Finite Group Databasebeta

← C23×#14817 #19162443

Subgroups — C23×#14817 #19162443

Order 5888.

1942 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#394C211yesmaximal, characteristic
2C2×C23×#393C211yesmaximal, characteristic, complemented
3C2×C23×#393C211yesmaximal, characteristic, complemented
4C2×C23×#391C211yesmaximal, characteristic, complemented
5C2×C23×#386C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
7C23×#1443C211yesmaximal, characteristic, complemented
8C23×#1442C211yesmaximal, characteristic, complemented
9C23×#1440C211yesmaximal, characteristic, complemented
10C23×#1440C211yesmaximal, characteristic, complemented
11C23×#1438C211yesmaximal, characteristic
12C23×#1437C211yesmaximal, characteristic, complemented
13C23×#1437C211yesmaximal, characteristic, complemented
14C23×#1434C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C23C2211yescharacteristic
17C23×D4×C23C2211yescharacteristic
18C24×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×#393—24no—
35C23×#393—24no—
36C23×#391—24no—
37C23×#386—24no—
38C4×C22⋊C4×C23—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
55C2×C23×#95C2211yescharacteristic
56C2×C23×#95C2211yescharacteristic
57C25×C23C2311yescharacteristic
58C25×C23C2311yescharacteristic
59C22×Q8×C23—22no—
60C22×Q8×C23—22no—
61C22×Q8×C23—22no—
62C22×Q8×C23—22no—
63C22×Q8×C23—22no—
64C22×Q8×C23—41no—
65C22×Q8×C23—41no—
66C22×D4×C23—22no—
67C22×D4×C23—22no—
68C22×D4×C23—22no—
69C22×D4×C23—22no—
70C22×D4×C23—22no—
71C22×D4×C23—41no—
72C22×D4×C23—41no—
73C23×C4×C23—22no—
74C23×C4×C23—22no—
75C23×C4×C23—22no—
76C23×C4×C23—22no—
77C23×C4×C23—22no—
78C23×C4×C23—41no—
79C23×C4×C23—41no—
80C23×C4×C23C2311yescharacteristic
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
93C2×C4⋊C4×C23—22no—
94C2×C4⋊C4×C23—22no—
95C2×C4⋊C4×C23—41no—
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—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—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×C23D414yes—
129C2×C42×C23—22no—
130C2×C42×C23—22no—
131C2×C42×C23—22no—
132C2×C42×C23—22no—
133C2×C42×C23—41no—
134C2×C42×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—22no—
144C23×#95—22no—
145C23×#95—22no—
146C23×#95—22no—
147C23×#95—22no—
148C23×#95—41no—
149C23×#95—41no—
150C23×#95—41no—
151C23×#95D414yes—
152C23×#95D414yescomplemented
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×C23—21no—
178C24×C23—21no—
179C24×C23C2×D412yes—
180C24×C23#4112yes—
181C24×C23#4112yes—
182C24×C23#4112yes—
183C24×C23C2411yescharacteristic
184C2×Q8×C23—28no—
185C2×Q8×C23—44no—
186C2×Q8×C23—44no—
187C2×Q8×C23—44no—
188C2×Q8×C23—44no—
189C2×Q8×C23—44no—
190C2×Q8×C23—44no—
191C2×D4×C23—28no—
192C2×D4×C23—44no—
193C2×D4×C23—44no—
194C2×D4×C23—44no—
195C2×D4×C23—44no—
196C2×D4×C23—44no—
197C2×D4×C23—44no—
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—28no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—21no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—21no—
238C22×C4×C23—21no—
239C22×C4×C23—21no—
240C22×C4×C23—21no—
241C22×C4×C23—21no—
242C22×C4×C23—21no—
243C22×C4×C23—21no—
244C22×C4×C23—21no—
245C22×C4×C23—21no—
246C22×C4×C23—21no—
247C22×C4×C23—21no—
248C22×C4×C23—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—21no—
276C22×C4×C23—21no—
277C22×C4×C23—44no—
278C22×C4×C23—44no—
279C22×C4×C23—44no—
280C22×C4×C23—44no—
281C22×C4×C23—44no—
282C22×C4×C23—44no—
283C22×C4×C23C2×D412yes—
284C22×C4×C23C2×D412yes—
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×C23#4112yes—
292C22×C4×C23#4112yes—
293C22×C4×C23#4112yes—
294C22×C4×C23#4112yes—
295C22×C4×C23#4112yes—
296C4⋊C4×C23—44no—
297C22⋊C4×C23—28no—
298C22⋊C4×C23—28no—
299C22⋊C4×C23—44no—
300C22⋊C4×C23—44no—
301C22⋊C4×C23—44no—
302C22⋊C4×C23—44no—
303C22⋊C4×C23—44no—
304C22⋊C4×C23—44no—
305C22⋊C4×C23—44no—
306C22⋊C4×C23—44no—
307C22⋊C4×C23—44no—
308C42×C23—44no—
309C42×C23—44no—
310#14817C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
331C23×C23—22no—
332C23×C23—22no—
333C23×C23—22no—
334C23×C23—22no—
335C23×C23—22no—
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×C23—41no—
375C23×C23—41no—
376C23×C23—41no—
377C23×C23—41no—
378C23×C23—41no—
379C23×C23—41no—
380C23×C23#12414yes—
381C23×C23C22×D411yescharacteristic
382C23×C23C22×D411yescharacteristic
383C23×C23C22×D411yescharacteristic
384C23×C23C2×#4111yescharacteristic
385C23×C23C2×#4111yescharacteristic
386C23×C23C2×#4111yescharacteristic
387C23×C23C2×#4111yescharacteristic
388C23×C23C2×#4111yescharacteristic
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×C232−1+411yescharacteristic
396Q8×C23—416no—
397D4×C23—416no—
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—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—416no—
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—41no—
483C2×C4×C23—41no—
484C2×C4×C23—41no—
485C2×C4×C23—41no—
486C2×C4×C23—41no—
487C2×C4×C23—41no—
488C2×C4×C23#12114yes—
489C2×C4×C23#12414yes—
490C2×#394C2×C2311yescharacteristic
491C2×#393C2×C2311yescharacteristic, complemented
492C2×#393C2×C2311yescharacteristic, complemented
493C2×#391C2×C2311yescharacteristic, complemented
494C2×#386C2×C2311yescharacteristic
495C2×C4×C22⋊C4C2×C2311yescharacteristic, complemented
496#1443C2×C2311yescharacteristic, complemented
497#1442C2×C2311yescharacteristic, complemented
498#1440C2×C2311yescharacteristic, complemented
499#1440C2×C2311yescharacteristic, complemented
500#1438C2×C2311yescharacteristic
501#1437C2×C2311yescharacteristic, complemented
502#1437C2×C2311yescharacteristic, complemented
503#1434C2×C2311yescharacteristic, complemented
504C22⋊#95C2×C2311yescharacteristic, complemented
505C22×C23—24no—
506C22×C23—24no—
507C22×C23—24no—
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—42no—
521C22×C23—42no—
522C22×C23—42no—
523C22×C23—42no—
524C22×C23—42no—
525C22×C23—42no—
526C22×C23—42no—
527C22×C23—81no—
528C22×C23—81no—
529C22×C23—81no—
530C22×C23—81no—
531C22×C23—81no—
532C22×C23—81no—
533C22×C23—81no—
534C22×C23—81no—
535C22×C23C2×#12111yescharacteristic
536C22×C23#52511yescharacteristic
537C22×C23#52511yescharacteristic
538C22×C23#52511yescharacteristic
539C22×C23#52511yescharacteristic
540C22×C23C2×#12411yescharacteristic
541C22×C23C2×#12411yescharacteristic
542C22×C23#52911yescharacteristic
543C22×C23#52911yescharacteristic
544C22×C23#52911yescharacteristic
545C22×C23#52911yescharacteristic
546C22×C23#52911yescharacteristic
547C22×C23#53211yescharacteristic
548C22×C23#53811yescharacteristic
549C22×C23#53811yescharacteristic
550C22×C23#53811yescharacteristic
551C22×C23#53911yescharacteristic
552C22×C23#54211yescharacteristic
553C22×C23#54211yescharacteristic
554C22×C23D4211yescharacteristic
555C22×C23D4211yescharacteristic
556C22×C23#54611yescharacteristic
557C22×C23#54611yescharacteristic
558C22×C23#54611yescharacteristic
559C22×C23#54611yescharacteristic
560C22×C23#54611yescharacteristic
561C22×C23#54711yescharacteristic
562C22×C23#54811yescharacteristic
563C22×C23#54811yescharacteristic
564C22×C23#55111yescharacteristic
565C22×C23#55111yescharacteristic
566C22×C23#55111yescharacteristic
567C22×C23#55211yescharacteristic
568C22×C23#55511yescharacteristic
569C22×C23#55911yescharacteristic
570C4×C23—24no—
571C4×C23—24no—
572C4×C23—42no—
573C4×C23—42no—
574C4×C23—42no—
575C4×C23—42no—
576C4×C23—42no—
577C4×C23—42no—
578C4×C23—42no—
579C4×C23—81no—
580C4×C23—81no—
581C4×C23—81no—
582C4×C23—81no—
583C23×Q8C22×C2311yescharacteristic
584C23×D4C22×C2311yescharacteristic
585C24×C4C22×C2311yescharacteristic
586C22×C4⋊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
595C22×C22⋊C4C22×C2311yescharacteristic
596C22×C22⋊C4C22×C2311yescharacteristic
597C22×C22⋊C4C22×C2311yescharacteristic
598C22×C42C22×C2311yescharacteristic
599C22×C42C22×C2311yescharacteristic
600#394—24no—
601#393—24no—
602#393—24no—
603#391—24no—
604#386—24no—
605C4×C22⋊C4—24no—
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×#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×C23—44no—
625C2×C23—82no—
626C2×C23#239811yescharacteristic
627C2×C23#242411yescharacteristic
628C2×C23#242711yescharacteristic
629C2×C23#245811yescharacteristic
630C2×C23#245911yescharacteristic
631C2×C23#246311yescharacteristic
632C2×C23#247211yescharacteristic
633C2×C23#247211yescharacteristic
634C2×C23#247711yescharacteristic
635C2×C23#248811yescharacteristic
636C2×C23#249111yescharacteristic
637C2×C23#255711yescharacteristic
638C2×C23#257211yescharacteristic
639C2×C23#265311yescharacteristic
640C2×C23#285011yescharacteristic
641C25C23×C2311yescharacteristic
642C25C23×C2311yescharacteristic
643C22×Q8—22no—
644C22×Q8—22no—
645C22×Q8—22no—
646C22×Q8—22no—
647C22×Q8—22no—
648C22×Q8—41no—
649C22×Q8—41no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—41no—
656C22×D4—41no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—41no—
663C23×C4—41no—
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
674C23×C4C23×C2311yescharacteristic
675C23×C4C23×C2311yescharacteristic
676C23×C4C23×C2311yescharacteristic
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—41no—
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—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—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4D4×C2314yes—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—22no—
716C2×C42—22no—
717C2×C42—41no—
718C2×C42—41no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—41no—
733#95—41no—
734#95—41no—
735#95D4×C2314yes—
736#95D4×C2314yescomplemented
737C23#1481711yescharacteristic, direct product factor, Sylow
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—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24C2×D4×C2312yes—
765C24#41×C2312yes—
766C24#41×C2312yes—
767C24#41×C2312yes—
768C24C24×C2311yescharacteristic
769C2×Q8—28no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—44no—
776C2×D4—28no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
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—28no—
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—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—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—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4C2×D4×C2312yes—
869C22×C4C2×D4×C2312yes—
870C22×C4C2×D4×C2312yes—
871C22×C4C2×D4×C2312yes—
872C22×C4C2×D4×C2312yes—
873C22×C4C2×D4×C2312yes—
874C22×C4C2×D4×C2312yes—
875C22×C4C2×D4×C2312yes—
876C22×C4#41×C2312yes—
877C22×C4#41×C2312yes—
878C22×C4#41×C2312yes—
879C22×C4#41×C2312yes—
880C22×C4#41×C2312yes—
881C4⋊C4—44no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C42—44no—
894C42—44no—
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—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—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—
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—
964C23C23×#12414yes—
965C23C22×D4×C2311yescharacteristic
966C23C22×D4×C2311yescharacteristic
967C23C22×D4×C2311yescharacteristic
968C23C2×#41×C2311yescharacteristic
969C23C2×#41×C2311yescharacteristic
970C23C2×#41×C2311yescharacteristic
971C23C2×#41×C2311yescharacteristic
972C23C2×#41×C2311yescharacteristic
973C23C2×#41×C2311yescharacteristic
974C23C2×#41×C2311yescharacteristic
975C23C2×#41×C2311yescharacteristic
976C23C23×H(5,𝔽2)11yescharacteristic
977C23C23×H(5,𝔽2)11yescharacteristic
978C23C23×H(5,𝔽2)11yescharacteristic
979C23C23×2−1+411yescharacteristic
980Q8—416no—
981D4—416no—
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—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—416no—
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×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×C4C23×#12114yes—
1073C2×C4C23×#12414yes—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
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—81no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22C2×C23×#12111yescharacteristic
1105C22C23×#52511yescharacteristic
1106C22C23×#52511yescharacteristic
1107C22C23×#52511yescharacteristic
1108C22C23×#52511yescharacteristic
1109C22C2×C23×#12411yescharacteristic
1110C22C2×C23×#12411yescharacteristic
1111C22C23×#52911yescharacteristic
1112C22C23×#52911yescharacteristic
1113C22C23×#52911yescharacteristic
1114C22C23×#52911yescharacteristic
1115C22C23×#52911yescharacteristic
1116C22C23×#53211yescharacteristic
1117C22C23×#53811yescharacteristic
1118C22C23×#53811yescharacteristic
1119C22C23×#53811yescharacteristic
1120C22C23×#53911yescharacteristic
1121C22C23×#54211yescharacteristic
1122C22C23×#54211yescharacteristic
1123C22D42×C2311yescharacteristic
1124C22D42×C2311yescharacteristic
1125C22C23×#54611yescharacteristic
1126C22C23×#54611yescharacteristic
1127C22C23×#54611yescharacteristic
1128C22C23×#54611yescharacteristic
1129C22C23×#54611yescharacteristic
1130C22C23×#54711yescharacteristic
1131C22C23×#54811yescharacteristic
1132C22C23×#54811yescharacteristic
1133C22C23×#55111yescharacteristic
1134C22C23×#55111yescharacteristic
1135C22C23×#55111yescharacteristic
1136C22C23×#55211yescharacteristic
1137C22C23×#55511yescharacteristic
1138C22C23×#55911yescharacteristic
1139C4—24no—
1140C4—24no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C2—44no—
1153C2—82no—
1154C2C23×#239811yescharacteristic
1155C2C23×#242411yescharacteristic
1156C2C23×#242711yescharacteristic
1157C2C23×#245811yescharacteristic
1158C2C23×#245911yescharacteristic
1159C2C23×#246311yescharacteristic
1160C2C23×#247211yescharacteristic
1161C2C23×#247211yescharacteristic
1162C2C23×#247711yescharacteristic
1163C2C23×#248811yescharacteristic
1164C2C23×#249111yescharacteristic
1165C2C23×#255711yescharacteristic
1166C2C23×#257211yescharacteristic
1167C2C23×#265311yescharacteristic
1168C2C23×#285011yescharacteristic
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
2. C2×C23×#393C2semidirect
3. C2×C23×#393C2semidirect
4. C2×C23×#391C2semidirect
6. C2×C4×C22⋊C4×C23C2semidirect
7. C23×#1443C2semidirect
8. C23×#1442C2semidirect
9. C23×#1440C2semidirect
10. C23×#1440C2semidirect
12. C23×#1437C2semidirect
13. C23×#1437C2semidirect
14. C23×#1434C2semidirect
15. C23×C22⋊#95C2semidirect
152. C23×#95D4semidirect
310. #14817C23direct (N × H)
491. C2×#393C2×C23semidirect
492. C2×#393C2×C23semidirect
493. C2×#391C2×C23semidirect
495. C2×C4×C22⋊C4C2×C23semidirect
496. #1443C2×C23semidirect
497. #1442C2×C23semidirect
498. #1440C2×C23semidirect
499. #1440C2×C23semidirect
501. #1437C2×C23semidirect
502. #1437C2×C23semidirect
503. #1434C2×C23semidirect
504. C22⋊#95C2×C23semidirect
736. #95D4×C23semidirect
737. C23#14817direct (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×#3932
C2×C23×#3912
C2×C23×#3862
C2×C4×C22⋊C4×C232
C23×#14432
C23×#14422
C23×#14402
C23×#14382
C23×#14372
C23×#14342
C23×C22⋊#952
#1481723