Finite Group Databasebeta

← C23×#14374 #19162000

Subgroups — C23×#14374 #19162000

Order 5888.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#390C211yesmaximal, characteristic
2C2×C23×#388C211yesmaximal, characteristic, complemented
3C2×C23×#386C211yesmaximal, characteristic
4C2×C23×#381C211yesmaximal, characteristic, complemented
5C2×C23×#380C211yesmaximal, characteristic, complemented
6C23×#1444C211yesmaximal, characteristic, complemented
7C23×#1440C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1438C211yesmaximal, characteristic
12C23×#1437C211yesmaximal, characteristic, complemented
13C23×#1436C211yesmaximal, characteristic, complemented
14C23×#1436C211yesmaximal, characteristic, complemented
15C23×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C4⋊C4×C23C2211yescharacteristic
22C22×C22⋊C4×C23C2211yescharacteristic
23C22×C22⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C22⋊C4×C23C2211yescharacteristic
32C22×C22⋊C4×C23C2211yescharacteristic
33C22×C42×C23C2211yescharacteristic
34C22×C42×C23C2211yescharacteristic
35C23×#390—24no—
36C23×#388—24no—
37C23×#386C418yescomplemented
38C23×#381—24no—
39C23×#380—24no—
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
54C2×C23×#95C2211yescharacteristic
55C2×C23×#95C2211yescharacteristic
56C25×C23C2311yescharacteristic
57C25×C23C2311yescharacteristic
58C22×D4×C23—22no—
59C22×D4×C23—22no—
60C22×D4×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23—41no—
63C22×D4×C23—41no—
64C22×D4×C23C2×C414yes—
65C23×C4×C23—22no—
66C23×C4×C23—22no—
67C23×C4×C23—22no—
68C23×C4×C23—22no—
69C23×C4×C23—41no—
70C23×C4×C23—41no—
71C23×C4×C23C2×C414yes—
72C23×C4×C23C2311yescharacteristic
73C23×C4×C23C2311yescharacteristic
74C23×C4×C23C2311yescharacteristic
75C23×C4×C23C2311yescharacteristic
76C23×C4×C23C2311yescharacteristic
77C23×C4×C23C2311yescharacteristic
78C23×C4×C23C2311yescharacteristic
79C23×C4×C23C2311yescharacteristic
80C23×C4×C23C2311yescharacteristic
81C23×C4×C23C2311yescharacteristic
82C23×C4×C23C2311yescharacteristic
83C23×C4×C23C2311yescharacteristic
84C23×C4×C23C2311yescharacteristic
85C2×C4⋊C4×C23—22no—
86C2×C4⋊C4×C23—22no—
87C2×C4⋊C4×C23—22no—
88C2×C4⋊C4×C23—22no—
89C2×C4⋊C4×C23—22no—
90C2×C4⋊C4×C23—22no—
91C2×C4⋊C4×C23—41no—
92C2×C4⋊C4×C23—41no—
93C2×C4⋊C4×C23—41no—
94C2×C4⋊C4×C23—41no—
95C2×C4⋊C4×C23—41no—
96C2×C4⋊C4×C23—41no—
97C2×C22⋊C4×C23—22no—
98C2×C22⋊C4×C23—22no—
99C2×C22⋊C4×C23—22no—
100C2×C22⋊C4×C23—22no—
101C2×C22⋊C4×C23—22no—
102C2×C22⋊C4×C23—22no—
103C2×C22⋊C4×C23—22no—
104C2×C22⋊C4×C23—22no—
105C2×C22⋊C4×C23—22no—
106C2×C22⋊C4×C23—22no—
107C2×C22⋊C4×C23—22no—
108C2×C22⋊C4×C23—41no—
109C2×C22⋊C4×C23—41no—
110C2×C22⋊C4×C23—41no—
111C2×C22⋊C4×C23—41no—
112C2×C22⋊C4×C23—41no—
113C2×C22⋊C4×C23—41no—
114C2×C22⋊C4×C23—41no—
115C2×C22⋊C4×C23—41no—
116C2×C22⋊C4×C23—41no—
117C2×C22⋊C4×C23—41no—
118C2×C22⋊C4×C23—41no—
119C2×C22⋊C4×C23—41no—
120C2×C22⋊C4×C23—41no—
121C2×C22⋊C4×C23—41no—
122C2×C22⋊C4×C23—41no—
123C2×C22⋊C4×C23—41no—
124C2×C22⋊C4×C23—41no—
125C2×C22⋊C4×C23—41no—
126C2×C22⋊C4×C23C2×C414yes—
127C2×C22⋊C4×C23C2×C414yes—
128C2×C22⋊C4×C23C2×C414yes—
129C2×C22⋊C4×C23D414yes—
130C2×C42×C23—22no—
131C2×C42×C23—22no—
132C2×C42×C23—22no—
133C2×C42×C23—41no—
134C2×C42×C23—41no—
135C2×C42×C23—41no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—22no—
139C23×#95—22no—
140C23×#95—22no—
141C23×#95—22no—
142C23×#95—22no—
143C23×#95—22no—
144C23×#95—41no—
145C23×#95—41no—
146C23×#95—41no—
147C23×#95—41no—
148C23×#95—41no—
149C23×#95C2×C414yes—
150C23×#95C2×C414yes—
151C23×#95D414yescomplemented
152C24×C23—21no—
153C24×C23—21no—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23—21no—
157C24×C23—21no—
158C24×C23—21no—
159C24×C23—21no—
160C24×C23—21no—
161C24×C23—21no—
162C24×C23—21no—
163C24×C23—21no—
164C24×C23—21no—
165C24×C23—21no—
166C24×C23—21no—
167C24×C23—21no—
168C24×C23—21no—
169C24×C23—21no—
170C24×C23—21no—
171C24×C23—21no—
172C24×C23—21no—
173C24×C23—21no—
174C24×C23—21no—
175C24×C23—21no—
176C24×C23—21no—
177C24×C23—21no—
178C24×C23C22×C412yes—
179C24×C23C22×C412yes—
180C24×C23C2×D412yes—
181C24×C23#4112yes—
182C24×C23C2411yescharacteristic
183C2×D4×C23—28no—
184C2×D4×C23—28no—
185C2×D4×C23—44no—
186C2×D4×C23—44no—
187C2×D4×C23—44no—
188C2×D4×C23—44no—
189C2×D4×C23—44no—
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—28no—
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—21no—
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—21no—
239C22×C4×C23—21no—
240C22×C4×C23—21no—
241C22×C4×C23—28no—
242C22×C4×C23—21no—
243C22×C4×C23—21no—
244C22×C4×C23—21no—
245C22×C4×C23—21no—
246C22×C4×C23—21no—
247C22×C4×C23—21no—
248C22×C4×C23—21no—
249C22×C4×C23—21no—
250C22×C4×C23—21no—
251C22×C4×C23—21no—
252C22×C4×C23—21no—
253C22×C4×C23—21no—
254C22×C4×C23—21no—
255C22×C4×C23—21no—
256C22×C4×C23—21no—
257C22×C4×C23—21no—
258C22×C4×C23—21no—
259C22×C4×C23—21no—
260C22×C4×C23—21no—
261C22×C4×C23—21no—
262C22×C4×C23—21no—
263C22×C4×C23—21no—
264C22×C4×C23—21no—
265C22×C4×C23—21no—
266C22×C4×C23—21no—
267C22×C4×C23—21no—
268C22×C4×C23—21no—
269C22×C4×C23—21no—
270C22×C4×C23—44no—
271C22×C4×C23—44no—
272C22×C4×C23—44no—
273C22×C4×C23—44no—
274C22×C4×C23—44no—
275C22×C4×C23C22×C412yes—
276C22×C4×C23C22×C412yes—
277C22×C4×C23C22×C412yes—
278C22×C4×C23C22×C412yes—
279C22×C4×C23C22×C412yes—
280C22×C4×C23C2×D412yes—
281C22×C4×C23C2×D412yes—
282C22×C4×C23C2×D412yes—
283C22×C4×C23C2×D412yes—
284C22×C4×C23C2×D412yes—
285C22×C4×C23#4112yes—
286C22×C4×C23#4112yes—
287C22×C4×C23#4112yes—
288C4⋊C4×C23—44no—
289C4⋊C4×C23—44no—
290C4⋊C4×C23—44no—
291C4⋊C4×C23—44no—
292C22⋊C4×C23—28no—
293C22⋊C4×C23—44no—
294C22⋊C4×C23—44no—
295C22⋊C4×C23—44no—
296C22⋊C4×C23—44no—
297C22⋊C4×C23—44no—
298C22⋊C4×C23—44no—
299C22⋊C4×C23—44no—
300C22⋊C4×C23—44no—
301C22⋊C4×C23—44no—
302C22⋊C4×C23—44no—
303C42×C23—44no—
304C42×C23—44no—
305#14374C2311yesmaximal, characteristic, direct product factor, Sylow
306C23×C23—22no—
307C23×C23—22no—
308C23×C23—22no—
309C23×C23—22no—
310C23×C23—22no—
311C23×C23—22no—
312C23×C23—22no—
313C23×C23—22no—
314C23×C23—22no—
315C23×C23—22no—
316C23×C23—22no—
317C23×C23—22no—
318C23×C23—22no—
319C23×C23—22no—
320C23×C23—22no—
321C23×C23—22no—
322C23×C23—22no—
323C23×C23—22no—
324C23×C23—22no—
325C23×C23—22no—
326C23×C23—22no—
327C23×C23—22no—
328C23×C23—22no—
329C23×C23—22no—
330C23×C23—22no—
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—41no—
344C23×C23—41no—
345C23×C23—41no—
346C23×C23—41no—
347C23×C23—41no—
348C23×C23—41no—
349C23×C23—41no—
350C23×C23—41no—
351C23×C23—41no—
352C23×C23—41no—
353C23×C23—41no—
354C23×C23—41no—
355C23×C23—41no—
356C23×C23—41no—
357C23×C23—41no—
358C23×C23—41no—
359C23×C23—41no—
360C23×C23—41no—
361C23×C23—41no—
362C23×C23—41no—
363C23×C23—41no—
364C23×C23—41no—
365C23×C23—41no—
366C23×C23—41no—
367C23×C23—41no—
368C23×C23—41no—
369C23×C23—41no—
370C23×C23—41no—
371C23×C23—41no—
372C23×C23—41no—
373C23×C23—41no—
374C23×C23—41no—
375C23×C23C4×D414yes—
376C23×C23C23×C411yescharacteristic
377C23×C23C22×D411yescharacteristic
378C23×C23C22×D411yescharacteristic
379C23×C23C2×#4111yescharacteristic
380C23×C23C2×#4111yescharacteristic
381C23×C23C2×#4111yescharacteristic
382C23×C23C2×#4111yescharacteristic
383C23×C23H(5,𝔽2)11yescharacteristic
384C23×C23H(5,𝔽2)11yescharacteristic
385C23×C23H(5,𝔽2)11yescharacteristic
386C23×C23H(5,𝔽2)11yescharacteristic
387C23×C23H(5,𝔽2)11yescharacteristic
388C23×C23H(5,𝔽2)11yescharacteristic
389C23×C232−1+411yescharacteristic
390C23×C232−1+411yescharacteristic
391D4×C23—416no—
392C2×C4×C23—22no—
393C2×C4×C23—22no—
394C2×C4×C23—22no—
395C2×C4×C23—22no—
396C2×C4×C23—22no—
397C2×C4×C23—22no—
398C2×C4×C23—22no—
399C2×C4×C23—22no—
400C2×C4×C23—22no—
401C2×C4×C23—22no—
402C2×C4×C23—22no—
403C2×C4×C23—22no—
404C2×C4×C23—22no—
405C2×C4×C23—22no—
406C2×C4×C23—22no—
407C2×C4×C23—22no—
408C2×C4×C23—22no—
409C2×C4×C23—22no—
410C2×C4×C23—22no—
411C2×C4×C23—22no—
412C2×C4×C23—22no—
413C2×C4×C23—22no—
414C2×C4×C23—22no—
415C2×C4×C23—22no—
416C2×C4×C23—22no—
417C2×C4×C23—22no—
418C2×C4×C23—22no—
419C2×C4×C23—22no—
420C2×C4×C23—22no—
421C2×C4×C23—22no—
422C2×C4×C23—22no—
423C2×C4×C23—22no—
424C2×C4×C23—22no—
425C2×C4×C23—416no—
426C2×C4×C23—41no—
427C2×C4×C23—41no—
428C2×C4×C23—41no—
429C2×C4×C23—41no—
430C2×C4×C23—41no—
431C2×C4×C23—41no—
432C2×C4×C23—41no—
433C2×C4×C23—41no—
434C2×C4×C23—41no—
435C2×C4×C23—41no—
436C2×C4×C23—41no—
437C2×C4×C23—41no—
438C2×C4×C23—41no—
439C2×C4×C23—41no—
440C2×C4×C23—41no—
441C2×C4×C23—41no—
442C2×C4×C23—41no—
443C2×C4×C23—41no—
444C2×C4×C23—41no—
445C2×C4×C23—41no—
446C2×C4×C23—41no—
447C2×C4×C23—41no—
448C2×C4×C23—41no—
449C2×C4×C23—41no—
450C2×C4×C23—41no—
451C2×C4×C23—41no—
452C2×C4×C23—41no—
453C2×C4×C23—41no—
454C2×C4×C23—41no—
455C2×C4×C23—41no—
456C2×C4×C23—41no—
457C2×C4×C23—41no—
458C2×C4×C23—41no—
459C2×C4×C23—41no—
460C2×C4×C23—41no—
461C2×C4×C23—41no—
462C2×C4×C23—41no—
463C2×C4×C23—41no—
464C2×C4×C23—41no—
465C2×C4×C23—41no—
466C2×C4×C23—41no—
467C2×C4×C23—41no—
468C2×C4×C23—41no—
469C2×C4×C23—41no—
470C2×C4×C23—41no—
471C2×C4×C23—41no—
472C2×C4×C23—41no—
473C2×C4×C23—41no—
474C2×C4×C23—41no—
475C2×C4×C23—41no—
476C2×C4×C23—41no—
477C2×C4×C23—41no—
478C2×C4×C23—41no—
479C2×C4×C23—41no—
480C2×C4×C23—41no—
481C2×C4×C23—41no—
482C2×C4×C23#11714yes—
483C2×C4×C23C4×D414yes—
484C2×#390C2×C2311yescharacteristic
485C2×#388C2×C2311yescharacteristic, complemented
486C2×#386C2×C2311yescharacteristic
487C2×#381C2×C2311yescharacteristic, complemented
488C2×#380C2×C2311yescharacteristic, complemented
489#1444C2×C2311yescharacteristic, complemented
490#1440C2×C2311yescharacteristic, complemented
491#1439C2×C2311yescharacteristic, complemented
492#1439C2×C2311yescharacteristic, complemented
493#1439C2×C2311yescharacteristic, complemented
494#1438C2×C2311yescharacteristic
495#1437C2×C2311yescharacteristic, complemented
496#1436C2×C2311yescharacteristic, complemented
497#1436C2×C2311yescharacteristic, complemented
498#1434C2×C2311yescharacteristic, complemented
499C22×C23—24no—
500C22×C23—24no—
501C22×C23—24no—
502C22×C23—42no—
503C22×C23—42no—
504C22×C23—42no—
505C22×C23—42no—
506C22×C23—42no—
507C22×C23—42no—
508C22×C23—42no—
509C22×C23—42no—
510C22×C23—42no—
511C22×C23—42no—
512C22×C23—42no—
513C22×C23—42no—
514C22×C23—42no—
515C22×C23—42no—
516C22×C23—42no—
517C22×C23—42no—
518C22×C23—42no—
519C22×C23—42no—
520C22×C23—42no—
521C22×C23—81no—
522C22×C23—81no—
523C22×C23—81no—
524C22×C23—81no—
525C22×C23—81no—
526C22×C23—81no—
527C22×C23—81no—
528C22×C23—81no—
529C22×C23C2×#11711yescharacteristic
530C22×C23C2×C4×D411yescharacteristic
531C22×C23C2×C4×D411yescharacteristic
532C22×C23#51811yescharacteristic
533C22×C23#51811yescharacteristic
534C22×C23#52011yescharacteristic
535C22×C23#52011yescharacteristic
536C22×C23#53411yescharacteristic
537C22×C23#53511yescharacteristic
538C22×C23#53611yescharacteristic
539C22×C23#53711yescharacteristic
540C22×C23#53911yescharacteristic
541C22×C23#53911yescharacteristic
542C22×C23#54011yescharacteristic
543C22×C23#54011yescharacteristic
544C22×C23#54011yescharacteristic
545C22×C23#54211yescharacteristic
546C22×C23#54211yescharacteristic
547C22×C23#54211yescharacteristic
548C22×C23D4211yescharacteristic
549C22×C23#54611yescharacteristic
550C22×C23#54611yescharacteristic
551C22×C23#54611yescharacteristic
552C22×C23#54611yescharacteristic
553C22×C23#54711yescharacteristic
554C22×C23#55011yescharacteristic
555C22×C23#55111yescharacteristic
556C22×C23#55111yescharacteristic
557C22×C23#55111yescharacteristic
558C22×C23#55511yescharacteristic
559C22×C23#55611yescharacteristic
560C22×C23#56011yescharacteristic
561C22×C23#56011yescharacteristic
562C22×C23#56211yescharacteristic
563C22×C23#56211yescharacteristic
564C4×C23—24no—
565C4×C23—24no—
566C4×C23—42no—
567C4×C23—42no—
568C4×C23—42no—
569C4×C23—42no—
570C4×C23—42no—
571C4×C23—42no—
572C4×C23—42no—
573C4×C23—81no—
574C4×C23—81no—
575C4×C23—81no—
576C4×C23—81no—
577C23×D4C22×C2311yescharacteristic
578C24×C4C22×C2311yescharacteristic
579C22×C4⋊C4C22×C2311yescharacteristic
580C22×C4⋊C4C22×C2311yescharacteristic
581C22×C4⋊C4C22×C2311yescharacteristic
582C22×C4⋊C4C22×C2311yescharacteristic
583C22×C22⋊C4C22×C2311yescharacteristic
584C22×C22⋊C4C22×C2311yescharacteristic
585C22×C22⋊C4C22×C2311yescharacteristic
586C22×C22⋊C4C22×C2311yescharacteristic
587C22×C22⋊C4C22×C2311yescharacteristic
588C22×C22⋊C4C22×C2311yescharacteristic
589C22×C22⋊C4C22×C2311yescharacteristic
590C22×C22⋊C4C22×C2311yescharacteristic
591C22×C22⋊C4C22×C2311yescharacteristic
592C22×C22⋊C4C22×C2311yescharacteristic
593C22×C22⋊C4C22×C2311yescharacteristic
594C22×C42C22×C2311yescharacteristic
595C22×C42C22×C2311yescharacteristic
596#390—24no—
597#388—24no—
598#386C4×C2318yescomplemented
599#381—24no—
600#380—24no—
601C2×#95C22×C2311yescharacteristic
602C2×#95C22×C2311yescharacteristic
603C2×#95C22×C2311yescharacteristic
604C2×#95C22×C2311yescharacteristic
605C2×#95C22×C2311yescharacteristic
606C2×#95C22×C2311yescharacteristic
607C2×#95C22×C2311yescharacteristic
608C2×#95C22×C2311yescharacteristic
609C2×#95C22×C2311yescharacteristic
610C2×#95C22×C2311yescharacteristic
611C2×#95C22×C2311yescharacteristic
612C2×#95C22×C2311yescharacteristic
613C2×#95C22×C2311yescharacteristic
614C2×#95C22×C2311yescharacteristic
615C2×#95C22×C2311yescharacteristic
616C2×#95C22×C2311yescharacteristic
617C2×C23—44no—
618C2×C23—82no—
619C2×C23#231911yescharacteristic
620C2×C23#232211yescharacteristic
621C2×C23#232411yescharacteristic
622C2×C23#234211yescharacteristic
623C2×C23#235411yescharacteristic
624C2×C23#235811yescharacteristic
625C2×C23#237711yescharacteristic
626C2×C23#267211yescharacteristic
627C2×C23#267311yescharacteristic
628C2×C23#269911yescharacteristic
629C2×C23#270011yescharacteristic
630C2×C23#270511yescharacteristic
631C2×C23#270611yescharacteristic
632C2×C23#273711yescharacteristic
633C2×C23#274011yescharacteristic
634C25C23×C2311yescharacteristic
635C25C23×C2311yescharacteristic
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—41no—
641C22×D4—41no—
642C22×D4C2×C4×C2314yes—
643C23×C4—22no—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—41no—
648C23×C4—41no—
649C23×C4C2×C4×C2314yes—
650C23×C4C23×C2311yescharacteristic
651C23×C4C23×C2311yescharacteristic
652C23×C4C23×C2311yescharacteristic
653C23×C4C23×C2311yescharacteristic
654C23×C4C23×C2311yescharacteristic
655C23×C4C23×C2311yescharacteristic
656C23×C4C23×C2311yescharacteristic
657C23×C4C23×C2311yescharacteristic
658C23×C4C23×C2311yescharacteristic
659C23×C4C23×C2311yescharacteristic
660C23×C4C23×C2311yescharacteristic
661C23×C4C23×C2311yescharacteristic
662C23×C4C23×C2311yescharacteristic
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4C2×C4×C2314yes—
705C2×C22⋊C4C2×C4×C2314yes—
706C2×C22⋊C4C2×C4×C2314yes—
707C2×C22⋊C4D4×C2314yes—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—41no—
713C2×C42—41no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—41no—
723#95—41no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95C2×C4×C2314yes—
728#95C2×C4×C2314yes—
729#95D4×C2314yescomplemented
730C23#1437411yescharacteristic, direct product factor, Sylow
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24C22×C4×C2312yes—
758C24C22×C4×C2312yes—
759C24C2×D4×C2312yes—
760C24#41×C2312yes—
761C24C24×C2311yescharacteristic
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—28no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—28no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4C22×C4×C2312yes—
855C22×C4C22×C4×C2312yes—
856C22×C4C22×C4×C2312yes—
857C22×C4C22×C4×C2312yes—
858C22×C4C22×C4×C2312yes—
859C22×C4C2×D4×C2312yes—
860C22×C4C2×D4×C2312yes—
861C22×C4C2×D4×C2312yes—
862C22×C4C2×D4×C2312yes—
863C22×C4C2×D4×C2312yes—
864C22×C4#41×C2312yes—
865C22×C4#41×C2312yes—
866C22×C4#41×C2312yes—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C42—44no—
883C42—44no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23C4×D4×C2314yes—
954C23C23×C4×C2311yescharacteristic
955C23C22×D4×C2311yescharacteristic
956C23C22×D4×C2311yescharacteristic
957C23C2×#41×C2311yescharacteristic
958C23C2×#41×C2311yescharacteristic
959C23C2×#41×C2311yescharacteristic
960C23C2×#41×C2311yescharacteristic
961C23C23×H(5,𝔽2)11yescharacteristic
962C23C23×H(5,𝔽2)11yescharacteristic
963C23C23×H(5,𝔽2)11yescharacteristic
964C23C23×H(5,𝔽2)11yescharacteristic
965C23C23×H(5,𝔽2)11yescharacteristic
966C23C23×H(5,𝔽2)11yescharacteristic
967C23C23×2−1+411yescharacteristic
968C23C23×2−1+411yescharacteristic
969D4—416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—416no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4C23×#11714yes—
1061C2×C4C4×D4×C2314yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22C2×C23×#11711yescharacteristic
1093C22C2×C4×D4×C2311yescharacteristic
1094C22C2×C4×D4×C2311yescharacteristic
1095C22C23×#51811yescharacteristic
1096C22C23×#51811yescharacteristic
1097C22C23×#52011yescharacteristic
1098C22C23×#52011yescharacteristic
1099C22C23×#53411yescharacteristic
1100C22C23×#53511yescharacteristic
1101C22C23×#53611yescharacteristic
1102C22C23×#53711yescharacteristic
1103C22C23×#53911yescharacteristic
1104C22C23×#53911yescharacteristic
1105C22C23×#54011yescharacteristic
1106C22C23×#54011yescharacteristic
1107C22C23×#54011yescharacteristic
1108C22C23×#54211yescharacteristic
1109C22C23×#54211yescharacteristic
1110C22C23×#54211yescharacteristic
1111C22D42×C2311yescharacteristic
1112C22C23×#54611yescharacteristic
1113C22C23×#54611yescharacteristic
1114C22C23×#54611yescharacteristic
1115C22C23×#54611yescharacteristic
1116C22C23×#54711yescharacteristic
1117C22C23×#55011yescharacteristic
1118C22C23×#55111yescharacteristic
1119C22C23×#55111yescharacteristic
1120C22C23×#55111yescharacteristic
1121C22C23×#55511yescharacteristic
1122C22C23×#55611yescharacteristic
1123C22C23×#56011yescharacteristic
1124C22C23×#56011yescharacteristic
1125C22C23×#56211yescharacteristic
1126C22C23×#56211yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C2—44no—
1141C2—82no—
1142C2C23×#231911yescharacteristic
1143C2C23×#232211yescharacteristic
1144C2C23×#232411yescharacteristic
1145C2C23×#234211yescharacteristic
1146C2C23×#235411yescharacteristic
1147C2C23×#235811yescharacteristic
1148C2C23×#237711yescharacteristic
1149C2C23×#267211yescharacteristic
1150C2C23×#267311yescharacteristic
1151C2C23×#269911yescharacteristic
1152C2C23×#270011yescharacteristic
1153C2C23×#270511yescharacteristic
1154C2C23×#270611yescharacteristic
1155C2C23×#273711yescharacteristic
1156C2C23×#274011yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC23×D4×C23C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C23×#388C2semidirect
4. C2×C23×#381C2semidirect
5. C2×C23×#380C2semidirect
6. C23×#1444C2semidirect
7. C23×#1440C2semidirect
8. C23×#1439C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
12. C23×#1437C2semidirect
13. C23×#1436C2semidirect
14. C23×#1436C2semidirect
15. C23×#1434C2semidirect
37. C23×#386C4semidirect
151. C23×#95D4semidirect
305. #14374C23direct (N × H)
485. C2×#388C2×C23semidirect
487. C2×#381C2×C23semidirect
488. C2×#380C2×C23semidirect
489. #1444C2×C23semidirect
490. #1440C2×C23semidirect
491. #1439C2×C23semidirect
492. #1439C2×C23semidirect
493. #1439C2×C23semidirect
495. #1437C2×C23semidirect
496. #1436C2×C23semidirect
497. #1436C2×C23semidirect
498. #1434C2×C23semidirect
598. #386C4×C23semidirect
729. #95D4×C23semidirect
730. C23#14374direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3902
C2×C23×#3882
C2×C23×#3862
C2×C23×#3812
C2×C23×#3802
C23×#14442
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14362
C23×#14342
#1437423