Finite Group Databasebeta

← #11633816

Subgroups — #11633816

Order 768.

2458 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#533C211yesmaximal, characteristic, complemented
2C2×#5726C211yesmaximal, characteristic, complemented
3#83260C211yesmaximal, characteristic, complemented
4#83260C211yesmaximal, characteristic, complemented
5#83229C211yesmaximal, characteristic, complemented
6#83061C212yesmaximal, complemented
7#83028C212yesmaximal, complemented
8#82812C212yesmaximal, complemented
9#82798C214yesmaximal, complemented
10#82777C212yesmaximal, complemented
11#82497C214yesmaximal, complemented
12#82493C212yesmaximal, complemented
13#82457C212yesmaximal, complemented
14#82276C212yesmaximal, complemented
15#82272C212yesmaximal, complemented
16C4×#930C211yesmaximal, characteristic, complemented
17C4×#930C211yesmaximal, characteristic, complemented
18#59034—31nomaximal, Sylow
19C22×#239C2212yes—
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×#946C2212yes—
31C2×Q8×Dic3C2212yes—
32C2×#930C2211yescharacteristic
33C2×#930C2211yescharacteristic
34C2×C4×#67C2212yes—
35C2×C4×#67C2212yes—
36#5726—28no—
37C2×#895C2212yes—
38C2×#894C2214yes—
39C2×D3×C4⋊C4C2212yes—
40C2×C4×D12C2211yescharacteristic
41C2×C4×D12C2211yescharacteristic
42#5231C2214yes—
43#5231C2214yes—
44#5229C2212yes—
45#5213C2212yes—
46#5213C2212yes—
47#5212C2211yescharacteristic
48#5212C2211yescharacteristic
49#4992C2214yes—
50#4991C2214yes—
51#4990C2214yes—
52#4989C2214yes—
53#4988C2212yes—
54#4988C2214yes—
55#4988C2212yes—
56#4987C2212yes—
57#4987C2214yes—
58#4987C2212yes—
59#4987C2212yes—
60#4987C2212yes—
61#4985C2214yes—
62#4984C2212yes—
63#4982C2214yes—
64#4980C2214yes—
65#4977C2212yes—
66#4977C2212yes—
67Dic3×C4⋊C4C2212yes—
68#4961C2214yes—
69#4960C2214yes—
70#4956C2214yes—
71#4945C2214yes—
72#4940C2214yes—
73#4940C2212yes—
74#4940C2212yes—
75#4939C2211yescharacteristic
76#4939C2214yes—
77#4939C2211yescharacteristic
78C4×(C2×D3)⋊C4C2212yes—
79C4×(C2×D3)⋊C4C2214yes—
80C4×(C2×D3)⋊C4C2212yes—
81C4×C4⋊Dic3C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83#4933C2214yes—
84#4928C2211yescharacteristic
85#4928C2211yescharacteristic
86C2×#547—31no—
87C2×#533D311yescharacteristic, complemented
88#2696—34no—
89#2563—31no—
90#2563—31no—
91#2536—32no—
92#2490—32no—
93#2458—34no—
94#2442—32no—
95#2421—32no—
96#2414—32no—
97#2407—32no—
98#2365—31no—
99#2352—32no—
100#2341—32no—
101C4×#121—31no—
102C4×#121—31no—
103C22×C3×Q8C2312yes—
104C22×C3×Q8C2312yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C22×#67C2312yes—
110C2×#239—28no—
111C2×#239—28no—
112C2×#239—44no—
113C22×D12C2311yescharacteristic
114C22×D12C2314yes—
115C22×D12C2311yescharacteristic
116C22×C4×D3C2312yes—
117C22×C4×D3C2312yes—
118C22×C4×D3C2314yes—
119C3×C4⋊Q8—24no—
120C3×C4⋊Q8D418yescomplemented
121C3×#125—28no—
122C3×C22⋊Q8—28no—
123C3×C22⋊Q8—28no—
124C3×C4×Q8—28no—
125C3×C4×Q8—28no—
126C3×#117—28no—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2314yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C42—24no—
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C2×C3×C42C2314yes—
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C2×#217C2312yes—
141C2×#217C2312yes—
142#946—28no—
143Q8×Dic3—44no—
144#930—24no—
145#930—24no—
146C4×#67—28no—
147C4×#67—44no—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2312yes—
151C2×(C2×D3)⋊C4C2312yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2312yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×C4⋊Dic3C2311yescharacteristic
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4⋊Dic3C2314yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2312yes—
171C2×C4×Dic3C2312yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2314yes—
174#895—28no—
175#894—216no—
176D3×C4⋊C4—28no—
177C4×D12—24no—
178C4×D12—24no—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C22×#41—32no—
192#547—68no—
193#533—28no—
194C2×C4⋊Q8C2×D311yescharacteristic
195C2×C4⋊Q8C2×D311yescharacteristic
196C2×#125C2×D312yes—
197C2×#123—34no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8C2×D312yes—
200C2×C22⋊Q8C2×D312yes—
201C2×#121—31no—
202C2×#121—31no—
203C2×#121—32no—
204C2×C4×Q8—32no—
205C2×C4×Q8C2×D312yes—
206C2×C4×Q8C2×D312yes—
207C2×C4×D4—32no—
208C2×C4×D4—32no—
209C2×C4×D4—31no—
210C2×C4×D4—31no—
211C2×#117C2×D312yes—
212C22×C4⋊C4—32no—
213C22×C42C2×D311yescharacteristic
214#400—34no—
215#398—34no—
216#397—34no—
217#394—34no—
218#394—34no—
219#393—34no—
220#393—34no—
221#392—34no—
222#391—32no—
223#390—32no—
224#390—32no—
225#390—34no—
226#390—31no—
227#390—34no—
228#390—31no—
229#389—32no—
230#389—31no—
231#389—31no—
232#388—34no—
233#388—34no—
234#388—34no—
235#388—32no—
236#388—32no—
237#387—34no—
238#387—34no—
239#386—32no—
240#386—32no—
241#386—34no—
242#385—34no—
243#382—32no—
244#382—32no—
245#380—31no—
246#380—31no—
247#380—32no—
248#380—32no—
249#380—32no—
250#380—32no—
251#380—34no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4—31no—
254C4×C4⋊C4—31no—
255C4×C22⋊C4—34no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—32no—
258C24×C3C2411yescharacteristic
259C23×D3C2412yes—
260C23×D3C2412yes—
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8—42no—
265C2×C3×Q8—42no—
266C2×C3×Q8C2×D418yes—
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—41no—
274C22×C3×C4—41no—
275C22×C3×C4#4114yescomplemented
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2414yes—
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2414yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C2×#67—24no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—42no—
288C2×#67—42no—
289C2×#67—42no—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C22×Dic3C2412yes—
295C22×Dic3C2412yes—
296#239—432no—
297C2×D12—22no—
298C2×D12—22no—
299C2×D12—28no—
300C2×D12—22no—
301C2×D12—28no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—44no—
305C2×D12#4114yes—
306C2×C4×D3—28no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—28no—
310C2×C4×D3—24no—
311C2×C4×D3—24no—
312C2×C4×D3—24no—
313C2×C4×D3—24no—
314C2×C4×D3—44no—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—28no—
317C3×C4⋊C4—28no—
318C3×C4⋊C4—24no—
319C3×C4⋊C4C2×D418yes—
320C3×C4⋊C4C2×D418yes—
321C3×C22⋊C4—28no—
322C3×C42—22no—
323C3×C42—22no—
324C3×C42—22no—
325C3×C42—28no—
326C3×C42C2×D414yes—
327#217—24no—
328#217—42no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—24no—
332(C2×D3)⋊C4—28no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—42no—
336(C2×D3)⋊C4—42no—
337(C2×D3)⋊C4—44no—
338(C2×D3)⋊C4—44no—
339(C2×D3)⋊C4—44no—
340(C2×D3)⋊C4—44no—
341(C2×D3)⋊C4—42no—
342C4⋊Dic3—22no—
343C4⋊Dic3—22no—
344C4⋊Dic3—22no—
345C4⋊Dic3—22no—
346C4⋊Dic3—22no—
347C4⋊Dic3—22no—
348C4⋊Dic3—44no—
349Dic3⋊C4—28no—
350Dic3⋊C4—24no—
351Dic3⋊C4—42no—
352C4×Dic3—24no—
353C4×Dic3—24no—
354C4×Dic3—44no—
355C2×#41—68no—
356C2×#41—68no—
357C2×#41—124no—
358C22×Q8C22×D312yes—
359C22×Q8C22×D312yes—
360C22×D4—32no—
361C22×D4—32no—
362C22×D4—31no—
363C22×D4—31no—
364C22×D4—34no—
365C23×C4—32no—
366C23×C4—32no—
367C23×C4—34no—
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C4⋊Q8—24no—
372C4⋊Q8#6718yescomplemented
373#125—28no—
374#123—616no—
375C22⋊Q8—28no—
376C22⋊Q8—28no—
377C22⋊Q8—68no—
378#121—64no—
379#121—64no—
380#121—68no—
381C4×Q8—28no—
382C4×Q8—28no—
383C4×Q8—124no—
384C4×D4—68no—
385C4×D4—64no—
386C4×D4—64no—
387C4×D4—124no—
388#117—28no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—68no—
400C2×C4⋊C4C22×D312yes—
401C2×C4⋊C4C22×D314yes—
402C2×C4⋊C4C22×D314yes—
403C2×C4⋊C4C22×D312yes—
404C2×C4⋊C4C22×D312yes—
405C2×C4⋊C4C22×D312yes—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4C22×D314yes—
422C2×C42—24no—
423C2×C42—32no—
424C2×C42—32no—
425C2×C42—34no—
426C2×C42C22×D314yes—
427C2×C42C22×D311yescharacteristic
428C2×C42C22×D311yescharacteristic
429C2×C42C22×D311yescharacteristic
430C2×C42C22×D311yescharacteristic
431#95—32no—
432#95—34no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—32no—
437#95—32no—
438#95—34no—
439#95—34no—
440#95—34no—
441#95—34no—
442#95—34no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3C2×#4112yes—
450C23×C3C2511yescharacteristic
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3C2×#4114yes—
465C3×Q8—216no—
466C3×Q8—48no—
467C2×C3×C4—21no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—28no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—24no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—44no—
484C2×C3×C4—44no—
485C2×C3×C4C22×D418yes—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C22×D412yes—
489C2×C3×C4C2×#4112yes—
490C2×C3×C4C2×#4112yes—
491C2×C3×C4C2×#4112yes—
492C2×C3×C4H(5,𝔽2)12yes—
493C2×C3×C42−1+412yes—
494#67—48no—
495#67—48no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514D12—28no—
515D12—416no—
516D12—44no—
517C4×D3—416no—
518C4×D3—48no—
519C4×D3—48no—
520C24—32no—
521C24—32no—
522C24C23×D311yescharacteristic
523#41—1232no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—24no—
527C2×Q8—42no—
528C2×Q8—42no—
529C2×Q8C2×#6718yes—
530C2×D4—34no—
531C2×D4—68no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—64no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—62no—
538C2×D4—62no—
539C2×D4—62no—
540C2×D4—68no—
541C2×D4—124no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—32no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—32no—
555C22×C4—32no—
556C22×C4—32no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—68no—
560C22×C4—64no—
561C22×C4—64no—
562C22×C4—64no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—68no—
566C22×C4—64no—
567C22×C4—124no—
568C22×C4#23914yescomplemented
569C22×C4C23×D311yescharacteristic
570C22×C4C23×D314yes—
571C22×C4C23×D311yescharacteristic
572C22×C4C23×D311yescharacteristic
573C22×C4C23×D311yescharacteristic
574C22×C4C23×D314yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C4⋊C4—24no—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—24no—
581C4⋊C4—64no—
582C4⋊C4—62no—
583C4⋊C4—62no—
584C4⋊C4—62no—
585C4⋊C4—62no—
586C4⋊C4—62no—
587C4⋊C4—68no—
588C4⋊C4—62no—
589C4⋊C4—122no—
590C4⋊C4—124no—
591C4⋊C4C2×#6718yes—
592C4⋊C4C2×#6718yes—
593C22⋊C4—28no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—64no—
600C22⋊C4—68no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—124no—
605C22⋊C4—124no—
606C22⋊C4—124no—
607C22⋊C4—124no—
608C22⋊C4—122no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—28no—
613C42—64no—
614C42—64no—
615C42—124no—
616C42C2×#6714yes—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3C23×D411yescharacteristic
625C22×C3C22×#4111yescharacteristic
626C22×C3C22×#4111yescharacteristic
627C22×C3C2×H(5,𝔽2)11yescharacteristic
628C22×C3C2×2−1+411yescharacteristic
629C22×C3#58511yescharacteristic
630C22×C3#58511yescharacteristic
631C2×D3—24no—
632C2×D3—24no—
633C2×D3—24no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—42no—
645C3×C4—28no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—44no—
651C3×C4#54614yes—
652C3×C4#54814yes—
653Dic3—42no—
654Dic3—42no—
655Dic3—42no—
656Dic3—42no—
657Dic3—42no—
658Dic3—42no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—34no—
666C23—62no—
667C23—62no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—62no—
672C23—62no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23C2×#23912yes—
680C23C24×D311yescharacteristic
681Q8—216no—
682Q8—48no—
683D4—68no—
684D4—1216no—
685D4—128no—
686D4—128no—
687D4—124no—
688C2×C4—21no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—28no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—24no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—1216no—
725C2×C4—128no—
726C2×C4—128no—
727C2×C4C2×#23912yes—
728C2×C4C2×#23912yes—
729C2×C4#100712yes—
730C2×C4D3×#4112yes—
731C2×C4#100912yes—
732C2×C4C22×#6712yes—
733C2×C4C22×#6718yes—
734C2×C4C22×#6712yes—
735C2×C4C22×#6712yes—
736C2×C3—42no—
737C2×C3C2×#54611yescharacteristic
738C2×C3C2×#54811yescharacteristic
739C2×C3#347511yescharacteristic
740C2×C3#348711yescharacteristic
741C2×C3#350611yescharacteristic
742C2×C3#351511yescharacteristic
743C2×C3#354711yescharacteristic
744D3—44no—
745D3—82no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—64no—
754C22—64no—
755C22—64no—
756C22—122no—
757C22—122no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—122no—
762C22—122no—
763C22—122no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22C22×#23911yescharacteristic
768C22C2×#100711yescharacteristic
769C22C2×D3×#4111yescharacteristic
770C22C2×#100911yescharacteristic
771C22#596411yescharacteristic
772C22#596411yescharacteristic
773C22C23×#6711yescharacteristic
774C4—22no—
775C4—28no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—44no—
780C4—122no—
781C4—122no—
782C4—122no—
783C4—122no—
784C4—122no—
785C4—122no—
786C4#581714yes—
787C4#582914yes—
788C3#5903411yescharacteristic, complemented, Sylow
789C2—42no—
790C2—124no—
791C2—242no—
792C2#8625911yescharacteristic
793C2#8627611yescharacteristic
794C2#8628411yescharacteristic
795C2#8628711yescharacteristic
796C2C2×#581711yescharacteristic
797C2C2×#582911yescharacteristic
798C2#8727411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#533C2
hypercenterC2×#533D3
hypocenterC3#59034
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×#5726C2semidirect
3. #83260C2semidirect
4. #83260C2semidirect
5. #83229C2semidirect
6. #83061C2semidirect
7. #83028C2semidirect
8. #82812C2semidirect
9. #82798C2semidirect
10. #82777C2semidirect
11. #82497C2semidirect
12. #82493C2semidirect
13. #82457C2semidirect
14. #82276C2semidirect
15. #82272C2semidirect
16. C4×#930C2semidirect
17. C4×#930C2semidirect
87. C2×#533D3semidirect
120. C3×C4⋊Q8D4semidirect
275. C22×C3×C4#41semidirect
372. C4⋊Q8#67semidirect
568. C22×C4#239semidirect
788. C3#59034semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5332
C2×#57262
#832602
#832292
#830612
#830282
#828122
#827982
#827772
#824972
#824932
#824572
#822762
#822722
C4×#9302
#590343