Finite Group Databasebeta

← C23×#18434 #19166060

Subgroups — C23×#18434 #19166060

Order 5888.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3560C211yesmaximal, characteristic, complemented
2C23×#3213C211yesmaximal, characteristic, complemented
3C23×#3211C211yesmaximal, characteristic, complemented
4C23×#2662C211yesmaximal, characteristic, complemented
5C23×#1606C211yesmaximal, characteristic, complemented
6C23×#1604C211yesmaximal, characteristic, complemented
7C23×#1603C211yesmaximal, characteristic, complemented
8C23×#1601C211yesmaximal, characteristic, complemented
9C23×#1600C211yesmaximal, characteristic, complemented
10C23×#1598C211yesmaximal, characteristic, complemented
11C23×#1597C211yesmaximal, characteristic, complemented
12C23×#1595C211yesmaximal, characteristic, complemented
13C23×#1509C211yesmaximal, characteristic, complemented
14C23×#1502C211yesmaximal, characteristic, complemented
15C23×#1473C211yesmaximal, characteristic, complemented
16C23×#563—21no—
17C23×#560—21no—
18C23×#553—21no—
19C23×#553—21no—
20C23×#551—21no—
21C23×#547—21no—
22C23×#546—21no—
23C23×#546—21no—
24C23×#542—21no—
25C23×#539—21no—
26C23×#539C2211yescharacteristic
27C23×#538—21no—
28C23×#538—21no—
29C23×#538C2211yescharacteristic
30C23×#537C2211yescharacteristic
31C23×#534C2211yescharacteristic
32C23×#532C2211yescharacteristic
33C23×#529C2211yescharacteristic
34C2×C23×#126C2211yescharacteristic
35C2×C23×#124C2211yescharacteristic, complemented
36C23×#496—21no—
37C23×#495—21no—
38C23×#489—21no—
39C23×#488—21no—
40C23×#464—21no—
41C23×#463—21no—
42C23×#463—21no—
43C23×#463—21no—
44C23×#451C2211yescharacteristic, complemented
45C23×#450C2211yescharacteristic, complemented
46C23×#448C2211yescharacteristic
47C23×#448C2211yescharacteristic
48C23×#448C2211yescharacteristic, complemented
49C23×#447C2211yescharacteristic
50C23×#447C2211yescharacteristic
51C23×#447C2211yescharacteristic, complemented
52C23×#432C2211yescharacteristic, complemented
53C23×#431C2211yescharacteristic, complemented
54C23×#396—21no—
55C23×#395C2211yescharacteristic, complemented
56C23×#394—21no—
57C23×#394C2211yescharacteristic, complemented
58C23×#393C2211yescharacteristic
59C23×#392C2211yescharacteristic
60C23×#390—21no—
61C23×#388—21no—
62C4×C4⋊C4×C23C2211yescharacteristic, complemented
63C23×#328C2211yescharacteristic, complemented
64C23×#328C2211yescharacteristic, complemented
65C23×#327C2211yescharacteristic
66C23×#327C2211yescharacteristic
67C23×#327C2211yescharacteristic
68C23×#327C2211yescharacteristic
69C23×#327C2211yescharacteristic, complemented
70C23×#327C2211yescharacteristic, complemented
71C23×#324C2211yescharacteristic, complemented
72C23×#324C2211yescharacteristic, complemented
73C23×#323C2211yescharacteristic
74C23×#323C2211yescharacteristic
75C2×#41×C23—21no—
76C2×#41×C23—21no—
77C22×Q8×C23C2311yescharacteristic
78C22×D4×C23—21no—
79C22×D4×C23—21no—
80C22×D4×C23C2311yescharacteristic
81C2×Q16×C23—21no—
82C2×SD16×C23—21no—
83C2×SD16×C23—21no—
84C2×SD16×C23—21no—
85C2×SD16×C23—21no—
86C2×D8×C23—21no—
87C2×D8×C23—21no—
88C2×D8×C23—21no—
89C23×C4⋊Q8—21no—
90C23×C4⋊Q8D411yescharacteristic, complemented
91C23×#127D411yescharacteristic, complemented
92C23×#126—21no—
93C23×#126—21no—
94C23×#126—21no—
95C23×#126—21no—
96C23×#126—21no—
97C23×#126—21no—
98C23×#126—21no—
99C23×#126—21no—
100C23×#126—21no—
101C23×#125—21no—
102C23×#125—21no—
103C23×#125D411yescharacteristic, complemented
104C23×#124—21no—
105C23×#124—21no—
106C23×#124—21no—
107C23×#124—21no—
108C23×#124—21no—
109C23×#124—21no—
110C23×#124—21no—
111C23×#124—21no—
112C23×#124D411yescharacteristic, complemented
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×#123—21no—
122C23×#123—21no—
123C23×#123—21no—
124C23×#123—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⋊Q8C2311yescharacteristic
133C23×#121—21no—
134C23×#121—21no—
135C23×#121—21no—
136C23×#121—21no—
137C23×#121—21no—
138C23×#121—21no—
139C23×#121—21no—
140C23×#121—21no—
141C23×#121—21no—
142C23×#121—21no—
143C23×#121—21no—
144C23×#121—21no—
145C23×#121C2311yescharacteristic
146C23×#121C2311yescharacteristic
147C23×#121C2311yescharacteristic
148C23×#120—21no—
149C23×#120—21no—
150C23×#120—21no—
151C23×#120—21no—
152C23×#120—21no—
153C4×Q8×C23D411yescharacteristic, complemented
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—
161C4×D4×C23—21no—
162C4×D4×C23D411yescharacteristic, complemented
163C4×D4×C23D411yescharacteristic, complemented
164C4×D4×C23D411yescharacteristic, complemented
165C23×#117—21no—
166C23×#117—21no—
167C2×C4⋊C4×C23—21no—
168C2×C4⋊C4×C23—21no—
169C2×C4⋊C4×C23—21no—
170C2×C4⋊C4×C23D411yescharacteristic
171C2×C4⋊C4×C23D411yescharacteristic
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
184C2×C42×C23—21no—
185C2×C42×C23C2311yescharacteristic
186C23×C4⋊C8—21no—
187C23×C4⋊C8—21no—
188C23×#103—21no—
189C23×#103—21no—
190C23×#103—21no—
191C23×#103—21no—
192C23×#102—21no—
193C23×#102—21no—
194C23×#102—21no—
195C23×#102—21no—
196C23×C22⋊C8C2311yescharacteristic
197C23×C22⋊C8C2311yescharacteristic
198C23×C22⋊C8C2311yescharacteristic
199C23×C22⋊C8C2311yescharacteristic
200C23×#97—21no—
201C4×C8×C23—21no—
202C23×#95—21no—
203C23×#95—21no—
204C23×#95C2311yescharacteristic
205C23×#95C2311yescharacteristic
206C24×C23—21no—
207C24×C23—21no—
208C24×C23C2×D411yescharacteristic
209#41×C23—81no—
210#41×C23—81no—
211#41×C23—81no—
212#41×C23—81no—
213C2×Q8×C23—21no—
214C2×Q8×C23—21no—
215C2×Q8×C23—21no—
216C2×Q8×C23—21no—
217C2×Q8×C23—81no—
218C2×Q8×C23C2×D411yescharacteristic
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—21no—
228C2×D4×C23—21no—
229C2×D4×C23—21no—
230C2×D4×C23—21no—
231C2×D4×C23—21no—
232C2×D4×C23—21no—
233C2×D4×C23—42no—
234C2×D4×C23—81no—
235C2×D4×C23—81no—
236C2×D4×C23—81no—
237C2×D4×C23—81no—
238C2×D4×C23—81no—
239C2×D4×C23C2×D411yescharacteristic
240C2×D4×C23C2×D411yescharacteristic
241C2×D4×C23C2×D411yescharacteristic
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×C23C2×D411yescharacteristic
254C22×C4×C23C2×D411yescharacteristic
255C22×C4×C23C2×D411yescharacteristic
256C22×C4×C23C2×D411yescharacteristic
257C22×C4×C23C2×D411yescharacteristic
258C22×C4×C23C2411yescharacteristic
259Q16×C23—81no—
260SD16×C23—81no—
261SD16×C23—81no—
262SD16×C23—81no—
263SD16×C23—81no—
264D8×C23—81no—
265D8×C23—81no—
266D8×C23—81no—
267C2×C8×C23—21no—
268C2×C8×C23—21no—
269C2×C8×C23—21no—
270C2×C8×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—42no—
289C4⋊C4×C23—81no—
290C4⋊C4×C23C2×D411yescharacteristic
291C4⋊C4×C23C2×D411yescharacteristic
292C4⋊C4×C23C2×D411yescharacteristic
293C4⋊C4×C23C2×D411yescharacteristic
294C22⋊C4×C23—21no—
295C22⋊C4×C23—21no—
296C22⋊C4×C23—21no—
297C22⋊C4×C23—21no—
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—42no—
320C22⋊C4×C23—41no—
321C22⋊C4×C23—41no—
322C22⋊C4×C23—41no—
323C22⋊C4×C23—41no—
324C22⋊C4×C23—81no—
325C22⋊C4×C23—81no—
326C22⋊C4×C23—81no—
327C42×C23—21no—
328C42×C23—21no—
329C42×C23—21no—
330C42×C23—81no—
331C42×C23C2×D411yescharacteristic
332C42×C23C2×D411yescharacteristic
333C42×C23C2×D411yescharacteristic
334C42×C23C2×D411yescharacteristic
335#18434C2311yesmaximal, characteristic, direct product factor, Sylow
336C23×C23—21no—
337C23×C23—21no—
338C23×C23—21no—
339C23×C23—21no—
340C23×C23—21no—
341C23×C23—21no—
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—81no—
352C23×C23—81no—
353C23×C23—81no—
354C23×C23C22×D411yescharacteristic
355Q8×C23—41no—
356Q8×C23—41no—
357Q8×C23—41no—
358Q8×C23—41no—
359Q8×C23—41no—
360Q8×C23—81no—
361Q8×C23—81no—
362D4×C23—41no—
363D4×C23—41no—
364D4×C23—41no—
365D4×C23—41no—
366D4×C23—41no—
367D4×C23—41no—
368D4×C23—41no—
369D4×C23—41no—
370D4×C23—41no—
371D4×C23—41no—
372D4×C23—41no—
373D4×C23—41no—
374D4×C23—41no—
375D4×C23—81no—
376D4×C23—81no—
377D4×C23—81no—
378D4×C23—81no—
379D4×C23—81no—
380D4×C23—81no—
381D4×C23—81no—
382D4×C23—81no—
383D4×C23—81no—
384D4×C23—84no—
385C2×C4×C23—21no—
386C2×C4×C23—21no—
387C2×C4×C23—22no—
388C2×C4×C23—21no—
389C2×C4×C23—21no—
390C2×C4×C23—21no—
391C2×C4×C23—21no—
392C2×C4×C23—21no—
393C2×C4×C23—21no—
394C2×C4×C23—21no—
395C2×C4×C23—21no—
396C2×C4×C23—21no—
397C2×C4×C23—21no—
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—41no—
407C2×C4×C23—41no—
408C2×C4×C23—41no—
409C2×C4×C23—41no—
410C2×C4×C23—81no—
411C2×C4×C23—81no—
412C2×C4×C23—81no—
413C2×C4×C23—81no—
414C2×C4×C23—81no—
415C2×C4×C23—81no—
416C2×C4×C23—81no—
417C2×C4×C23—81no—
418C2×C4×C23#12011yescharacteristic
419C2×C4×C23#12011yescharacteristic
420C2×C4×C23#12011yescharacteristic
421C2×C4×C23#12011yescharacteristic
422C2×C4×C23C22×D411yescharacteristic
423C2×C4×C23C22×D411yescharacteristic
424C8×C23—41no—
425C8×C23—41no—
426C8×C23—41no—
427C8×C23—41no—
428#3560C2×C2311yescharacteristic, complemented
429#3213C2×C2311yescharacteristic, complemented
430#3211C2×C2311yescharacteristic, complemented
431#2662C2×C2311yescharacteristic, complemented
432#1606C2×C2311yescharacteristic, complemented
433#1604C2×C2311yescharacteristic, complemented
434#1603C2×C2311yescharacteristic, complemented
435#1601C2×C2311yescharacteristic, complemented
436#1600C2×C2311yescharacteristic, complemented
437#1598C2×C2311yescharacteristic, complemented
438#1597C2×C2311yescharacteristic, complemented
439#1595C2×C2311yescharacteristic, complemented
440#1509C2×C2311yescharacteristic, complemented
441#1502C2×C2311yescharacteristic, complemented
442#1473C2×C2311yescharacteristic, complemented
443C22×C23—21no—
444C22×C23—21no—
445C22×C23—41no—
446C22×C23—41no—
447C22×C23—41no—
448C22×C23—41no—
449C22×C23—41no—
450C22×C23—41no—
451C22×C23—41no—
452C22×C23—41no—
453C22×C23—41no—
454C22×C23—41no—
455C22×C23—41no—
456C22×C23—41no—
457C22×C23—81no—
458C22×C23—81no—
459C22×C23—81no—
460C22×C23—81no—
461C22×C23—81no—
462C22×C23—81no—
463C22×C23—81no—
464C22×C23—81no—
465C22×C23—81no—
466C22×C23—162no—
467C22×C23C2×#12011yescharacteristic
468C22×C23#57611yescharacteristic
469C22×C23#57711yescharacteristic
470C4×C23—21no—
471C4×C23—21no—
472C4×C23—21no—
473C4×C23—21no—
474C4×C23—21no—
475C4×C23—21no—
476C4×C23—42no—
477C4×C23—41no—
478C4×C23—41no—
479C4×C23—41no—
480C4×C23—41no—
481C4×C23—41no—
482C4×C23—41no—
483C4×C23—41no—
484C4×C23—41no—
485C4×C23—81no—
486C4×C23—81no—
487#563—21no—
488#560—21no—
489#553—21no—
490#553—21no—
491#551—21no—
492#547—21no—
493#546—21no—
494#546—21no—
495#542—21no—
496#539—21no—
497#539C22×C2311yescharacteristic
498#538—21no—
499#538—21no—
500#538C22×C2311yescharacteristic
501#537C22×C2311yescharacteristic
502#534C22×C2311yescharacteristic
503#532C22×C2311yescharacteristic
504#529C22×C2311yescharacteristic
505C2×#126C22×C2311yescharacteristic
506C2×#124C22×C2311yescharacteristic, complemented
507#496—21no—
508#495—21no—
509#489—21no—
510#488—21no—
511#464—21no—
512#463—21no—
513#463—21no—
514#463—21no—
515#451C22×C2311yescharacteristic, complemented
516#450C22×C2311yescharacteristic, complemented
517#448C22×C2311yescharacteristic
518#448C22×C2311yescharacteristic
519#448C22×C2311yescharacteristic, complemented
520#447C22×C2311yescharacteristic
521#447C22×C2311yescharacteristic
522#447C22×C2311yescharacteristic, complemented
523#432C22×C2311yescharacteristic, complemented
524#431C22×C2311yescharacteristic, complemented
525#396—21no—
526#395C22×C2311yescharacteristic, complemented
527#394—21no—
528#394C22×C2311yescharacteristic, complemented
529#393C22×C2311yescharacteristic
530#392C22×C2311yescharacteristic
531#390—21no—
532#388—21no—
533C4×C4⋊C4C22×C2311yescharacteristic, complemented
534#328C22×C2311yescharacteristic, complemented
535#328C22×C2311yescharacteristic, complemented
536#327C22×C2311yescharacteristic
537#327C22×C2311yescharacteristic
538#327C22×C2311yescharacteristic
539#327C22×C2311yescharacteristic
540#327C22×C2311yescharacteristic, complemented
541#327C22×C2311yescharacteristic, complemented
542#324C22×C2311yescharacteristic, complemented
543#324C22×C2311yescharacteristic, complemented
544#323C22×C2311yescharacteristic
545#323C22×C2311yescharacteristic
546C2×C23—21no—
547C2×C23—21no—
548C2×C23—81no—
549C2×C23—81no—
550C2×C23—81no—
551C2×C23—81no—
552C2×C23—161no—
553C2×C23#301211yescharacteristic
554C2×C23#301811yescharacteristic
555C2×C23#302711yescharacteristic
556C2×#41—21no—
557C2×#41—21no—
558C22×Q8C23×C2311yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4C23×C2311yescharacteristic
562C2×Q16—21no—
563C2×SD16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×D8—21no—
568C2×D8—21no—
569C2×D8—21no—
570C4⋊Q8—21no—
571C4⋊Q8D4×C2311yescharacteristic, complemented
572#127D4×C2311yescharacteristic, complemented
573#126—21no—
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#125—21no—
583#125—21no—
584#125D4×C2311yescharacteristic, complemented
585#124—21no—
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124D4×C2311yescharacteristic, complemented
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8C23×C2311yescharacteristic
614#121—21no—
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#121—21no—
624#121—21no—
625#121—21no—
626#121C23×C2311yescharacteristic
627#121C23×C2311yescharacteristic
628#121C23×C2311yescharacteristic
629#120—21no—
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634C4×Q8D4×C2311yescharacteristic, complemented
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4D4×C2311yescharacteristic, complemented
644C4×D4D4×C2311yescharacteristic, complemented
645C4×D4D4×C2311yescharacteristic, complemented
646#117—21no—
647#117—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4D4×C2311yescharacteristic
652C2×C4⋊C4D4×C2311yescharacteristic
653C2×C4⋊C4C23×C2311yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C2311yescharacteristic
663C2×C22⋊C4D4×C2311yescharacteristic
664C2×C22⋊C4C23×C2311yescharacteristic
665C2×C42—21no—
666C2×C42C23×C2311yescharacteristic
667C4⋊C8—21no—
668C4⋊C8—21no—
669#103—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#102—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677C22⋊C8C23×C2311yescharacteristic
678C22⋊C8C23×C2311yescharacteristic
679C22⋊C8C23×C2311yescharacteristic
680C22⋊C8C23×C2311yescharacteristic
681#97—21no—
682C4×C8—21no—
683#95—21no—
684#95—21no—
685#95C23×C2311yescharacteristic
686#95C23×C2311yescharacteristic
687C23#1843411yescharacteristic, direct product factor, Sylow
688C24—21no—
689C24—21no—
690C24C2×D4×C2311yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C2311yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C2311yescharacteristic
722C2×D4C2×D4×C2311yescharacteristic
723C2×D4C2×D4×C2311yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C2311yescharacteristic
736C22×C4C2×D4×C2311yescharacteristic
737C22×C4C2×D4×C2311yescharacteristic
738C22×C4C2×D4×C2311yescharacteristic
739C22×C4C2×D4×C2311yescharacteristic
740C22×C4C24×C2311yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C2311yescharacteristic
773C4⋊C4C2×D4×C2311yescharacteristic
774C4⋊C4C2×D4×C2311yescharacteristic
775C4⋊C4C2×D4×C2311yescharacteristic
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—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C2311yescharacteristic
814C42C2×D4×C2311yescharacteristic
815C42C2×D4×C2311yescharacteristic
816C42C2×D4×C2311yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C2311yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4C23×#12011yescharacteristic
900C2×C4C23×#12011yescharacteristic
901C2×C4C23×#12011yescharacteristic
902C2×C4C23×#12011yescharacteristic
903C2×C4C22×D4×C2311yescharacteristic
904C2×C4C22×D4×C2311yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×C23×#12011yescharacteristic
934C22C23×#57611yescharacteristic
935C22C23×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C23×#301211yescharacteristic
961C2C23×#301811yescharacteristic
962C2C23×#302711yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC22×C4C24×C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#3560C2semidirect
2. C23×#3213C2semidirect
3. C23×#3211C2semidirect
4. C23×#2662C2semidirect
5. C23×#1606C2semidirect
6. C23×#1604C2semidirect
7. C23×#1603C2semidirect
8. C23×#1601C2semidirect
9. C23×#1600C2semidirect
10. C23×#1598C2semidirect
11. C23×#1597C2semidirect
12. C23×#1595C2semidirect
13. C23×#1509C2semidirect
14. C23×#1502C2semidirect
15. C23×#1473C2semidirect
35. C2×C23×#124C22semidirect
44. C23×#451C22semidirect
45. C23×#450C22semidirect
48. C23×#448C22semidirect
51. C23×#447C22semidirect
52. C23×#432C22semidirect
53. C23×#431C22semidirect
55. C23×#395C22semidirect
57. C23×#394C22semidirect
62. C4×C4⋊C4×C23C22semidirect
63. C23×#328C22semidirect
64. C23×#328C22semidirect
69. C23×#327C22semidirect
70. C23×#327C22semidirect
71. C23×#324C22semidirect
72. C23×#324C22semidirect
90. C23×C4⋊Q8D4semidirect
91. C23×#127D4semidirect
103. C23×#125D4semidirect
112. C23×#124D4semidirect
153. C4×Q8×C23D4semidirect
162. C4×D4×C23D4semidirect
163. C4×D4×C23D4semidirect
164. C4×D4×C23D4semidirect
335. #18434C23direct (N × H)
428. #3560C2×C23semidirect
429. #3213C2×C23semidirect
430. #3211C2×C23semidirect
431. #2662C2×C23semidirect
432. #1606C2×C23semidirect
433. #1604C2×C23semidirect
434. #1603C2×C23semidirect
435. #1601C2×C23semidirect
436. #1600C2×C23semidirect
437. #1598C2×C23semidirect
438. #1597C2×C23semidirect
439. #1595C2×C23semidirect
440. #1509C2×C23semidirect
441. #1502C2×C23semidirect
442. #1473C2×C23semidirect
506. C2×#124C22×C23semidirect
515. #451C22×C23semidirect
516. #450C22×C23semidirect
519. #448C22×C23semidirect
522. #447C22×C23semidirect
523. #432C22×C23semidirect
524. #431C22×C23semidirect
526. #395C22×C23semidirect
528. #394C22×C23semidirect
533. C4×C4⋊C4C22×C23semidirect
534. #328C22×C23semidirect
535. #328C22×C23semidirect
540. #327C22×C23semidirect
541. #327C22×C23semidirect
542. #324C22×C23semidirect
543. #324C22×C23semidirect
571. C4⋊Q8D4×C23semidirect
572. #127D4×C23semidirect
584. #125D4×C23semidirect
593. #124D4×C23semidirect
634. C4×Q8D4×C23semidirect
643. C4×D4D4×C23semidirect
644. C4×D4D4×C23semidirect
645. C4×D4D4×C23semidirect
687. C23#18434direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35602
C23×#32132
C23×#32112
C23×#26622
C23×#16062
C23×#16042
C23×#16032
C23×#16012
C23×#16002
C23×#15982
C23×#15972
C23×#15952
C23×#15092
C23×#15022
C23×#14732
#1843423