Finite Group Databasebeta

← #11069137

Subgroups — #11069137

Order 768.

2276 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5582C212yesmaximal, complemented
2C3×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
3C4×#946C211yesmaximal, characteristic, complemented
4#82476C211yesmaximal, characteristic, complemented
5#82469C212yesmaximal, complemented
6#76257C214yesmaximal, complemented
7#76249C212yesmaximal, complemented
8#76121C214yesmaximal, complemented
9#76010C212yesmaximal, complemented
10#74375C211yesmaximal, characteristic
11#74362C212yesmaximal, complemented
12#74335C211yesmaximal, characteristic, complemented
13#74334C212yesmaximal, complemented
14#73788C212yesmaximal, complemented
15#73753C211yesmaximal, characteristic, complemented
16#73693C212yesmaximal, complemented
17#73653C211yesmaximal, characteristic, complemented
18#39351—31nomaximal, Sylow
19C2×C3×C4×Q8C2212yes—
20C2×C3×C4×Q8C2211yescharacteristic
21C2×#947C2212yes—
22C2×#946C2211yescharacteristic
23#5582—216no—
24C2×#896C2214yes—
25C2×#896C2214yes—
26C2×#895C2212yes—
27C2×#895C2212yes—
28C2×#895C2212yes—
29C2×#894C2214yes—
30C2×#893C2212yes—
31C2×#888C2212yes—
32C2×#888C2212yes—
33C2×#876C2214yes—
34C2×#875C2214yes—
35C2×#874C2211yescharacteristic
36C2×C4×D12C2212yes—
37C2×#872C2212yes—
38C2×C42×D3C2211yescharacteristic
39C3×#389C2214yes—
40C3×#389C2212yes—
41C3×#384C2212yes—
42C3×#384C2211yescharacteristic
43C3×C4×C4⋊C4C2211yescharacteristic
44C3×C4×C4⋊C4C2212yes—
45#5229C2211yescharacteristic
46#4993C2214yes—
47#4993C2214yes—
48#4992C2214yes—
49#4991C2214yes—
50#4991C2214yes—
51#4989C2212yes—
52#4989C2214yes—
53#4988C2212yes—
54#4988C2212yes—
55#4988C2212yes—
56#4988C2212yes—
57#4988C2212yes—
58#4987C2211yescharacteristic
59#4987C2211yescharacteristic
60#4987C2211yescharacteristic
61#4979C2214yes—
62#4978C2212yes—
63#4975C2211yescharacteristic
64#4975C2211yescharacteristic
65#4972C2212yes—
66#4972C2211yescharacteristic
67#4972C2212yes—
68#4940C2214yes—
69#4940C2214yes—
70#4939C2212yes—
71#4939C2212yes—
72#4939C2212yes—
73C4×(C2×D3)⋊C4C2212yes—
74C4×C4⋊Dic3C2211yescharacteristic
75C4×C4⋊Dic3C2211yescharacteristic
76C4×Dic3⋊C4C2212yes—
77C4×Dic3⋊C4C2212yes—
78#4676C2214yes—
79#4675C2214yes—
80#4673C2214yes—
81#4672C2214yes—
82#4667C2212yes—
83#4665C2214yes—
84#4650C2212yes—
85C2×#542—32no—
86#2856—31no—
87#2723—34no—
88#2672—34no—
89#2624—32no—
90#2551—31no—
91#2548—31no—
92#2542—32no—
93#2512—32no—
94#2491—32no—
95#2452—32no—
96#2448—32no—
97#2422—32no—
98#2366—31no—
99Q8×C4⋊C4D311yescharacteristic, complemented
100C4×C22⋊Q8—31no—
101#2285—31no—
102C22×C3×Q8C2311yescharacteristic
103C22×D12C2312yes—
104C22×D12C2312yes—
105C22×D12C2312yes—
106C22×D12C2314yes—
107C22×C4×D3C2311yescharacteristic
108C22×C4×D3C2311yescharacteristic
109C22×C4×D3C2311yescharacteristic
110C22×C4×D3C2314yes—
111C22×Dic6C2314yes—
112C3×C4×Q8—28no—
113C3×C4×Q8—24no—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2312yes—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2314yes—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2314yes—
123C2×C3×C42C2312yes—
124C2×C3×C42C2312yes—
125C2×C3×C42C2314yes—
126C2×C3×C42C2311yescharacteristic
127#947—28no—
128#946D418yescomplemented
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2312yes—
131C2×(C2×D3)⋊C4C2312yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2314yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×Dic3⋊C4C2312yes—
148C2×Dic3⋊C4C2312yes—
149C2×Dic3⋊C4C2312yes—
150C2×Dic3⋊C4C2312yes—
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2312yes—
153C2×Dic3⋊C4C2314yes—
154C2×Dic3⋊C4C2312yes—
155C2×C4×Dic3C2311yescharacteristic
156C2×C4×Dic3C2311yescharacteristic
157C2×C4×Dic3C2311yescharacteristic
158C2×C4×Dic3C2312yes—
159C2×C4×Dic3C2312yes—
160#896—216no—
161#896—48no—
162#895—28no—
163#895—44no—
164#895—44no—
165#894—216no—
166#893—44no—
167#888—28no—
168#888—44no—
169#876—216no—
170#875—216no—
171#874—24no—
172C4×D12—28no—
173#872—28no—
174C42×D3—24no—
175C3×#95C2312yes—
176C3×#95C2314yes—
177C3⋊#95C2312yes—
178C3⋊#95C2312yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186#542—616no—
187C2×C4⋊Q8—32no—
188C2×C4⋊Q8—32no—
189C2×#127—31no—
190C2×#126—34no—
191C2×#124—32no—
192C2×#124—34no—
193C2×#123—34no—
194C2×C22⋊Q8—31no—
195C2×C22⋊Q8—34no—
196C2×C22⋊Q8—34no—
197C2×#121—32no—
198C2×#121—32no—
199C2×#121—32no—
200C2×C4×Q8C2×D312yes—
201C2×C4×Q8C2×D311yescharacteristic
202C2×C4×D4—32no—
203C2×C4×D4—32no—
204C2×#117—32no—
205C22×C42—31no—
206#399—34no—
207#399—34no—
208#397—34no—
209#397—34no—
210#396—34no—
211#395—34no—
212#394—34no—
213#394—34no—
214#394—34no—
215#393—34no—
216#391—31no—
217#390—32no—
218#390—32no—
219#390—32no—
220#390—32no—
221#390—32no—
222#390—32no—
223#390—32no—
224#390—32no—
225#389—32no—
226#389—32no—
227#389—31no—
228#389C2×D312yes—
229#389C2×D314yes—
230#388—34no—
231#388—34no—
232#387—32no—
233#386—34no—
234#385—32no—
235#385—34no—
236#384—31no—
237#384—31no—
238#384C2×D311yescharacteristic
239#384C2×D312yes—
240#382—32no—
241#380—31no—
242#380—31no—
243#380—31no—
244#380—32no—
245C4×C4⋊C4—31no—
246C4×C4⋊C4—32no—
247C4×C4⋊C4—32no—
248C4×C4⋊C4—31no—
249C4×C4⋊C4C2×D311yescharacteristic
250C4×C4⋊C4C2×D312yes—
251C4×C22⋊C4—32no—
252C23×D3C2414yes—
253C23×D3C2411yescharacteristic
254C2×C3×Q8—22no—
255C2×C3×Q8—22no—
256C2×C3×Q8C2×D414yes—
257C22×C3×C4C2412yes—
258C22×C3×C4C2412yes—
259C22×C3×C4C2414yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2412yes—
262C22×C3×C4C2411yescharacteristic
263C22×C3×C4C2411yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C22×Dic3C2411yescharacteristic
266C22×Dic3C2412yes—
267C22×Dic3C2412yes—
268C22×Dic3C2412yes—
269C22×Dic3C2411yescharacteristic
270C22×Dic3C2412yes—
271C22×Dic3C2411yescharacteristic
272C2×D12—24no—
273C2×D12—24no—
274C2×D12—24no—
275C2×D12—24no—
276C2×D12—24no—
277C2×D12—24no—
278C2×D12—28no—
279C2×D12—24no—
280C2×D12—42no—
281C2×D12—44no—
282C2×D12—44no—
283C2×D12—42no—
284C2×C4×D3—22no—
285C2×C4×D3—22no—
286C2×C4×D3—22no—
287C2×C4×D3—22no—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×C4×D3—28no—
292C2×C4×D3—41no—
293C2×C4×D3—44no—
294C2×C4×D3—44no—
295C2×C4×D3C2×D414yes—
296C2×Dic6—28no—
297C2×Dic6—44no—
298C2×Dic6—44no—
299C3×C4⋊C4—24no—
300C3×C4⋊C4—28no—
301C3×C4⋊C4—24no—
302C3×C4⋊C4—22no—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—42no—
307C3×C4⋊C4—44no—
308C3×C42—24no—
309C3×C42—28no—
310C3×C42—24no—
311C3×C42#4114yes—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—28no—
315(C2×D3)⋊C4—28no—
316(C2×D3)⋊C4—28no—
317(C2×D3)⋊C4—28no—
318(C2×D3)⋊C4—28no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4—44no—
322(C2×D3)⋊C4—44no—
323(C2×D3)⋊C4—44no—
324(C2×D3)⋊C4—42no—
325(C2×D3)⋊C4C2×D418yes—
326C4⋊Dic3—22no—
327C4⋊Dic3—22no—
328C4⋊Dic3—22no—
329C4⋊Dic3C2×D414yes—
330Dic3⋊C4—24no—
331Dic3⋊C4—24no—
332Dic3⋊C4—28no—
333Dic3⋊C4—24no—
334Dic3⋊C4—24no—
335Dic3⋊C4—44no—
336Dic3⋊C4—42no—
337Dic3⋊C4C2×D418yes—
338C4×Dic3—24no—
339C4×Dic3—22no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—24no—
343C22×Q8—34no—
344C22×Q8C22×D311yescharacteristic
345C22×D4—32no—
346C22×D4—32no—
347C22×D4—34no—
348C22×D4—32no—
349C23×C4—31no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—34no—
353C4⋊Q8—68no—
354C4⋊Q8—124no—
355#127—64no—
356#126—616no—
357#124—616no—
358#124—68no—
359#123—616no—
360C22⋊Q8—38no—
361C22⋊Q8—616no—
362C22⋊Q8—128no—
363#121—68no—
364#121—124no—
365#121—124no—
366C4×Q8—28no—
367C4×Q8—24no—
368C4×D4—68no—
369C4×D4—124no—
370#117—68no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—34no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4C22×D311yescharacteristic
384C2×C4⋊C4C22×D312yes—
385C2×C4⋊C4C22×D314yes—
386C2×C4⋊C4C22×D311yescharacteristic
387C2×C4⋊C4C22×D312yes—
388C2×C4⋊C4C22×D312yes—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D312yes—
391C2×C4⋊C4C22×D314yes—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—34no—
398C2×C22⋊C4—34no—
399C2×C22⋊C4—34no—
400C2×C22⋊C4—34no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C42—32no—
407C2×C42—32no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—64no—
412C2×C42C22×D312yes—
413C2×C42C22×D314yes—
414C2×C42C22×D312yes—
415C2×C42C22×D311yescharacteristic
416#95—32no—
417#95—32no—
418#95—32no—
419#95—32no—
420#95—32no—
421#95—32no—
422#95—32no—
423#95—32no—
424#95—34no—
425#95C22×D312yes—
426#95C22×D314yes—
427C23×C3C2511yescharacteristic
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—24no—
438C22×D3—24no—
439C22×D3—24no—
440C22×D3—24no—
441C22×D3C22×D412yes—
442C3×Q8—28no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—24no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4C22×D414yes—
460C2×C3×C4C22×D412yes—
461C2×C3×C4C2×#4112yes—
462C2×C3×C4C2×#4112yes—
463C2×C3×C4C2×#4112yes—
464C2×C3×C4H(5,𝔽2)12yes—
465C2×C3×C42−1+412yes—
466C2×C3×C42−1+412yes—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—21no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—21no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3C22×D412yes—
486C2×Dic3C22×D414yes—
487C2×Dic3H(5,𝔽2)12yes—
488D12—48no—
489D12—48no—
490D12—84no—
491D12—88no—
492C4×D3—28no—
493C4×D3—44no—
494C4×D3—44no—
495C4×D3—88no—
496Dic6—88no—
497C24—31no—
498C24—34no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—68no—
502C2×Q8—124no—
503C2×Q8—124no—
504C2×Q8D3×D414yes—
505C2×D4—68no—
506C2×D4—64no—
507C2×D4—64no—
508C2×D4—64no—
509C2×D4—64no—
510C2×D4—64no—
511C2×D4—64no—
512C2×D4—64no—
513C2×D4—122no—
514C2×D4—124no—
515C2×D4—124no—
516C2×D4—122no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—32no—
520C22×C4—34no—
521C22×C4—31no—
522C22×C4—32no—
523C22×C4—32no—
524C22×C4—32no—
525C22×C4—62no—
526C22×C4—68no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—121no—
534C22×C4—124no—
535C22×C4—124no—
536C22×C4C23×D312yes—
537C22×C4C23×D312yes—
538C22×C4C23×D312yes—
539C22×C4C23×D314yes—
540C22×C4C23×D311yescharacteristic
541C22×C4C23×D312yes—
542C22×C4C23×D311yescharacteristic
543C22×C4C23×D311yescharacteristic
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—24no—
547C4⋊C4—28no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—24no—
551C4⋊C4—34no—
552C4⋊C4—38no—
553C4⋊C4—42no—
554C4⋊C4—44no—
555C4⋊C4—64no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—64no—
559C4⋊C4—68no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—62no—
563C4⋊C4—124no—
564C4⋊C4—122no—
565C22⋊C4—38no—
566C22⋊C4—68no—
567C22⋊C4—68no—
568C22⋊C4—68no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—124no—
574C22⋊C4—124no—
575C22⋊C4—124no—
576C22⋊C4—122no—
577C22⋊C4—124no—
578C22⋊C4—124no—
579C42—24no—
580C42—24no—
581C42—28no—
582C42—62no—
583C42—62no—
584C42—62no—
585C42—64no—
586C42—64no—
587C42#23514yes—
588C22×C3C23×D411yescharacteristic
589C22×C3C22×#4111yescharacteristic
590C22×C3C2×H(5,𝔽2)11yescharacteristic
591C22×C3C2×H(5,𝔽2)11yescharacteristic
592C22×C3C2×2−1+411yescharacteristic
593C22×C3C2×2−1+411yescharacteristic
594C22×C3#58511yescharacteristic
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—44no—
605C2×D3—44no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C3×C4—24no—
610C3×C4—22no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—44no—
614C3×C4—42no—
615C3×C4#54214yescomplemented
616C3×C4#54714yes—
617Dic3—22no—
618Dic3—22no—
619Dic3—24no—
620Dic3—41no—
621Dic3—42no—
622Dic3—42no—
623Dic3—42no—
624C23—32no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—64no—
632C23—64no—
633C23—64no—
634C23—64no—
635C23—64no—
636C23—64no—
637C23—64no—
638C23C24×D311yescharacteristic
639Q8—28no—
640Q8—248no—
641D4—128no—
642D4—128no—
643D4—244no—
644D4—248no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—34no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—61no—
670C2×C4—68no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—61no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—124no—
684C2×C4—124no—
685C2×C4—248no—
686C2×C4C2×#23512yes—
687C2×C4C2×#23512yes—
688C2×C4C2×#23512yes—
689C2×C4C2×D3×D414yes—
690C2×C4C2×D3×D412yes—
691C2×C4#100712yes—
692C2×C4#100712yes—
693C2×C4#100912yes—
694C2×C3C2×#54211yescharacteristic
695C2×C3C2×#54711yescharacteristic
696C2×C3#349411yescharacteristic
697C2×C3#349711yescharacteristic
698C2×C3#349811yescharacteristic
699C2×C3#355011yescharacteristic
700C2×C3#355411yescharacteristic
701D3—42no—
702D3—84no—
703C22—62no—
704C22—62no—
705C22—62no—
706C22—121no—
707C22—121no—
708C22—121no—
709C22—121no—
710C22—124no—
711C22—124no—
712C22—124no—
713C22—124no—
714C22—124no—
715C22—124no—
716C22—124no—
717C22C22×#23511yescharacteristic
718C22C22×D3×D411yescharacteristic
719C22C2×#100711yescharacteristic
720C22C2×#100711yescharacteristic
721C22C2×#100911yescharacteristic
722C22D3×H(5,𝔽2)11yescharacteristic
723C22#596811yescharacteristic
724C4—22no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—44no—
730C4—62no—
731C4—62no—
732C4—64no—
733C4—121no—
734C4—122no—
735C4—122no—
736C4—122no—
737C4#550714yes—
738C4#558214yescomplemented
739C3#3935111yescharacteristic, complemented, Sylow
740C2—122no—
741C2—244no—
742C2C2×#550711yescharacteristic
743C2C2×#558211yescharacteristic
744C2#8590311yescharacteristic
745C2#8676011yescharacteristic
746C2#8677011yescharacteristic
747C2#8703511yescharacteristic
748C2#8704411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×Q8×C4⋊C4C2
prime radical#74375C2
hypercenterQ8×C4⋊C4D3
hypocenterC3#39351
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#5582C2semidirect
2. C3×Q8×C4⋊C4C2semidirect
3. C4×#946C2semidirect
4. #82476C2semidirect
5. #82469C2semidirect
6. #76257C2semidirect
7. #76249C2semidirect
8. #76121C2semidirect
9. #76010C2semidirect
11. #74362C2semidirect
12. #74335C2semidirect
13. #74334C2semidirect
14. #73788C2semidirect
15. #73753C2semidirect
16. #73693C2semidirect
17. #73653C2semidirect
99. Q8×C4⋊C4D3semidirect
128. #946D4semidirect
615. C3×C4#542semidirect
738. C4#5582semidirect
739. C3#39351semidirect

Maximal subgroups

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

subgroupindex
C2×#55822
C3×Q8×C4⋊C42
C4×#9462
#824762
#824692
#762572
#762492
#761212
#760102
#743752
#743622
#743352
#743342
#737882
#737532
#736932
#736532
#393513