Finite Group Databasebeta

← #10968223

Subgroups — #10968223

Order 768.

2650 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×D3×C22⋊Q8C211yesmaximal, characteristic
2C22×#896C211yesmaximal, characteristic
3C3×#2583C211yesmaximal, characteristic, complemented
4#82785C211yesmaximal, characteristic, complemented
5#82181C211yesmaximal, characteristic, complemented
6#77966C212yesmaximal, complemented
7#77765C212yesmaximal, complemented
8#77258C212yesmaximal, complemented
9#77173C212yesmaximal, complemented
10#76288C214yesmaximal, complemented
11#76247C214yesmaximal, complemented
12#74591C212yesmaximal
13#74591C212yesmaximal
14#74460C212yesmaximal, complemented
15#74412C212yesmaximal, complemented
16C4×D3×C22⋊C4C211yesmaximal, characteristic
17#73547C211yesmaximal, characteristic, complemented
18#35011—31nomaximal, Sylow
19C22×D3×Q8C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×Dic3⋊C4C2211yescharacteristic
29C22×Dic3⋊C4C2211yescharacteristic
30D3×C22⋊Q8—28no—
31C2×#897C2211yescharacteristic
32C2×#896—28no—
33C2×#896C2212yes—
34C2×#896C2212yes—
35C2×#896C2212yes—
36C2×#896C2212yes—
37C2×#896C2212yes—
38C2×D3×C4⋊C4C2211yescharacteristic
39C2×D3×C4⋊C4C2212yes—
40C2×#888C2214yescomplemented
41C2×D3×C22⋊C4C2212yes—
42C2×D3×C22⋊C4C2212yes—
43C2×#878C2212yes—
44C2×C42×D3C2212yes—
45C3×#398C2212yescomplemented
46C3×#395C2212yescomplemented
47C3×#389C2214yescomplemented
48C3×#385C2212yes—
49C3×#385C2212yes—
50C3×C4×C22⋊C4C2211yescharacteristic
51#5230C2212yescomplemented
52#5210C2212yes—
53#5210C2212yes—
54C4×#217C2211yescharacteristic
55#4989C2214yes—
56#4989C2214yes—
57#4987C2214yes—
58#4987C2214yes—
59#4983C2212yescomplemented
60#4982C2214yescomplemented
61#4981C2212yescomplemented
62#4979C2212yescomplemented
63#4979C2214yescomplemented
64#4976C2214yescomplemented
65#4976C2214yescomplemented
66#4975C2214yescomplemented
67#4950C2212yes—
68#4950C2212yes—
69#4946C2212yes—
70#4946C2212yes—
71Dic3×C22⋊C4C2212yes—
72C4×(C2×D3)⋊C4C2212yes—
73#4928C2214yescomplemented
74#4668C2214yes—
75#4668C2214yes—
76#4667C2214yes—
77#4667C2214yes—
78#4666C2212yes—
79D3×#95C2212yes—
80#4661C2212yescomplemented
81#4657C2214yescomplemented
82#4656C2212yescomplemented
83#4656C2214yescomplemented
84#4646C2214yescomplemented
85#4646C2214yescomplemented
86C22×C22⋊Q8—31no—
87C22×C22⋊Q8—31no—
88#2857—34no—
89#2659—32no—
90#2659—32no—
91#2583—34no—
92#2583—31no—
93#2583—31no—
94#2583—31no—
95#2583D311yescharacteristic, complemented
96#2502—32no—
97#2502—32no—
98#2434—32no—
99#2434—32no—
100#2315—32no—
101#2315—32no—
102C2×C4×C22⋊C4—31no—
103C24×D3C2311yescharacteristic
104C22×C3×Q8C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C2×D3×Q8—24no—
112C2×D3×Q8—44no—
113C22×C4×D3—44no—
114C22×C4×D3D418yes—
115C22×C4×D3C2311yescharacteristic
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2312yes—
118C22×C4×D3C2312yes—
119C22×C4×D3C2311yescharacteristic
120C22×C4×D3C2311yescharacteristic
121C22×C4×D3C2314yes—
122C22×Dic6—24no—
123C22×Dic6—44no—
124C22×Dic6C2312yes—
125C22×Dic6C2312yes—
126C22×Dic6C2312yes—
127C22×Dic6C2311yescharacteristic
128C3×C22⋊Q8—24no—
129C2×C3×C4⋊C4—24no—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C42C2312yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141#946—24no—
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—24no—
144C2×(C2×D3)⋊C4C2312yes—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2312yes—
149C2×(C2×D3)⋊C4C2312yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2314yes—
155#924—24no—
156C2×Dic3⋊C4—24no—
157C2×Dic3⋊C4—24no—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×C4×Dic3C2314yes—
170C2×C4×Dic3C2312yes—
171#897—24no—
172#896—28no—
173#896—28no—
174#896—28no—
175#896—28no—
176#896—28no—
177D3×C4⋊C4—28no—
178D3×C4⋊C4—24no—
179#888—48no—
180D3×C22⋊C4—28no—
181D3×C22⋊C4Q8116yescomplemented
182#878—28no—
183C42×D3—44no—
184C3×#95C2314yes—
185C3×#95C2314yes—
186C3×#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C3⋊#95C2312yes—
195C23×Q8—31no—
196C23×Q8—31no—
197C24×C4—31no—
198C2×C4⋊Q8—34no—
199C2×C22⋊Q8—31no—
200C2×C22⋊Q8—31no—
201C2×C22⋊Q8—32no—
202C2×C22⋊Q8—32no—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8—31no—
206C2×C22⋊Q8—32no—
207C2×C22⋊Q8—32no—
208C2×C22⋊Q8—68no—
209C2×C22⋊Q8—68no—
210C2×C22⋊Q8C2×D311yescharacteristic
211C22×C4⋊C4—31no—
212C22×C4⋊C4—31no—
213C22×C4⋊C4—32no—
214C22×C4⋊C4—31no—
215C22×C4⋊C4C2×D311yescharacteristic
216C22×C22⋊C4—32no—
217C22×C22⋊C4—31no—
218C22×C22⋊C4—31no—
219C22×C22⋊C4—32no—
220C22×C42—32no—
221#398—32no—
222#398—34no—
223#398—32no—
224#398—34no—
225#398—32no—
226#398C2×D312yescomplemented
227#395—32no—
228#395—34no—
229#395—32no—
230#395—34no—
231#395—32no—
232#395C2×D312yescomplemented
233#391—34no—
234#391—34no—
235#389—34no—
236#389—34no—
237#389—34no—
238#389C2×D314yescomplemented
239#385—32no—
240#385—32no—
241#385—34no—
242#385—34no—
243#385—32no—
244#385—32no—
245#385—32no—
246#385—32no—
247#385—34no—
248#385—34no—
249#385C2×D312yes—
250#385C2×D312yes—
251#384—34no—
252#380—34no—
253#380—34no—
254#380—34no—
255#380—34no—
256C4×C22⋊C4—31no—
257C4×C22⋊C4—32no—
258C4×C22⋊C4—32no—
259C4×C22⋊C4—32no—
260C4×C22⋊C4C2×D311yescharacteristic
261C2×#95—32no—
262C24×C3C2411yescharacteristic
263C23×D3—42no—
264C23×D3—42no—
265C23×D3C2×D414yes—
266C23×D3C2×Q818yes—
267C23×D3C2411yescharacteristic
268C23×D3C2411yescharacteristic
269C2×C3×Q8—22no—
270C2×C3×Q8—42no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—42no—
276C22×C3×C4C2×D414yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2414yes—
284C22×Dic3—24no—
285C22×Dic3—22no—
286C22×Dic3—22no—
287C22×Dic3—42no—
288C22×Dic3—42no—
289C22×Dic3C2×D414yes—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C22×Dic3C2411yescharacteristic
295C22×Dic3C2414yes—
296C22×Dic3C2411yescharacteristic
297D3×Q8—416no—
298C2×C4×D3—24no—
299C2×C4×D3—24no—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—416no—
303C2×C4×D3—44no—
304C2×C4×D3—42no—
305C2×C4×D3—42no—
306C2×C4×D3—44no—
307C2×C4×D3—44no—
308C2×C4×D3—44no—
309C2×C4×D3C2×D414yes—
310C2×C4×D3C2×D414yes—
311C2×C4×D3C2×D414yes—
312C2×C4×D3C2×D414yes—
313C2×C4×D3C2×Q8116yescomplemented
314C2×Dic6—22no—
315C2×Dic6—24no—
316C2×Dic6—24no—
317C2×Dic6—24no—
318C2×Dic6—28no—
319C2×Dic6—28no—
320C2×Dic6—44no—
321C2×Dic6—42no—
322C2×Dic6—416no—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—24no—
327C3×C4⋊C4—44no—
328C3×C4⋊C4—44no—
329C3×C22⋊C4—24no—
330C3×C22⋊C4C2×Q818yescomplemented
331C3×C42—42no—
332#217—24no—
333#217C2×Q818yescomplemented
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4C2×Q8116yescomplemented
341C4⋊Dic3—22no—
342C4⋊Dic3—24no—
343C4⋊Dic3—44no—
344C4⋊Dic3—44no—
345Dic3⋊C4—24no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—24no—
349Dic3⋊C4—24no—
350Dic3⋊C4—24no—
351Dic3⋊C4—24no—
352Dic3⋊C4—44no—
353Dic3⋊C4—44no—
354Dic3⋊C4—44no—
355Dic3⋊C4—44no—
356C4×Dic3—28no—
357C4×Dic3—42no—
358C25—31no—
359C22×Q8—32no—
360C22×Q8—32no—
361C22×Q8—32no—
362C22×Q8—31no—
363C22×Q8—64no—
364C22×Q8—64no—
365C22×Q8—124no—
366C22×Q8—124no—
367C22×Q8C22×D311yescharacteristic
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4—38no—
372C23×C4—34no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—32no—
378C23×C4—32no—
379C23×C4—124no—
380C23×C4C22×D311yescharacteristic
381C23×C4C22×D311yescharacteristic
382C23×C4C22×D311yescharacteristic
383C4⋊Q8—128no—
384C22⋊Q8—24no—
385C22⋊Q8—68no—
386C22⋊Q8—68no—
387C22⋊Q8—68no—
388C22⋊Q8—68no—
389C22⋊Q8—68no—
390C22⋊Q8—68no—
391C22⋊Q8—64no—
392C22⋊Q8—64no—
393C22⋊Q8—64no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—64no—
411C2×C4⋊C4—68no—
412C2×C4⋊C4—64no—
413C2×C4⋊C4—64no—
414C2×C4⋊C4C22×D312yes—
415C2×C4⋊C4C22×D311yescharacteristic
416C2×C4⋊C4C22×D312yes—
417C2×C4⋊C4C22×D312yes—
418C2×C4⋊C4C22×D314yes—
419C2×C4⋊C4C22×D314yes—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—316no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—32no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—68no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4C22×D312yes—
434C2×C22⋊C4C22×D312yes—
435C2×C42—34no—
436C2×C42—32no—
437C2×C42—124no—
438C2×C42C22×D312yes—
439#95—32no—
440#95—34no—
441#95—34no—
442#95—34no—
443#95—34no—
444#95—34no—
445#95—34no—
446#95—34no—
447#95C22×D312yes—
448#95C22×D314yes—
449#95C22×D314yes—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3C22×D412yes—
453C23×C3C22×Q814yes—
454C23×C3C2511yescharacteristic
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—44no—
460C22×D3—44no—
461C22×D3—416no—
462C22×D3C4⋊Q8116yescomplemented
463C22×D3C22×D412yes—
464C22×D3C22×D412yes—
465C22×D3C22×Q814yes—
466C22×D3C22×Q814yes—
467C3×Q8—44no—
468C2×C3×C4—24no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—24no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—22no—
481C2×C3×C4—44no—
482C2×C3×C4—44no—
483C2×C3×C4—44no—
484C2×C3×C4C22×D412yes—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C22×Q818yes—
487C2×Dic3—24no—
488C2×Dic3—22no—
489C2×Dic3—24no—
490C2×Dic3—28no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—24no—
496C2×Dic3—24no—
497C2×Dic3—22no—
498C2×Dic3—24no—
499C2×Dic3—22no—
500C2×Dic3—44no—
501C2×Dic3—44no—
502C2×Dic3C22×D412yes—
503C2×Dic3C22×D412yes—
504C2×Dic3C22×Q818yes—
505C2×Dic3H(5,𝔽2)14yes—
506C4×D3—28no—
507C4×D3—28no—
508C4×D3—44no—
509C4×D3—44no—
510C4×D3—416no—
511C4×D3—48no—
512C4×D3—48no—
513Dic6—48no—
514Dic6—44no—
515Dic6—48no—
516Dic6—48no—
517C24—31no—
518C24—31no—
519C24—34no—
520C24—38no—
521C24—122no—
522C24—122no—
523C24C23×D311yescharacteristic
524C2×Q8—22no—
525C2×Q8—42no—
526C2×Q8—64no—
527C2×Q8—64no—
528C2×Q8—64no—
529C2×Q8—68no—
530C2×Q8—68no—
531C2×Q8—62no—
532C2×Q8—122no—
533C2×Q8—124no—
534C2×Q8—1216no—
535C2×Q8—1216no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—31no—
539C22×C4—34no—
540C22×C4—34no—
541C22×C4—31no—
542C22×C4—34no—
543C22×C4—34no—
544C22×C4—34no—
545C22×C4—34no—
546C22×C4—316no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—64no—
555C22×C4—64no—
556C22×C4—64no—
557C22×C4—64no—
558C22×C4—64no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—124no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—124no—
565C22×C4—124no—
566C22×C4—124no—
567C22×C4—1216no—
568C22×C4—122no—
569C22×C4—122no—
570C22×C4D3×D414yes—
571C22×C4C23×D312yes—
572C22×C4C23×D312yes—
573C22×C4C23×D312yes—
574C22×C4C23×D312yes—
575C22×C4C23×D311yescharacteristic
576C22×C4C23×D311yescharacteristic
577C22×C4C23×D314yes—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—62no—
593C4⋊C4—124no—
594C4⋊C4—124no—
595C4⋊C4—124no—
596C4⋊C4—124no—
597C4⋊C4—124no—
598C4⋊C4—124no—
599C22⋊C4—24no—
600C22⋊C4—38no—
601C22⋊C4—316no—
602C22⋊C4—64no—
603C22⋊C4—64no—
604C22⋊C4—64no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4D3×Q818yescomplemented
610C42—42no—
611C42—68no—
612C42—122no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—28no—
616C22×C3C2×C4⋊Q814yes—
617C22×C3C23×D411yescharacteristic
618C22×C3C23×Q812yes—
619C22×C3C2×H(5,𝔽2)12yes—
620C22×C3#58512yes—
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—22no—
625C2×D3—28no—
626C2×D3—28no—
627C2×D3—416no—
628C2×D3C2×C4⋊Q814yes—
629C2×D3C2×C4⋊Q814yes—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—28no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—42no—
637Dic3—22no—
638Dic3—28no—
639Dic3—42no—
640Dic3—42no—
641Dic3—42no—
642Dic3—42no—
643Dic3#53414yes—
644C23—22no—
645C23—22no—
646C23—32no—
647C23—32no—
648C23—34no—
649C23—34no—
650C23—316no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—124no—
656C23—124no—
657C23—1216no—
658C23C2×D3×D412yes—
659C23C2×D3×Q814yes—
660C23C24×D311yescharacteristic
661Q8—44no—
662Q8—124no—
663Q8—128no—
664Q8—128no—
665Q8—128no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—32no—
680C2×C4—34no—
681C2×C4—32no—
682C2×C4—38no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—68no—
687C2×C4—68no—
688C2×C4—68no—
689C2×C4—64no—
690C2×C4—64no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—62no—
699C2×C4—64no—
700C2×C4—64no—
701C2×C4—124no—
702C2×C4—124no—
703C2×C4—1216no—
704C2×C4—128no—
705C2×C4—128no—
706C2×C4—124no—
707C2×C4—124no—
708C2×C4C2×D3×D412yes—
709C2×C4C2×D3×D412yes—
710C2×C4C2×D3×Q818yes—
711C2×C3—24no—
712C2×C3C22×C4⋊Q811yescharacteristic
713C2×C3C2×#53411yescharacteristic
714C2×C3#344911yescharacteristic
715C2×C3#350114yes—
716D3—24no—
717D3—24no—
718C22—22no—
719C22—22no—
720C22—28no—
721C22—34no—
722C22—34no—
723C22—62no—
724C22—62no—
725C22—62no—
726C22—62no—
727C22—68no—
728C22—68no—
729C22—1216no—
730C22D3×C4⋊Q814yes—
731C22C22×D3×D411yescharacteristic
732C22C22×D3×Q812yes—
733C22#596412yes—
734C22D3×H(5,𝔽2)12yes—
735C4—22no—
736C4—22no—
737C4—28no—
738C4—34no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—62no—
744C4—68no—
745C4—122no—
746C4—122no—
747C4—122no—
748C4—122no—
749C3#3501111yescharacteristic, complemented, Sylow
750C2—24no—
751C2—64no—
752C2—64no—
753C2#8603511yescharacteristic
754C2C2×D3×C4⋊Q811yescharacteristic
755C2D3×#53411yescharacteristic
756C2#8694914yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2583C2
prime radicalC24×D3C23
hypercenter#2583D3
hypocenterC3#35011
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2583

Complements

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

NH ≅ G/Ntype
3. C3×#2583C2semidirect
4. #82785C2semidirect
5. #82181C2semidirect
6. #77966C2semidirect
7. #77765C2semidirect
8. #77258C2semidirect
9. #77173C2semidirect
10. #76288C2semidirect
11. #76247C2semidirect
14. #74460C2semidirect
15. #74412C2semidirect
17. #73547C2semidirect
40. C2×#888C22semidirect
45. C3×#398C22semidirect
46. C3×#395C22semidirect
47. C3×#389C22semidirect
51. #5230C22semidirect
59. #4983C22semidirect
60. #4982C22semidirect
61. #4981C22semidirect
62. #4979C22semidirect
63. #4979C22semidirect
64. #4976C22semidirect
65. #4976C22semidirect
66. #4975C22semidirect
73. #4928C22semidirect
80. #4661C22semidirect
81. #4657C22semidirect
82. #4656C22semidirect
83. #4656C22semidirect
84. #4646C22semidirect
85. #4646C22semidirect
95. #2583D3semidirect
181. D3×C22⋊C4Q8semidirect
226. #398C2×D3semidirect
232. #395C2×D3semidirect
238. #389C2×D3semidirect
313. C2×C4×D3C2×Q8semidirect
330. C3×C22⋊C4C2×Q8semidirect
333. #217C2×Q8semidirect
340. (C2×D3)⋊C4C2×Q8semidirect
462. C22×D3C4⋊Q8semidirect
609. C22⋊C4D3×Q8semidirect
749. C3#35011semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊Q82
C22×#8962
C3×#25832
#827852
#821812
#779662
#777652
#772582
#771732
#762882
#762472
#745912
#744602
#744122
C4×D3×C22⋊C42
#735472
#350113