Finite Group Databasebeta

← C23×#18448 #19166074

Subgroups — C23×#18448 #19166074

Order 5888.

968 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3535C211yesmaximal, characteristic, complemented
2C23×#3193C211yesmaximal, characteristic, complemented
3C23×#3188C211yesmaximal, characteristic, complemented
4C23×#2813C211yesmaximal, characteristic, complemented
5C23×#1618C211yesmaximal, characteristic, complemented
6C23×#1617C211yesmaximal, characteristic, complemented
7C23×#1615C211yesmaximal, characteristic, complemented
8C23×#1614C211yesmaximal, characteristic, complemented
9C23×#1600C211yesmaximal, characteristic, complemented
10C23×#1599C211yesmaximal, characteristic, complemented
11C23×#1597C211yesmaximal, characteristic, complemented
12C23×#1596C211yesmaximal, characteristic, complemented
13C23×#1520C211yesmaximal, characteristic, complemented
14C23×#1513C211yesmaximal, characteristic, complemented
15C23×#1468C211yesmaximal, characteristic, complemented
16C23×#563—21no—
17C23×#562—21no—
18C23×#554—21no—
19C23×#552—21no—
20C23×#551—21no—
21C23×#551—21no—
22C23×#547—21no—
23C23×#546—21no—
24C23×#544C2211yescharacteristic
25C23×#543C2211yescharacteristic
26C23×#542—21no—
27C23×#539—21no—
28C23×#539—21no—
29C23×#539C2211yescharacteristic
30C23×#538C2211yescharacteristic
31C23×#536—21no—
32C23×#525C2211yescharacteristic
33C2×C23×#123C2211yescharacteristic
34C2×C23×C22⋊Q8C2211yescharacteristic
35C2×C23×#121C2211yescharacteristic
36C23×#484C2211yescharacteristic
37C23×#484C2211yescharacteristic
38C23×#484C2211yescharacteristic
39C23×#482—21no—
40C23×#481C2211yescharacteristic
41C23×#480—21no—
42C23×#468—21no—
43C23×#468—21no—
44C23×#466—21no—
45C23×#465—21no—
46C23×#450C2211yescharacteristic
47C23×#450C2211yescharacteristic
48C23×#450C2211yescharacteristic
49C23×#449—21no—
50C23×#448—21no—
51C23×#447C2211yescharacteristic
52C23×#407C2211yescharacteristic
53C2×C23×C22⋊C8C2211yescharacteristic
54C23×#400C2211yescharacteristic
55C23×#399C2211yescharacteristic
56C23×#396—21no—
57C23×#394—21no—
58C23×#394—21no—
59C23×#394C2211yescharacteristic
60C23×#392—21no—
61C23×#392C2211yescharacteristic
62C23×#380C2211yescharacteristic
63C23×#328C2211yescharacteristic
64C23×#328C2211yescharacteristic
65C23×#328C2211yescharacteristic
66C23×#328C2211yescharacteristic
67C23×#328C2211yescharacteristic
68C23×#328C2211yescharacteristic
69C23×#327C2211yescharacteristic
70C23×#327C2211yescharacteristic
71C23×#324C2211yescharacteristic
72C23×#324C2211yescharacteristic
73C23×#323C2211yescharacteristic
74C23×#323C2211yescharacteristic
75C2×#41×C23—21no—
76C2×#41×C23D411yescharacteristic, complemented
77C22×Q8×C23D411yescharacteristic, complemented
78C22×D4×C23—21no—
79C22×D4×C23—21no—
80C22×D4×C23D411yescharacteristic
81C22×D4×C23C2311yescharacteristic
82C23×C4×C23C2311yescharacteristic
83C2×SD16×C23—21no—
84C2×SD16×C23—21no—
85C2×SD16×C23—21no—
86C2×D8×C23—21no—
87C2×M16×C23—21no—
88C22×C8×C23—21no—
89C23×C4⋊Q8—21no—
90C23×C4⋊Q8—21no—
91C23×C4⋊Q8—21no—
92C23×#126—21no—
93C23×#126—21no—
94C23×#126—21no—
95C23×#126—21no—
96C23×#126—21no—
97C23×#126—21no—
98C23×#125—21no—
99C23×#125—21no—
100C23×#125—21no—
101C23×#125—21no—
102C23×#125—21no—
103C23×#124—21no—
104C23×#124—21no—
105C23×#124—21no—
106C23×#124—21no—
107C23×#123—21no—
108C23×#123—21no—
109C23×#123—21no—
110C23×#123—21no—
111C23×#123—21no—
112C23×#123—21no—
113C23×#123—21no—
114C23×#123—21no—
115C23×#123—21no—
116C23×#123—21no—
117C23×#123—21no—
118C23×#123—21no—
119C23×#123—21no—
120C23×#123—21no—
121C23×C22⋊Q8—21no—
122C23×C22⋊Q8—21no—
123C23×C22⋊Q8—21no—
124C23×C22⋊Q8—21no—
125C23×C22⋊Q8—21no—
126C23×C22⋊Q8—21no—
127C23×C22⋊Q8—21no—
128C23×C22⋊Q8—21no—
129C23×C22⋊Q8—21no—
130C23×C22⋊Q8—21no—
131C23×C22⋊Q8—21no—
132C23×C22⋊Q8—21no—
133C23×C22⋊Q8—21no—
134C23×C22⋊Q8—21no—
135C23×C22⋊Q8D411yescharacteristic, complemented
136C23×C22⋊Q8D411yescharacteristic, complemented
137C23×C22⋊Q8D411yescharacteristic, complemented
138C23×C22⋊Q8C2311yescharacteristic
139C23×C22⋊Q8C2311yescharacteristic
140C23×C22⋊Q8C2311yescharacteristic
141C23×#121—21no—
142C23×#121—21no—
143C23×#121—21no—
144C23×#121—21no—
145C23×#121—21no—
146C23×#121—21no—
147C23×#121—21no—
148C23×#121—21no—
149C23×#121D411yescharacteristic, complemented
150C23×#121C2311yescharacteristic
151C23×#120—21no—
152C23×#120—21no—
153C4×Q8×C23—21no—
154C4×D4×C23—21no—
155C4×D4×C23—21no—
156C4×D4×C23—21no—
157C4×D4×C23—21no—
158C4×D4×C23—21no—
159C4×D4×C23—21no—
160C4×D4×C23—21no—
161C23×#117—21no—
162C23×#117—21no—
163C23×#117—21no—
164C23×#117D411yescharacteristic, complemented
165C2×C4⋊C4×C23—21no—
166C2×C4⋊C4×C23—21no—
167C2×C4⋊C4×C23—21no—
168C2×C4⋊C4×C23—21no—
169C2×C4⋊C4×C23D411yescharacteristic
170C2×C4⋊C4×C23D411yescharacteristic, complemented
171C2×C4⋊C4×C23C2311yescharacteristic
172C2×C4⋊C4×C23C2311yescharacteristic
173C2×C22⋊C4×C23—21no—
174C2×C22⋊C4×C23—21no—
175C2×C22⋊C4×C23—21no—
176C2×C22⋊C4×C23—21no—
177C2×C22⋊C4×C23—21no—
178C2×C22⋊C4×C23—21no—
179C2×C22⋊C4×C23—21no—
180C2×C22⋊C4×C23—21no—
181C2×C22⋊C4×C23D411yescharacteristic
182C2×C22⋊C4×C23D411yescharacteristic
183C2×C22⋊C4×C23C2311yescharacteristic
184C23×#107—21no—
185C23×#107—21no—
186C23×#107—21no—
187C23×#106—21no—
188C23×#103—21no—
189C23×#103—21no—
190C23×#103—21no—
191C23×#102—21no—
192C23×#102—21no—
193C23×#102—21no—
194C23×#102—21no—
195C23×#102—21no—
196C23×C22⋊C8—21no—
197C23×C22⋊C8—21no—
198C23×C22⋊C8C2311yescharacteristic
199C23×C22⋊C8C2311yescharacteristic
200C23×C22⋊C8C2311yescharacteristic
201C23×C22⋊C8C2311yescharacteristic
202C23×#95—21no—
203C23×#95—21no—
204C23×#95C2311yescharacteristic
205C23×#95C2311yescharacteristic
206C24×C23—21no—
207C24×C23C2×D411yescharacteristic
208C24×C23C2×D411yescharacteristic
209#41×C23—82no—
210#41×C23—81no—
211C2×Q8×C23—21no—
212C2×Q8×C23—21no—
213C2×Q8×C23—21no—
214C2×Q8×C23—81no—
215C2×Q8×C23C2×D411yescharacteristic
216C2×Q8×C23C2×D411yescharacteristic
217C2×Q8×C23C2×D411yescharacteristic
218C2×D4×C23—21no—
219C2×D4×C23—21no—
220C2×D4×C23—21no—
221C2×D4×C23—21no—
222C2×D4×C23—21no—
223C2×D4×C23—21no—
224C2×D4×C23—21no—
225C2×D4×C23—21no—
226C2×D4×C23—21no—
227C2×D4×C23—41no—
228C2×D4×C23—41no—
229C2×D4×C23—81no—
230C2×D4×C23—81no—
231C2×D4×C23—81no—
232C2×D4×C23—81no—
233C2×D4×C23—81no—
234C2×D4×C23—81no—
235C2×D4×C23—81no—
236C2×D4×C23C2×D411yescharacteristic
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—81no—
248C22×C4×C23C2×D411yescharacteristic
249C22×C4×C23C2×D411yescharacteristic
250C22×C4×C23C2×D411yescharacteristic
251C22×C4×C23C2×D411yescharacteristic
252C22×C4×C23C2×D411yescharacteristic
253C22×C4×C23C2×D411yescharacteristic
254C22×C4×C23C2×D411yescharacteristic
255C22×C4×C23C2×D411yescharacteristic
256C22×C4×C23C2411yescharacteristic
257SD16×C23—81no—
258SD16×C23—81no—
259SD16×C23—81no—
260D8×C23—81no—
261M16×C23—81no—
262C2×C8×C23—21no—
263C2×C8×C23—21no—
264C2×C8×C23—21no—
265C2×C8×C23—21no—
266C2×C8×C23—81no—
267C4⋊C4×C23—21no—
268C4⋊C4×C23—21no—
269C4⋊C4×C23—21no—
270C4⋊C4×C23—21no—
271C4⋊C4×C23—21no—
272C4⋊C4×C23—21no—
273C4⋊C4×C23—21no—
274C4⋊C4×C23—21no—
275C4⋊C4×C23—21no—
276C4⋊C4×C23—21no—
277C4⋊C4×C23—21no—
278C4⋊C4×C23—21no—
279C4⋊C4×C23—21no—
280C4⋊C4×C23—21no—
281C4⋊C4×C23—21no—
282C4⋊C4×C23—21no—
283C4⋊C4×C23—21no—
284C4⋊C4×C23—21no—
285C4⋊C4×C23—21no—
286C4⋊C4×C23—21no—
287C4⋊C4×C23—21no—
288C4⋊C4×C23—21no—
289C4⋊C4×C23—21no—
290C4⋊C4×C23—21no—
291C4⋊C4×C23—21no—
292C4⋊C4×C23—81no—
293C4⋊C4×C23—81no—
294C4⋊C4×C23C2×D411yescharacteristic
295C4⋊C4×C23C2×D411yescharacteristic
296C4⋊C4×C23C2×D411yescharacteristic
297C4⋊C4×C23C2×D411yescharacteristic
298C22⋊C4×C23—21no—
299C22⋊C4×C23—21no—
300C22⋊C4×C23—21no—
301C22⋊C4×C23—21no—
302C22⋊C4×C23—21no—
303C22⋊C4×C23—21no—
304C22⋊C4×C23—21no—
305C22⋊C4×C23—21no—
306C22⋊C4×C23—21no—
307C22⋊C4×C23—21no—
308C22⋊C4×C23—21no—
309C22⋊C4×C23—21no—
310C22⋊C4×C23—21no—
311C22⋊C4×C23—21no—
312C22⋊C4×C23—21no—
313C22⋊C4×C23—21no—
314C22⋊C4×C23—21no—
315C22⋊C4×C23—21no—
316C22⋊C4×C23—21no—
317C22⋊C4×C23—21no—
318C22⋊C4×C23—21no—
319C22⋊C4×C23—21no—
320C22⋊C4×C23—21no—
321C22⋊C4×C23—41no—
322C22⋊C4×C23—41no—
323C22⋊C4×C23—81no—
324C22⋊C4×C23—81no—
325C22⋊C4×C23—81no—
326C22⋊C4×C23—81no—
327C22⋊C4×C23—81no—
328C42×C23—21no—
329C42×C23—21no—
330C42×C23—21no—
331C42×C23—21no—
332C42×C23—21no—
333#18448C2311yesmaximal, characteristic, direct product factor, Sylow
334C23×C23—21no—
335C23×C23—21no—
336C23×C23—21no—
337C23×C23—21no—
338C23×C23—21no—
339C23×C23—21no—
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#12011yescharacteristic
352C23×C23#12011yescharacteristic
353C23×C23C22×D411yescharacteristic
354Q8×C23—41no—
355Q8×C23—41no—
356Q8×C23—41no—
357Q8×C23—81no—
358Q8×C23—81no—
359Q8×C23—81no—
360D4×C23—41no—
361D4×C23—41no—
362D4×C23—41no—
363D4×C23—41no—
364D4×C23—41no—
365D4×C23—42no—
366D4×C23—42no—
367D4×C23—41no—
368D4×C23—41no—
369D4×C23—81no—
370D4×C23—81no—
371D4×C23—81no—
372D4×C23—81no—
373D4×C23—82no—
374D4×C23—82no—
375D4×C23—84no—
376C2×C4×C23—21no—
377C2×C4×C23—21no—
378C2×C4×C23—21no—
379C2×C4×C23—21no—
380C2×C4×C23—21no—
381C2×C4×C23—21no—
382C2×C4×C23—21no—
383C2×C4×C23—21no—
384C2×C4×C23—21no—
385C2×C4×C23—21no—
386C2×C4×C23—21no—
387C2×C4×C23—21no—
388C2×C4×C23—41no—
389C2×C4×C23—41no—
390C2×C4×C23—41no—
391C2×C4×C23—41no—
392C2×C4×C23—41no—
393C2×C4×C23—41no—
394C2×C4×C23—42no—
395C2×C4×C23—41no—
396C2×C4×C23—41no—
397C2×C4×C23—41no—
398C2×C4×C23—41no—
399C2×C4×C23—41no—
400C2×C4×C23—41no—
401C2×C4×C23—41no—
402C2×C4×C23—41no—
403C2×C4×C23—41no—
404C2×C4×C23—41no—
405C2×C4×C23—41no—
406C2×C4×C23—81no—
407C2×C4×C23—81no—
408C2×C4×C23—81no—
409C2×C4×C23—81no—
410C2×C4×C23—81no—
411C2×C4×C23—81no—
412C2×C4×C23#12011yescharacteristic
413C2×C4×C23#12011yescharacteristic
414C2×C4×C23C22×D411yescharacteristic
415C2×C4×C23C22×D411yescharacteristic
416C8×C23—41no—
417C8×C23—41no—
418C8×C23—41no—
419C8×C23—41no—
420#3535C2×C2311yescharacteristic, complemented
421#3193C2×C2311yescharacteristic, complemented
422#3188C2×C2311yescharacteristic, complemented
423#2813C2×C2311yescharacteristic, complemented
424#1618C2×C2311yescharacteristic, complemented
425#1617C2×C2311yescharacteristic, complemented
426#1615C2×C2311yescharacteristic, complemented
427#1614C2×C2311yescharacteristic, complemented
428#1600C2×C2311yescharacteristic, complemented
429#1599C2×C2311yescharacteristic, complemented
430#1597C2×C2311yescharacteristic, complemented
431#1596C2×C2311yescharacteristic, complemented
432#1520C2×C2311yescharacteristic, complemented
433#1513C2×C2311yescharacteristic, complemented
434#1468C2×C2311yescharacteristic, complemented
435C22×C23—21no—
436C22×C23—21no—
437C22×C23—21no—
438C22×C23—21no—
439C22×C23—21no—
440C22×C23—21no—
441C22×C23—21no—
442C22×C23—21no—
443C22×C23—41no—
444C22×C23—41no—
445C22×C23—41no—
446C22×C23—41no—
447C22×C23—41no—
448C22×C23—41no—
449C22×C23—81no—
450C22×C23—81no—
451C22×C23—81no—
452C22×C23—81no—
453C22×C23—81no—
454C22×C23—81no—
455C22×C23—81no—
456C22×C23—81no—
457C22×C23—81no—
458C22×C23—81no—
459C22×C23—81no—
460C22×C23C2×#12011yescharacteristic
461C22×C23#57711yescharacteristic
462C22×C23#57811yescharacteristic
463C4×C23—21no—
464C4×C23—21no—
465C4×C23—21no—
466C4×C23—21no—
467C4×C23—41no—
468C4×C23—41no—
469C4×C23—41no—
470C4×C23—41no—
471C4×C23—41no—
472C4×C23—41no—
473C4×C23—41no—
474C4×C23—41no—
475C4×C23—41no—
476C4×C23—41no—
477C4×C23—81no—
478C4×C23—81no—
479C4×C23—81no—
480#563—21no—
481#562—21no—
482#554—21no—
483#552—21no—
484#551—21no—
485#551—21no—
486#547—21no—
487#546—21no—
488#544C22×C2311yescharacteristic
489#543C22×C2311yescharacteristic
490#542—21no—
491#539—21no—
492#539—21no—
493#539C22×C2311yescharacteristic
494#538C22×C2311yescharacteristic
495#536—21no—
496#525C22×C2311yescharacteristic
497C2×#123C22×C2311yescharacteristic
498C2×C22⋊Q8C22×C2311yescharacteristic
499C2×#121C22×C2311yescharacteristic
500#484C22×C2311yescharacteristic
501#484C22×C2311yescharacteristic
502#484C22×C2311yescharacteristic
503#482—21no—
504#481C22×C2311yescharacteristic
505#480—21no—
506#468—21no—
507#468—21no—
508#466—21no—
509#465—21no—
510#450C22×C2311yescharacteristic
511#450C22×C2311yescharacteristic
512#450C22×C2311yescharacteristic
513#449—21no—
514#448—21no—
515#447C22×C2311yescharacteristic
516#407C22×C2311yescharacteristic
517C2×C22⋊C8C22×C2311yescharacteristic
518#400C22×C2311yescharacteristic
519#399C22×C2311yescharacteristic
520#396—21no—
521#394—21no—
522#394—21no—
523#394C22×C2311yescharacteristic
524#392—21no—
525#392C22×C2311yescharacteristic
526#380C22×C2311yescharacteristic
527#328C22×C2311yescharacteristic
528#328C22×C2311yescharacteristic
529#328C22×C2311yescharacteristic
530#328C22×C2311yescharacteristic
531#328C22×C2311yescharacteristic
532#328C22×C2311yescharacteristic
533#327C22×C2311yescharacteristic
534#327C22×C2311yescharacteristic
535#324C22×C2311yescharacteristic
536#324C22×C2311yescharacteristic
537#323C22×C2311yescharacteristic
538#323C22×C2311yescharacteristic
539C2×C23—21no—
540C2×C23—21no—
541C2×C23—41no—
542C2×C23—41no—
543C2×C23—81no—
544C2×C23—81no—
545C2×C23—161no—
546C2×C23#301311yescharacteristic
547C2×C23#302111yescharacteristic
548C2×C23#302611yescharacteristic
549C2×#41—21no—
550C2×#41D4×C2311yescharacteristic, complemented
551C22×Q8D4×C2311yescharacteristic, complemented
552C22×D4—21no—
553C22×D4—21no—
554C22×D4D4×C2311yescharacteristic
555C22×D4C23×C2311yescharacteristic
556C23×C4C23×C2311yescharacteristic
557C2×SD16—21no—
558C2×SD16—21no—
559C2×SD16—21no—
560C2×D8—21no—
561C2×M16—21no—
562C22×C8—21no—
563C4⋊Q8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#124—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8D4×C2311yescharacteristic, complemented
610C22⋊Q8D4×C2311yescharacteristic, complemented
611C22⋊Q8D4×C2311yescharacteristic, complemented
612C22⋊Q8C23×C2311yescharacteristic
613C22⋊Q8C23×C2311yescharacteristic
614C22⋊Q8C23×C2311yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121D4×C2311yescharacteristic, complemented
624#121C23×C2311yescharacteristic
625#120—21no—
626#120—21no—
627C4×Q8—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635#117—21no—
636#117—21no—
637#117—21no—
638#117D4×C2311yescharacteristic, complemented
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C2311yescharacteristic
644C2×C4⋊C4D4×C2311yescharacteristic, complemented
645C2×C4⋊C4C23×C2311yescharacteristic
646C2×C4⋊C4C23×C2311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C2311yescharacteristic
656C2×C22⋊C4D4×C2311yescharacteristic
657C2×C22⋊C4C23×C2311yescharacteristic
658#107—21no—
659#107—21no—
660#107—21no—
661#106—21no—
662#103—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670C22⋊C8—21no—
671C22⋊C8—21no—
672C22⋊C8C23×C2311yescharacteristic
673C22⋊C8C23×C2311yescharacteristic
674C22⋊C8C23×C2311yescharacteristic
675C22⋊C8C23×C2311yescharacteristic
676#95—21no—
677#95—21no—
678#95C23×C2311yescharacteristic
679#95C23×C2311yescharacteristic
680C23#1844811yescharacteristic, direct product factor, Sylow
681C24—21no—
682C24C2×D4×C2311yescharacteristic
683C24C2×D4×C2311yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C2311yescharacteristic
691C2×Q8C2×D4×C2311yescharacteristic
692C2×Q8C2×D4×C2311yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C2311yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C2311yescharacteristic
724C22×C4C2×D4×C2311yescharacteristic
725C22×C4C2×D4×C2311yescharacteristic
726C22×C4C2×D4×C2311yescharacteristic
727C22×C4C2×D4×C2311yescharacteristic
728C22×C4C2×D4×C2311yescharacteristic
729C22×C4C2×D4×C2311yescharacteristic
730C22×C4C2×D4×C2311yescharacteristic
731C22×C4C24×C2311yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C2311yescharacteristic
770C4⋊C4C2×D4×C2311yescharacteristic
771C4⋊C4C2×D4×C2311yescharacteristic
772C4⋊C4C2×D4×C2311yescharacteristic
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—41no—
797C22⋊C4—41no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C22⋊C4—81no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C23×#12011yescharacteristic
826C23C23×#12011yescharacteristic
827C23C22×D4×C2311yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—82no—
848D4—82no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4C23×#12011yescharacteristic
887C2×C4C23×#12011yescharacteristic
888C2×C4C22×D4×C2311yescharacteristic
889C2×C4C22×D4×C2311yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×C23×#12011yescharacteristic
920C22C23×#57711yescharacteristic
921C22C23×#57811yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C23×#301311yescharacteristic
947C2C23×#302111yescharacteristic
948C2C23×#302611yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC22×C4C24×C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#3535C2semidirect
2. C23×#3193C2semidirect
3. C23×#3188C2semidirect
4. C23×#2813C2semidirect
5. C23×#1618C2semidirect
6. C23×#1617C2semidirect
7. C23×#1615C2semidirect
8. C23×#1614C2semidirect
9. C23×#1600C2semidirect
10. C23×#1599C2semidirect
11. C23×#1597C2semidirect
12. C23×#1596C2semidirect
13. C23×#1520C2semidirect
14. C23×#1513C2semidirect
15. C23×#1468C2semidirect
76. C2×#41×C23D4semidirect
77. C22×Q8×C23D4semidirect
135. C23×C22⋊Q8D4semidirect
136. C23×C22⋊Q8D4semidirect
137. C23×C22⋊Q8D4semidirect
149. C23×#121D4semidirect
164. C23×#117D4semidirect
170. C2×C4⋊C4×C23D4semidirect
333. #18448C23direct (N × H)
420. #3535C2×C23semidirect
421. #3193C2×C23semidirect
422. #3188C2×C23semidirect
423. #2813C2×C23semidirect
424. #1618C2×C23semidirect
425. #1617C2×C23semidirect
426. #1615C2×C23semidirect
427. #1614C2×C23semidirect
428. #1600C2×C23semidirect
429. #1599C2×C23semidirect
430. #1597C2×C23semidirect
431. #1596C2×C23semidirect
432. #1520C2×C23semidirect
433. #1513C2×C23semidirect
434. #1468C2×C23semidirect
550. C2×#41D4×C23semidirect
551. C22×Q8D4×C23semidirect
609. C22⋊Q8D4×C23semidirect
610. C22⋊Q8D4×C23semidirect
611. C22⋊Q8D4×C23semidirect
623. #121D4×C23semidirect
638. #117D4×C23semidirect
644. C2×C4⋊C4D4×C23semidirect
680. C23#18448direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35352
C23×#31932
C23×#31882
C23×#28132
C23×#16182
C23×#16172
C23×#16152
C23×#16142
C23×#16002
C23×#15992
C23×#15972
C23×#15962
C23×#15202
C23×#15132
C23×#14682
#1844823