Finite Group Databasebeta

← C23×#14114 #19161740

Subgroups — C23×#14114 #19161740

Order 5888.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#388C211yesmaximal, characteristic
2C2×C23×#388C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C23C211yesmaximal, characteristic
4C23×#1442C211yesmaximal, characteristic, complemented
5C23×#1441C211yesmaximal, characteristic, complemented
6C23×#1439C211yesmaximal, characteristic
7C23×#1439C211yesmaximal, characteristic
8C23×#1436C211yesmaximal, characteristic, complemented
9C23×#1436C211yesmaximal, characteristic, complemented
10C23×#1436C211yesmaximal, characteristic, complemented
11C23×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×#1434C211yesmaximal, characteristic, complemented
13C23×C22⋊#95C211yesmaximal, characteristic
14C23×C22⋊#95C211yesmaximal, characteristic
15C4×C23×#95C211yesmaximal, characteristic, complemented
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
29C22×C42×C23C2211yescharacteristic
30C22×C42×C23C2211yescharacteristic
31C23×#388—24no—
32C23×#388C418yescomplemented
33C4×C22⋊C4×C23—24no—
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—22no—
60C23×C4×C23—41no—
61C23×C4×C23—41no—
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—22no—
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×C23—41no—
87C2×C4⋊C4×C23C2×C414yescomplemented
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—41no—
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×C23C2×C414yes—
102C2×C22⋊C4×C23C2×C414yes—
103C2×C22⋊C4×C23C2×C414yes—
104C2×C22⋊C4×C23D414yes—
105C2×C22⋊C4×C23Q814yes—
106C2×C42×C23—22no—
107C2×C42×C23—22no—
108C2×C42×C23—22no—
109C2×C42×C23—22no—
110C2×C42×C23—22no—
111C2×C42×C23—22no—
112C2×C42×C23—41no—
113C2×C42×C23—41no—
114C2×C42×C23—41no—
115C2×C42×C23—41no—
116C2×C42×C23—41no—
117C2×C42×C23C2×C414yescomplemented
118C23×#95—22no—
119C23×#95—22no—
120C23×#95—22no—
121C23×#95—22no—
122C23×#95—22no—
123C23×#95—22no—
124C23×#95—22no—
125C23×#95—22no—
126C23×#95—22no—
127C23×#95—22no—
128C23×#95—22no—
129C23×#95—22no—
130C23×#95—22no—
131C23×#95—41no—
132C23×#95—41no—
133C23×#95—41no—
134C23×#95—41no—
135C23×#95—41no—
136C23×#95C2×C414yescomplemented
137C23×#95C2×C414yescomplemented
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×C23—21no—
147C24×C23—21no—
148C24×C23—21no—
149C24×C23—21no—
150C24×C23C22×C412yes—
151C24×C23C2×D412yes—
152C24×C23C2×Q812yes—
153C24×C23C2411yescharacteristic
154C22×C4×C23—21no—
155C22×C4×C23—21no—
156C22×C4×C23—21no—
157C22×C4×C23—21no—
158C22×C4×C23—21no—
159C22×C4×C23—21no—
160C22×C4×C23—21no—
161C22×C4×C23—21no—
162C22×C4×C23—21no—
163C22×C4×C23—21no—
164C22×C4×C23—21no—
165C22×C4×C23—21no—
166C22×C4×C23—28no—
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—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—44no—
236C22×C4×C23—44no—
237C22×C4×C23—44no—
238C22×C4×C23—44no—
239C22×C4×C23—44no—
240C22×C4×C23—44no—
241C22×C4×C23C22×C412yes—
242C22×C4×C23C22×C412yes—
243C22×C4×C23C22×C412yes—
244C22×C4×C23C22×C412yes—
245C22×C4×C23C22×C412yes—
246C22×C4×C23C22×C412yes—
247C22×C4×C23C2×D412yes—
248C22×C4×C23C2×D412yes—
249C22×C4×C23C2×Q812yes—
250C22×C4×C23C2×Q812yes—
251C22×C4×C23#4112yes—
252C22×C4×C23#4112yes—
253C22×C4×C23#4112yes—
254C22×C4×C23#4112yes—
255C22×C4×C23#4112yes—
256C22×C4×C23#4112yes—
257C22×C4×C23#4112yes—
258C22×C4×C23#4112yes—
259C4⋊C4×C23—44no—
260C4⋊C4×C23—44no—
261C4⋊C4×C23—44no—
262C4⋊C4×C23—44no—
263C22⋊C4×C23—28no—
264C22⋊C4×C23—44no—
265C22⋊C4×C23—44no—
266C22⋊C4×C23—44no—
267C22⋊C4×C23—44no—
268C22⋊C4×C23C4⋊C4116yescomplemented
269C42×C23—44no—
270C42×C23—44no—
271C42×C23—44no—
272C42×C23—44no—
273#14114C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
287C23×C23—22no—
288C23×C23—22no—
289C23×C23—22no—
290C23×C23—22no—
291C23×C23—22no—
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—41no—
303C23×C23—41no—
304C23×C23—41no—
305C23×C23—41no—
306C23×C23—41no—
307C23×C23—41no—
308C23×C23C2×C4⋊C414yes—
309C23×C23C23×C411yescharacteristic
310C23×C23C22×D411yescharacteristic
311C23×C23C22×Q811yescharacteristic
312C23×C23C2×#4111yescharacteristic
313C23×C23C2×#4111yescharacteristic
314C23×C23C2×#4111yescharacteristic
315C23×C23C2×#4111yescharacteristic
316C23×C23C2×#4111yescharacteristic
317C23×C23C2×#4111yescharacteristic
318C23×C23C2×#4111yescharacteristic
319C23×C23C2×#4111yescharacteristic
320C23×C23H(5,𝔽2)11yescharacteristic
321C23×C23H(5,𝔽2)11yescharacteristic
322C23×C23H(5,𝔽2)11yescharacteristic
323C23×C23H(5,𝔽2)11yescharacteristic
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—22no—
352C2×C4×C23—22no—
353C2×C4×C23—22no—
354C2×C4×C23—22no—
355C2×C4×C23—22no—
356C2×C4×C23—22no—
357C2×C4×C23—22no—
358C2×C4×C23—22no—
359C2×C4×C23—22no—
360C2×C4×C23—22no—
361C2×C4×C23—22no—
362C2×C4×C23—22no—
363C2×C4×C23—22no—
364C2×C4×C23—22no—
365C2×C4×C23—22no—
366C2×C4×C23—22no—
367C2×C4×C23—22no—
368C2×C4×C23—22no—
369C2×C4×C23—416no—
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×C23—41no—
417C2×C4×C23—41no—
418C2×C4×C23—41no—
419C2×C4×C23—41no—
420C2×C4×C23C2×C4⋊C414yes—
421C2×C4×C23C2×C4⋊C414yes—
422C2×C4×C23#12614yes—
423C2×#388C2×C2311yescharacteristic
424C2×#388C2×C2311yescharacteristic
425C2×C4×C22⋊C4C2×C2311yescharacteristic
426#1442C2×C2311yescharacteristic, complemented
427#1441C2×C2311yescharacteristic, complemented
428#1439C2×C2311yescharacteristic
429#1439C2×C2311yescharacteristic
430#1436C2×C2311yescharacteristic, complemented
431#1436C2×C2311yescharacteristic, complemented
432#1436C2×C2311yescharacteristic, complemented
433C4⋊#95C2×C2311yescharacteristic, complemented
434#1434C2×C2311yescharacteristic, complemented
435C22⋊#95C2×C2311yescharacteristic
436C22⋊#95C2×C2311yescharacteristic
437C4×#95C2×C2311yescharacteristic, complemented
438C22×C23—24no—
439C22×C23—24no—
440C22×C23—24no—
441C22×C23—42no—
442C22×C23—42no—
443C22×C23—42no—
444C22×C23—42no—
445C22×C23—42no—
446C22×C23—42no—
447C22×C23—42no—
448C22×C23—42no—
449C22×C23—42no—
450C22×C23—42no—
451C22×C23—42no—
452C22×C23—42no—
453C22×C23C22×C4⋊C411yescharacteristic
454C22×C23C4×#4111yescharacteristic
455C22×C23C4×#4111yescharacteristic
456C22×C23C4×#4111yescharacteristic
457C22×C23C4×#4111yescharacteristic
458C22×C23#51811yescharacteristic
459C22×C23#51811yescharacteristic
460C22×C23#52511yescharacteristic
461C22×C23#52511yescharacteristic
462C22×C23C2×#12611yescharacteristic
463C22×C23#52911yescharacteristic
464C22×C23#52911yescharacteristic
465C22×C23#52911yescharacteristic
466C22×C23#53311yescharacteristic
467C22×C23#53311yescharacteristic
468C22×C23#53811yescharacteristic
469C22×C23#53811yescharacteristic
470C22×C23#54011yescharacteristic
471C22×C23#54011yescharacteristic
472C22×C23#54611yescharacteristic
473C22×C23#54611yescharacteristic
474C22×C23#54611yescharacteristic
475C22×C23#54611yescharacteristic
476C22×C23#55111yescharacteristic
477C22×C23#55111yescharacteristic
478C22×C23#55111yescharacteristic
479C22×C23#55311yescharacteristic
480C22×C23#55311yescharacteristic
481C22×C23#55411yescharacteristic
482C22×C23#55411yescharacteristic
483C22×C23#55411yescharacteristic
484C22×C23#55411yescharacteristic
485C22×C23#55511yescharacteristic
486C22×C23#55511yescharacteristic
487C22×C23#55911yescharacteristic
488C4×C23—24no—
489C4×C23—24no—
490C4×C23—24no—
491C4×C23—42no—
492C4×C23—42no—
493C4×C23—42no—
494C4×C23—42no—
495C4×C23—42no—
496C4×C23—42no—
497C4×C23—42no—
498C4×C23—42no—
499C4×C23—42no—
500C4×C23—81no—
501C4×C23—81no—
502C24×C4C22×C2311yescharacteristic
503C22×C4⋊C4C22×C2311yescharacteristic
504C22×C4⋊C4C22×C2311yescharacteristic
505C22×C4⋊C4C22×C2311yescharacteristic
506C22×C4⋊C4C22×C2311yescharacteristic
507C22×C22⋊C4C22×C2311yescharacteristic
508C22×C22⋊C4C22×C2311yescharacteristic
509C22×C22⋊C4C22×C2311yescharacteristic
510C22×C22⋊C4C22×C2311yescharacteristic
511C22×C22⋊C4C22×C2311yescharacteristic
512C22×C22⋊C4C22×C2311yescharacteristic
513C22×C42C22×C2311yescharacteristic
514C22×C42C22×C2311yescharacteristic
515C22×C42C22×C2311yescharacteristic
516C22×C42C22×C2311yescharacteristic
517#388—24no—
518#388C4×C2318yescomplemented
519C4×C22⋊C4—24no—
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×#95C22×C2311yescharacteristic
535C2×#95C22×C2311yescharacteristic
536C2×#95C22×C2311yescharacteristic
537C2×#95C22×C2311yescharacteristic
538C2×#95C22×C2311yescharacteristic
539C2×#95C22×C2311yescharacteristic
540C2×C23—44no—
541C2×C23#229611yescharacteristic
542C2×C23C4×#12611yescharacteristic
543C2×C23#233311yescharacteristic
544C2×C23#234911yescharacteristic
545C2×C23#234911yescharacteristic
546C2×C23#237211yescharacteristic
547C2×C23#237411yescharacteristic
548C2×C23#245711yescharacteristic
549C2×C23#245911yescharacteristic
550C2×C23#247611yescharacteristic
551C2×C23#248011yescharacteristic
552C2×C23#249711yescharacteristic
553C2×C23#252211yescharacteristic
554C2×C23#257411yescharacteristic
555C2×C23#258911yescharacteristic
556C25C23×C2311yescharacteristic
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4C23×C2311yescharacteristic
565C23×C4C23×C2311yescharacteristic
566C23×C4C23×C2311yescharacteristic
567C23×C4C23×C2311yescharacteristic
568C23×C4C23×C2311yescharacteristic
569C23×C4C23×C2311yescharacteristic
570C23×C4C23×C2311yescharacteristic
571C23×C4C23×C2311yescharacteristic
572C23×C4C23×C2311yescharacteristic
573C23×C4C23×C2311yescharacteristic
574C23×C4C23×C2311yescharacteristic
575C23×C4C23×C2311yescharacteristic
576C23×C4C23×C2311yescharacteristic
577C23×C4C23×C2311yescharacteristic
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4C2×C4×C2314yescomplemented
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4C2×C4×C2314yes—
604C2×C22⋊C4C2×C4×C2314yes—
605C2×C22⋊C4C2×C4×C2314yes—
606C2×C22⋊C4D4×C2314yes—
607C2×C22⋊C4Q8×C2314yes—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42C2×C4×C2314yescomplemented
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95C2×C4×C2314yescomplemented
639#95C2×C4×C2314yescomplemented
640C23#1411411yescharacteristic, direct product factor, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C2312yes—
654C24C2×D4×C2312yes—
655C24C2×Q8×C2312yes—
656C24C24×C2311yescharacteristic
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—28no—
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—21no—
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—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4C22×C4×C2312yes—
745C22×C4C22×C4×C2312yes—
746C22×C4C22×C4×C2312yes—
747C22×C4C22×C4×C2312yes—
748C22×C4C22×C4×C2312yes—
749C22×C4C22×C4×C2312yes—
750C22×C4C2×D4×C2312yes—
751C22×C4C2×D4×C2312yes—
752C22×C4C2×Q8×C2312yes—
753C22×C4C2×Q8×C2312yes—
754C22×C4#41×C2312yes—
755C22×C4#41×C2312yes—
756C22×C4#41×C2312yes—
757C22×C4#41×C2312yes—
758C22×C4#41×C2312yes—
759C22×C4#41×C2312yes—
760C22×C4#41×C2312yes—
761C22×C4#41×C2312yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4C4⋊C4×C23116yescomplemented
772C42—44no—
773C42—44no—
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C2314yes—
811C23C23×C4×C2311yescharacteristic
812C23C22×D4×C2311yescharacteristic
813C23C22×Q8×C2311yescharacteristic
814C23C2×#41×C2311yescharacteristic
815C23C2×#41×C2311yescharacteristic
816C23C2×#41×C2311yescharacteristic
817C23C2×#41×C2311yescharacteristic
818C23C2×#41×C2311yescharacteristic
819C23C2×#41×C2311yescharacteristic
820C23C2×#41×C2311yescharacteristic
821C23C2×#41×C2311yescharacteristic
822C23C23×H(5,𝔽2)11yescharacteristic
823C23C23×H(5,𝔽2)11yescharacteristic
824C23C23×H(5,𝔽2)11yescharacteristic
825C23C23×H(5,𝔽2)11yescharacteristic
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—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—416no—
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×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4C2×C4⋊C4×C2314yes—
923C2×C4C2×C4⋊C4×C2314yes—
924C2×C4C23×#12614yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C2311yescharacteristic
941C22C4×#41×C2311yescharacteristic
942C22C4×#41×C2311yescharacteristic
943C22C4×#41×C2311yescharacteristic
944C22C4×#41×C2311yescharacteristic
945C22C23×#51811yescharacteristic
946C22C23×#51811yescharacteristic
947C22C23×#52511yescharacteristic
948C22C23×#52511yescharacteristic
949C22C2×C23×#12611yescharacteristic
950C22C23×#52911yescharacteristic
951C22C23×#52911yescharacteristic
952C22C23×#52911yescharacteristic
953C22C23×#53311yescharacteristic
954C22C23×#53311yescharacteristic
955C22C23×#53811yescharacteristic
956C22C23×#53811yescharacteristic
957C22C23×#54011yescharacteristic
958C22C23×#54011yescharacteristic
959C22C23×#54611yescharacteristic
960C22C23×#54611yescharacteristic
961C22C23×#54611yescharacteristic
962C22C23×#54611yescharacteristic
963C22C23×#55111yescharacteristic
964C22C23×#55111yescharacteristic
965C22C23×#55111yescharacteristic
966C22C23×#55311yescharacteristic
967C22C23×#55311yescharacteristic
968C22C23×#55411yescharacteristic
969C22C23×#55411yescharacteristic
970C22C23×#55411yescharacteristic
971C22C23×#55411yescharacteristic
972C22C23×#55511yescharacteristic
973C22C23×#55511yescharacteristic
974C22C23×#55911yescharacteristic
975C4—24no—
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C23×#229611yescharacteristic
991C2C4×C23×#12611yescharacteristic
992C2C23×#233311yescharacteristic
993C2C23×#234911yescharacteristic
994C2C23×#234911yescharacteristic
995C2C23×#237211yescharacteristic
996C2C23×#237411yescharacteristic
997C2C23×#245711yescharacteristic
998C2C23×#245911yescharacteristic
999C2C23×#247611yescharacteristic
1000C2C23×#248011yescharacteristic
1001C2C23×#249711yescharacteristic
1002C2C23×#252211yescharacteristic
1003C2C23×#257411yescharacteristic
1004C2C23×#258911yescharacteristic
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
4. C23×#1442C2semidirect
5. C23×#1441C2semidirect
8. C23×#1436C2semidirect
9. C23×#1436C2semidirect
10. C23×#1436C2semidirect
11. C23×C4⋊#95C2semidirect
12. C23×#1434C2semidirect
15. C4×C23×#95C2semidirect
32. C23×#388C4semidirect
87. C2×C4⋊C4×C23C2×C4semidirect
117. C2×C42×C23C2×C4semidirect
136. C23×#95C2×C4semidirect
137. C23×#95C2×C4semidirect
268. C22⋊C4×C23C4⋊C4semidirect
273. #14114C23direct (N × H)
426. #1442C2×C23semidirect
427. #1441C2×C23semidirect
430. #1436C2×C23semidirect
431. #1436C2×C23semidirect
432. #1436C2×C23semidirect
433. C4⋊#95C2×C23semidirect
434. #1434C2×C23semidirect
437. C4×#95C2×C23semidirect
518. #388C4×C23semidirect
589. C2×C4⋊C4C2×C4×C23semidirect
619. C2×C42C2×C4×C23semidirect
638. #95C2×C4×C23semidirect
639. #95C2×C4×C23semidirect
640. C23#14114direct (N × H)
771. C22⋊C4C4⋊C4×C23semidirect

Maximal subgroups

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

subgroupindex
C2×C23×#3882
C2×C4×C22⋊C4×C232
C23×#14422
C23×#14412
C23×#14392
C23×#14362
C23×C4⋊#952
C23×#14342
C23×C22⋊#952
C4×C23×#952
#1411423