Finite Group Databasebeta

← C23×#24467 #19172093

Subgroups — C23×#24467 #19172093

Order 5888.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3488C211yesmaximal, characteristic
2C23×#3056C211yesmaximal, characteristic, complemented
3C2×C23×#455C211yesmaximal, characteristic, complemented
4C23×#3007C211yesmaximal, characteristic, complemented
5C22×C23×#104C211yesmaximal, characteristic, complemented
6C23×#2850C211yesmaximal, characteristic, complemented
7C23×#2040C211yesmaximal, characteristic, complemented
8C23×#2037C211yesmaximal, characteristic, complemented
9C23×#2007C211yesmaximal, characteristic, complemented
10C23×#2004C211yesmaximal, characteristic, complemented
11C23×#1900C211yesmaximal, characteristic, complemented
12C23×#1896C211yesmaximal, characteristic, complemented
13C23×#1882C211yesmaximal, characteristic, complemented
14C23×#1860C211yesmaximal, characteristic, complemented
15C23×#1792C211yesmaximal, characteristic, complemented
16C2×C23×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C23C2211yescharacteristic
18C2×C23×#137C2211yescharacteristic
19C2×C23×#137C2211yescharacteristic, complemented
20C2×C23×#137C2211yescharacteristic, complemented
21C22×M16×C23C2211yescharacteristic, complemented
22C23×#550—21no—
23C23×#548—21no—
24C23×#546—21no—
25C23×#546—22no—
26D42×C23—22no—
27D42×C23—21no—
28C23×#537—21no—
29C23×#537C2211yescharacteristic
30C23×#535—21no—
31C23×#535C2211yescharacteristic
32C2×C23×#124C2211yescharacteristic, complemented
33C23×#525—21no—
34C23×#525C2211yescharacteristic
35C2×C23×C22⋊Q8C2211yescharacteristic, complemented
36C2×C23×#121—21no—
37C2×C23×#121C2211yescharacteristic
38C23×#520C2211yescharacteristic
39C22×C42×C23C2211yescharacteristic, complemented
40C23×#470—21no—
41C23×#468—21no—
42C23×#467—21no—
43C23×#465—21no—
44C23×#455—24no—
45C23×#452—21no—
46C23×#452—21no—
47C23×#451—21no—
48C23×#450—21no—
49C23×#428C2211yescharacteristic, complemented
50C2×C23×#104—24no—
51C2×C23×#104C2211yescharacteristic
52C2×C23×#104C2211yescharacteristic
53C2×C23×#104C2211yescharacteristic, complemented
54C2×C23×#104C2211yescharacteristic, complemented
55C2×C23×#104C2211yescharacteristic, complemented
56C2×C23×#104C2211yescharacteristic, complemented
57C23×#419C2211yescharacteristic, complemented
58C23×#417C2211yescharacteristic
59C23×#417C2211yescharacteristic, complemented
60C23×#417C2211yescharacteristic, complemented
61C2×C23×#100C2211yescharacteristic, complemented
62C2×C23×#100C2211yescharacteristic, complemented
63C23×#407C2211yescharacteristic, complemented
64C23×#391C2211yescharacteristic, complemented
65C23×#390C2211yescharacteristic, complemented
66C23×#388—22no—
67C23×#386—22no—
68C23×#382C2211yescharacteristic, complemented
69C23×#343C2211yescharacteristic, complemented
70C23×#343C2211yescharacteristic, complemented
71C23×#339C2211yescharacteristic, complemented
72C23×#339C2211yescharacteristic, complemented
73C23×H(5,𝔽2)—22no—
74C23×H(5,𝔽2)—22no—
75C23×H(5,𝔽2)—41no—
76C23×H(5,𝔽2)—41no—
77C2×#41×C23—21no—
78C2×#41×C23—21no—
79C2×#41×C23—21no—
80C2×#41×C23—21no—
81C2×#41×C23—22no—
82C2×#41×C23—22no—
83C2×#41×C23—41no—
84C2×#41×C23—41no—
85C2×#41×C23D411yescharacteristic
86C2×#41×C23D411yescharacteristic
87C2×#41×C23C2311yescharacteristic
88C2×#41×C23C2311yescharacteristic
89C2×#41×C23C2311yescharacteristic
90C22×Q8×C23D411yescharacteristic
91C22×Q8×C23C2311yescharacteristic
92C22×D4×C23—21no—
93C22×D4×C23—22no—
94C22×D4×C23—22no—
95C22×D4×C23—21no—
96C22×D4×C23—21no—
97C22×D4×C23D411yescharacteristic
98C22×D4×C23D412yes—
99C22×D4×C23C2311yescharacteristic
100C23×C4×C23—21no—
101C23×C4×C23—21no—
102C23×C4×C23C2311yescharacteristic
103C23×#137—22no—
104C23×#137—22no—
105C23×#137—22no—
106C23×#137—41no—
107C23×#137—41no—
108C23×#137—41no—
109C2×Q16×C23—21no—
110C2×Q16×C23—21no—
111C2×Q16×C23—21no—
112C2×SD16×C23—21no—
113C2×SD16×C23—21no—
114C2×SD16×C23—21no—
115C2×M16×C23—21no—
116C2×M16×C23—22no—
117C2×M16×C23—41no—
118C2×M16×C23C2311yescharacteristic
119C2×M16×C23C2311yescharacteristic
120C2×M16×C23C2311yescharacteristic
121C2×M16×C23C2311yescharacteristic
122C22×C8×C23—21no—
123C23×#127—22no—
124C23×#127—21no—
125C23×#124—22no—
126C23×#124—21no—
127C23×#124—22no—
128C23×#124—41no—
129C23×#123—22no—
130C23×#123—21no—
131C23×C22⋊Q8—22no—
132C23×C22⋊Q8—21no—
133C23×C22⋊Q8—21no—
134C23×C22⋊Q8—21no—
135C23×C22⋊Q8—21no—
136C23×C22⋊Q8—21no—
137C23×C22⋊Q8—21no—
138C23×C22⋊Q8D411yescharacteristic
139C23×C22⋊Q8D411yescharacteristic
140C23×#121—22no—
141C23×#121—22no—
142C23×#121—22no—
143C23×#121—22no—
144C23×#121—22no—
145C23×#121—21no—
146C23×#121—21no—
147C23×#121—21no—
148C23×#121—21no—
149C23×#121—21no—
150C23×#121—21no—
151C23×#121—22no—
152C23×#121—21no—
153C23×#121—21no—
154C23×#121D411yescharacteristic
155C23×#121D411yescharacteristic
156C23×#120—22no—
157C23×#120—22no—
158C23×#120—22no—
159C23×#120—21no—
160C23×#120—22no—
161C4×Q8×C23—21no—
162C4×D4×C23—22no—
163C4×D4×C23—22no—
164C4×D4×C23—21no—
165C4×D4×C23—21no—
166C4×D4×C23—21no—
167C4×D4×C23—22no—
168C23×#117—21no—
169C23×#117C2311yescharacteristic
170C2×C4⋊C4×C23—21no—
171C2×C4⋊C4×C23—21no—
172C2×C4⋊C4×C23C2311yescharacteristic
173C2×C4⋊C4×C23C2311yescharacteristic
174C2×C22⋊C4×C23—22no—
175C2×C22⋊C4×C23—21no—
176C2×C22⋊C4×C23—22no—
177C2×C22⋊C4×C23—22no—
178C2×C22⋊C4×C23D412yes—
179C2×C42×C23—22no—
180C2×C42×C23—21no—
181C2×C42×C23—41no—
182C2×C42×C23C2311yescharacteristic
183C2×C42×C23C2311yescharacteristic
184C23×#107—21no—
185C23×#106—21no—
186C23×#104—22no—
187C23×#104—22no—
188C23×#104—22no—
189C23×#104—22no—
190C23×#104—41no—
191C23×#104D414yescomplemented
192C23×#103—21no—
193C23×#103—21no—
194C23×#103—21no—
195C23×#103—21no—
196C23×#103—21no—
197C23×#102—21no—
198C23×#102—21no—
199C23×#102—21no—
200C23×#100—22no—
201C23×#100—41no—
202C23×C22⋊C8—21no—
203C23×C22⋊C8—21no—
204C23×#95—22no—
205C23×#95—22no—
206C24×C23—22no—
207C24×C23—21no—
208C24×C23C2×D411yescharacteristic
209C24×C23C2×D412yes—
210#41×C23—21no—
211#41×C23—21no—
212#41×C23—22no—
213#41×C23—22no—
214#41×C23—21no—
215#41×C23—21no—
216#41×C23—21no—
217#41×C23—21no—
218#41×C23—21no—
219#41×C23—21no—
220#41×C23—21no—
221#41×C23—21no—
222#41×C23—42no—
223#41×C23—42no—
224#41×C23—41no—
225#41×C23—41no—
226#41×C23—42no—
227#41×C23—42no—
228#41×C23—42no—
229#41×C23—42no—
230#41×C23—42no—
231#41×C23—42no—
232#41×C23C2×D412yes—
233#41×C23#4112yes—
234C2×Q8×C23—21no—
235C2×Q8×C23—22no—
236C2×Q8×C23—21no—
237C2×Q8×C23—21no—
238C2×Q8×C23—21no—
239C2×Q8×C23—21no—
240C2×Q8×C23—21no—
241C2×Q8×C23—21no—
242C2×Q8×C23—41no—
243C2×Q8×C23C2×D411yescharacteristic
244C2×Q8×C23C2×D411yescharacteristic
245C2×Q8×C23C2×D411yescharacteristic
246C2×D4×C23—21no—
247C2×D4×C23—22no—
248C2×D4×C23—22no—
249C2×D4×C23—22no—
250C2×D4×C23—22no—
251C2×D4×C23—21no—
252C2×D4×C23—21no—
253C2×D4×C23—21no—
254C2×D4×C23—21no—
255C2×D4×C23—21no—
256C2×D4×C23—22no—
257C2×D4×C23—22no—
258C2×D4×C23—22no—
259C2×D4×C23—21no—
260C2×D4×C23—22no—
261C2×D4×C23—21no—
262C2×D4×C23—21no—
263C2×D4×C23—21no—
264C2×D4×C23—21no—
265C2×D4×C23—21no—
266C2×D4×C23—21no—
267C2×D4×C23—21no—
268C2×D4×C23—41no—
269C2×D4×C23—42no—
270C2×D4×C23—42no—
271C2×D4×C23—42no—
272C2×D4×C23—42no—
273C2×D4×C23—44no—
274C2×D4×C23—44no—
275C2×D4×C23—42no—
276C2×D4×C23—42no—
277C2×D4×C23—44no—
278C2×D4×C23—84no—
279C2×D4×C23C2×D411yescharacteristic
280C2×D4×C23C2×D411yescharacteristic
281C2×D4×C23C2×D411yescharacteristic
282C22×C4×C23—21no—
283C22×C4×C23—21no—
284C22×C4×C23—21no—
285C22×C4×C23—21no—
286C22×C4×C23—21no—
287C22×C4×C23—22no—
288C22×C4×C23—21no—
289C22×C4×C23—21no—
290C22×C4×C23—21no—
291C22×C4×C23—22no—
292C22×C4×C23—21no—
293C22×C4×C23—21no—
294C22×C4×C23—21no—
295C22×C4×C23—21no—
296C22×C4×C23—21no—
297C22×C4×C23—21no—
298C22×C4×C23—42no—
299C22×C4×C23—42no—
300C22×C4×C23—42no—
301C22×C4×C23—42no—
302C22×C4×C23—42no—
303C22×C4×C23C2×D411yescharacteristic
304C22×C4×C23C2×D411yescharacteristic
305C22×C4×C23C2×D411yescharacteristic
306C22×C4×C23C2×D411yescharacteristic
307C22×C4×C23C2×D411yescharacteristic
308C22×C4×C23C2×D412yes—
309C22×C4×C23C2411yescharacteristic
310Q16×C23—42no—
311Q16×C23—42no—
312Q16×C23—42no—
313SD16×C23—42no—
314SD16×C23—42no—
315SD16×C23—42no—
316M16×C23—21no—
317M16×C23—21no—
318M16×C23—21no—
319M16×C23—21no—
320M16×C23—21no—
321M16×C23—21no—
322M16×C23—21no—
323M16×C23—42no—
324M16×C23C2×D412yescomplemented
325C2×C8×C23—21no—
326C2×C8×C23—21no—
327C2×C8×C23—21no—
328C2×C8×C23—21no—
329C2×C8×C23—42no—
330C4⋊C4×C23—22no—
331C4⋊C4×C23—22no—
332C4⋊C4×C23—21no—
333C4⋊C4×C23—21no—
334C4⋊C4×C23—21no—
335C4⋊C4×C23—21no—
336C4⋊C4×C23—21no—
337C4⋊C4×C23—21no—
338C4⋊C4×C23—41no—
339C4⋊C4×C23—41no—
340C4⋊C4×C23C2×D411yescharacteristic
341C4⋊C4×C23C2×D411yescharacteristic
342C22⋊C4×C23—22no—
343C22⋊C4×C23—22no—
344C22⋊C4×C23—22no—
345C22⋊C4×C23—22no—
346C22⋊C4×C23—22no—
347C22⋊C4×C23—21no—
348C22⋊C4×C23—21no—
349C22⋊C4×C23—21no—
350C22⋊C4×C23—21no—
351C22⋊C4×C23—22no—
352C22⋊C4×C23—22no—
353C22⋊C4×C23—21no—
354C22⋊C4×C23—44no—
355C22⋊C4×C23—44no—
356C22⋊C4×C23—41no—
357C22⋊C4×C23—41no—
358C42×C23—22no—
359C42×C23—21no—
360C42×C23—21no—
361C42×C23—21no—
362C42×C23—21no—
363C42×C23—42no—
364C42×C23C2×D412yescomplemented
365#24467C2311yesmaximal, characteristic, direct product factor, Sylow
366C23×C23—21no—
367C23×C23—21no—
368C23×C23—21no—
369C23×C23—22no—
370C23×C23—22no—
371C23×C23—21no—
372C23×C23—21no—
373C23×C23—22no—
374C23×C23—22no—
375C23×C23—41no—
376C23×C23—42no—
377C23×C23—44no—
378C23×C23—42no—
379C23×C23—42no—
380C23×C23—42no—
381C23×C23—81no—
382C23×C23—82no—
383C23×C23—82no—
384C23×C23#12011yescharacteristic
385C23×C23#12011yescharacteristic
386C23×C23C22×D411yescharacteristic
387Q8×C23—21no—
388Q8×C23—21no—
389Q8×C23—21no—
390Q8×C23—21no—
391Q8×C23—21no—
392Q8×C23—42no—
393Q8×C23—41no—
394Q8×C23—41no—
395Q8×C23—41no—
396Q8×C23—41no—
397Q8×C23#12112yes—
398D4×C23—22no—
399D4×C23—22no—
400D4×C23—21no—
401D4×C23—21no—
402D4×C23—21no—
403D4×C23—21no—
404D4×C23—21no—
405D4×C23—42no—
406D4×C23—42no—
407D4×C23—44no—
408D4×C23—42no—
409D4×C23—44no—
410D4×C23—41no—
411D4×C23—41no—
412D4×C23—41no—
413D4×C23—41no—
414D4×C23—44no—
415D4×C23—42no—
416D4×C23—41no—
417D4×C23—41no—
418D4×C23—41no—
419D4×C23—41no—
420D4×C23—81no—
421D4×C23—82no—
422D4×C23—82no—
423D4×C23—82no—
424D4×C23—82no—
425D4×C23#12112yes—
426C2×C4×C23—21no—
427C2×C4×C23—21no—
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—22no—
436C2×C4×C23—21no—
437C2×C4×C23—21no—
438C2×C4×C23—22no—
439C2×C4×C23—22no—
440C2×C4×C23—21no—
441C2×C4×C23—22no—
442C2×C4×C23—21no—
443C2×C4×C23—21no—
444C2×C4×C23—21no—
445C2×C4×C23—22no—
446C2×C4×C23—42no—
447C2×C4×C23—42no—
448C2×C4×C23—42no—
449C2×C4×C23—44no—
450C2×C4×C23—41no—
451C2×C4×C23—41no—
452C2×C4×C23—41no—
453C2×C4×C23—48no—
454C2×C4×C23—41no—
455C2×C4×C23—41no—
456C2×C4×C23—41no—
457C2×C4×C23—41no—
458C2×C4×C23—41no—
459C2×C4×C23—42no—
460C2×C4×C23—42no—
461C2×C4×C23—41no—
462C2×C4×C23—41no—
463C2×C4×C23—41no—
464C2×C4×C23—41no—
465C2×C4×C23—82no—
466C2×C4×C23#12011yescharacteristic
467C2×C4×C23#12011yescharacteristic
468C2×C4×C23C22×D411yescharacteristic
469C2×C4×C23C22×D411yescharacteristic
470C2×C4×C23C22×D411yescharacteristic
471C2×C4×C23C2×#4111yescharacteristic
472C2×C4×C23H(5,𝔽2)11yescharacteristic
473C2×C4×C23H(5,𝔽2)11yescharacteristic
474C8×C23—22no—
475C8×C23—41no—
476C8×C23—41no—
477C8×C23—41no—
478#3488C2×C2311yescharacteristic
479#3056C2×C2311yescharacteristic, complemented
480C2×#455C2×C2311yescharacteristic, complemented
481#3007C2×C2311yescharacteristic, complemented
482C22×#104C2×C2311yescharacteristic, complemented
483#2850C2×C2311yescharacteristic, complemented
484#2040C2×C2311yescharacteristic, complemented
485#2037C2×C2311yescharacteristic, complemented
486#2007C2×C2311yescharacteristic, complemented
487#2004C2×C2311yescharacteristic, complemented
488#1900C2×C2311yescharacteristic, complemented
489#1896C2×C2311yescharacteristic, complemented
490#1882C2×C2311yescharacteristic, complemented
491#1860C2×C2311yescharacteristic, complemented
492#1792C2×C2311yescharacteristic, complemented
493C22×C23—21no—
494C22×C23—21no—
495C22×C23—21no—
496C22×C23—21no—
497C22×C23—21no—
498C22×C23—22no—
499C22×C23—21no—
500C22×C23—21no—
501C22×C23—42no—
502C22×C23—42no—
503C22×C23—41no—
504C22×C23—41no—
505C22×C23—41no—
506C22×C23—41no—
507C22×C23—42no—
508C22×C23—42no—
509C22×C23—41no—
510C22×C23—41no—
511C22×C23—41no—
512C22×C23—42no—
513C22×C23—41no—
514C22×C23—84no—
515C22×C23—82no—
516C22×C23—82no—
517C22×C23—164no—
518C22×C23#45512yescomplemented
519C22×C23C2×#12011yescharacteristic
520C22×C23D4211yescharacteristic
521C22×C23#54611yescharacteristic
522C4×C23—21no—
523C4×C23—21no—
524C4×C23—22no—
525C4×C23—42no—
526C4×C23—42no—
527C4×C23—41no—
528C4×C23—41no—
529C4×C23—42no—
530C4×C23—41no—
531C4×C23—41no—
532C4×C23—81no—
533C4×C23—81no—
534C4×C23C2×#12111yescharacteristic
535C4×C23#53411yescharacteristic
536C4×C23D4211yescharacteristic
537C4×C23#54611yescharacteristic
538C2×H(5,𝔽2)C22×C2311yescharacteristic
539C22×#41C22×C2311yescharacteristic
540C2×#137C22×C2311yescharacteristic
541C2×#137C22×C2311yescharacteristic, complemented
542C2×#137C22×C2311yescharacteristic, complemented
543C22×M16C22×C2311yescharacteristic, complemented
544#550—21no—
545#548—21no—
546#546—21no—
547#546—22no—
548D42—22no—
549D42—21no—
550#537—21no—
551#537C22×C2311yescharacteristic
552#535—21no—
553#535C22×C2311yescharacteristic
554C2×#124C22×C2311yescharacteristic, complemented
555#525—21no—
556#525C22×C2311yescharacteristic
557C2×C22⋊Q8C22×C2311yescharacteristic, complemented
558C2×#121—21no—
559C2×#121C22×C2311yescharacteristic
560#520C22×C2311yescharacteristic
561C22×C42C22×C2311yescharacteristic, complemented
562#470—21no—
563#468—21no—
564#467—21no—
565#465—21no—
566#455—24no—
567#452—21no—
568#452—21no—
569#451—21no—
570#450—21no—
571#428C22×C2311yescharacteristic, complemented
572C2×#104—24no—
573C2×#104C22×C2311yescharacteristic
574C2×#104C22×C2311yescharacteristic
575C2×#104C22×C2311yescharacteristic, complemented
576C2×#104C22×C2311yescharacteristic, complemented
577C2×#104C22×C2311yescharacteristic, complemented
578C2×#104C22×C2311yescharacteristic, complemented
579#419C22×C2311yescharacteristic, complemented
580#417C22×C2311yescharacteristic
581#417C22×C2311yescharacteristic, complemented
582#417C22×C2311yescharacteristic, complemented
583C2×#100C22×C2311yescharacteristic, complemented
584C2×#100C22×C2311yescharacteristic, complemented
585#407C22×C2311yescharacteristic, complemented
586#391C22×C2311yescharacteristic, complemented
587#390C22×C2311yescharacteristic, complemented
588#388—22no—
589#386—22no—
590#382C22×C2311yescharacteristic, complemented
591#343C22×C2311yescharacteristic, complemented
592#343C22×C2311yescharacteristic, complemented
593#339C22×C2311yescharacteristic, complemented
594#339C22×C2311yescharacteristic, complemented
595C2×C23—21no—
596C2×C23—21no—
597C2×C23—22no—
598C2×C23—41no—
599C2×C23—42no—
600C2×C23—81no—
601C2×C23—82no—
602C2×C23—81no—
603C2×C23#241011yescharacteristic
604C2×C23C2×#45511yescharacteristic
605C2×C23#301811yescharacteristic
606H(5,𝔽2)—22no—
607H(5,𝔽2)—22no—
608H(5,𝔽2)—41no—
609H(5,𝔽2)—41no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—41no—
617C2×#41—41no—
618C2×#41D4×C2311yescharacteristic
619C2×#41D4×C2311yescharacteristic
620C2×#41C23×C2311yescharacteristic
621C2×#41C23×C2311yescharacteristic
622C2×#41C23×C2311yescharacteristic
623C22×Q8D4×C2311yescharacteristic
624C22×Q8C23×C2311yescharacteristic
625C22×D4—21no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—21no—
629C22×D4—21no—
630C22×D4D4×C2311yescharacteristic
631C22×D4D4×C2312yes—
632C22×D4C23×C2311yescharacteristic
633C23×C4—21no—
634C23×C4—21no—
635C23×C4C23×C2311yescharacteristic
636#137—22no—
637#137—22no—
638#137—22no—
639#137—41no—
640#137—41no—
641#137—41no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×SD16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×M16—21no—
649C2×M16—22no—
650C2×M16—41no—
651C2×M16C23×C2311yescharacteristic
652C2×M16C23×C2311yescharacteristic
653C2×M16C23×C2311yescharacteristic
654C2×M16C23×C2311yescharacteristic
655C22×C8—21no—
656#127—22no—
657#127—21no—
658#124—22no—
659#124—21no—
660#124—22no—
661#124—41no—
662#123—22no—
663#123—21no—
664C22⋊Q8—22no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8D4×C2311yescharacteristic
672C22⋊Q8D4×C2311yescharacteristic
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—22no—
685#121—21no—
686#121—21no—
687#121D4×C2311yescharacteristic
688#121D4×C2311yescharacteristic
689#120—22no—
690#120—22no—
691#120—22no—
692#120—21no—
693#120—22no—
694C4×Q8—21no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—22no—
699C4×D4—21no—
700C4×D4—21no—
701#117—21no—
702#117C23×C2311yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4C23×C2311yescharacteristic
706C2×C4⋊C4C23×C2311yescharacteristic
707C2×C22⋊C4—22no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4D4×C2312yes—
712C2×C42—22no—
713C2×C42—21no—
714C2×C42—41no—
715C2×C42C23×C2311yescharacteristic
716C2×C42C23×C2311yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C2314yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738#95—22no—
739C23#2446711yescharacteristic, direct product factor, Sylow
740C24—22no—
741C24—21no—
742C24C2×D4×C2311yescharacteristic
743C24C2×D4×C2312yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C2312yes—
767#41#41×C2312yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C2311yescharacteristic
778C2×Q8C2×D4×C2311yescharacteristic
779C2×Q8C2×D4×C2311yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C2311yescharacteristic
814C2×D4C2×D4×C2311yescharacteristic
815C2×D4C2×D4×C2311yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C2311yescharacteristic
838C22×C4C2×D4×C2311yescharacteristic
839C22×C4C2×D4×C2311yescharacteristic
840C22×C4C2×D4×C2311yescharacteristic
841C22×C4C2×D4×C2311yescharacteristic
842C22×C4C2×D4×C2312yes—
843C22×C4C24×C2311yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C2312yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C2311yescharacteristic
875C4⋊C4C2×D4×C2311yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C2312yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23C23×#12011yescharacteristic
918C23C23×#12011yescharacteristic
919C23C22×D4×C2311yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8C23×#12112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4C23×#12112yes—
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—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4C23×#12011yescharacteristic
1000C2×C4C23×#12011yescharacteristic
1001C2×C4C22×D4×C2311yescharacteristic
1002C2×C4C22×D4×C2311yescharacteristic
1003C2×C4C22×D4×C2311yescharacteristic
1004C2×C4C2×#41×C2311yescharacteristic
1005C2×C4C23×H(5,𝔽2)11yescharacteristic
1006C2×C4C23×H(5,𝔽2)11yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C23×#45512yescomplemented
1037C22C2×C23×#12011yescharacteristic
1038C22D42×C2311yescharacteristic
1039C22C23×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×C23×#12111yescharacteristic
1053C4C23×#53411yescharacteristic
1054C4D42×C2311yescharacteristic
1055C4C23×#54611yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C23×#241011yescharacteristic
1065C2C2×C23×#45511yescharacteristic
1066C2C23×#301811yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC23×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#3056C2semidirect
3. C2×C23×#455C2semidirect
4. C23×#3007C2semidirect
5. C22×C23×#104C2semidirect
6. C23×#2850C2semidirect
7. C23×#2040C2semidirect
8. C23×#2037C2semidirect
9. C23×#2007C2semidirect
10. C23×#2004C2semidirect
11. C23×#1900C2semidirect
12. C23×#1896C2semidirect
13. C23×#1882C2semidirect
14. C23×#1860C2semidirect
15. C23×#1792C2semidirect
19. C2×C23×#137C22semidirect
20. C2×C23×#137C22semidirect
21. C22×M16×C23C22semidirect
32. C2×C23×#124C22semidirect
35. C2×C23×C22⋊Q8C22semidirect
39. C22×C42×C23C22semidirect
49. C23×#428C22semidirect
53. C2×C23×#104C22semidirect
54. C2×C23×#104C22semidirect
55. C2×C23×#104C22semidirect
56. C2×C23×#104C22semidirect
57. C23×#419C22semidirect
59. C23×#417C22semidirect
60. C23×#417C22semidirect
61. C2×C23×#100C22semidirect
62. C2×C23×#100C22semidirect
63. C23×#407C22semidirect
64. C23×#391C22semidirect
65. C23×#390C22semidirect
68. C23×#382C22semidirect
69. C23×#343C22semidirect
70. C23×#343C22semidirect
71. C23×#339C22semidirect
72. C23×#339C22semidirect
191. C23×#104D4semidirect
324. M16×C23C2×D4semidirect
364. C42×C23C2×D4semidirect
365. #24467C23direct (N × H)
479. #3056C2×C23semidirect
480. C2×#455C2×C23semidirect
481. #3007C2×C23semidirect
482. C22×#104C2×C23semidirect
483. #2850C2×C23semidirect
484. #2040C2×C23semidirect
485. #2037C2×C23semidirect
486. #2007C2×C23semidirect
487. #2004C2×C23semidirect
488. #1900C2×C23semidirect
489. #1896C2×C23semidirect
490. #1882C2×C23semidirect
491. #1860C2×C23semidirect
492. #1792C2×C23semidirect
518. C22×C23#455semidirect
541. C2×#137C22×C23semidirect
542. C2×#137C22×C23semidirect
543. C22×M16C22×C23semidirect
554. C2×#124C22×C23semidirect
557. C2×C22⋊Q8C22×C23semidirect
561. C22×C42C22×C23semidirect
571. #428C22×C23semidirect
575. C2×#104C22×C23semidirect
576. C2×#104C22×C23semidirect
577. C2×#104C22×C23semidirect
578. C2×#104C22×C23semidirect
579. #419C22×C23semidirect
581. #417C22×C23semidirect
582. #417C22×C23semidirect
583. C2×#100C22×C23semidirect
584. C2×#100C22×C23semidirect
585. #407C22×C23semidirect
586. #391C22×C23semidirect
587. #390C22×C23semidirect
590. #382C22×C23semidirect
591. #343C22×C23semidirect
592. #343C22×C23semidirect
593. #339C22×C23semidirect
594. #339C22×C23semidirect
724. #104D4×C23semidirect
739. C23#24467direct (N × H)
858. M16C2×D4×C23semidirect
898. C42C2×D4×C23semidirect
1036. C22C23×#455semidirect

Maximal subgroups

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

subgroupindex
C23×#34882
C23×#30562
C2×C23×#4552
C23×#30072
C22×C23×#1042
C23×#28502
C23×#20402
C23×#20372
C23×#20072
C23×#20042
C23×#19002
C23×#18962
C23×#18822
C23×#18602
C23×#17922
#2446723