Finite Group Databasebeta

← #11634174

Subgroups — #11634174

Order 768.

2238 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic, complemented
2C2×#5728C211yesmaximal, characteristic, complemented
3#83230C211yesmaximal, characteristic, complemented
4#83058C212yesmaximal, complemented
5#83037C212yesmaximal, complemented
6#82807C214yesmaximal, complemented
7#82780C212yesmaximal, complemented
8#82757C212yesmaximal, complemented
9#82754C214yesmaximal, complemented
10C4×#946C211yesmaximal, characteristic, complemented
11#82475C211yesmaximal, characteristic, complemented
12C4×#938C211yesmaximal, characteristic
13#82379C211yesmaximal, characteristic, complemented
14#82363C212yesmaximal, complemented
15#82341C212yesmaximal
16#82194C212yesmaximal, complemented
17#82162C212yesmaximal, complemented
18#59052—31nomaximal, Sylow
19C3×#554—28no—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#125C2212yes—
22C2×C3×C22⋊Q8C2214yes—
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×C4×Q8C2211yescharacteristic
25C2×C3×C4×D4C2212yes—
26C2×C3×C4×D4C2211yescharacteristic
27C22×C3×C4⋊C4C2212yes—
28C2×#946C2211yescharacteristic
29C2×#946C2212yes—
30C2×Q8×Dic3C2212yes—
31C2×#944C2212yes—
32C2×#938C2211yescharacteristic
33C2×C4×#67C2212yes—
34C2×#924C2212yes—
35C2×#924C2212yes—
36#5728—28no—
37C2×#897C2212yes—
38C2×#892C2212yes—
39C2×#890C2212yes—
40C2×#887C2212yes—
41C2×C42×D3C2211yescharacteristic
42C2×#869C2211yescharacteristic
43#5229C2214yes—
44#5229C2211yescharacteristic
45#5221C2212yes—
46#5221C2211yescharacteristic
47#5213C2214yes—
48#5212C2214yes—
49#5210C2214yes—
50C4×#217C2214yes—
51C4×#217C2212yes—
52#4994C2214yes—
53#4993C2214yes—
54#4989C2212yes—
55#4987C2211yescharacteristic
56#4987C2211yescharacteristic
57#4984C2212yes—
58#4984C2212yes—
59#4983C2214yes—
60#4981C2214yes—
61#4981C2214yes—
62#4978C2212yes—
63#4978C2214yes—
64#4976C2214yes—
65#4975C2214yes—
66#4975C2212yes—
67Dic3×C4⋊C4C2212yes—
68Dic3×C4⋊C4C2212yes—
69#4973C2212yes—
70#4972C2211yescharacteristic
71#4972C2214yes—
72#4972C2211yescharacteristic
73#4957C2214yes—
74#4956C2212yes—
75#4949C2214yes—
76#4949C2214yes—
77#4948C2214yes—
78#4944C2212yes—
79#4944C2214yes—
80C4×(C2×D3)⋊C4C2212yes—
81C4×C4⋊Dic3C2211yescharacteristic
82C4×C4⋊Dic3C2211yescharacteristic
83C4×Dic3⋊C4C2212yes—
84#4928C2212yes—
85#4928C2212yes—
86C2×#554D311yescharacteristic, complemented
87C2×#533—31no—
88#2732—34no—
89#2552—32no—
90#2546—31no—
91#2542—32no—
92#2542—31no—
93#2454—32no—
94#2441—32no—
95#2429—32no—
96#2423—34no—
97#2417—32no—
98#2369—31no—
99#2363—32no—
100#2360—32no—
101C4×C22⋊Q8—31no—
102C4×#121—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×Q8C2312yes—
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4C2312yes—
107C23×C3×C4C2314yes—
108C22×#67C2312yes—
109C22×C4×D3C2311yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×C4×D3C2311yescharacteristic
112C22×Dic6C2312yes—
113C3×C4⋊Q8D418yescomplemented
114C3×#125—28no—
115C3×C22⋊Q8—216no—
116C3×C22⋊Q8—28no—
117C3×C4×Q8—24no—
118C3×C4×D4—28no—
119C3×C4×D4—24no—
120C2×C3×C4⋊C4—28no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2314yes—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C42C2312yes—
131C2×C3×C42C2311yescharacteristic
132C2×#217C2314yes—
133C2×#217C2314yes—
134C2×#217C2312yes—
135C2×#217C2312yes—
136C2×#217C2312yes—
137#946—28no—
138#946—24no—
139Q8×Dic3—28no—
140#944—44no—
141#938Q818yescomplemented
142C4×#67—44no—
143C2×(C2×D3)⋊C4C2312yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2312yes—
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2314yes—
152C2×C4⋊Dic3C2314yes—
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2311yescharacteristic
155#924—28no—
156#924—44no—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2314yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2314yes—
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2314yes—
170C2×C4×Dic3C2311yescharacteristic
171C2×C4×Dic3C2314yes—
172#897—28no—
173#892—28no—
174#890—28no—
175#887—28no—
176C42×D3—24no—
177#869—24no—
178C3⋊#95C2314yes—
179C3⋊#95C2314yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190#554—28no—
191#533—68no—
192C2×C4⋊Q8—32no—
193C2×C4⋊Q8—31no—
194C2×C4⋊Q8C2×D311yescharacteristic
195C2×#125—32no—
196C2×#125C2×D312yes—
197C2×C22⋊Q8—32no—
198C2×C22⋊Q8—31no—
199C2×C22⋊Q8—32no—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8—32no—
202C2×C22⋊Q8C2×D314yes—
203C2×C22⋊Q8C2×D312yes—
204C2×#121—31no—
205C2×C4×Q8—32no—
206C2×C4×Q8—32no—
207C2×C4×Q8C2×D311yescharacteristic
208C2×C4×D4—32no—
209C2×C4×D4C2×D312yes—
210C2×C4×D4C2×D311yescharacteristic
211C2×#117—32no—
212C22×C4⋊C4C2×D312yes—
213C22×C42—31no—
214#399—34no—
215#399—34no—
216#399—34no—
217#398—34no—
218#398—34no—
219#398—34no—
220#396—34no—
221#396—34no—
222#391—34no—
223#391—31no—
224#391—32no—
225#390—32no—
226#390—31no—
227#390—34no—
228#389—31no—
229#389—34no—
230#389—32no—
231#389—32no—
232#389—34no—
233#389—31no—
234#389—32no—
235#389—32no—
236#388—34no—
237#388—32no—
238#387—34no—
239#387—32no—
240#386—34no—
241#386—32no—
242#385—34no—
243#385—32no—
244#384—34no—
245#384—32no—
246#380—34no—
247#380—31no—
248#380—31no—
249C4×C4⋊C4—32no—
250C4×C4⋊C4—32no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—31no—
253C4×C4⋊C4—32no—
254C4×C22⋊C4—34no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—32no—
257C24×C3C2412yes—
258C23×D3C2411yescharacteristic
259C2×C3×Q8—22no—
260C2×C3×Q8—22no—
261C2×C3×Q8—22no—
262C2×C3×Q8—42no—
263C2×C3×Q8—42no—
264C2×C3×Q8C2×D418yes—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4C2×Q814yes—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4—24no—
271C22×C3×C4—28no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4C2412yes—
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2414yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C2×#67—42no—
282C2×#67—42no—
283C2×#67C2×Q818yes—
284C22×Dic3C2412yes—
285C22×Dic3C2412yes—
286C22×Dic3C2411yescharacteristic
287C22×Dic3C2411yescharacteristic
288C22×Dic3C2414yes—
289C22×Dic3C2411yescharacteristic
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C2×C4×D3—22no—
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—22no—
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3—41no—
299C2×C4×D3—41no—
300C2×C4×D3C2×Q814yes—
301C2×Dic6—24no—
302C2×Dic6—24no—
303C2×Dic6—24no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—28no—
306C3×C4⋊C4—22no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—28no—
309C3×C4⋊C4C2×D418yes—
310C3×C4⋊C4C2×D418yes—
311C3×C22⋊C4—28no—
312C3×C22⋊C4—24no—
313C3×C42—24no—
314C3×C42C2×D414yes—
315#217—28no—
316#217—44no—
317#217—42no—
318#217—42no—
319#217C2×Q818yes—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—24no—
322(C2×D3)⋊C4—42no—
323(C2×D3)⋊C4—42no—
324C4⋊Dic3—24no—
325C4⋊Dic3—24no—
326C4⋊Dic3—28no—
327C4⋊Dic3—22no—
328C4⋊Dic3—22no—
329C4⋊Dic3—44no—
330C4⋊Dic3C2×Q814yes—
331C4⋊Dic3#4114yes—
332Dic3⋊C4—28no—
333Dic3⋊C4—28no—
334Dic3⋊C4—24no—
335Dic3⋊C4—42no—
336Dic3⋊C4—44no—
337Dic3⋊C4—42no—
338Dic3⋊C4—44no—
339Dic3⋊C4—44no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—28no—
344C4×Dic3—24no—
345C4×Dic3—24no—
346C4×Dic3—44no—
347C22×Q8—32no—
348C22×Q8C22×D311yescharacteristic
349C22×Q8C22×D312yes—
350C22×D4—32no—
351C22×D4C22×D311yescharacteristic
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4C22×D312yes—
356C23×C4C22×D314yes—
357C4⋊Q8—64no—
358C4⋊Q8—124no—
359C4⋊Q8#6718yescomplemented
360#125—28no—
361#125—68no—
362C22⋊Q8—216no—
363C22⋊Q8—28no—
364C22⋊Q8—68no—
365C22⋊Q8—64no—
366C22⋊Q8—68no—
367C22⋊Q8—68no—
368C22⋊Q8—124no—
369#121—38no—
370C4×Q8—24no—
371C4×Q8—68no—
372C4×Q8—68no—
373C4×D4—28no—
374C4×D4—24no—
375C4×D4—124no—
376#117—68no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—32no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—34no—
390C2×C4⋊C4—34no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D314yes—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D312yes—
398C2×C4⋊C4C22×D314yes—
399C2×C4⋊C4C22×D312yes—
400C2×C4⋊C4C22×D312yes—
401C2×C22⋊C4—32no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—32no—
410C2×C22⋊C4C22×D312yes—
411C2×C22⋊C4C22×D314yes—
412C2×C42—34no—
413C2×C42—32no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—31no—
417C2×C42—32no—
418C2×C42—34no—
419C2×C42—64no—
420C2×C42C22×D312yes—
421C2×C42C22×D311yescharacteristic
422#95—32no—
423#95—32no—
424#95—32no—
425#95—34no—
426#95—32no—
427#95—32no—
428#95—34no—
429#95—32no—
430#95—32no—
431#95—34no—
432#95—32no—
433#95—34no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3C22×Q814yes—
441C23×C3C2511yescharacteristic
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3C22×Q812yes—
449C3×Q8—48no—
450C3×Q8—44no—
451C3×D4—28no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
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—48no—
466C2×C3×C4—88no—
467C2×C3×C4C22×D418yes—
468C2×C3×C4C22×D412yes—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C22×Q812yes—
472C2×C3×C4C2×#4112yes—
473C2×C3×C4H(5,𝔽2)12yes—
474C2×C3×C42−1+412yes—
475#67—48no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—24no—
485C2×Dic3—21no—
486C2×Dic3—24no—
487C2×Dic3—22no—
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—21no—
497C2×Dic3C22×Q814yes—
498C2×Dic3C22×Q812yes—
499C2×Dic3C2×#4114yes—
500C4×D3—28no—
501C4×D3—44no—
502C4×D3—44no—
503Dic6—48no—
504C24—31no—
505C24C23×D312yes—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—64no—
512C2×Q8—64no—
513C2×Q8—64no—
514C2×Q8C2×#6718yes—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—38no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4D3×Q814yes—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—28no—
525C22×C4—31no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—34no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—34no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—121no—
543C22×C4—121no—
544C22×C4C23×D312yes—
545C22×C4C23×D312yes—
546C22×C4C23×D312yes—
547C22×C4C23×D311yescharacteristic
548C22×C4C23×D314yes—
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C4⋊C4—22no—
552C4⋊C4—28no—
553C4⋊C4—22no—
554C4⋊C4—24no—
555C4⋊C4—28no—
556C4⋊C4—34no—
557C4⋊C4—34no—
558C4⋊C4—64no—
559C4⋊C4—68no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—64no—
563C4⋊C4—68no—
564C4⋊C4—68no—
565C4⋊C4—64no—
566C4⋊C4—122no—
567C4⋊C4—124no—
568C4⋊C4—124no—
569C4⋊C4—124no—
570C4⋊C4—122no—
571C4⋊C4—124no—
572C4⋊C4C2×#6718yes—
573C4⋊C4C2×#6718yes—
574C22⋊C4—28no—
575C22⋊C4—24no—
576C22⋊C4—38no—
577C22⋊C4—64no—
578C22⋊C4—68no—
579C22⋊C4—68no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—124no—
584C22⋊C4—122no—
585C42—24no—
586C42—64no—
587C42—64no—
588C42—62no—
589C42—62no—
590C42—62no—
591C42—68no—
592C42—124no—
593C42C2×#6714yes—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—24no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3C23×D411yescharacteristic
602C22×C3C23×Q811yescharacteristic
603C22×C3C22×#4111yescharacteristic
604C22×C3C2×H(5,𝔽2)11yescharacteristic
605C22×C3C2×2−1+411yescharacteristic
606C22×C3#58511yescharacteristic
607C22×C3#58511yescharacteristic
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C3×C4—22no—
616C3×C4—28no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4D4×Q814yes—
621C3×C4#55014yes—
622Dic3—22no—
623Dic3—24no—
624Dic3—24no—
625Dic3—44no—
626Dic3—41no—
627Dic3—41no—
628Dic3—42no—
629Dic3—42no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—32no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23C2×D3×Q814yes—
644C23C24×D311yescharacteristic
645Q8—48no—
646Q8—44no—
647Q8—128no—
648D4—28no—
649D4—128no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—32no—
664C2×C4—34no—
665C2×C4—34no—
666C2×C4—48no—
667C2×C4—62no—
668C2×C4—61no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—61no—
673C2×C4—68no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—64no—
677C2×C4—61no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4—64no—
682C2×C4—61no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—64no—
689C2×C4—88no—
690C2×C4—124no—
691C2×C4—124no—
692C2×C4C2×D3×Q812yes—
693C2×C4#100712yes—
694C2×C4D3×#4112yes—
695C2×C4#100912yes—
696C2×C4C22×#6712yes—
697C2×C4C22×#6718yes—
698C2×C4C22×#6712yes—
699C2×C4C22×#6712yes—
700C2×C3—44no—
701C2×C3C2×D4×Q811yescharacteristic
702C2×C3C2×#55011yescharacteristic
703C2×C3Q8×#4111yescharacteristic
704C2×C3#348511yescharacteristic
705C2×C3#350111yescharacteristic
706C2×C3#351511yescharacteristic
707C2×C3#354711yescharacteristic
708D3—42no—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—62no—
717C22—62no—
718C22—62no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22C22×D3×Q811yescharacteristic
724C22C2×#100711yescharacteristic
725C22C2×D3×#4111yescharacteristic
726C22C2×#100911yescharacteristic
727C22#596611yescharacteristic
728C22#596611yescharacteristic
729C22C23×#6711yescharacteristic
730C4—28no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—64no—
736C4—64no—
737C4—62no—
738C4—122no—
739C4—122no—
740C4—121no—
741C4—124no—
742C4—121no—
743C4Q8×#6714yes—
744C4#583414yes—
745C3#5905211yescharacteristic, complemented, Sylow
746C2—44no—
747C2—122no—
748C2#8692311yescharacteristic
749C2#8693111yescharacteristic
750C2#8694811yescharacteristic
751C2#8695411yescharacteristic
752C2C2×Q8×#6711yescharacteristic
753C2C2×#583411yescharacteristic
754C2#8728011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#554C2
prime radicalC2×#938C22
hypercenterC2×#554D3
hypocenterC3#59052
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C3×#554C2semidirect
2. C2×#5728C2semidirect
3. #83230C2semidirect
4. #83058C2semidirect
5. #83037C2semidirect
6. #82807C2semidirect
7. #82780C2semidirect
8. #82757C2semidirect
9. #82754C2semidirect
10. C4×#946C2semidirect
11. #82475C2semidirect
13. #82379C2semidirect
14. #82363C2semidirect
16. #82194C2semidirect
17. #82162C2semidirect
86. C2×#554D3semidirect
113. C3×C4⋊Q8D4semidirect
141. #938Q8semidirect
359. C4⋊Q8#67semidirect
745. C3#59052semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5542
C2×#57282
#832302
#830582
#830372
#828072
#827802
#827572
#827542
C4×#9462
#824752
C4×#9382
#823792
#823632
#823412
#821942
#821622
#590523