Finite Group Databasebeta

← C23×#14371 #19161997

Subgroups — C23×#14371 #19161997

Order 5888.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#387C211yesmaximal, characteristic, complemented
2C2×C23×#381C211yesmaximal, characteristic
3C2×C23×#380C211yesmaximal, characteristic
4C23×#1445C211yesmaximal, characteristic, complemented
5C23×#1443C211yesmaximal, characteristic, complemented
6C23×#1442C211yesmaximal, characteristic, complemented
7C23×#1441C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic
9C23×#1439C211yesmaximal, characteristic
10C23×#1437C211yesmaximal, characteristic
11C23×#1437C211yesmaximal, characteristic
12C23×#1436C211yesmaximal, characteristic, complemented
13C23×#1436C211yesmaximal, characteristic, complemented
14C23×#1434C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C23C2211yescharacteristic
17C22×C4⋊C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C22⋊C4×C23C2211yescharacteristic
22C22×C22⋊C4×C23C2211yescharacteristic
23C22×C22⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C42×C23C2211yescharacteristic
28C22×C42×C23C2211yescharacteristic
29C23×#387—24no—
30C23×#381—24no—
31C23×#380C418yescomplemented
32C2×C23×#95C2211yescharacteristic
33C2×C23×#95C2211yescharacteristic
34C2×C23×#95C2211yescharacteristic
35C2×C23×#95C2211yescharacteristic
36C2×C23×#95C2211yescharacteristic
37C2×C23×#95C2211yescharacteristic
38C2×C23×#95C2211yescharacteristic
39C2×C23×#95C2211yescharacteristic
40C2×C23×#95C2211yescharacteristic
41C2×C23×#95C2211yescharacteristic
42C2×C23×#95C2211yescharacteristic
43C2×C23×#95C2211yescharacteristic
44C2×C23×#95C2211yescharacteristic
45C2×C23×#95C2211yescharacteristic
46C2×C23×#95C2211yescharacteristic
47C2×C23×#95C2211yescharacteristic
48C2×C23×#95C2211yescharacteristic
49C2×C23×#95C2211yescharacteristic
50C2×C23×#95C2211yescharacteristic
51C2×C23×#95C2211yescharacteristic
52C2×C23×#95C2211yescharacteristic
53C2×C23×#95C2211yescharacteristic
54C25×C23C2311yescharacteristic
55C23×C4×C23—22no—
56C23×C4×C23—22no—
57C23×C4×C23—22no—
58C23×C4×C23—22no—
59C23×C4×C23—41no—
60C23×C4×C23—41no—
61C23×C4×C23C2×C414yes—
62C23×C4×C23C2311yescharacteristic
63C23×C4×C23C2311yescharacteristic
64C23×C4×C23C2311yescharacteristic
65C23×C4×C23C2311yescharacteristic
66C23×C4×C23C2311yescharacteristic
67C23×C4×C23C2311yescharacteristic
68C23×C4×C23C2311yescharacteristic
69C23×C4×C23C2311yescharacteristic
70C23×C4×C23C2311yescharacteristic
71C23×C4×C23C2311yescharacteristic
72C23×C4×C23C2311yescharacteristic
73C23×C4×C23C2311yescharacteristic
74C23×C4×C23C2311yescharacteristic
75C23×C4×C23C2311yescharacteristic
76C2×C4⋊C4×C23—22no—
77C2×C4⋊C4×C23—22no—
78C2×C4⋊C4×C23—22no—
79C2×C4⋊C4×C23—22no—
80C2×C4⋊C4×C23—41no—
81C2×C4⋊C4×C23—41no—
82C2×C4⋊C4×C23—41no—
83C2×C4⋊C4×C23—41no—
84C2×C4⋊C4×C23—41no—
85C2×C4⋊C4×C23—41no—
86C2×C4⋊C4×C23C2×C414yes—
87C2×C4⋊C4×C23C2×C414yes—
88C2×C22⋊C4×C23—22no—
89C2×C22⋊C4×C23—22no—
90C2×C22⋊C4×C23—22no—
91C2×C22⋊C4×C23—22no—
92C2×C22⋊C4×C23—22no—
93C2×C22⋊C4×C23—22no—
94C2×C22⋊C4×C23—22no—
95C2×C22⋊C4×C23—22no—
96C2×C22⋊C4×C23—41no—
97C2×C22⋊C4×C23—41no—
98C2×C22⋊C4×C23—41no—
99C2×C22⋊C4×C23—41no—
100C2×C22⋊C4×C23—41no—
101C2×C22⋊C4×C23—41no—
102C2×C22⋊C4×C23—41no—
103C2×C22⋊C4×C23—41no—
104C2×C22⋊C4×C23C2×C414yes—
105C2×C22⋊C4×C23C2×C414yes—
106C2×C42×C23—22no—
107C2×C42×C23—22no—
108C2×C42×C23—41no—
109C2×C42×C23—41no—
110C2×C42×C23—41no—
111C2×C42×C23—41no—
112C23×#95—22no—
113C23×#95—22no—
114C23×#95—22no—
115C23×#95—22no—
116C23×#95—22no—
117C23×#95—22no—
118C23×#95—22no—
119C23×#95—22no—
120C23×#95—22no—
121C23×#95—41no—
122C23×#95—41no—
123C23×#95—41no—
124C23×#95—41no—
125C23×#95—41no—
126C23×#95—41no—
127C23×#95—41no—
128C23×#95—41no—
129C23×#95—41no—
130C23×#95—41no—
131C23×#95C2×C414yes—
132C23×#95C2×C414yes—
133C23×#95D414yes—
134C24×C23—21no—
135C24×C23—21no—
136C24×C23—21no—
137C24×C23—21no—
138C24×C23—21no—
139C24×C23—21no—
140C24×C23—21no—
141C24×C23—21no—
142C24×C23—21no—
143C24×C23—21no—
144C24×C23—21no—
145C24×C23—21no—
146C24×C23C22×C412yes—
147C24×C23#4112yes—
148C24×C23#4112yes—
149C24×C23C2411yescharacteristic
150C22×C4×C23—21no—
151C22×C4×C23—21no—
152C22×C4×C23—21no—
153C22×C4×C23—21no—
154C22×C4×C23—28no—
155C22×C4×C23—21no—
156C22×C4×C23—21no—
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—21no—
164C22×C4×C23—21no—
165C22×C4×C23—21no—
166C22×C4×C23—21no—
167C22×C4×C23—21no—
168C22×C4×C23—21no—
169C22×C4×C23—21no—
170C22×C4×C23—21no—
171C22×C4×C23—21no—
172C22×C4×C23—21no—
173C22×C4×C23—21no—
174C22×C4×C23—21no—
175C22×C4×C23—21no—
176C22×C4×C23—21no—
177C22×C4×C23—21no—
178C22×C4×C23—21no—
179C22×C4×C23—21no—
180C22×C4×C23—21no—
181C22×C4×C23—21no—
182C22×C4×C23—21no—
183C22×C4×C23—21no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—21no—
187C22×C4×C23—21no—
188C22×C4×C23—21no—
189C22×C4×C23—21no—
190C22×C4×C23—21no—
191C22×C4×C23—21no—
192C22×C4×C23—21no—
193C22×C4×C23—21no—
194C22×C4×C23—21no—
195C22×C4×C23—21no—
196C22×C4×C23—21no—
197C22×C4×C23—21no—
198C22×C4×C23—21no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—21no—
204C22×C4×C23—21no—
205C22×C4×C23—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—28no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
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—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—21no—
238C22×C4×C23—44no—
239C22×C4×C23—44no—
240C22×C4×C23—44no—
241C22×C4×C23—44no—
242C22×C4×C23—44no—
243C22×C4×C23C22×C412yes—
244C22×C4×C23C22×C412yes—
245C22×C4×C23C22×C412yes—
246C22×C4×C23C22×C412yes—
247C22×C4×C23C22×C412yes—
248C22×C4×C23C22×C412yes—
249C22×C4×C23C2×D412yes—
250C22×C4×C23C2×D412yes—
251C22×C4×C23C2×D412yes—
252C22×C4×C23#4112yes—
253C22×C4×C23#4112yes—
254C22×C4×C23#4112yes—
255C4⋊C4×C23—28no—
256C4⋊C4×C23—44no—
257C4⋊C4×C23—44no—
258C4⋊C4×C23—44no—
259C22⋊C4×C23—44no—
260C22⋊C4×C23—44no—
261C22⋊C4×C23—44no—
262C22⋊C4×C23—44no—
263C22⋊C4×C23—44no—
264C22⋊C4×C23—44no—
265C42×C23—44no—
266C42×C23—44no—
267#14371C2311yesmaximal, characteristic, direct product factor, Sylow
268C23×C23—22no—
269C23×C23—22no—
270C23×C23—22no—
271C23×C23—22no—
272C23×C23—22no—
273C23×C23—22no—
274C23×C23—22no—
275C23×C23—22no—
276C23×C23—22no—
277C23×C23—22no—
278C23×C23—22no—
279C23×C23—22no—
280C23×C23—22no—
281C23×C23—22no—
282C23×C23—22no—
283C23×C23—22no—
284C23×C23—22no—
285C23×C23—22no—
286C23×C23—41no—
287C23×C23—41no—
288C23×C23—41no—
289C23×C23—41no—
290C23×C23—41no—
291C23×C23—41no—
292C23×C23—41no—
293C23×C23—41no—
294C23×C23—41no—
295C23×C23—41no—
296C23×C23—41no—
297C23×C23—41no—
298C23×C23—41no—
299C23×C23—41no—
300C23×C23—41no—
301C23×C23—41no—
302C23×C23#11714yes—
303C23×C23C23×C411yescharacteristic
304C23×C23C22×D411yescharacteristic
305C23×C23C2×#4111yescharacteristic
306C23×C23C2×#4111yescharacteristic
307C23×C23C2×#4111yescharacteristic
308C23×C23C2×#4111yescharacteristic
309C23×C23C2×#4111yescharacteristic
310C23×C23H(5,𝔽2)11yescharacteristic
311C23×C23H(5,𝔽2)11yescharacteristic
312C23×C23H(5,𝔽2)11yescharacteristic
313C23×C23H(5,𝔽2)11yescharacteristic
314C23×C23H(5,𝔽2)11yescharacteristic
315C23×C232−1+411yescharacteristic
316C23×C232−1+411yescharacteristic
317C23×C232−1+411yescharacteristic
318C2×C4×C23—22no—
319C2×C4×C23—22no—
320C2×C4×C23—22no—
321C2×C4×C23—22no—
322C2×C4×C23—22no—
323C2×C4×C23—22no—
324C2×C4×C23—22no—
325C2×C4×C23—22no—
326C2×C4×C23—22no—
327C2×C4×C23—22no—
328C2×C4×C23—22no—
329C2×C4×C23—22no—
330C2×C4×C23—22no—
331C2×C4×C23—22no—
332C2×C4×C23—22no—
333C2×C4×C23—22no—
334C2×C4×C23—22no—
335C2×C4×C23—22no—
336C2×C4×C23—22no—
337C2×C4×C23—22no—
338C2×C4×C23—22no—
339C2×C4×C23—22no—
340C2×C4×C23—22no—
341C2×C4×C23—22no—
342C2×C4×C23—22no—
343C2×C4×C23—22no—
344C2×C4×C23—22no—
345C2×C4×C23—22no—
346C2×C4×C23—22no—
347C2×C4×C23—22no—
348C2×C4×C23—22no—
349C2×C4×C23—22no—
350C2×C4×C23—22no—
351C2×C4×C23—416no—
352C2×C4×C23—41no—
353C2×C4×C23—41no—
354C2×C4×C23—41no—
355C2×C4×C23—41no—
356C2×C4×C23—41no—
357C2×C4×C23—41no—
358C2×C4×C23—41no—
359C2×C4×C23—41no—
360C2×C4×C23—41no—
361C2×C4×C23—41no—
362C2×C4×C23—41no—
363C2×C4×C23—41no—
364C2×C4×C23—41no—
365C2×C4×C23—41no—
366C2×C4×C23—41no—
367C2×C4×C23—41no—
368C2×C4×C23—41no—
369C2×C4×C23—41no—
370C2×C4×C23—41no—
371C2×C4×C23—41no—
372C2×C4×C23—41no—
373C2×C4×C23—41no—
374C2×C4×C23—41no—
375C2×C4×C23—41no—
376C2×C4×C23—41no—
377C2×C4×C23—41no—
378C2×C4×C23—41no—
379C2×C4×C23—41no—
380C2×C4×C23—41no—
381C2×C4×C23—41no—
382C2×C4×C23—41no—
383C2×C4×C23—41no—
384C2×C4×C23—41no—
385C2×C4×C23—41no—
386C2×C4×C23—41no—
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—41no—
407C2×C4×C23—41no—
408C2×C4×C23—41no—
409C2×C4×C23—41no—
410C2×C4×C23—41no—
411C2×C4×C23—41no—
412C2×C4×C23—41no—
413C2×C4×C23—41no—
414C2×C4×C23—41no—
415C2×C4×C23—41no—
416C2×C4×C23C4×D414yes—
417C2×#387C2×C2311yescharacteristic, complemented
418C2×#381C2×C2311yescharacteristic
419C2×#380C2×C2311yescharacteristic
420#1445C2×C2311yescharacteristic, complemented
421#1443C2×C2311yescharacteristic, complemented
422#1442C2×C2311yescharacteristic, complemented
423#1441C2×C2311yescharacteristic, complemented
424#1439C2×C2311yescharacteristic
425#1439C2×C2311yescharacteristic
426#1437C2×C2311yescharacteristic
427#1437C2×C2311yescharacteristic
428#1436C2×C2311yescharacteristic, complemented
429#1436C2×C2311yescharacteristic, complemented
430#1434C2×C2311yescharacteristic, complemented
431C22⋊#95C2×C2311yescharacteristic
432C22×C23—24no—
433C22×C23—24no—
434C22×C23—24no—
435C22×C23—42no—
436C22×C23—42no—
437C22×C23—42no—
438C22×C23—42no—
439C22×C23—42no—
440C22×C23—42no—
441C22×C23—42no—
442C22×C23—42no—
443C22×C23—42no—
444C22×C23—42no—
445C22×C23—42no—
446C22×C23—42no—
447C22×C23C2×#11711yescharacteristic
448C22×C23C2×C4×D411yescharacteristic
449C22×C23C4×#4111yescharacteristic
450C22×C23#51811yescharacteristic
451C22×C23#51811yescharacteristic
452C22×C23#51911yescharacteristic
453C22×C23#52011yescharacteristic
454C22×C23#53611yescharacteristic
455C22×C23#53711yescharacteristic
456C22×C23#53911yescharacteristic
457C22×C23#53911yescharacteristic
458C22×C23#53911yescharacteristic
459C22×C23#53911yescharacteristic
460C22×C23#53911yescharacteristic
461C22×C23#53911yescharacteristic
462C22×C23#54111yescharacteristic
463C22×C23#54211yescharacteristic
464C22×C23#54211yescharacteristic
465C22×C23#54211yescharacteristic
466C22×C23#54611yescharacteristic
467C22×C23#54611yescharacteristic
468C22×C23#54611yescharacteristic
469C22×C23#55011yescharacteristic
470C22×C23#55111yescharacteristic
471C22×C23#55111yescharacteristic
472C22×C23#55111yescharacteristic
473C22×C23#55111yescharacteristic
474C22×C23#55211yescharacteristic
475C22×C23#55211yescharacteristic
476C22×C23#55311yescharacteristic
477C22×C23#55511yescharacteristic
478C22×C23#56011yescharacteristic
479C22×C23#56011yescharacteristic
480C22×C23#56211yescharacteristic
481C22×C23#56211yescharacteristic
482C4×C23—24no—
483C4×C23—42no—
484C4×C23—42no—
485C4×C23—42no—
486C4×C23—42no—
487C4×C23—42no—
488C4×C23—42no—
489C4×C23—42no—
490C4×C23—42no—
491C4×C23—42no—
492C4×C23—81no—
493C4×C23—81no—
494C4×C23—81no—
495C4×C23—81no—
496C24×C4C22×C2311yescharacteristic
497C22×C4⋊C4C22×C2311yescharacteristic
498C22×C4⋊C4C22×C2311yescharacteristic
499C22×C4⋊C4C22×C2311yescharacteristic
500C22×C4⋊C4C22×C2311yescharacteristic
501C22×C22⋊C4C22×C2311yescharacteristic
502C22×C22⋊C4C22×C2311yescharacteristic
503C22×C22⋊C4C22×C2311yescharacteristic
504C22×C22⋊C4C22×C2311yescharacteristic
505C22×C22⋊C4C22×C2311yescharacteristic
506C22×C22⋊C4C22×C2311yescharacteristic
507C22×C42C22×C2311yescharacteristic
508C22×C42C22×C2311yescharacteristic
509#387—24no—
510#381—24no—
511#380C4×C2318yescomplemented
512C2×#95C22×C2311yescharacteristic
513C2×#95C22×C2311yescharacteristic
514C2×#95C22×C2311yescharacteristic
515C2×#95C22×C2311yescharacteristic
516C2×#95C22×C2311yescharacteristic
517C2×#95C22×C2311yescharacteristic
518C2×#95C22×C2311yescharacteristic
519C2×#95C22×C2311yescharacteristic
520C2×#95C22×C2311yescharacteristic
521C2×#95C22×C2311yescharacteristic
522C2×#95C22×C2311yescharacteristic
523C2×#95C22×C2311yescharacteristic
524C2×#95C22×C2311yescharacteristic
525C2×#95C22×C2311yescharacteristic
526C2×#95C22×C2311yescharacteristic
527C2×#95C22×C2311yescharacteristic
528C2×#95C22×C2311yescharacteristic
529C2×#95C22×C2311yescharacteristic
530C2×#95C22×C2311yescharacteristic
531C2×#95C22×C2311yescharacteristic
532C2×#95C22×C2311yescharacteristic
533C2×#95C22×C2311yescharacteristic
534C2×C23—44no—
535C2×C23#231311yescharacteristic
536C2×C23#232311yescharacteristic
537C2×C23#233211yescharacteristic
538C2×C23#234211yescharacteristic
539C2×C23#234311yescharacteristic
540C2×C23#236311yescharacteristic
541C2×C23#237711yescharacteristic
542C2×C23#268711yescharacteristic
543C2×C23#269311yescharacteristic
544C2×C23#269411yescharacteristic
545C2×C23#270511yescharacteristic
546C2×C23#273711yescharacteristic
547C2×C23#273911yescharacteristic
548C2×C23#274411yescharacteristic
549C2×C23#274611yescharacteristic
550C25C23×C2311yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4C2×C4×C2314yes—
558C23×C4C23×C2311yescharacteristic
559C23×C4C23×C2311yescharacteristic
560C23×C4C23×C2311yescharacteristic
561C23×C4C23×C2311yescharacteristic
562C23×C4C23×C2311yescharacteristic
563C23×C4C23×C2311yescharacteristic
564C23×C4C23×C2311yescharacteristic
565C23×C4C23×C2311yescharacteristic
566C23×C4C23×C2311yescharacteristic
567C23×C4C23×C2311yescharacteristic
568C23×C4C23×C2311yescharacteristic
569C23×C4C23×C2311yescharacteristic
570C23×C4C23×C2311yescharacteristic
571C23×C4C23×C2311yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4C2×C4×C2314yes—
583C2×C4⋊C4C2×C4×C2314yes—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4C2×C4×C2314yes—
601C2×C22⋊C4C2×C4×C2314yes—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42—41no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95C2×C4×C2314yes—
628#95C2×C4×C2314yes—
629#95D4×C2314yes—
630C23#1437111yescharacteristic, direct product factor, Sylow
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C22×C4×C2312yes—
644C24#41×C2312yes—
645C24#41×C2312yes—
646C24C24×C2311yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—28no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—28no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
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—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4C22×C4×C2312yes—
741C22×C4C22×C4×C2312yes—
742C22×C4C22×C4×C2312yes—
743C22×C4C22×C4×C2312yes—
744C22×C4C22×C4×C2312yes—
745C22×C4C22×C4×C2312yes—
746C22×C4C2×D4×C2312yes—
747C22×C4C2×D4×C2312yes—
748C22×C4C2×D4×C2312yes—
749C22×C4#41×C2312yes—
750C22×C4#41×C2312yes—
751C22×C4#41×C2312yes—
752C4⋊C4—28no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—44no—
761C22⋊C4—44no—
762C42—44no—
763C42—44no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23C23×#11714yes—
799C23C23×C4×C2311yescharacteristic
800C23C22×D4×C2311yescharacteristic
801C23C2×#41×C2311yescharacteristic
802C23C2×#41×C2311yescharacteristic
803C23C2×#41×C2311yescharacteristic
804C23C2×#41×C2311yescharacteristic
805C23C2×#41×C2311yescharacteristic
806C23C23×H(5,𝔽2)11yescharacteristic
807C23C23×H(5,𝔽2)11yescharacteristic
808C23C23×H(5,𝔽2)11yescharacteristic
809C23C23×H(5,𝔽2)11yescharacteristic
810C23C23×H(5,𝔽2)11yescharacteristic
811C23C23×2−1+411yescharacteristic
812C23C23×2−1+411yescharacteristic
813C23C23×2−1+411yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—416no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
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×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4C4×D4×C2314yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×C23×#11711yescharacteristic
929C22C2×C4×D4×C2311yescharacteristic
930C22C4×#41×C2311yescharacteristic
931C22C23×#51811yescharacteristic
932C22C23×#51811yescharacteristic
933C22C23×#51911yescharacteristic
934C22C23×#52011yescharacteristic
935C22C23×#53611yescharacteristic
936C22C23×#53711yescharacteristic
937C22C23×#53911yescharacteristic
938C22C23×#53911yescharacteristic
939C22C23×#53911yescharacteristic
940C22C23×#53911yescharacteristic
941C22C23×#53911yescharacteristic
942C22C23×#53911yescharacteristic
943C22C23×#54111yescharacteristic
944C22C23×#54211yescharacteristic
945C22C23×#54211yescharacteristic
946C22C23×#54211yescharacteristic
947C22C23×#54611yescharacteristic
948C22C23×#54611yescharacteristic
949C22C23×#54611yescharacteristic
950C22C23×#55011yescharacteristic
951C22C23×#55111yescharacteristic
952C22C23×#55111yescharacteristic
953C22C23×#55111yescharacteristic
954C22C23×#55111yescharacteristic
955C22C23×#55211yescharacteristic
956C22C23×#55211yescharacteristic
957C22C23×#55311yescharacteristic
958C22C23×#55511yescharacteristic
959C22C23×#56011yescharacteristic
960C22C23×#56011yescharacteristic
961C22C23×#56211yescharacteristic
962C22C23×#56211yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—81no—
974C4—81no—
975C4—81no—
976C4—81no—
977C2—44no—
978C2C23×#231311yescharacteristic
979C2C23×#232311yescharacteristic
980C2C23×#233211yescharacteristic
981C2C23×#234211yescharacteristic
982C2C23×#234311yescharacteristic
983C2C23×#236311yescharacteristic
984C2C23×#237711yescharacteristic
985C2C23×#268711yescharacteristic
986C2C23×#269311yescharacteristic
987C2C23×#269411yescharacteristic
988C2C23×#270511yescharacteristic
989C2C23×#273711yescharacteristic
990C2C23×#273911yescharacteristic
991C2C23×#274411yescharacteristic
992C2C23×#274611yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC25×C23C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C23×#387C2semidirect
4. C23×#1445C2semidirect
5. C23×#1443C2semidirect
6. C23×#1442C2semidirect
7. C23×#1441C2semidirect
12. C23×#1436C2semidirect
13. C23×#1436C2semidirect
14. C23×#1434C2semidirect
31. C23×#380C4semidirect
267. #14371C23direct (N × H)
417. C2×#387C2×C23semidirect
420. #1445C2×C23semidirect
421. #1443C2×C23semidirect
422. #1442C2×C23semidirect
423. #1441C2×C23semidirect
428. #1436C2×C23semidirect
429. #1436C2×C23semidirect
430. #1434C2×C23semidirect
511. #380C4×C23semidirect
630. C23#14371direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3872
C2×C23×#3812
C2×C23×#3802
C23×#14452
C23×#14432
C23×#14422
C23×#14412
C23×#14392
C23×#14372
C23×#14362
C23×#14342
C23×C22⋊#952
#1437123