Finite Group Databasebeta

← #11633967

Subgroups — #11633967

Order 768.

2378 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5728C211yesmaximal, characteristic, complemented
2C2×Q8×D12C211yesmaximal, characteristic, complemented
3C3×#2568C211yesmaximal, characteristic, complemented
4#83240C211yesmaximal, characteristic, complemented
5C4×#946C211yesmaximal, characteristic, complemented
6#78237C214yesmaximal, complemented
7#78143C214yesmaximal, complemented
8#76633C212yesmaximal, complemented
9#76624C212yesmaximal
10#76619C212yesmaximal, complemented
11#76614C212yesmaximal, complemented
12#76508C212yesmaximal, complemented
13#76493C212yesmaximal, complemented
14#74240C212yesmaximal, complemented
15#74232C212yesmaximal, complemented
16C4×#895C211yesmaximal, characteristic
17#73651C211yesmaximal, characteristic, complemented
18#59042—31nomaximal, Sylow
19C22×D3×Q8C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22C2×#947C2212yes—
23C2×#946C2211yescharacteristic
24C2×#946C2212yes—
25C2×Q8×Dic3C2212yes—
26#5728—28no—
27Q8×D12—28no—
28C2×#897C2212yes—
29C2×#897C2212yes—
30C2×#897C2214yes—
31C2×#895C2211yescharacteristic
32C2×#892C2212yes—
33C2×#890C2212yes—
34C2×#887C2212yes—
35C2×C4×D12C2211yescharacteristic
36C2×C4×D12C2212yes—
37C2×C4×D12C2212yes—
38C2×C42×D3C2211yescharacteristic
39C2×#869C2212yes—
40C2×#869C2211yescharacteristic
41C2×C4×Dic6C2212yes—
42C3×#400C2214yes—
43C3×#391C2212yes—
44C3×#391C2212yes—
45C3×#391C2212yes—
46C3×#382C2212yes—
47C3×C4×C4⋊C4C2211yescharacteristic
48#5229C2212yes—
49#5229C2211yescharacteristic
50#4992C2214yes—
51#4989C2212yes—
52#4988C2211yescharacteristic
53#4987C2211yescharacteristic
54#4987C2212yes—
55#4987C2211yescharacteristic
56#4987C2212yes—
57#4984C2211yescharacteristic
58#4978C2212yes—
59Dic3×C4⋊C4C2212yes—
60#4972C2211yescharacteristic
61#4972C2212yes—
62C4×(C2×D3)⋊C4C2212yes—
63C4×(C2×D3)⋊C4C2212yes—
64C4×C4⋊Dic3C2211yescharacteristic
65C4×Dic3⋊C4C2212yes—
66#4929C2212yes—
67#4675C2214yes—
68#4673C2214yes—
69#4672C2214yes—
70#4670C2214yes—
71#4670C2214yes—
72#4670C2212yes—
73#4669C2214yes—
74#4668C2214yes—
75#4667C2214yes—
76#4666C2214yes—
77#4665C2212yes—
78#4665C2214yes—
79#4661C2214yes—
80#4660C2214yes—
81#4656C2214yes—
82#4655C2214yes—
83#4654C2214yes—
84#4646C2214yes—
85#4646C2214yes—
86C2×D4×Q8—31no—
87C2×#533—31no—
88#2690—34no—
89#2568D311yescharacteristic, complemented
90#2547—31no—
91#2536—32no—
92#2492—32no—
93#2477—34no—
94#2451—32no—
95#2427—32no—
96#2421—32no—
97#2409—32no—
98#2367—32no—
99#2365—31no—
100Q8×C22⋊C4—32no—
101C4×C22⋊Q8—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×Q8C2311yescharacteristic
105C2×D3×Q8—28no—
106C2×D3×Q8—28no—
107C2×D3×Q8—44no—
108C22×D12C2312yes—
109C22×D12C2311yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×C4×D3C2312yes—
112C22×C4×D3C2311yescharacteristic
113C22×C4×D3C2311yescharacteristic
114C22×C4×D3C2314yes—
115C22×Dic6C2314yes—
116C22×Dic6C2312yes—
117C3×C4⋊Q8—24no—
118C3×C4×Q8—24no—
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C42C2312yes—
126C2×C3×C42C2312yes—
127C2×C3×C42C2311yescharacteristic
128#947—28no—
129#946—24no—
130#946—28no—
131Q8×Dic3—28no—
132C2×(C2×D3)⋊C4C2312yes—
133C2×(C2×D3)⋊C4C2312yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2312yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×C4⋊Dic3C2314yes—
144C2×C4⋊Dic3C2314yes—
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2312yes—
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2312yes—
153C2×Dic3⋊C4C2312yes—
154C2×Dic3⋊C4C2314yes—
155C2×C4×Dic3C2314yes—
156C2×C4×Dic3C2311yescharacteristic
157C2×C4×Dic3C2311yescharacteristic
158C2×C4×Dic3C2312yes—
159C2×C4×Dic3C2311yescharacteristic
160C2×C4×Dic3C2314yes—
161#897—28no—
162#897—28no—
163#897—216no—
164#895—24no—
165#892—28no—
166#890—28no—
167#887—28no—
168C4×D12—24no—
169C4×D12—28no—
170C4×D12—44no—
171C42×D3—24no—
172#869—28no—
173#869D418yescomplemented
174C4×Dic6—44no—
175C3×#95C2314yes—
176C3×#95C2314yes—
177C3×#95C2312yes—
178C3×#95C2314yes—
179C3×#95C2314yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191C23×Q8—32no—
192D4×Q8—68no—
193#533—68no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8—32no—
196C2×C4⋊Q8C2×D311yescharacteristic
197C2×#125—32no—
198C2×#124—32no—
199C2×C22⋊Q8—31no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—32no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—34no—
204C2×#121—31no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×Q8—32no—
208C2×C4×Q8C2×D311yescharacteristic
209C2×C4×D4—32no—
210C2×C4×D4—31no—
211C2×C4×D4—32no—
212C2×#117—32no—
213C22×C42—31no—
214#400—34no—
215#400C2×D314yes—
216#398—34no—
217#397—34no—
218#397—34no—
219#395—34no—
220#394—34no—
221#393—34no—
222#391—31no—
223#391—32no—
224#391—32no—
225#391—34no—
226#391—34no—
227#391C2×D312yes—
228#391C2×D312yes—
229#391C2×D312yes—
230#390—31no—
231#389—32no—
232#389—31no—
233#389—31no—
234#388—34no—
235#388—34no—
236#388—32no—
237#388—34no—
238#387—32no—
239#387—34no—
240#387—34no—
241#386—34no—
242#386—32no—
243#385—32no—
244#385—34no—
245#382C2×D312yes—
246#380—32no—
247#380—32no—
248#380—31no—
249#380—31no—
250#380—34no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—31no—
253C4×C4⋊C4—32no—
254C4×C4⋊C4C2×D311yescharacteristic
255C4×C22⋊C4—32no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—34no—
258C23×D3C2412yes—
259C23×D3C2411yescharacteristic
260C2×C3×Q8—22no—
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8—22no—
264C2×C3×Q8—24no—
265C2×C3×Q8#4114yes—
266C22×C3×C4C2412yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2414yes—
269C22×C3×C4C2412yes—
270C22×C3×C4C2411yescharacteristic
271C22×C3×C4C2412yes—
272C22×C3×C4C2411yescharacteristic
273C22×C3×C4C2411yescharacteristic
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276C22×Dic3C2411yescharacteristic
277C22×Dic3C2412yes—
278C22×Dic3C2411yescharacteristic
279C22×Dic3C2414yes—
280C22×Dic3C2411yescharacteristic
281D3×Q8—432no—
282C2×D12—22no—
283C2×D12—22no—
284C2×D12—24no—
285C2×D12—24no—
286C2×D12—42no—
287C2×D12#4114yes—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—22no—
292C2×C4×D3—22no—
293C2×C4×D3—24no—
294C2×C4×D3—22no—
295C2×C4×D3—22no—
296C2×C4×D3—28no—
297C2×C4×D3—24no—
298C2×C4×D3—22no—
299C2×C4×D3—24no—
300C2×C4×D3—22no—
301C2×C4×D3—28no—
302C2×C4×D3—44no—
303C2×Dic6—24no—
304C2×Dic6—24no—
305C2×Dic6—28no—
306C2×Dic6—28no—
307C2×Dic6—44no—
308C2×Dic6C2×D418yes—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—24no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—22no—
313C3×C4⋊C4—22no—
314C3×C4⋊C4—22no—
315C3×C42—24no—
316C3×C42—24no—
317C3×C42C2×D414yes—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—28no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—24no—
323(C2×D3)⋊C4—24no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—28no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—42no—
328(C2×D3)⋊C4—42no—
329C4⋊Dic3—22no—
330C4⋊Dic3—22no—
331C4⋊Dic3—22no—
332C4⋊Dic3—28no—
333C4⋊Dic3—28no—
334C4⋊Dic3—42no—
335C4⋊Dic3C2×D418yes—
336C4⋊Dic3C2×D418yes—
337Dic3⋊C4—24no—
338Dic3⋊C4—28no—
339Dic3⋊C4—24no—
340Dic3⋊C4—44no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—24no—
345C4×Dic3—28no—
346C4×Dic3—44no—
347C22×Q8—32no—
348C22×Q8—34no—
349C22×Q8—68no—
350C22×Q8—68no—
351C22×Q8—124no—
352C22×Q8C22×D312yes—
353C22×Q8C22×D311yescharacteristic
354C22×D4—31no—
355C22×D4—32no—
356C23×C4—31no—
357C23×C4—31no—
358C23×C4—32no—
359C23×C4—31no—
360C23×C4—34no—
361C4⋊Q8—24no—
362C4⋊Q8—38no—
363C4⋊Q8—68no—
364#125—68no—
365#124—68no—
366C22⋊Q8—616no—
367C22⋊Q8—68no—
368C22⋊Q8—68no—
369C22⋊Q8—68no—
370C22⋊Q8—64no—
371#121—64no—
372C4×Q8—24no—
373C4×Q8—68no—
374C4×Q8—68no—
375C4×Q8—124no—
376C4×D4—68no—
377C4×D4—64no—
378C4×D4—124no—
379#117—68no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4C22×D312yes—
393C2×C4⋊C4C22×D312yes—
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D312yes—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—34no—
399C2×C22⋊C4—32no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—32no—
402C2×C22⋊C4—32no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C42—34no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—32no—
413C2×C42—31no—
414C2×C42—34no—
415C2×C42—64no—
416C2×C42C22×D312yes—
417C2×C42C22×D312yes—
418C2×C42C22×D311yescharacteristic
419#95—32no—
420#95—32no—
421#95—32no—
422#95—32no—
423#95—32no—
424#95—32no—
425#95—32no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—34no—
430#95C22×D314yes—
431#95C22×D312yes—
432#95C22×D314yes—
433#95C22×D314yes—
434#95C22×D314yes—
435C23×C3C2511yescharacteristic
436C22×D3—21no—
437C22×D3—22no—
438C22×D3—21no—
439C22×D3—22no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3C2×#4114yes—
449C22×D32−1+412yes—
450C3×Q8—28no—
451C3×Q8—48no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—24no—
457C2×C3×C4—22no—
458C2×C3×C4—24no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—24no—
468C2×C3×C4C22×D412yes—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C2×#4114yes—
472C2×C3×C4C2×#4112yes—
473C2×C3×C4C2×#4112yes—
474C2×C3×C4H(5,𝔽2)12yes—
475C2×C3×C42−1+412yes—
476C2×Dic3—21no—
477C2×Dic3—24no—
478C2×Dic3—24no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—22no—
487C2×Dic3—21no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—21no—
495C2×Dic3C22×D418yes—
496C2×Dic32−1+412yes—
497D12—28no—
498D12—48no—
499C4×D3—28no—
500C4×D3—416no—
501C4×D3—44no—
502C4×D3—48no—
503C4×D3—44no—
504Dic6—216no—
505Dic6—416no—
506C24—32no—
507C24—31no—
508C2×Q8—22no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—22no—
512C2×Q8—24no—
513C2×Q8—38no—
514C2×Q8—68no—
515C2×Q8—64no—
516C2×Q8—68no—
517C2×Q8—64no—
518C2×Q8—124no—
519C2×Q8—1232no—
520C2×Q8#23914yes—
521C2×D4—34no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4—62no—
525C2×D4—62no—
526C2×D4—122no—
527C22×C4—31no—
528C22×C4—34no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—32no—
533C22×C4—31no—
534C22×C4—62no—
535C22×C4—68no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—64no—
541C22×C4—62no—
542C22×C4—68no—
543C22×C4—64no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—64no—
547C22×C4—62no—
548C22×C4—124no—
549C22×C4C23×D312yes—
550C22×C4C23×D312yes—
551C22×C4C23×D314yes—
552C22×C4C23×D312yes—
553C22×C4C23×D311yescharacteristic
554C22×C4C23×D312yes—
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D311yescharacteristic
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—22no—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—38no—
564C4⋊C4—38no—
565C4⋊C4—68no—
566C4⋊C4—68no—
567C4⋊C4—68no—
568C4⋊C4—64no—
569C4⋊C4—62no—
570C4⋊C4—64no—
571C4⋊C4—62no—
572C4⋊C4—62no—
573C4⋊C4—122no—
574C4⋊C4—124no—
575C22⋊C4—68no—
576C22⋊C4—68no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—68no—
580C22⋊C4—68no—
581C22⋊C4—64no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C42—24no—
587C42—24no—
588C42—68no—
589C42—62no—
590C42—62no—
591C42—62no—
592C42—64no—
593C42—124no—
594C42D3×D414yes—
595C22×C3C23×D411yescharacteristic
596C22×C3C22×#4111yescharacteristic
597C22×C3C22×#4111yescharacteristic
598C22×C3C2×H(5,𝔽2)11yescharacteristic
599C22×C3C2×2−1+411yescharacteristic
600C22×C3C2×2−1+411yescharacteristic
601C22×C3C2×2−1+411yescharacteristic
602C2×D3—24no—
603C2×D3—24no—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—24no—
607C2×D3—22no—
608C2×D3—42no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—41no—
615C2×D3—42no—
616C3×C4—24no—
617C3×C4—22no—
618C3×C4—44no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4#54614yes—
623C3×C4#54814yes—
624Dic3—28no—
625Dic3—22no—
626Dic3—42no—
627Dic3—41no—
628Dic3—41no—
629Dic3—42no—
630Dic3—42no—
631C23—34no—
632C23—32no—
633C23—61no—
634C23—62no—
635C23—61no—
636C23—62no—
637C23—61no—
638C23—61no—
639C23—62no—
640C23—61no—
641C23—62no—
642C23—62no—
643C23—61no—
644C23—62no—
645C23C24×D311yescharacteristic
646Q8—28no—
647Q8—48no—
648Q8—616no—
649Q8—1216no—
650D4—68no—
651D4—128no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—38no—
669C2×C4—32no—
670C2×C4—68no—
671C2×C4—61no—
672C2×C4—64no—
673C2×C4—64no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—61no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—1216no—
691C2×C4—124no—
692C2×C4—128no—
693C2×C4—124no—
694C2×C4C2×D3×D412yes—
695C2×C4C2×D3×D412yes—
696C2×C4C2×D3×D412yes—
697C2×C4C2×#23914yes—
698C2×C4C2×#23912yes—
699C2×C4D3×#4112yes—
700C2×C4#100912yes—
701C2×C4#101012yes—
702C2×C3C2×#54611yescharacteristic
703C2×C3C2×#54811yescharacteristic
704C2×C3#348211yescharacteristic
705C2×C3#348611yescharacteristic
706C2×C3#352011yescharacteristic
707C2×C3#352311yescharacteristic
708C2×C3#355011yescharacteristic
709D3—44no—
710D3—42no—
711C22—64no—
712C22—62no—
713C22—62no—
714C22—64no—
715C22—64no—
716C22—62no—
717C22—121no—
718C22—122no—
719C22—121no—
720C22—122no—
721C22—122no—
722C22—121no—
723C22—121no—
724C22—122no—
725C22C22×D3×D411yescharacteristic
726C22C22×#23911yescharacteristic
727C22C2×D3×#4111yescharacteristic
728C22C2×#100911yescharacteristic
729C22C2×#101011yescharacteristic
730C22D3×2−1+411yescharacteristic
731C22D3×2−1+411yescharacteristic
732C4—22no—
733C4—24no—
734C4—44no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—62no—
739C4—68no—
740C4—121no—
741C4—122no—
742C4—122no—
743C4—121no—
744C4—122no—
745C4#563014yes—
746C4#567714yes—
747C3#5904211yescharacteristic, complemented, Sylow
748C2—124no—
749C2—122no—
750C2C2×#563011yescharacteristic
751C2C2×#567711yescharacteristic
752C2#8635511yescharacteristic
753C2#8699011yescharacteristic
754C2#8699511yescharacteristic
755C2#8701711yescharacteristic
756C2#8702411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2568C2
prime radicalC2×#895C22
hypercenter#2568D3
hypocenterC3#59042
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2568

Complements

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

NH ≅ G/Ntype
1. C2×#5728C2semidirect
2. C2×Q8×D12C2semidirect
3. C3×#2568C2semidirect
4. #83240C2semidirect
5. C4×#946C2semidirect
6. #78237C2semidirect
7. #78143C2semidirect
8. #76633C2semidirect
10. #76619C2semidirect
11. #76614C2semidirect
12. #76508C2semidirect
13. #76493C2semidirect
14. #74240C2semidirect
15. #74232C2semidirect
17. #73651C2semidirect
89. #2568D3semidirect
173. #869D4semidirect
747. C3#59042semidirect

Maximal subgroups

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

subgroupindex
C2×#57282
C2×Q8×D122
C3×#25682
#832402
C4×#9462
#782372
#781432
#766332
#766242
#766192
#766142
#765082
#764932
#742402
#742322
C4×#8952
#736512
#590423