Finite Group Databasebeta

← C23×#14096 #19161722

Subgroups — C23×#14096 #19161722

Order 5888.

2266 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×C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
6C23×#1445C211yesmaximal, characteristic, complemented
7C23×#1440C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1438C211yesmaximal, characteristic
10C23×#1437C211yesmaximal, characteristic, complemented
11C23×#1436C211yesmaximal, characteristic, complemented
12C23×#1436C211yesmaximal, 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×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×C42×C23C2211yescharacteristic
36C22×C42×C23C2211yescharacteristic
37C22×C42×C23C2211yescharacteristic
38C23×#388—24no—
39C23×#386—24no—
40C4×C22⋊C4×C23—24no—
41C4×C22⋊C4×C23—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—22no—
75C23×C4×C23—22no—
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—41no—
102C2×C4⋊C4×C23C2×C414yescomplemented
103C2×C4⋊C4×C23C2×C414yescomplemented
104C2×C22⋊C4×C23—22no—
105C2×C22⋊C4×C23—22no—
106C2×C22⋊C4×C23—22no—
107C2×C22⋊C4×C23—22no—
108C2×C22⋊C4×C23—22no—
109C2×C22⋊C4×C23—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—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×C23C2×C414yes—
129C2×C22⋊C4×C23C2×C414yes—
130C2×C22⋊C4×C23C2×C414yescomplemented
131C2×C22⋊C4×C23D414yes—
132C2×C22⋊C4×C23D414yes—
133C2×C22⋊C4×C23D414yes—
134C2×C42×C23—22no—
135C2×C42×C23—22no—
136C2×C42×C23—22no—
137C2×C42×C23—22no—
138C2×C42×C23—22no—
139C2×C42×C23—22no—
140C2×C42×C23—41no—
141C2×C42×C23—41no—
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—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×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—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—28no—
210C22×C4×C23—28no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—21no—
238C22×C4×C23—21no—
239C22×C4×C23—21no—
240C22×C4×C23—21no—
241C22×C4×C23—21no—
242C22×C4×C23—21no—
243C22×C4×C23—21no—
244C22×C4×C23—21no—
245C22×C4×C23—21no—
246C22×C4×C23—21no—
247C22×C4×C23—21no—
248C22×C4×C23—21no—
249C22×C4×C23—21no—
250C22×C4×C23—21no—
251C22×C4×C23—21no—
252C22×C4×C23—21no—
253C22×C4×C23—21no—
254C22×C4×C23—21no—
255C22×C4×C23—21no—
256C22×C4×C23—21no—
257C22×C4×C23—21no—
258C22×C4×C23—21no—
259C22×C4×C23—28no—
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—44no—
275C22×C4×C23—44no—
276C22×C4×C23—44no—
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×C23C22×C412yes—
286C22×C4×C23C22×C412yes—
287C22×C4×C23C22×C412yes—
288C22×C4×C23C22×C412yes—
289C22×C4×C23C22×C412yes—
290C22×C4×C23C2×D412yes—
291C22×C4×C23C2×D412yes—
292C22×C4×C23C2×D412yes—
293C22×C4×C23C2×D412yes—
294C22×C4×C23C2×D412yes—
295C22×C4×C23C2×D412yes—
296C22×C4×C23#4112yes—
297C22×C4×C23#4112yes—
298C22×C4×C23#4112yes—
299C22×C4×C23#4112yes—
300C22×C4×C23#4112yes—
301C22×C4×C23#4112yes—
302C4⋊C4×C23—28no—
303C4⋊C4×C23—28no—
304C4⋊C4×C23—44no—
305C22⋊C4×C23—28no—
306C22⋊C4×C23—28no—
307C22⋊C4×C23—28no—
308C22⋊C4×C23—28no—
309C22⋊C4×C23—28no—
310C22⋊C4×C23—44no—
311C22⋊C4×C23—44no—
312C22⋊C4×C23—44no—
313C22⋊C4×C23—44no—
314C22⋊C4×C23C22⋊C4116yescomplemented
315C42×C23—44no—
316C42×C23—44no—
317C42×C23—44no—
318#14096C2311yesmaximal, 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×C23C2×#4111yescharacteristic
397C23×C23C2×#4111yescharacteristic
398C23×C23C2×#4111yescharacteristic
399C23×C23C2×#4111yescharacteristic
400C23×C23H(5,𝔽2)11yescharacteristic
401C23×C23H(5,𝔽2)11yescharacteristic
402C23×C23H(5,𝔽2)11yescharacteristic
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—22no—
439C2×C4×C23—22no—
440C2×C4×C23—22no—
441C2×C4×C23—22no—
442C2×C4×C23—22no—
443C2×C4×C23—22no—
444C2×C4×C23—22no—
445C2×C4×C23—22no—
446C2×C4×C23—22no—
447C2×C4×C23—416no—
448C2×C4×C23—416no—
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×C23C2×C22⋊C414yes—
496C2×C4×C23C2×C22⋊C414yes—
497C2×C4×C23#12314yescomplemented
498C22×#123C2×C2311yescharacteristic
499C2×#388C2×C2311yescharacteristic, complemented
500C2×#386C2×C2311yescharacteristic
501C2×C4×C22⋊C4C2×C2311yescharacteristic, complemented
502C2×C4×C22⋊C4C2×C2311yescharacteristic, complemented
503#1445C2×C2311yescharacteristic, complemented
504#1440C2×C2311yescharacteristic, complemented
505#1439C2×C2311yescharacteristic, complemented
506#1438C2×C2311yescharacteristic
507#1437C2×C2311yescharacteristic, complemented
508#1436C2×C2311yescharacteristic, complemented
509#1436C2×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×C23C4×#4111yescharacteristic
547C22×C23C4×#4111yescharacteristic
548C22×C23#51811yescharacteristic
549C22×C23#52011yescharacteristic
550C22×C23C2×#12311yescharacteristic
551C22×C23#52511yescharacteristic
552C22×C23#52511yescharacteristic
553C22×C23#52511yescharacteristic
554C22×C23#52911yescharacteristic
555C22×C23#52911yescharacteristic
556C22×C23#53211yescharacteristic
557C22×C23#53211yescharacteristic
558C22×C23#53811yescharacteristic
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#55111yescharacteristic
574C22×C23#55211yescharacteristic
575C22×C23#55311yescharacteristic
576C22×C23#55311yescharacteristic
577C22×C23#55911yescharacteristic
578C4×C23—24no—
579C4×C23—24no—
580C4×C23—24no—
581C4×C23—42no—
582C4×C23—42no—
583C4×C23—42no—
584C4×C23—42no—
585C4×C23—42no—
586C4×C23—42no—
587C4×C23—42no—
588C4×C23—42no—
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×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×C22⋊C4C22×C2311yescharacteristic
609C22×C22⋊C4C22×C2311yescharacteristic
610C22×C42C22×C2311yescharacteristic
611C22×C42C22×C2311yescharacteristic
612C22×C42C22×C2311yescharacteristic
613#388—24no—
614#386—24no—
615C4×C22⋊C4—24no—
616C4×C22⋊C4—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#229711yescharacteristic
636C2×C23C4×#12311yescharacteristic
637C2×C23#233511yescharacteristic
638C2×C23D4×C22⋊C411yescharacteristic
639C2×C23#233911yescharacteristic
640C2×C23#235911yescharacteristic
641C2×C23#237411yescharacteristic
642C2×C23#241811yescharacteristic
643C2×C23#242211yescharacteristic
644C2×C23#245511yescharacteristic
645C2×C23#245711yescharacteristic
646C2×C23#246411yescharacteristic
647C2×C23#247011yescharacteristic
648C2×C23#255311yescharacteristic
649C2×C23#255711yescharacteristic
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—22no—
667C23×C4—22no—
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—41no—
694C2×C4⋊C4C2×C4×C2314yescomplemented
695C2×C4⋊C4C2×C4×C2314yescomplemented
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—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⋊C4C2×C4×C2314yes—
721C2×C22⋊C4C2×C4×C2314yes—
722C2×C22⋊C4C2×C4×C2314yescomplemented
723C2×C22⋊C4D4×C2314yes—
724C2×C22⋊C4D4×C2314yes—
725C2×C22⋊C4D4×C2314yes—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—41no—
733C2×C42—41no—
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—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751C23#1409611yescharacteristic, 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—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—28no—
803C22×C4—28no—
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—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—28no—
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—44no—
868C22×C4—44no—
869C22×C4—44no—
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×C4C22×C4×C2312yes—
879C22×C4C22×C4×C2312yes—
880C22×C4C22×C4×C2312yes—
881C22×C4C22×C4×C2312yes—
882C22×C4C22×C4×C2312yes—
883C22×C4C2×D4×C2312yes—
884C22×C4C2×D4×C2312yes—
885C22×C4C2×D4×C2312yes—
886C22×C4C2×D4×C2312yes—
887C22×C4C2×D4×C2312yes—
888C22×C4C2×D4×C2312yes—
889C22×C4#41×C2312yes—
890C22×C4#41×C2312yes—
891C22×C4#41×C2312yes—
892C22×C4#41×C2312yes—
893C22×C4#41×C2312yes—
894C22×C4#41×C2312yes—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—44no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4C22⋊C4×C23116yescomplemented
908C42—44no—
909C42—44no—
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
988C23C2×#41×C2311yescharacteristic
989C23C2×#41×C2311yescharacteristic
990C23C2×#41×C2311yescharacteristic
991C23C2×#41×C2311yescharacteristic
992C23C23×H(5,𝔽2)11yescharacteristic
993C23C23×H(5,𝔽2)11yescharacteristic
994C23C23×H(5,𝔽2)11yescharacteristic
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—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—416no—
1040C2×C4—416no—
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×C4C2×C22⋊C4×C2314yes—
1088C2×C4C2×C22⋊C4×C2314yes—
1089C2×C4C23×#12314yescomplemented
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
1123C22C4×#41×C2311yescharacteristic
1124C22C4×#41×C2311yescharacteristic
1125C22C23×#51811yescharacteristic
1126C22C23×#52011yescharacteristic
1127C22C2×C23×#12311yescharacteristic
1128C22C23×#52511yescharacteristic
1129C22C23×#52511yescharacteristic
1130C22C23×#52511yescharacteristic
1131C22C23×#52911yescharacteristic
1132C22C23×#52911yescharacteristic
1133C22C23×#53211yescharacteristic
1134C22C23×#53211yescharacteristic
1135C22C23×#53811yescharacteristic
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×#55111yescharacteristic
1151C22C23×#55211yescharacteristic
1152C22C23×#55311yescharacteristic
1153C22C23×#55311yescharacteristic
1154C22C23×#55911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—44no—
1170C2C23×#229711yescharacteristic
1171C2C4×C23×#12311yescharacteristic
1172C2C23×#233511yescharacteristic
1173C2D4×C22⋊C4×C2311yescharacteristic
1174C2C23×#233911yescharacteristic
1175C2C23×#235911yescharacteristic
1176C2C23×#237411yescharacteristic
1177C2C23×#241811yescharacteristic
1178C2C23×#242211yescharacteristic
1179C2C23×#245511yescharacteristic
1180C2C23×#245711yescharacteristic
1181C2C23×#246411yescharacteristic
1182C2C23×#247011yescharacteristic
1183C2C23×#255311yescharacteristic
1184C2C23×#255711yescharacteristic
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×C4×C22⋊C4×C23C2semidirect
5. C2×C4×C22⋊C4×C23C2semidirect
6. C23×#1445C2semidirect
7. C23×#1440C2semidirect
8. C23×#1439C2semidirect
10. C23×#1437C2semidirect
11. C23×#1436C2semidirect
12. C23×#1436C2semidirect
13. C23×C4⋊#95C2semidirect
14. C23×C22⋊#95C2semidirect
15. C23×C22⋊#95C2semidirect
21. C2×C23×#123C4semidirect
80. C23×C4×C23C2×C4semidirect
102. C2×C4⋊C4×C23C2×C4semidirect
103. C2×C4⋊C4×C23C2×C4semidirect
130. C2×C22⋊C4×C23C2×C4semidirect
314. C22⋊C4×C23C22⋊C4semidirect
318. #14096C23direct (N × H)
497. C2×C4×C23#123semidirect
499. C2×#388C2×C23semidirect
501. C2×C4×C22⋊C4C2×C23semidirect
502. C2×C4×C22⋊C4C2×C23semidirect
503. #1445C2×C23semidirect
504. #1440C2×C23semidirect
505. #1439C2×C23semidirect
507. #1437C2×C23semidirect
508. #1436C2×C23semidirect
509. #1436C2×C23semidirect
510. C4⋊#95C2×C23semidirect
511. C22⋊#95C2×C23semidirect
512. C22⋊#95C2×C23semidirect
596. C2×#123C4×C23semidirect
672. C23×C4C2×C4×C23semidirect
694. C2×C4⋊C4C2×C4×C23semidirect
695. C2×C4⋊C4C2×C4×C23semidirect
722. C2×C22⋊C4C2×C4×C23semidirect
751. C23#14096direct (N × H)
907. C22⋊C4C22⋊C4×C23semidirect
1089. C2×C4C23×#123semidirect

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×C4×C22⋊C4×C232
C23×#14452
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14362
C23×C4⋊#952
C23×C22⋊#952
#1409623