C2×D4×C23—42no—
205C2×D4×C23—42no—
206C2×D4×C23—42no—
207C2×D4×C23—42no—
208C2×D4×C23—42no—
209C2×D4×C23—42no—
210C2×D4×C23—42no—
211C2×D4×C23—42no—
212C2×D4×C23—42no—
213C2×D4×C23—42no—
214C2×D4×C23—42no—
215C2×D4×C23—42no—
216C2×D4×C23—42no—
217C2×D4×C23—42no—
218C2×D4×C23C2×D412yes—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—24no—
228C22×C4×C23—22no—
229C22×C4×C23—22no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—22no—
234C22×C4×C23—22no—
235C22×C4×C23—22no—
236C22×C4×C23—22no—
237C22×C4×C23—21no—
238C22×C4×C23—21no—
239C22×C4×C23—21no—
240C22×C4×C23—21no—
241C22×C4×C23—21no—
242C22×C4×C23—21no—
243C22×C4×C23—21no—
244C22×C4×C23—21no—
245C22×C4×C23—21no—
246C22×C4×C23—41no—
247C22×C4×C23—41no—
248C22×C4×C23—41no—
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×C23C2×D411yescharacteristic
256C22×C4×C23C2×D411yescharacteristic
257C22×C4×C23C2×D412yes—
258C22×C4×C23C2×D412yes—
259C22×C4×C23C2×D411yescharacteristic
260C22×C4×C23C2×D412yes—
261C22×C4×C23#4112yes—
262C22×C4×C23C2411yescharacteristic
263SD16×C23—44no—
264D8×C23—44no—
265M16×C23—44no—
266M16×C23—44no—
267C2×C8×C23—21no—
268C2×C8×C23—21no—
269C2×C8×C23—21no—
270C2×C8×C23—21no—
271C2×C8×C23—21no—
272C2×C8×C23—21no—
273C2×C8×C23—21no—
274C2×C8×C23—21no—
275C2×C8×C23—21no—
276C2×C8×C23—21no—
277C2×C8×C23C2×D412yes—
278C2×C8×C23C2×D412yes—
279C4⋊C4×C23—24no—
280C4⋊C4×C23—24no—
281C4⋊C4×C23—21no—
282C4⋊C4×C23—21no—
283C4⋊C4×C23—21no—
284C4⋊C4×C23—21no—
285C4⋊C4×C23—21no—
286C4⋊C4×C23—21no—
287C4⋊C4×C23—21no—
288C4⋊C4×C23—21no—
289C4⋊C4×C23C2×D412yes—
290C4⋊C4×C23C2×D412yes—
291C22⋊C4×C23—24no—
292C22⋊C4×C23—24no—
293C22⋊C4×C23—24no—
294C22⋊C4×C23—24no—
295C22⋊C4×C23—24no—
296C22⋊C4×C23—42no—
297C22⋊C4×C23—42no—
298C22⋊C4×C23—42no—
299C22⋊C4×C23—42no—
300C22⋊C4×C23—42no—
301C22⋊C4×C23—42no—
302C42×C23—24no—
303#24388C2311yesmaximal, characteristic, direct product factor, Sylow
304C23×C23—21no—
305C23×C23—21no—
306C23×C23—21no—
307C23×C23—21no—
308C23×C23—21no—
309C23×C23—21no—
310C23×C23—21no—
311C23×C23—21no—
312C23×C23—21no—
313C23×C23—21no—
314C23×C23—21no—
315C23×C23—21no—
316C23×C23—21no—
317C23×C23—21no—
318C23×C23—21no—
319C23×C23—21no—
320C23×C23—21no—
321C23×C23—21no—
322C23×C23—22no—
323C23×C23—44no—
324C23×C23—44no—
325C23×C23—44no—
326C23×C23—44no—
327C23×C23—44no—
328C23×C23—44no—
329C23×C23—44no—
330C23×C23—41no—
331C23×C23—41no—
332C23×C23—41no—
333C23×C23—41no—
334C23×C23—41no—
335C23×C23—41no—
336C23×C23—41no—
337C23×C23—41no—
338C23×C23—41no—
339C23×C23—41no—
340C23×C23—41no—
341C23×C23—41no—
342C23×C23—41no—
343C23×C23#12012yes—
344C23×C23#12112yes—
345C23×C23AGL(1,ℤ/8)12yes—
346C23×C23C22×D411yescharacteristic
347Q8×C23—22no—
348Q8×C23—22no—
349Q8×C23—41no—
350Q8×C23—41no—
351D4×C23—22no—
352D4×C23—22no—
353D4×C23—48no—
354D4×C23—48no—
355D4×C23—48no—
356D4×C23—41no—
357D4×C23—41no—
358D4×C23—41no—
359D4×C23—41no—
360D4×C23—41no—
361D4×C23—41no—
362D4×C23—84no—
363D4×C23—84no—
364D4×C23—84no—
365C2×C4×C23—21no—
366C2×C4×C23—21no—
367C2×C4×C23—21no—
368C2×C4×C23—21no—
369C2×C4×C23—22no—
370C2×C4×C23—22no—
371C2×C4×C23—22no—
372C2×C4×C23—22no—
373C2×C4×C23—22no—
374C2×C4×C23—22no—
375C2×C4×C23—22no—
376C2×C4×C23—22no—
377C2×C4×C23—22no—
378C2×C4×C23—22no—
379C2×C4×C23—21no—
380C2×C4×C23—22no—
381C2×C4×C23—21no—
382C2×C4×C23—21no—
383C2×C4×C23—44no—
384C2×C4×C23—44no—
385C2×C4×C23—44no—
386C2×C4×C23—48no—
387C2×C4×C23—41no—
388C2×C4×C23—41no—
389C2×C4×C23—41no—
390C2×C4×C23—41no—
391C2×C4×C23—41no—
392C2×C4×C23—41no—
393C2×C4×C23—41no—
394C2×C4×C23—41no—
395C2×C4×C23—41no—
396C2×C4×C23—41no—
397C2×C4×C23—41no—
398C2×C4×C23—41no—
399C2×C4×C23—41no—
400C2×C4×C23—41no—
401C2×C4×C23—41no—
402C2×C4×C23—41no—
403C2×C4×C23—41no—
404C2×C4×C23—41no—
405C2×C4×C23—41no—
406C2×C4×C23#12012yes—
407C2×C4×C23#12112yes—
408C2×C4×C23C22×D411yescharacteristic
409C2×C4×C23C22×D411yescharacteristic
410C2×C4×C23C22×D411yescharacteristic
411C2×C4×C23C2×#4111yescharacteristic
412C2×C4×C23H(5,𝔽2)11yescharacteristic
413C2×C4×C23H(5,𝔽2)11yescharacteristic
414C8×C23—22no—
415C8×C23—22no—
416C8×C23—41no—
417C8×C23—41no—
418C2×#525C2×C2311yescharacteristic, complemented
419C2×#469C2×C2311yescharacteristic, complemented
420C2×#468C2×C2311yescharacteristic, complemented
421C2×#449C2×C2311yescharacteristic, complemented
422C2×#407C2×C2311yescharacteristic, complemented
423#2847C2×C2311yescharacteristic, complemented
424#2035C2×C2311yescharacteristic, complemented
425#2033C2×C2311yescharacteristic, complemented
426#2000C2×C2311yescharacteristic, complemented
427#1999C2×C2311yescharacteristic, complemented
428#1895C2×C2311yescharacteristic, complemented
429#1894C2×C2311yescharacteristic, complemented
430#1875C2×C2311yescharacteristic, complemented
431#1854C2×C2311yescharacteristic, complemented
432#1788C2×C2311yescharacteristic, complemented
433C22×C23—22no—
434C22×C23—22no—
435C22×C23—22no—
436C22×C23—22no—
437C22×C23—22no—
438C22×C23—22no—
439C22×C23—22no—
440C22×C23—22no—
441C22×C23—22no—
442C22×C23—416no—
443C22×C23—41no—
444C22×C23—41no—
445C22×C23—41no—
446C22×C23—41no—
447C22×C23—41no—
448C22×C23—41no—
449C22×C23—41no—
450C22×C23—41no—
451C22×C23—41no—
452C22×C23—41no—
453C22×C23—41no—
454C22×C23—41no—
455C22×C23—42no—
456C22×C23—42no—
457C22×C23—42no—
458C22×C23—81no—
459C22×C23—81no—
460C22×C23—81no—
461C22×C23—81no—
462C22×C23—81no—
463C22×C23—81no—
464C22×C23—81no—
465C22×C23—81no—
466C22×C23—81no—
467C22×C23—81no—
468C22×C23—81no—
469C22×C23C2×#12011yescharacteristic
470C22×C23C2×#12111yescharacteristic
471C22×C23#53411yescharacteristic
472C22×C23C2×AGL(1,ℤ/8)11yescharacteristic
473C22×C23#57511yescharacteristic
474C22×C23#57511yescharacteristic
475C22×C23#57511yescharacteristic
476C4×C23—22no—
477C4×C23—22no—
478C4×C23—41no—
479C4×C23—42no—
480C4×C23—42no—
481C4×C23—42no—
482C4×C23—81no—
483C4×C23—81no—
484C4×C23—81no—
485C4×C23D4211yescharacteristic
486C4×C23D4211yescharacteristic
487C4×C23#54611yescharacteristic
488C4×C23#54611yescharacteristic
489C22×#41C22×C2311yescharacteristic
490C24×C4C22×C2311yescharacteristic
491C22×SD16C22×C2311yescharacteristic, complemented
492C22×D8C22×C2311yescharacteristic, complemented
493C22×M16C22×C2311yescharacteristic
494C22×M16C22×C2311yescharacteristic
495#525—24no—
496#525—24no—
497C2×#123—21no—
498C2×C22⋊Q8C22×C2311yescharacteristic
499C2×C22⋊Q8C22×C2311yescharacteristic
500C2×#121C22×C2311yescharacteristic
501C2×#121C22×C2311yescharacteristic
502C2×#121C22×C2311yescharacteristic
503C2×#121C22×C2311yescharacteristic
504C2×#121C22×C2311yescharacteristic
505C2×#120—21no—
506C2×#120—21no—
507C2×C4×D4—21no—
508C2×C4×D4—21no—
509C2×#117C22×C2311yescharacteristic
510#469—24no—
511#468—24no—
512#449—24no—
513C2×#107C22×C2311yescharacteristic, complemented
514C2×#106C22×C2311yescharacteristic, complemented
515C2×#103C22×C2311yescharacteristic, complemented
516C2×#103C22×C2311yescharacteristic, complemented
517C2×#103C22×C2311yescharacteristic, complemented
518C2×#102C22×C2311yescharacteristic, complemented
519C2×#102C22×C2311yescharacteristic, complemented
520C2×#102C22×C2311yescharacteristic, complemented
521C2×#102C22×C2311yescharacteristic, complemented
522C2×#102C22×C2311yescharacteristic, complemented
523#407—24no—
524C2×C22⋊C8C22×C2311yescharacteristic
525C2×C22⋊C8C22×C2311yescharacteristic
526C2×C22⋊C8C22×C2311yescharacteristic
527C2×C22⋊C8C22×C2311yescharacteristic
528#386—21no—
529#386—21no—
530#386—21no—
531#380C22×C2311yescharacteristic
532#380C22×C2311yescharacteristic
533#380C22×C2311yescharacteristic
534#340C22×C2311yescharacteristic, complemented
535#340C22×C2311yescharacteristic, complemented
536#340C22×C2311yescharacteristic, complemented
537#340C22×C2311yescharacteristic, complemented
538C2×C23—42no—
539C2×C23—42no—
540C2×C23—42no—
541C2×C23—82no—
542C2×C23—161no—
543C2×C23#241011yescharacteristic
544C2×C23#300511yescharacteristic
545C2×C23#300611yescharacteristic
546C2×C23#305411yescharacteristic
547C2×C23#305511yescharacteristic
548C2×C23#319411yescharacteristic
549C2×C23#319711yescharacteristic
550C25D4×C2311yescharacteristic
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—41no—
556C2×#41—41no—
557C22×Q8C23×C2311yescharacteristic
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4C23×C2311yescharacteristic
565C22×D4C23×C2311yescharacteristic
566C23×C4—21no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4D4×C2311yescharacteristic
574C23×C4D4×C2311yescharacteristic
575C23×C4D4×C2311yescharacteristic
576C23×C4C23×C2311yescharacteristic
577C23×C4C23×C2311yescharacteristic
578C23×C4C23×C2311yescharacteristic
579C2×SD16—22no—
580C2×SD16—22no—
581C2×SD16—41no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×M16—22no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—22no—
589C2×M16—41no—
590C2×M16—41no—
591C22×C8C23×C2311yescharacteristic
592C22×C8C23×C2311yescharacteristic
593C22×C8C23×C2311yescharacteristic
594C22×C8C23×C2311yescharacteristic
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8D4×C2314yescomplemented
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—41no—
608#121—41no—
609#121D4×C2314yescomplemented
610#120—28no—
611#120—44no—
612C4×D4—28no—
613C4×D4—28no—
614#117—22no—
615#117—22no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4C23×C2311yescharacteristic
619C2×C4⋊C4C23×C2311yescharacteristic
620C2×C4⋊C4C23×C2311yescharacteristic
621C2×C4⋊C4C23×C2311yescharacteristic
622C2×C4⋊C4C23×C2311yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C42—21no—
635#107—22no—
636#106—22no—
637#103—22no—
638#103—22no—
639#103—41no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—41no—
645C22⋊C8—22no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8D4×C2314yescomplemented
649#95—21no—
650#95—21no—
651#95—21no—
652C23#2438811yescharacteristic, direct product factor, Sylow
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24—41no—
662C24C2×D4×C2311yescharacteristic
663C24C2×D4×C2311yescharacteristic
664C24C2×D4×C2311yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C2312yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C2312yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C2311yescharacteristic
742C22×C4C2×D4×C2311yescharacteristic
743C22×C4C2×D4×C2312yes—
744C22×C4C2×D4×C2312yes—
745C22×C4C2×D4×C2311yescharacteristic
746C22×C4C2×D4×C2312yes—
747C22×C4#41×C2312yes—
748C22×C4C24×C2311yescharacteristic
749SD16—44no—
750D8—44no—
751M16—44no—
752M16—44no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8C2×D4×C2312yes—
764C2×C8C2×D4×C2312yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C2312yes—
776C4⋊C4C2×D4×C2312yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—22no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23C23×#12012yes—
829C23C23×#12112yes—
830C23C23×AGL(1,ℤ/8)12yes—
831C23C22×D4×C2311yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4C23×#12012yes—
892C2×C4C23×#12112yes—
893C2×C4C22×D4×C2311yescharacteristic
894C2×C4C22×D4×C2311yescharacteristic
895C2×C4C22×D4×C2311yescharacteristic
896C2×C4C2×#41×C2311yescharacteristic
897C2×C4C23×H(5,𝔽2)11yescharacteristic
898C2×C4C23×H(5,𝔽2)11yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—416no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22C2×C23×#12011yescharacteristic
940C22C2×C23×#12111yescharacteristic
941C22C23×#53411yescharacteristic
942C22C2×C23×AGL(1,ℤ/8)11yescharacteristic
943C22C23×#57511yescharacteristic
944C22C23×#57511yescharacteristic
945C22C23×#57511yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C2311yescharacteristic
956C4D42×C2311yescharacteristic
957C4C23×#54611yescharacteristic
958C4C23×#54611yescharacteristic
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C23×#241011yescharacteristic
965C2C23×#300511yescharacteristic
966C2C23×#300611yescharacteristic
967C2C23×#305411yescharacteristic
968C2C23×#305511yescharacteristic
969C2C23×#319411yescharacteristic
970C2C23×#319711yescharacteristic
subgroupG/H
center, socleC23×C23C22×D4
commutator, Frattini, cosocleC22×C4C24×C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C24×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C23×#525C2semidirect
2. C2×C23×#469C2semidirect
3. C2×C23×#468C2semidirect
4. C2×C23×#449C2semidirect
5. C2×C23×#407C2semidirect
6. C23×#2847C2semidirect
7. C23×#2035C2semidirect
8. C23×#2033C2semidirect
9. C23×#2000C2semidirect
10. C23×#1999C2semidirect
11. C23×#1895C2semidirect
12. C23×#1894C2semidirect
13. C23×#1875C2semidirect
14. C23×#1854C2semidirect
15. C23×#1788C2semidirect
18. C22×SD16×C23C22semidirect
19. C22×D8×C23C22semidirect
40. C2×C23×#107C22semidirect
41. C2×C23×#106C22semidirect
42. C2×C23×#103C22semidirect
43. C2×C23×#103C22semidirect
44. C2×C23×#103C22semidirect
45. C2×C23×#102C22semidirect
46. C2×C23×#102C22semidirect
47. C2×C23×#102C22semidirect
48. C2×C23×#102C22semidirect
49. C2×C23×#102C22semidirect
61. C23×#340C22semidirect
62. C23×#340C22semidirect
63. C23×#340C22semidirect
64. C23×#340C22semidirect
114. C23×C22⋊Q8D4semidirect
124. C23×#121D4semidirect
163. C23×C22⋊C8D4semidirect
303. #24388C23direct (N × H)
418. C2×#525C2×C23semidirect
419. C2×#469C2×C23semidirect
420. C2×#468C2×C23semidirect
421. C2×#449C2×C23semidirect
422. C2×#407C2×C23semidirect
423. #2847C2×C23semidirect
424. #2035C2×C23semidirect
425. #2033C2×C23semidirect
426. #2000C2×C23semidirect
427. #1999C2×C23semidirect
428. #1895C2×C23semidirect
429. #1894C2×C23semidirect
430. #1875C2×C23semidirect
431. #1854C2×C23semidirect
432. #1788C2×C23semidirect
491. C22×SD16C22×C23semidirect
492. C22×D8C22×C23semidirect
513. C2×#107C22×C23semidirect
514. C2×#106C22×C23semidirect
515. C2×#103C22×C23semidirect
516. C2×#103C22×C23semidirect
517. C2×#103C22×C23semidirect
518. C2×#102C22×C23semidirect
519. C2×#102C22×C23semidirect
520. C2×#102C22×C23semidirect
521. C2×#102C22×C23semidirect
522. C2×#102C22×C23semidirect
534. #340C22×C23semidirect
535. #340C22×C23semidirect
536. #340C22×C23semidirect
537. #340C22×C23semidirect
599. C22⋊Q8D4×C23semidirect
609. #121D4×C23semidirect
648. C22⋊C8D4×C23semidirect
652. C23#24388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#5252
C2×C23×#4692
C2×C23×#4682
C2×C23×#4492
C2×C23×#4072
C23×#28472
C23×#20352
C23×#20332
C23×#20002
C23×#19992
C23×#18952
C23×#18942
C23×#18752
C23×#18542
C23×#17882
#2438823