Finite Group Databasebeta

← C23×#26741 #19174367

Subgroups — C23×#26741 #19174367

Order 5888.

820 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#2491C211yesmaximal, characteristic
2C23×#2360C211yesmaximal, characteristic, complemented
3C23×#2055C211yesmaximal, characteristic, complemented
4C23×#2035C211yesmaximal, characteristic, complemented
5C23×#2024C211yesmaximal, characteristic, complemented
6C23×#2000C211yesmaximal, characteristic
7C23×#1987C211yesmaximal, characteristic, complemented
8C23×#1936C211yesmaximal, characteristic, complemented
9C23×#1926C211yesmaximal, characteristic, complemented
10C23×#1924C211yesmaximal, characteristic, complemented
11C23×#1919C211yesmaximal, characteristic, complemented
12C23×#1880C211yesmaximal, characteristic, complemented
13C23×#1874C211yesmaximal, characteristic
14C23×#1823C211yesmaximal, characteristic, complemented
15C23×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C23C2211yescharacteristic
17C2×C23×C4⋊Q8C2211yescharacteristic
18C2×C23×#124—21no—
19C2×C23×C22⋊Q8C2211yescharacteristic
20C2×C23×#121C2211yescharacteristic
21C2×C4×Q8×C23C2211yescharacteristic
22C22×C4⋊C4×C23C2211yescharacteristic
23C2×C23×#106C2211yescharacteristic
24C2×C23×C4⋊C8C2211yescharacteristic
25C2×C23×#103C2211yescharacteristic
26C2×C23×#103C2211yescharacteristic
27C2×C23×#103C2211yescharacteristic
28C2×C23×#102C2211yescharacteristic
29C2×C23×#102C2211yescharacteristic
30C2×C23×#102C2211yescharacteristic
31C2×C23×C22⋊C8C2211yescharacteristic
32C2×C23×C22⋊C8C2211yescharacteristic
33C2×C23×#97C2211yescharacteristic
34C23×#394—21no—
35C23×#393—21no—
36C23×#391C2211yescharacteristic
37C23×#390C2211yescharacteristic
38C23×#390C2211yescharacteristic
39C23×#389—21no—
40C23×#389C2211yescharacteristic
41C23×#388—21no—
42C23×#387—21no—
43C23×#385—21no—
44C23×#380C2211yescharacteristic
45C4×C4⋊C4×C23C2211yescharacteristic
46C4×C4⋊C4×C23C2211yescharacteristic
47C4×C22⋊C4×C23—21no—
48C4×C22⋊C4×C23C2211yescharacteristic
49C23×#340C2211yescharacteristic
50C23×#340C2211yescharacteristic
51C23×#340C2211yescharacteristic
52C23×#340C2211yescharacteristic
53C23×#340C2211yescharacteristic
54C23×#340C2211yescharacteristic
55C23×#340C2211yescharacteristic
56C23×#340C2211yescharacteristic
57C23×#336C2211yescharacteristic
58C23×#336C2211yescharacteristic
59C22×Q8×C23—21no—
60C22×Q8×C23C2311yescharacteristic
61C22×D4×C23—21no—
62C22×D4×C23C2311yescharacteristic
63C23×C4×C23—21no—
64C23×C4×C23C2311yescharacteristic
65C2×SD16×C23—22no—
66C2×SD16×C23—41no—
67C2×SD16×C23—41no—
68C22×C8×C23C2311yescharacteristic
69C22×C8×C23C2311yescharacteristic
70C22×C8×C23C2311yescharacteristic
71C22×C8×C23C2311yescharacteristic
72C23×C4⋊Q8—22no—
73C23×C4⋊Q8—41no—
74C23×#124—44no—
75C23×C22⋊Q8—22no—
76C23×C22⋊Q8—22no—
77C23×#121—22no—
78C23×#121—41no—
79C4×Q8×C23—22no—
80C4×Q8×C23—41no—
81C2×C4⋊C4×C23—21no—
82C2×C4⋊C4×C23—22no—
83C2×C4⋊C4×C23—21no—
84C2×C4⋊C4×C23—21no—
85C2×C4⋊C4×C23—21no—
86C2×C4⋊C4×C23—21no—
87C2×C4⋊C4×C23—41no—
88C2×C4⋊C4×C23C2311yescharacteristic
89C2×C4⋊C4×C23C2311yescharacteristic
90C2×C4⋊C4×C23C2311yescharacteristic
91C2×C4⋊C4×C23C2311yescharacteristic
92C2×C4⋊C4×C23C2311yescharacteristic
93C2×C4⋊C4×C23C2311yescharacteristic
94C2×C22⋊C4×C23—21no—
95C2×C22⋊C4×C23—21no—
96C2×C22⋊C4×C23—21no—
97C2×C22⋊C4×C23—21no—
98C2×C22⋊C4×C23—21no—
99C2×C22⋊C4×C23—21no—
100C2×C22⋊C4×C23—21no—
101C2×C22⋊C4×C23D411yescharacteristic
102C2×C22⋊C4×C23D411yescharacteristic
103C2×C42×C23—21no—
104C2×C42×C23—21no—
105C2×C42×C23—21no—
106C2×C42×C23C2311yescharacteristic
107C2×C42×C23C2311yescharacteristic
108C23×#106—22no—
109C23×C4⋊C8—41no—
110C23×#103—22no—
111C23×#103—22no—
112C23×#103—41no—
113C23×#102—22no—
114C23×#102—22no—
115C23×#102—41no—
116C23×C22⋊C8—41no—
117C23×C22⋊C8—41no—
118C23×#97—41no—
119C23×#95—21no—
120C23×#95—21no—
121C23×#95—21no—
122C23×#95—21no—
123C23×#95—21no—
124C23×#95—21no—
125C23×#95D411yescharacteristic
126C23×#95D411yescharacteristic
127C24×C23—21no—
128C24×C23C2×D411yescharacteristic
129C2×Q8×C23—21no—
130C2×Q8×C23—21no—
131C2×Q8×C23—21no—
132C2×Q8×C23—21no—
133C2×Q8×C23—21no—
134C2×Q8×C23—42no—
135C2×Q8×C23—42no—
136C2×Q8×C23—81no—
137C2×Q8×C23#4112yes—
138C2×D4×C23—21no—
139C2×D4×C23—21no—
140C2×D4×C23—21no—
141C2×D4×C23—21no—
142C2×D4×C23—21no—
143C2×D4×C23—21no—
144C2×D4×C23—42no—
145C2×D4×C23—42no—
146C2×D4×C23—81no—
147C22×C4×C23—21no—
148C22×C4×C23—21no—
149C22×C4×C23—21no—
150C22×C4×C23—21no—
151C22×C4×C23—21no—
152C22×C4×C23—21no—
153C22×C4×C23—21no—
154C22×C4×C23—21no—
155C22×C4×C23—21no—
156C22×C4×C23—21no—
157C22×C4×C23—21no—
158C22×C4×C23—21no—
159C22×C4×C23—21no—
160C22×C4×C23—42no—
161C22×C4×C23—42no—
162C22×C4×C23—81no—
163C22×C4×C23C2×D411yescharacteristic
164C22×C4×C23C2×D411yescharacteristic
165C22×C4×C23C2×D411yescharacteristic
166C22×C4×C23C2×D411yescharacteristic
167C22×C4×C23C2×D411yescharacteristic
168C22×C4×C23C2411yescharacteristic
169SD16×C23—44no—
170C2×C8×C23—21no—
171C2×C8×C23—21no—
172C2×C8×C23—21no—
173C2×C8×C23—21no—
174C2×C8×C23—21no—
175C2×C8×C23—21no—
176C2×C8×C23—21no—
177C2×C8×C23—21no—
178C2×C8×C23—21no—
179C2×C8×C23—21no—
180C2×C8×C23—21no—
181C2×C8×C23—21no—
182C4⋊C4×C23—24no—
183C4⋊C4×C23—21no—
184C4⋊C4×C23—21no—
185C4⋊C4×C23—21no—
186C4⋊C4×C23—21no—
187C4⋊C4×C23—21no—
188C4⋊C4×C23—21no—
189C4⋊C4×C23—21no—
190C4⋊C4×C23—21no—
191C4⋊C4×C23—21no—
192C4⋊C4×C23—42no—
193C4⋊C4×C23—42no—
194C4⋊C4×C23—42no—
195C4⋊C4×C23—81no—
196C4⋊C4×C23#4112yes—
197C4⋊C4×C23#4112yes—
198C4⋊C4×C23#4112yes—
199C22⋊C4×C23—24no—
200C22⋊C4×C23—22no—
201C22⋊C4×C23—22no—
202C22⋊C4×C23—42no—
203C22⋊C4×C23—42no—
204C22⋊C4×C23—42no—
205C22⋊C4×C23—42no—
206C22⋊C4×C23—42no—
207C22⋊C4×C23—81no—
208C42×C23—21no—
209C42×C23—21no—
210C42×C23—21no—
211C42×C23—21no—
212C42×C23—42no—
213C42×C23—42no—
214C42×C23—81no—
215#26741C2311yesmaximal, characteristic, direct product factor, Sylow
216C23×C23—21no—
217C23×C23—21no—
218C23×C23—21no—
219C23×C23—21no—
220C23×C23—21no—
221C23×C23—21no—
222C23×C23—41no—
223C23×C23—41no—
224C23×C23—41no—
225C23×C23—41no—
226C23×C23—41no—
227C23×C23—41no—
228C23×C23—41no—
229C23×C23AGL(1,ℤ/8)12yes—
230C23×C23C22×D411yescharacteristic
231Q8×C23—22no—
232Q8×C23—22no—
233Q8×C23—41no—
234Q8×C23—41no—
235Q8×C23—84no—
236D4×C23—41no—
237D4×C23—41no—
238D4×C23—41no—
239D4×C23—41no—
240D4×C23—84no—
241C2×C4×C23—21no—
242C2×C4×C23—21no—
243C2×C4×C23—22no—
244C2×C4×C23—22no—
245C2×C4×C23—21no—
246C2×C4×C23—21no—
247C2×C4×C23—21no—
248C2×C4×C23—21no—
249C2×C4×C23—22no—
250C2×C4×C23—21no—
251C2×C4×C23—22no—
252C2×C4×C23—21no—
253C2×C4×C23—21no—
254C2×C4×C23—21no—
255C2×C4×C23—21no—
256C2×C4×C23—21no—
257C2×C4×C23—21no—
258C2×C4×C23—21no—
259C2×C4×C23—41no—
260C2×C4×C23—41no—
261C2×C4×C23—41no—
262C2×C4×C23—41no—
263C2×C4×C23—41no—
264C2×C4×C23—41no—
265C2×C4×C23—41no—
266C2×C4×C23—41no—
267C2×C4×C23—41no—
268C2×C4×C23—41no—
269C2×C4×C23—41no—
270C2×C4×C23—41no—
271C2×C4×C23—41no—
272C2×C4×C23—41no—
273C2×C4×C23—41no—
274C2×C4×C23—41no—
275C2×C4×C23—41no—
276C2×C4×C23—41no—
277C2×C4×C23—41no—
278C2×C4×C23—41no—
279C2×C4×C23—41no—
280C2×C4×C23—84no—
281C2×C4×C23#13712yes—
282C2×C4×C23C2×#4111yescharacteristic
283C2×C4×C23C2×#4111yescharacteristic
284C2×C4×C23C2×#4111yescharacteristic
285C2×C4×C23C2×#4111yescharacteristic
286C2×C4×C23H(5,𝔽2)11yescharacteristic
287C2×C4×C23H(5,𝔽2)11yescharacteristic
288C8×C23—41no—
289C8×C23—41no—
290C8×C23—41no—
291C8×C23—41no—
292#2491C2×C2311yescharacteristic
293#2360C2×C2311yescharacteristic, complemented
294#2055C2×C2311yescharacteristic, complemented
295#2035C2×C2311yescharacteristic, complemented
296#2024C2×C2311yescharacteristic, complemented
297#2000C2×C2311yescharacteristic
298#1987C2×C2311yescharacteristic, complemented
299#1936C2×C2311yescharacteristic, complemented
300#1926C2×C2311yescharacteristic, complemented
301#1924C2×C2311yescharacteristic, complemented
302#1919C2×C2311yescharacteristic, complemented
303#1880C2×C2311yescharacteristic, complemented
304#1874C2×C2311yescharacteristic
305#1823C2×C2311yescharacteristic, complemented
306#1763C2×C2311yescharacteristic, complemented
307C22×C23—22no—
308C22×C23—22no—
309C22×C23—22no—
310C22×C23—41no—
311C22×C23—41no—
312C22×C23—41no—
313C22×C23—41no—
314C22×C23—81no—
315C22×C23—81no—
316C22×C23—81no—
317C22×C23—81no—
318C22×C23—81no—
319C22×C23—81no—
320C22×C23—81no—
321C22×C23#52511yescharacteristic
322C22×C23#54611yescharacteristic
323C22×C23#54611yescharacteristic
324C22×C23C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C23C2×#13711yescharacteristic
326C22×C23#57711yescharacteristic
327C22×C23#57711yescharacteristic
328C4×C23—22no—
329C4×C23—41no—
330C4×C23—42no—
331C4×C23—41no—
332C4×C23—42no—
333C4×C23—41no—
334C4×C23—42no—
335C4×C23—41no—
336C4×C23—42no—
337C4×C23—81no—
338C4×C23—81no—
339C4×C23—81no—
340C4×C23#52911yescharacteristic
341C4×C23#53811yescharacteristic
342C4×C23#55511yescharacteristic
343C4×C23#55911yescharacteristic
344C22×SD16C22×C2311yescharacteristic
345C2×C4⋊Q8C22×C2311yescharacteristic
346C2×#124—21no—
347C2×C22⋊Q8C22×C2311yescharacteristic
348C2×#121C22×C2311yescharacteristic
349C2×C4×Q8C22×C2311yescharacteristic
350C22×C4⋊C4C22×C2311yescharacteristic
351C2×#106C22×C2311yescharacteristic
352C2×C4⋊C8C22×C2311yescharacteristic
353C2×#103C22×C2311yescharacteristic
354C2×#103C22×C2311yescharacteristic
355C2×#103C22×C2311yescharacteristic
356C2×#102C22×C2311yescharacteristic
357C2×#102C22×C2311yescharacteristic
358C2×#102C22×C2311yescharacteristic
359C2×C22⋊C8C22×C2311yescharacteristic
360C2×C22⋊C8C22×C2311yescharacteristic
361C2×#97C22×C2311yescharacteristic
362#394—21no—
363#393—21no—
364#391C22×C2311yescharacteristic
365#390C22×C2311yescharacteristic
366#390C22×C2311yescharacteristic
367#389—21no—
368#389C22×C2311yescharacteristic
369#388—21no—
370#387—21no—
371#385—21no—
372#380C22×C2311yescharacteristic
373C4×C4⋊C4C22×C2311yescharacteristic
374C4×C4⋊C4C22×C2311yescharacteristic
375C4×C22⋊C4—21no—
376C4×C22⋊C4C22×C2311yescharacteristic
377#340C22×C2311yescharacteristic
378#340C22×C2311yescharacteristic
379#340C22×C2311yescharacteristic
380#340C22×C2311yescharacteristic
381#340C22×C2311yescharacteristic
382#340C22×C2311yescharacteristic
383#340C22×C2311yescharacteristic
384#340C22×C2311yescharacteristic
385#336C22×C2311yescharacteristic
386#336C22×C2311yescharacteristic
387C2×C23—42no—
388C2×C23—161no—
389C2×C23#245911yescharacteristic
390C2×C23#311211yescharacteristic
391C2×C23#312511yescharacteristic
392C2×C23#330611yescharacteristic
393C2×C23#331011yescharacteristic
394C2×C23#331611yescharacteristic
395C2×C23#332911yescharacteristic
396C22×Q8—21no—
397C22×Q8C23×C2311yescharacteristic
398C22×D4—21no—
399C22×D4C23×C2311yescharacteristic
400C23×C4—21no—
401C23×C4C23×C2311yescharacteristic
402C2×SD16—22no—
403C2×SD16—41no—
404C2×SD16—41no—
405C22×C8C23×C2311yescharacteristic
406C22×C8C23×C2311yescharacteristic
407C22×C8C23×C2311yescharacteristic
408C22×C8C23×C2311yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8—41no—
411#124—44no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414#121—22no—
415#121—41no—
416C4×Q8—22no—
417C4×Q8—41no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4C23×C2311yescharacteristic
426C2×C4⋊C4C23×C2311yescharacteristic
427C2×C4⋊C4C23×C2311yescharacteristic
428C2×C4⋊C4C23×C2311yescharacteristic
429C2×C4⋊C4C23×C2311yescharacteristic
430C2×C4⋊C4C23×C2311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C2311yescharacteristic
439C2×C22⋊C4D4×C2311yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C2311yescharacteristic
444C2×C42C23×C2311yescharacteristic
445#106—22no—
446C4⋊C8—41no—
447#103—22no—
448#103—22no—
449#103—41no—
450#102—22no—
451#102—22no—
452#102—41no—
453C22⋊C8—41no—
454C22⋊C8—41no—
455#97—41no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95D4×C2311yescharacteristic
463#95D4×C2311yescharacteristic
464C23#2674111yescharacteristic, direct product factor, Sylow
465C24—21no—
466C24C2×D4×C2311yescharacteristic
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—81no—
475C2×Q8#41×C2312yes—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—81no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4C2×D4×C2311yescharacteristic
502C22×C4C2×D4×C2311yescharacteristic
503C22×C4C2×D4×C2311yescharacteristic
504C22×C4C2×D4×C2311yescharacteristic
505C22×C4C2×D4×C2311yescharacteristic
506C22×C4C24×C2311yescharacteristic
507SD16—44no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4#41×C2312yes—
535C4⋊C4#41×C2312yes—
536C4⋊C4#41×C2312yes—
537C22⋊C4—24no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—81no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—42no—
552C42—81no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23C23×AGL(1,ℤ/8)12yes—
567C23C22×D4×C2311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—84no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—84no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—84no—
618C2×C4C23×#13712yes—
619C2×C4C2×#41×C2311yescharacteristic
620C2×C4C2×#41×C2311yescharacteristic
621C2×C4C2×#41×C2311yescharacteristic
622C2×C4C2×#41×C2311yescharacteristic
623C2×C4C23×H(5,𝔽2)11yescharacteristic
624C2×C4C23×H(5,𝔽2)11yescharacteristic
625C8—41no—
626C8—41no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C23×#52511yescharacteristic
644C22C23×#54611yescharacteristic
645C22C23×#54611yescharacteristic
646C22C2×C23×AGL(1,ℤ/8)11yescharacteristic
647C22C2×C23×#13711yescharacteristic
648C22C23×#57711yescharacteristic
649C22C23×#57711yescharacteristic
650C4—22no—
651C4—41no—
652C4—42no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4C23×#52911yescharacteristic
663C4C23×#53811yescharacteristic
664C4C23×#55511yescharacteristic
665C4C23×#55911yescharacteristic
666C2—42no—
667C2—161no—
668C2C23×#245911yescharacteristic
669C2C23×#311211yescharacteristic
670C2C23×#312511yescharacteristic
671C2C23×#330611yescharacteristic
672C2C23×#331011yescharacteristic
673C2C23×#331611yescharacteristic
674C2C23×#332911yescharacteristic
subgroupG/H
center, socleC23×C23C22×D4
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC2×C23×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C4×C22⋊C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#2360C2semidirect
3. C23×#2055C2semidirect
4. C23×#2035C2semidirect
5. C23×#2024C2semidirect
7. C23×#1987C2semidirect
8. C23×#1936C2semidirect
9. C23×#1926C2semidirect
10. C23×#1924C2semidirect
11. C23×#1919C2semidirect
12. C23×#1880C2semidirect
14. C23×#1823C2semidirect
15. C23×#1763C2semidirect
215. #26741C23direct (N × H)
293. #2360C2×C23semidirect
294. #2055C2×C23semidirect
295. #2035C2×C23semidirect
296. #2024C2×C23semidirect
298. #1987C2×C23semidirect
299. #1936C2×C23semidirect
300. #1926C2×C23semidirect
301. #1924C2×C23semidirect
302. #1919C2×C23semidirect
303. #1880C2×C23semidirect
305. #1823C2×C23semidirect
306. #1763C2×C23semidirect
464. C23#26741direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#24912
C23×#23602
C23×#20552
C23×#20352
C23×#20242
C23×#20002
C23×#19872
C23×#19362
C23×#19262
C23×#19242
C23×#19192
C23×#18802
C23×#18742
C23×#18232
C23×#17632
#2674123