Finite Group Databasebeta

← C23×#16562 #19164188

Subgroups — C23×#16562 #19164188

Order 5888.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#396C211yesmaximal, characteristic, complemented
2C2×C23×#386C211yesmaximal, characteristic
3C2×C23×#385C211yesmaximal, characteristic, complemented
4C2×C23×#380C211yesmaximal, characteristic, complemented
5C23×#1445C211yesmaximal, characteristic, complemented
6C23×#1442C211yesmaximal, characteristic, complemented
7C23×#1441C211yesmaximal, characteristic, complemented
8C23×#1441C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1439C211yesmaximal, characteristic, complemented
13C23×#1439C211yesmaximal, characteristic, complemented
14C23×#1438C211yesmaximal, characteristic
15C23×#1438C211yesmaximal, characteristic
16C23×D4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C4⋊C4×C23C2211yescharacteristic
22C22×C4⋊C4×C23C2211yescharacteristic
23C22×C4⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C22⋊C4×C23C2211yescharacteristic
32C22×C22⋊C4×C23C2211yescharacteristic
33C22×C22⋊C4×C23C2211yescharacteristic
34C22×C22⋊C4×C23C2211yescharacteristic
35C23×#396—24no—
36C23×#386—24no—
37C23×#385—24no—
38C23×#380—24no—
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—41no—
60C22×D4×C23—41no—
61C22×D4×C23—41no—
62C22×D4×C23—41no—
63C22×D4×C23Q814yes—
64C23×C4×C23—22no—
65C23×C4×C23—22no—
66C23×C4×C23—41no—
67C23×C4×C23—41no—
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—22no—
88C2×C4⋊C4×C23—22no—
89C2×C4⋊C4×C23—22no—
90C2×C4⋊C4×C23—22no—
91C2×C4⋊C4×C23—41no—
92C2×C4⋊C4×C23—41no—
93C2×C4⋊C4×C23—41no—
94C2×C4⋊C4×C23—41no—
95C2×C4⋊C4×C23—41no—
96C2×C4⋊C4×C23—41no—
97C2×C4⋊C4×C23—41no—
98C2×C4⋊C4×C23—41no—
99C2×C4⋊C4×C23—41no—
100C2×C4⋊C4×C23—41no—
101C2×C4⋊C4×C23D414yescomplemented
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—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—41no—
120C2×C22⋊C4×C23—41no—
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—
135C23×#95—22no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—22no—
139C23×#95—22no—
140C23×#95—22no—
141C23×#95—22no—
142C23×#95—22no—
143C23×#95—41no—
144C23×#95—41no—
145C23×#95—41no—
146C23×#95—41no—
147C23×#95—41no—
148C23×#95—41no—
149C23×#95—41no—
150C23×#95—41no—
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×C23—21no—
174C24×C23—21no—
175C24×C23—21no—
176C24×C23—21no—
177C24×C23C2×D412yes—
178C24×C23C2×Q812yes—
179C24×C23C2×Q812yes—
180C24×C23#4112yes—
181C24×C23C2411yescharacteristic
182C2×D4×C23—28no—
183C2×D4×C23—44no—
184C2×D4×C23—44no—
185C2×D4×C23—44no—
186C2×D4×C23—44no—
187C2×D4×C23—44no—
188C2×D4×C23—44no—
189C22×C4×C23—21no—
190C22×C4×C23—21no—
191C22×C4×C23—21no—
192C22×C4×C23—21no—
193C22×C4×C23—21no—
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—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—28no—
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—21no—
268C22×C4×C23—21no—
269C22×C4×C23—21no—
270C22×C4×C23—21no—
271C22×C4×C23—21no—
272C22×C4×C23—44no—
273C22×C4×C23—44no—
274C22×C4×C23—44no—
275C22×C4×C23—44no—
276C22×C4×C23—44no—
277C22×C4×C23—44no—
278C22×C4×C23C2×D412yes—
279C22×C4×C23C2×D412yes—
280C22×C4×C23C2×D412yes—
281C22×C4×C23C2×D412yes—
282C22×C4×C23C2×D412yes—
283C22×C4×C23C2×Q812yes—
284C22×C4×C23#4112yes—
285C22×C4×C23#4112yes—
286C22×C4×C23#4112yes—
287C4⋊C4×C23—44no—
288C4⋊C4×C23—44no—
289C4⋊C4×C23—44no—
290C4⋊C4×C23—44no—
291C4⋊C4×C23—44no—
292C4⋊C4×C23—44no—
293C22⋊C4×C23—28no—
294C22⋊C4×C23—44no—
295C22⋊C4×C23—44no—
296C22⋊C4×C23—44no—
297C22⋊C4×C23—44no—
298C22⋊C4×C23—44no—
299C22⋊C4×C23—44no—
300C22⋊C4×C23—44no—
301C22⋊C4×C23—44no—
302C22⋊C4×C23—44no—
303C22⋊C4×C23—44no—
304#16562C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
325C23×C23—22no—
326C23×C23—22no—
327C23×C23—22no—
328C23×C23—22no—
329C23×C23—22no—
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—41no—
369C23×C23—41no—
370C23×C23—41no—
371C23×C23—41no—
372C23×C23—41no—
373C23×C23—41no—
374C23×C23C22⋊Q814yes—
375C23×C23C22×D411yescharacteristic
376C23×C23C22×D411yescharacteristic
377C23×C23C22×Q811yescharacteristic
378C23×C23C2×#4111yescharacteristic
379C23×C23C2×#4111yescharacteristic
380C23×C23C2×#4111yescharacteristic
381C23×C23C2×#4111yescharacteristic
382C23×C23H(5,𝔽2)11yescharacteristic
383C23×C23H(5,𝔽2)11yescharacteristic
384C23×C23H(5,𝔽2)11yescharacteristic
385C23×C23H(5,𝔽2)11yescharacteristic
386C23×C23H(5,𝔽2)11yescharacteristic
387C23×C23H(5,𝔽2)11yescharacteristic
388C23×C23H(5,𝔽2)11yescharacteristic
389C23×C232−1+411yescharacteristic
390D4×C23—416no—
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—22no—
413C2×C4×C23—22no—
414C2×C4×C23—22no—
415C2×C4×C23—416no—
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—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#12114yes—
483C2×#396C2×C2311yescharacteristic, complemented
484C2×#386C2×C2311yescharacteristic
485C2×#385C2×C2311yescharacteristic, complemented
486C2×#380C2×C2311yescharacteristic, complemented
487#1445C2×C2311yescharacteristic, complemented
488#1442C2×C2311yescharacteristic, complemented
489#1441C2×C2311yescharacteristic, complemented
490#1441C2×C2311yescharacteristic, complemented
491#1439C2×C2311yescharacteristic, complemented
492#1439C2×C2311yescharacteristic, complemented
493#1439C2×C2311yescharacteristic, complemented
494#1439C2×C2311yescharacteristic, complemented
495#1439C2×C2311yescharacteristic, complemented
496#1438C2×C2311yescharacteristic
497#1438C2×C2311yescharacteristic
498C22×C23—24no—
499C22×C23—24no—
500C22×C23—24no—
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—42no—
515C22×C23—42no—
516C22×C23—42no—
517C22×C23—42no—
518C22×C23—42no—
519C22×C23—42no—
520C22×C23—81no—
521C22×C23—81no—
522C22×C23—81no—
523C22×C23—81no—
524C22×C23—81no—
525C22×C23—81no—
526C22×C23—81no—
527C22×C23—81no—
528C22×C23C2×#12111yescharacteristic
529C22×C23C2×C22⋊Q811yescharacteristic
530C22×C23#52511yescharacteristic
531C22×C23#53411yescharacteristic
532C22×C23#53411yescharacteristic
533C22×C23#53411yescharacteristic
534C22×C23#53511yescharacteristic
535C22×C23#53511yescharacteristic
536C22×C23#53711yescharacteristic
537C22×C23#53811yescharacteristic
538C22×C23#53811yescharacteristic
539C22×C23#53811yescharacteristic
540C22×C23#53811yescharacteristic
541C22×C23#53811yescharacteristic
542C22×C23#53911yescharacteristic
543C22×C23#54011yescharacteristic
544C22×C23#54211yescharacteristic
545C22×C23#54311yescharacteristic
546C22×C23#54311yescharacteristic
547C22×C23#54611yescharacteristic
548C22×C23#54611yescharacteristic
549C22×C23D4×Q811yescharacteristic
550C22×C23#55011yescharacteristic
551C22×C23#55211yescharacteristic
552C22×C23#55311yescharacteristic
553C22×C23#55311yescharacteristic
554C22×C23#55311yescharacteristic
555C22×C23#55411yescharacteristic
556C22×C23#55411yescharacteristic
557C22×C23#55411yescharacteristic
558C22×C23#55511yescharacteristic
559C22×C23#56011yescharacteristic
560C22×C23#56011yescharacteristic
561C22×C23#56211yescharacteristic
562C22×C23#56211yescharacteristic
563C4×C23—24no—
564C4×C23—42no—
565C4×C23—42no—
566C4×C23—42no—
567C4×C23—42no—
568C4×C23—42no—
569C4×C23—42no—
570C4×C23—81no—
571C4×C23—81no—
572C4×C23—81no—
573C4×C23—81no—
574C4×C23—81no—
575C4×C23—81no—
576C23×D4C22×C2311yescharacteristic
577C24×C4C22×C2311yescharacteristic
578C22×C4⋊C4C22×C2311yescharacteristic
579C22×C4⋊C4C22×C2311yescharacteristic
580C22×C4⋊C4C22×C2311yescharacteristic
581C22×C4⋊C4C22×C2311yescharacteristic
582C22×C4⋊C4C22×C2311yescharacteristic
583C22×C4⋊C4C22×C2311yescharacteristic
584C22×C22⋊C4C22×C2311yescharacteristic
585C22×C22⋊C4C22×C2311yescharacteristic
586C22×C22⋊C4C22×C2311yescharacteristic
587C22×C22⋊C4C22×C2311yescharacteristic
588C22×C22⋊C4C22×C2311yescharacteristic
589C22×C22⋊C4C22×C2311yescharacteristic
590C22×C22⋊C4C22×C2311yescharacteristic
591C22×C22⋊C4C22×C2311yescharacteristic
592C22×C22⋊C4C22×C2311yescharacteristic
593C22×C22⋊C4C22×C2311yescharacteristic
594C22×C22⋊C4C22×C2311yescharacteristic
595#396—24no—
596#386—24no—
597#385—24no—
598#380—24no—
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×#95C22×C2311yescharacteristic
610C2×#95C22×C2311yescharacteristic
611C2×#95C22×C2311yescharacteristic
612C2×#95C22×C2311yescharacteristic
613C2×#95C22×C2311yescharacteristic
614C2×#95C22×C2311yescharacteristic
615C2×C23—44no—
616C2×C23—82no—
617C2×C23#241411yescharacteristic
618C2×C23#241711yescharacteristic
619C2×C23#257911yescharacteristic
620C2×C23#261711yescharacteristic
621C2×C23#262611yescharacteristic
622C2×C23#263011yescharacteristic
623C2×C23#268811yescharacteristic
624C2×C23#269211yescharacteristic
625C2×C23#271411yescharacteristic
626C2×C23#273211yescharacteristic
627C2×C23#277911yescharacteristic
628C2×C23#278011yescharacteristic
629C2×C23#278111yescharacteristic
630C2×C23#278411yescharacteristic
631C2×C23#281311yescharacteristic
632C25C23×C2311yescharacteristic
633C25C23×C2311yescharacteristic
634C22×D4—22no—
635C22×D4—22no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4Q8×C2314yes—
641C23×C4—22no—
642C23×C4—22no—
643C23×C4—41no—
644C23×C4—41no—
645C23×C4—41no—
646C23×C4—41no—
647C23×C4D4×C2314yes—
648C23×C4C23×C2311yescharacteristic
649C23×C4C23×C2311yescharacteristic
650C23×C4C23×C2311yescharacteristic
651C23×C4C23×C2311yescharacteristic
652C23×C4C23×C2311yescharacteristic
653C23×C4C23×C2311yescharacteristic
654C23×C4C23×C2311yescharacteristic
655C23×C4C23×C2311yescharacteristic
656C23×C4C23×C2311yescharacteristic
657C23×C4C23×C2311yescharacteristic
658C23×C4C23×C2311yescharacteristic
659C23×C4C23×C2311yescharacteristic
660C23×C4C23×C2311yescharacteristic
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4D4×C2314yescomplemented
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95—41no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95—41no—
728C23#1656211yescharacteristic, direct product factor, Sylow
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—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24C2×D4×C2312yes—
756C24C2×Q8×C2312yes—
757C24C2×Q8×C2312yes—
758C24#41×C2312yes—
759C24C24×C2311yescharacteristic
760C2×D4—28no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
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—21no—
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—28no—
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—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4C2×D4×C2312yes—
857C22×C4C2×D4×C2312yes—
858C22×C4C2×D4×C2312yes—
859C22×C4C2×D4×C2312yes—
860C22×C4C2×D4×C2312yes—
861C22×C4C2×Q8×C2312yes—
862C22×C4#41×C2312yes—
863C22×C4#41×C2312yes—
864C22×C4#41×C2312yes—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C22⋊C4—28no—
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—
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—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
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—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23C23×C22⋊Q814yes—
952C23C22×D4×C2311yescharacteristic
953C23C22×D4×C2311yescharacteristic
954C23C22×Q8×C2311yescharacteristic
955C23C2×#41×C2311yescharacteristic
956C23C2×#41×C2311yescharacteristic
957C23C2×#41×C2311yescharacteristic
958C23C2×#41×C2311yescharacteristic
959C23C23×H(5,𝔽2)11yescharacteristic
960C23C23×H(5,𝔽2)11yescharacteristic
961C23C23×H(5,𝔽2)11yescharacteristic
962C23C23×H(5,𝔽2)11yescharacteristic
963C23C23×H(5,𝔽2)11yescharacteristic
964C23C23×H(5,𝔽2)11yescharacteristic
965C23C23×H(5,𝔽2)11yescharacteristic
966C23C23×2−1+411yescharacteristic
967D4—416no—
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—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—416no—
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×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×C4C23×#12114yes—
1060C22—24no—
1061C22—24no—
1062C22—24no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22C2×C23×#12111yescharacteristic
1091C22C2×C23×C22⋊Q811yescharacteristic
1092C22C23×#52511yescharacteristic
1093C22C23×#53411yescharacteristic
1094C22C23×#53411yescharacteristic
1095C22C23×#53411yescharacteristic
1096C22C23×#53511yescharacteristic
1097C22C23×#53511yescharacteristic
1098C22C23×#53711yescharacteristic
1099C22C23×#53811yescharacteristic
1100C22C23×#53811yescharacteristic
1101C22C23×#53811yescharacteristic
1102C22C23×#53811yescharacteristic
1103C22C23×#53811yescharacteristic
1104C22C23×#53911yescharacteristic
1105C22C23×#54011yescharacteristic
1106C22C23×#54211yescharacteristic
1107C22C23×#54311yescharacteristic
1108C22C23×#54311yescharacteristic
1109C22C23×#54611yescharacteristic
1110C22C23×#54611yescharacteristic
1111C22D4×Q8×C2311yescharacteristic
1112C22C23×#55011yescharacteristic
1113C22C23×#55211yescharacteristic
1114C22C23×#55311yescharacteristic
1115C22C23×#55311yescharacteristic
1116C22C23×#55311yescharacteristic
1117C22C23×#55411yescharacteristic
1118C22C23×#55411yescharacteristic
1119C22C23×#55411yescharacteristic
1120C22C23×#55511yescharacteristic
1121C22C23×#56011yescharacteristic
1122C22C23×#56011yescharacteristic
1123C22C23×#56211yescharacteristic
1124C22C23×#56211yescharacteristic
1125C4—24no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—81no—
1134C4—81no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C2—44no—
1139C2—82no—
1140C2C23×#241411yescharacteristic
1141C2C23×#241711yescharacteristic
1142C2C23×#257911yescharacteristic
1143C2C23×#261711yescharacteristic
1144C2C23×#262611yescharacteristic
1145C2C23×#263011yescharacteristic
1146C2C23×#268811yescharacteristic
1147C2C23×#269211yescharacteristic
1148C2C23×#271411yescharacteristic
1149C2C23×#273211yescharacteristic
1150C2C23×#277911yescharacteristic
1151C2C23×#278011yescharacteristic
1152C2C23×#278111yescharacteristic
1153C2C23×#278411yescharacteristic
1154C2C23×#281311yescharacteristic
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
1. C2×C23×#396C2semidirect
3. C2×C23×#385C2semidirect
4. C2×C23×#380C2semidirect
5. C23×#1445C2semidirect
6. C23×#1442C2semidirect
7. C23×#1441C2semidirect
8. C23×#1441C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
11. C23×#1439C2semidirect
12. C23×#1439C2semidirect
13. C23×#1439C2semidirect
101. C2×C4⋊C4×C23D4semidirect
304. #16562C23direct (N × H)
483. C2×#396C2×C23semidirect
485. C2×#385C2×C23semidirect
486. C2×#380C2×C23semidirect
487. #1445C2×C23semidirect
488. #1442C2×C23semidirect
489. #1441C2×C23semidirect
490. #1441C2×C23semidirect
491. #1439C2×C23semidirect
492. #1439C2×C23semidirect
493. #1439C2×C23semidirect
494. #1439C2×C23semidirect
495. #1439C2×C23semidirect
678. C2×C4⋊C4D4×C23semidirect
728. C23#16562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3962
C2×C23×#3862
C2×C23×#3852
C2×C23×#3802
C23×#14452
C23×#14422
C23×#14412
C23×#14392
C23×#14382
#1656223