Finite Group Databasebeta

← C23×#14359 #19161985

Subgroups — C23×#14359 #19161985

Order 5888.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C23×#123C211yesmaximal, characteristic
2C2×C23×#388C211yesmaximal, characteristic, complemented
3C2×C23×#386C211yesmaximal, characteristic
4C2×C23×#385C211yesmaximal, characteristic, complemented
5C2×C23×#380C211yesmaximal, characteristic, complemented
6C23×#1445C211yesmaximal, characteristic, complemented
7C23×#1441C211yesmaximal, characteristic, complemented
8C23×#1441C211yesmaximal, characteristic, complemented
9C23×#1440C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1438C211yesmaximal, characteristic
12C23×#1437C211yesmaximal, characteristic, complemented
13C23×C4⋊#95C211yesmaximal, characteristic, complemented
14C23×C22⋊#95C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C24×C4×C23C2211yescharacteristic
19C2×C23×#123—24no—
20C2×C23×#123—24no—
21C2×C23×#123C418yescomplemented
22C22×C4⋊C4×C23C2211yescharacteristic
23C22×C4⋊C4×C23C2211yescharacteristic
24C22×C4⋊C4×C23C2211yescharacteristic
25C22×C4⋊C4×C23C2211yescharacteristic
26C22×C4⋊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×C22⋊C4×C23C2211yescharacteristic
37C22×C42×C23C2211yescharacteristic
38C23×#388—24no—
39C23×#386—24no—
40C23×#385—24no—
41C23×#380—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
56C2×C23×#95C2211yescharacteristic
57C2×C23×#95C2211yescharacteristic
58C25×C23C2311yescharacteristic
59C25×C23C2311yescharacteristic
60C22×D4×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23—22no—
63C22×D4×C23—22no—
64C22×D4×C23—41no—
65C22×D4×C23—41no—
66C22×D4×C23C2×C414yes—
67C23×C4×C23—22no—
68C23×C4×C23—22no—
69C23×C4×C23—22no—
70C23×C4×C23—22no—
71C23×C4×C23—22no—
72C23×C4×C23—22no—
73C23×C4×C23—22no—
74C23×C4×C23—41no—
75C23×C4×C23—41no—
76C23×C4×C23—41no—
77C23×C4×C23—41no—
78C23×C4×C23—41no—
79C23×C4×C23—41no—
80C23×C4×C23C2×C414yescomplemented
81C23×C4×C23C2311yescharacteristic
82C23×C4×C23C2311yescharacteristic
83C23×C4×C23C2311yescharacteristic
84C23×C4×C23C2311yescharacteristic
85C23×C4×C23C2311yescharacteristic
86C23×C4×C23C2311yescharacteristic
87C23×C4×C23C2311yescharacteristic
88C23×C4×C23C2311yescharacteristic
89C23×C4×C23C2311yescharacteristic
90C23×C4×C23C2311yescharacteristic
91C23×C4×C23C2311yescharacteristic
92C23×C4×C23C2311yescharacteristic
93C23×C4×C23C2311yescharacteristic
94C23×#123—232no—
95C2×C4⋊C4×C23—22no—
96C2×C4⋊C4×C23—22no—
97C2×C4⋊C4×C23—22no—
98C2×C4⋊C4×C23—22no—
99C2×C4⋊C4×C23—22no—
100C2×C4⋊C4×C23—22no—
101C2×C4⋊C4×C23—22no—
102C2×C4⋊C4×C23—22no—
103C2×C4⋊C4×C23—22no—
104C2×C4⋊C4×C23—22no—
105C2×C4⋊C4×C23—41no—
106C2×C4⋊C4×C23—41no—
107C2×C4⋊C4×C23—41no—
108C2×C4⋊C4×C23C2×C414yescomplemented
109C2×C4⋊C4×C23C2×C414yescomplemented
110C2×C22⋊C4×C23—22no—
111C2×C22⋊C4×C23—22no—
112C2×C22⋊C4×C23—22no—
113C2×C22⋊C4×C23—22no—
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—41no—
125C2×C22⋊C4×C23—41no—
126C2×C22⋊C4×C23—41no—
127C2×C22⋊C4×C23—41no—
128C2×C22⋊C4×C23—41no—
129C2×C22⋊C4×C23—41no—
130C2×C22⋊C4×C23—41no—
131C2×C22⋊C4×C23—41no—
132C2×C22⋊C4×C23—41no—
133C2×C22⋊C4×C23—41no—
134C2×C22⋊C4×C23C2×C414yes—
135C2×C22⋊C4×C23C2×C414yes—
136C2×C22⋊C4×C23C2×C414yescomplemented
137C2×C22⋊C4×C23D414yes—
138C2×C22⋊C4×C23D414yes—
139C2×C22⋊C4×C23D414yes—
140C2×C42×C23—22no—
141C2×C42×C23—22no—
142C2×C42×C23—41no—
143C23×#95—22no—
144C23×#95—22no—
145C23×#95—22no—
146C23×#95—22no—
147C23×#95—22no—
148C23×#95—22no—
149C23×#95—22no—
150C23×#95—22no—
151C23×#95—41no—
152C23×#95—41no—
153C23×#95—41no—
154C23×#95—41no—
155C23×#95—41no—
156C23×#95—41no—
157C23×#95—41no—
158C23×#95—41no—
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×C23—21no—
181C24×C23—21no—
182C24×C23—21no—
183C24×C23C22×C412yes—
184C24×C23C22×C412yes—
185C24×C23C2×D412yes—
186C24×C23C2×D412yes—
187C24×C23C2×D412yes—
188C24×C23#4112yes—
189C24×C23C2411yescharacteristic
190C2×D4×C23—28no—
191C2×D4×C23—28no—
192C2×D4×C23—44no—
193C2×D4×C23—44no—
194C2×D4×C23—44no—
195C2×D4×C23—44no—
196C2×D4×C23—44no—
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—28no—
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—28no—
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—44no—
278C22×C4×C23—44no—
279C22×C4×C23—44no—
280C22×C4×C23—44no—
281C22×C4×C23—44no—
282C22×C4×C23—44no—
283C22×C4×C23—44no—
284C22×C4×C23—44no—
285C22×C4×C23—44no—
286C22×C4×C23—44no—
287C22×C4×C23—44no—
288C22×C4×C23—44no—
289C22×C4×C23C22×C412yes—
290C22×C4×C23C22×C412yes—
291C22×C4×C23C22×C412yes—
292C22×C4×C23C22×C412yes—
293C22×C4×C23C22×C412yes—
294C22×C4×C23C2×D412yes—
295C22×C4×C23C2×D412yes—
296C22×C4×C23C2×D412yes—
297C22×C4×C23C2×D412yes—
298C22×C4×C23C2×D412yes—
299C22×C4×C23C2×D412yes—
300C22×C4×C23#4112yes—
301C22×C4×C23#4112yes—
302C4⋊C4×C23—28no—
303C4⋊C4×C23—28no—
304C4⋊C4×C23—44no—
305C4⋊C4×C23—44no—
306C4⋊C4×C23—44no—
307C22⋊C4×C23—28no—
308C22⋊C4×C23—28no—
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×C23C22⋊C4116yescomplemented
317C42×C23—44no—
318#14359C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
332C23×C23—22no—
333C23×C23—22no—
334C23×C23—22no—
335C23×C23—22no—
336C23×C23—22no—
337C23×C23—22no—
338C23×C23—22no—
339C23×C23—22no—
340C23×C23—22no—
341C23×C23—22no—
342C23×C23—22no—
343C23×C23—22no—
344C23×C23—22no—
345C23×C23—22no—
346C23×C23—22no—
347C23×C23—22no—
348C23×C23—22no—
349C23×C23—22no—
350C23×C23—22no—
351C23×C23—22no—
352C23×C23—22no—
353C23×C23—22no—
354C23×C23—22no—
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×C23—41no—
376C23×C23—41no—
377C23×C23—41no—
378C23×C23—41no—
379C23×C23—41no—
380C23×C23—41no—
381C23×C23—41no—
382C23×C23—41no—
383C23×C23—41no—
384C23×C23—41no—
385C23×C23—41no—
386C23×C23—41no—
387C23×C23C2×C22⋊C414yes—
388C23×C23C4×D414yes—
389C23×C23C23×C411yescharacteristic
390C23×C23C22×D411yescharacteristic
391C23×C23C22×D411yescharacteristic
392C23×C23C22×D411yescharacteristic
393C23×C23C2×#4111yescharacteristic
394C23×C23C2×#4111yescharacteristic
395C23×C23C2×#4111yescharacteristic
396C23×C23H(5,𝔽2)11yescharacteristic
397C23×C23H(5,𝔽2)11yescharacteristic
398C23×C23H(5,𝔽2)11yescharacteristic
399C23×C23H(5,𝔽2)11yescharacteristic
400C23×C23H(5,𝔽2)11yescharacteristic
401C23×C232−1+411yescharacteristic
402C23×C232−1+411yescharacteristic
403C23×C232−1+411yescharacteristic
404D4×C23—416no—
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—22no—
428C2×C4×C23—22no—
429C2×C4×C23—22no—
430C2×C4×C23—22no—
431C2×C4×C23—22no—
432C2×C4×C23—22no—
433C2×C4×C23—22no—
434C2×C4×C23—22no—
435C2×C4×C23—22no—
436C2×C4×C23—22no—
437C2×C4×C23—22no—
438C2×C4×C23—416no—
439C2×C4×C23—416no—
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—41no—
483C2×C4×C23—41no—
484C2×C4×C23—41no—
485C2×C4×C23—41no—
486C2×C4×C23—41no—
487C2×C4×C23—41no—
488C2×C4×C23—41no—
489C2×C4×C23—41no—
490C2×C4×C23—41no—
491C2×C4×C23—41no—
492C2×C4×C23—41no—
493C2×C4×C23—41no—
494C2×C4×C23—41no—
495C2×C4×C23—41no—
496C2×C4×C23C2×C22⋊C414yes—
497C2×C4×C23C2×C22⋊C414yes—
498C22×#123C2×C2311yescharacteristic
499C2×#388C2×C2311yescharacteristic, complemented
500C2×#386C2×C2311yescharacteristic
501C2×#385C2×C2311yescharacteristic, complemented
502C2×#380C2×C2311yescharacteristic, complemented
503#1445C2×C2311yescharacteristic, complemented
504#1441C2×C2311yescharacteristic, complemented
505#1441C2×C2311yescharacteristic, complemented
506#1440C2×C2311yescharacteristic, complemented
507#1439C2×C2311yescharacteristic, complemented
508#1438C2×C2311yescharacteristic
509#1437C2×C2311yescharacteristic, complemented
510C4⋊#95C2×C2311yescharacteristic, complemented
511C22⋊#95C2×C2311yescharacteristic, complemented
512C22⋊#95C2×C2311yescharacteristic, complemented
513C22×C23—24no—
514C22×C23—24no—
515C22×C23—24no—
516C22×C23—24no—
517C22×C23—24no—
518C22×C23—24no—
519C22×C23—42no—
520C22×C23—42no—
521C22×C23—42no—
522C22×C23—42no—
523C22×C23—42no—
524C22×C23—42no—
525C22×C23—42no—
526C22×C23—42no—
527C22×C23—42no—
528C22×C23—42no—
529C22×C23—42no—
530C22×C23—42no—
531C22×C23—42no—
532C22×C23—42no—
533C22×C23—42no—
534C22×C23—42no—
535C22×C23—42no—
536C22×C23—42no—
537C22×C23—42no—
538C22×C23—42no—
539C22×C23—42no—
540C22×C23—42no—
541C22×C23—42no—
542C22×C23—42no—
543C22×C23C22×C22⋊C411yescharacteristic
544C22×C23C2×C4×D411yescharacteristic
545C22×C23C4×#4111yescharacteristic
546C22×C23#51811yescharacteristic
547C22×C23#52011yescharacteristic
548C22×C23#52011yescharacteristic
549C22×C23#52011yescharacteristic
550C22×C23#53411yescharacteristic
551C22×C23#53511yescharacteristic
552C22×C23#53611yescharacteristic
553C22×C23#53611yescharacteristic
554C22×C23#53711yescharacteristic
555C22×C23#53711yescharacteristic
556C22×C23#53811yescharacteristic
557C22×C23#53911yescharacteristic
558C22×C23#53911yescharacteristic
559C22×C23#53911yescharacteristic
560C22×C23#54011yescharacteristic
561C22×C23#54211yescharacteristic
562C22×C23D4211yescharacteristic
563C22×C23D4211yescharacteristic
564C22×C23#54611yescharacteristic
565C22×C23#54611yescharacteristic
566C22×C23#54611yescharacteristic
567C22×C23#54611yescharacteristic
568C22×C23#54611yescharacteristic
569C22×C23#54711yescharacteristic
570C22×C23#54711yescharacteristic
571C22×C23#54711yescharacteristic
572C22×C23#55111yescharacteristic
573C22×C23#55211yescharacteristic
574C22×C23#56011yescharacteristic
575C22×C23#56211yescharacteristic
576C22×C23#56211yescharacteristic
577C22×C23#56311yescharacteristic
578C4×C23—24no—
579C4×C23—24no—
580C4×C23—42no—
581C4×C23—42no—
582C4×C23—42no—
583C4×C23—42no—
584C4×C23—42no—
585C4×C23—42no—
586C4×C23—42no—
587C4×C23—81no—
588C4×C23—81no—
589C4×C23—81no—
590C4×C23—81no—
591C23×D4C22×C2311yescharacteristic
592C24×C4C22×C2311yescharacteristic
593C24×C4C22×C2311yescharacteristic
594C2×#123—24no—
595C2×#123—24no—
596C2×#123C4×C2318yescomplemented
597C22×C4⋊C4C22×C2311yescharacteristic
598C22×C4⋊C4C22×C2311yescharacteristic
599C22×C4⋊C4C22×C2311yescharacteristic
600C22×C4⋊C4C22×C2311yescharacteristic
601C22×C4⋊C4C22×C2311yescharacteristic
602C22×C22⋊C4C22×C2311yescharacteristic
603C22×C22⋊C4C22×C2311yescharacteristic
604C22×C22⋊C4C22×C2311yescharacteristic
605C22×C22⋊C4C22×C2311yescharacteristic
606C22×C22⋊C4C22×C2311yescharacteristic
607C22×C22⋊C4C22×C2311yescharacteristic
608C22×C22⋊C4C22×C2311yescharacteristic
609C22×C22⋊C4C22×C2311yescharacteristic
610C22×C22⋊C4C22×C2311yescharacteristic
611C22×C22⋊C4C22×C2311yescharacteristic
612C22×C42C22×C2311yescharacteristic
613#388—24no—
614#386—24no—
615#385—24no—
616#380—24no—
617C2×#95C22×C2311yescharacteristic
618C2×#95C22×C2311yescharacteristic
619C2×#95C22×C2311yescharacteristic
620C2×#95C22×C2311yescharacteristic
621C2×#95C22×C2311yescharacteristic
622C2×#95C22×C2311yescharacteristic
623C2×#95C22×C2311yescharacteristic
624C2×#95C22×C2311yescharacteristic
625C2×#95C22×C2311yescharacteristic
626C2×#95C22×C2311yescharacteristic
627C2×#95C22×C2311yescharacteristic
628C2×#95C22×C2311yescharacteristic
629C2×#95C22×C2311yescharacteristic
630C2×#95C22×C2311yescharacteristic
631C2×#95C22×C2311yescharacteristic
632C2×#95C22×C2311yescharacteristic
633C2×C23—44no—
634C2×C23—44no—
635C2×C23#231111yescharacteristic
636C2×C23#232211yescharacteristic
637C2×C23#233511yescharacteristic
638C2×C23D4×C22⋊C411yescharacteristic
639C2×C23#233911yescharacteristic
640C2×C23#235911yescharacteristic
641C2×C23#237611yescharacteristic
642C2×C23#267111yescharacteristic
643C2×C23#267211yescharacteristic
644C2×C23#267811yescharacteristic
645C2×C23#268011yescharacteristic
646C2×C23#268711yescharacteristic
647C2×C23#269311yescharacteristic
648C2×C23#269511yescharacteristic
649C2×C23#270611yescharacteristic
650C25C23×C2311yescharacteristic
651C25C23×C2311yescharacteristic
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—41no—
657C22×D4—41no—
658C22×D4C2×C4×C2314yes—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—41no—
667C23×C4—41no—
668C23×C4—41no—
669C23×C4—41no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4C2×C4×C2314yescomplemented
673C23×C4C23×C2311yescharacteristic
674C23×C4C23×C2311yescharacteristic
675C23×C4C23×C2311yescharacteristic
676C23×C4C23×C2311yescharacteristic
677C23×C4C23×C2311yescharacteristic
678C23×C4C23×C2311yescharacteristic
679C23×C4C23×C2311yescharacteristic
680C23×C4C23×C2311yescharacteristic
681C23×C4C23×C2311yescharacteristic
682C23×C4C23×C2311yescharacteristic
683C23×C4C23×C2311yescharacteristic
684C23×C4C23×C2311yescharacteristic
685C23×C4C23×C2311yescharacteristic
686#123—232no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—41no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4—41no—
700C2×C4⋊C4C2×C4×C2314yescomplemented
701C2×C4⋊C4C2×C4×C2314yescomplemented
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4C2×C4×C2314yes—
727C2×C22⋊C4C2×C4×C2314yes—
728C2×C22⋊C4C2×C4×C2314yescomplemented
729C2×C22⋊C4D4×C2314yes—
730C2×C22⋊C4D4×C2314yes—
731C2×C22⋊C4D4×C2314yes—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—41no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751C23#1435911yescharacteristic, direct product factor, Sylow
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C22×C4×C2312yes—
777C24C22×C4×C2312yes—
778C24C2×D4×C2312yes—
779C24C2×D4×C2312yes—
780C24C2×D4×C2312yes—
781C24#41×C2312yes—
782C24C24×C2311yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
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—28no—
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×C4—21no—
841C22×C4—28no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—44no—
871C22×C4—44no—
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—
882C22×C4C22×C4×C2312yes—
883C22×C4C22×C4×C2312yes—
884C22×C4C22×C4×C2312yes—
885C22×C4C22×C4×C2312yes—
886C22×C4C22×C4×C2312yes—
887C22×C4C2×D4×C2312yes—
888C22×C4C2×D4×C2312yes—
889C22×C4C2×D4×C2312yes—
890C22×C4C2×D4×C2312yes—
891C22×C4C2×D4×C2312yes—
892C22×C4C2×D4×C2312yes—
893C22×C4#41×C2312yes—
894C22×C4#41×C2312yes—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4C22⋊C4×C23116yescomplemented
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C2×C22⋊C4×C2314yes—
980C23C4×D4×C2314yes—
981C23C23×C4×C2311yescharacteristic
982C23C22×D4×C2311yescharacteristic
983C23C22×D4×C2311yescharacteristic
984C23C22×D4×C2311yescharacteristic
985C23C2×#41×C2311yescharacteristic
986C23C2×#41×C2311yescharacteristic
987C23C2×#41×C2311yescharacteristic
988C23C23×H(5,𝔽2)11yescharacteristic
989C23C23×H(5,𝔽2)11yescharacteristic
990C23C23×H(5,𝔽2)11yescharacteristic
991C23C23×H(5,𝔽2)11yescharacteristic
992C23C23×H(5,𝔽2)11yescharacteristic
993C23C23×2−1+411yescharacteristic
994C23C23×2−1+411yescharacteristic
995C23C23×2−1+411yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—416no—
1031C2×C4—416no—
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×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4C2×C22⋊C4×C2314yes—
1089C2×C4C2×C22⋊C4×C2314yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C22×C22⋊C4×C2311yescharacteristic
1121C22C2×C4×D4×C2311yescharacteristic
1122C22C4×#41×C2311yescharacteristic
1123C22C23×#51811yescharacteristic
1124C22C23×#52011yescharacteristic
1125C22C23×#52011yescharacteristic
1126C22C23×#52011yescharacteristic
1127C22C23×#53411yescharacteristic
1128C22C23×#53511yescharacteristic
1129C22C23×#53611yescharacteristic
1130C22C23×#53611yescharacteristic
1131C22C23×#53711yescharacteristic
1132C22C23×#53711yescharacteristic
1133C22C23×#53811yescharacteristic
1134C22C23×#53911yescharacteristic
1135C22C23×#53911yescharacteristic
1136C22C23×#53911yescharacteristic
1137C22C23×#54011yescharacteristic
1138C22C23×#54211yescharacteristic
1139C22D42×C2311yescharacteristic
1140C22D42×C2311yescharacteristic
1141C22C23×#54611yescharacteristic
1142C22C23×#54611yescharacteristic
1143C22C23×#54611yescharacteristic
1144C22C23×#54611yescharacteristic
1145C22C23×#54611yescharacteristic
1146C22C23×#54711yescharacteristic
1147C22C23×#54711yescharacteristic
1148C22C23×#54711yescharacteristic
1149C22C23×#55111yescharacteristic
1150C22C23×#55211yescharacteristic
1151C22C23×#56011yescharacteristic
1152C22C23×#56211yescharacteristic
1153C22C23×#56211yescharacteristic
1154C22C23×#56311yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—44no—
1170C2C23×#231111yescharacteristic
1171C2C23×#232211yescharacteristic
1172C2C23×#233511yescharacteristic
1173C2D4×C22⋊C4×C2311yescharacteristic
1174C2C23×#233911yescharacteristic
1175C2C23×#235911yescharacteristic
1176C2C23×#237611yescharacteristic
1177C2C23×#267111yescharacteristic
1178C2C23×#267211yescharacteristic
1179C2C23×#267811yescharacteristic
1180C2C23×#268011yescharacteristic
1181C2C23×#268711yescharacteristic
1182C2C23×#269311yescharacteristic
1183C2C23×#269511yescharacteristic
1184C2C23×#270611yescharacteristic
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×#385C2semidirect
5. C2×C23×#380C2semidirect
6. C23×#1445C2semidirect
7. C23×#1441C2semidirect
8. C23×#1441C2semidirect
9. C23×#1440C2semidirect
10. C23×#1439C2semidirect
12. C23×#1437C2semidirect
13. C23×C4⋊#95C2semidirect
14. C23×C22⋊#95C2semidirect
15. C23×C22⋊#95C2semidirect
21. C2×C23×#123C4semidirect
80. C23×C4×C23C2×C4semidirect
108. C2×C4⋊C4×C23C2×C4semidirect
109. C2×C4⋊C4×C23C2×C4semidirect
136. C2×C22⋊C4×C23C2×C4semidirect
316. C22⋊C4×C23C22⋊C4semidirect
318. #14359C23direct (N × H)
499. C2×#388C2×C23semidirect
501. C2×#385C2×C23semidirect
502. C2×#380C2×C23semidirect
503. #1445C2×C23semidirect
504. #1441C2×C23semidirect
505. #1441C2×C23semidirect
506. #1440C2×C23semidirect
507. #1439C2×C23semidirect
509. #1437C2×C23semidirect
510. C4⋊#95C2×C23semidirect
511. C22⋊#95C2×C23semidirect
512. C22⋊#95C2×C23semidirect
596. C2×#123C4×C23semidirect
672. C23×C4C2×C4×C23semidirect
700. C2×C4⋊C4C2×C4×C23semidirect
701. C2×C4⋊C4C2×C4×C23semidirect
728. C2×C22⋊C4C2×C4×C23semidirect
751. C23#14359direct (N × H)
909. C22⋊C4C22⋊C4×C23semidirect

Maximal subgroups

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

subgroupindex
C22×C23×#1232
C2×C23×#3882
C2×C23×#3862
C2×C23×#3852
C2×C23×#3802
C23×#14452
C23×#14412
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×C4⋊#952
C23×C22⋊#952
#1435923