Finite Group Databasebeta

← C23×#14360 #19161986

Subgroups — C23×#14360 #19161986

Order 5888.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C23×#123C211yesmaximal, characteristic
2C2×C23×#390C211yesmaximal, characteristic
3C2×C23×#389C211yesmaximal, characteristic, complemented
4C2×C23×#387C211yesmaximal, characteristic, complemented
5C2×C23×#380C211yesmaximal, characteristic, complemented
6C23×#1441C211yesmaximal, characteristic, complemented
7C23×#1439C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1438C211yesmaximal, characteristic
12C23×#1437C211yesmaximal, characteristic, complemented
13C23×#1437C211yesmaximal, characteristic, complemented
14C23×#1436C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C2×C23×#123—24no—
19C2×C23×#123—24no—
20C2×C23×#123C418yescomplemented
21C22×C4⋊C4×C23C2211yescharacteristic
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×C22⋊C4×C23C2211yescharacteristic
38C22×C42×C23C2211yescharacteristic
39C22×C42×C23C2211yescharacteristic
40C23×#390—24no—
41C23×#389—24no—
42C23×#387—24no—
43C23×#380—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
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—41no—
72C23×C4×C23—41no—
73C23×C4×C23C2×C414yes—
74C23×C4×C23C2311yescharacteristic
75C23×C4×C23C2311yescharacteristic
76C23×C4×C23C2311yescharacteristic
77C23×C4×C23C2311yescharacteristic
78C23×C4×C23C2311yescharacteristic
79C23×C4×C23C2311yescharacteristic
80C23×C4×C23C2311yescharacteristic
81C23×C4×C23C2311yescharacteristic
82C23×C4×C23C2311yescharacteristic
83C23×C4×C23C2311yescharacteristic
84C23×C4×C23C2311yescharacteristic
85C23×C4×C23C2311yescharacteristic
86C23×C4×C23C2311yescharacteristic
87C23×#123—232no—
88C2×C4⋊C4×C23—22no—
89C2×C4⋊C4×C23—22no—
90C2×C4⋊C4×C23—22no—
91C2×C4⋊C4×C23—22no—
92C2×C4⋊C4×C23—22no—
93C2×C4⋊C4×C23—22no—
94C2×C4⋊C4×C23—22no—
95C2×C4⋊C4×C23—22no—
96C2×C4⋊C4×C23—22no—
97C2×C4⋊C4×C23—41no—
98C2×C4⋊C4×C23—41no—
99C2×C4⋊C4×C23—41no—
100C2×C4⋊C4×C23—41no—
101C2×C4⋊C4×C23—41no—
102C2×C4⋊C4×C23C2×C414yes—
103C2×C4⋊C4×C23C2×C414yes—
104C2×C4⋊C4×C23D414yes—
105C2×C4⋊C4×C23D414yes—
106C2×C22⋊C4×C23—22no—
107C2×C22⋊C4×C23—22no—
108C2×C22⋊C4×C23—22no—
109C2×C22⋊C4×C23—22no—
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—41no—
122C2×C22⋊C4×C23—41no—
123C2×C22⋊C4×C23—41no—
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×C23—41no—
135C2×C22⋊C4×C23C2×C414yes—
136C2×C22⋊C4×C23C2×C414yes—
137C2×C22⋊C4×C23C2×C414yes—
138C2×C22⋊C4×C23D414yes—
139C2×C42×C23—22no—
140C2×C42×C23—22no—
141C2×C42×C23—22no—
142C2×C42×C23—41no—
143C2×C42×C23—41no—
144C2×C42×C23—41no—
145C23×#95—22no—
146C23×#95—22no—
147C23×#95—22no—
148C23×#95—22no—
149C23×#95—22no—
150C23×#95—22no—
151C23×#95—22no—
152C23×#95—22no—
153C23×#95—22no—
154C23×#95—22no—
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×C23—21no—
184C24×C23—21no—
185C24×C23C22×C412yes—
186C24×C23C22×C412yes—
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—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—28no—
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—28no—
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—44no—
276C22×C4×C23—44no—
277C22×C4×C23—44no—
278C22×C4×C23—44no—
279C22×C4×C23—44no—
280C22×C4×C23C22×C412yes—
281C22×C4×C23C22×C412yes—
282C22×C4×C23C22×C412yes—
283C22×C4×C23C22×C412yes—
284C22×C4×C23C22×C412yes—
285C22×C4×C23C2×D412yes—
286C22×C4×C23C2×D412yes—
287C22×C4×C23C2×D412yes—
288C22×C4×C23C2×D412yes—
289C22×C4×C23C2×D412yes—
290C22×C4×C23C2×D412yes—
291C22×C4×C23C2×D412yes—
292C22×C4×C23C2×D412yes—
293C22×C4×C23#4112yes—
294C22×C4×C23#4112yes—
295C4⋊C4×C23—28no—
296C4⋊C4×C23—44no—
297C4⋊C4×C23—44no—
298C4⋊C4×C23—44no—
299C4⋊C4×C23—44no—
300C4⋊C4×C23C22⋊C4116yescomplemented
301C22⋊C4×C23—28no—
302C22⋊C4×C23—28no—
303C22⋊C4×C23—28no—
304C22⋊C4×C23—44no—
305C22⋊C4×C23—44no—
306C22⋊C4×C23—44no—
307C22⋊C4×C23—44no—
308C22⋊C4×C23—44no—
309C22⋊C4×C23—44no—
310C22⋊C4×C23—44no—
311C22⋊C4×C23—44no—
312C42×C23—44no—
313C42×C23—44no—
314#14360C2311yesmaximal, characteristic, direct product factor, Sylow
315C23×C23—22no—
316C23×C23—22no—
317C23×C23—22no—
318C23×C23—22no—
319C23×C23—22no—
320C23×C23—22no—
321C23×C23—22no—
322C23×C23—22no—
323C23×C23—22no—
324C23×C23—22no—
325C23×C23—22no—
326C23×C23—22no—
327C23×C23—22no—
328C23×C23—22no—
329C23×C23—22no—
330C23×C23—22no—
331C23×C23—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—41no—
341C23×C23—41no—
342C23×C23—41no—
343C23×C23—41no—
344C23×C23—41no—
345C23×C23—41no—
346C23×C23—41no—
347C23×C23—41no—
348C23×C23—41no—
349C23×C23—41no—
350C23×C23—41no—
351C23×C23—41no—
352C23×C23—41no—
353C23×C23—41no—
354C23×C23—41no—
355C23×C23—41no—
356C23×C23—41no—
357C23×C23—41no—
358C23×C23—41no—
359C23×C23—41no—
360C23×C23—41no—
361C23×C23—41no—
362C23×C23—41no—
363C23×C23—41no—
364C23×C23—41no—
365C23×C23—41no—
366C23×C23—41no—
367C23×C23—41no—
368C23×C23—41no—
369C23×C23—41no—
370C23×C23—41no—
371C23×C23—41no—
372C23×C23—41no—
373C23×C23—41no—
374C23×C23—41no—
375C23×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×C23C4×D414yes—
385C23×C23C23×C411yescharacteristic
386C23×C23C22×D411yescharacteristic
387C23×C23C22×D411yescharacteristic
388C23×C23C22×D411yescharacteristic
389C23×C23C2×#4111yescharacteristic
390C23×C23C2×#4111yescharacteristic
391C23×C23C2×#4111yescharacteristic
392C23×C23H(5,𝔽2)11yescharacteristic
393C23×C23H(5,𝔽2)11yescharacteristic
394C23×C23H(5,𝔽2)11yescharacteristic
395C23×C23H(5,𝔽2)11yescharacteristic
396C23×C23H(5,𝔽2)11yescharacteristic
397C23×C232−1+411yescharacteristic
398C23×C232−1+411yescharacteristic
399C23×C232−1+411yescharacteristic
400D4×C23—416no—
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—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—416no—
438C2×C4×C23—41no—
439C2×C4×C23—41no—
440C2×C4×C23—41no—
441C2×C4×C23—41no—
442C2×C4×C23—41no—
443C2×C4×C23—41no—
444C2×C4×C23—41no—
445C2×C4×C23—41no—
446C2×C4×C23—41no—
447C2×C4×C23—41no—
448C2×C4×C23—41no—
449C2×C4×C23—41no—
450C2×C4×C23—41no—
451C2×C4×C23—41no—
452C2×C4×C23—41no—
453C2×C4×C23—41no—
454C2×C4×C23—41no—
455C2×C4×C23—41no—
456C2×C4×C23—41no—
457C2×C4×C23—41no—
458C2×C4×C23—41no—
459C2×C4×C23—41no—
460C2×C4×C23—41no—
461C2×C4×C23—41no—
462C2×C4×C23—41no—
463C2×C4×C23—41no—
464C2×C4×C23—41no—
465C2×C4×C23—41no—
466C2×C4×C23—41no—
467C2×C4×C23—41no—
468C2×C4×C23—41no—
469C2×C4×C23—41no—
470C2×C4×C23—41no—
471C2×C4×C23—41no—
472C2×C4×C23—41no—
473C2×C4×C23—41no—
474C2×C4×C23—41no—
475C2×C4×C23—41no—
476C2×C4×C23—41no—
477C2×C4×C23—41no—
478C2×C4×C23—41no—
479C2×C4×C23—41no—
480C2×C4×C23—41no—
481C2×C4×C23—41no—
482C2×C4×C23—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×C23C2×C22⋊C414yes—
491C2×C4×C23C2×C22⋊C414yes—
492C2×C4×C23C2×C22⋊C414yes—
493C22×#123C2×C2311yescharacteristic
494C2×#390C2×C2311yescharacteristic
495C2×#389C2×C2311yescharacteristic, complemented
496C2×#387C2×C2311yescharacteristic, complemented
497C2×#380C2×C2311yescharacteristic, complemented
498#1441C2×C2311yescharacteristic, complemented
499#1439C2×C2311yescharacteristic, complemented
500#1439C2×C2311yescharacteristic, complemented
501#1439C2×C2311yescharacteristic, complemented
502#1439C2×C2311yescharacteristic, complemented
503#1438C2×C2311yescharacteristic
504#1437C2×C2311yescharacteristic, complemented
505#1437C2×C2311yescharacteristic, complemented
506#1436C2×C2311yescharacteristic, complemented
507C22⋊#95C2×C2311yescharacteristic, complemented
508C22×C23—24no—
509C22×C23—24no—
510C22×C23—24no—
511C22×C23—42no—
512C22×C23—42no—
513C22×C23—42no—
514C22×C23—42no—
515C22×C23—42no—
516C22×C23—42no—
517C22×C23—42no—
518C22×C23—42no—
519C22×C23—42no—
520C22×C23—42no—
521C22×C23—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—81no—
531C22×C23—81no—
532C22×C23—81no—
533C22×C23—81no—
534C22×C23—81no—
535C22×C23—81no—
536C22×C23—81no—
537C22×C23—81no—
538C22×C23C22×C22⋊C411yescharacteristic
539C22×C23C2×C4×D411yescharacteristic
540C22×C23C4×#4111yescharacteristic
541C22×C23#51811yescharacteristic
542C22×C23#52011yescharacteristic
543C22×C23#52011yescharacteristic
544C22×C23#52011yescharacteristic
545C22×C23#53411yescharacteristic
546C22×C23#53511yescharacteristic
547C22×C23#53611yescharacteristic
548C22×C23#53611yescharacteristic
549C22×C23#53711yescharacteristic
550C22×C23#53711yescharacteristic
551C22×C23#53811yescharacteristic
552C22×C23#53911yescharacteristic
553C22×C23#53911yescharacteristic
554C22×C23#53911yescharacteristic
555C22×C23#54011yescharacteristic
556C22×C23#54211yescharacteristic
557C22×C23D4211yescharacteristic
558C22×C23D4211yescharacteristic
559C22×C23#54611yescharacteristic
560C22×C23#54611yescharacteristic
561C22×C23#54611yescharacteristic
562C22×C23#54711yescharacteristic
563C22×C23#54811yescharacteristic
564C22×C23#54811yescharacteristic
565C22×C23#55011yescharacteristic
566C22×C23#55011yescharacteristic
567C22×C23#55111yescharacteristic
568C22×C23#55211yescharacteristic
569C22×C23#56011yescharacteristic
570C22×C23#56211yescharacteristic
571C22×C23#56211yescharacteristic
572C22×C23#56311yescharacteristic
573C4×C23—24no—
574C4×C23—24no—
575C4×C23—24no—
576C4×C23—42no—
577C4×C23—42no—
578C4×C23—42no—
579C4×C23—42no—
580C4×C23—42no—
581C4×C23—42no—
582C4×C23—81no—
583C4×C23—81no—
584C4×C23—81no—
585C4×C23—81no—
586C23×D4C22×C2311yescharacteristic
587C24×C4C22×C2311yescharacteristic
588C2×#123—24no—
589C2×#123—24no—
590C2×#123C4×C2318yescomplemented
591C22×C4⋊C4C22×C2311yescharacteristic
592C22×C4⋊C4C22×C2311yescharacteristic
593C22×C4⋊C4C22×C2311yescharacteristic
594C22×C4⋊C4C22×C2311yescharacteristic
595C22×C4⋊C4C22×C2311yescharacteristic
596C22×C4⋊C4C22×C2311yescharacteristic
597C22×C22⋊C4C22×C2311yescharacteristic
598C22×C22⋊C4C22×C2311yescharacteristic
599C22×C22⋊C4C22×C2311yescharacteristic
600C22×C22⋊C4C22×C2311yescharacteristic
601C22×C22⋊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×C42C22×C2311yescharacteristic
609C22×C42C22×C2311yescharacteristic
610#390—24no—
611#389—24no—
612#387—24no—
613#380—24no—
614C2×#95C22×C2311yescharacteristic
615C2×#95C22×C2311yescharacteristic
616C2×#95C22×C2311yescharacteristic
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×C23—44no—
629C2×C23—82no—
630C2×C23#231111yescharacteristic
631C2×C23#232211yescharacteristic
632C2×C23#233511yescharacteristic
633C2×C23D4×C22⋊C411yescharacteristic
634C2×C23#234111yescharacteristic
635C2×C23#235911yescharacteristic
636C2×C23#237611yescharacteristic
637C2×C23#267311yescharacteristic
638C2×C23#267411yescharacteristic
639C2×C23#268111yescharacteristic
640C2×C23#268211yescharacteristic
641C2×C23#269411yescharacteristic
642C2×C23#269611yescharacteristic
643C2×C23#270511yescharacteristic
644C2×C23#270711yescharacteristic
645C25C23×C2311yescharacteristic
646C25C23×C2311yescharacteristic
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—41no—
652C22×D4—41no—
653C22×D4C2×C4×C2314yes—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—41no—
659C23×C4—41no—
660C23×C4C2×C4×C2314yes—
661C23×C4C23×C2311yescharacteristic
662C23×C4C23×C2311yescharacteristic
663C23×C4C23×C2311yescharacteristic
664C23×C4C23×C2311yescharacteristic
665C23×C4C23×C2311yescharacteristic
666C23×C4C23×C2311yescharacteristic
667C23×C4C23×C2311yescharacteristic
668C23×C4C23×C2311yescharacteristic
669C23×C4C23×C2311yescharacteristic
670C23×C4C23×C2311yescharacteristic
671C23×C4C23×C2311yescharacteristic
672C23×C4C23×C2311yescharacteristic
673C23×C4C23×C2311yescharacteristic
674#123—232no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4C2×C4×C2314yes—
690C2×C4⋊C4C2×C4×C2314yes—
691C2×C4⋊C4D4×C2314yes—
692C2×C4⋊C4D4×C2314yes—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
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—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
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⋊C4C2×C4×C2314yes—
723C2×C22⋊C4C2×C4×C2314yes—
724C2×C22⋊C4C2×C4×C2314yes—
725C2×C22⋊C4D4×C2314yes—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—41no—
731C2×C42—41no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—41no—
743#95—41no—
744#95—41no—
745#95—41no—
746C23#1436011yescharacteristic, direct product factor, Sylow
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
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—
773C24C22×C4×C2312yes—
774C24C22×C4×C2312yes—
775C24C2×D4×C2312yes—
776C24#41×C2312yes—
777C24C24×C2311yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
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—28no—
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—28no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—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—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4C22×C4×C2312yes—
869C22×C4C22×C4×C2312yes—
870C22×C4C22×C4×C2312yes—
871C22×C4C22×C4×C2312yes—
872C22×C4C22×C4×C2312yes—
873C22×C4C2×D4×C2312yes—
874C22×C4C2×D4×C2312yes—
875C22×C4C2×D4×C2312yes—
876C22×C4C2×D4×C2312yes—
877C22×C4C2×D4×C2312yes—
878C22×C4C2×D4×C2312yes—
879C22×C4C2×D4×C2312yes—
880C22×C4C2×D4×C2312yes—
881C22×C4#41×C2312yes—
882C22×C4#41×C2312yes—
883C4⋊C4—28no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4C22⋊C4×C23116yescomplemented
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C42—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
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—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
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—
971C23C4×D4×C2314yes—
972C23C23×C4×C2311yescharacteristic
973C23C22×D4×C2311yescharacteristic
974C23C22×D4×C2311yescharacteristic
975C23C22×D4×C2311yescharacteristic
976C23C2×#41×C2311yescharacteristic
977C23C2×#41×C2311yescharacteristic
978C23C2×#41×C2311yescharacteristic
979C23C23×H(5,𝔽2)11yescharacteristic
980C23C23×H(5,𝔽2)11yescharacteristic
981C23C23×H(5,𝔽2)11yescharacteristic
982C23C23×H(5,𝔽2)11yescharacteristic
983C23C23×H(5,𝔽2)11yescharacteristic
984C23C23×2−1+411yescharacteristic
985C23C23×2−1+411yescharacteristic
986C23C23×2−1+411yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—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—416no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×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×C4C2×C22⋊C4×C2314yes—
1078C2×C4C2×C22⋊C4×C2314yes—
1079C2×C4C2×C22⋊C4×C2314yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C22⋊C4×C2311yescharacteristic
1111C22C2×C4×D4×C2311yescharacteristic
1112C22C4×#41×C2311yescharacteristic
1113C22C23×#51811yescharacteristic
1114C22C23×#52011yescharacteristic
1115C22C23×#52011yescharacteristic
1116C22C23×#52011yescharacteristic
1117C22C23×#53411yescharacteristic
1118C22C23×#53511yescharacteristic
1119C22C23×#53611yescharacteristic
1120C22C23×#53611yescharacteristic
1121C22C23×#53711yescharacteristic
1122C22C23×#53711yescharacteristic
1123C22C23×#53811yescharacteristic
1124C22C23×#53911yescharacteristic
1125C22C23×#53911yescharacteristic
1126C22C23×#53911yescharacteristic
1127C22C23×#54011yescharacteristic
1128C22C23×#54211yescharacteristic
1129C22D42×C2311yescharacteristic
1130C22D42×C2311yescharacteristic
1131C22C23×#54611yescharacteristic
1132C22C23×#54611yescharacteristic
1133C22C23×#54611yescharacteristic
1134C22C23×#54711yescharacteristic
1135C22C23×#54811yescharacteristic
1136C22C23×#54811yescharacteristic
1137C22C23×#55011yescharacteristic
1138C22C23×#55011yescharacteristic
1139C22C23×#55111yescharacteristic
1140C22C23×#55211yescharacteristic
1141C22C23×#56011yescharacteristic
1142C22C23×#56211yescharacteristic
1143C22C23×#56211yescharacteristic
1144C22C23×#56311yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C23×#231111yescharacteristic
1161C2C23×#232211yescharacteristic
1162C2C23×#233511yescharacteristic
1163C2D4×C22⋊C4×C2311yescharacteristic
1164C2C23×#234111yescharacteristic
1165C2C23×#235911yescharacteristic
1166C2C23×#237611yescharacteristic
1167C2C23×#267311yescharacteristic
1168C2C23×#267411yescharacteristic
1169C2C23×#268111yescharacteristic
1170C2C23×#268211yescharacteristic
1171C2C23×#269411yescharacteristic
1172C2C23×#269611yescharacteristic
1173C2C23×#270511yescharacteristic
1174C2C23×#270711yescharacteristic
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×#387C2semidirect
5. C2×C23×#380C2semidirect
6. C23×#1441C2semidirect
7. C23×#1439C2semidirect
8. C23×#1439C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
12. C23×#1437C2semidirect
13. C23×#1437C2semidirect
14. C23×#1436C2semidirect
15. C23×C22⋊#95C2semidirect
20. C2×C23×#123C4semidirect
300. C4⋊C4×C23C22⋊C4semidirect
314. #14360C23direct (N × H)
495. C2×#389C2×C23semidirect
496. C2×#387C2×C23semidirect
497. C2×#380C2×C23semidirect
498. #1441C2×C23semidirect
499. #1439C2×C23semidirect
500. #1439C2×C23semidirect
501. #1439C2×C23semidirect
502. #1439C2×C23semidirect
504. #1437C2×C23semidirect
505. #1437C2×C23semidirect
506. #1436C2×C23semidirect
507. C22⋊#95C2×C23semidirect
590. C2×#123C4×C23semidirect
746. C23#14360direct (N × H)
888. C4⋊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×#3902
C2×C23×#3892
C2×C23×#3872
C2×C23×#3802
C23×#14412
C23×#14392
C23×#14382
C23×#14372
C23×#14362
C23×C22⋊#952
#1436023