Finite Group Databasebeta

← C23×#14519 #19162145

Subgroups — C23×#14519 #19162145

Order 5888.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#392C211yesmaximal, characteristic
2C2×C23×#390C211yesmaximal, characteristic, complemented
3C2×C23×#386C211yesmaximal, characteristic, complemented
4C2×C23×#386C211yesmaximal, characteristic, complemented
5C2×C23×#386C211yesmaximal, characteristic, complemented
6C2×C23×#386C211yesmaximal, characteristic, complemented
7C2×C23×#385C211yesmaximal, characteristic, complemented
8C23×#1442C211yesmaximal, characteristic, complemented
9C23×#1440C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1438C211yesmaximal, characteristic, complemented
13C23×#1437C211yesmaximal, characteristic, complemented
14C23×#1434C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C23×D4×C23C2211yescharacteristic
18C23×D4×C23C2211yescharacteristic
19C24×C4×C23C2211yescharacteristic
20C24×C4×C23C2211yescharacteristic
21C22×C4⋊C4×C23C2211yescharacteristic
22C22×C4⋊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×C22⋊C4×C23C2211yescharacteristic
35C22×C22⋊C4×C23C2211yescharacteristic
36C22×C42×C23C2211yescharacteristic
37C23×#392C418yescomplemented
38C23×#390—24no—
39C23×#386—24no—
40C23×#386—24no—
41C23×#386—24no—
42C23×#386—24no—
43C23×#385—24no—
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
56C2×C23×#95C2211yescharacteristic
57C2×C23×#95C2211yescharacteristic
58C25×C23C2311yescharacteristic
59C25×C23C2311yescharacteristic
60C25×C23C2311yescharacteristic
61C22×D4×C23—22no—
62C22×D4×C23—22no—
63C22×D4×C23—22no—
64C22×D4×C23—22no—
65C22×D4×C23—22no—
66C22×D4×C23—22no—
67C22×D4×C23—22no—
68C22×D4×C23—22no—
69C22×D4×C23—22no—
70C22×D4×C23—22no—
71C22×D4×C23—41no—
72C22×D4×C23—41no—
73C22×D4×C23—41no—
74C22×D4×C23—41no—
75C22×D4×C23—41no—
76C22×D4×C23—41no—
77C22×D4×C23—41no—
78C22×D4×C23—41no—
79C22×D4×C23C2×C414yes—
80C22×D4×C23C2×C414yescomplemented
81C22×D4×C23C2×C414yescomplemented
82C23×C4×C23—22no—
83C23×C4×C23—22no—
84C23×C4×C23—22no—
85C23×C4×C23—22no—
86C23×C4×C23—22no—
87C23×C4×C23—22no—
88C23×C4×C23—41no—
89C23×C4×C23—41no—
90C23×C4×C23—41no—
91C23×C4×C23—41no—
92C23×C4×C23—41no—
93C23×C4×C23—41no—
94C23×C4×C23—41no—
95C23×C4×C23—41no—
96C23×C4×C23C2311yescharacteristic
97C23×C4×C23C2311yescharacteristic
98C23×C4×C23C2311yescharacteristic
99C23×C4×C23C2311yescharacteristic
100C23×C4×C23C2311yescharacteristic
101C23×C4×C23C2311yescharacteristic
102C23×C4×C23C2311yescharacteristic
103C23×C4×C23C2311yescharacteristic
104C23×C4×C23C2311yescharacteristic
105C23×C4×C23C2311yescharacteristic
106C23×C4×C23C2311yescharacteristic
107C23×C4×C23C2311yescharacteristic
108C2×C4⋊C4×C23—22no—
109C2×C4⋊C4×C23—22no—
110C2×C4⋊C4×C23—22no—
111C2×C4⋊C4×C23—41no—
112C2×C4⋊C4×C23—41no—
113C2×C4⋊C4×C23—41no—
114C2×C22⋊C4×C23—22no—
115C2×C22⋊C4×C23—22no—
116C2×C22⋊C4×C23—22no—
117C2×C22⋊C4×C23—22no—
118C2×C22⋊C4×C23—22no—
119C2×C22⋊C4×C23—22no—
120C2×C22⋊C4×C23—22no—
121C2×C22⋊C4×C23—22no—
122C2×C22⋊C4×C23—22no—
123C2×C22⋊C4×C23—22no—
124C2×C22⋊C4×C23—22no—
125C2×C22⋊C4×C23—22no—
126C2×C22⋊C4×C23—22no—
127C2×C22⋊C4×C23—22no—
128C2×C22⋊C4×C23—22no—
129C2×C22⋊C4×C23—22no—
130C2×C22⋊C4×C23—41no—
131C2×C22⋊C4×C23—41no—
132C2×C22⋊C4×C23—41no—
133C2×C22⋊C4×C23—41no—
134C2×C22⋊C4×C23—41no—
135C2×C22⋊C4×C23—41no—
136C2×C22⋊C4×C23—41no—
137C2×C22⋊C4×C23—41no—
138C2×C22⋊C4×C23—41no—
139C2×C22⋊C4×C23—41no—
140C2×C22⋊C4×C23—41no—
141C2×C22⋊C4×C23—41no—
142C2×C22⋊C4×C23—41no—
143C2×C22⋊C4×C23—41no—
144C2×C22⋊C4×C23—41no—
145C2×C22⋊C4×C23—41no—
146C2×C22⋊C4×C23—41no—
147C2×C22⋊C4×C23—41no—
148C2×C22⋊C4×C23C2×C414yescomplemented
149C2×C22⋊C4×C23C2×C414yescomplemented
150C2×C22⋊C4×C23C2×C414yescomplemented
151C2×C22⋊C4×C23D414yescomplemented
152C2×C22⋊C4×C23D414yescomplemented
153C2×C42×C23—22no—
154C2×C42×C23—22no—
155C2×C42×C23—41no—
156C23×#95—22no—
157C23×#95—22no—
158C23×#95—22no—
159C23×#95—22no—
160C23×#95—22no—
161C23×#95—22no—
162C23×#95—22no—
163C23×#95—22no—
164C23×#95—41no—
165C23×#95—41no—
166C23×#95—41no—
167C23×#95—41no—
168C23×#95C2×C414yescomplemented
169C23×#95D414yescomplemented
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×C23—21no—
181C24×C23—21no—
182C24×C23—21no—
183C24×C23—21no—
184C24×C23—21no—
185C24×C23—21no—
186C24×C23—21no—
187C24×C23—21no—
188C24×C23—21no—
189C24×C23—21no—
190C24×C23—21no—
191C24×C23—21no—
192C24×C23—21no—
193C24×C23—21no—
194C24×C23—21no—
195C24×C23—21no—
196C24×C23—21no—
197C24×C23—21no—
198C24×C23—21no—
199C24×C23—21no—
200C24×C23—21no—
201C24×C23—21no—
202C24×C23—21no—
203C24×C23—21no—
204C24×C23—21no—
205C24×C23—21no—
206C24×C23—21no—
207C24×C23—21no—
208C24×C23C22×C412yes—
209C24×C23C22×C412yes—
210C24×C23C22×C412yes—
211C24×C23C2×D412yes—
212C24×C23C2×D412yes—
213C24×C23#4112yes—
214C24×C23#4112yes—
215C24×C23C2411yescharacteristic
216C2×D4×C23—28no—
217C2×D4×C23—28no—
218C2×D4×C23—28no—
219C2×D4×C23—28no—
220C2×D4×C23—28no—
221C2×D4×C23—44no—
222C2×D4×C23—44no—
223C2×D4×C23—44no—
224C2×D4×C23—44no—
225C2×D4×C23—44no—
226C2×D4×C23—44no—
227C2×D4×C23—44no—
228C2×D4×C23—44no—
229C2×D4×C23—44no—
230C2×D4×C23—44no—
231C2×D4×C23—44no—
232C2×D4×C23—44no—
233C2×D4×C23—44no—
234C2×D4×C23—44no—
235C2×D4×C23—44no—
236C2×D4×C23—44no—
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×C23—21no—
267C22×C4×C23—21no—
268C22×C4×C23—21no—
269C22×C4×C23—21no—
270C22×C4×C23—21no—
271C22×C4×C23—21no—
272C22×C4×C23—21no—
273C22×C4×C23—21no—
274C22×C4×C23—21no—
275C22×C4×C23—21no—
276C22×C4×C23—21no—
277C22×C4×C23—21no—
278C22×C4×C23—21no—
279C22×C4×C23—21no—
280C22×C4×C23—21no—
281C22×C4×C23—21no—
282C22×C4×C23—21no—
283C22×C4×C23—21no—
284C22×C4×C23—21no—
285C22×C4×C23—21no—
286C22×C4×C23—21no—
287C22×C4×C23—21no—
288C22×C4×C23—21no—
289C22×C4×C23—21no—
290C22×C4×C23—21no—
291C22×C4×C23—21no—
292C22×C4×C23—21no—
293C22×C4×C23—21no—
294C22×C4×C23—21no—
295C22×C4×C23—21no—
296C22×C4×C23—21no—
297C22×C4×C23—21no—
298C22×C4×C23—21no—
299C22×C4×C23—21no—
300C22×C4×C23—21no—
301C22×C4×C23—21no—
302C22×C4×C23—21no—
303C22×C4×C23—21no—
304C22×C4×C23—21no—
305C22×C4×C23—21no—
306C22×C4×C23—21no—
307C22×C4×C23—21no—
308C22×C4×C23—21no—
309C22×C4×C23—44no—
310C22×C4×C23—44no—
311C22×C4×C23—44no—
312C22×C4×C23—44no—
313C22×C4×C23—44no—
314C22×C4×C23—44no—
315C22×C4×C23—44no—
316C22×C4×C23—44no—
317C22×C4×C23—44no—
318C22×C4×C23—44no—
319C22×C4×C23—44no—
320C22×C4×C23—44no—
321C22×C4×C23—44no—
322C22×C4×C23—44no—
323C22×C4×C23C22×C412yes—
324C22×C4×C23C22×C412yes—
325C22×C4×C23C22×C412yes—
326C22×C4×C23C22×C412yes—
327C22×C4×C23C2×D412yes—
328C22×C4×C23C2×D412yes—
329C22×C4×C23C2×D412yes—
330C22×C4×C23C2×D412yes—
331C22×C4×C23C2×D412yes—
332C22×C4×C23C2×D412yes—
333C22×C4×C23C2×D412yes—
334C22×C4×C23#4112yes—
335C4⋊C4×C23—44no—
336C4⋊C4×C23—44no—
337C22⋊C4×C23—28no—
338C22⋊C4×C23—44no—
339C22⋊C4×C23—44no—
340C22⋊C4×C23—44no—
341C22⋊C4×C23—44no—
342C22⋊C4×C23—44no—
343C22⋊C4×C23—44no—
344C22⋊C4×C23—44no—
345C22⋊C4×C23—44no—
346C22⋊C4×C23—44no—
347C22⋊C4×C23—44no—
348C22⋊C4×C23—44no—
349C22⋊C4×C23—44no—
350C42×C23—44no—
351#14519C2311yesmaximal, characteristic, direct product factor, Sylow
352C23×C23—22no—
353C23×C23—22no—
354C23×C23—22no—
355C23×C23—22no—
356C23×C23—22no—
357C23×C23—22no—
358C23×C23—22no—
359C23×C23—22no—
360C23×C23—22no—
361C23×C23—22no—
362C23×C23—22no—
363C23×C23—22no—
364C23×C23—22no—
365C23×C23—22no—
366C23×C23—22no—
367C23×C23—22no—
368C23×C23—22no—
369C23×C23—22no—
370C23×C23—22no—
371C23×C23—22no—
372C23×C23—22no—
373C23×C23—22no—
374C23×C23—22no—
375C23×C23—22no—
376C23×C23—22no—
377C23×C23—22no—
378C23×C23—22no—
379C23×C23—22no—
380C23×C23—22no—
381C23×C23—22no—
382C23×C23—22no—
383C23×C23—22no—
384C23×C23—22no—
385C23×C23—22no—
386C23×C23—22no—
387C23×C23—22no—
388C23×C23—22no—
389C23×C23—22no—
390C23×C23—22no—
391C23×C23—22no—
392C23×C23—22no—
393C23×C23—22no—
394C23×C23—22no—
395C23×C23—41no—
396C23×C23—41no—
397C23×C23—41no—
398C23×C23—41no—
399C23×C23—41no—
400C23×C23—41no—
401C23×C23—41no—
402C23×C23—41no—
403C23×C23—41no—
404C23×C23—41no—
405C23×C23—41no—
406C23×C23—41no—
407C23×C23—41no—
408C23×C23—41no—
409C23×C23—41no—
410C23×C23—41no—
411C23×C23—41no—
412C23×C23—41no—
413C23×C23—41no—
414C23×C23—41no—
415C23×C23—41no—
416C23×C23—41no—
417C23×C23—41no—
418C23×C23—41no—
419C23×C23—41no—
420C23×C23—41no—
421C23×C23—41no—
422C23×C23—41no—
423C23×C23—41no—
424C23×C23—41no—
425C23×C23—41no—
426C23×C23—41no—
427C23×C23—41no—
428C23×C23—41no—
429C23×C23—41no—
430C23×C23—41no—
431C23×C23—41no—
432C23×C23—41no—
433C23×C23—41no—
434C23×C23—41no—
435C23×C23—41no—
436C23×C23—41no—
437C23×C23—41no—
438C23×C23—41no—
439C23×C23—41no—
440C23×C23—41no—
441C23×C23—41no—
442C23×C23—41no—
443C23×C23—41no—
444C23×C23—41no—
445C23×C23—41no—
446C23×C23—41no—
447C23×C23—41no—
448C23×C23—41no—
449C23×C23—41no—
450C23×C23—41no—
451C23×C23—41no—
452C23×C23—41no—
453C23×C23—41no—
454C23×C23—41no—
455C23×C23C4×D414yes—
456C23×C23C4×D414yes—
457C23×C23C23×C411yescharacteristic
458C23×C23C22×D411yescharacteristic
459C23×C23C22×D411yescharacteristic
460C23×C23C22×D411yescharacteristic
461C23×C23C2×#4111yescharacteristic
462C23×C23C2×#4111yescharacteristic
463C23×C23C2×#4111yescharacteristic
464C23×C23H(5,𝔽2)11yescharacteristic
465C23×C23H(5,𝔽2)11yescharacteristic
466C23×C23H(5,𝔽2)11yescharacteristic
467C23×C23H(5,𝔽2)11yescharacteristic
468C23×C23H(5,𝔽2)11yescharacteristic
469C23×C23H(5,𝔽2)11yescharacteristic
470C23×C23H(5,𝔽2)11yescharacteristic
471C23×C232−1+411yescharacteristic
472D4×C23—416no—
473D4×C23—416no—
474D4×C23—416no—
475C2×C4×C23—22no—
476C2×C4×C23—22no—
477C2×C4×C23—22no—
478C2×C4×C23—22no—
479C2×C4×C23—22no—
480C2×C4×C23—22no—
481C2×C4×C23—22no—
482C2×C4×C23—22no—
483C2×C4×C23—22no—
484C2×C4×C23—22no—
485C2×C4×C23—22no—
486C2×C4×C23—22no—
487C2×C4×C23—22no—
488C2×C4×C23—22no—
489C2×C4×C23—22no—
490C2×C4×C23—22no—
491C2×C4×C23—22no—
492C2×C4×C23—22no—
493C2×C4×C23—22no—
494C2×C4×C23—22no—
495C2×C4×C23—22no—
496C2×C4×C23—22no—
497C2×C4×C23—22no—
498C2×C4×C23—22no—
499C2×C4×C23—22no—
500C2×C4×C23—22no—
501C2×C4×C23—22no—
502C2×C4×C23—22no—
503C2×C4×C23—22no—
504C2×C4×C23—22no—
505C2×C4×C23—22no—
506C2×C4×C23—22no—
507C2×C4×C23—22no—
508C2×C4×C23—416no—
509C2×C4×C23—416no—
510C2×C4×C23—41no—
511C2×C4×C23—41no—
512C2×C4×C23—41no—
513C2×C4×C23—41no—
514C2×C4×C23—41no—
515C2×C4×C23—41no—
516C2×C4×C23—41no—
517C2×C4×C23—41no—
518C2×C4×C23—41no—
519C2×C4×C23—41no—
520C2×C4×C23—41no—
521C2×C4×C23—41no—
522C2×C4×C23—41no—
523C2×C4×C23—41no—
524C2×C4×C23—41no—
525C2×C4×C23—41no—
526C2×C4×C23—41no—
527C2×C4×C23—41no—
528C2×C4×C23—41no—
529C2×C4×C23—41no—
530C2×C4×C23—41no—
531C2×C4×C23—41no—
532C2×C4×C23—41no—
533C2×C4×C23—41no—
534C2×C4×C23—41no—
535C2×C4×C23—41no—
536C2×C4×C23—41no—
537C2×C4×C23—41no—
538C2×C4×C23—41no—
539C2×C4×C23—41no—
540C2×C4×C23—41no—
541C2×C4×C23—41no—
542C2×C4×C23—41no—
543C2×C4×C23—41no—
544C2×C4×C23—41no—
545C2×C4×C23—41no—
546C2×C4×C23—41no—
547C2×C4×C23—41no—
548C2×C4×C23—41no—
549C2×C4×C23—41no—
550C2×C4×C23—41no—
551C2×C4×C23—41no—
552C2×C4×C23—41no—
553C2×C4×C23—41no—
554C2×C4×C23—41no—
555C2×C4×C23—41no—
556C2×C4×C23—41no—
557C2×C4×C23—41no—
558C2×C4×C23—41no—
559C2×C4×C23—41no—
560C2×C4×C23C4×D414yes—
561C2×#392C2×C2311yescharacteristic
562C2×#390C2×C2311yescharacteristic, complemented
563C2×#386C2×C2311yescharacteristic, complemented
564C2×#386C2×C2311yescharacteristic, complemented
565C2×#386C2×C2311yescharacteristic, complemented
566C2×#386C2×C2311yescharacteristic, complemented
567C2×#385C2×C2311yescharacteristic, complemented
568#1442C2×C2311yescharacteristic, complemented
569#1440C2×C2311yescharacteristic, complemented
570#1439C2×C2311yescharacteristic, complemented
571#1439C2×C2311yescharacteristic, complemented
572#1438C2×C2311yescharacteristic, complemented
573#1437C2×C2311yescharacteristic, complemented
574#1434C2×C2311yescharacteristic, complemented
575C22⋊#95C2×C2311yescharacteristic, complemented
576C22×C23—24no—
577C22×C23—24no—
578C22×C23—24no—
579C22×C23—24no—
580C22×C23—24no—
581C22×C23—24no—
582C22×C23—42no—
583C22×C23—42no—
584C22×C23—42no—
585C22×C23—42no—
586C22×C23—42no—
587C22×C23—42no—
588C22×C23—42no—
589C22×C23—42no—
590C22×C23—42no—
591C22×C23—42no—
592C22×C23—42no—
593C22×C23—42no—
594C22×C23—42no—
595C22×C23—42no—
596C22×C23—42no—
597C22×C23—42no—
598C22×C23—42no—
599C22×C23—42no—
600C22×C23—42no—
601C22×C23—42no—
602C22×C23—42no—
603C22×C23—42no—
604C22×C23—42no—
605C22×C23—42no—
606C22×C23—42no—
607C22×C23—42no—
608C22×C23—42no—
609C22×C23—42no—
610C22×C23—42no—
611C22×C23—42no—
612C22×C23—42no—
613C22×C23—81no—
614C22×C23—81no—
615C22×C23—81no—
616C22×C23—81no—
617C22×C23—81no—
618C22×C23—81no—
619C22×C23—81no—
620C22×C23—81no—
621C22×C23C2×C4×D411yescharacteristic
622C22×C23C2×C4×D411yescharacteristic
623C22×C23C2×C4×D411yescharacteristic
624C22×C23#51811yescharacteristic
625C22×C23#51811yescharacteristic
626C22×C23#51811yescharacteristic
627C22×C23#52011yescharacteristic
628C22×C23#53411yescharacteristic
629C22×C23#53411yescharacteristic
630C22×C23#53511yescharacteristic
631C22×C23#53511yescharacteristic
632C22×C23#53511yescharacteristic
633C22×C23#53711yescharacteristic
634C22×C23#53811yescharacteristic
635C22×C23#53811yescharacteristic
636C22×C23#53811yescharacteristic
637C22×C23#53911yescharacteristic
638C22×C23#54011yescharacteristic
639C22×C23#54011yescharacteristic
640C22×C23D4211yescharacteristic
641C22×C23D4211yescharacteristic
642C22×C23D4211yescharacteristic
643C22×C23#54611yescharacteristic
644C22×C23#54611yescharacteristic
645C22×C23#54611yescharacteristic
646C22×C23#54611yescharacteristic
647C22×C23#54711yescharacteristic
648C22×C23#54811yescharacteristic
649C22×C23#55111yescharacteristic
650C22×C23#55111yescharacteristic
651C22×C23#55311yescharacteristic
652C22×C23#56011yescharacteristic
653C22×C23#56011yescharacteristic
654C22×C23#56211yescharacteristic
655C22×C23#56211yescharacteristic
656C4×C23—24no—
657C4×C23—42no—
658C4×C23—42no—
659C4×C23—42no—
660C4×C23—42no—
661C4×C23—42no—
662C4×C23—42no—
663C4×C23—42no—
664C4×C23—42no—
665C4×C23—42no—
666C4×C23—81no—
667C4×C23—81no—
668C23×D4C22×C2311yescharacteristic
669C23×D4C22×C2311yescharacteristic
670C23×D4C22×C2311yescharacteristic
671C24×C4C22×C2311yescharacteristic
672C24×C4C22×C2311yescharacteristic
673C22×C4⋊C4C22×C2311yescharacteristic
674C22×C4⋊C4C22×C2311yescharacteristic
675C22×C22⋊C4C22×C2311yescharacteristic
676C22×C22⋊C4C22×C2311yescharacteristic
677C22×C22⋊C4C22×C2311yescharacteristic
678C22×C22⋊C4C22×C2311yescharacteristic
679C22×C22⋊C4C22×C2311yescharacteristic
680C22×C22⋊C4C22×C2311yescharacteristic
681C22×C22⋊C4C22×C2311yescharacteristic
682C22×C22⋊C4C22×C2311yescharacteristic
683C22×C22⋊C4C22×C2311yescharacteristic
684C22×C22⋊C4C22×C2311yescharacteristic
685C22×C22⋊C4C22×C2311yescharacteristic
686C22×C22⋊C4C22×C2311yescharacteristic
687C22×C22⋊C4C22×C2311yescharacteristic
688C22×C42C22×C2311yescharacteristic
689#392C4×C2318yescomplemented
690#390—24no—
691#386—24no—
692#386—24no—
693#386—24no—
694#386—24no—
695#385—24no—
696C2×#95C22×C2311yescharacteristic
697C2×#95C22×C2311yescharacteristic
698C2×#95C22×C2311yescharacteristic
699C2×#95C22×C2311yescharacteristic
700C2×#95C22×C2311yescharacteristic
701C2×#95C22×C2311yescharacteristic
702C2×#95C22×C2311yescharacteristic
703C2×#95C22×C2311yescharacteristic
704C2×#95C22×C2311yescharacteristic
705C2×#95C22×C2311yescharacteristic
706C2×#95C22×C2311yescharacteristic
707C2×#95C22×C2311yescharacteristic
708C2×#95C22×C2311yescharacteristic
709C2×#95C22×C2311yescharacteristic
710C2×C23—44no—
711C2×C23—44no—
712C2×C23—82no—
713C2×C23#232111yescharacteristic
714C2×C23#232511yescharacteristic
715C2×C23#232811yescharacteristic
716C2×C23#235811yescharacteristic
717C2×C23#235811yescharacteristic
718C2×C23#236111yescharacteristic
719C2×C23#237711yescharacteristic
720C2×C23#266911yescharacteristic
721C2×C23#267111yescharacteristic
722C2×C23#267611yescharacteristic
723C2×C23#267811yescharacteristic
724C2×C23#268811yescharacteristic
725C2×C23#269611yescharacteristic
726C2×C23#270611yescharacteristic
727C2×C23#274911yescharacteristic
728C25C23×C2311yescharacteristic
729C25C23×C2311yescharacteristic
730C25C23×C2311yescharacteristic
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4C2×C4×C2314yes—
750C22×D4C2×C4×C2314yescomplemented
751C22×D4C2×C4×C2314yescomplemented
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—41no—
759C23×C4—41no—
760C23×C4—41no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4C23×C2311yescharacteristic
767C23×C4C23×C2311yescharacteristic
768C23×C4C23×C2311yescharacteristic
769C23×C4C23×C2311yescharacteristic
770C23×C4C23×C2311yescharacteristic
771C23×C4C23×C2311yescharacteristic
772C23×C4C23×C2311yescharacteristic
773C23×C4C23×C2311yescharacteristic
774C23×C4C23×C2311yescharacteristic
775C23×C4C23×C2311yescharacteristic
776C23×C4C23×C2311yescharacteristic
777C23×C4C23×C2311yescharacteristic
778C2×C4⋊C4—22no—
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—41no—
782C2×C4⋊C4—41no—
783C2×C4⋊C4—41no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4C2×C4×C2314yescomplemented
819C2×C22⋊C4C2×C4×C2314yescomplemented
820C2×C22⋊C4C2×C4×C2314yescomplemented
821C2×C22⋊C4D4×C2314yescomplemented
822C2×C22⋊C4D4×C2314yescomplemented
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—41no—
835#95—41no—
836#95—41no—
837#95—41no—
838#95C2×C4×C2314yescomplemented
839#95D4×C2314yescomplemented
840C23#1451911yescharacteristic, direct product factor, Sylow
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24C22×C4×C2312yes—
880C24C22×C4×C2312yes—
881C24C22×C4×C2312yes—
882C24C2×D4×C2312yes—
883C24C2×D4×C2312yes—
884C24#41×C2312yes—
885C24#41×C2312yes—
886C24C24×C2311yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4C22×C4×C2312yes—
995C22×C4C22×C4×C2312yes—
996C22×C4C22×C4×C2312yes—
997C22×C4C22×C4×C2312yes—
998C22×C4C2×D4×C2312yes—
999C22×C4C2×D4×C2312yes—
1000C22×C4C2×D4×C2312yes—
1001C22×C4C2×D4×C2312yes—
1002C22×C4C2×D4×C2312yes—
1003C22×C4C2×D4×C2312yes—
1004C22×C4C2×D4×C2312yes—
1005C22×C4#41×C2312yes—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C42—44no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23C4×D4×C2314yes—
1126C23C4×D4×C2314yes—
1127C23C23×C4×C2311yescharacteristic
1128C23C22×D4×C2311yescharacteristic
1129C23C22×D4×C2311yescharacteristic
1130C23C22×D4×C2311yescharacteristic
1131C23C2×#41×C2311yescharacteristic
1132C23C2×#41×C2311yescharacteristic
1133C23C2×#41×C2311yescharacteristic
1134C23C23×H(5,𝔽2)11yescharacteristic
1135C23C23×H(5,𝔽2)11yescharacteristic
1136C23C23×H(5,𝔽2)11yescharacteristic
1137C23C23×H(5,𝔽2)11yescharacteristic
1138C23C23×H(5,𝔽2)11yescharacteristic
1139C23C23×H(5,𝔽2)11yescharacteristic
1140C23C23×H(5,𝔽2)11yescharacteristic
1141C23C23×2−1+411yescharacteristic
1142D4—416no—
1143D4—416no—
1144D4—416no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—416no—
1179C2×C4—416no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4C4×D4×C2314yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×C4×D4×C2311yescharacteristic
1277C22C2×C4×D4×C2311yescharacteristic
1278C22C2×C4×D4×C2311yescharacteristic
1279C22C23×#51811yescharacteristic
1280C22C23×#51811yescharacteristic
1281C22C23×#51811yescharacteristic
1282C22C23×#52011yescharacteristic
1283C22C23×#53411yescharacteristic
1284C22C23×#53411yescharacteristic
1285C22C23×#53511yescharacteristic
1286C22C23×#53511yescharacteristic
1287C22C23×#53511yescharacteristic
1288C22C23×#53711yescharacteristic
1289C22C23×#53811yescharacteristic
1290C22C23×#53811yescharacteristic
1291C22C23×#53811yescharacteristic
1292C22C23×#53911yescharacteristic
1293C22C23×#54011yescharacteristic
1294C22C23×#54011yescharacteristic
1295C22D42×C2311yescharacteristic
1296C22D42×C2311yescharacteristic
1297C22D42×C2311yescharacteristic
1298C22C23×#54611yescharacteristic
1299C22C23×#54611yescharacteristic
1300C22C23×#54611yescharacteristic
1301C22C23×#54611yescharacteristic
1302C22C23×#54711yescharacteristic
1303C22C23×#54811yescharacteristic
1304C22C23×#55111yescharacteristic
1305C22C23×#55111yescharacteristic
1306C22C23×#55311yescharacteristic
1307C22C23×#56011yescharacteristic
1308C22C23×#56011yescharacteristic
1309C22C23×#56211yescharacteristic
1310C22C23×#56211yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2C23×#232111yescharacteristic
1327C2C23×#232511yescharacteristic
1328C2C23×#232811yescharacteristic
1329C2C23×#235811yescharacteristic
1330C2C23×#235811yescharacteristic
1331C2C23×#236111yescharacteristic
1332C2C23×#237711yescharacteristic
1333C2C23×#266911yescharacteristic
1334C2C23×#267111yescharacteristic
1335C2C23×#267611yescharacteristic
1336C2C23×#267811yescharacteristic
1337C2C23×#268811yescharacteristic
1338C2C23×#269611yescharacteristic
1339C2C23×#270611yescharacteristic
1340C2C23×#274911yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC2×C23×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C23×#390C2semidirect
3. C2×C23×#386C2semidirect
4. C2×C23×#386C2semidirect
5. C2×C23×#386C2semidirect
6. C2×C23×#386C2semidirect
7. C2×C23×#385C2semidirect
8. C23×#1442C2semidirect
9. C23×#1440C2semidirect
10. C23×#1439C2semidirect
11. C23×#1439C2semidirect
12. C23×#1438C2semidirect
13. C23×#1437C2semidirect
14. C23×#1434C2semidirect
15. C23×C22⋊#95C2semidirect
37. C23×#392C4semidirect
80. C22×D4×C23C2×C4semidirect
81. C22×D4×C23C2×C4semidirect
148. C2×C22⋊C4×C23C2×C4semidirect
149. C2×C22⋊C4×C23C2×C4semidirect
150. C2×C22⋊C4×C23C2×C4semidirect
151. C2×C22⋊C4×C23D4semidirect
152. C2×C22⋊C4×C23D4semidirect
168. C23×#95C2×C4semidirect
169. C23×#95D4semidirect
351. #14519C23direct (N × H)
562. C2×#390C2×C23semidirect
563. C2×#386C2×C23semidirect
564. C2×#386C2×C23semidirect
565. C2×#386C2×C23semidirect
566. C2×#386C2×C23semidirect
567. C2×#385C2×C23semidirect
568. #1442C2×C23semidirect
569. #1440C2×C23semidirect
570. #1439C2×C23semidirect
571. #1439C2×C23semidirect
572. #1438C2×C23semidirect
573. #1437C2×C23semidirect
574. #1434C2×C23semidirect
575. C22⋊#95C2×C23semidirect
689. #392C4×C23semidirect
750. C22×D4C2×C4×C23semidirect
751. C22×D4C2×C4×C23semidirect
818. C2×C22⋊C4C2×C4×C23semidirect
819. C2×C22⋊C4C2×C4×C23semidirect
820. C2×C22⋊C4C2×C4×C23semidirect
821. C2×C22⋊C4D4×C23semidirect
822. C2×C22⋊C4D4×C23semidirect
838. #95C2×C4×C23semidirect
839. #95D4×C23semidirect
840. C23#14519direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3922
C2×C23×#3902
C2×C23×#3862
C2×C23×#3852
C23×#14422
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14342
C23×C22⋊#952
#1451923