Finite Group Databasebeta

← C23×#25587 #19173213

Subgroups — C23×#25587 #19173213

Order 5888.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3505C211yesmaximal, characteristic, complemented
2C23×#2561C211yesmaximal, characteristic, complemented
3C23×#2539C211yesmaximal, characteristic, complemented
4C23×#2534C211yesmaximal, characteristic, complemented
5C23×#2022C212yesmaximal, complemented
6C23×#2021C212yesmaximal, complemented
7C23×#1996C211yesmaximal, characteristic, complemented
8C23×#1964C211yesmaximal, characteristic, complemented
9C23×#1890C212yesmaximal, complemented
10C23×#1889C212yesmaximal, complemented
11C4×C23×#99C211yesmaximal, characteristic, complemented
12C23×#553—22no—
13C23×#553—21no—
14C23×#552—21no—
15C23×#551—22no—
16C23×#548—21no—
17C23×#546—21no—
18C23×#539—21no—
19C23×#538—21no—
20C23×#534C2212yes—
21C23×#529—21no—
22C23×#525—21no—
23C2×C23×#123C2212yes—
24C2×C23×#123C2211yescharacteristic
25C2×C23×C22⋊Q8C2211yescharacteristic
26C2×C23×#121C2211yescharacteristic
27C2×C23×#120C2212yes—
28C2×C23×#120C2211yescharacteristic
29C23×#518C2212yes—
30C2×C4×D4×C23C2211yescharacteristic
31C22×C22⋊C4×C23C2211yescharacteristic
32C2×C23×#99C2212yes—
33C2×C23×#99C2212yes—
34C2×C23×#99C2212yes—
35C23×#399—21no—
36C23×#397—21no—
37C23×#396—21no—
38C23×#394—21no—
39C23×#393—21no—
40C23×#392—21no—
41C23×#390—22no—
42C23×#388—22no—
43C23×#388—21no—
44C23×#386—21no—
45C23×#381C2211yescharacteristic
46C23×#381C2212yes—
47C23×#380C2211yescharacteristic
48C23×#379C2211yescharacteristic
49C23×#379C2212yes—
50C4×C22⋊C4×C23C2211yescharacteristic
51C4×C22⋊C4×C23C2211yescharacteristic
52C23×#342C2212yes—
53C23×#342C2212yes—
54C23×#342C2212yes—
55C25×C23C2311yescharacteristic
56C2×#41×C23—21no—
57C22×Q8×C23D411yescharacteristic, complemented
58C22×D4×C23—21no—
59C22×D4×C23—22no—
60C22×D4×C23D411yescharacteristic, complemented
61C22×D4×C23C2311yescharacteristic
62C22×D4×C23C2312yes—
63C23×C4×C23D411yescharacteristic, complemented
64C23×C4×C23C2311yescharacteristic
65C23×C4×C23C2311yescharacteristic
66C23×#126—22no—
67C23×#126—22no—
68C23×#126—22no—
69C23×#125—21no—
70C23×#125—22no—
71C23×#124—22no—
72C23×#124—21no—
73C23×#123—22no—
74C23×#123—22no—
75C23×#123—22no—
76C23×#123—22no—
77C23×#123—22no—
78C23×#123—24no—
79C23×#123—42no—
80C23×#123—42no—
81C23×C22⋊Q8—22no—
82C23×C22⋊Q8—21no—
83C23×C22⋊Q8—21no—
84C23×C22⋊Q8—21no—
85C23×C22⋊Q8—21no—
86C23×C22⋊Q8—21no—
87C23×#121—21no—
88C23×#121—22no—
89C23×#121—21no—
90C23×#121—22no—
91C23×#121—21no—
92C23×#121—22no—
93C23×#121—21no—
94C23×#121—21no—
95C23×#120—22no—
96C23×#120—22no—
97C23×#120—24no—
98C23×#120—42no—
99C23×#120—42no—
100C4×Q8×C23—21no—
101C4×D4×C23—22no—
102C4×D4×C23—21no—
103C4×D4×C23—21no—
104C4×D4×C23—22no—
105C4×D4×C23—21no—
106C4×D4×C23—21no—
107C4×D4×C23—21no—
108C4×D4×C23—22no—
109C4×D4×C23—22no—
110C4×D4×C23—22no—
111C23×#117—22no—
112C23×#117—21no—
113C23×#117—22no—
114C2×C4⋊C4×C23—21no—
115C2×C4⋊C4×C23—22no—
116C2×C4⋊C4×C23—21no—
117C2×C4⋊C4×C23D411yescharacteristic, complemented
118C2×C4⋊C4×C23D412yescomplemented
119C2×C4⋊C4×C23D411yescharacteristic, complemented
120C2×C4⋊C4×C23D411yescharacteristic, complemented
121C2×C22⋊C4×C23—22no—
122C2×C22⋊C4×C23—21no—
123C2×C22⋊C4×C23—22no—
124C2×C22⋊C4×C23—21no—
125C2×C22⋊C4×C23—22no—
126C2×C22⋊C4×C23—21no—
127C2×C22⋊C4×C23—21no—
128C2×C22⋊C4×C23—21no—
129C2×C22⋊C4×C23—21no—
130C2×C22⋊C4×C23—22no—
131C2×C22⋊C4×C23—21no—
132C2×C22⋊C4×C23—21no—
133C2×C22⋊C4×C23—21no—
134C2×C22⋊C4×C23—21no—
135C2×C22⋊C4×C23—22no—
136C2×C22⋊C4×C23D412yescomplemented
137C2×C22⋊C4×C23D411yescharacteristic, complemented
138C2×C22⋊C4×C23C2311yescharacteristic
139C2×C22⋊C4×C23C2311yescharacteristic
140C2×C22⋊C4×C23C2312yes—
141C2×C22⋊C4×C23C2311yescharacteristic
142C2×C22⋊C4×C23C2312yes—
143C2×C22⋊C4×C23C2312yes—
144C2×C42×C23—21no—
145C2×C42×C23—21no—
146C2×C42×C23D411yescharacteristic, complemented
147C23×#99—24no—
148C23×#99—42no—
149C23×#99—42no—
150C23×#95—21no—
151C23×#95—21no—
152C23×#95—21no—
153C23×#95—21no—
154C23×#95—22no—
155C23×#95—21no—
156C23×#95—22no—
157C24×C23—21no—
158C24×C23—21no—
159C24×C23—21no—
160C24×C23—22no—
161C24×C23—22no—
162C24×C23—42no—
163C24×C23—81no—
164C24×C23C2×D412yes—
165C24×C23C2×D411yescharacteristic
166C24×C23C2411yescharacteristic
167#41×C23—82no—
168C2×Q8×C23—21no—
169C2×Q8×C23—21no—
170C2×Q8×C23—81no—
171C2×D4×C23—21no—
172C2×D4×C23—22no—
173C2×D4×C23—21no—
174C2×D4×C23—22no—
175C2×D4×C23—22no—
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—44no—
186C2×D4×C23—42no—
187C2×D4×C23—44no—
188C2×D4×C23—42no—
189C2×D4×C23—81no—
190C2×D4×C23—82no—
191C2×D4×C23—81no—
192C22×C4×C23—22no—
193C22×C4×C23—22no—
194C22×C4×C23—22no—
195C22×C4×C23—21no—
196C22×C4×C23—21no—
197C22×C4×C23—22no—
198C22×C4×C23—21no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—22no—
204C22×C4×C23—22no—
205C22×C4×C23—81no—
206C22×C4×C23—81no—
207C22×C4×C23C2×D411yescharacteristic
208C22×C4×C23C2×D412yes—
209C22×C4×C23C2×D411yescharacteristic
210C22×C4×C23C2×D412yes—
211C22×C4×C23C2×D411yescharacteristic
212C22×C4×C23C2×D412yes—
213C22×C4×C23C2×D411yescharacteristic
214C22×C4×C23C2×D411yescharacteristic
215C22×C4×C23C2×D411yescharacteristic
216C22×C4×C23C2×D411yescharacteristic
217C22×C4×C23C2×D411yescharacteristic
218C22×C4×C23C2×D411yescharacteristic
219C4⋊C4×C23—22no—
220C4⋊C4×C23—22no—
221C4⋊C4×C23—22no—
222C4⋊C4×C23—22no—
223C4⋊C4×C23—21no—
224C4⋊C4×C23—22no—
225C4⋊C4×C23—21no—
226C4⋊C4×C23—21no—
227C4⋊C4×C23—21no—
228C4⋊C4×C23—21no—
229C4⋊C4×C23—22no—
230C4⋊C4×C23—21no—
231C4⋊C4×C23—44no—
232C4⋊C4×C23—42no—
233C4⋊C4×C23—81no—
234C22⋊C4×C23—22no—
235C22⋊C4×C23—22no—
236C22⋊C4×C23—22no—
237C22⋊C4×C23—22no—
238C22⋊C4×C23—22no—
239C22⋊C4×C23—22no—
240C22⋊C4×C23—21no—
241C22⋊C4×C23—22no—
242C22⋊C4×C23—21no—
243C22⋊C4×C23—22no—
244C22⋊C4×C23—22no—
245C22⋊C4×C23—22no—
246C22⋊C4×C23—21no—
247C22⋊C4×C23—21no—
248C22⋊C4×C23—22no—
249C22⋊C4×C23—22no—
250C22⋊C4×C23—22no—
251C22⋊C4×C23—22no—
252C22⋊C4×C23—22no—
253C22⋊C4×C23—44no—
254C22⋊C4×C23—44no—
255C22⋊C4×C23—42no—
256C22⋊C4×C23—44no—
257C22⋊C4×C23—42no—
258C22⋊C4×C23—42no—
259C22⋊C4×C23—41no—
260C22⋊C4×C23—41no—
261C22⋊C4×C23—41no—
262C22⋊C4×C23—41no—
263C22⋊C4×C23—81no—
264C22⋊C4×C23—82no—
265C22⋊C4×C23#4114yescomplemented
266C42×C23—22no—
267C42×C23—22no—
268C42×C23—21no—
269C42×C23—21no—
270C42×C23—81no—
271C42×C23—81no—
272#25587C2311yesmaximal, characteristic, direct product factor, Sylow
273C23×C23—22no—
274C23×C23—22no—
275C23×C23—22no—
276C23×C23—22no—
277C23×C23—21no—
278C23×C23—21no—
279C23×C23—21no—
280C23×C23—22no—
281C23×C23—22no—
282C23×C23—41no—
283C23×C23—41no—
284C23×C23—41no—
285C23×C23—41no—
286C23×C23—42no—
287C23×C23—41no—
288C23×C23—41no—
289C23×C23—42no—
290C23×C23—41no—
291C23×C23—41no—
292C23×C23—41no—
293C23×C23—42no—
294C23×C23—42no—
295C23×C23—41no—
296C23×C23—41no—
297C23×C23—41no—
298C23×C23—42no—
299C23×C23—42no—
300C23×C23—84no—
301C23×C23—84no—
302C23×C23C22×D411yescharacteristic
303C23×C23C22×D411yescharacteristic
304C23×C23C22×D411yescharacteristic
305C23×C23C2×#4112yes—
306C23×C23H(5,𝔽2)12yes—
307Q8×C23—42no—
308Q8×C23—81no—
309D4×C23—42no—
310D4×C23—42no—
311D4×C23—42no—
312D4×C23—42no—
313D4×C23—42no—
314D4×C23—42no—
315D4×C23—42no—
316D4×C23—81no—
317D4×C23—82no—
318D4×C23—82no—
319D4×C23—88no—
320D4×C23—84no—
321C2×C4×C23—21no—
322C2×C4×C23—22no—
323C2×C4×C23—21no—
324C2×C4×C23—21no—
325C2×C4×C23—22no—
326C2×C4×C23—22no—
327C2×C4×C23—21no—
328C2×C4×C23—21no—
329C2×C4×C23—24no—
330C2×C4×C23—22no—
331C2×C4×C23—22no—
332C2×C4×C23—41no—
333C2×C4×C23—41no—
334C2×C4×C23—41no—
335C2×C4×C23—41no—
336C2×C4×C23—41no—
337C2×C4×C23—41no—
338C2×C4×C23—42no—
339C2×C4×C23—42no—
340C2×C4×C23—42no—
341C2×C4×C23—41no—
342C2×C4×C23—42no—
343C2×C4×C23—41no—
344C2×C4×C23—42no—
345C2×C4×C23—42no—
346C2×C4×C23—42no—
347C2×C4×C23—41no—
348C2×C4×C23—41no—
349C2×C4×C23—41no—
350C2×C4×C23—41no—
351C2×C4×C23—41no—
352C2×C4×C23—41no—
353C2×C4×C23—41no—
354C2×C4×C23—41no—
355C2×C4×C23—41no—
356C2×C4×C23—42no—
357C2×C4×C23—42no—
358C2×C4×C23—42no—
359C2×C4×C23—81no—
360C2×C4×C23—82no—
361C2×C4×C23—82no—
362C2×C4×C23#12011yescharacteristic
363C2×C4×C23#12011yescharacteristic
364C2×C4×C23#12011yescharacteristic
365C2×C4×C23#12011yescharacteristic
366#3505C2×C2311yescharacteristic, complemented
367#2561C2×C2311yescharacteristic, complemented
368#2539C2×C2311yescharacteristic, complemented
369#2534C2×C2311yescharacteristic, complemented
370#2022C2×C2312yescomplemented
371#2021C2×C2312yescomplemented
372#1996C2×C2311yescharacteristic, complemented
373#1964C2×C2311yescharacteristic, complemented
374#1890C2×C2312yescomplemented
375#1889C2×C2312yescomplemented
376C4×#99C2×C2311yescharacteristic, complemented
377C22×C23—21no—
378C22×C23—21no—
379C22×C23—21no—
380C22×C23—21no—
381C22×C23—21no—
382C22×C23—21no—
383C22×C23—42no—
384C22×C23—42no—
385C22×C23—42no—
386C22×C23—44no—
387C22×C23—42no—
388C22×C23—44no—
389C22×C23—42no—
390C22×C23—41no—
391C22×C23—42no—
392C22×C23—42no—
393C22×C23—41no—
394C22×C23—42no—
395C22×C23—41no—
396C22×C23—42no—
397C22×C23—82no—
398C22×C23—82no—
399C22×C23—81no—
400C22×C23—82no—
401C22×C23—81no—
402C22×C23—82no—
403C22×C23—81no—
404C22×C23—81no—
405C22×C23—81no—
406C22×C23C2×#12011yescharacteristic
407C22×C23#53211yescharacteristic
408C22×C23#53511yescharacteristic
409C22×C23#54612yes—
410C22×C23#55012yes—
411C4×C23—21no—
412C4×C23—21no—
413C4×C23—21no—
414C4×C23—21no—
415C4×C23—44no—
416C4×C23—41no—
417C4×C23—42no—
418C4×C23—41no—
419C4×C23—42no—
420C4×C23—41no—
421C4×C23—42no—
422C4×C23—81no—
423C4×C23—82no—
424C4×C23—81no—
425C4×C23—81no—
426#553—22no—
427#553—21no—
428#552—21no—
429#551—22no—
430#548—21no—
431#546—21no—
432#539—21no—
433#538—21no—
434#534C22×C2312yes—
435#529—21no—
436#525—21no—
437C2×#123C22×C2312yes—
438C2×#123C22×C2311yescharacteristic
439C2×C22⋊Q8C22×C2311yescharacteristic
440C2×#121C22×C2311yescharacteristic
441C2×#120C22×C2312yes—
442C2×#120C22×C2311yescharacteristic
443#518C22×C2312yes—
444C2×C4×D4C22×C2311yescharacteristic
445C22×C22⋊C4C22×C2311yescharacteristic
446C2×#99C22×C2312yes—
447C2×#99C22×C2312yes—
448C2×#99C22×C2312yes—
449#399—21no—
450#397—21no—
451#396—21no—
452#394—21no—
453#393—21no—
454#392—21no—
455#390—22no—
456#388—22no—
457#388—21no—
458#386—21no—
459#381C22×C2312yes—
460#381C22×C2311yescharacteristic
461#380C22×C2311yescharacteristic
462#379C22×C2312yes—
463#379C22×C2311yescharacteristic
464C4×C22⋊C4C22×C2311yescharacteristic
465C4×C22⋊C4C22×C2311yescharacteristic
466#342C22×C2312yes—
467#342C22×C2312yes—
468#342C22×C2312yes—
469C2×C23—22no—
470C2×C23—21no—
471C2×C23—22no—
472C2×C23—21no—
473C2×C23—82no—
474C2×C23—81no—
475C2×C23—82no—
476C2×C23#243111yescharacteristic
477C2×C23#302511yescharacteristic
478C2×C23#302611yescharacteristic
479C25C23×C2311yescharacteristic
480C2×#41—21no—
481C22×Q8D4×C2311yescharacteristic, complemented
482C22×D4—21no—
483C22×D4—22no—
484C22×D4D4×C2311yescharacteristic, complemented
485C22×D4C23×C2311yescharacteristic
486C22×D4C23×C2312yes—
487C23×C4D4×C2311yescharacteristic, complemented
488C23×C4C23×C2311yescharacteristic
489C23×C4C23×C2311yescharacteristic
490#126—22no—
491#126—22no—
492#126—22no—
493#125—21no—
494#125—22no—
495#124—21no—
496#124—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—24no—
503#123—42no—
504#123—42no—
505C22⋊Q8—21no—
506C22⋊Q8—22no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511#121—21no—
512#121—22no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—22no—
518#121—22no—
519#120—22no—
520#120—22no—
521#120—24no—
522#120—42no—
523#120—42no—
524C4×Q8—21no—
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535#117—21no—
536#117—22no—
537#117—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C2311yescharacteristic, complemented
542C2×C4⋊C4D4×C2311yescharacteristic, complemented
543C2×C4⋊C4D4×C2312yescomplemented
544C2×C4⋊C4D4×C2311yescharacteristic, complemented
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4D4×C2311yescharacteristic, complemented
561C2×C22⋊C4D4×C2312yescomplemented
562C2×C22⋊C4C23×C2311yescharacteristic
563C2×C22⋊C4C23×C2311yescharacteristic
564C2×C22⋊C4C23×C2312yes—
565C2×C22⋊C4C23×C2311yescharacteristic
566C2×C22⋊C4C23×C2312yes—
567C2×C22⋊C4C23×C2312yes—
568C2×C42—21no—
569C2×C42—21no—
570C2×C42D4×C2311yescharacteristic, complemented
571#99—24no—
572#99—42no—
573#99—42no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—22no—
579#95—21no—
580#95—22no—
581C23#2558711yescharacteristic, direct product factor, Sylow
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C2312yes—
590C24C2×D4×C2311yescharacteristic
591C24C24×C2311yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C2311yescharacteristic
633C22×C4C2×D4×C2312yes—
634C22×C4C2×D4×C2311yescharacteristic
635C22×C4C2×D4×C2312yes—
636C22×C4C2×D4×C2311yescharacteristic
637C22×C4C2×D4×C2312yes—
638C22×C4C2×D4×C2311yescharacteristic
639C22×C4C2×D4×C2311yescharacteristic
640C22×C4C2×D4×C2311yescharacteristic
641C22×C4C2×D4×C2311yescharacteristic
642C22×C4C2×D4×C2311yescharacteristic
643C22×C4C2×D4×C2311yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C2314yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C2311yescharacteristic
727C23C22×D4×C2311yescharacteristic
728C23C22×D4×C2311yescharacteristic
729C23C2×#41×C2312yes—
730C23C23×H(5,𝔽2)12yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4C23×#12011yescharacteristic
787C2×C4C23×#12011yescharacteristic
788C2×C4C23×#12011yescharacteristic
789C2×C4C23×#12011yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×C23×#12011yescharacteristic
820C22C23×#53211yescharacteristic
821C22C23×#53511yescharacteristic
822C22C23×#54612yes—
823C22C23×#55012yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C23×#243111yescharacteristic
847C2C23×#302511yescharacteristic
848C2C23×#302611yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC24C24×C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×#3505C2semidirect
2. C23×#2561C2semidirect
3. C23×#2539C2semidirect
4. C23×#2534C2semidirect
5. C23×#2022C2semidirect
6. C23×#2021C2semidirect
7. C23×#1996C2semidirect
8. C23×#1964C2semidirect
9. C23×#1890C2semidirect
10. C23×#1889C2semidirect
11. C4×C23×#99C2semidirect
57. C22×Q8×C23D4semidirect
60. C22×D4×C23D4semidirect
63. C23×C4×C23D4semidirect
117. C2×C4⋊C4×C23D4semidirect
118. C2×C4⋊C4×C23D4semidirect
119. C2×C4⋊C4×C23D4semidirect
120. C2×C4⋊C4×C23D4semidirect
136. C2×C22⋊C4×C23D4semidirect
137. C2×C22⋊C4×C23D4semidirect
146. C2×C42×C23D4semidirect
265. C22⋊C4×C23#41semidirect
272. #25587C23direct (N × H)
366. #3505C2×C23semidirect
367. #2561C2×C23semidirect
368. #2539C2×C23semidirect
369. #2534C2×C23semidirect
370. #2022C2×C23semidirect
371. #2021C2×C23semidirect
372. #1996C2×C23semidirect
373. #1964C2×C23semidirect
374. #1890C2×C23semidirect
375. #1889C2×C23semidirect
376. C4×#99C2×C23semidirect
481. C22×Q8D4×C23semidirect
484. C22×D4D4×C23semidirect
487. C23×C4D4×C23semidirect
541. C2×C4⋊C4D4×C23semidirect
542. C2×C4⋊C4D4×C23semidirect
543. C2×C4⋊C4D4×C23semidirect
544. C2×C4⋊C4D4×C23semidirect
560. C2×C22⋊C4D4×C23semidirect
561. C2×C22⋊C4D4×C23semidirect
570. C2×C42D4×C23semidirect
581. C23#25587direct (N × H)
690. C22⋊C4#41×C23semidirect

Maximal subgroups

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

subgroupindex
C23×#35052
C23×#25612
C23×#25392
C23×#25342
C23×#20222
C23×#20212
C23×#19962
C23×#19642
C23×#18902
C23×#18892
C4×C23×#992
#2558723