Finite Group Databasebeta

← C23×#14563 #19162189

Subgroups — C23×#14563 #19162189

Order 5888.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#394C211yesmaximal, characteristic
2C2×C23×#390C211yesmaximal, characteristic
3C2×C23×#389C211yesmaximal, characteristic, complemented
4C2×C23×#388C211yesmaximal, characteristic, complemented
5C2×C23×#388C211yesmaximal, characteristic, complemented
6C23×#1439C211yesmaximal, characteristic, complemented
7C23×#1439C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1438C211yesmaximal, characteristic
11C23×#1437C211yesmaximal, characteristic, complemented
12C23×#1437C211yesmaximal, characteristic, complemented
13C23×#1436C211yesmaximal, characteristic, complemented
14C23×#1436C211yesmaximal, characteristic, complemented
15C23×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C22×C4⋊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×C22⋊C4×C23C2211yescharacteristic
34C22×C42×C23C2211yescharacteristic
35C22×C42×C23C2211yescharacteristic
36C22×C42×C23C2211yescharacteristic
37C23×#394C418yescomplemented
38C23×#390—24no—
39C23×#389—24no—
40C23×#388—24no—
41C23×#388—24no—
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—41no—
61C22×D4×C23—41no—
62C22×D4×C23—41no—
63C22×D4×C23—41no—
64C22×D4×C23C2×C414yes—
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
76C23×C4×C23C2311yescharacteristic
77C23×C4×C23C2311yescharacteristic
78C2×C4⋊C4×C23—22no—
79C2×C4⋊C4×C23—22no—
80C2×C4⋊C4×C23—22no—
81C2×C4⋊C4×C23—22no—
82C2×C4⋊C4×C23—22no—
83C2×C4⋊C4×C23—22no—
84C2×C4⋊C4×C23—22no—
85C2×C4⋊C4×C23—41no—
86C2×C4⋊C4×C23—41no—
87C2×C4⋊C4×C23—41no—
88C2×C4⋊C4×C23—41no—
89C2×C4⋊C4×C23—41no—
90C2×C4⋊C4×C23—41no—
91C2×C4⋊C4×C23C2×C414yes—
92C2×C4⋊C4×C23D414yes—
93C2×C22⋊C4×C23—22no—
94C2×C22⋊C4×C23—22no—
95C2×C22⋊C4×C23—22no—
96C2×C22⋊C4×C23—22no—
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—22no—
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×C23C2×C414yes—
126C2×C22⋊C4×C23C2×C414yes—
127C2×C22⋊C4×C23C2×C414yes—
128C2×C22⋊C4×C23C2×C414yes—
129C2×C42×C23—22no—
130C2×C42×C23—22no—
131C2×C42×C23—22no—
132C2×C42×C23—22no—
133C2×C42×C23—41no—
134C2×C42×C23—41no—
135C2×C42×C23—41no—
136C2×C42×C23—41no—
137C2×C42×C23—41no—
138C23×#95—22no—
139C23×#95—22no—
140C23×#95—22no—
141C23×#95—22no—
142C23×#95—22no—
143C23×#95—22no—
144C23×#95—22no—
145C23×#95—41no—
146C23×#95—41no—
147C23×#95—41no—
148C23×#95—41no—
149C23×#95—41no—
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×C23—21no—
179C24×C23—21no—
180C24×C23C22×C412yes—
181C24×C23C22×C412yes—
182C24×C23C2411yescharacteristic
183C2×D4×C23—28no—
184C2×D4×C23—44no—
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—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—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—21no—
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×C23C22×C412yes—
267C22×C4×C23C22×C412yes—
268C22×C4×C23C22×C412yes—
269C22×C4×C23C22×C412yes—
270C22×C4×C23C22×C412yes—
271C22×C4×C23C2×D412yes—
272C22×C4×C23C2×D412yes—
273C22×C4×C23C2×D412yes—
274C22×C4×C23C2×D412yes—
275C22×C4×C23C2×D412yes—
276C22×C4×C23C2×D412yes—
277C22×C4×C23#4112yes—
278C22×C4×C23#4112yes—
279C22×C4×C23#4112yes—
280C22×C4×C23#4112yes—
281C4⋊C4×C23—28no—
282C4⋊C4×C23—44no—
283C4⋊C4×C23—44no—
284C4⋊C4×C23—44no—
285C4⋊C4×C23—44no—
286C22⋊C4×C23—28no—
287C22⋊C4×C23—28no—
288C22⋊C4×C23—44no—
289C22⋊C4×C23—44no—
290C22⋊C4×C23—44no—
291C22⋊C4×C23—44no—
292C22⋊C4×C23—44no—
293C22⋊C4×C23—44no—
294C22⋊C4×C23—44no—
295C22⋊C4×C23—44no—
296C22⋊C4×C23—44no—
297C22⋊C4×C23—44no—
298C42×C23—44no—
299C42×C23—44no—
300C42×C23—44no—
301#14563C2311yesmaximal, characteristic, direct product factor, Sylow
302C23×C23—22no—
303C23×C23—22no—
304C23×C23—22no—
305C23×C23—22no—
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—41no—
317C23×C23—41no—
318C23×C23—41no—
319C23×C23—41no—
320C23×C23—41no—
321C23×C23—41no—
322C23×C23—41no—
323C23×C23—41no—
324C23×C23—41no—
325C23×C23—41no—
326C23×C23—41no—
327C23×C23—41no—
328C23×C23—41no—
329C23×C23—41no—
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—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×C23C23×C411yescharacteristic
373C23×C23C22×D411yescharacteristic
374C23×C23C22×D411yescharacteristic
375C23×C23C2×#4111yescharacteristic
376C23×C23C2×#4111yescharacteristic
377C23×C23C2×#4111yescharacteristic
378C23×C23C2×#4111yescharacteristic
379C23×C23H(5,𝔽2)11yescharacteristic
380C23×C23H(5,𝔽2)11yescharacteristic
381C23×C23H(5,𝔽2)11yescharacteristic
382C23×C23H(5,𝔽2)11yescharacteristic
383C23×C23H(5,𝔽2)11yescharacteristic
384C23×C23H(5,𝔽2)11yescharacteristic
385C23×C232−1+411yescharacteristic
386C23×C232−1+411yescharacteristic
387D4×C23—416no—
388C2×C4×C23—22no—
389C2×C4×C23—22no—
390C2×C4×C23—22no—
391C2×C4×C23—22no—
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—22no—
426C2×C4×C23—22no—
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×C23C4×D414yes—
478C2×C4×C23C4×D414yes—
479C2×#394C2×C2311yescharacteristic
480C2×#390C2×C2311yescharacteristic
481C2×#389C2×C2311yescharacteristic, complemented
482C2×#388C2×C2311yescharacteristic, complemented
483C2×#388C2×C2311yescharacteristic, complemented
484#1439C2×C2311yescharacteristic, complemented
485#1439C2×C2311yescharacteristic, complemented
486#1439C2×C2311yescharacteristic, complemented
487#1439C2×C2311yescharacteristic, complemented
488#1438C2×C2311yescharacteristic
489#1437C2×C2311yescharacteristic, complemented
490#1437C2×C2311yescharacteristic, complemented
491#1436C2×C2311yescharacteristic, complemented
492#1436C2×C2311yescharacteristic, complemented
493#1436C2×C2311yescharacteristic, complemented
494C22×C23—42no—
495C22×C23—42no—
496C22×C23—42no—
497C22×C23—42no—
498C22×C23—42no—
499C22×C23—42no—
500C22×C23—42no—
501C22×C23—42no—
502C22×C23—42no—
503C22×C23—42no—
504C22×C23—42no—
505C22×C23—42no—
506C22×C23—42no—
507C22×C23—42no—
508C22×C23—81no—
509C22×C23—81no—
510C22×C23—81no—
511C22×C23—81no—
512C22×C23—81no—
513C22×C23—81no—
514C22×C23—81no—
515C22×C23—81no—
516C22×C23—81no—
517C22×C23—81no—
518C22×C23—81no—
519C22×C23—81no—
520C22×C23—81no—
521C22×C23—81no—
522C22×C23—81no—
523C22×C23—81no—
524C22×C23C2×C4×D411yescharacteristic
525C22×C23C2×C4×D411yescharacteristic
526C22×C23C4×#4111yescharacteristic
527C22×C23#51811yescharacteristic
528C22×C23#51811yescharacteristic
529C22×C23#52011yescharacteristic
530C22×C23#52011yescharacteristic
531C22×C23#53411yescharacteristic
532C22×C23#53511yescharacteristic
533C22×C23#53511yescharacteristic
534C22×C23#53711yescharacteristic
535C22×C23#53811yescharacteristic
536C22×C23#53811yescharacteristic
537C22×C23#53811yescharacteristic
538C22×C23#53911yescharacteristic
539C22×C23#54011yescharacteristic
540C22×C23#54011yescharacteristic
541C22×C23#54211yescharacteristic
542C22×C23#54211yescharacteristic
543C22×C23D4211yescharacteristic
544C22×C23#54611yescharacteristic
545C22×C23#54611yescharacteristic
546C22×C23#54711yescharacteristic
547C22×C23#54811yescharacteristic
548C22×C23#54811yescharacteristic
549C22×C23#55011yescharacteristic
550C22×C23#55311yescharacteristic
551C22×C23#55311yescharacteristic
552C22×C23#55511yescharacteristic
553C22×C23#55611yescharacteristic
554C22×C23#55911yescharacteristic
555C22×C23#56011yescharacteristic
556C22×C23#56211yescharacteristic
557C22×C23#56211yescharacteristic
558C22×C23#56311yescharacteristic
559C4×C23—24no—
560C4×C23—24no—
561C4×C23—42no—
562C4×C23—42no—
563C4×C23—42no—
564C4×C23—42no—
565C4×C23—42no—
566C4×C23—42no—
567C4×C23—42no—
568C4×C23—42no—
569C4×C23—42no—
570C4×C23—81no—
571C4×C23—81no—
572C23×D4C22×C2311yescharacteristic
573C22×C4⋊C4C22×C2311yescharacteristic
574C22×C4⋊C4C22×C2311yescharacteristic
575C22×C4⋊C4C22×C2311yescharacteristic
576C22×C4⋊C4C22×C2311yescharacteristic
577C22×C4⋊C4C22×C2311yescharacteristic
578C22×C22⋊C4C22×C2311yescharacteristic
579C22×C22⋊C4C22×C2311yescharacteristic
580C22×C22⋊C4C22×C2311yescharacteristic
581C22×C22⋊C4C22×C2311yescharacteristic
582C22×C22⋊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×C42C22×C2311yescharacteristic
591C22×C42C22×C2311yescharacteristic
592C22×C42C22×C2311yescharacteristic
593#394C4×C2318yescomplemented
594#390—24no—
595#389—24no—
596#388—24no—
597#388—24no—
598C2×#95C22×C2311yescharacteristic
599C2×#95C22×C2311yescharacteristic
600C2×#95C22×C2311yescharacteristic
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×C23—82no—
613C2×C23—82no—
614C2×C23#232111yescharacteristic
615C2×C23#232411yescharacteristic
616C2×C23#233511yescharacteristic
617C2×C23#236111yescharacteristic
618C2×C23#236311yescharacteristic
619C2×C23#236711yescharacteristic
620C2×C23#237611yescharacteristic
621C2×C23#267311yescharacteristic
622C2×C23#267611yescharacteristic
623C2×C23#271011yescharacteristic
624C2×C23#271111yescharacteristic
625C2×C23#272711yescharacteristic
626C2×C23#273111yescharacteristic
627C2×C23#280011yescharacteristic
628C2×C23#280311yescharacteristic
629C25C23×C2311yescharacteristic
630C25C23×C2311yescharacteristic
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—41no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4—41no—
637C22×D4C2×C4×C2314yes—
638C23×C4C23×C2311yescharacteristic
639C23×C4C23×C2311yescharacteristic
640C23×C4C23×C2311yescharacteristic
641C23×C4C23×C2311yescharacteristic
642C23×C4C23×C2311yescharacteristic
643C23×C4C23×C2311yescharacteristic
644C23×C4C23×C2311yescharacteristic
645C23×C4C23×C2311yescharacteristic
646C23×C4C23×C2311yescharacteristic
647C23×C4C23×C2311yescharacteristic
648C23×C4C23×C2311yescharacteristic
649C23×C4C23×C2311yescharacteristic
650C23×C4C23×C2311yescharacteristic
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4C2×C4×C2314yes—
665C2×C4⋊C4D4×C2314yes—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
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—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
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⋊C4C2×C4×C2314yes—
699C2×C22⋊C4C2×C4×C2314yes—
700C2×C22⋊C4C2×C4×C2314yes—
701C2×C22⋊C4C2×C4×C2314yes—
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—41no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42—41no—
710C2×C42—41no—
711#95—22no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—41no—
719#95—41no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95C2×C4×C2314yes—
724#95D4×C2314yescomplemented
725C23#1456311yescharacteristic, direct product factor, Sylow
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
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—
754C24C22×C4×C2312yes—
755C24C22×C4×C2312yes—
756C24C24×C2311yescharacteristic
757C2×D4—28no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
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—21no—
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—21no—
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×C4C22×C4×C2312yes—
841C22×C4C22×C4×C2312yes—
842C22×C4C22×C4×C2312yes—
843C22×C4C22×C4×C2312yes—
844C22×C4C22×C4×C2312yes—
845C22×C4C2×D4×C2312yes—
846C22×C4C2×D4×C2312yes—
847C22×C4C2×D4×C2312yes—
848C22×C4C2×D4×C2312yes—
849C22×C4C2×D4×C2312yes—
850C22×C4C2×D4×C2312yes—
851C22×C4#41×C2312yes—
852C22×C4#41×C2312yes—
853C22×C4#41×C2312yes—
854C22×C4#41×C2312yes—
855C4⋊C4—28no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C42—44no—
873C42—44no—
874C42—44no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
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—
945C23C23×C4×C2311yescharacteristic
946C23C22×D4×C2311yescharacteristic
947C23C22×D4×C2311yescharacteristic
948C23C2×#41×C2311yescharacteristic
949C23C2×#41×C2311yescharacteristic
950C23C2×#41×C2311yescharacteristic
951C23C2×#41×C2311yescharacteristic
952C23C23×H(5,𝔽2)11yescharacteristic
953C23C23×H(5,𝔽2)11yescharacteristic
954C23C23×H(5,𝔽2)11yescharacteristic
955C23C23×H(5,𝔽2)11yescharacteristic
956C23C23×H(5,𝔽2)11yescharacteristic
957C23C23×H(5,𝔽2)11yescharacteristic
958C23C23×2−1+411yescharacteristic
959C23C23×2−1+411yescharacteristic
960D4—416no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
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—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
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×C4C4×D4×C2314yes—
1051C2×C4C4×D4×C2314yes—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22C2×C4×D4×C2311yescharacteristic
1083C22C2×C4×D4×C2311yescharacteristic
1084C22C4×#41×C2311yescharacteristic
1085C22C23×#51811yescharacteristic
1086C22C23×#51811yescharacteristic
1087C22C23×#52011yescharacteristic
1088C22C23×#52011yescharacteristic
1089C22C23×#53411yescharacteristic
1090C22C23×#53511yescharacteristic
1091C22C23×#53511yescharacteristic
1092C22C23×#53711yescharacteristic
1093C22C23×#53811yescharacteristic
1094C22C23×#53811yescharacteristic
1095C22C23×#53811yescharacteristic
1096C22C23×#53911yescharacteristic
1097C22C23×#54011yescharacteristic
1098C22C23×#54011yescharacteristic
1099C22C23×#54211yescharacteristic
1100C22C23×#54211yescharacteristic
1101C22D42×C2311yescharacteristic
1102C22C23×#54611yescharacteristic
1103C22C23×#54611yescharacteristic
1104C22C23×#54711yescharacteristic
1105C22C23×#54811yescharacteristic
1106C22C23×#54811yescharacteristic
1107C22C23×#55011yescharacteristic
1108C22C23×#55311yescharacteristic
1109C22C23×#55311yescharacteristic
1110C22C23×#55511yescharacteristic
1111C22C23×#55611yescharacteristic
1112C22C23×#55911yescharacteristic
1113C22C23×#56011yescharacteristic
1114C22C23×#56211yescharacteristic
1115C22C23×#56211yescharacteristic
1116C22C23×#56311yescharacteristic
1117C4—24no—
1118C4—24no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—81no—
1129C4—81no—
1130C2—82no—
1131C2—82no—
1132C2C23×#232111yescharacteristic
1133C2C23×#232411yescharacteristic
1134C2C23×#233511yescharacteristic
1135C2C23×#236111yescharacteristic
1136C2C23×#236311yescharacteristic
1137C2C23×#236711yescharacteristic
1138C2C23×#237611yescharacteristic
1139C2C23×#267311yescharacteristic
1140C2C23×#267611yescharacteristic
1141C2C23×#271011yescharacteristic
1142C2C23×#271111yescharacteristic
1143C2C23×#272711yescharacteristic
1144C2C23×#273111yescharacteristic
1145C2C23×#280011yescharacteristic
1146C2C23×#280311yescharacteristic
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
3. C2×C23×#389C2semidirect
4. C2×C23×#388C2semidirect
5. C2×C23×#388C2semidirect
6. C23×#1439C2semidirect
7. C23×#1439C2semidirect
8. C23×#1439C2semidirect
9. C23×#1439C2semidirect
11. C23×#1437C2semidirect
12. C23×#1437C2semidirect
13. C23×#1436C2semidirect
14. C23×#1436C2semidirect
15. C23×#1436C2semidirect
37. C23×#394C4semidirect
151. C23×#95D4semidirect
301. #14563C23direct (N × H)
481. C2×#389C2×C23semidirect
482. C2×#388C2×C23semidirect
483. C2×#388C2×C23semidirect
484. #1439C2×C23semidirect
485. #1439C2×C23semidirect
486. #1439C2×C23semidirect
487. #1439C2×C23semidirect
489. #1437C2×C23semidirect
490. #1437C2×C23semidirect
491. #1436C2×C23semidirect
492. #1436C2×C23semidirect
493. #1436C2×C23semidirect
593. #394C4×C23semidirect
724. #95D4×C23semidirect
725. C23#14563direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3942
C2×C23×#3902
C2×C23×#3892
C2×C23×#3882
C23×#14392
C23×#14382
C23×#14372
C23×#14362
#1456323