Finite Group Databasebeta

← #10957205

Subgroups — #10957205

Order 768.

3124 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic
2C2×#5827C212yesmaximal, complemented
3#84088C212yesmaximal, complemented
4#83229C211yesmaximal, characteristic, complemented
5Dic3×C4⋊Q8C211yesmaximal, characteristic, complemented
6#82838C214yesmaximal, complemented
7#82836C214yesmaximal, complemented
8#82747C212yesmaximal, complemented
9#82744C212yesmaximal, complemented
10#82636C212yesmaximal, complemented
11Dic3×#121C212yesmaximal, complemented
12D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
13D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
14#82319C211yesmaximal, characteristic, complemented
15C4×D4×Dic3C211yesmaximal, characteristic, complemented
16#82159C212yesmaximal, complemented
17C2×#4984C212yesmaximal, complemented
18#34308—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C3×#547C4116yescomplemented
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#123C2214yes—
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×#121C2212yes—
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C22×C3×C4⋊C4C2212yes—
28#5827—216no—
29C2×Q8×Dic3C2212yes—
30C2×Q8×Dic3C2212yes—
31C2×D4×Dic3C2211yescharacteristic
32C2×D4×Dic3C2212yes—
33C2×D4×Dic3C2214yes—
34C2×D4×Dic3C2214yes—
35C2×D4×Dic3C2212yes—
36C2×D4×Dic3C2211yescharacteristic
37C2×#926C2212yes—
38C2×#926C2214yes—
39C22×C4⋊Dic3C2212yes—
40C22×C4⋊Dic3C2214yes—
41C22×C4⋊Dic3C2212yes—
42C22×C4×Dic3C2212yes—
43#5229C2212yes—
44#5229C2212yes—
45#5221C2211yescharacteristic
46#5221C2211yescharacteristic
47#5220C2214yes—
48#5220C2214yes—
49#5212C2212yes—
50#5212C2212yes—
51#5211C2214yes—
52C4×#217C2212yes—
53C4×#217C2212yes—
54C2×C3⋊#95C2214yes—
55#4984C2212yes—
56#4984C2212yes—
57#4984C2212yes—
58#4984C2212yes—
59#4984C2214yes—
60#4984C2214yes—
61#4984C2211yescharacteristic
62#4984C2211yescharacteristic
63#4984C2212yes—
64#4980C2214yes—
65#4980C2214yes—
66#4980C2214yes—
67Dic3×C4⋊C4C2212yes—
68Dic3×C4⋊C4C2212yes—
69Dic3×C4⋊C4C2212yes—
70Dic3×C4⋊C4C2211yescharacteristic
71Dic3×C4⋊C4C2211yescharacteristic
72#4951C2214yes—
73#4951C2214yes—
74#4951C2212yes—
75#4951C2212yes—
76#4950C2214yes—
77#4950C2214yes—
78#4950C2214yes—
79Dic3×C22⋊C4C2214yes—
80Dic3×C22⋊C4C2212yes—
81Dic3×C22⋊C4C2212yes—
82#4935C2211yescharacteristic
83C4×C4⋊Dic3C2211yescharacteristic
84C4×C4⋊Dic3C2211yescharacteristic
85C42×Dic3C2211yescharacteristic
86C2×#547D311yescharacteristic
87C2×#520—32no—
88#2365—31no—
89#2361—32no—
90#2360—32no—
91#2359—34no—
92D4×C4⋊C4—31no—
93D4×C4⋊C4—31no—
94#2344—32no—
95#2339—32no—
96#2323—32no—
97#2322—34no—
98C4×C4⋊Q8—31no—
99C4×#121—32no—
100#2293—31no—
101C2×#389—32no—
102C42×D4—31no—
103C2×C3×#41—28no—
104C2×C3×#41—28no—
105C2×C3×#41C2×C4116yescomplemented
106C22×C3×Q8C2312yes—
107C22×C3×D4C2314yes—
108C22×C3×D4C2311yescharacteristic
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4C2314yes—
111C23×C3×C4C2312yes—
112C23×C3×C4C2312yes—
113C23×Dic3C2312yes—
114C23×Dic3C2314yes—
115C23×Dic3C2314yes—
116C23×Dic3C2312yes—
117C3×C4⋊Q8C2×C418yescomplemented
118C3×#123C2×C4132yescomplemented
119C3×C22⋊Q8C2×C4116yescomplemented
120C3×#121C2×C4116yescomplemented
121C3×C4×D4C2×C418yescomplemented
122C3×C4×D4C2×C418yescomplemented
123C2×C3×C4⋊C4C2×C4116yescomplemented
124C2×C3×C4⋊C4C2312yes—
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2314yes—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C42C2311yescharacteristic
133C2×#217C2312yes—
134C2×#217C2312yes—
135C2×#217C2314yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2314yes—
140C2×#217C2312yes—
141Q8×Dic3—28no—
142Q8×Dic3—28no—
143D4×Dic3—28no—
144D4×Dic3—24no—
145D4×Dic3—216no—
146D4×Dic3—216no—
147D4×Dic3—44no—
148D4×Dic3D418yescomplemented
149#926—216no—
150#926—28no—
151C2×C4⋊Dic3—216no—
152C2×C4⋊Dic3—28no—
153C2×C4⋊Dic3—44no—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2314yes—
160C2×C4⋊Dic3C2314yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2312yes—
163C2×C4⋊Dic3C2314yes—
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2314yes—
166C2×C4⋊Dic3C2311yescharacteristic
167C2×C4×Dic3—44no—
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2311yescharacteristic
170C2×C4×Dic3C2311yescharacteristic
171C2×C4×Dic3C2311yescharacteristic
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2314yes—
175C2×C4×Dic3C2314yes—
176C2×C4×Dic3C2311yescharacteristic
177C2×C4×Dic3C2312yes—
178C2×C4×Dic3C2312yes—
179C2×C4×Dic3C2311yescharacteristic
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C3⋊#95C2314yes—
192C22×#41C2×D312yes—
193#547Dic3116yescomplemented
194C2×C4⋊Q8C2×D311yescharacteristic
195C2×#123C2×D314yes—
196C2×C22⋊Q8C2×D312yes—
197C2×#121C2×D312yes—
198#520—616no—
199C2×C4×Q8—32no—
200C2×C4×Q8—32no—
201C2×C4×D4—31no—
202C2×C4×D4—34no—
203C2×C4×D4—31no—
204C2×C4×D4—32no—
205C2×C4×D4—34no—
206C2×C4×D4—32no—
207C2×C4×D4C2×D311yescharacteristic
208C2×C4×D4C2×D311yescharacteristic
209C2×#117—32no—
210C2×#117—34no—
211C22×C4⋊C4—34no—
212C22×C4⋊C4—32no—
213C22×C4⋊C4—32no—
214C22×C4⋊C4C2×D312yes—
215C22×C42—32no—
216#391—32no—
217#391—32no—
218#390—31no—
219#390—31no—
220#389—32no—
221#389—32no—
222#389—34no—
223#389—32no—
224#389—31no—
225#389—32no—
226#389—34no—
227#389—32no—
228#389—31no—
229#388—32no—
230#388—34no—
231#388—34no—
232#388—32no—
233#387—34no—
234#387—34no—
235#387—34no—
236#386—34no—
237#386—34no—
238#385—34no—
239#385—34no—
240#385—34no—
241#384—31no—
242#381—34no—
243#380—32no—
244#380—32no—
245C4×C4⋊C4—32no—
246C4×C4⋊C4—32no—
247C4×C4⋊C4—31no—
248C4×C4⋊C4—32no—
249C4×C4⋊C4—31no—
250C4×C4⋊C4—31no—
251C4×C4⋊C4—31no—
252C4×C22⋊C4—32no—
253C4×C22⋊C4—32no—
254C4×C22⋊C4—32no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—34no—
257C2×#95—34no—
258C43—31no—
259C24×C3C2412yes—
260C24×C3C2412yes—
261C3×#41—264no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8C22×C418yes—
265C2×C3×D4—28no—
266C2×C3×D4—28no—
267C2×C3×D4—22no—
268C2×C3×D4—22no—
269C2×C3×D4C22×C414yes—
270C2×C3×D4C22×C4116yes—
271C2×C3×D4C22×C414yes—
272C2×C3×D4C2×D414yes—
273C2×C3×D4#4114yes—
274C22×C3×C4—28no—
275C22×C3×C4—28no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—24no—
279C22×C3×C4—24no—
280C22×C3×C4C22×C418yes—
281C22×C3×C4C22×C4116yes—
282C22×C3×C4C22×C418yes—
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2412yes—
285C22×C3×C4C2414yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C22×Dic3—24no—
290C22×Dic3—28no—
291C22×Dic3—24no—
292C22×Dic3—28no—
293C22×Dic3—42no—
294C22×Dic3—42no—
295C22×Dic3—42no—
296C22×Dic3—44no—
297C22×Dic3—44no—
298C22×Dic3—44no—
299C22×Dic3—44no—
300C22×Dic3C2×D418yes—
301C22×Dic3C2411yescharacteristic
302C22×Dic3C2412yes—
303C22×Dic3C2412yes—
304C22×Dic3C2412yes—
305C22×Dic3C2414yes—
306C22×Dic3C2411yescharacteristic
307C22×Dic3C2412yes—
308C22×Dic3C2411yescharacteristic
309C22×Dic3C2411yescharacteristic
310C3×C4⋊C4C22×C414yes—
311C3×C4⋊C4C22×C418yes—
312C3×C4⋊C4C22×C4116yes—
313C3×C4⋊C4C22×C414yes—
314C3×C4⋊C4C22×C418yes—
315C3×C22⋊C4C22×C418yes—
316C3×C22⋊C4C22×C418yes—
317C3×C22⋊C4C22×C4116yes—
318C3×C42C22×C414yes—
319#217—28no—
320#217—24no—
321#217—24no—
322#217—24no—
323#217—24no—
324#217—44no—
325#217—42no—
326#217C2×D418yes—
327C4⋊Dic3—24no—
328C4⋊Dic3—22no—
329C4⋊Dic3—22no—
330C4⋊Dic3—24no—
331C4⋊Dic3—22no—
332C4⋊Dic3—28no—
333C4⋊Dic3—24no—
334C4⋊Dic3—28no—
335C4⋊Dic3—28no—
336C4⋊Dic3—24no—
337C4⋊Dic3—44no—
338C4⋊Dic3—42no—
339C4⋊Dic3C2×D414yes—
340C4×Dic3—24no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—24no—
344C4×Dic3—22no—
345C4×Dic3—28no—
346C4×Dic3—28no—
347C4×Dic3—22no—
348C4×Dic3—42no—
349C4×Dic3—42no—
350C4×Dic3—41no—
351C4×Dic3C2×D414yes—
352C2×#41—28no—
353C2×#41—28no—
354C2×#41C2×Dic3116yescomplemented
355C22×Q8C22×D312yes—
356C22×D4C22×D311yescharacteristic
357C22×D4C22×D314yes—
358C22×D4C22×D311yescharacteristic
359C23×C4—32no—
360C23×C4—32no—
361C23×C4—34no—
362C23×C4—34no—
363C23×C4C22×D314yes—
364C23×C4C22×D312yes—
365C23×C4C22×D312yes—
366C4⋊Q8C2×Dic318yescomplemented
367#123C2×Dic3132yescomplemented
368C22⋊Q8C2×Dic3116yescomplemented
369#121C2×Dic3116yescomplemented
370C4×Q8—68no—
371C4×Q8—68no—
372C4×D4—38no—
373C4×D4—616no—
374C4×D4—616no—
375C4×D4—68no—
376C4×D4—64no—
377C4×D4—124no—
378C4×D4C2×Dic318yescomplemented
379C4×D4C2×Dic318yescomplemented
380#117—68no—
381#117—616no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—34no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—68no—
396C2×C4⋊C4—616no—
397C2×C4⋊C4—124no—
398C2×C4⋊C4C2×Dic3116yescomplemented
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C4⋊C4C22×D312yes—
401C2×C4⋊C4C22×D314yes—
402C2×C4⋊C4C22×D311yescharacteristic
403C2×C4⋊C4C22×D312yes—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—34no—
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⋊C4C22×D312yes—
413C2×C22⋊C4C22×D312yes—
414C2×C22⋊C4C22×D314yes—
415C2×C42—31no—
416C2×C42—34no—
417C2×C42—32no—
418C2×C42—34no—
419C2×C42—31no—
420C2×C42—32no—
421C2×C42—31no—
422C2×C42—31no—
423C2×C42—31no—
424C2×C42—31no—
425C2×C42—32no—
426C2×C42—32no—
427C2×C42—124no—
428C2×C42C22×D311yescharacteristic
429#95—32no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—34no—
437#95—32no—
438#95—34no—
439#95—34no—
440#95—32no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3C23×C414yes—
452C23×C3C23×C414yes—
453C23×C3C22×D414yes—
454C23×C3C2×#4114yes—
455C23×C3C2511yescharacteristic
456C3×Q8—216no—
457C3×D4—232no—
458C3×D4—28no—
459C3×D4C4×D4116yescomplemented
460C2×C3×C4—232no—
461C2×C3×C4—24no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—24no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—216no—
470C2×C3×C4—216no—
471C2×C3×C4C23×C412yes—
472C2×C3×C4C23×C414yes—
473C2×C3×C4C23×C414yes—
474C2×C3×C4C23×C418yes—
475C2×C3×C4C23×C412yes—
476C2×C3×C4C23×C412yes—
477C2×C3×C4C22×D412yes—
478C2×C3×C4C2×#4112yes—
479C2×C3×C4H(5,𝔽2)12yes—
480C2×C3×C42−1+412yes—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—22no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—24no—
492C2×Dic3—21no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—24no—
497C2×Dic3—21no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—21no—
502C2×Dic3—24no—
503C2×Dic3—22no—
504C2×Dic3—48no—
505C2×Dic3—48no—
506C2×Dic3—88no—
507C2×Dic3—88no—
508C2×Dic3C22×D412yes—
509C2×Dic3C22×D414yes—
510C2×Dic3C22×D412yes—
511C2×Dic32−1+412yes—
512C24C23×D312yes—
513C24C23×D312yes—
514#41—264no—
515C2×Q8—24no—
516C2×Q8—24no—
517C2×Q8C22×Dic318yes—
518C2×D4—28no—
519C2×D4—28no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4D3×D414yes—
523C2×D4#23714yes—
524C2×D4C22×Dic314yes—
525C2×D4C22×Dic3116yes—
526C2×D4C22×Dic314yes—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—31no—
534C22×C4—31no—
535C22×C4—32no—
536C22×C4—31no—
537C22×C4—38no—
538C22×C4—31no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—34no—
542C22×C4—32no—
543C22×C4—64no—
544C22×C4—68no—
545C22×C4—64no—
546C22×C4—68no—
547C22×C4—122no—
548C22×C4—122no—
549C22×C4—122no—
550C22×C4—124no—
551C22×C4—124no—
552C22×C4—124no—
553C22×C4—124no—
554C22×C4C22×Dic318yes—
555C22×C4C22×Dic3116yes—
556C22×C4C22×Dic318yes—
557C22×C4C23×D311yescharacteristic
558C22×C4C23×D312yes—
559C22×C4C23×D314yes—
560C22×C4C23×D312yes—
561C22×C4C23×D311yescharacteristic
562C22×C4C23×D311yescharacteristic
563C4⋊C4—34no—
564C4⋊C4—64no—
565C4⋊C4—68no—
566C4⋊C4—68no—
567C4⋊C4—68no—
568C4⋊C4—64no—
569C4⋊C4—64no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—64no—
573C4⋊C4—62no—
574C4⋊C4—124no—
575C4⋊C4—122no—
576C4⋊C4C22×Dic314yes—
577C4⋊C4C22×Dic318yes—
578C4⋊C4C22×Dic3116yes—
579C4⋊C4C22×Dic314yes—
580C4⋊C4C22×Dic318yes—
581C22⋊C4—38no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—64no—
585C22⋊C4—68no—
586C22⋊C4—64no—
587C22⋊C4—124no—
588C22⋊C4—122no—
589C22⋊C4C22×Dic318yes—
590C22⋊C4C22×Dic318yes—
591C22⋊C4C22×Dic3116yes—
592C42—34no—
593C42—68no—
594C42—68no—
595C42—62no—
596C42—64no—
597C42—62no—
598C42—62no—
599C42—64no—
600C42—62no—
601C42—122no—
602C42—122no—
603C42—121no—
604C42C22×Dic314yes—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—24no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3C2×C4×D418yes—
619C22×C3C24×C411yescharacteristic
620C22×C3C23×D411yescharacteristic
621C22×C3C22×#4111yescharacteristic
622C22×C3C2×H(5,𝔽2)11yescharacteristic
623C22×C3C2×2−1+411yescharacteristic
624C22×C3C2×2−1+411yescharacteristic
625C22×C3#58511yescharacteristic
626C3×C4—24no—
627C3×C4—28no—
628C3×C4—24no—
629C3×C4—22no—
630C3×C4C2×C4×D414yes—
631C3×C4#52014yescomplemented
632Dic3—22no—
633Dic3—24no—
634Dic3—22no—
635Dic3—22no—
636Dic3—42no—
637Dic3—44no—
638Dic3—42no—
639Dic3—41no—
640Dic3—42no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23C2×D3×D414yes—
652C23C2×#23714yes—
653C23C23×Dic314yes—
654C23C23×Dic314yes—
655C23C24×D311yescharacteristic
656Q8—216no—
657D4—232no—
658D4—28no—
659D4D4×Dic3116yescomplemented
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—232no—
669C2×C4—216no—
670C2×C4—216no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—34no—
674C2×C4—32no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—62no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—64no—
685C2×C4—62no—
686C2×C4—61no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—64no—
690C2×C4—62no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—61no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—128no—
699C2×C4—128no—
700C2×C4—248no—
701C2×C4—248no—
702C2×C4C2×D3×D412yes—
703C2×C4C2×#23712yes—
704C2×C4#100912yes—
705C2×C4#101012yes—
706C2×C4C23×Dic312yes—
707C2×C4C23×Dic314yes—
708C2×C4C23×Dic314yes—
709C2×C4C23×Dic318yes—
710C2×C4C23×Dic312yes—
711C2×C4C23×Dic312yes—
712C2×C3—28no—
713C2×C3—44no—
714C2×C3C22×C4×D411yescharacteristic
715C2×C3C2×#52011yescharacteristic
716C2×C3C4×2−1+411yescharacteristic
717C2×C3#349611yescharacteristic
718C2×C3#349911yescharacteristic
719C2×C3#351511yescharacteristic
720C2×C3#352011yescharacteristic
721C22—24no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22C2×D4×Dic318yes—
735C22C22×D3×D411yescharacteristic
736C22C22×#23711yescharacteristic
737C22C2×#100911yescharacteristic
738C22C2×#101011yescharacteristic
739C22D3×2−1+411yescharacteristic
740C22#596811yescharacteristic
741C22C24×Dic311yescharacteristic
742C4—24no—
743C4—28no—
744C4—24no—
745C4—22no—
746C4—62no—
747C4—62no—
748C4—62no—
749C4—64no—
750C4—122no—
751C4—121no—
752C4—122no—
753C4—124no—
754C4—122no—
755C4C2×D4×Dic314yes—
756C4#582714yescomplemented
757C3#3430811yescharacteristic, complemented, Sylow
758C2—28no—
759C2—44no—
760C2#8667911yescharacteristic
761C2#8668311yescharacteristic
762C2#8668511yescharacteristic
763C2#8670211yescharacteristic
764C2C22×D4×Dic311yescharacteristic
765C2C2×#582711yescharacteristic
766C2Dic3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
Fitting, prime radicalC2×C3×#547C2
socle, cosocleC23×C3C25
hypercenterC2×#547D3
hypocenterC3#34308
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
2. C2×#5827C2semidirect
3. #84088C2semidirect
4. #83229C2semidirect
5. Dic3×C4⋊Q8C2semidirect
6. #82838C2semidirect
7. #82836C2semidirect
8. #82747C2semidirect
9. #82744C2semidirect
10. #82636C2semidirect
11. Dic3×#121C2semidirect
12. D4×C4⋊Dic3C2semidirect
13. D4×C4⋊Dic3C2semidirect
14. #82319C2semidirect
15. C4×D4×Dic3C2semidirect
16. #82159C2semidirect
17. C2×#4984C2semidirect
20. C3×#547C4semidirect
105. C2×C3×#41C2×C4semidirect
117. C3×C4⋊Q8C2×C4semidirect
118. C3×#123C2×C4semidirect
119. C3×C22⋊Q8C2×C4semidirect
120. C3×#121C2×C4semidirect
121. C3×C4×D4C2×C4semidirect
122. C3×C4×D4C2×C4semidirect
123. C2×C3×C4⋊C4C2×C4semidirect
148. D4×Dic3D4semidirect
193. #547Dic3semidirect
354. C2×#41C2×Dic3semidirect
366. C4⋊Q8C2×Dic3semidirect
367. #123C2×Dic3semidirect
368. C22⋊Q8C2×Dic3semidirect
369. #121C2×Dic3semidirect
378. C4×D4C2×Dic3semidirect
379. C4×D4C2×Dic3semidirect
398. C2×C4⋊C4C2×Dic3semidirect
459. C3×D4C4×D4semidirect
631. C3×C4#520semidirect
659. D4D4×Dic3semidirect
756. C4#5827semidirect
757. C3#34308semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C2×#58272
#840882
#832292
Dic3×C4⋊Q82
#828382
#828362
#827472
#827442
#826362
Dic3×#1212
D4×C4⋊Dic32
#823192
C4×D4×Dic32
#821592
C2×#49842
#343083