Finite Group Databasebeta

← C23×#18252 #19165878

Subgroups — C23×#18252 #19165878

Order 5888.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3534C211yesmaximal, characteristic, complemented
2C23×#3006C211yesmaximal, characteristic, complemented
3C23×#3002C211yesmaximal, characteristic, complemented
4C23×#2430C211yesmaximal, 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×#1504C211yesmaximal, characteristic, complemented
14C2×C23×#327C211yesmaximal, characteristic, complemented
15C23×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C23C2211yescharacteristic, complemented
17C2×C23×AGL(1,ℤ/8)—21no—
18C2×C23×#135—21no—
19C23×#562—21no—
20C23×#560—21no—
21C23×#553—21no—
22C23×#551—21no—
23C23×#546—21no—
24C23×#546—21no—
25C23×#546—21no—
26D42×C23—21no—
27C23×#540—21no—
28C23×#539—21no—
29C23×#539C2211yescharacteristic
30C23×#538—21no—
31C23×#538C2211yescharacteristic
32C23×#537C2211yescharacteristic
33C23×#534—21no—
34C23×#534C2211yescharacteristic
35C23×#525C2211yescharacteristic
36C2×C23×#123C2211yescharacteristic
37C2×C23×#121—21no—
38C2×C23×#121C2211yescharacteristic
39C23×#452—21no—
40C23×#451C2211yescharacteristic, complemented
41C23×#450C2211yescharacteristic, complemented
42C23×#449—21no—
43C23×#449—21no—
44C23×#449—21no—
45C23×#448C2211yescharacteristic
46C23×#448C2211yescharacteristic, complemented
47C23×#448C2211yescharacteristic, complemented
48C23×#447C2211yescharacteristic
49C23×#447C2211yescharacteristic, complemented
50C23×#447C2211yescharacteristic, complemented
51C23×#417—21no—
52C23×#416—21no—
53C23×#407C2211yescharacteristic, complemented
54C2×C23×C22⋊C8C2211yescharacteristic, complemented
55C23×#395C2211yescharacteristic, complemented
56C23×#394C2211yescharacteristic, complemented
57C23×#393C2211yescharacteristic, complemented
58C23×#392C2211yescharacteristic, complemented
59C23×#386—21no—
60C23×#386—21no—
61C23×#385—21no—
62C2×C23×#95C2211yescharacteristic, complemented
63C23×#328C2211yescharacteristic, complemented
64C23×#328C2211yescharacteristic, complemented
65C23×#327C2211yescharacteristic
66C23×#327C2211yescharacteristic
67C23×#327C2211yescharacteristic, complemented
68C23×#327C2211yescharacteristic, complemented
69C23×#327C2211yescharacteristic, complemented
70C23×#327C2211yescharacteristic, complemented
71C23×#324C2211yescharacteristic, complemented
72C23×#324C2211yescharacteristic, complemented
73C23×#323C2211yescharacteristic, complemented
74C23×#323C2211yescharacteristic, complemented
75C2×#41×C23—21no—
76C2×#41×C23—21no—
77C2×#41×C23—21no—
78C2×#41×C23—21no—
79C2×#41×C23—21no—
80C2×#41×C23—44no—
81C2×#41×C23D411yescharacteristic, complemented
82C22×Q8×C23C2311yescharacteristic
83C22×D4×C23—21no—
84C22×D4×C23—21no—
85C22×D4×C23—21no—
86C22×D4×C23—21no—
87C22×D4×C23—21no—
88C22×D4×C23D411yescharacteristic
89C22×D4×C23D411yescharacteristic, complemented
90C22×D4×C23C2311yescharacteristic
91C23×C4×C23—21no—
92C23×C4×C23—21no—
93C23×C4×C23C2311yescharacteristic
94C23×AGL(1,ℤ/8)—44no—
95C23×#135—44no—
96C2×Q16×C23—21no—
97C2×SD16×C23—21no—
98C2×SD16×C23—21no—
99C2×SD16×C23—21no—
100C2×SD16×C23—21no—
101C2×D8×C23—21no—
102C2×D8×C23—21no—
103C2×D8×C23—21no—
104C2×M16×C23—21no—
105C22×C8×C23—21no—
106C23×#127—21no—
107C23×#126—21no—
108C23×#126—21no—
109C23×#126—21no—
110C23×#126—21no—
111C23×#125—21no—
112C23×#125—21no—
113C23×#124—21no—
114C23×#124—21no—
115C23×#124—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×#123—21no—
126C23×#123—21no—
127C23×#123—21no—
128C23×#123—21no—
129C23×#123—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⋊Q8C2311yescharacteristic
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×#121—21no—
146C23×#121—21no—
147C23×#121—21no—
148C23×#121—21no—
149C23×#121—21no—
150C23×#121—21no—
151C23×#121—21no—
152C23×#121—44no—
153C23×#121D411yescharacteristic, complemented
154C23×#121D411yescharacteristic, complemented
155C23×#121D411yescharacteristic, complemented
156C23×#121C2311yescharacteristic
157C23×#121C2311yescharacteristic
158C23×#121C2311yescharacteristic
159C23×#120—21no—
160C23×#120—21no—
161C23×#120—21no—
162C23×#120—21no—
163C23×#120—21no—
164C23×#120—21no—
165C23×#120—21no—
166C23×#120—21no—
167C4×D4×C23—21no—
168C4×D4×C23—21no—
169C4×D4×C23—21no—
170C4×D4×C23—21no—
171C4×D4×C23—21no—
172C4×D4×C23—21no—
173C4×D4×C23—21no—
174C4×D4×C23—21no—
175C23×#117—21no—
176C23×#117D411yescharacteristic, complemented
177C2×C4⋊C4×C23—21no—
178C2×C4⋊C4×C23D411yescharacteristic
179C2×C4⋊C4×C23D411yescharacteristic, complemented
180C2×C4⋊C4×C23C2311yescharacteristic
181C2×C22⋊C4×C23—21no—
182C2×C22⋊C4×C23—21no—
183C2×C22⋊C4×C23—21no—
184C2×C22⋊C4×C23—21no—
185C2×C22⋊C4×C23—21no—
186C2×C22⋊C4×C23—21no—
187C2×C22⋊C4×C23—21no—
188C2×C22⋊C4×C23D411yescharacteristic
189C2×C22⋊C4×C23D411yescharacteristic
190C2×C22⋊C4×C23C2311yescharacteristic
191C23×#103—21no—
192C23×#103—21no—
193C23×#103—21no—
194C23×#103—21no—
195C23×#102—21no—
196C23×#102—21no—
197C23×#102—21no—
198C23×#102—21no—
199C23×C22⋊C8—21no—
200C23×C22⋊C8—21no—
201C23×C22⋊C8C2311yescharacteristic
202C23×C22⋊C8C2311yescharacteristic
203C23×C22⋊C8C2311yescharacteristic
204C23×C22⋊C8C2311yescharacteristic
205C23×#95—21no—
206C23×#95—21no—
207C23×#95—21no—
208C23×#95C2311yescharacteristic
209C23×#95C2311yescharacteristic
210C24×C23—21no—
211C24×C23—21no—
212C24×C23—21no—
213C24×C23C2×D411yescharacteristic
214C24×C23C2×D411yescharacteristic
215#41×C23—24no—
216#41×C23—24no—
217#41×C23—42no—
218#41×C23—42no—
219#41×C23—42no—
220#41×C23—42no—
221#41×C23—42no—
222#41×C23—42no—
223#41×C23—42no—
224#41×C23—81no—
225#41×C23—81no—
226C2×Q8×C23—21no—
227C2×Q8×C23—21no—
228C2×Q8×C23—21no—
229C2×Q8×C23—42no—
230C2×Q8×C23C2×D411yescharacteristic
231C2×D4×C23—24no—
232C2×D4×C23—21no—
233C2×D4×C23—21no—
234C2×D4×C23—21no—
235C2×D4×C23—21no—
236C2×D4×C23—21no—
237C2×D4×C23—21no—
238C2×D4×C23—21no—
239C2×D4×C23—21no—
240C2×D4×C23—21no—
241C2×D4×C23—21no—
242C2×D4×C23—21no—
243C2×D4×C23—21no—
244C2×D4×C23—21no—
245C2×D4×C23—21no—
246C2×D4×C23—21no—
247C2×D4×C23—21no—
248C2×D4×C23—21no—
249C2×D4×C23—21no—
250C2×D4×C23—21no—
251C2×D4×C23—42no—
252C2×D4×C23—42no—
253C2×D4×C23—42no—
254C2×D4×C23—42no—
255C2×D4×C23—41no—
256C2×D4×C23—41no—
257C2×D4×C23—42no—
258C2×D4×C23—42no—
259C2×D4×C23—81no—
260C2×D4×C23—81no—
261C2×D4×C23—81no—
262C2×D4×C23—81no—
263C2×D4×C23—81no—
264C2×D4×C23—82no—
265C2×D4×C23C2×D411yescharacteristic
266C2×D4×C23C2×D411yescharacteristic
267C2×D4×C23C2×D411yescharacteristic
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—21no—
278C22×C4×C23—42no—
279C22×C4×C23—42no—
280C22×C4×C23—42no—
281C22×C4×C23—42no—
282C22×C4×C23—41no—
283C22×C4×C23—41no—
284C22×C4×C23—42no—
285C22×C4×C23—81no—
286C22×C4×C23C2×D411yescharacteristic
287C22×C4×C23C2×D411yescharacteristic
288C22×C4×C23C2×D411yescharacteristic
289C22×C4×C23C2×D411yescharacteristic
290C22×C4×C23C2×D411yescharacteristic
291C22×C4×C23C2×D411yescharacteristic
292C22×C4×C23C2×D411yescharacteristic
293C22×C4×C23C2×D411yescharacteristic
294C22×C4×C23C2411yescharacteristic
295Q16×C23—42no—
296SD16×C23—42no—
297SD16×C23—42no—
298SD16×C23—42no—
299SD16×C23—42no—
300D8×C23—42no—
301D8×C23—42no—
302D8×C23—42no—
303M16×C23—42no—
304C2×C8×C23—21no—
305C2×C8×C23—21no—
306C2×C8×C23—21no—
307C2×C8×C23—21no—
308C2×C8×C23—42no—
309C4⋊C4×C23—21no—
310C4⋊C4×C23—21no—
311C4⋊C4×C23—21no—
312C4⋊C4×C23—21no—
313C4⋊C4×C23—21no—
314C4⋊C4×C23—21no—
315C4⋊C4×C23—21no—
316C4⋊C4×C23—21no—
317C4⋊C4×C23—21no—
318C4⋊C4×C23—21no—
319C4⋊C4×C23—21no—
320C4⋊C4×C23—21no—
321C4⋊C4×C23—21no—
322C4⋊C4×C23—42no—
323C4⋊C4×C23C2×D411yescharacteristic
324C4⋊C4×C23C2×D411yescharacteristic
325C4⋊C4×C23C2×D411yescharacteristic
326C4⋊C4×C23C2×D411yescharacteristic
327C22⋊C4×C23—21no—
328C22⋊C4×C23—21no—
329C22⋊C4×C23—21no—
330C22⋊C4×C23—21no—
331C22⋊C4×C23—21no—
332C22⋊C4×C23—21no—
333C22⋊C4×C23—21no—
334C22⋊C4×C23—21no—
335C22⋊C4×C23—21no—
336C22⋊C4×C23—21no—
337C22⋊C4×C23—21no—
338C22⋊C4×C23—21no—
339C22⋊C4×C23—21no—
340C22⋊C4×C23—21no—
341C22⋊C4×C23—21no—
342C22⋊C4×C23—21no—
343C22⋊C4×C23—21no—
344C22⋊C4×C23—21no—
345C22⋊C4×C23—21no—
346C22⋊C4×C23—21no—
347C22⋊C4×C23—21no—
348C22⋊C4×C23—21no—
349C22⋊C4×C23—21no—
350C22⋊C4×C23—21no—
351C22⋊C4×C23—21no—
352C22⋊C4×C23—42no—
353C22⋊C4×C23—42no—
354C22⋊C4×C23—42no—
355C22⋊C4×C23—81no—
356C42×C23—21no—
357C42×C23—21no—
358C42×C23—21no—
359#18252C2311yesmaximal, characteristic, direct product factor, Sylow
360C23×C23—21no—
361C23×C23—21no—
362C23×C23—22no—
363C23×C23—22no—
364C23×C23—21no—
365C23×C23—21no—
366C23×C23—21no—
367C23×C23—21no—
368C23×C23—21no—
369C23×C23—21no—
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—42no—
380C23×C23—81no—
381C23×C23—81no—
382C23×C23—81no—
383C23×C23—81no—
384C23×C23—81no—
385C23×C23#12011yescharacteristic
386C23×C23#12011yescharacteristic
387C23×C23C22×D411yescharacteristic
388Q8×C23—22no—
389Q8×C23—22no—
390Q8×C23—41no—
391Q8×C23—41no—
392Q8×C23—41no—
393Q8×C23—81no—
394D4×C23—22no—
395D4×C23—22no—
396D4×C23—41no—
397D4×C23—41no—
398D4×C23—41no—
399D4×C23—41no—
400D4×C23—41no—
401D4×C23—44no—
402D4×C23—41no—
403D4×C23—41no—
404D4×C23—41no—
405D4×C23—41no—
406D4×C23—41no—
407D4×C23—41no—
408D4×C23—44no—
409D4×C23—42no—
410D4×C23—42no—
411D4×C23—81no—
412D4×C23—81no—
413D4×C23—81no—
414D4×C23—81no—
415D4×C23—81no—
416D4×C23—81no—
417D4×C23—81no—
418D4×C23—81no—
419D4×C23—81no—
420D4×C23—81no—
421D4×C23—81no—
422D4×C23—81no—
423D4×C23—84no—
424C2×C4×C23—22no—
425C2×C4×C23—22no—
426C2×C4×C23—22no—
427C2×C4×C23—22no—
428C2×C4×C23—21no—
429C2×C4×C23—21no—
430C2×C4×C23—21no—
431C2×C4×C23—21no—
432C2×C4×C23—21no—
433C2×C4×C23—21no—
434C2×C4×C23—21no—
435C2×C4×C23—21no—
436C2×C4×C23—21no—
437C2×C4×C23—21no—
438C2×C4×C23—41no—
439C2×C4×C23—41no—
440C2×C4×C23—41no—
441C2×C4×C23—41no—
442C2×C4×C23—44no—
443C2×C4×C23—44no—
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—81no—
454C2×C4×C23—81no—
455C2×C4×C23—81no—
456C2×C4×C23—81no—
457C2×C4×C23—81no—
458C2×C4×C23—81no—
459C2×C4×C23—81no—
460C2×C4×C23—84no—
461C2×C4×C23#12011yescharacteristic
462C2×C4×C23#12011yescharacteristic
463C2×C4×C23C22×D411yescharacteristic
464C2×C4×C23C22×D411yescharacteristic
465C8×C23—41no—
466C8×C23—41no—
467C8×C23—41no—
468C8×C23—41no—
469#3534C2×C2311yescharacteristic, complemented
470#3006C2×C2311yescharacteristic, complemented
471#3002C2×C2311yescharacteristic, complemented
472#2430C2×C2311yescharacteristic, complemented
473#1606C2×C2311yescharacteristic, complemented
474#1604C2×C2311yescharacteristic, complemented
475#1603C2×C2311yescharacteristic, complemented
476#1601C2×C2311yescharacteristic, complemented
477#1600C2×C2311yescharacteristic, complemented
478#1598C2×C2311yescharacteristic, complemented
479#1597C2×C2311yescharacteristic, complemented
480#1595C2×C2311yescharacteristic, complemented
481#1504C2×C2311yescharacteristic, complemented
482C2×#327C2×C2311yescharacteristic, complemented
483#1468C2×C2311yescharacteristic, complemented
484C22×C23—21no—
485C22×C23—21no—
486C22×C23—21no—
487C22×C23—21no—
488C22×C23—21no—
489C22×C23—21no—
490C22×C23—21no—
491C22×C23—42no—
492C22×C23—42no—
493C22×C23—42no—
494C22×C23—42no—
495C22×C23—41no—
496C22×C23—41no—
497C22×C23—41no—
498C22×C23—41no—
499C22×C23—41no—
500C22×C23—41no—
501C22×C23—41no—
502C22×C23—41no—
503C22×C23—42no—
504C22×C23—41no—
505C22×C23—41no—
506C22×C23—41no—
507C22×C23—41no—
508C22×C23—81no—
509C22×C23—81no—
510C22×C23—81no—
511C22×C23—81no—
512C22×C23—81no—
513C22×C23—81no—
514C22×C23—162no—
515C22×C23—162no—
516C22×C23B(4,𝔽2)12yes—
517C22×C23C2×#12011yescharacteristic
518C22×C23#57611yescharacteristic
519C22×C23#57711yescharacteristic
520C4×C23—21no—
521C4×C23—21no—
522C4×C23—21no—
523C4×C23—21no—
524C4×C23—42no—
525C4×C23—41no—
526C4×C23—41no—
527C4×C23—41no—
528C4×C23—41no—
529C4×C23—41no—
530C4×C23—41no—
531C4×C23—42no—
532C4×C23—41no—
533C4×C23—41no—
534C4×C23—81no—
535C22×#41C22×C2311yescharacteristic, complemented
536C2×AGL(1,ℤ/8)—21no—
537C2×#135—21no—
538#562—21no—
539#560—21no—
540#553—21no—
541#551—21no—
542#546—21no—
543#546—21no—
544#546—21no—
545D42—21no—
546#540—21no—
547#539—21no—
548#539C22×C2311yescharacteristic
549#538—21no—
550#538C22×C2311yescharacteristic
551#537C22×C2311yescharacteristic
552#534—21no—
553#534C22×C2311yescharacteristic
554#525C22×C2311yescharacteristic
555C2×#123C22×C2311yescharacteristic
556C2×#121—21no—
557C2×#121C22×C2311yescharacteristic
558#452—21no—
559#451C22×C2311yescharacteristic, complemented
560#450C22×C2311yescharacteristic, complemented
561#449—21no—
562#449—21no—
563#449—21no—
564#448C22×C2311yescharacteristic
565#448C22×C2311yescharacteristic, complemented
566#448C22×C2311yescharacteristic, complemented
567#447C22×C2311yescharacteristic
568#447C22×C2311yescharacteristic, complemented
569#447C22×C2311yescharacteristic, complemented
570#417—21no—
571#416—21no—
572#407C22×C2311yescharacteristic, complemented
573C2×C22⋊C8C22×C2311yescharacteristic, complemented
574#395C22×C2311yescharacteristic, complemented
575#394C22×C2311yescharacteristic, complemented
576#393C22×C2311yescharacteristic, complemented
577#392C22×C2311yescharacteristic, complemented
578#386—21no—
579#386—21no—
580#385—21no—
581C2×#95C22×C2311yescharacteristic, complemented
582#328C22×C2311yescharacteristic, complemented
583#328C22×C2311yescharacteristic, complemented
584#327C22×C2311yescharacteristic
585#327C22×C2311yescharacteristic
586#327C22×C2311yescharacteristic, complemented
587#327C22×C2311yescharacteristic, complemented
588#327C22×C2311yescharacteristic, complemented
589#327C22×C2311yescharacteristic, complemented
590#324C22×C2311yescharacteristic, complemented
591#324C22×C2311yescharacteristic, complemented
592#323C22×C2311yescharacteristic, complemented
593#323C22×C2311yescharacteristic, complemented
594C2×C23—21no—
595C2×C23—21no—
596C2×C23—22no—
597C2×C23—41no—
598C2×C23—82no—
599C2×C23—81no—
600C2×C23—81no—
601C2×C23—81no—
602C2×C23—81no—
603C2×C23#301211yescharacteristic
604C2×C23#301811yescharacteristic
605C2×C23C2×B(4,𝔽2)11yescharacteristic
606C2×#41—21no—
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—44no—
612C2×#41D4×C2311yescharacteristic, complemented
613C22×Q8C23×C2311yescharacteristic
614C22×D4—21no—
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C2311yescharacteristic
620C22×D4D4×C2311yescharacteristic, complemented
621C22×D4C23×C2311yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4C23×C2311yescharacteristic
625AGL(1,ℤ/8)—44no—
626#135—44no—
627C2×Q16—21no—
628C2×SD16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×D8—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×M16—21no—
636C22×C8—21no—
637#127—21no—
638#126—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#125—21no—
643#125—21no—
644#124—21no—
645#124—21no—
646#124—21no—
647#123—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8D4×C2311yescharacteristic, complemented
667C22⋊Q8C23×C2311yescharacteristic
668#121—21no—
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—44no—
684#121D4×C2311yescharacteristic, complemented
685#121D4×C2311yescharacteristic, complemented
686#121D4×C2311yescharacteristic, complemented
687#121C23×C2311yescharacteristic
688#121C23×C2311yescharacteristic
689#121C23×C2311yescharacteristic
690#120—21no—
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706#117—21no—
707#117D4×C2311yescharacteristic, complemented
708C2×C4⋊C4—21no—
709C2×C4⋊C4D4×C2311yescharacteristic
710C2×C4⋊C4D4×C2311yescharacteristic, complemented
711C2×C4⋊C4C23×C2311yescharacteristic
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4D4×C2311yescharacteristic
720C2×C22⋊C4D4×C2311yescharacteristic
721C2×C22⋊C4C23×C2311yescharacteristic
722#103—21no—
723#103—21no—
724#103—21no—
725#103—21no—
726#102—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730C22⋊C8—21no—
731C22⋊C8—21no—
732C22⋊C8C23×C2311yescharacteristic
733C22⋊C8C23×C2311yescharacteristic
734C22⋊C8C23×C2311yescharacteristic
735C22⋊C8C23×C2311yescharacteristic
736#95—21no—
737#95—21no—
738#95—21no—
739#95C23×C2311yescharacteristic
740#95C23×C2311yescharacteristic
741C23#1825211yescharacteristic, direct product factor, Sylow
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C2311yescharacteristic
746C24C2×D4×C2311yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C2311yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C2311yescharacteristic
798C2×D4C2×D4×C2311yescharacteristic
799C2×D4C2×D4×C2311yescharacteristic
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—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C2311yescharacteristic
819C22×C4C2×D4×C2311yescharacteristic
820C22×C4C2×D4×C2311yescharacteristic
821C22×C4C2×D4×C2311yescharacteristic
822C22×C4C2×D4×C2311yescharacteristic
823C22×C4C2×D4×C2311yescharacteristic
824C22×C4C2×D4×C2311yescharacteristic
825C22×C4C2×D4×C2311yescharacteristic
826C22×C4C24×C2311yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C2311yescharacteristic
856C4⋊C4C2×D4×C2311yescharacteristic
857C4⋊C4C2×D4×C2311yescharacteristic
858C4⋊C4C2×D4×C2311yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23C23×#12011yescharacteristic
917C23C23×#12011yescharacteristic
918C23C22×D4×C2311yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—44no—
940D4—42no—
941D4—42no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4C23×#12011yescharacteristic
993C2×C4C23×#12011yescharacteristic
994C2×C4C22×D4×C2311yescharacteristic
995C2×C4C22×D4×C2311yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C23×B(4,𝔽2)12yes—
1033C22C2×C23×#12011yescharacteristic
1034C22C23×#57611yescharacteristic
1035C22C23×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C23×#301211yescharacteristic
1061C2C23×#301811yescharacteristic
1062C2C2×C23×B(4,𝔽2)11yescharacteristic
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×#3534C2semidirect
2. C23×#3006C2semidirect
3. C23×#3002C2semidirect
4. C23×#2430C2semidirect
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×#1504C2semidirect
14. C2×C23×#327C2semidirect
15. C23×#1468C2semidirect
16. C22×#41×C23C22semidirect
40. C23×#451C22semidirect
41. C23×#450C22semidirect
46. C23×#448C22semidirect
47. C23×#448C22semidirect
49. C23×#447C22semidirect
50. C23×#447C22semidirect
53. C23×#407C22semidirect
54. C2×C23×C22⋊C8C22semidirect
55. C23×#395C22semidirect
56. C23×#394C22semidirect
57. C23×#393C22semidirect
58. C23×#392C22semidirect
62. C2×C23×#95C22semidirect
63. C23×#328C22semidirect
64. C23×#328C22semidirect
67. C23×#327C22semidirect
68. C23×#327C22semidirect
69. C23×#327C22semidirect
70. C23×#327C22semidirect
71. C23×#324C22semidirect
72. C23×#324C22semidirect
73. C23×#323C22semidirect
74. C23×#323C22semidirect
81. C2×#41×C23D4semidirect
89. C22×D4×C23D4semidirect
135. C23×C22⋊Q8D4semidirect
153. C23×#121D4semidirect
154. C23×#121D4semidirect
155. C23×#121D4semidirect
176. C23×#117D4semidirect
179. C2×C4⋊C4×C23D4semidirect
359. #18252C23direct (N × H)
469. #3534C2×C23semidirect
470. #3006C2×C23semidirect
471. #3002C2×C23semidirect
472. #2430C2×C23semidirect
473. #1606C2×C23semidirect
474. #1604C2×C23semidirect
475. #1603C2×C23semidirect
476. #1601C2×C23semidirect
477. #1600C2×C23semidirect
478. #1598C2×C23semidirect
479. #1597C2×C23semidirect
480. #1595C2×C23semidirect
481. #1504C2×C23semidirect
482. C2×#327C2×C23semidirect
483. #1468C2×C23semidirect
535. C22×#41C22×C23semidirect
559. #451C22×C23semidirect
560. #450C22×C23semidirect
565. #448C22×C23semidirect
566. #448C22×C23semidirect
568. #447C22×C23semidirect
569. #447C22×C23semidirect
572. #407C22×C23semidirect
573. C2×C22⋊C8C22×C23semidirect
574. #395C22×C23semidirect
575. #394C22×C23semidirect
576. #393C22×C23semidirect
577. #392C22×C23semidirect
581. C2×#95C22×C23semidirect
582. #328C22×C23semidirect
583. #328C22×C23semidirect
586. #327C22×C23semidirect
587. #327C22×C23semidirect
588. #327C22×C23semidirect
589. #327C22×C23semidirect
590. #324C22×C23semidirect
591. #324C22×C23semidirect
592. #323C22×C23semidirect
593. #323C22×C23semidirect
612. C2×#41D4×C23semidirect
620. C22×D4D4×C23semidirect
666. C22⋊Q8D4×C23semidirect
684. #121D4×C23semidirect
685. #121D4×C23semidirect
686. #121D4×C23semidirect
707. #117D4×C23semidirect
710. C2×C4⋊C4D4×C23semidirect
741. C23#18252direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35342
C23×#30062
C23×#30022
C23×#24302
C23×#16062
C23×#16042
C23×#16032
C23×#16012
C23×#16002
C23×#15982
C23×#15972
C23×#15952
C23×#15042
C2×C23×#3272
C23×#14682
#1825223