Finite Group Databasebeta

← #11069394

Subgroups — #11069394

Order 768.

2560 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5634C212yesmaximal, complemented
2C3×#2857C211yesmaximal, characteristic, complemented
3#83236C212yesmaximal, complemented
4#82822C212yesmaximal, complemented
5C4×#924C211yesmaximal, characteristic, complemented
6C2×#4939C211yesmaximal, characteristic
7#76564C214yesmaximal, complemented
8#76261C212yesmaximal, complemented
9#76134C212yesmaximal, complemented
10#76059C212yesmaximal, complemented
11#76011C212yesmaximal, complemented
12#74334C212yesmaximal, complemented
13#74007C212yesmaximal
14#73899C212yesmaximal, complemented
15#73896C214yesmaximal, complemented
16#39367—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic, complemented
19C2×C3×C22⋊Q8C2212yes—
20C22×C3×C42C2211yescharacteristic
21C2×#946C2214yescomplemented
22C22×(C2×D3)⋊C4C2212yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×C4⋊Dic3C2211yescharacteristic
25C2×#924C2211yescharacteristic
26#5634—216no—
27C2×#897C2214yescomplemented
28C2×#896C2214yescomplemented
29C2×#896C2214yescomplemented
30C2×#896C2214yescomplemented
31C2×#893C2212yes—
32C2×#893C2212yes—
33C2×#888C2212yescomplemented
34C2×D3×C22⋊C4C2214yes—
35C2×#878C2214yes—
36C2×C4×Dic6C2211yescharacteristic, complemented
37C3×#391C2212yescomplemented
38C3×#389C2212yescomplemented
39C3×#389C2212yescomplemented
40C3×#384C2211yescharacteristic, complemented
41C3×#380C2212yes—
42C3×#380C2212yes—
43#5231C2214yescomplemented
44#5212C2211yescharacteristic
45#5210C2212yes—
46C4×#217C2212yes—
47#4994C2214yescomplemented
48#4994C2214yescomplemented
49#4994C2214yescomplemented
50#4993C2214yescomplemented
51#4993C2214yescomplemented
52#4989C2214yescomplemented
53#4988C2212yes—
54#4988C2212yes—
55#4984C2212yescomplemented
56#4975C2212yescomplemented
57#4972C2212yescomplemented
58#4955C2214yes—
59#4946C2214yes—
60#4939C2212yes—
61#4939C2212yes—
62#4939C2212yes—
63#4939C2212yes—
64C4×C4⋊Dic3C2211yescharacteristic, complemented
65#4933C2212yescomplemented
66C4×Dic3⋊C4C2212yescomplemented
67#4929C2211yescharacteristic, complemented
68#4928C2211yescharacteristic, complemented
69#4676C2214yescomplemented
70#4673C2214yescomplemented
71#4668C2214yescomplemented
72#4667C2214yescomplemented
73#4665C2214yes—
74#4665C2214yes—
75#4657C2214yescomplemented
76#4656C2214yescomplemented
77C2×#543—32no—
78#2857D311yescharacteristic, complemented
79#2732—32no—
80#2692—34no—
81#2683—32no—
82#2626—32no—
83#2542—32no—
84#2538—32no—
85#2452—32no—
86#2452—32no—
87#2440—32no—
88#2437—34no—
89D4×C22⋊C4—32no—
90C4×C22⋊Q8—31no—
91C2×#390—31no—
92C24×D3C2312yes—
93C22×C3×Q8C2312yes—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×Dic3C2312yes—
98C22×D12—42no—
99C22×D12—42no—
100C22×D12Q818yescomplemented
101C22×D12C2312yes—
102C22×D12C2312yes—
103C22×C4×D3C2314yes—
104C22×C4×D3C2314yes—
105C22×Dic6C2314yes—
106C22×Dic6C2311yescharacteristic
107C3×C4⋊Q8—42no—
108C3×C22⋊Q8—28no—
109C2×C3×C4⋊C4C2312yes—
110C2×C3×C4⋊C4C2312yes—
111C2×C3×C4⋊C4C2312yes—
112C2×C3×C4⋊C4C2312yes—
113C2×C3×C4⋊C4C2314yes—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C22⋊C4C2314yes—
116C2×C3×C42—42no—
117C2×C3×C42C2311yescharacteristic
118C2×C3×C42C2311yescharacteristic
119C2×C3×C42C2311yescharacteristic
120C2×C3×C42C2311yescharacteristic
121C2×#217C2312yes—
122C2×#217C2312yes—
123#946—216no—
124C2×(C2×D3)⋊C4—28no—
125C2×(C2×D3)⋊C4—44no—
126C2×(C2×D3)⋊C4C2314yes—
127C2×(C2×D3)⋊C4C2314yes—
128C2×(C2×D3)⋊C4C2314yes—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×C4⋊Dic3—42no—
137C2×C4⋊Dic3C2314yes—
138C2×C4⋊Dic3C2312yes—
139C2×C4⋊Dic3C2312yes—
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4⋊Dic3C2311yescharacteristic
143#924D418yescomplemented
144C2×Dic3⋊C4C2314yes—
145C2×Dic3⋊C4C2314yes—
146C2×Dic3⋊C4C2312yes—
147C2×Dic3⋊C4C2314yes—
148C2×Dic3⋊C4C2314yes—
149C2×Dic3⋊C4C2312yes—
150C2×Dic3⋊C4C2312yes—
151C2×C4×Dic3C2312yes—
152C2×C4×Dic3C2312yes—
153#897—216no—
154#896—216no—
155#896—216no—
156#896—48no—
157#893—44no—
158#893—44no—
159#888—44no—
160D3×C22⋊C4—216no—
161#878—216no—
162C4×Dic6—42no—
163C3×#95C2314yes—
164C3×#95C2314yes—
165C3⋊#95C2312yes—
166C3⋊#95C2314yes—
167C3⋊#95C2312yes—
168C3⋊#95C2314yes—
169C3⋊#95C2312yes—
170C3⋊#95C2312yes—
171C3⋊#95C2312yes—
172C23×D4—31no—
173#543—616no—
174C2×C4⋊Q8—32no—
175C2×C4⋊Q8C2×D311yescharacteristic, complemented
176C2×C22⋊Q8—31no—
177C2×C22⋊Q8—34no—
178C2×C22⋊Q8—34no—
179C2×C22⋊Q8—34no—
180C2×C22⋊Q8—34no—
181C2×C22⋊Q8—34no—
182C2×C22⋊Q8—34no—
183C2×C22⋊Q8C2×D312yes—
184C2×C4×Q8—31no—
185C2×C4×D4—32no—
186C2×C4×D4—32no—
187C22×C4⋊C4—31no—
188C22×C22⋊C4—32no—
189C22×C22⋊C4—32no—
190C22×C22⋊C4—34no—
191C22×C42C2×D311yescharacteristic
192#399—34no—
193#399—34no—
194#398—34no—
195#396—34no—
196#396—34no—
197#396—34no—
198#396—34no—
199#395—34no—
200#393—34no—
201#393—34no—
202#391—31no—
203#391C2×D312yescomplemented
204#390—32no—
205#390—32no—
206#390—32no—
207#390—32no—
208#390—32no—
209#390—32no—
210#389—32no—
211#389—32no—
212#389—31no—
213#389C2×D312yescomplemented
214#389C2×D312yescomplemented
215#387—32no—
216#386—34no—
217#386—34no—
218#385—32no—
219#385—34no—
220#385—34no—
221#385—34no—
222#384—32no—
223#384C2×D311yescharacteristic, complemented
224#380—31no—
225#380—34no—
226#380C2×D312yes—
227#380C2×D312yes—
228#379—34no—
229C4×C4⋊C4—32no—
230C4×C4⋊C4—31no—
231C4×C22⋊C4—32no—
232C24×C3C2411yescharacteristic
233C23×D3—24no—
234C23×D3—24no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3C2×Q818yes—
240C23×D3C2414yes—
241C2×C3×Q8—24no—
242C2×C3×Q8—42no—
243C2×C3×Q8—42no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—41no—
249C22×C3×C4—41no—
250C22×C3×C4—41no—
251C22×C3×C4C2×D414yes—
252C22×C3×C4C2×Q814yes—
253C22×C3×C4C2411yescharacteristic
254C22×C3×C4C2414yes—
255C22×C3×C4C2414yes—
256C22×C3×C4C2411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C22×Dic3—24no—
262C22×Dic3—42no—
263C22×Dic3—42no—
264C22×Dic3C2412yes—
265C22×Dic3C2412yes—
266C22×Dic3C2414yes—
267C22×Dic3C2412yes—
268C22×Dic3C2412yes—
269C2×D12—24no—
270C2×D12—24no—
271C2×D12—416no—
272C2×D12—42no—
273C2×D12—42no—
274C2×D12C2×Q818yes—
275C2×D12C2×Q818yes—
276C2×C4×D3—28no—
277C2×C4×D3—28no—
278C2×C4×D3—44no—
279C2×C4×D3—44no—
280C2×C4×D3—44no—
281C2×C4×D3—44no—
282C2×Dic6—28no—
283C2×Dic6—41no—
284C2×Dic6—41no—
285C2×Dic6—44no—
286C2×Dic6—44no—
287C2×Dic6C2×D414yescomplemented
288C3×C4⋊C4—24no—
289C3×C4⋊C4—28no—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—42no—
294C3×C22⋊C4—28no—
295C3×C42—22no—
296C3×C42—22no—
297C3×C42—41no—
298C3×C42—41no—
299#217—24no—
300#217C2×D418yes—
301(C2×D3)⋊C4—28no—
302(C2×D3)⋊C4—28no—
303(C2×D3)⋊C4—28no—
304(C2×D3)⋊C4—28no—
305(C2×D3)⋊C4—28no—
306(C2×D3)⋊C4—44no—
307(C2×D3)⋊C4—44no—
308(C2×D3)⋊C4—44no—
309(C2×D3)⋊C4—44no—
310(C2×D3)⋊C4—44no—
311C4⋊Dic3—24no—
312C4⋊Dic3—28no—
313C4⋊Dic3—41no—
314C4⋊Dic3—42no—
315C4⋊Dic3—41no—
316C4⋊Dic3C2×D414yescomplemented
317Dic3⋊C4—24no—
318Dic3⋊C4—28no—
319Dic3⋊C4—28no—
320Dic3⋊C4—42no—
321Dic3⋊C4—44no—
322Dic3⋊C4—44no—
323Dic3⋊C4C2×D418yescomplemented
324C4×Dic3—24no—
325C4×Dic3—24no—
326C25—32no—
327C22×Q8—31no—
328C22×Q8—34no—
329C22×Q8C22×D312yes—
330C22×D4—38no—
331C22×D4—32no—
332C22×D4—32no—
333C22×D4—122no—
334C22×D4—122no—
335C23×C4—32no—
336C23×C4—34no—
337C23×C4—34no—
338C23×C4C22×D311yescharacteristic
339C23×C4C22×D311yescharacteristic
340C23×C4C22×D311yescharacteristic
341C4⋊Q8—42no—
342C4⋊Q8—124no—
343C22⋊Q8—28no—
344C22⋊Q8—38no—
345C22⋊Q8—616no—
346C22⋊Q8—616no—
347C22⋊Q8—616no—
348C22⋊Q8—616no—
349C22⋊Q8—616no—
350C22⋊Q8—128no—
351C4×Q8—122no—
352C4×D4—124no—
353C4×D4—124no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—34no—
358C2×C4⋊C4—34no—
359C2×C4⋊C4—34no—
360C2×C4⋊C4—32no—
361C2×C4⋊C4—32no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—34no—
365C2×C4⋊C4—34no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—122no—
368C2×C4⋊C4C22×D312yes—
369C2×C4⋊C4C22×D312yes—
370C2×C4⋊C4C22×D312yes—
371C2×C4⋊C4C22×D314yes—
372C2×C4⋊C4C22×D312yes—
373C2×C4⋊C4C22×D312yes—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—34no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—34no—
381C2×C22⋊C4—34no—
382C2×C22⋊C4—34no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—616no—
387C2×C22⋊C4—68no—
388C2×C22⋊C4—124no—
389C2×C22⋊C4C22×D314yes—
390C2×C42—32no—
391C2×C42—32no—
392C2×C42—42no—
393C2×C42C22×D311yescharacteristic
394C2×C42C22×D311yescharacteristic
395C2×C42C22×D311yescharacteristic
396C2×C42C22×D311yescharacteristic
397#95—32no—
398#95—32no—
399#95—32no—
400#95—32no—
401#95—32no—
402#95—34no—
403#95—34no—
404#95C22×D314yes—
405#95C22×D314yes—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3C22×D412yes—
411C23×C3C22×Q812yes—
412C23×C32−1+412yes—
413C23×C3C2511yescharacteristic
414C22×D3—24no—
415C22×D3—24no—
416C22×D3—24no—
417C22×D3—24no—
418C22×D3—24no—
419C22×D3—24no—
420C22×D3—216no—
421C22×D3—48no—
422C22×D3—48no—
423C22×D3—84no—
424C22×D3—84no—
425C22×D3—84no—
426C22×D3—84no—
427C22×D3C22×Q818yes—
428C3×Q8—84no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—28no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—21no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—21no—
444C2×C3×C4—24no—
445C2×C3×C4—21no—
446C2×C3×C4—24no—
447C2×C3×C4—44no—
448C2×C3×C4—44no—
449C2×C3×C4C22×D412yes—
450C2×C3×C4C22×D412yes—
451C2×C3×C4C22×Q812yes—
452C2×C3×C4C22×Q812yes—
453C2×C3×C4H(5,𝔽2)12yes—
454C2×C3×C4H(5,𝔽2)12yes—
455C2×C3×C4H(5,𝔽2)12yes—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—24no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—24no—
465C2×Dic3—24no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—84no—
470C2×Dic3C22×D414yes—
471C2×Dic3C22×D414yes—
472D12—216no—
473D12—48no—
474C4×D3—88no—
475C4×D3—88no—
476Dic6—44no—
477Dic6—88no—
478C24—34no—
479C24—38no—
480C24—64no—
481C24—64no—
482C24—122no—
483C24—122no—
484C24—122no—
485C24—122no—
486C24C23×D311yescharacteristic
487C2×Q8—24no—
488C2×Q8—34no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—68no—
492C2×Q8—121no—
493C2×Q8—121no—
494C2×Q8—124no—
495C2×Q8—124no—
496C2×D4—38no—
497C2×D4—38no—
498C2×D4—64no—
499C2×D4—64no—
500C2×D4—1216no—
501C2×D4—122no—
502C2×D4—122no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—34no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—68no—
516C22×C4—68no—
517C22×C4—64no—
518C22×C4—124no—
519C22×C4—124no—
520C22×C4—124no—
521C22×C4—124no—
522C22×C4—122no—
523C22×C4—122no—
524C22×C4D3×D414yes—
525C22×C4D3×Q814yes—
526C22×C4C23×D311yescharacteristic
527C22×C4C23×D314yes—
528C22×C4C23×D314yes—
529C22×C4C23×D311yescharacteristic
530C22×C4C23×D311yescharacteristic
531C22×C4C23×D311yescharacteristic
532C22×C4C23×D311yescharacteristic
533C22×C4C23×D311yescharacteristic
534C4⋊C4—24no—
535C4⋊C4—28no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—38no—
540C4⋊C4—34no—
541C4⋊C4—42no—
542C4⋊C4—68no—
543C4⋊C4—68no—
544C4⋊C4—68no—
545C4⋊C4—64no—
546C4⋊C4—64no—
547C4⋊C4—122no—
548C4⋊C4—122no—
549C4⋊C4—121no—
550C4⋊C4—124no—
551C4⋊C4—124no—
552C4⋊C4—121no—
553C22⋊C4—28no—
554C22⋊C4—38no—
555C22⋊C4—68no—
556C22⋊C4—68no—
557C22⋊C4—64no—
558C22⋊C4—68no—
559C22⋊C4—68no—
560C22⋊C4—68no—
561C22⋊C4—124no—
562C22⋊C4—124no—
563C22⋊C4—124no—
564C22⋊C4—124no—
565C22⋊C4—124no—
566C42—22no—
567C42—22no—
568C42—41no—
569C42—41no—
570C42—64no—
571C42—64no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3D4×Q814yes—
579C22×C3C23×D411yescharacteristic
580C22×C3C23×Q811yescharacteristic
581C22×C3C2×H(5,𝔽2)11yescharacteristic
582C22×C3C2×H(5,𝔽2)11yescharacteristic
583C22×C3C2×H(5,𝔽2)11yescharacteristic
584C22×C3C2×2−1+411yescharacteristic
585C22×C3#58511yescharacteristic
586C2×D3—28no—
587C2×D3—28no—
588C2×D3—28no—
589C2×D3—44no—
590C2×D3—44no—
591C2×D3—44no—
592C2×D3—44no—
593C2×D3—816no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—44no—
599C3×C4—44no—
600C3×C4—41no—
601C3×C4#54314yescomplemented
602Dic3—24no—
603Dic3—24no—
604Dic3—44no—
605Dic3—42no—
606Dic3—42no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—38no—
612C23—64no—
613C23—64no—
614C23—64no—
615C23—64no—
616C23—64no—
617C23—64no—
618C23—616no—
619C23—128no—
620C23—128no—
621C23—244no—
622C23—244no—
623C23—244no—
624C23—244no—
625C23C2×D3×D412yes—
626C23C2×D3×Q812yes—
627C23#100712yes—
628C23C24×D311yescharacteristic
629Q8—84no—
630Q8—124no—
631Q8—248no—
632D4—616no—
633D4—128no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—28no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—21no—
646C2×C4—24no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—34no—
653C2×C4—34no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—64no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—64no—
666C2×C4—62no—
667C2×C4—64no—
668C2×C4—62no—
669C2×C4—248no—
670C2×C4—248no—
671C2×C4—244no—
672C2×C4C2×D3×D412yes—
673C2×C4C2×D3×D412yes—
674C2×C4#100412yes—
675C2×C4C2×D3×Q812yes—
676C2×C4C2×D3×Q812yes—
677C2×C4#100912yes—
678C2×C4#100912yes—
679C2×C3—24no—
680C2×C3C2×#54311yescharacteristic
681C2×C3C2×D4×Q811yescharacteristic
682C2×C3#349611yescharacteristic
683C2×C3#349811yescharacteristic
684C2×C3#350111yescharacteristic
685C2×C3#353611yescharacteristic
686C2×C3#356111yescharacteristic
687D3—48no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—68no—
695C22—68no—
696C22—68no—
697C22—124no—
698C22—124no—
699C22—124no—
700C22—124no—
701C22—2416no—
702C22#572714yes—
703C22C22×D3×D411yescharacteristic
704C22C2×#100411yescharacteristic
705C22C22×D3×Q811yescharacteristic
706C22C2×#100711yescharacteristic
707C22C2×#100911yescharacteristic
708C22C2×#100911yescharacteristic
709C22#596411yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—44no—
715C4—44no—
716C4—41no—
717C4—64no—
718C4—64no—
719C4—122no—
720C4—124no—
721C4—122no—
722C4#563414yescomplemented
723C3#3936711yescharacteristic, complemented, Sylow
724C2—24no—
725C2—128no—
726C2#8595011yescharacteristic
727C2C2×#563411yescharacteristic
728C2#8599011yescharacteristic
729C2C2×#572711yescharacteristic
730C2#8624211yescharacteristic
731C2#8628011yescharacteristic
732C2#8629111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2857C2
prime radicalC23×D12C22
hypercenter#2857D3
hypocenterC3#39367
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×#5634C2semidirect
2. C3×#2857C2semidirect
3. #83236C2semidirect
4. #82822C2semidirect
5. C4×#924C2semidirect
7. #76564C2semidirect
8. #76261C2semidirect
9. #76134C2semidirect
10. #76059C2semidirect
11. #76011C2semidirect
12. #74334C2semidirect
14. #73899C2semidirect
15. #73896C2semidirect
18. C2×C3×C4⋊Q8C22semidirect
21. C2×#946C22semidirect
27. C2×#897C22semidirect
28. C2×#896C22semidirect
29. C2×#896C22semidirect
30. C2×#896C22semidirect
33. C2×#888C22semidirect
36. C2×C4×Dic6C22semidirect
37. C3×#391C22semidirect
38. C3×#389C22semidirect
39. C3×#389C22semidirect
40. C3×#384C22semidirect
43. #5231C22semidirect
47. #4994C22semidirect
48. #4994C22semidirect
49. #4994C22semidirect
50. #4993C22semidirect
51. #4993C22semidirect
52. #4989C22semidirect
55. #4984C22semidirect
56. #4975C22semidirect
57. #4972C22semidirect
64. C4×C4⋊Dic3C22semidirect
65. #4933C22semidirect
66. C4×Dic3⋊C4C22semidirect
67. #4929C22semidirect
68. #4928C22semidirect
69. #4676C22semidirect
70. #4673C22semidirect
71. #4668C22semidirect
72. #4667C22semidirect
75. #4657C22semidirect
76. #4656C22semidirect
78. #2857D3semidirect
100. C22×D12Q8semidirect
143. #924D4semidirect
175. C2×C4⋊Q8C2×D3semidirect
203. #391C2×D3semidirect
213. #389C2×D3semidirect
214. #389C2×D3semidirect
223. #384C2×D3semidirect
287. C2×Dic6C2×D4semidirect
316. C4⋊Dic3C2×D4semidirect
323. Dic3⋊C4C2×D4semidirect
601. C3×C4#543semidirect
722. C4#5634semidirect
723. C3#39367semidirect

Maximal subgroups

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

subgroupindex
C2×#56342
C3×#28572
#832362
#828222
C4×#9242
C2×#49392
#765642
#762612
#761342
#760592
#760112
#743342
#740072
#738992
#738962
#393673