Finite Group Databasebeta

← C23×#22160 #19169786

Subgroups — C23×#22160 #19169786

Order 5888.

880 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#460C211yesmaximal, characteristic
2C23×#2328C211yesmaximal, characteristic
3C23×#2320C211yesmaximal, characteristic, complemented
4C23×#1982C211yesmaximal, characteristic
5C23×#1973C211yesmaximal, characteristic, complemented
6C23×#1968C211yesmaximal, characteristic, complemented
7C23×#1949C211yesmaximal, characteristic, complemented
8C23×#1936C211yesmaximal, characteristic, complemented
9C23×#1934C211yesmaximal, characteristic, complemented
10C23×#1877C211yesmaximal, characteristic, complemented
11C23×#1877C211yesmaximal, characteristic, complemented
12C23×#1864C211yesmaximal, characteristic, complemented
13C23×#1862C211yesmaximal, characteristic, complemented
14C23×#1805C211yesmaximal, characteristic, complemented
15C23×#1768C211yesmaximal, characteristic, complemented
16C22×SD16×C23C2211yescharacteristic
17C22×SD16×C23C2211yescharacteristic
18C2×C23×#127C2211yescharacteristic
19C2×C4×Q8×C23C2211yescharacteristic
20C2×C4×D4×C23C2211yescharacteristic
21C2×C4×D4×C23C2211yescharacteristic
22C23×#460C418yescomplemented
23C2×C23×#107C2211yescharacteristic
24C2×C23×#106C2211yescharacteristic
25C2×C23×C4⋊C8C2211yescharacteristic
26C2×C23×C4⋊C8C2211yescharacteristic
27C2×C23×#103C2211yescharacteristic
28C2×C23×#103C2211yescharacteristic
29C2×C23×#102C2211yescharacteristic
30C2×C23×#102C2211yescharacteristic
31C2×C23×#102C2211yescharacteristic
32C2×C23×#102C2211yescharacteristic
33C2×C23×#102C2211yescharacteristic
34C2×C23×#102C2211yescharacteristic
35C2×C23×#97C2211yescharacteristic
36C2×C4×C8×C23C2211yescharacteristic
37C23×#391C2211yescharacteristic
38C23×#391C2211yescharacteristic
39C23×#390C2211yescharacteristic
40C23×#390C2211yescharacteristic
41C23×#389C2211yescharacteristic
42C23×#389C2211yescharacteristic
43C23×#387—21no—
44C23×#387—21no—
45C23×#386—21no—
46C23×#386—21no—
47C23×#386—21no—
48C23×#386—21no—
49C23×#383—21no—
50C23×#382—21no—
51C23×#382C2211yescharacteristic
52C4×C4⋊C4×C23C2211yescharacteristic
53C23×#376C2211yescharacteristic
54C23×#340C2211yescharacteristic
55C23×#340C2211yescharacteristic
56C23×#340C2211yescharacteristic
57C23×#340C2211yescharacteristic
58C23×#336C2211yescharacteristic
59C23×#336C2211yescharacteristic
60C22×Q8×C23C2311yescharacteristic
61C22×D4×C23—21no—
62C22×D4×C23—21no—
63C22×D4×C23C2311yescharacteristic
64C22×D4×C23C2311yescharacteristic
65C23×C4×C23—21no—
66C23×C4×C23—21no—
67C2×SD16×C23—41no—
68C2×SD16×C23—41no—
69C2×SD16×C23—41no—
70C2×SD16×C23—41no—
71C2×SD16×C23C2×C414yescomplemented
72C2×SD16×C23C2×C414yescomplemented
73C22×C8×C23C2311yescharacteristic
74C22×C8×C23C2311yescharacteristic
75C22×C8×C23C2311yescharacteristic
76C22×C8×C23C2311yescharacteristic
77C23×#127—22no—
78C23×#127C2×C414yes—
79C4×Q8×C23—22no—
80C4×Q8×C23C2×C414yescomplemented
81C4×D4×C23—41no—
82C4×D4×C23—41no—
83C4×D4×C23—41no—
84C4×D4×C23—41no—
85C2×C4⋊C4×C23—21no—
86C2×C4⋊C4×C23—21no—
87C2×C4⋊C4×C23—21no—
88C2×C4⋊C4×C23C2311yescharacteristic
89C2×C4⋊C4×C23C2311yescharacteristic
90C2×C4⋊C4×C23C2311yescharacteristic
91C2×C4⋊C4×C23C2311yescharacteristic
92C2×C4⋊C4×C23C2311yescharacteristic
93C2×C22⋊C4×C23—21no—
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×C42×C23—21no—
100C2×C42×C23—21no—
101C2×C42×C23C2311yescharacteristic
102C2×C42×C23C2311yescharacteristic
103C2×C42×C23C2311yescharacteristic
104C23×#107—41no—
105C23×#106—41no—
106C23×C4⋊C8—22no—
107C23×C4⋊C8C2×C414yescomplemented
108C23×#103—41no—
109C23×#103—41no—
110C23×#102—41no—
111C23×#102—41no—
112C23×#102—41no—
113C23×#102—41no—
114C23×#102C2×C414yescomplemented
115C23×#102C2×C414yescomplemented
116C23×#97—41no—
117C4×C8×C23—41no—
118C23×#95—21no—
119C23×#95—21no—
120C23×#95—21no—
121C23×#95—21no—
122C23×#95—21no—
123C23×#95—21no—
124C23×#95—21no—
125C23×#95—21no—
126C23×#95—21no—
127C23×#95D411yescharacteristic
128C23×#95D411yescharacteristic
129C23×#95D411yescharacteristic
130C23×#95D411yescharacteristic
131C24×C23—21no—
132C24×C23—21no—
133C2×Q8×C23—21no—
134C2×Q8×C23—21no—
135C2×Q8×C23—21no—
136C2×Q8×C23—21no—
137C2×Q8×C23—21no—
138C2×Q8×C23C22×C412yes—
139C2×D4×C23—24no—
140C2×D4×C23—24no—
141C2×D4×C23—21no—
142C2×D4×C23—21no—
143C2×D4×C23—21no—
144C2×D4×C23—21no—
145C2×D4×C23—21no—
146C2×D4×C23—21no—
147C2×D4×C23—21no—
148C2×D4×C23—21no—
149C2×D4×C23—21no—
150C2×D4×C23—21no—
151C2×D4×C23—81no—
152C2×D4×C23—81no—
153C2×D4×C23—81no—
154C2×D4×C23—81no—
155C2×D4×C23C22×C412yes—
156C2×D4×C23C22×C412yes—
157C22×C4×C23—21no—
158C22×C4×C23—21no—
159C22×C4×C23—21no—
160C22×C4×C23—21no—
161C22×C4×C23—21no—
162C22×C4×C23—21no—
163C22×C4×C23—42no—
164C22×C4×C23—42no—
165C22×C4×C23—81no—
166C22×C4×C23—81no—
167C22×C4×C23—81no—
168C22×C4×C23—81no—
169C22×C4×C23C2×D411yescharacteristic
170C22×C4×C23C2×D411yescharacteristic
171C22×C4×C23C2×D411yescharacteristic
172C22×C4×C23C2×D411yescharacteristic
173C22×C4×C23C2×D411yescharacteristic
174C22×C4×C23C2×D411yescharacteristic
175C22×C4×C23C2411yescharacteristic
176SD16×C23—44no—
177SD16×C23—44no—
178C2×C8×C23—21no—
179C2×C8×C23—21no—
180C2×C8×C23—21no—
181C2×C8×C23—21no—
182C2×C8×C23—21no—
183C2×C8×C23—21no—
184C2×C8×C23—21no—
185C2×C8×C23—21no—
186C2×C8×C23—21no—
187C2×C8×C23—21no—
188C2×C8×C23C22×C412yes—
189C2×C8×C23C22×C412yes—
190C4⋊C4×C23—24no—
191C4⋊C4×C23—21no—
192C4⋊C4×C23—21no—
193C4⋊C4×C23—21no—
194C4⋊C4×C23—21no—
195C4⋊C4×C23—21no—
196C4⋊C4×C23—21no—
197C4⋊C4×C23—21no—
198C4⋊C4×C23—21no—
199C4⋊C4×C23—21no—
200C4⋊C4×C23—81no—
201C4⋊C4×C23—81no—
202C4⋊C4×C23C22×C412yes—
203C22⋊C4×C23—42no—
204C22⋊C4×C23—42no—
205C22⋊C4×C23—81no—
206C22⋊C4×C23—81no—
207C22⋊C4×C23—81no—
208C22⋊C4×C23—81no—
209C42×C23—24no—
210C42×C23—21no—
211C42×C23—21no—
212C42×C23—21no—
213C42×C23—21no—
214C42×C23—81no—
215C42×C23C22×C412yes—
216C42×C23#4112yes—
217#22160C2311yesmaximal, characteristic, direct product factor, Sylow
218C23×C23—22no—
219C23×C23—22no—
220C23×C23—41no—
221C23×C23—41no—
222C23×C23—41no—
223C23×C23—41no—
224C23×C23—41no—
225C23×C23—41no—
226C23×C23—41no—
227C23×C23—41no—
228C23×C23—41no—
229C23×C23—41no—
230C23×C23—41no—
231C23×C23—41no—
232C23×C23C22×D411yescharacteristic
233Q8×C23—22no—
234Q8×C23—22no—
235Q8×C23—41no—
236Q8×C23—41no—
237D4×C23—22no—
238D4×C23—22no—
239D4×C23—22no—
240D4×C23—22no—
241D4×C23—41no—
242D4×C23—41no—
243D4×C23—41no—
244D4×C23—41no—
245D4×C23—84no—
246D4×C23—84no—
247C2×C4×C23—21no—
248C2×C4×C23—21no—
249C2×C4×C23—21no—
250C2×C4×C23—21no—
251C2×C4×C23—22no—
252C2×C4×C23—22no—
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—21no—
260C2×C4×C23—21no—
261C2×C4×C23—21no—
262C2×C4×C23—21no—
263C2×C4×C23—21no—
264C2×C4×C23—21no—
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—41no—
281C2×C4×C23—84no—
282C2×C4×C23—84no—
283C2×C4×C23C4×D412yes—
284C2×C4×C23C4×D412yes—
285C2×C4×C23C23×C411yescharacteristic
286C2×C4×C23C2×#4111yescharacteristic
287C2×C4×C23H(5,𝔽2)11yescharacteristic
288C2×C4×C23H(5,𝔽2)11yescharacteristic
289C2×C4×C23H(5,𝔽2)11yescharacteristic
290C2×C4×C232−1+411yescharacteristic
291C8×C23—22no—
292C8×C23—22no—
293C8×C23—41no—
294C8×C23—41no—
295C2×#460C2×C2311yescharacteristic
296#2328C2×C2311yescharacteristic
297#2320C2×C2311yescharacteristic, complemented
298#1982C2×C2311yescharacteristic
299#1973C2×C2311yescharacteristic, complemented
300#1968C2×C2311yescharacteristic, complemented
301#1949C2×C2311yescharacteristic, complemented
302#1936C2×C2311yescharacteristic, complemented
303#1934C2×C2311yescharacteristic, complemented
304#1877C2×C2311yescharacteristic, complemented
305#1877C2×C2311yescharacteristic, complemented
306#1864C2×C2311yescharacteristic, complemented
307#1862C2×C2311yescharacteristic, complemented
308#1805C2×C2311yescharacteristic, complemented
309#1768C2×C2311yescharacteristic, complemented
310C22×C23—42no—
311C22×C23—42no—
312C22×C23—42no—
313C22×C23—42no—
314C22×C23—42no—
315C22×C23—42no—
316C22×C23—81no—
317C22×C23—81no—
318C22×C23—81no—
319C22×C23—81no—
320C22×C23—81no—
321C22×C23—81no—
322C22×C23—81no—
323C22×C23—81no—
324C22×C23C2×C4×D411yescharacteristic
325C22×C23#53511yescharacteristic
326C22×C23#53711yescharacteristic
327C22×C23#57611yescharacteristic
328C22×C23#57711yescharacteristic
329C22×C23#57711yescharacteristic
330C22×C23#57711yescharacteristic
331C4×C23—22no—
332C4×C23—22no—
333C4×C23—42no—
334C4×C23—42no—
335C4×C23—41no—
336C4×C23—41no—
337C4×C23—41no—
338C4×C23—41no—
339C4×C23—81no—
340C4×C23—81no—
341C4×C23—81no—
342C4×C23—81no—
343C4×C23#51811yescharacteristic
344C4×C23#52011yescharacteristic
345C4×C23#54011yescharacteristic
346C4×C23#54211yescharacteristic
347C22×SD16C22×C2311yescharacteristic
348C22×SD16C22×C2311yescharacteristic
349C2×#127C22×C2311yescharacteristic
350C2×C4×Q8C22×C2311yescharacteristic
351C2×C4×D4C22×C2311yescharacteristic
352C2×C4×D4C22×C2311yescharacteristic
353#460C4×C2318yescomplemented
354C2×#107C22×C2311yescharacteristic
355C2×#106C22×C2311yescharacteristic
356C2×C4⋊C8C22×C2311yescharacteristic
357C2×C4⋊C8C22×C2311yescharacteristic
358C2×#103C22×C2311yescharacteristic
359C2×#103C22×C2311yescharacteristic
360C2×#102C22×C2311yescharacteristic
361C2×#102C22×C2311yescharacteristic
362C2×#102C22×C2311yescharacteristic
363C2×#102C22×C2311yescharacteristic
364C2×#102C22×C2311yescharacteristic
365C2×#102C22×C2311yescharacteristic
366C2×#97C22×C2311yescharacteristic
367C2×C4×C8C22×C2311yescharacteristic
368#391C22×C2311yescharacteristic
369#391C22×C2311yescharacteristic
370#390C22×C2311yescharacteristic
371#390C22×C2311yescharacteristic
372#389C22×C2311yescharacteristic
373#389C22×C2311yescharacteristic
374#387—21no—
375#387—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#383—21no—
381#382—21no—
382#382C22×C2311yescharacteristic
383C4×C4⋊C4C22×C2311yescharacteristic
384#376C22×C2311yescharacteristic
385#340C22×C2311yescharacteristic
386#340C22×C2311yescharacteristic
387#340C22×C2311yescharacteristic
388#340C22×C2311yescharacteristic
389#336C22×C2311yescharacteristic
390#336C22×C2311yescharacteristic
391C2×C23—82no—
392C2×C23—82no—
393C2×C23#232411yescharacteristic
394C2×C23#294611yescharacteristic
395C2×C23#294911yescharacteristic
396C2×C23#322211yescharacteristic
397C2×C23#322411yescharacteristic
398C2×C23#325711yescharacteristic
399C2×C23#326011yescharacteristic
400C22×Q8C23×C2311yescharacteristic
401C22×D4—21no—
402C22×D4—21no—
403C22×D4C23×C2311yescharacteristic
404C22×D4C23×C2311yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C2×SD16—41no—
408C2×SD16—41no—
409C2×SD16—41no—
410C2×SD16—41no—
411C2×SD16C2×C4×C2314yescomplemented
412C2×SD16C2×C4×C2314yescomplemented
413C22×C8C23×C2311yescharacteristic
414C22×C8C23×C2311yescharacteristic
415C22×C8C23×C2311yescharacteristic
416C22×C8C23×C2311yescharacteristic
417#127—22no—
418#127C2×C4×C2314yes—
419C4×Q8—22no—
420C4×Q8C2×C4×C2314yescomplemented
421C4×D4—41no—
422C4×D4—41no—
423C4×D4—41no—
424C4×D4—41no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4C23×C2311yescharacteristic
429C2×C4⋊C4C23×C2311yescharacteristic
430C2×C4⋊C4C23×C2311yescharacteristic
431C2×C4⋊C4C23×C2311yescharacteristic
432C2×C4⋊C4C23×C2311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42C23×C2311yescharacteristic
442C2×C42C23×C2311yescharacteristic
443C2×C42C23×C2311yescharacteristic
444#107—41no—
445#106—41no—
446C4⋊C8—22no—
447C4⋊C8C2×C4×C2314yescomplemented
448#103—41no—
449#103—41no—
450#102—41no—
451#102—41no—
452#102—41no—
453#102—41no—
454#102C2×C4×C2314yescomplemented
455#102C2×C4×C2314yescomplemented
456#97—41no—
457C4×C8—41no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95D4×C2311yescharacteristic
468#95D4×C2311yescharacteristic
469#95D4×C2311yescharacteristic
470#95D4×C2311yescharacteristic
471C23#2216011yescharacteristic, direct product factor, Sylow
472C24—21no—
473C24—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C22×C4×C2312yes—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—81no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4C22×C4×C2312yes—
497C2×D4C22×C4×C2312yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4C2×D4×C2311yescharacteristic
511C22×C4C2×D4×C2311yescharacteristic
512C22×C4C2×D4×C2311yescharacteristic
513C22×C4C2×D4×C2311yescharacteristic
514C22×C4C2×D4×C2311yescharacteristic
515C22×C4C2×D4×C2311yescharacteristic
516C22×C4C24×C2311yescharacteristic
517SD16—44no—
518SD16—44no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8C22×C4×C2312yes—
530C2×C8C22×C4×C2312yes—
531C4⋊C4—24no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—81no—
542C4⋊C4—81no—
543C4⋊C4C22×C4×C2312yes—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—81no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C42—24no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—81no—
556C42C22×C4×C2312yes—
557C42#41×C2312yes—
558C23—22no—
559C23—22no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×D4×C2311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—22no—
578D4—22no—
579D4—22no—
580D4—22no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—84no—
586D4—84no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
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—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—84no—
623C2×C4C4×D4×C2312yes—
624C2×C4C4×D4×C2312yes—
625C2×C4C23×C4×C2311yescharacteristic
626C2×C4C2×#41×C2311yescharacteristic
627C2×C4C23×H(5,𝔽2)11yescharacteristic
628C2×C4C23×H(5,𝔽2)11yescharacteristic
629C2×C4C23×H(5,𝔽2)11yescharacteristic
630C2×C4C23×2−1+411yescharacteristic
631C8—22no—
632C8—22no—
633C8—41no—
634C8—41no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C2×C4×D4×C2311yescharacteristic
650C22C23×#53511yescharacteristic
651C22C23×#53711yescharacteristic
652C22C23×#57611yescharacteristic
653C22C23×#57711yescharacteristic
654C22C23×#57711yescharacteristic
655C22C23×#57711yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4C23×#51811yescharacteristic
669C4C23×#52011yescharacteristic
670C4C23×#54011yescharacteristic
671C4C23×#54211yescharacteristic
672C2—82no—
673C2—82no—
674C2C23×#232411yescharacteristic
675C2C23×#294611yescharacteristic
676C2C23×#294911yescharacteristic
677C2C23×#322211yescharacteristic
678C2C23×#322411yescharacteristic
679C2C23×#325711yescharacteristic
680C2C23×#326011yescharacteristic
subgroupG/H
center, socleC23×C23C22×D4
commutatorC2×C4C23×C4×C23
Frattini, cosocleC22×C4C24×C23
prime radicalC2×C23×#127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C23×#376 ◁ G

Complements

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

NH ≅ G/Ntype
3. C23×#2320C2semidirect
5. C23×#1973C2semidirect
6. C23×#1968C2semidirect
7. C23×#1949C2semidirect
8. C23×#1936C2semidirect
9. C23×#1934C2semidirect
10. C23×#1877C2semidirect
11. C23×#1877C2semidirect
12. C23×#1864C2semidirect
13. C23×#1862C2semidirect
14. C23×#1805C2semidirect
15. C23×#1768C2semidirect
22. C23×#460C4semidirect
71. C2×SD16×C23C2×C4semidirect
72. C2×SD16×C23C2×C4semidirect
80. C4×Q8×C23C2×C4semidirect
107. C23×C4⋊C8C2×C4semidirect
114. C23×#102C2×C4semidirect
115. C23×#102C2×C4semidirect
217. #22160C23direct (N × H)
297. #2320C2×C23semidirect
299. #1973C2×C23semidirect
300. #1968C2×C23semidirect
301. #1949C2×C23semidirect
302. #1936C2×C23semidirect
303. #1934C2×C23semidirect
304. #1877C2×C23semidirect
305. #1877C2×C23semidirect
306. #1864C2×C23semidirect
307. #1862C2×C23semidirect
308. #1805C2×C23semidirect
309. #1768C2×C23semidirect
353. #460C4×C23semidirect
411. C2×SD16C2×C4×C23semidirect
412. C2×SD16C2×C4×C23semidirect
420. C4×Q8C2×C4×C23semidirect
447. C4⋊C8C2×C4×C23semidirect
454. #102C2×C4×C23semidirect
455. #102C2×C4×C23semidirect
471. C23#22160direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#4602
C23×#23282
C23×#23202
C23×#19822
C23×#19732
C23×#19682
C23×#19492
C23×#19362
C23×#19342
C23×#18772
C23×#18642
C23×#18622
C23×#18052
C23×#17682
#2216023