Finite Group Databasebeta

← C23×#24471 #19172097

Subgroups — C23×#24471 #19172097

Order 5888.

1444 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×#3488C211yesmaximal, characteristic
2C23×#3056C211yesmaximal, characteristic, complemented
3C2×C23×#455C211yesmaximal, characteristic, complemented
4C23×#3007C211yesmaximal, characteristic, complemented
5C2×C23×#421C211yesmaximal, characteristic, complemented
6C23×#2620C211yesmaximal, characteristic, complemented
7C23×#2039C211yesmaximal, characteristic, complemented
8C23×#2037C211yesmaximal, characteristic, complemented
9C23×#2007C211yesmaximal, characteristic, complemented
10C23×#2004C211yesmaximal, characteristic, complemented
11C23×#1900C211yesmaximal, characteristic, complemented
12C23×#1897C211yesmaximal, characteristic, complemented
13C23×#1882C211yesmaximal, characteristic, complemented
14C23×#1859C211yesmaximal, 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
39C2×C23×#117C2211yescharacteristic, 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
50C23×#421—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×#396—22no—
65C23×#394—22no—
66C23×#391C2211yescharacteristic, complemented
67C23×#390C2211yescharacteristic, complemented
68C23×#384C2211yescharacteristic, 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×C23C2311yescharacteristic
102C23×#137—22no—
103C23×#137—22no—
104C23×#137—22no—
105C23×#137—41no—
106C23×#137—41no—
107C23×#137—41no—
108C2×Q16×C23—21no—
109C2×Q16×C23—21no—
110C2×Q16×C23—21no—
111C2×SD16×C23—21no—
112C2×SD16×C23—21no—
113C2×SD16×C23—21no—
114C2×M16×C23—21no—
115C2×M16×C23—22no—
116C2×M16×C23—41no—
117C2×M16×C23C2311yescharacteristic
118C2×M16×C23C2311yescharacteristic
119C2×M16×C23C2311yescharacteristic
120C2×M16×C23C2311yescharacteristic
121C22×C8×C23—21no—
122C23×#127—22no—
123C23×#127—21no—
124C23×#124—22no—
125C23×#124—21no—
126C23×#124—22no—
127C23×#124—41no—
128C23×#123—22no—
129C23×#123—21no—
130C23×C22⋊Q8—22no—
131C23×C22⋊Q8—21no—
132C23×C22⋊Q8—21no—
133C23×C22⋊Q8—21no—
134C23×C22⋊Q8—21no—
135C23×C22⋊Q8—21no—
136C23×C22⋊Q8—21no—
137C23×C22⋊Q8D411yescharacteristic
138C23×C22⋊Q8D411yescharacteristic
139C23×#121—22no—
140C23×#121—22no—
141C23×#121—22no—
142C23×#121—22no—
143C23×#121—22no—
144C23×#121—21no—
145C23×#121—21no—
146C23×#121—21no—
147C23×#121—21no—
148C23×#121—21no—
149C23×#121—21no—
150C23×#121—22no—
151C23×#121—21no—
152C23×#121—21no—
153C23×#121D411yescharacteristic
154C23×#121D411yescharacteristic
155C23×#120—22no—
156C23×#120—22no—
157C23×#120—22no—
158C23×#120—21no—
159C23×#120—22no—
160C4×Q8×C23—21no—
161C4×D4×C23—22no—
162C4×D4×C23—22no—
163C4×D4×C23—21no—
164C4×D4×C23—21no—
165C4×D4×C23—21no—
166C4×D4×C23—22no—
167C23×#117—21no—
168C23×#117—22no—
169C23×#117—41no—
170C23×#117C2311yescharacteristic
171C2×C4⋊C4×C23—21no—
172C2×C4⋊C4×C23—21no—
173C2×C4⋊C4×C23—21no—
174C2×C4⋊C4×C23—22no—
175C2×C4⋊C4×C23C2311yescharacteristic
176C2×C4⋊C4×C23C2311yescharacteristic
177C2×C22⋊C4×C23—22no—
178C2×C22⋊C4×C23—21no—
179C2×C22⋊C4×C23—21no—
180C2×C22⋊C4×C23—22no—
181C2×C22⋊C4×C23—22no—
182C2×C22⋊C4×C23D412yes—
183C2×C42×C23C2311yescharacteristic
184C2×C42×C23C2311yescharacteristic
185C23×#107—21no—
186C23×#106—21no—
187C23×#104—22no—
188C23×#104—22no—
189C23×#104—22no—
190C23×#104—22no—
191C23×#104—41no—
192C23×#104D414yescomplemented
193C23×#103—21no—
194C23×#103—21no—
195C23×#103—21no—
196C23×#103—21no—
197C23×#103—21no—
198C23×#102—21no—
199C23×#102—21no—
200C23×#102—21no—
201C23×#100—22no—
202C23×#100—41no—
203C23×C22⋊C8—21no—
204C23×C22⋊C8—21no—
205C23×#95—22no—
206C24×C23—22no—
207C24×C23—21no—
208C24×C23C2×D412yes—
209C24×C23C2×D411yescharacteristic
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—82no—
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—22no—
291C22×C4×C23—21no—
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×C23C2×D411yescharacteristic
301C22×C4×C23C2×D411yescharacteristic
302C22×C4×C23C2×D411yescharacteristic
303C22×C4×C23C2×D411yescharacteristic
304C22×C4×C23C2×D411yescharacteristic
305C22×C4×C23C2×D412yes—
306C22×C4×C23C2411yescharacteristic
307Q16×C23—42no—
308Q16×C23—42no—
309Q16×C23—42no—
310SD16×C23—42no—
311SD16×C23—42no—
312SD16×C23—42no—
313M16×C23—21no—
314M16×C23—21no—
315M16×C23—21no—
316M16×C23—21no—
317M16×C23—21no—
318M16×C23—21no—
319M16×C23—21no—
320M16×C23—42no—
321M16×C23C2×D412yescomplemented
322C2×C8×C23—21no—
323C2×C8×C23—21no—
324C2×C8×C23—21no—
325C2×C8×C23—21no—
326C2×C8×C23—42no—
327C4⋊C4×C23—22no—
328C4⋊C4×C23—22no—
329C4⋊C4×C23—21no—
330C4⋊C4×C23—21no—
331C4⋊C4×C23—21no—
332C4⋊C4×C23—21no—
333C4⋊C4×C23—21no—
334C4⋊C4×C23—21no—
335C4⋊C4×C23—42no—
336C4⋊C4×C23—41no—
337C4⋊C4×C23—41no—
338C4⋊C4×C23—82no—
339C4⋊C4×C23C2×D411yescharacteristic
340C4⋊C4×C23C2×D411yescharacteristic
341C22⋊C4×C23—22no—
342C22⋊C4×C23—22no—
343C22⋊C4×C23—22no—
344C22⋊C4×C23—22no—
345C22⋊C4×C23—22no—
346C22⋊C4×C23—21no—
347C22⋊C4×C23—21no—
348C22⋊C4×C23—21no—
349C22⋊C4×C23—21no—
350C22⋊C4×C23—22no—
351C22⋊C4×C23—22no—
352C22⋊C4×C23—21no—
353C22⋊C4×C23—42no—
354C22⋊C4×C23—44no—
355C22⋊C4×C23—41no—
356C22⋊C4×C23—41no—
357C22⋊C4×C23—82no—
358C42×C23—22no—
359C42×C23—21no—
360C42×C23—21no—
361C42×C23—21no—
362C42×C23—21no—
363C42×C23C2×D412yescomplemented
364#24471C2311yesmaximal, characteristic, direct product factor, Sylow
365C23×C23—21no—
366C23×C23—21no—
367C23×C23—21no—
368C23×C23—22no—
369C23×C23—21no—
370C23×C23—21no—
371C23×C23—22no—
372C23×C23—22no—
373C23×C23—41no—
374C23×C23—41no—
375C23×C23—42no—
376C23×C23—42no—
377C23×C23—44no—
378C23×C23—42no—
379C23×C23—42no—
380C23×C23—81no—
381C23×C23—82no—
382C23×C23—82no—
383C23×C23#12011yescharacteristic
384C23×C23#12011yescharacteristic
385C23×C23C22×D411yescharacteristic
386Q8×C23—21no—
387Q8×C23—21no—
388Q8×C23—21no—
389Q8×C23—21no—
390Q8×C23—21no—
391Q8×C23—42no—
392Q8×C23—41no—
393Q8×C23—41no—
394Q8×C23—41no—
395Q8×C23—41no—
396Q8×C23#12112yes—
397D4×C23—22no—
398D4×C23—22no—
399D4×C23—21no—
400D4×C23—21no—
401D4×C23—21no—
402D4×C23—21no—
403D4×C23—21no—
404D4×C23—42no—
405D4×C23—42no—
406D4×C23—44no—
407D4×C23—42no—
408D4×C23—44no—
409D4×C23—44no—
410D4×C23—42no—
411D4×C23—41no—
412D4×C23—41no—
413D4×C23—41no—
414D4×C23—41no—
415D4×C23—41no—
416D4×C23—41no—
417D4×C23—41no—
418D4×C23—41no—
419D4×C23—81no—
420D4×C23—82no—
421D4×C23—82no—
422D4×C23—82no—
423D4×C23—82no—
424D4×C23#12112yes—
425C2×C4×C23—21no—
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—22no—
435C2×C4×C23—21no—
436C2×C4×C23—21no—
437C2×C4×C23—22no—
438C2×C4×C23—21no—
439C2×C4×C23—22no—
440C2×C4×C23—21no—
441C2×C4×C23—21no—
442C2×C4×C23—21no—
443C2×C4×C23—22no—
444C2×C4×C23—42no—
445C2×C4×C23—42no—
446C2×C4×C23—42no—
447C2×C4×C23—44no—
448C2×C4×C23—41no—
449C2×C4×C23—41no—
450C2×C4×C23—41no—
451C2×C4×C23—41no—
452C2×C4×C23—41no—
453C2×C4×C23—41no—
454C2×C4×C23—42no—
455C2×C4×C23—41no—
456C2×C4×C23—42no—
457C2×C4×C23—41no—
458C2×C4×C23—41no—
459C2×C4×C23—41no—
460C2×C4×C23—41no—
461C2×C4×C23—41no—
462C2×C4×C23—41no—
463C2×C4×C23—82no—
464C2×C4×C23#12011yescharacteristic
465C2×C4×C23#12011yescharacteristic
466C2×C4×C23C22×D411yescharacteristic
467C2×C4×C23C22×D411yescharacteristic
468C2×C4×C23C22×D411yescharacteristic
469C2×C4×C23C2×#4111yescharacteristic
470C2×C4×C23H(5,𝔽2)11yescharacteristic
471C2×C4×C23H(5,𝔽2)11yescharacteristic
472C8×C23—22no—
473C8×C23—41no—
474C8×C23—41no—
475C8×C23—41no—
476#3488C2×C2311yescharacteristic
477#3056C2×C2311yescharacteristic, complemented
478C2×#455C2×C2311yescharacteristic, complemented
479#3007C2×C2311yescharacteristic, complemented
480C2×#421C2×C2311yescharacteristic, complemented
481#2620C2×C2311yescharacteristic, complemented
482#2039C2×C2311yescharacteristic, complemented
483#2037C2×C2311yescharacteristic, complemented
484#2007C2×C2311yescharacteristic, complemented
485#2004C2×C2311yescharacteristic, complemented
486#1900C2×C2311yescharacteristic, complemented
487#1897C2×C2311yescharacteristic, complemented
488#1882C2×C2311yescharacteristic, complemented
489#1859C2×C2311yescharacteristic, complemented
490#1792C2×C2311yescharacteristic, complemented
491C22×C23—21no—
492C22×C23—21no—
493C22×C23—21no—
494C22×C23—21no—
495C22×C23—22no—
496C22×C23—21no—
497C22×C23—21no—
498C22×C23—21no—
499C22×C23—21no—
500C22×C23—41no—
501C22×C23—41no—
502C22×C23—41no—
503C22×C23—41no—
504C22×C23—42no—
505C22×C23—42no—
506C22×C23—41no—
507C22×C23—41no—
508C22×C23—41no—
509C22×C23—42no—
510C22×C23—41no—
511C22×C23—81no—
512C22×C23—81no—
513C22×C23—82no—
514C22×C23—82no—
515C22×C23—84no—
516C22×C23—164no—
517C22×C23C2×#12011yescharacteristic
518C22×C23D4211yescharacteristic
519C22×C23#54611yescharacteristic
520C4×C23—21no—
521C4×C23—21no—
522C4×C23—22no—
523C4×C23—42no—
524C4×C23—41no—
525C4×C23—41no—
526C4×C23—42no—
527C4×C23—41no—
528C4×C23—41no—
529C4×C23—81no—
530C4×C23—81no—
531C4×C23—81no—
532C4×C23C2×#12111yescharacteristic
533C4×C23#53411yescharacteristic
534C4×C23D4211yescharacteristic
535C4×C23#54611yescharacteristic
536C2×H(5,𝔽2)C22×C2311yescharacteristic
537C22×#41C22×C2311yescharacteristic
538C2×#137C22×C2311yescharacteristic
539C2×#137C22×C2311yescharacteristic, complemented
540C2×#137C22×C2311yescharacteristic, complemented
541C22×M16C22×C2311yescharacteristic, complemented
542#550—21no—
543#548—21no—
544#546—21no—
545#546—22no—
546D42—22no—
547D42—21no—
548#537—21no—
549#537C22×C2311yescharacteristic
550#535—21no—
551#535C22×C2311yescharacteristic
552C2×#124C22×C2311yescharacteristic, complemented
553#525—21no—
554#525C22×C2311yescharacteristic
555C2×C22⋊Q8C22×C2311yescharacteristic, complemented
556C2×#121—21no—
557C2×#121C22×C2311yescharacteristic
558#520C22×C2311yescharacteristic
559C2×#117C22×C2311yescharacteristic, complemented
560#470—21no—
561#468—21no—
562#467—21no—
563#465—21no—
564#455—24no—
565#452—21no—
566#452—21no—
567#451—21no—
568#450—21no—
569#428C22×C2311yescharacteristic, complemented
570#421—24no—
571C2×#104C22×C2311yescharacteristic
572C2×#104C22×C2311yescharacteristic
573C2×#104C22×C2311yescharacteristic, complemented
574C2×#104C22×C2311yescharacteristic, complemented
575C2×#104C22×C2311yescharacteristic, complemented
576C2×#104C22×C2311yescharacteristic, complemented
577#419C22×C2311yescharacteristic, complemented
578#417C22×C2311yescharacteristic
579#417C22×C2311yescharacteristic, complemented
580#417C22×C2311yescharacteristic, complemented
581C2×#100C22×C2311yescharacteristic, complemented
582C2×#100C22×C2311yescharacteristic, complemented
583#407C22×C2311yescharacteristic, complemented
584#396—22no—
585#394—22no—
586#391C22×C2311yescharacteristic, complemented
587#390C22×C2311yescharacteristic, complemented
588#384C22×C2311yescharacteristic, complemented
589#343C22×C2311yescharacteristic, complemented
590#343C22×C2311yescharacteristic, complemented
591#339C22×C2311yescharacteristic, complemented
592#339C22×C2311yescharacteristic, complemented
593C2×C23—21no—
594C2×C23—21no—
595C2×C23—41no—
596C2×C23—41no—
597C2×C23—42no—
598C2×C23—81no—
599C2×C23—82no—
600C2×C23—81no—
601C2×C23#241011yescharacteristic
602C2×C23#301911yescharacteristic
603C2×C23#302211yescharacteristic
604H(5,𝔽2)—22no—
605H(5,𝔽2)—22no—
606H(5,𝔽2)—41no—
607H(5,𝔽2)—41no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—22no—
613C2×#41—22no—
614C2×#41—41no—
615C2×#41—41no—
616C2×#41D4×C2311yescharacteristic
617C2×#41D4×C2311yescharacteristic
618C2×#41C23×C2311yescharacteristic
619C2×#41C23×C2311yescharacteristic
620C2×#41C23×C2311yescharacteristic
621C22×Q8D4×C2311yescharacteristic
622C22×Q8C23×C2311yescharacteristic
623C22×D4—21no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—21no—
627C22×D4—21no—
628C22×D4D4×C2311yescharacteristic
629C22×D4D4×C2312yes—
630C22×D4C23×C2311yescharacteristic
631C23×C4—21no—
632C23×C4C23×C2311yescharacteristic
633#137—22no—
634#137—22no—
635#137—22no—
636#137—41no—
637#137—41no—
638#137—41no—
639C2×Q16—21no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×SD16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×M16—21no—
646C2×M16—22no—
647C2×M16—41no—
648C2×M16C23×C2311yescharacteristic
649C2×M16C23×C2311yescharacteristic
650C2×M16C23×C2311yescharacteristic
651C2×M16C23×C2311yescharacteristic
652C22×C8—21no—
653#127—22no—
654#127—21no—
655#124—22no—
656#124—21no—
657#124—22no—
658#124—41no—
659#123—22no—
660#123—21no—
661C22⋊Q8—22no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8D4×C2311yescharacteristic
669C22⋊Q8D4×C2311yescharacteristic
670#121—22no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—22no—
682#121—21no—
683#121—21no—
684#121D4×C2311yescharacteristic
685#121D4×C2311yescharacteristic
686#120—22no—
687#120—22no—
688#120—22no—
689#120—21no—
690#120—22no—
691C4×Q8—21no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—21no—
695C4×D4—22no—
696C4×D4—21no—
697C4×D4—21no—
698#117—21no—
699#117—22no—
700#117—41no—
701#117C23×C2311yescharacteristic
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4C23×C2311yescharacteristic
707C2×C4⋊C4C23×C2311yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4D4×C2312yes—
714C2×C42C23×C2311yescharacteristic
715C2×C42C23×C2311yescharacteristic
716#107—21no—
717#106—21no—
718#104—22no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—41no—
723#104D4×C2314yescomplemented
724#103—21no—
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#102—21no—
730#102—21no—
731#102—21no—
732#100—22no—
733#100—41no—
734C22⋊C8—21no—
735C22⋊C8—21no—
736#95—22no—
737C23#2447111yescharacteristic, direct product factor, Sylow
738C24—22no—
739C24—21no—
740C24C2×D4×C2312yes—
741C24C2×D4×C2311yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C2312yes—
765#41#41×C2312yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C2311yescharacteristic
776C2×Q8C2×D4×C2311yescharacteristic
777C2×Q8C2×D4×C2311yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C2311yescharacteristic
812C2×D4C2×D4×C2311yescharacteristic
813C2×D4C2×D4×C2311yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C2311yescharacteristic
833C22×C4C2×D4×C2311yescharacteristic
834C22×C4C2×D4×C2311yescharacteristic
835C22×C4C2×D4×C2311yescharacteristic
836C22×C4C2×D4×C2311yescharacteristic
837C22×C4C2×D4×C2312yes—
838C22×C4C24×C2311yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C2312yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C2311yescharacteristic
872C4⋊C4C2×D4×C2311yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C2312yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23C23×#12011yescharacteristic
915C23C23×#12011yescharacteristic
916C23C22×D4×C2311yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8C23×#12112yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4C23×#12112yes—
956C2×C4—21no—
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—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4C23×#12011yescharacteristic
996C2×C4C23×#12011yescharacteristic
997C2×C4C22×D4×C2311yescharacteristic
998C2×C4C22×D4×C2311yescharacteristic
999C2×C4C22×D4×C2311yescharacteristic
1000C2×C4C2×#41×C2311yescharacteristic
1001C2×C4C23×H(5,𝔽2)11yescharacteristic
1002C2×C4C23×H(5,𝔽2)11yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×C23×#12011yescharacteristic
1034C22D42×C2311yescharacteristic
1035C22C23×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×C23×#12111yescharacteristic
1049C4C23×#53411yescharacteristic
1050C4D42×C2311yescharacteristic
1051C4C23×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C23×#241011yescharacteristic
1061C2C23×#301911yescharacteristic
1062C2C23×#302211yescharacteristic
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. C2×C23×#421C2semidirect
6. C23×#2620C2semidirect
7. C23×#2039C2semidirect
8. C23×#2037C2semidirect
9. C23×#2007C2semidirect
10. C23×#2004C2semidirect
11. C23×#1900C2semidirect
12. C23×#1897C2semidirect
13. C23×#1882C2semidirect
14. C23×#1859C2semidirect
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. C2×C23×#117C22semidirect
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
66. C23×#391C22semidirect
67. C23×#390C22semidirect
68. C23×#384C22semidirect
69. C23×#343C22semidirect
70. C23×#343C22semidirect
71. C23×#339C22semidirect
72. C23×#339C22semidirect
192. C23×#104D4semidirect
321. M16×C23C2×D4semidirect
363. C42×C23C2×D4semidirect
364. #24471C23direct (N × H)
477. #3056C2×C23semidirect
478. C2×#455C2×C23semidirect
479. #3007C2×C23semidirect
480. C2×#421C2×C23semidirect
481. #2620C2×C23semidirect
482. #2039C2×C23semidirect
483. #2037C2×C23semidirect
484. #2007C2×C23semidirect
485. #2004C2×C23semidirect
486. #1900C2×C23semidirect
487. #1897C2×C23semidirect
488. #1882C2×C23semidirect
489. #1859C2×C23semidirect
490. #1792C2×C23semidirect
539. C2×#137C22×C23semidirect
540. C2×#137C22×C23semidirect
541. C22×M16C22×C23semidirect
552. C2×#124C22×C23semidirect
555. C2×C22⋊Q8C22×C23semidirect
559. C2×#117C22×C23semidirect
569. #428C22×C23semidirect
573. C2×#104C22×C23semidirect
574. C2×#104C22×C23semidirect
575. C2×#104C22×C23semidirect
576. C2×#104C22×C23semidirect
577. #419C22×C23semidirect
579. #417C22×C23semidirect
580. #417C22×C23semidirect
581. C2×#100C22×C23semidirect
582. C2×#100C22×C23semidirect
583. #407C22×C23semidirect
586. #391C22×C23semidirect
587. #390C22×C23semidirect
588. #384C22×C23semidirect
589. #343C22×C23semidirect
590. #343C22×C23semidirect
591. #339C22×C23semidirect
592. #339C22×C23semidirect
723. #104D4×C23semidirect
737. C23#24471direct (N × H)
853. M16C2×D4×C23semidirect
895. C42C2×D4×C23semidirect

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
C2×C23×#4212
C23×#26202
C23×#20392
C23×#20372
C23×#20072
C23×#20042
C23×#19002
C23×#18972
C23×#18822
C23×#18592
C23×#17922
#2447123