Finite Group Databasebeta

← C23×#33553 #19181179

Subgroups — C23×#33553 #19181179

Order 5888.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3537C211yesmaximal, characteristic, complemented
2C23×#3027C211yesmaximal, characteristic, complemented
3C23×#3025C211yesmaximal, characteristic, complemented
4C23×#3021C211yesmaximal, characteristic, complemented
5C23×#2200C214yesmaximal, complemented
6C23×#2196C214yesmaximal, complemented
7C23×#2128C211yesmaximal, characteristic, complemented
8C23×#2122C211yesmaximal, characteristic, complemented
9C23×#2120C211yesmaximal, characteristic, complemented
10C23×#585C2211yescharacteristic, complemented
11C2×C23×AGL(1,ℤ/8)—21no—
12C23×#560—21no—
13C23×#560C2212yescomplemented
14C23×#553—21no—
15C23×#553—21no—
16D42×C23—21no—
17D42×C23—21no—
18D42×C23—21no—
19D42×C23C2212yescomplemented
20C23×#540—21no—
21C23×#538—22no—
22C23×#535—21no—
23C23×#535C2211yescharacteristic
24C23×#535C2211yescharacteristic
25C23×#534—22no—
26C23×#525—21no—
27C23×#525C2211yescharacteristic
28C2×C23×#121—21no—
29C23×#458—21no—
30C23×#458C2212yescomplemented
31C23×B(4,𝔽2)—21no—
32C23×B(4,𝔽2)—22no—
33C23×B(4,𝔽2)C2212yescomplemented
34C23×B(4,𝔽2)C2214yescomplemented
35C23×#454—22no—
36C23×#453C2214yescomplemented
37C23×#421—21no—
38C23×#413C2211yescharacteristic, complemented
39C23×#410—21no—
40C23×#410—21no—
41C23×#410C2211yescharacteristic, complemented
42C23×#410C2211yescharacteristic, complemented
43C23×#353C2214yescomplemented
44C23×#352C2212yescomplemented
45C23×AΣL(1,𝔽16)C2212yescomplemented
46C23×AΣL(1,𝔽16)C2214yescomplemented
47C23×2−1+4—21no—
48C23×2−1+4—41no—
49C23×H(5,𝔽2)—21no—
50C23×H(5,𝔽2)—21no—
51C23×H(5,𝔽2)—41no—
52C23×H(5,𝔽2)C2312yes—
53C2×#41×C23—21no—
54C2×#41×C23—21no—
55C2×#41×C23—21no—
56C2×#41×C23—42no—
57C2×#41×C23C2311yescharacteristic
58C22×D4×C23—21no—
59C22×D4×C23—22no—
60C22×D4×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23D411yescharacteristic, complemented
63C22×D4×C23D411yescharacteristic, complemented
64C23×C4×C23D411yescharacteristic, complemented
65C23×AGL(1,ℤ/8)—24no—
66C23×AGL(1,ℤ/8)—42no—
67C2×SD16×C23—41no—
68C2×D8×C23—41no—
69C2×M16×C23—21no—
70C23×#127—21no—
71C23×#127—21no—
72C23×#127—41no—
73C23×#127C2312yes—
74C23×#126—22no—
75C23×#126—22no—
76C23×#125—21no—
77C23×#124—21no—
78C23×#124—41no—
79C23×#124D412yescomplemented
80C23×#123—22no—
81C23×#123—22no—
82C23×#123—22no—
83C23×#123—22no—
84C23×#123—22no—
85C23×#123D411yescharacteristic, complemented
86C23×#123C2311yescharacteristic
87C23×C22⋊Q8—21no—
88C23×C22⋊Q8—41no—
89C23×#121—21no—
90C23×#121—21no—
91C23×#121—22no—
92C23×#121—22no—
93C23×#121—22no—
94C23×#121—22no—
95C23×#121—21no—
96C23×#121—21no—
97C23×#121—21no—
98C23×#121—22no—
99C23×#121—21no—
100C23×#121—21no—
101C23×#121—22no—
102C23×#121—22no—
103C23×#121—22no—
104C23×#121—42no—
105C23×#121—41no—
106C23×#120—22no—
107C23×#120—22no—
108C23×#120—22no—
109C23×#120—21no—
110C23×#120—21no—
111C23×#120—22no—
112C23×#120—22no—
113C23×#120—24no—
114C23×#120D411yescharacteristic, complemented
115C23×#120D412yescomplemented
116C23×#120C2312yes—
117C23×#120C2311yescharacteristic
118C4×D4×C23—22no—
119C4×D4×C23—21no—
120C4×D4×C23—21no—
121C4×D4×C23—21no—
122C4×D4×C23—21no—
123C4×D4×C23—22no—
124C4×D4×C23—42no—
125C23×#117—21no—
126C23×#117—21no—
127C23×#117D411yescharacteristic, complemented
128C23×#117D411yescharacteristic, complemented
129C23×#117D411yescharacteristic, complemented
130C2×C4⋊C4×C23—21no—
131C2×C22⋊C4×C23—22no—
132C23×#104—24no—
133C23×#101—21no—
134C23×#100C2312yes—
135C23×#99—21no—
136C23×#99—21no—
137C23×#99—24no—
138C23×#99—22no—
139C23×#99—22no—
140C23×#99C2312yes—
141C23×#99C2312yes—
142C24×C23—22no—
143C24×C23—21no—
144C24×C23C2×D411yescharacteristic
145C24×C23C2×D412yes—
146#41×C23—22no—
147#41×C23—22no—
148#41×C23—41no—
149#41×C23—41no—
150#41×C23—42no—
151#41×C23—41no—
152#41×C23—41no—
153#41×C23—41no—
154#41×C23—41no—
155#41×C23—41no—
156#41×C23—42no—
157#41×C23—42no—
158#41×C23—42no—
159#41×C23—41no—
160#41×C23—41no—
161#41×C23—41no—
162C2×Q8×C23—21no—
163C2×Q8×C23—21no—
164C2×Q8×C23—21no—
165C2×Q8×C23—42no—
166C2×Q8×C23C2×D411yescharacteristic
167C2×D4×C23—21no—
168C2×D4×C23—22no—
169C2×D4×C23—22no—
170C2×D4×C23—21no—
171C2×D4×C23—21no—
172C2×D4×C23—21no—
173C2×D4×C23—22no—
174C2×D4×C23—22no—
175C2×D4×C23—21no—
176C2×D4×C23—22no—
177C2×D4×C23—22no—
178C2×D4×C23—22no—
179C2×D4×C23—22no—
180C2×D4×C23—22no—
181C2×D4×C23—22no—
182C2×D4×C23—22no—
183C2×D4×C23—21no—
184C2×D4×C23—21no—
185C2×D4×C23—21no—
186C2×D4×C23—41no—
187C2×D4×C23—41no—
188C2×D4×C23—41no—
189C2×D4×C23—41no—
190C2×D4×C23—42no—
191C2×D4×C23—42no—
192C2×D4×C23—42no—
193C2×D4×C23—41no—
194C2×D4×C23—42no—
195C2×D4×C23—44no—
196C2×D4×C23—81no—
197C2×D4×C23—81no—
198C2×D4×C23—84no—
199C2×D4×C23—84no—
200C2×D4×C23—84no—
201C2×D4×C23C2×D411yescharacteristic
202C2×D4×C23C2×D411yescharacteristic
203C2×D4×C23C2×D412yes—
204C2×D4×C23C2411yescharacteristic
205C22×C4×C23—22no—
206C22×C4×C23—22no—
207C22×C4×C23—22no—
208C22×C4×C23—22no—
209C22×C4×C23—22no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—41no—
213C22×C4×C23—41no—
214C22×C4×C23—41no—
215C22×C4×C23C2×D411yescharacteristic
216C22×C4×C23C2×D411yescharacteristic
217C22×C4×C23C2×D411yescharacteristic
218C22×C4×C23C2×D411yescharacteristic
219SD16×C23—44no—
220D8×C23—44no—
221M16×C23—22no—
222M16×C23—41no—
223C2×C8×C23—41no—
224C4⋊C4×C23—22no—
225C4⋊C4×C23—22no—
226C4⋊C4×C23—22no—
227C4⋊C4×C23—21no—
228C4⋊C4×C23—21no—
229C4⋊C4×C23—21no—
230C4⋊C4×C23—21no—
231C4⋊C4×C23—21no—
232C4⋊C4×C23—41no—
233C4⋊C4×C23—41no—
234C4⋊C4×C23—42no—
235C22⋊C4×C23—22no—
236C22⋊C4×C23—22no—
237C22⋊C4×C23—22no—
238C22⋊C4×C23—22no—
239C22⋊C4×C23—21no—
240C22⋊C4×C23—21no—
241C22⋊C4×C23—21no—
242C22⋊C4×C23—22no—
243C22⋊C4×C23—22no—
244C22⋊C4×C23—21no—
245C22⋊C4×C23—22no—
246C22⋊C4×C23—21no—
247C22⋊C4×C23—22no—
248C22⋊C4×C23—22no—
249C22⋊C4×C23—22no—
250C22⋊C4×C23—42no—
251C22⋊C4×C23—44no—
252C22⋊C4×C23—42no—
253C22⋊C4×C23C2×D412yes—
254C22⋊C4×C23C2×D411yescharacteristic
255C22⋊C4×C23C2×D411yescharacteristic
256C42×C23—21no—
257C42×C23—21no—
258C42×C23—41no—
259C42×C23—41no—
260C42×C23C2×D412yes—
261#33553C2311yesmaximal, characteristic, direct product factor, Sylow
262C23×C23—21no—
263C23×C23—22no—
264C23×C23—22no—
265C23×C23—22no—
266C23×C23—22no—
267C23×C23—41no—
268C23×C23—42no—
269C23×C23—41no—
270C23×C23—44no—
271C23×C23—42no—
272C23×C23—81no—
273C23×C23—82no—
274C23×C23—82no—
275C23×C23—82no—
276C23×C23—82no—
277C23×C23#12011yescharacteristic
278C23×C23C22×D411yescharacteristic
279C23×C23C22×D411yescharacteristic
280Q8×C23—22no—
281Q8×C23—41no—
282Q8×C23—41no—
283Q8×C23—41no—
284Q8×C23—41no—
285D4×C23—22no—
286D4×C23—41no—
287D4×C23—41no—
288D4×C23—41no—
289D4×C23—42no—
290D4×C23—41no—
291D4×C23—41no—
292D4×C23—42no—
293D4×C23—42no—
294D4×C23—42no—
295D4×C23—42no—
296D4×C23—44no—
297D4×C23—44no—
298D4×C23—42no—
299D4×C23—42no—
300D4×C23—41no—
301D4×C23—41no—
302D4×C23—41no—
303D4×C23—41no—
304D4×C23—41no—
305D4×C23—81no—
306D4×C23—82no—
307D4×C23—82no—
308D4×C23—82no—
309D4×C23—82no—
310D4×C23—82no—
311D4×C23—82no—
312D4×C23—82no—
313D4×C23—84no—
314D4×C23—164no—
315C2×C4×C23—21no—
316C2×C4×C23—21no—
317C2×C4×C23—21no—
318C2×C4×C23—21no—
319C2×C4×C23—21no—
320C2×C4×C23—21no—
321C2×C4×C23—22no—
322C2×C4×C23—22no—
323C2×C4×C23—22no—
324C2×C4×C23—21no—
325C2×C4×C23—21no—
326C2×C4×C23—22no—
327C2×C4×C23—21no—
328C2×C4×C23—42no—
329C2×C4×C23—42no—
330C2×C4×C23—42no—
331C2×C4×C23—41no—
332C2×C4×C23—42no—
333C2×C4×C23—41no—
334C2×C4×C23—41no—
335C2×C4×C23—41no—
336C2×C4×C23—42no—
337C2×C4×C23—42no—
338C2×C4×C23—81no—
339C2×C4×C23—82no—
340C2×C4×C23—82no—
341C2×C4×C23—82no—
342C2×C4×C23#12011yescharacteristic
343C2×C4×C23#12011yescharacteristic
344C2×C4×C23#12011yescharacteristic
345C2×C4×C23C22×D411yescharacteristic
346C8×C23—42no—
347#3537C2×C2311yescharacteristic, complemented
348#3027C2×C2311yescharacteristic, complemented
349#3025C2×C2311yescharacteristic, complemented
350#3021C2×C2311yescharacteristic, complemented
351#2200C2×C2314yescomplemented
352#2196C2×C2314yescomplemented
353#2128C2×C2311yescharacteristic, complemented
354#2122C2×C2311yescharacteristic, complemented
355#2120C2×C2311yescharacteristic, complemented
356C22×C23—22no—
357C22×C23—21no—
358C22×C23—21no—
359C22×C23—21no—
360C22×C23—41no—
361C22×C23—41no—
362C22×C23—41no—
363C22×C23—41no—
364C22×C23—42no—
365C22×C23—42no—
366C22×C23—42no—
367C22×C23—42no—
368C22×C23—42no—
369C22×C23—41no—
370C22×C23—42no—
371C22×C23—42no—
372C22×C23—42no—
373C22×C23—81no—
374C22×C23—82no—
375C22×C23—82no—
376C22×C23—84no—
377C22×C23—161no—
378C22×C23—164no—
379C22×C23—162no—
380C22×C23C2×#12011yescharacteristic
381C4×C23—21no—
382C4×C23—21no—
383C4×C23—21no—
384C4×C23—42no—
385C4×C23—41no—
386C4×C23—41no—
387C4×C23—42no—
388C4×C23—42no—
389C4×C23—41no—
390C4×C23—82no—
391C4×C23—82no—
392C4×C23B(4,𝔽2)11yescharacteristic
393C4×C23B(4,𝔽2)11yescharacteristic
394#585C22×C2311yescharacteristic, complemented
395C2×AGL(1,ℤ/8)—21no—
396#560—21no—
397#560C22×C2312yescomplemented
398#553—21no—
399#553—21no—
400D42—21no—
401D42—21no—
402D42—21no—
403D42C22×C2312yescomplemented
404#540—21no—
405#538—22no—
406#535—21no—
407#535C22×C2311yescharacteristic
408#535C22×C2311yescharacteristic
409#534—22no—
410#525—21no—
411#525C22×C2311yescharacteristic
412C2×#121—21no—
413#458—21no—
414#458C22×C2312yescomplemented
415B(4,𝔽2)—21no—
416B(4,𝔽2)—22no—
417B(4,𝔽2)C22×C2312yescomplemented
418B(4,𝔽2)C22×C2314yescomplemented
419#454—22no—
420#453C22×C2314yescomplemented
421#421—21no—
422#413C22×C2311yescharacteristic, complemented
423#410—21no—
424#410—21no—
425#410C22×C2311yescharacteristic, complemented
426#410C22×C2311yescharacteristic, complemented
427#353C22×C2314yescomplemented
428#352C22×C2312yescomplemented
429AΣL(1,𝔽16)C22×C2312yescomplemented
430AΣL(1,𝔽16)C22×C2314yescomplemented
431C2×C23—21no—
432C2×C23—41no—
433C2×C23—41no—
434C2×C23—42no—
435C2×C23—41no—
436C2×C23—82no—
437C2×C23—82no—
438C2×C23—82no—
439C2×C23C2×B(4,𝔽2)11yescharacteristic
4402−1+4—21no—
4412−1+4—41no—
442H(5,𝔽2)—21no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—41no—
445H(5,𝔽2)C23×C2312yes—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—42no—
450C2×#41C23×C2311yescharacteristic
451C22×D4—21no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4D4×C2311yescharacteristic, complemented
456C22×D4D4×C2311yescharacteristic, complemented
457C23×C4D4×C2311yescharacteristic, complemented
458AGL(1,ℤ/8)—24no—
459AGL(1,ℤ/8)—42no—
460C2×SD16—41no—
461C2×D8—41no—
462C2×M16—21no—
463#127—21no—
464#127—21no—
465#127—41no—
466#127C23×C2312yes—
467#126—22no—
468#126—22no—
469#125—21no—
470#124—21no—
471#124—41no—
472#124D4×C2312yescomplemented
473#123—22no—
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123D4×C2311yescharacteristic, complemented
479#123C23×C2311yescharacteristic
480C22⋊Q8—21no—
481C22⋊Q8—41no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—22no—
486#121—22no—
487#121—21no—
488#121—22no—
489#121—21no—
490#121—21no—
491#121—22no—
492#121—21no—
493#121—21no—
494#121—22no—
495#121—22no—
496#121—22no—
497#121—42no—
498#121—41no—
499#120—22no—
500#120—22no—
501#120—22no—
502#120—21no—
503#120—21no—
504#120—22no—
505#120—22no—
506#120—24no—
507#120D4×C2311yescharacteristic, complemented
508#120D4×C2312yescomplemented
509#120C23×C2311yescharacteristic
510#120C23×C2312yes—
511C4×D4—22no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—22no—
517C4×D4—42no—
518#117—21no—
519#117—21no—
520#117D4×C2311yescharacteristic, complemented
521#117D4×C2311yescharacteristic, complemented
522#117D4×C2311yescharacteristic, complemented
523C2×C4⋊C4—21no—
524C2×C22⋊C4—22no—
525#104—24no—
526#101—21no—
527#100C23×C2312yes—
528#99—21no—
529#99—21no—
530#99—24no—
531#99—22no—
532#99—22no—
533#99C23×C2312yes—
534#99C23×C2312yes—
535C23#3355311yescharacteristic, direct product factor, Sylow
536C24—22no—
537C24—21no—
538C24C2×D4×C2311yescharacteristic
539C24C2×D4×C2312yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C2311yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C2311yescharacteristic
596C2×D4C2×D4×C2311yescharacteristic
597C2×D4C2×D4×C2312yes—
598C2×D4C24×C2311yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C2311yescharacteristic
610C22×C4C2×D4×C2311yescharacteristic
611C22×C4C2×D4×C2311yescharacteristic
612C22×C4C2×D4×C2311yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C2312yes—
648C22⋊C4C2×D4×C2311yescharacteristic
649C22⋊C4C2×D4×C2311yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C2312yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23C23×#12011yescharacteristic
671C23C22×D4×C2311yescharacteristic
672C23C22×D4×C2311yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4C23×#12011yescharacteristic
736C2×C4C23×#12011yescharacteristic
737C2×C4C23×#12011yescharacteristic
738C2×C4C22×D4×C2311yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×C23×#12011yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4C23×B(4,𝔽2)11yescharacteristic
777C4C23×B(4,𝔽2)11yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×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 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#3537C2semidirect
2. C23×#3027C2semidirect
3. C23×#3025C2semidirect
4. C23×#3021C2semidirect
5. C23×#2200C2semidirect
6. C23×#2196C2semidirect
7. C23×#2128C2semidirect
8. C23×#2122C2semidirect
9. C23×#2120C2semidirect
10. C23×#585C22semidirect
13. C23×#560C22semidirect
19. D42×C23C22semidirect
30. C23×#458C22semidirect
33. C23×B(4,𝔽2)C22semidirect
34. C23×B(4,𝔽2)C22semidirect
36. C23×#453C22semidirect
38. C23×#413C22semidirect
41. C23×#410C22semidirect
42. C23×#410C22semidirect
43. C23×#353C22semidirect
44. C23×#352C22semidirect
45. C23×AΣL(1,𝔽16)C22semidirect
46. C23×AΣL(1,𝔽16)C22semidirect
62. C22×D4×C23D4semidirect
63. C22×D4×C23D4semidirect
64. C23×C4×C23D4semidirect
79. C23×#124D4semidirect
85. C23×#123D4semidirect
114. C23×#120D4semidirect
115. C23×#120D4semidirect
127. C23×#117D4semidirect
128. C23×#117D4semidirect
129. C23×#117D4semidirect
261. #33553C23direct (N × H)
347. #3537C2×C23semidirect
348. #3027C2×C23semidirect
349. #3025C2×C23semidirect
350. #3021C2×C23semidirect
351. #2200C2×C23semidirect
352. #2196C2×C23semidirect
353. #2128C2×C23semidirect
354. #2122C2×C23semidirect
355. #2120C2×C23semidirect
394. #585C22×C23semidirect
397. #560C22×C23semidirect
403. D42C22×C23semidirect
414. #458C22×C23semidirect
417. B(4,𝔽2)C22×C23semidirect
418. B(4,𝔽2)C22×C23semidirect
420. #453C22×C23semidirect
422. #413C22×C23semidirect
425. #410C22×C23semidirect
426. #410C22×C23semidirect
427. #353C22×C23semidirect
428. #352C22×C23semidirect
429. AΣL(1,𝔽16)C22×C23semidirect
430. AΣL(1,𝔽16)C22×C23semidirect
455. C22×D4D4×C23semidirect
456. C22×D4D4×C23semidirect
457. C23×C4D4×C23semidirect
472. #124D4×C23semidirect
478. #123D4×C23semidirect
507. #120D4×C23semidirect
508. #120D4×C23semidirect
520. #117D4×C23semidirect
521. #117D4×C23semidirect
522. #117D4×C23semidirect
535. C23#33553direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35372
C23×#30272
C23×#30252
C23×#30212
C23×#22002
C23×#21962
C23×#21282
C23×#21222
C23×#21202
#3355323