Finite Group Databasebeta

← #10957249

Subgroups — #10957249

Order 768.

2860 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5727C211yesmaximal, characteristic
2C2×#5572C212yesmaximal, complemented
3C3×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
4#83229C211yesmaximal, characteristic, complemented
5#82488C212yesmaximal, complemented
6#76614C212yesmaximal, complemented
7#76491C212yesmaximal, complemented
8#75971C214yesmaximal, complemented
9#75967C212yesmaximal, complemented
10#75961C212yesmaximal
11#74324C211yesmaximal, characteristic
12#74323C211yesmaximal, characteristic, complemented
13#73652C212yesmaximal, complemented
14#73648C214yesmaximal, complemented
15#73639C212yesmaximal
16#73299C211yesmaximal, characteristic
17C42×Dic6C211yesmaximal, characteristic, complemented
18#34311—31nomaximal, Sylow
19C22×D3×Q8C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×Q8C2212yes—
22C2×#946C2212yes—
23C2×Q8×Dic3C2212yes—
24#5727C4116yescomplemented
25#5572—216no—
26C2×#896C2214yes—
27C2×#893C2212yes—
28C2×#892C2212yes—
29C2×#892C2214yes—
30C2×#888C2212yes—
31C2×#887C2212yes—
32C2×#887C2214yes—
33C2×C4×D12C2211yescharacteristic
34C2×#872C2212yes—
35C2×#872C2214yes—
36C2×C4×Dic6C2214yes—
37C2×C4×Dic6C2211yescharacteristic
38C2×C4×Dic6C2211yescharacteristic
39C2×C4×Dic6C2211yescharacteristic
40C3×#391C2212yes—
41C3×#389C2212yes—
42C3×#389C2212yes—
43C3×#384C2211yescharacteristic
44C3×C4×C4⋊C4C2212yes—
45C3×C4×C4⋊C4C2212yes—
46C3×C43C2211yescharacteristic
47#5229C2212yes—
48#4990C2214yes—
49#4990C2214yes—
50#4988C2212yes—
51#4987C2212yes—
52#4984C2212yes—
53#4980C2214yes—
54#4976C2214yes—
55#4976C2214yes—
56#4975C2212yes—
57Dic3×C4⋊C4C2212yes—
58Dic3×C4⋊C4C2212yes—
59Dic3×C4⋊C4C2212yes—
60#4972C2212yes—
61#4940C2214yes—
62#4940C2212yes—
63#4940C2212yes—
64#4939C2211yescharacteristic
65#4939C2211yescharacteristic
66C4×(C2×D3)⋊C4C2212yes—
67C4×C4⋊Dic3C2211yescharacteristic
68C4×C4⋊Dic3C2211yescharacteristic
69C4×C4⋊Dic3C2211yescharacteristic
70C4×C4⋊Dic3C2211yescharacteristic
71#4933C2214yes—
72C4×Dic3⋊C4C2212yes—
73C4×Dic3⋊C4C2212yes—
74C4×Dic3⋊C4C2212yes—
75C42×Dic3C2212yes—
76#4928C2211yescharacteristic
77#4928C2211yescharacteristic
78#4670C2214yes—
79#4669C2214yes—
80#4667C2214yes—
81#4666C2214yes—
82#4655C2214yes—
83#4649C2214yes—
84#4646C2214yes—
85#4646C2214yes—
86C2×D4×Q8—31no—
87C2×#519—32no—
88#2365—32no—
89#2365—31no—
90#2362—32no—
91#2362—34no—
92#2354—31no—
93#2354—32no—
94Q8×C4⋊C4—31no—
95Q8×C22⋊C4—32no—
96#2323—34no—
97#2323—32no—
98C4×C4⋊Q8—32no—
99C4×C4⋊Q8D311yescharacteristic, complemented
100#2293—32no—
101#2293—31no—
102C42×Q8—31no—
103C22×C3×Q8C2312yes—
104C2×D3×Q8—28no—
105C2×D3×Q8—28no—
106C2×D3×Q8C2×C4116yes—
107C22×D12C2311yescharacteristic
108C22×C4×D3C2314yes—
109C22×C4×D3C2312yes—
110C22×Dic6C2314yes—
111C22×Dic6C2311yescharacteristic
112C3×C4⋊Q8C2×C418yes—
113C3×C4×Q8—28no—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2312yes—
116C2×C3×C4⋊C4C2314yes—
117C2×C3×C4⋊C4C2312yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C42C2311yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2314yes—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C2×C3×C42C2311yescharacteristic
127C2×C3×C42C2311yescharacteristic
128#946C2×C4116yes—
129Q8×Dic3—28no—
130C2×(C2×D3)⋊C4C2312yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2312yes—
133C2×(C2×D3)⋊C4C2312yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2312yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×C4⋊Dic3C2314yes—
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×Dic3⋊C4C2312yes—
146C2×Dic3⋊C4C2314yes—
147C2×Dic3⋊C4C2312yes—
148C2×Dic3⋊C4C2312yes—
149C2×Dic3⋊C4C2314yes—
150C2×Dic3⋊C4C2314yes—
151C2×Dic3⋊C4C2312yes—
152C2×Dic3⋊C4C2312yes—
153C2×C4×Dic3C2312yes—
154C2×C4×Dic3C2314yes—
155C2×C4×Dic3C2312yes—
156C2×C4×Dic3C2314yes—
157C2×C4×Dic3C2314yes—
158C2×C4×Dic3C2312yes—
159C2×C4×Dic3C2312yes—
160C2×C4×Dic3C2312yes—
161C2×C4×Dic3C2312yes—
162C2×C4×Dic3C2312yes—
163#896C2×C4132yes—
164#893C2×C4116yes—
165#892—28no—
166#892—216no—
167#888C2×C4116yes—
168#887—28no—
169#887—216no—
170C4×D12C2×C418yes—
171#872—28no—
172#872—216no—
173C4×Dic6—24no—
174C4×Dic6—216no—
175C4×Dic6C2×C418yes—
176C4×Dic6D418yescomplemented
177C3×#95C2314yes—
178C3×#95C2314yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2314yes—
182C3⋊#95C2314yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189C23×Q8—32no—
190D4×Q8—316no—
191C2×C4⋊Q8—32no—
192C2×C4⋊Q8C2×D311yescharacteristic
193C2×C22⋊Q8—32no—
194C2×C22⋊Q8—34no—
195#519—616no—
196C2×C4×Q8—32no—
197C2×C4×Q8—34no—
198C2×C4×Q8—32no—
199C2×C4×Q8—31no—
200C2×C4×Q8—31no—
201C2×C4×Q8—31no—
202C2×C4×Q8—34no—
203C2×C4×Q8C2×D312yes—
204C2×C4×D4—32no—
205C2×C4×D4—31no—
206C2×#117—34no—
207C2×#117—32no—
208C2×#117—32no—
209C2×#117—34no—
210#391—32no—
211#391—34no—
212#391—34no—
213#391C2×D312yes—
214#390—32no—
215#390—31no—
216#390—31no—
217#389—34no—
218#389—32no—
219#389—34no—
220#389—32no—
221#389—31no—
222#389—31no—
223#389C2×D312yes—
224#389C2×D312yes—
225#388—34no—
226#388—34no—
227#388—32no—
228#388—34no—
229#388—32no—
230#388—34no—
231#388—34no—
232#387—34no—
233#387—34no—
234#387—34no—
235#384—32no—
236#384C2×D311yescharacteristic
237#380—32no—
238#380—34no—
239C4×C4⋊C4—32no—
240C4×C4⋊C4—32no—
241C4×C4⋊C4—32no—
242C4×C4⋊C4—32no—
243C4×C4⋊C4—31no—
244C4×C4⋊C4—31no—
245C4×C4⋊C4—32no—
246C4×C4⋊C4—31no—
247C4×C4⋊C4—32no—
248C4×C4⋊C4—31no—
249C4×C4⋊C4—34no—
250C4×C4⋊C4C2×D312yes—
251C4×C4⋊C4C2×D312yes—
252C4×C22⋊C4—32no—
253C4×C22⋊C4—34no—
254C43—32no—
255C43C2×D311yescharacteristic
256C23×D3C2412yes—
257C2×C3×Q8—24no—
258C2×C3×Q8—24no—
259C2×C3×Q8C22×C418yes—
260C22×C3×C4C2411yescharacteristic
261C22×C3×C4C2414yes—
262C22×C3×C4C2411yescharacteristic
263C22×C3×C4C2414yes—
264C22×C3×C4C2411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C22×C3×C4C2411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C22×C3×C4C2411yescharacteristic
269C22×Dic3C2412yes—
270C22×Dic3C2412yes—
271C22×Dic3C2412yes—
272C22×Dic3C2412yes—
273C22×Dic3C2412yes—
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276D3×Q8—264no—
277C2×D12—22no—
278C2×D12—22no—
279C2×D12C22×C414yes—
280C2×C4×D3—24no—
281C2×C4×D3—24no—
282C2×C4×D3—28no—
283C2×C4×D3—28no—
284C2×C4×D3C22×C418yes—
285C2×C4×D3C22×C4116yes—
286C2×Dic6—28no—
287C2×Dic6—28no—
288C2×Dic6C22×C4116yes—
289C2×Dic6C22×C414yes—
290C2×Dic6C2×D414yes—
291C2×Dic6#4114yes—
292C3×C4⋊C4—28no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—24no—
295C3×C4⋊C4—42no—
296C3×C4⋊C4C22×C418yes—
297C3×C4⋊C4C22×C418yes—
298C3×C42—28no—
299C3×C42—22no—
300C3×C42—22no—
301C3×C42—22no—
302C3×C42—22no—
303C3×C42—41no—
304C3×C42C22×C414yes—
305C3×C42C2×D414yes—
306(C2×D3)⋊C4—24no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—28no—
310(C2×D3)⋊C4—44no—
311(C2×D3)⋊C4—42no—
312(C2×D3)⋊C4C22×C418yes—
313(C2×D3)⋊C4C22×C4116yes—
314C4⋊Dic3—22no—
315C4⋊Dic3—22no—
316C4⋊Dic3—22no—
317C4⋊Dic3—28no—
318C4⋊Dic3C22×C414yes—
319C4⋊Dic3C22×C414yes—
320C4⋊Dic3C2×D414yes—
321Dic3⋊C4—24no—
322Dic3⋊C4—24no—
323Dic3⋊C4—28no—
324Dic3⋊C4—24no—
325Dic3⋊C4—44no—
326Dic3⋊C4C22×C418yes—
327Dic3⋊C4C22×C4116yes—
328Dic3⋊C4C2×D418yes—
329C4×Dic3—24no—
330C4×Dic3—24no—
331C4×Dic3—24no—
332C4×Dic3—28no—
333C4×Dic3—28no—
334C4×Dic3—28no—
335C4×Dic3—24no—
336C4×Dic3—42no—
337C4×Dic3C22×C418yes—
338C4×Dic3C2×D418yes—
339C22×Q8—316no—
340C22×Q8—31no—
341C22×Q8—34no—
342C22×Q8—68no—
343C22×Q8—68no—
344C22×Q8C22×D312yes—
345C22×D4—31no—
346C23×C4—34no—
347C23×C4—32no—
348C4⋊Q8—316no—
349C4⋊Q8C4×D318yes—
350C22⋊Q8—316no—
351C22⋊Q8—332no—
352C4×Q8—28no—
353C4×Q8—38no—
354C4×Q8—38no—
355C4×Q8—616no—
356C4×Q8—64no—
357C4×Q8—616no—
358C4×Q8—68no—
359C4×Q8—68no—
360C4×D4—316no—
361C4×D4—38no—
362#117—616no—
363#117—616no—
364#117—68no—
365#117—68no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—32no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—34no—
372C2×C4⋊C4—34no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—34no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4C22×D312yes—
382C2×C4⋊C4C22×D314yes—
383C2×C4⋊C4C22×D312yes—
384C2×C4⋊C4C22×D312yes—
385C2×C4⋊C4C22×D312yes—
386C2×C4⋊C4C22×D312yes—
387C2×C22⋊C4—34no—
388C2×C22⋊C4—32no—
389C2×C22⋊C4—34no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—32no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—32no—
395C2×C42—32no—
396C2×C42—32no—
397C2×C42—34no—
398C2×C42—32no—
399C2×C42—34no—
400C2×C42—34no—
401C2×C42—32no—
402C2×C42—32no—
403C2×C42—32no—
404C2×C42—32no—
405C2×C42C22×D314yes—
406C2×C42C22×D311yescharacteristic
407C2×C42C22×D311yescharacteristic
408C2×C42C22×D311yescharacteristic
409C2×C42C22×D311yescharacteristic
410C2×C42C22×D311yescharacteristic
411C2×C42C22×D311yescharacteristic
412C2×C42C22×D311yescharacteristic
413#95—32no—
414#95—32no—
415#95—34no—
416#95—32no—
417#95—32no—
418#95—32no—
419#95—34no—
420#95—34no—
421#95—34no—
422#95—32no—
423#95C22×D314yes—
424#95C22×D314yes—
425C23×C3C2511yescharacteristic
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—22no—
429C22×D3—22no—
430C22×D3—22no—
431C22×D3—22no—
432C22×D3C23×C414yes—
433C3×Q8—216no—
434C2×C3×C4—24no—
435C2×C3×C4—21no—
436C2×C3×C4—24no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—24no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—21no—
450C2×C3×C4C23×C412yes—
451C2×C3×C4C23×C418yes—
452C2×C3×C4C23×C412yes—
453C2×C3×C4C23×C412yes—
454C2×C3×C4C22×D412yes—
455C2×C3×C4C22×D412yes—
456C2×C3×C4C22×D412yes—
457C2×C3×C4C2×#4112yes—
458C2×C3×C42−1+412yes—
459C2×C3×C42−1+412yes—
460C2×C3×C42−1+412yes—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3C23×C414yes—
477C2×Dic3C23×C414yes—
478C2×Dic3C23×C414yes—
479C2×Dic3C22×D414yes—
480C2×Dic3C22×D414yes—
481C2×Dic3C2×#4114yes—
482D12—28no—
483C4×D3—216no—
484C4×D3—232no—
485Dic6—232no—
486Dic6C4×D4116yes—
487C24—32no—
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—34no—
491C2×Q8—316no—
492C2×Q8—34no—
493C2×Q8—34no—
494C2×Q8—68no—
495C2×Q8—68no—
496C2×Q8—664no—
497C2×Q8C2×C4×D318yes—
498C2×D4—34no—
499C2×D4—62no—
500C2×D4—62no—
501C22×C4—32no—
502C22×C4—32no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—316no—
506C22×C4—38no—
507C22×C4—32no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—68no—
511C22×C4—68no—
512C22×C4—64no—
513C22×C4—64no—
514C22×C4C23×D311yescharacteristic
515C22×C4C23×D314yes—
516C22×C4C23×D311yescharacteristic
517C22×C4C23×D314yes—
518C22×C4C23×D311yescharacteristic
519C22×C4C23×D311yescharacteristic
520C22×C4C23×D311yescharacteristic
521C22×C4C23×D311yescharacteristic
522C22×C4C23×D311yescharacteristic
523C4⋊C4—28no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—34no—
527C4⋊C4—38no—
528C4⋊C4—34no—
529C4⋊C4—316no—
530C4⋊C4—38no—
531C4⋊C4—34no—
532C4⋊C4—42no—
533C4⋊C4—68no—
534C4⋊C4—68no—
535C4⋊C4—64no—
536C4⋊C4—64no—
537C4⋊C4—64no—
538C4⋊C4—62no—
539C4⋊C4—62no—
540C4⋊C4—62no—
541C4⋊C4—124no—
542C4⋊C4C2×C4×D318yes—
543C4⋊C4C2×C4×D318yes—
544C22⋊C4—316no—
545C22⋊C4—38no—
546C22⋊C4—68no—
547C22⋊C4—64no—
548C22⋊C4—64no—
549C22⋊C4—64no—
550C22⋊C4—122no—
551C22⋊C4—124no—
552C42—28no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—38no—
558C42—38no—
559C42—41no—
560C42—68no—
561C42—68no—
562C42—68no—
563C42—64no—
564C42—64no—
565C42—64no—
566C42—64no—
567C42—122no—
568C42C2×C4×D314yes—
569C42D3×D414yes—
570C22×C3C24×C411yescharacteristic
571C22×C3C23×D411yescharacteristic
572C22×C3C22×#4111yescharacteristic
573C22×C3C2×2−1+411yescharacteristic
574C22×C3C2×2−1+411yescharacteristic
575C22×C3C2×2−1+411yescharacteristic
576C22×C3#58511yescharacteristic
577C2×D3—24no—
578C2×D3—24no—
579C2×D3—24no—
580C2×D3—42no—
581C2×D3—42no—
582C2×D3—42no—
583C2×D3—42no—
584C3×C4—28no—
585C3×C4—22no—
586C3×C4—22no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—44no—
590C3×C4—41no—
591C3×C4C2×C4×D414yes—
592C3×C4#51914yescomplemented
593Dic3—24no—
594Dic3—24no—
595Dic3—24no—
596Dic3—42no—
597Dic3—42no—
598Dic3—42no—
599Dic3C2×C4×D418yes—
600C23—34no—
601C23—62no—
602C23—62no—
603C23—62no—
604C23—62no—
605C23—62no—
606C23—62no—
607C23C24×D311yescharacteristic
608Q8—216no—
609Q8—316no—
610Q8—632no—
611D4—68no—
612C2×C4—24no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—24no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—24no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—24no—
626C2×C4—21no—
627C2×C4—24no—
628C2×C4—34no—
629C2×C4—34no—
630C2×C4—34no—
631C2×C4—34no—
632C2×C4—34no—
633C2×C4—34no—
634C2×C4—632no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—62no—
639C2×C4—62no—
640C2×C4—62no—
641C2×C4—616no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4C22×C4×D312yes—
652C2×C4C22×C4×D318yes—
653C2×C4C22×C4×D312yes—
654C2×C4C22×C4×D312yes—
655C2×C4C2×D3×D412yes—
656C2×C4C2×D3×D412yes—
657C2×C4C2×D3×D412yes—
658C2×C4#100712yes—
659C2×C4#100712yes—
660C2×C4D3×#4112yes—
661C2×C4#101012yes—
662C2×C3C22×C4×D411yescharacteristic
663C2×C3C2×#51911yescharacteristic
664C2×C3C4×2−1+411yescharacteristic
665C2×C3#349711yescharacteristic
666C2×C3#349911yescharacteristic
667C2×C3#351811yescharacteristic
668C2×C3#352311yescharacteristic
669D3—44no—
670C22—64no—
671C22—64no—
672C22—64no—
673C22—122no—
674C22—122no—
675C22—122no—
676C22—122no—
677C22C23×C4×D311yescharacteristic
678C22C22×D3×D411yescharacteristic
679C22C2×#100711yescharacteristic
680C22C2×#100711yescharacteristic
681C22C2×D3×#4111yescharacteristic
682C22C2×#101011yescharacteristic
683C22#596411yescharacteristic
684C4—28no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—38no—
690C4—44no—
691C4—41no—
692C4—64no—
693C4—64no—
694C4—64no—
695C4—122no—
696C4—122no—
697C4—122no—
698C4C4×D3×D414yes—
699C4#557214yescomplemented
700C3#3431111yescharacteristic, complemented, Sylow
701C2—124no—
702C2C2×C4×D3×D411yescharacteristic
703C2C4×#100711yescharacteristic
704C2C2×#557211yescharacteristic
705C2#8621411yescharacteristic
706C2#8622211yescharacteristic
707C2#8626511yescharacteristic
708C2#8626611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC3×C4×C4⋊Q8C2
socle, cosocleC23×C3C25
prime radicalC22×D12C23
hypercenterC4×C4⋊Q8D3
hypocenterC3#34311
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#5572C2semidirect
3. C3×C4×C4⋊Q8C2semidirect
4. #83229C2semidirect
5. #82488C2semidirect
6. #76614C2semidirect
7. #76491C2semidirect
8. #75971C2semidirect
9. #75967C2semidirect
12. #74323C2semidirect
13. #73652C2semidirect
14. #73648C2semidirect
17. C42×Dic6C2semidirect
24. #5727C4semidirect
99. C4×C4⋊Q8D3semidirect
176. C4×Dic6D4semidirect
592. C3×C4#519semidirect
699. C4#5572semidirect
700. C3#34311semidirect

Maximal subgroups

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

subgroupindex
C2×#57272
C2×#55722
C3×C4×C4⋊Q82
#832292
#824882
#766142
#764912
#759712
#759672
#759612
#743242
#743232
#736522
#736482
#736392
#732992
C42×Dic62
#343113