Finite Group Databasebeta

← C23×#33551 #19181177

Subgroups — C23×#33551 #19181177

Order 5888.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3532C211yesmaximal, characteristic, complemented
2C23×#3026C211yesmaximal, characteristic, complemented
3C2×C23×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C23×#3019C211yesmaximal, characteristic, complemented
5C23×#2200C212yesmaximal, complemented
6C23×#2199C212yesmaximal, complemented
7C23×#2197C212yesmaximal, complemented
8C23×#2196C212yesmaximal, complemented
9C23×#2127C211yesmaximal, characteristic, complemented
10C23×#2121C211yesmaximal, characteristic, complemented
11C2×C23×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
12C2×C23×H(5,𝔽2)C2211yescharacteristic, complemented
13C23×#575—21no—
14C23×H(3,𝔽4)C2211yescharacteristic, complemented
15C23×#560—21no—
16C23×#560C2211yescharacteristic, complemented
17C23×#551—21no—
18C23×#551C2211yescharacteristic, complemented
19C23×#546—21no—
20C23×#546—21no—
21C23×#546—21no—
22D42×C23—21no—
23D42×C23C2211yescharacteristic, complemented
24C23×#538—21no—
25C23×#538—21no—
26C23×#538—21no—
27C23×#535—21no—
28C23×#535C2211yescharacteristic
29C23×#534—21no—
30C23×#534—21no—
31C23×#534C2211yescharacteristic
32C2×C23×#120—21no—
33C2×C23×#120—21no—
34C2×C23×#120C2211yescharacteristic
35C23×#458—21no—
36C23×#458C2212yescomplemented
37C23×B(4,𝔽2)—21no—
38C23×B(4,𝔽2)—21no—
39C23×B(4,𝔽2)—21no—
40C23×B(4,𝔽2)C2212yes—
41C23×B(4,𝔽2)C2212yescomplemented
42C23×B(4,𝔽2)C2212yescomplemented
43C23×#455—21no—
44C23×#455C2212yescomplemented
45C23×#453—21no—
46C23×#453C2212yescomplemented
47C23×#421—21no—
48C2×C23×#100C2211yescharacteristic, complemented
49C2×C23×#99—21no—
50C2×C23×#99—21no—
51C2×C23×#99C2211yescharacteristic, complemented
52C2×C23×#99C2211yescharacteristic, complemented
53C23×#354C2212yescomplemented
54C23×#353C2212yescomplemented
55C23×#352C2212yescomplemented
56C23×AΣL(1,𝔽16)C2212yescomplemented
57C23×AΣL(1,𝔽16)C2212yescomplemented
58C23×AΣL(1,𝔽16)C2212yescomplemented
59C25×C23D411yescharacteristic, complemented
60C23×H(5,𝔽2)—21no—
61C23×H(5,𝔽2)—21no—
62C23×H(5,𝔽2)—21no—
63C23×H(5,𝔽2)—42no—
64C23×H(5,𝔽2)C2312yes—
65C2×#41×C23—21no—
66C2×#41×C23—21no—
67C2×#41×C23—41no—
68C2×#41×C23D411yescharacteristic, complemented
69C22×D4×C23—21no—
70C22×D4×C23—21no—
71C22×D4×C23—21no—
72C22×D4×C23—21no—
73C22×D4×C23—21no—
74C22×D4×C23—21no—
75C22×D4×C23—21no—
76C22×D4×C23—41no—
77C22×D4×C23—41no—
78C22×D4×C23D411yescharacteristic, complemented
79C22×D4×C23C2311yescharacteristic
80C23×#137—22no—
81C23×#137—41no—
82C23×AGL(1,ℤ/8)—22no—
83C23×AGL(1,ℤ/8)—41no—
84C23×#135—42no—
85C2×M16×C23—21no—
86C23×#127—21no—
87C23×#127D411yescharacteristic, complemented
88C23×#127C2311yescharacteristic
89C23×#126—21no—
90C23×#126—21no—
91C23×#126—21no—
92C23×#126—21no—
93C23×#124—21no—
94C23×#124—21no—
95C23×#124—21no—
96C23×#124—21no—
97C23×#124—21no—
98C23×#124D411yescharacteristic, complemented
99C23×#124C2311yescharacteristic
100C23×#123—21no—
101C23×#123—21no—
102C23×#123—21no—
103C23×#123—21no—
104C23×#123—21no—
105C23×#123—21no—
106C23×#123—21no—
107C23×#123—21no—
108C23×#123—22no—
109C23×#123—41no—
110C23×#123D411yescharacteristic, complemented
111C23×#123C2311yescharacteristic
112C23×C22⋊Q8—21no—
113C23×C22⋊Q8—21no—
114C23×C22⋊Q8—21no—
115C23×#121—21no—
116C23×#121—21no—
117C23×#121—21no—
118C23×#121—21no—
119C23×#121—21no—
120C23×#121—21no—
121C23×#121—21no—
122C23×#121—21no—
123C23×#121—21no—
124C23×#121—21no—
125C23×#121—21no—
126C23×#121—21no—
127C23×#121—21no—
128C23×#121—21no—
129C23×#121—21no—
130C23×#121—42no—
131C23×#120—21no—
132C23×#120—21no—
133C23×#120—21no—
134C23×#120—21no—
135C23×#120—21no—
136C23×#120—21no—
137C23×#120—21no—
138C23×#120—21no—
139C23×#120—21no—
140C23×#120—21no—
141C23×#120—21no—
142C23×#120—21no—
143C23×#120—21no—
144C23×#120—21no—
145C23×#120—22no—
146C23×#120—22no—
147C23×#120—22no—
148C23×#120—42no—
149C23×#120—41no—
150C23×#120D411yescharacteristic, complemented
151C23×#120D411yescharacteristic, complemented
152C23×#120D411yescharacteristic, complemented
153C23×#120C2311yescharacteristic
154C23×#120C2311yescharacteristic
155C23×#120C2311yescharacteristic
156C4×D4×C23—21no—
157C4×D4×C23—21no—
158C4×D4×C23—21no—
159C4×D4×C23—21no—
160C4×D4×C23—21no—
161C4×D4×C23—21no—
162C23×#117—21no—
163C23×#117D411yescharacteristic, complemented
164C2×C22⋊C4×C23—21no—
165C2×C22⋊C4×C23—21no—
166C2×C22⋊C4×C23—21no—
167C2×C22⋊C4×C23—21no—
168C2×C22⋊C4×C23—21no—
169C2×C22⋊C4×C23—21no—
170C2×C22⋊C4×C23—21no—
171C2×C22⋊C4×C23—41no—
172C2×C22⋊C4×C23D411yescharacteristic, complemented
173C2×C22⋊C4×C23D411yescharacteristic, complemented
174C23×#104—22no—
175C23×#104—22no—
176C23×#100—21no—
177C23×#100C2312yes—
178C23×#99—21no—
179C23×#99—21no—
180C23×#99—22no—
181C23×#99—22no—
182C23×#99—22no—
183C23×#99—22no—
184C23×#99C2312yes—
185C23×#99C2312yes—
186C24×C23—21no—
187C24×C23—21no—
188C24×C23—21no—
189C24×C23—21no—
190C24×C23—21no—
191C24×C23—41no—
192C24×C23—41no—
193C24×C23—82no—
194C24×C23C2×D411yescharacteristic
195C24×C23C2×D411yescharacteristic
196C24×C23C2×D411yescharacteristic
197C24×C23C2×D411yescharacteristic
198C24×C23C2×D411yescharacteristic, complemented
199#41×C23—22no—
200#41×C23—22no—
201#41×C23—42no—
202#41×C23—41no—
203#41×C23—42no—
204#41×C23—42no—
205#41×C23—41no—
206#41×C23—41no—
207#41×C23—42no—
208#41×C23—41no—
209#41×C23—82no—
210C2×Q8×C23—21no—
211C2×Q8×C23—21no—
212C2×Q8×C23C2×D411yescharacteristic, complemented
213C2×D4×C23—21no—
214C2×D4×C23—21no—
215C2×D4×C23—21no—
216C2×D4×C23—22no—
217C2×D4×C23—22no—
218C2×D4×C23—21no—
219C2×D4×C23—21no—
220C2×D4×C23—21no—
221C2×D4×C23—22no—
222C2×D4×C23—22no—
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—21no—
234C2×D4×C23—21no—
235C2×D4×C23—21no—
236C2×D4×C23—21no—
237C2×D4×C23—21no—
238C2×D4×C23—41no—
239C2×D4×C23—41no—
240C2×D4×C23—42no—
241C2×D4×C23—42no—
242C2×D4×C23—41no—
243C2×D4×C23—41no—
244C2×D4×C23—41no—
245C2×D4×C23—41no—
246C2×D4×C23—42no—
247C2×D4×C23—42no—
248C2×D4×C23—41no—
249C2×D4×C23—41no—
250C2×D4×C23—41no—
251C2×D4×C23—41no—
252C2×D4×C23—41no—
253C2×D4×C23—42no—
254C2×D4×C23—42no—
255C2×D4×C23—42no—
256C2×D4×C23—82no—
257C2×D4×C23—82no—
258C2×D4×C23—82no—
259C2×D4×C23—82no—
260C2×D4×C23—81no—
261C2×D4×C23—81no—
262C2×D4×C23—84no—
263C2×D4×C23C2×D411yescharacteristic
264C2×D4×C23C2×D411yescharacteristic
265C2×D4×C23C2×D411yescharacteristic
266C2×D4×C23C2×D411yescharacteristic, complemented
267C2×D4×C23C2411yescharacteristic
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—41no—
279C22×C4×C23—41no—
280C22×C4×C23—41no—
281C22×C4×C23C2×D411yescharacteristic
282C22×C4×C23C2×D411yescharacteristic, complemented
283Q16×C23—42no—
284SD16×C23—42no—
285SD16×C23—42no—
286D8×C23—42no—
287M16×C23—22no—
288M16×C23—41no—
289C2×C8×C23—41no—
290C4⋊C4×C23—21no—
291C4⋊C4×C23—21no—
292C4⋊C4×C23—21no—
293C4⋊C4×C23—21no—
294C4⋊C4×C23—21no—
295C4⋊C4×C23—21no—
296C4⋊C4×C23—21no—
297C4⋊C4×C23—21no—
298C4⋊C4×C23—21no—
299C4⋊C4×C23—42no—
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—21no—
322C22⋊C4×C23—21no—
323C22⋊C4×C23—21no—
324C22⋊C4×C23—21no—
325C22⋊C4×C23—22no—
326C22⋊C4×C23—22no—
327C22⋊C4×C23—42no—
328C22⋊C4×C23—42no—
329C22⋊C4×C23—42no—
330C22⋊C4×C23—41no—
331C22⋊C4×C23—41no—
332C22⋊C4×C23—42no—
333C22⋊C4×C23C2×D411yescharacteristic
334C22⋊C4×C23C2×D411yescharacteristic
335C22⋊C4×C23C2×D411yescharacteristic, complemented
336C22⋊C4×C23C2×D411yescharacteristic, complemented
337C42×C23—21no—
338C42×C23—21no—
339C42×C23C2×D411yescharacteristic, complemented
340C42×C23C2×D411yescharacteristic, complemented
341#33551C2311yesmaximal, characteristic, direct product factor, Sylow
342C23×C23—21no—
343C23×C23—21no—
344C23×C23—21no—
345C23×C23—21no—
346C23×C23—21no—
347C23×C23—22no—
348C23×C23—22no—
349C23×C23—21no—
350C23×C23—21no—
351C23×C23—21no—
352C23×C23—41no—
353C23×C23—41no—
354C23×C23—42no—
355C23×C23—42no—
356C23×C23—42no—
357C23×C23—41no—
358C23×C23—41no—
359C23×C23—42no—
360C23×C23—41no—
361C23×C23—44no—
362C23×C23—41no—
363C23×C23—41no—
364C23×C23—41no—
365C23×C23—81no—
366C23×C23—81no—
367C23×C23—81no—
368C23×C23—81no—
369C23×C23—81no—
370C23×C23—81no—
371C23×C23—81no—
372C23×C23—81no—
373C23×C23—81no—
374C23×C23—82no—
375C23×C23—82no—
376C23×C23—82no—
377C23×C23—82no—
378C23×C23—161no—
379C23×C23#12011yescharacteristic
380C23×C23#12011yescharacteristic
381C23×C23#12011yescharacteristic
382C23×C23C22×D411yescharacteristic
383C23×C23C22×D411yescharacteristic
384Q8×C23—22no—
385Q8×C23—41no—
386Q8×C23—41no—
387Q8×C23—81no—
388D4×C23—22no—
389D4×C23—41no—
390D4×C23—41no—
391D4×C23—41no—
392D4×C23—41no—
393D4×C23—41no—
394D4×C23—41no—
395D4×C23—42no—
396D4×C23—42no—
397D4×C23—42no—
398D4×C23—42no—
399D4×C23—42no—
400D4×C23—42no—
401D4×C23—42no—
402D4×C23—42no—
403D4×C23—42no—
404D4×C23—42no—
405D4×C23—41no—
406D4×C23—41no—
407D4×C23—41no—
408D4×C23—41no—
409D4×C23—81no—
410D4×C23—81no—
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—
424D4×C23—84no—
425D4×C23—162no—
426C2×C4×C23—21no—
427C2×C4×C23—21no—
428C2×C4×C23—22no—
429C2×C4×C23—22no—
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—42no—
439C2×C4×C23—42no—
440C2×C4×C23—41no—
441C2×C4×C23—41no—
442C2×C4×C23—42no—
443C2×C4×C23—41no—
444C2×C4×C23—41no—
445C2×C4×C23—42no—
446C2×C4×C23—42no—
447C2×C4×C23—81no—
448C2×C4×C23—81no—
449C2×C4×C23—81no—
450C2×C4×C23—81no—
451C2×C4×C23—81no—
452C2×C4×C23—81no—
453C2×C4×C23—81no—
454C2×C4×C23—82no—
455C2×C4×C23—161no—
456C2×C4×C23#12011yescharacteristic
457C2×C4×C23C22×D411yescharacteristic
458C8×C23—42no—
459#3532C2×C2311yescharacteristic, complemented
460#3026C2×C2311yescharacteristic, complemented
461C2×B(4,𝔽2)C2×C2311yescharacteristic, complemented
462#3019C2×C2311yescharacteristic, complemented
463#2200C2×C2312yescomplemented
464#2199C2×C2312yescomplemented
465#2197C2×C2312yescomplemented
466#2196C2×C2312yescomplemented
467#2127C2×C2311yescharacteristic, complemented
468#2121C2×C2311yescharacteristic, complemented
469C2×AΣL(1,𝔽16)C2×C2311yescharacteristic, complemented
470C22×C23—22no—
471C22×C23—21no—
472C22×C23—21no—
473C22×C23—21no—
474C22×C23—21no—
475C22×C23—41no—
476C22×C23—41no—
477C22×C23—41no—
478C22×C23—41no—
479C22×C23—41no—
480C22×C23—41no—
481C22×C23—42no—
482C22×C23—41no—
483C22×C23—41no—
484C22×C23—41no—
485C22×C23—41no—
486C22×C23—41no—
487C22×C23—41no—
488C22×C23—42no—
489C22×C23—41no—
490C22×C23—42no—
491C22×C23—42no—
492C22×C23—41no—
493C22×C23—41no—
494C22×C23—41no—
495C22×C23—81no—
496C22×C23—81no—
497C22×C23—81no—
498C22×C23—82no—
499C22×C23—82no—
500C22×C23—82no—
501C22×C23—81no—
502C22×C23—84no—
503C22×C23—82no—
504C22×C23—82no—
505C22×C23—82no—
506C22×C23—81no—
507C22×C23—162no—
508C22×C23—161no—
509C22×C23—161no—
510C22×C23B(4,𝔽2)11yescharacteristic
511C22×C23B(4,𝔽2)11yescharacteristic
512C22×C23C2×#12011yescharacteristic
513C4×C23—21no—
514C4×C23—21no—
515C4×C23—41no—
516C4×C23—41no—
517C4×C23—41no—
518C4×C23—41no—
519C4×C23—41no—
520C4×C23—41no—
521C4×C23—42no—
522C4×C23—41no—
523C4×C23—41no—
524C4×C23—82no—
525C4×C23—82no—
526C2×H(5,𝔽2)C22×C2311yescharacteristic, complemented
527#575—21no—
528H(3,𝔽4)C22×C2311yescharacteristic, complemented
529#560—21no—
530#560C22×C2311yescharacteristic, complemented
531#551—21no—
532#551C22×C2311yescharacteristic, complemented
533#546—21no—
534#546—21no—
535#546—21no—
536D42—21no—
537D42C22×C2311yescharacteristic, complemented
538#538—21no—
539#538—21no—
540#538—21no—
541#535—21no—
542#535C22×C2311yescharacteristic
543#534—21no—
544#534—21no—
545#534C22×C2311yescharacteristic
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C2311yescharacteristic
549#458—21no—
550#458C22×C2312yescomplemented
551B(4,𝔽2)—21no—
552B(4,𝔽2)—21no—
553B(4,𝔽2)—21no—
554B(4,𝔽2)C22×C2312yes—
555B(4,𝔽2)C22×C2312yescomplemented
556B(4,𝔽2)C22×C2312yescomplemented
557#455—21no—
558#455C22×C2312yescomplemented
559#453—21no—
560#453C22×C2312yescomplemented
561#421—21no—
562C2×#100C22×C2311yescharacteristic, complemented
563C2×#99—21no—
564C2×#99—21no—
565C2×#99C22×C2311yescharacteristic, complemented
566C2×#99C22×C2311yescharacteristic, complemented
567#354C22×C2312yescomplemented
568#353C22×C2312yescomplemented
569#352C22×C2312yescomplemented
570AΣL(1,𝔽16)C22×C2312yescomplemented
571AΣL(1,𝔽16)C22×C2312yescomplemented
572AΣL(1,𝔽16)C22×C2312yescomplemented
573C2×C23—21no—
574C2×C23—21no—
575C2×C23—21no—
576C2×C23—41no—
577C2×C23—41no—
578C2×C23—42no—
579C2×C23—41no—
580C2×C23—41no—
581C2×C23—81no—
582C2×C23—81no—
583C2×C23—81no—
584C2×C23—82no—
585C2×C23C2×B(4,𝔽2)11yescharacteristic
586C25D4×C2311yescharacteristic, complemented
587H(5,𝔽2)—21no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—42no—
591H(5,𝔽2)C23×C2312yes—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—41no—
595C2×#41D4×C2311yescharacteristic, complemented
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4D4×C2311yescharacteristic, complemented
606C22×D4C23×C2311yescharacteristic
607#137—22no—
608#137—41no—
609AGL(1,ℤ/8)—22no—
610AGL(1,ℤ/8)—41no—
611#135—42no—
612C2×M16—21no—
613#127—21no—
614#127D4×C2311yescharacteristic, complemented
615#127C23×C2311yescharacteristic
616#126—21no—
617#126—21no—
618#126—21no—
619#126—21no—
620#124—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124D4×C2311yescharacteristic, complemented
626#124C23×C2311yescharacteristic
627#123—21no—
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—22no—
636#123—41no—
637#123D4×C2311yescharacteristic, complemented
638#123C23×C2311yescharacteristic
639C22⋊Q8—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—42no—
658#120—21no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—22no—
673#120—22no—
674#120—22no—
675#120—42no—
676#120—41no—
677#120D4×C2311yescharacteristic, complemented
678#120D4×C2311yescharacteristic, complemented
679#120D4×C2311yescharacteristic, complemented
680#120C23×C2311yescharacteristic
681#120C23×C2311yescharacteristic
682#120C23×C2311yescharacteristic
683C4×D4—21no—
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689#117—21no—
690#117D4×C2311yescharacteristic, complemented
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4D4×C2311yescharacteristic, complemented
700C2×C22⋊C4D4×C2311yescharacteristic, complemented
701#104—22no—
702#104—22no—
703#100—21no—
704#100C23×C2312yes—
705#99—21no—
706#99—21no—
707#99—22no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99C23×C2312yes—
712#99C23×C2312yes—
713C23#3355111yescharacteristic, direct product factor, Sylow
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C2311yescharacteristic
723C24C2×D4×C2311yescharacteristic
724C24C2×D4×C2311yescharacteristic
725C24C2×D4×C2311yescharacteristic
726C24C2×D4×C2311yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C2311yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C2311yescharacteristic
792C2×D4C2×D4×C2311yescharacteristic
793C2×D4C2×D4×C2311yescharacteristic
794C2×D4C2×D4×C2311yescharacteristic, complemented
795C2×D4C24×C2311yescharacteristic
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—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C2311yescharacteristic
810C22×C4C2×D4×C2311yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
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—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C2311yescharacteristic
862C22⋊C4C2×D4×C2311yescharacteristic
863C22⋊C4C2×D4×C2311yescharacteristic, complemented
864C22⋊C4C2×D4×C2311yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C2311yescharacteristic, complemented
868C42C2×D4×C2311yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23C23×#12011yescharacteristic
907C23C23×#12011yescharacteristic
908C23C23×#12011yescharacteristic
909C23C22×D4×C2311yescharacteristic
910C23C22×D4×C2311yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—42no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4C23×#12011yescharacteristic
984C2×C4C22×D4×C2311yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22C23×B(4,𝔽2)11yescharacteristic
1027C22C23×B(4,𝔽2)11yescharacteristic
1028C22C2×C23×#12011yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×C23×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C23C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C23
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C23 ◁ C23×C23 ◁ C22×D4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#3532C2semidirect
2. C23×#3026C2semidirect
3. C2×C23×B(4,𝔽2)C2semidirect
4. C23×#3019C2semidirect
5. C23×#2200C2semidirect
6. C23×#2199C2semidirect
7. C23×#2197C2semidirect
8. C23×#2196C2semidirect
9. C23×#2127C2semidirect
10. C23×#2121C2semidirect
11. C2×C23×AΣL(1,𝔽16)C2semidirect
12. C2×C23×H(5,𝔽2)C22semidirect
14. C23×H(3,𝔽4)C22semidirect
16. C23×#560C22semidirect
18. C23×#551C22semidirect
23. D42×C23C22semidirect
36. C23×#458C22semidirect
41. C23×B(4,𝔽2)C22semidirect
42. C23×B(4,𝔽2)C22semidirect
44. C23×#455C22semidirect
46. C23×#453C22semidirect
48. C2×C23×#100C22semidirect
51. C2×C23×#99C22semidirect
52. C2×C23×#99C22semidirect
53. C23×#354C22semidirect
54. C23×#353C22semidirect
55. C23×#352C22semidirect
56. C23×AΣL(1,𝔽16)C22semidirect
57. C23×AΣL(1,𝔽16)C22semidirect
58. C23×AΣL(1,𝔽16)C22semidirect
59. C25×C23D4semidirect
68. C2×#41×C23D4semidirect
78. C22×D4×C23D4semidirect
87. C23×#127D4semidirect
98. C23×#124D4semidirect
110. C23×#123D4semidirect
150. C23×#120D4semidirect
151. C23×#120D4semidirect
152. C23×#120D4semidirect
163. C23×#117D4semidirect
172. C2×C22⋊C4×C23D4semidirect
173. C2×C22⋊C4×C23D4semidirect
198. C24×C23C2×D4semidirect
212. C2×Q8×C23C2×D4semidirect
266. C2×D4×C23C2×D4semidirect
282. C22×C4×C23C2×D4semidirect
335. C22⋊C4×C23C2×D4semidirect
336. C22⋊C4×C23C2×D4semidirect
339. C42×C23C2×D4semidirect
340. C42×C23C2×D4semidirect
341. #33551C23direct (N × H)
459. #3532C2×C23semidirect
460. #3026C2×C23semidirect
461. C2×B(4,𝔽2)C2×C23semidirect
462. #3019C2×C23semidirect
463. #2200C2×C23semidirect
464. #2199C2×C23semidirect
465. #2197C2×C23semidirect
466. #2196C2×C23semidirect
467. #2127C2×C23semidirect
468. #2121C2×C23semidirect
469. C2×AΣL(1,𝔽16)C2×C23semidirect
526. C2×H(5,𝔽2)C22×C23semidirect
528. H(3,𝔽4)C22×C23semidirect
530. #560C22×C23semidirect
532. #551C22×C23semidirect
537. D42C22×C23semidirect
550. #458C22×C23semidirect
555. B(4,𝔽2)C22×C23semidirect
556. B(4,𝔽2)C22×C23semidirect
558. #455C22×C23semidirect
560. #453C22×C23semidirect
562. C2×#100C22×C23semidirect
565. C2×#99C22×C23semidirect
566. C2×#99C22×C23semidirect
567. #354C22×C23semidirect
568. #353C22×C23semidirect
569. #352C22×C23semidirect
570. AΣL(1,𝔽16)C22×C23semidirect
571. AΣL(1,𝔽16)C22×C23semidirect
572. AΣL(1,𝔽16)C22×C23semidirect
586. C25D4×C23semidirect
595. C2×#41D4×C23semidirect
605. C22×D4D4×C23semidirect
614. #127D4×C23semidirect
625. #124D4×C23semidirect
637. #123D4×C23semidirect
677. #120D4×C23semidirect
678. #120D4×C23semidirect
679. #120D4×C23semidirect
690. #117D4×C23semidirect
699. C2×C22⋊C4D4×C23semidirect
700. C2×C22⋊C4D4×C23semidirect
713. C23#33551direct (N × H)
726. C24C2×D4×C23semidirect
740. C2×Q8C2×D4×C23semidirect
794. C2×D4C2×D4×C23semidirect
810. C22×C4C2×D4×C23semidirect
863. C22⋊C4C2×D4×C23semidirect
864. C22⋊C4C2×D4×C23semidirect
867. C42C2×D4×C23semidirect
868. C42C2×D4×C23semidirect

Maximal subgroups

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

subgroupindex
C23×#35322
C23×#30262
C2×C23×B(4,𝔽2)2
C23×#30192
C23×#22002
C23×#21992
C23×#21972
C23×#21962
C23×#21272
C23×#21212
C2×C23×AΣL(1,𝔽16)2
#3355123