Finite Group Databasebeta

← #11633958

Subgroups — #11633958

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×C3×#533C211yesmaximal, characteristic, complemented
2C2×#5727C211yesmaximal, characteristic, complemented
3#83244C211yesmaximal, characteristic, complemented
4#83240C211yesmaximal, characteristic, complemented
5#83229C211yesmaximal, characteristic, complemented
6#83068C214yesmaximal, complemented
7#82777C212yesmaximal, complemented
8#82773C212yesmaximal, complemented
9#82756C212yesmaximal
10#82751C212yesmaximal, complemented
11#82493C212yesmaximal, complemented
12Q8×(C2×D3)⋊C4C212yesmaximal, complemented
13#82470C212yesmaximal, complemented
14#82466C212yesmaximal, complemented
15#82281C214yesmaximal, complemented
16C4×#924C211yesmaximal, characteristic, complemented
17C4×#930C211yesmaximal, characteristic
18#59042—31nomaximal, Sylow
19C22×D3×Q8C2212yes—
20C3×#533—28no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×C4⋊Q8C2211yescharacteristic
23C2×C3×#125C2212yes—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×C22⋊Q8C2212yes—
26C2×C3×C4×Q8C2212yes—
27C2×C3×C4×Q8C2212yes—
28C2×C3×#117C2212yes—
29C22×C3×C42C2211yescharacteristic
30C2×#947C2212yes—
31C2×#946C2212yes—
32C2×Q8×Dic3C2212yes—
33C2×#930C2211yescharacteristic
34C2×C4×#67C2212yes—
35C2×#924C2211yescharacteristic
36#5727—28no—
37C2×#896C2214yes—
38C2×#893C2212yes—
39C2×#888C2212yes—
40C2×C4×D12C2211yescharacteristic
41C2×C4×Dic6C2211yescharacteristic
42#5229C2212yes—
43#5229C2212yes—
44#5229C2212yes—
45#5229C2212yes—
46#5213C2212yes—
47#5212C2211yescharacteristic
48#5212C2211yescharacteristic
49#5210C2212yes—
50C4×#217C2212yes—
51#4992C2214yes—
52#4992C2214yes—
53#4990C2214yes—
54#4989C2214yes—
55#4987C2212yes—
56#4987C2212yes—
57#4987C2214yes—
58#4985C2214yes—
59#4985C2214yes—
60#4984C2212yes—
61#4982C2214yes—
62#4980C2214yes—
63#4979C2214yes—
64#4977C2212yes—
65Dic3×C4⋊C4C2212yes—
66#4973C2212yes—
67#4973C2214yes—
68#4961C2214yes—
69#4956C2214yes—
70#4947C2214yes—
71#4945C2214yes—
72#4940C2214yes—
73#4940C2212yes—
74#4939C2211yescharacteristic
75C4×(C2×D3)⋊C4C2214yes—
76C4×(C2×D3)⋊C4C2212yes—
77C4×C4⋊Dic3C2211yescharacteristic
78C4×C4⋊Dic3C2211yescharacteristic
79#4933C2214yes—
80#4933C2212yes—
81C4×Dic3⋊C4C2212yes—
82#4929C2214yes—
83#4929C2211yescharacteristic
84#4928C2211yescharacteristic
85#4928C2211yescharacteristic
86C2×D4×Q8—31no—
87C2×#533D311yescharacteristic, complemented
88#2690—34no—
89#2568—31no—
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×Q8C2312yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C2×D3×Q8—28no—
110C2×D3×Q8—28no—
111C2×D3×Q8—44no—
112C22×D12C2311yescharacteristic
113C22×C4×D3C2312yes—
114C22×C4×D3C2314yes—
115C22×Dic6C2314yes—
116C22×Dic6C2311yescharacteristic
117C3×C4⋊Q8—24no—
118C3×C4⋊Q8D418yescomplemented
119C3×#125—28no—
120C3×C22⋊Q8—28no—
121C3×C22⋊Q8—28no—
122C3×C4×Q8—28no—
123C3×C4×Q8—28no—
124C3×#117—28no—
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C42—24no—
133C2×C3×C42C2311yescharacteristic
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2314yes—
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C2×#217C2312yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141#947—28no—
142#946—28no—
143Q8×Dic3—44no—
144#930—24no—
145C4×#67—44no—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2314yes—
160#924—24no—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2312yes—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2314yes—
170#896—216no—
171#893—28no—
172#888—28no—
173C4×D12—24no—
174C4×Dic6—24no—
175C3⋊#95C2312yes—
176C3⋊#95C2312yes—
177C3⋊#95C2312yes—
178C3⋊#95C2312yes—
179C3⋊#95C2314yes—
180C3⋊#95C2314yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C23×Q8—32no—
192D4×Q8—68no—
193#533—28no—
194C2×C4⋊Q8—32no—
195C2×C4⋊Q8C2×D311yescharacteristic
196C2×C4⋊Q8C2×D311yescharacteristic
197C2×#125C2×D312yes—
198C2×#124—32no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—31no—
201C2×C22⋊Q8—34no—
202C2×C22⋊Q8C2×D312yes—
203C2×C22⋊Q8C2×D312yes—
204C2×#121—31no—
205C2×C4×Q8—32no—
206C2×C4×Q8—31no—
207C2×C4×Q8C2×D312yes—
208C2×C4×Q8C2×D312yes—
209C2×C4×D4—32no—
210C2×C4×D4—32no—
211C2×C4×D4—31no—
212C2×#117C2×D312yes—
213C22×C42C2×D311yescharacteristic
214#400—34no—
215#400—34no—
216#398—34no—
217#397—34no—
218#397—34no—
219#395—34no—
220#394—34no—
221#393—34no—
222#391—32no—
223#391—32no—
224#391—32no—
225#391—32no—
226#391—32no—
227#391—34no—
228#391—31no—
229#391—34no—
230#390—31no—
231#389—32no—
232#389—31no—
233#389—31no—
234#388—34no—
235#388—34no—
236#388—34no—
237#388—32no—
238#387—34no—
239#387—34no—
240#387—32no—
241#386—32no—
242#386—34no—
243#385—32no—
244#385—34no—
245#382—32no—
246#380—31no—
247#380—31no—
248#380—34no—
249#380—32no—
250#380—32no—
251C4×C4⋊C4—32no—
252C4×C4⋊C4—31no—
253C4×C4⋊C4—31no—
254C4×C4⋊C4—32no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—34no—
257C4×C22⋊C4—32no—
258C24×C3C2411yescharacteristic
259C23×D3C2412yes—
260C2×C3×Q8—24no—
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8—24no—
265C2×C3×Q8C2×D418yes—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2414yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2414yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C2×#67—24no—
284C2×#67—24no—
285C2×#67—42no—
286C22×Dic3C2412yes—
287C22×Dic3C2412yes—
288C22×Dic3C2412yes—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293D3×Q8—432no—
294C2×D12—22no—
295C2×D12—22no—
296C2×D12#4114yes—
297C2×C4×D3—24no—
298C2×C4×D3—28no—
299C2×C4×D3—24no—
300C2×C4×D3—24no—
301C2×C4×D3—28no—
302C2×C4×D3—44no—
303C2×Dic6—22no—
304C2×Dic6—22no—
305C2×Dic6—28no—
306C2×Dic6—28no—
307C2×Dic6—44no—
308C2×Dic6#4114yes—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—28no—
311C3×C4⋊C4—28no—
312C3×C4⋊C4—24no—
313C3×C4⋊C4C2×D418yes—
314C3×C4⋊C4C2×D418yes—
315C3×C22⋊C4—28no—
316C3×C42—22no—
317C3×C42—22no—
318C3×C42—22no—
319C3×C42—28no—
320C3×C42C2×D414yes—
321#217—24no—
322#217—24no—
323#217—42no—
324(C2×D3)⋊C4—24no—
325(C2×D3)⋊C4—28no—
326(C2×D3)⋊C4—28no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—28no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—42no—
331C4⋊Dic3—22no—
332C4⋊Dic3—22no—
333C4⋊Dic3—22no—
334C4⋊Dic3—22no—
335C4⋊Dic3—22no—
336C4⋊Dic3—22no—
337C4⋊Dic3—44no—
338Dic3⋊C4—24no—
339Dic3⋊C4—28no—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342Dic3⋊C4—42no—
343C4×Dic3—24no—
344C4×Dic3—24no—
345C4×Dic3—24no—
346C4×Dic3—44no—
347C22×Q8—31no—
348C22×Q8—34no—
349C22×Q8—68no—
350C22×Q8—68no—
351C22×Q8—124no—
352C22×Q8C22×D312yes—
353C22×Q8C22×D312yes—
354C22×D4—32no—
355C22×D4—31no—
356C23×C4—32no—
357C23×C4—34no—
358C23×C4C22×D311yescharacteristic
359C23×C4C22×D311yescharacteristic
360C23×C4C22×D311yescharacteristic
361C4⋊Q8—24no—
362C4⋊Q8—68no—
363C4⋊Q8#6718yescomplemented
364#125—28no—
365#124—68no—
366C22⋊Q8—28no—
367C22⋊Q8—28no—
368C22⋊Q8—64no—
369C22⋊Q8—68no—
370C22⋊Q8—616no—
371#121—64no—
372C4×Q8—28no—
373C4×Q8—28no—
374C4×Q8—64no—
375C4×Q8—124no—
376C4×D4—68no—
377C4×D4—64no—
378C4×D4—124no—
379#117—28no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4C22×D312yes—
393C2×C4⋊C4C22×D314yes—
394C2×C4⋊C4C22×D314yes—
395C2×C4⋊C4C22×D312yes—
396C2×C4⋊C4C22×D312yes—
397C2×C4⋊C4C22×D312yes—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—32no—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—34no—
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⋊C4C22×D314yes—
409C2×C42—24no—
410C2×C42—32no—
411C2×C42—32no—
412C2×C42—32no—
413C2×C42—34no—
414C2×C42C22×D314yes—
415C2×C42C22×D311yescharacteristic
416C2×C42C22×D311yescharacteristic
417C2×C42C22×D311yescharacteristic
418C2×C42C22×D311yescharacteristic
419#95—32no—
420#95—32no—
421#95—32no—
422#95—34no—
423#95—32no—
424#95—32no—
425#95—32no—
426#95—32no—
427#95—34no—
428#95—32no—
429#95—34no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—34no—
434#95—34no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C32−1+412yes—
442C23×C3C2511yescharacteristic
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3—22no—
449C22×D3C2×#4114yes—
450C3×Q8—216no—
451C3×Q8—48no—
452C2×C3×C4—28no—
453C2×C3×C4—21no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—24no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—24no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—24no—
468C2×C3×C4—44no—
469C2×C3×C4—44no—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C22×D418yes—
472C2×C3×C4C22×D412yes—
473C2×C3×C4C22×D412yes—
474C2×C3×C4C2×#4112yes—
475C2×C3×C4C2×#4112yes—
476C2×C3×C4H(5,𝔽2)12yes—
477C2×C3×C42−1+412yes—
478C2×C3×C42−1+412yes—
479#67—48no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3C2×#4114yes—
501D12—28no—
502C4×D3—416no—
503C4×D3—48no—
504Dic6—28no—
505Dic6—416no—
506C24—32no—
507C24C23×D311yescharacteristic
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—24no—
512C2×Q8—24no—
513C2×Q8—34no—
514C2×Q8—68no—
515C2×Q8—62no—
516C2×Q8—62no—
517C2×Q8—68no—
518C2×Q8—124no—
519C2×Q8—1232no—
520C2×Q8C2×#6718yes—
521C2×D4—34no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4—62no—
525C2×D4—62no—
526C2×D4—122no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—68no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—68no—
547C22×C4—64no—
548C22×C4—124no—
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D314yes—
551C22×C4C23×D311yescharacteristic
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D311yescharacteristic
554C22×C4C23×D314yes—
555C22×C4C23×D311yescharacteristic
556C22×C4C23×D311yescharacteristic
557C4⋊C4—24no—
558C4⋊C4—28no—
559C4⋊C4—28no—
560C4⋊C4—24no—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—62no—
564C4⋊C4—62no—
565C4⋊C4—62no—
566C4⋊C4—62no—
567C4⋊C4—62no—
568C4⋊C4—64no—
569C4⋊C4—62no—
570C4⋊C4—68no—
571C4⋊C4—122no—
572C4⋊C4—124no—
573C4⋊C4C2×#6718yes—
574C4⋊C4C2×#6718yes—
575C22⋊C4—28no—
576C22⋊C4—64no—
577C22⋊C4—68no—
578C22⋊C4—68no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—64no—
582C22⋊C4—68no—
583C22⋊C4—64no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—28no—
590C42—64no—
591C42—64no—
592C42—64no—
593C42—124no—
594C42C2×#6714yes—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3C23×D411yescharacteristic
603C22×C3C22×#4111yescharacteristic
604C22×C3C22×#4111yescharacteristic
605C22×C3C2×H(5,𝔽2)11yescharacteristic
606C22×C3C2×2−1+411yescharacteristic
607C22×C3C2×2−1+411yescharacteristic
608C22×C3C2×2−1+411yescharacteristic
609C2×D3—24no—
610C2×D3—24no—
611C2×D3—24no—
612C2×D3—42no—
613C2×D3—42no—
614C2×D3—42no—
615C2×D3—42no—
616C3×C4—28no—
617C3×C4—22no—
618C3×C4—22no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—44no—
622C3×C4#54614yes—
623C3×C4#54814yes—
624Dic3—24no—
625Dic3—42no—
626Dic3—42no—
627Dic3—42no—
628Dic3—42no—
629Dic3—42no—
630Dic3—42no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—34no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23#100712yes—
645C23C24×D311yescharacteristic
646Q8—216no—
647Q8—48no—
648Q8—68no—
649Q8—1216no—
650D4—68no—
651D4—128no—
652C2×C4—28no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—24no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—24no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—24no—
668C2×C4—34no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—1216no—
692C2×C4—128no—
693C2×C4#100712yes—
694C2×C4D3×#4112yes—
695C2×C4D3×#4112yes—
696C2×C4#100912yes—
697C2×C4#101012yes—
698C2×C4C22×#6712yes—
699C2×C4C22×#6718yes—
700C2×C4C22×#6712yes—
701C2×C4C22×#6712yes—
702C2×C3—42no—
703C2×C3C2×#54611yescharacteristic
704C2×C3C2×#54811yescharacteristic
705C2×C3#348211yescharacteristic
706C2×C3#348611yescharacteristic
707C2×C3#352011yescharacteristic
708C2×C3#352311yescharacteristic
709C2×C3#355011yescharacteristic
710D3—44no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—64no—
719C22—64no—
720C22—64no—
721C22—122no—
722C22—122no—
723C22—122no—
724C22—122no—
725C22C2×#100711yescharacteristic
726C22C2×#100711yescharacteristic
727C22C2×D3×#4111yescharacteristic
728C22C2×D3×#4111yescharacteristic
729C22C2×#100911yescharacteristic
730C22C2×#101011yescharacteristic
731C22C23×#6711yescharacteristic
732C4—22no—
733C4—22no—
734C4—28no—
735C4—41no—
736C4—41no—
737C4—44no—
738C4—64no—
739C4—122no—
740C4—122no—
741C4—122no—
742C4—122no—
743C4—122no—
744C4—122no—
745C4#582914yes—
746C4#583114yes—
747C3#5904211yescharacteristic, complemented, Sylow
748C2—42no—
749C2—124no—
750C2#8626611yescharacteristic
751C2#8626711yescharacteristic
752C2#8627811yescharacteristic
753C2#8628511yescharacteristic
754C2#8725111yescharacteristic
755C2C2×#582911yescharacteristic
756C2C2×#583111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#533C2
prime radicalC2×#930C22
hypercenterC2×#533D3
hypocenterC3#59042
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C3×#533C2semidirect
2. C2×#5727C2semidirect
3. #83244C2semidirect
4. #83240C2semidirect
5. #83229C2semidirect
6. #83068C2semidirect
7. #82777C2semidirect
8. #82773C2semidirect
10. #82751C2semidirect
11. #82493C2semidirect
12. Q8×(C2×D3)⋊C4C2semidirect
13. #82470C2semidirect
14. #82466C2semidirect
15. #82281C2semidirect
16. C4×#924C2semidirect
87. C2×#533D3semidirect
118. C3×C4⋊Q8D4semidirect
363. C4⋊Q8#67semidirect
747. C3#59042semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5332
C2×#57272
#832442
#832402
#832292
#830682
#827772
#827732
#827562
#827512
#824932
Q8×(C2×D3)⋊C42
#824702
#824662
#822812
C4×#9242
C4×#9302
#590423