Finite Group Databasebeta

← C23×#14838 #19162464

Subgroups — C23×#14838 #19162464

Order 5888.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#394C211yesmaximal, characteristic
2C2×C23×#386C211yesmaximal, characteristic
3C2×C23×#381C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
5C23×#1443C211yesmaximal, characteristic, complemented
6C23×#1442C211yesmaximal, characteristic, complemented
7C23×#1440C211yesmaximal, characteristic, complemented
8C23×#1440C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1438C211yesmaximal, characteristic
12C23×#1437C211yesmaximal, characteristic, complemented
13C23×#1437C211yesmaximal, characteristic, complemented
14C23×C4⋊#95C211yesmaximal, characteristic, complemented
15C23×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C22⋊C4×C23C2211yescharacteristic
21C22×C22⋊C4×C23C2211yescharacteristic
22C22×C22⋊C4×C23C2211yescharacteristic
23C22×C22⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C42×C23C2211yescharacteristic
32C22×C42×C23C2211yescharacteristic
33C23×#394—24no—
34C23×#386—24no—
35C23×#381—24no—
36C4×C22⋊C4×C23—24no—
37C2×C23×#95C2211yescharacteristic
38C2×C23×#95C2211yescharacteristic
39C2×C23×#95C2211yescharacteristic
40C2×C23×#95C2211yescharacteristic
41C2×C23×#95C2211yescharacteristic
42C2×C23×#95C2211yescharacteristic
43C2×C23×#95C2211yescharacteristic
44C2×C23×#95C2211yescharacteristic
45C2×C23×#95C2211yescharacteristic
46C2×C23×#95C2211yescharacteristic
47C2×C23×#95C2211yescharacteristic
48C2×C23×#95C2211yescharacteristic
49C2×C23×#95C2211yescharacteristic
50C2×C23×#95C2211yescharacteristic
51C2×C23×#95C2211yescharacteristic
52C2×C23×#95C2211yescharacteristic
53C2×C23×#95C2211yescharacteristic
54C2×C23×#95C2211yescharacteristic
55C25×C23C2311yescharacteristic
56C25×C23C2311yescharacteristic
57C22×D4×C23—22no—
58C22×D4×C23—22no—
59C22×D4×C23—22no—
60C22×D4×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23—41no—
63C22×D4×C23—41no—
64C23×C4×C23—22no—
65C23×C4×C23—22no—
66C23×C4×C23—22no—
67C23×C4×C23—22no—
68C23×C4×C23—41no—
69C23×C4×C23—41no—
70C23×C4×C23D414yes—
71C23×C4×C23C2311yescharacteristic
72C23×C4×C23C2311yescharacteristic
73C23×C4×C23C2311yescharacteristic
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
84C2×C4⋊C4×C23—22no—
85C2×C4⋊C4×C23—22no—
86C2×C4⋊C4×C23—22no—
87C2×C4⋊C4×C23—41no—
88C2×C4⋊C4×C23—41no—
89C2×C4⋊C4×C23—41no—
90C2×C22⋊C4×C23—22no—
91C2×C22⋊C4×C23—22no—
92C2×C22⋊C4×C23—22no—
93C2×C22⋊C4×C23—22no—
94C2×C22⋊C4×C23—22no—
95C2×C22⋊C4×C23—22no—
96C2×C22⋊C4×C23—22no—
97C2×C22⋊C4×C23—22no—
98C2×C22⋊C4×C23—22no—
99C2×C22⋊C4×C23—22no—
100C2×C22⋊C4×C23—22no—
101C2×C22⋊C4×C23—22no—
102C2×C22⋊C4×C23—22no—
103C2×C22⋊C4×C23—22no—
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—41no—
113C2×C22⋊C4×C23—41no—
114C2×C22⋊C4×C23—41no—
115C2×C22⋊C4×C23—41no—
116C2×C22⋊C4×C23—41no—
117C2×C22⋊C4×C23—41no—
118C2×C22⋊C4×C23—41no—
119C2×C22⋊C4×C23—41no—
120C2×C22⋊C4×C23—41no—
121C2×C22⋊C4×C23—41no—
122C2×C22⋊C4×C23D414yes—
123C2×C42×C23—22no—
124C2×C42×C23—22no—
125C2×C42×C23—22no—
126C2×C42×C23—22no—
127C2×C42×C23—41no—
128C2×C42×C23—41no—
129C23×#95—22no—
130C23×#95—22no—
131C23×#95—22no—
132C23×#95—22no—
133C23×#95—22no—
134C23×#95—22no—
135C23×#95—22no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—22no—
139C23×#95—22no—
140C23×#95—22no—
141C23×#95—22no—
142C23×#95—41no—
143C23×#95—41no—
144C23×#95—41no—
145C23×#95—41no—
146C23×#95—41no—
147C24×C23—21no—
148C24×C23—21no—
149C24×C23—21no—
150C24×C23—21no—
151C24×C23—21no—
152C24×C23—21no—
153C24×C23—21no—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23—21no—
157C24×C23—21no—
158C24×C23—21no—
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×C23C2×D412yes—
174C24×C23C2×D412yes—
175C24×C23#4112yes—
176C24×C23#4112yes—
177C24×C23C2411yescharacteristic
178C2×D4×C23—28no—
179C2×D4×C23—44no—
180C2×D4×C23—44no—
181C2×D4×C23—44no—
182C2×D4×C23—44no—
183C2×D4×C23—44no—
184C2×D4×C23—44no—
185C22×C4×C23—21no—
186C22×C4×C23—21no—
187C22×C4×C23—21no—
188C22×C4×C23—21no—
189C22×C4×C23—21no—
190C22×C4×C23—21no—
191C22×C4×C23—21no—
192C22×C4×C23—21no—
193C22×C4×C23—28no—
194C22×C4×C23—21no—
195C22×C4×C23—21no—
196C22×C4×C23—21no—
197C22×C4×C23—21no—
198C22×C4×C23—21no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—21no—
204C22×C4×C23—21no—
205C22×C4×C23—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—21no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—28no—
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—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—44no—
268C22×C4×C23—44no—
269C22×C4×C23—44no—
270C22×C4×C23—44no—
271C22×C4×C23—44no—
272C22×C4×C23C2×D412yes—
273C22×C4×C23C2×D412yes—
274C22×C4×C23C2×D412yes—
275C22×C4×C23C2×D412yes—
276C22×C4×C23#4112yes—
277C22×C4×C23#4112yes—
278C22×C4×C23#4112yes—
279C22×C4×C23#4112yes—
280C22×C4×C23#4112yes—
281C22×C4×C23#4112yes—
282C22×C4×C23#4112yes—
283C4⋊C4×C23—44no—
284C4⋊C4×C23—44no—
285C22⋊C4×C23—28no—
286C22⋊C4×C23—28no—
287C22⋊C4×C23—44no—
288C22⋊C4×C23—44no—
289C22⋊C4×C23—44no—
290C22⋊C4×C23—44no—
291C22⋊C4×C23—44no—
292C22⋊C4×C23—44no—
293C22⋊C4×C23—44no—
294C22⋊C4×C23—44no—
295C22⋊C4×C23—44no—
296C42×C23—44no—
297C42×C23—44no—
298#14838C2311yesmaximal, characteristic, direct product factor, Sylow
299C23×C23—22no—
300C23×C23—22no—
301C23×C23—22no—
302C23×C23—22no—
303C23×C23—22no—
304C23×C23—22no—
305C23×C23—22no—
306C23×C23—22no—
307C23×C23—22no—
308C23×C23—22no—
309C23×C23—22no—
310C23×C23—22no—
311C23×C23—22no—
312C23×C23—22no—
313C23×C23—22no—
314C23×C23—22no—
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—41no—
325C23×C23—41no—
326C23×C23—41no—
327C23×C23—41no—
328C23×C23—41no—
329C23×C23—41no—
330C23×C23—41no—
331C23×C23—41no—
332C23×C23—41no—
333C23×C23—41no—
334C23×C23—41no—
335C23×C23—41no—
336C23×C23—41no—
337C23×C23—41no—
338C23×C23—41no—
339C23×C23—41no—
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#12114yes—
369C23×C23C22×D411yescharacteristic
370C23×C23C22×D411yescharacteristic
371C23×C23C2×#4111yescharacteristic
372C23×C23C2×#4111yescharacteristic
373C23×C23C2×#4111yescharacteristic
374C23×C23C2×#4111yescharacteristic
375C23×C23C2×#4111yescharacteristic
376C23×C23C2×#4111yescharacteristic
377C23×C23C2×#4111yescharacteristic
378C23×C23C2×#4111yescharacteristic
379C23×C23C2×#4111yescharacteristic
380C23×C23H(5,𝔽2)11yescharacteristic
381C23×C23H(5,𝔽2)11yescharacteristic
382C23×C23H(5,𝔽2)11yescharacteristic
383C23×C23H(5,𝔽2)11yescharacteristic
384D4×C23—416no—
385C2×C4×C23—22no—
386C2×C4×C23—22no—
387C2×C4×C23—22no—
388C2×C4×C23—22no—
389C2×C4×C23—22no—
390C2×C4×C23—22no—
391C2×C4×C23—22no—
392C2×C4×C23—22no—
393C2×C4×C23—22no—
394C2×C4×C23—22no—
395C2×C4×C23—22no—
396C2×C4×C23—22no—
397C2×C4×C23—22no—
398C2×C4×C23—22no—
399C2×C4×C23—22no—
400C2×C4×C23—22no—
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—416no—
413C2×C4×C23—41no—
414C2×C4×C23—41no—
415C2×C4×C23—41no—
416C2×C4×C23—41no—
417C2×C4×C23—41no—
418C2×C4×C23—41no—
419C2×C4×C23—41no—
420C2×C4×C23—41no—
421C2×C4×C23—41no—
422C2×C4×C23—41no—
423C2×C4×C23—41no—
424C2×C4×C23—41no—
425C2×C4×C23—41no—
426C2×C4×C23—41no—
427C2×C4×C23—41no—
428C2×C4×C23—41no—
429C2×C4×C23—41no—
430C2×C4×C23—41no—
431C2×C4×C23—41no—
432C2×C4×C23—41no—
433C2×C4×C23—41no—
434C2×C4×C23—41no—
435C2×C4×C23—41no—
436C2×C4×C23—41no—
437C2×C4×C23—41no—
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#12314yes—
476C2×C4×C23#12314yes—
477C2×#394C2×C2311yescharacteristic
478C2×#386C2×C2311yescharacteristic
479C2×#381C2×C2311yescharacteristic, complemented
480C2×C4×C22⋊C4C2×C2311yescharacteristic, complemented
481#1443C2×C2311yescharacteristic, complemented
482#1442C2×C2311yescharacteristic, complemented
483#1440C2×C2311yescharacteristic, complemented
484#1440C2×C2311yescharacteristic, complemented
485#1439C2×C2311yescharacteristic, complemented
486#1439C2×C2311yescharacteristic, complemented
487#1438C2×C2311yescharacteristic
488#1437C2×C2311yescharacteristic, complemented
489#1437C2×C2311yescharacteristic, complemented
490C4⋊#95C2×C2311yescharacteristic, complemented
491#1434C2×C2311yescharacteristic, complemented
492C22×C23—24no—
493C22×C23—24no—
494C22×C23—24no—
495C22×C23—42no—
496C22×C23—42no—
497C22×C23—42no—
498C22×C23—42no—
499C22×C23—42no—
500C22×C23—42no—
501C22×C23—42no—
502C22×C23—42no—
503C22×C23—42no—
504C22×C23—42no—
505C22×C23—42no—
506C22×C23—42no—
507C22×C23—42no—
508C22×C23—42no—
509C22×C23—42no—
510C22×C23—42no—
511C22×C23—42no—
512C22×C23—42no—
513C22×C23—42no—
514C22×C23—81no—
515C22×C23—81no—
516C22×C23—81no—
517C22×C23—81no—
518C22×C23—81no—
519C22×C23—81no—
520C22×C23—81no—
521C22×C23—81no—
522C22×C23C2×#12111yescharacteristic
523C22×C23C2×#12311yescharacteristic
524C22×C23C2×#12311yescharacteristic
525C22×C23#52511yescharacteristic
526C22×C23#52511yescharacteristic
527C22×C23#52911yescharacteristic
528C22×C23#52911yescharacteristic
529C22×C23#52911yescharacteristic
530C22×C23#52911yescharacteristic
531C22×C23#52911yescharacteristic
532C22×C23#52911yescharacteristic
533C22×C23#53211yescharacteristic
534C22×C23#53211yescharacteristic
535C22×C23#53411yescharacteristic
536C22×C23#53511yescharacteristic
537C22×C23#53811yescharacteristic
538C22×C23#53811yescharacteristic
539C22×C23#54011yescharacteristic
540C22×C23#54011yescharacteristic
541C22×C23#54611yescharacteristic
542C22×C23#54611yescharacteristic
543C22×C23#54611yescharacteristic
544C22×C23#54611yescharacteristic
545C22×C23#55111yescharacteristic
546C22×C23#55111yescharacteristic
547C22×C23#55111yescharacteristic
548C22×C23#55111yescharacteristic
549C22×C23#55111yescharacteristic
550C22×C23#55311yescharacteristic
551C22×C23#55311yescharacteristic
552C22×C23#55311yescharacteristic
553C22×C23#55311yescharacteristic
554C22×C23#55511yescharacteristic
555C22×C23#55511yescharacteristic
556C22×C23#55911yescharacteristic
557C4×C23—24no—
558C4×C23—24no—
559C4×C23—42no—
560C4×C23—42no—
561C4×C23—42no—
562C4×C23—42no—
563C4×C23—42no—
564C4×C23—81no—
565C4×C23—81no—
566C4×C23—81no—
567C4×C23—81no—
568C4×C23—81no—
569C4×C23—81no—
570C23×D4C22×C2311yescharacteristic
571C24×C4C22×C2311yescharacteristic
572C22×C4⋊C4C22×C2311yescharacteristic
573C22×C4⋊C4C22×C2311yescharacteristic
574C22×C22⋊C4C22×C2311yescharacteristic
575C22×C22⋊C4C22×C2311yescharacteristic
576C22×C22⋊C4C22×C2311yescharacteristic
577C22×C22⋊C4C22×C2311yescharacteristic
578C22×C22⋊C4C22×C2311yescharacteristic
579C22×C22⋊C4C22×C2311yescharacteristic
580C22×C22⋊C4C22×C2311yescharacteristic
581C22×C22⋊C4C22×C2311yescharacteristic
582C22×C22⋊C4C22×C2311yescharacteristic
583C22×C22⋊C4C22×C2311yescharacteristic
584C22×C22⋊C4C22×C2311yescharacteristic
585C22×C42C22×C2311yescharacteristic
586C22×C42C22×C2311yescharacteristic
587#394—24no—
588#386—24no—
589#381—24no—
590C4×C22⋊C4—24no—
591C2×#95C22×C2311yescharacteristic
592C2×#95C22×C2311yescharacteristic
593C2×#95C22×C2311yescharacteristic
594C2×#95C22×C2311yescharacteristic
595C2×#95C22×C2311yescharacteristic
596C2×#95C22×C2311yescharacteristic
597C2×#95C22×C2311yescharacteristic
598C2×#95C22×C2311yescharacteristic
599C2×#95C22×C2311yescharacteristic
600C2×#95C22×C2311yescharacteristic
601C2×#95C22×C2311yescharacteristic
602C2×#95C22×C2311yescharacteristic
603C2×#95C22×C2311yescharacteristic
604C2×#95C22×C2311yescharacteristic
605C2×#95C22×C2311yescharacteristic
606C2×#95C22×C2311yescharacteristic
607C2×#95C22×C2311yescharacteristic
608C2×#95C22×C2311yescharacteristic
609C2×C23—44no—
610C2×C23—82no—
611C2×C23#239511yescharacteristic
612C2×C23#241111yescharacteristic
613C2×C23#241211yescharacteristic
614C2×C23#242011yescharacteristic
615C2×C23#244411yescharacteristic
616C2×C23#245711yescharacteristic
617C2×C23#245911yescharacteristic
618C2×C23#250011yescharacteristic
619C2×C23#251611yescharacteristic
620C2×C23#252611yescharacteristic
621C2×C23#257211yescharacteristic
622C2×C23#257611yescharacteristic
623C2×C23#260211yescharacteristic
624C2×C23#266111yescharacteristic
625C2×C23#285411yescharacteristic
626C25C23×C2311yescharacteristic
627C25C23×C2311yescharacteristic
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—41no—
634C22×D4—41no—
635C23×C4—22no—
636C23×C4—22no—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—41no—
640C23×C4—41no—
641C23×C4D4×C2314yes—
642C23×C4C23×C2311yescharacteristic
643C23×C4C23×C2311yescharacteristic
644C23×C4C23×C2311yescharacteristic
645C23×C4C23×C2311yescharacteristic
646C23×C4C23×C2311yescharacteristic
647C23×C4C23×C2311yescharacteristic
648C23×C4C23×C2311yescharacteristic
649C23×C4C23×C2311yescharacteristic
650C23×C4C23×C2311yescharacteristic
651C23×C4C23×C2311yescharacteristic
652C23×C4C23×C2311yescharacteristic
653C23×C4C23×C2311yescharacteristic
654C23×C4C23×C2311yescharacteristic
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4D4×C2314yes—
694C2×C42—22no—
695C2×C42—22no—
696C2×C42—22no—
697C2×C42—22no—
698C2×C42—41no—
699C2×C42—41no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—22no—
710#95—22no—
711#95—22no—
712#95—22no—
713#95—41no—
714#95—41no—
715#95—41no—
716#95—41no—
717#95—41no—
718C23#1483811yescharacteristic, direct product factor, Sylow
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C2312yes—
746C24C2×D4×C2312yes—
747C24#41×C2312yes—
748C24#41×C2312yes—
749C24C24×C2311yescharacteristic
750C2×D4—28no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—28no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
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—28no—
797C22×C4—21no—
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—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4C2×D4×C2312yes—
845C22×C4C2×D4×C2312yes—
846C22×C4C2×D4×C2312yes—
847C22×C4C2×D4×C2312yes—
848C22×C4#41×C2312yes—
849C22×C4#41×C2312yes—
850C22×C4#41×C2312yes—
851C22×C4#41×C2312yes—
852C22×C4#41×C2312yes—
853C22×C4#41×C2312yes—
854C22×C4#41×C2312yes—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C42—44no—
869C42—44no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23C23×#12114yes—
940C23C22×D4×C2311yescharacteristic
941C23C22×D4×C2311yescharacteristic
942C23C2×#41×C2311yescharacteristic
943C23C2×#41×C2311yescharacteristic
944C23C2×#41×C2311yescharacteristic
945C23C2×#41×C2311yescharacteristic
946C23C2×#41×C2311yescharacteristic
947C23C2×#41×C2311yescharacteristic
948C23C2×#41×C2311yescharacteristic
949C23C2×#41×C2311yescharacteristic
950C23C2×#41×C2311yescharacteristic
951C23C23×H(5,𝔽2)11yescharacteristic
952C23C23×H(5,𝔽2)11yescharacteristic
953C23C23×H(5,𝔽2)11yescharacteristic
954C23C23×H(5,𝔽2)11yescharacteristic
955D4—416no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—416no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
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×C4C23×#12314yes—
1047C2×C4C23×#12314yes—
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22C2×C23×#12111yescharacteristic
1079C22C2×C23×#12311yescharacteristic
1080C22C2×C23×#12311yescharacteristic
1081C22C23×#52511yescharacteristic
1082C22C23×#52511yescharacteristic
1083C22C23×#52911yescharacteristic
1084C22C23×#52911yescharacteristic
1085C22C23×#52911yescharacteristic
1086C22C23×#52911yescharacteristic
1087C22C23×#52911yescharacteristic
1088C22C23×#52911yescharacteristic
1089C22C23×#53211yescharacteristic
1090C22C23×#53211yescharacteristic
1091C22C23×#53411yescharacteristic
1092C22C23×#53511yescharacteristic
1093C22C23×#53811yescharacteristic
1094C22C23×#53811yescharacteristic
1095C22C23×#54011yescharacteristic
1096C22C23×#54011yescharacteristic
1097C22C23×#54611yescharacteristic
1098C22C23×#54611yescharacteristic
1099C22C23×#54611yescharacteristic
1100C22C23×#54611yescharacteristic
1101C22C23×#55111yescharacteristic
1102C22C23×#55111yescharacteristic
1103C22C23×#55111yescharacteristic
1104C22C23×#55111yescharacteristic
1105C22C23×#55111yescharacteristic
1106C22C23×#55311yescharacteristic
1107C22C23×#55311yescharacteristic
1108C22C23×#55311yescharacteristic
1109C22C23×#55311yescharacteristic
1110C22C23×#55511yescharacteristic
1111C22C23×#55511yescharacteristic
1112C22C23×#55911yescharacteristic
1113C4—24no—
1114C4—24no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C2—44no—
1127C2—82no—
1128C2C23×#239511yescharacteristic
1129C2C23×#241111yescharacteristic
1130C2C23×#241211yescharacteristic
1131C2C23×#242011yescharacteristic
1132C2C23×#244411yescharacteristic
1133C2C23×#245711yescharacteristic
1134C2C23×#245911yescharacteristic
1135C2C23×#250011yescharacteristic
1136C2C23×#251611yescharacteristic
1137C2C23×#252611yescharacteristic
1138C2C23×#257211yescharacteristic
1139C2C23×#257611yescharacteristic
1140C2C23×#260211yescharacteristic
1141C2C23×#266111yescharacteristic
1142C2C23×#285411yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutator, Frattini, cosocleC24C24×C23
prime radicalC23×D4×C23C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C23×#381C2semidirect
4. C2×C4×C22⋊C4×C23C2semidirect
5. C23×#1443C2semidirect
6. C23×#1442C2semidirect
7. C23×#1440C2semidirect
8. C23×#1440C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
12. C23×#1437C2semidirect
13. C23×#1437C2semidirect
14. C23×C4⋊#95C2semidirect
15. C23×#1434C2semidirect
298. #14838C23direct (N × H)
479. C2×#381C2×C23semidirect
480. C2×C4×C22⋊C4C2×C23semidirect
481. #1443C2×C23semidirect
482. #1442C2×C23semidirect
483. #1440C2×C23semidirect
484. #1440C2×C23semidirect
485. #1439C2×C23semidirect
486. #1439C2×C23semidirect
488. #1437C2×C23semidirect
489. #1437C2×C23semidirect
490. C4⋊#95C2×C23semidirect
491. #1434C2×C23semidirect
718. C23#14838direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3942
C2×C23×#3862
C2×C23×#3812
C2×C4×C22⋊C4×C232
C23×#14432
C23×#14422
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×C4⋊#952
C23×#14342
#1483823