Finite Group Databasebeta

← D3×#5731 #11901564

Subgroups — D3×#5731 #11901564

Order 1152.

2104 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596202C211yesmaximal, characteristic, complemented
2C3×#5731C211yesmaximal, characteristic, complemented
3C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
4D3×#946C212yesmaximal
5D3×Q8×Dic3C212yesmaximal, complemented
6#10595354C212yesmaximal, complemented
7#10595349C212yesmaximal, complemented
8D3×#898C214yesmaximal
9#10594446C214yesmaximal, complemented
10D3×#889C214yesmaximal, complemented
11#10594316C214yesmaximal, complemented
12D3×#872C211yesmaximal, characteristic
13D3×#870C211yesmaximal, characteristic, complemented
14#10593867C211yesmaximal, characteristic, complemented
15#10593862C211yesmaximal, characteristic, complemented
16D3×#541—31nomaximal
17C2×#5731—31nomaximal
18C2×C3×D3×Q8C2212yes—
19C2×C4×D32C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21#64155C2212yes—
22Q8×C3⋊Dic3C2212yescomplemented
23#64107C2214yes—
24#64098C2214yescomplemented
25#64081C2211yescharacteristic
26#64079C2211yescharacteristic, complemented
27C3×#946C2212yes—
28C3×Q8×Dic3C2212yescomplemented
29C3×#944C2212yescomplemented
30C3×#898C2214yes—
31C3×D3×C4⋊C4C2214yes—
32C3×#889C2214yescomplemented
33C3×#888C2214yescomplemented
34C3×#872C2211yescharacteristic
35C3×C42×D3C2211yescharacteristic
36C3×#870C2211yescharacteristic, complemented
37C3×#869C2211yescharacteristic, complemented
38D3×(C2×D3)⋊C4C2214yes—
39D3×(C2×D3)⋊C4C2212yes—
40D3×C4⋊Dic3C2214yes—
41D3×C4⋊Dic3C2212yes—
42#63888C2214yes—
43#63887C2214yes—
44#63877C2212yes—
45D3×Dic3⋊C4C2214yes—
46D3×Dic3⋊C4C2214yes—
47D3×Dic3⋊C4C2212yes—
48C4×D3×Dic3C2211yescharacteristic
49C4×D3×Dic3C2214yes—
50#63874C2211yescharacteristic
51#63871C2212yes—
52#63870C2214yescomplemented
53#63869C2212yescomplemented
54#63868C2214yes—
55#63867C2214yescomplemented
56#63867C2214yescomplemented
57#63862C2214yes—
58#63861C2214yes—
59#63858C2214yes—
60#63856C2212yes—
61#63855C2211yescharacteristic
62#63848C2214yes—
63#63848C2214yes—
64#63847C2214yescomplemented
65#63847C2214yescomplemented
66#63846C2214yescomplemented
67#63845C2214yescomplemented
68#63843C2214yescomplemented
69#63843C2212yescomplemented
70Dic3×Dic6C2214yescomplemented
71Dic3×Dic6C2212yescomplemented
72#63836C2212yes—
73C3×#541—31no—
74C2×C3×C4⋊Q8—31no—
75C2×#946—32no—
76C2×Q8×Dic3—32no—
77#5731—31no—
78#5731—31no—
79#5731—32no—
80#5731—32no—
81#5731—34no—
82#5731—34no—
83#5731—31no—
84#5731—31no—
85#5731—61no—
86#5731D311yescharacteristic, direct product factor
87D3×C4⋊Q8D311yescharacteristic, complemented
88D3×#126—34no—
89#5701—34no—
90#5698—31no—
91#5696—34no—
92D3×#125—34no—
93D3×#125—31no—
94D3×C22⋊Q8—32no—
95#5625—32no—
96#5583—32no—
97C4×D3×Q8—32no—
98D3×#117—31no—
99#5518—31no—
100C2×#898—34no—
101C2×#889—34no—
102C2×#872—31no—
103C2×#870—31no—
104C22×D32C2311yescharacteristic
105C2×C32×Q8C2312yes—
106C2×C4×C3⋊D3C2311yescharacteristic
107C3×D3×Q8—28no—
108C2×C3×C4×D3C2314yes—
109C2×C3×C4×D3C2312yes—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2314yes—
113C2×C3×Dic6C2312yes—
114C2×#624C2311yescharacteristic
115C2×D3×Dic3C2311yescharacteristic
116C2×D3×Dic3C2311yescharacteristic
117C2×D3×Dic3C2312yes—
118C2×D3×Dic3C2314yes—
119C4×D32—24no—
120C32×C4⋊C4C2314yes—
121C32×C42C2311yescharacteristic
122#3752C2312yes—
123#3752C2314yes—
124C4⋊(C3⋊Dic3)C2312yes—
125C4⋊(C3⋊Dic3)C2314yes—
126#3750C2314yes—
127#3750C2312yes—
128#3750C2314yes—
129C4×C3⋊Dic3C2311yescharacteristic
130C4×C3⋊Dic3C2314yes—
131C3×(C2×D3)⋊C4C2314yes—
132C3×(C2×D3)⋊C4C2312yes—
133C3×C4⋊Dic3C2314yes—
134C3×C4⋊Dic3C2314yes—
135C3×C4⋊Dic3C2312yes—
136C3×Dic3⋊C4C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2312yes—
140C3×Dic3⋊C4C2314yes—
141C3×C4×Dic3C2312yes—
142C3×C4×Dic3C2314yes—
143C3×C4×Dic3C2311yescharacteristic
144C3×C4×Dic3C2311yescharacteristic
145#3724C2314yes—
146#3724C2312yes—
147#3724C2314yes—
148Dic3⋊Dic3C2312yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154#3722C2312yes—
155#3722C2314yes—
156(C2×D3)⋊Dic3C2312yes—
157(C2×D3)⋊Dic3C2314yes—
158Dic32C2312yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#541—91noSylow
162C22×C3×Q8—32no—
163C2×D3×Q8C2×D312yes—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C3×C4⋊Q8—21no—
167C3×C4⋊Q8—32no—
168C3×C4⋊Q8—34no—
169C3×C4⋊Q8—31no—
170C3×C4⋊Q8C2×D311yescharacteristic, complemented
171C3×C4⋊Q8C2×D311yescharacteristic, complemented
172C3×#126—34no—
173C3×#125—34no—
174C3×#125—31no—
175C3×C22⋊Q8—32no—
176C3×C4×Q8—32no—
177C3×#117—31no—
178C2×C3×C4⋊C4—34no—
179C2×C3×C42—31no—
180#946—32no—
181#946—32no—
182#946—32no—
183#946—34no—
184#946—32no—
185#946—34no—
186#946—62no—
187#946C2×D312yes—
188Q8×Dic3—32no—
189Q8×Dic3—32no—
190Q8×Dic3—32no—
191Q8×Dic3—34no—
192Q8×Dic3—34no—
193Q8×Dic3—32no—
194Q8×Dic3—62no—
195Q8×Dic3C2×D312yescomplemented
196#944C2×D312yescomplemented
197C2×(C2×D3)⋊C4—32no—
198C2×(C2×D3)⋊C4—34no—
199#926—31no—
200C2×C4⋊Dic3—32no—
201C2×C4⋊Dic3—34no—
202#924—32no—
203C2×Dic3⋊C4—34no—
204C2×Dic3⋊C4—32no—
205C2×Dic3⋊C4—34no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—34no—
208#898—34no—
209#898—34no—
210#898—34no—
211#898—34no—
212#898—34no—
213#898—34no—
214#898—34no—
215#898—34no—
216#898—34no—
217#898—34no—
218#898—64no—
219#898C2×D314yes—
220#897—32no—
221#896—34no—
222#892—32no—
223D3×C4⋊C4—34no—
224D3×C4⋊C4—32no—
225D3×C4⋊C4—34no—
226D3×C4⋊C4—34no—
227D3×C4⋊C4—32no—
228D3×C4⋊C4C2×D314yes—
229#890—34no—
230#890—34no—
231#890—32no—
232#889—34no—
233#889—34no—
234#889—34no—
235#889—34no—
236#889—34no—
237#889—34no—
238#889—34no—
239#889—34no—
240#889—34no—
241#889—34no—
242#889—34no—
243#889—34no—
244#889—64no—
245#889C2×D314yescomplemented
246#888C2×D314yescomplemented
247#887—34no—
248#887—32no—
249D3×C22⋊C4—32no—
250D3×C22⋊C4—34no—
251#879—34no—
252#879—34no—
253#879—34no—
254#878—34no—
255#877—32no—
256#876—34no—
257#872—31no—
258#872—31no—
259#872—31no—
260#872—32no—
261#872—32no—
262#872—31no—
263#872—31no—
264#872—61no—
265#872C2×D311yescharacteristic
266C42×D3—34no—
267C42×D3—31no—
268C42×D3C2×D311yescharacteristic
269#870—31no—
270#870—31no—
271#870—32no—
272#870—34no—
273#870—34no—
274#870—61no—
275#870C2×D311yescharacteristic, complemented
276#869C2×D311yescharacteristic, complemented
277C4×Dic6—34no—
278C4×Dic6—32no—
279C22×C3⋊D3C2411yescharacteristic
280C22×C3×D3C2411yescharacteristic
281C22×C3×D3C2411yescharacteristic
282C2×D32—22no—
283C2×D32—24no—
284C32×Q8—24no—
285C2×C32×C4C2412yes—
286C2×C32×C4C2414yes—
287C2×C32×C4C2411yescharacteristic
288C2×C3⋊Dic3C2412yes—
289C2×C3⋊Dic3C2414yes—
290C2×C3⋊Dic3C2411yescharacteristic
291C4×C3⋊D3—22no—
292C2×C3×Dic3C2412yes—
293C2×C3×Dic3C2414yes—
294C2×C3×Dic3C2414yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2411yescharacteristic
297C2×C3×Dic3C2411yescharacteristic
298C3×C4×D3—28no—
299C3×C4×D3—24no—
300C3×C4×D3—22no—
301C3×C4×D3#4114yes—
302C3×Dic6—24no—
303C3×Dic6—28no—
304#624—22no—
305D3×Dic3—22no—
306D3×Dic3—24no—
307D3×Dic3—28no—
308D3×Dic3—22no—
309#541—31no—
310#541—91no—
311#541—92no—
312#541—92no—
313#541—94no—
314#541—91no—
315#541—94no—
316#541—91no—
317C2×C4⋊Q8—31no—
318C2×#126—94no—
319C2×#125—91no—
320C2×#125—94no—
321C2×C22⋊Q8—92no—
322C2×C4×Q8—92no—
323C2×#117—91no—
324C23×D3—31no—
325C23×D3—31no—
326C2×C3×Q8—22no—
327C2×C3×Q8—34no—
328C2×C3×Q8—32no—
329C2×C3×Q8—68no—
330C2×C3×Q8C22×D312yes—
331C2×C3×Q8C22×D312yes—
332C22×C3×C4—31no—
333C22×C3×C4—34no—
334C22×C3×C4—32no—
335C22×C3×C4—31no—
336C22×Dic3—31no—
337C22×Dic3—32no—
338C22×Dic3—34no—
339C22×Dic3—31no—
340D3×Q8—28no—
341C2×C4×D3—32no—
342C2×C4×D3—34no—
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—31no—
349C2×C4×D3—61no—
350C2×C4×D3—64no—
351C2×C4×D3—64no—
352C2×C4×D3C22×D314yes—
353C2×C4×D3C22×D312yes—
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6C22×D312yes—
357C2×Dic6C22×D314yes—
358C3×C4⋊C4—24no—
359C3×C4⋊C4—34no—
360C3×C4⋊C4—32no—
361C3×C4⋊C4—32no—
362C3×C4⋊C4—34no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4C22×D314yes—
368C3×C4⋊C4C22×D314yes—
369C3×C22⋊C4—32no—
370C3×C22⋊C4—34no—
371C3×C42—21no—
372C3×C42—31no—
373C3×C42—34no—
374C3×C42—32no—
375C3×C42—31no—
376C3×C42C22×D311yescharacteristic
377C3×C42C22×D311yescharacteristic
378#217—32no—
379#217—34no—
380(C2×D3)⋊C4—32no—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—32no—
383(C2×D3)⋊C4—32no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4—32no—
387(C2×D3)⋊C4—32no—
388(C2×D3)⋊C4—34no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—64no—
392(C2×D3)⋊C4C22×D312yes—
393(C2×D3)⋊C4C22×D314yes—
394C4⋊Dic3—32no—
395C4⋊Dic3—34no—
396C4⋊Dic3—32no—
397C4⋊Dic3—34no—
398C4⋊Dic3—34no—
399C4⋊Dic3—34no—
400C4⋊Dic3—34no—
401C4⋊Dic3—32no—
402C4⋊Dic3—34no—
403C4⋊Dic3—34no—
404C4⋊Dic3—62no—
405C4⋊Dic3—64no—
406C4⋊Dic3C22×D314yes—
407C4⋊Dic3C22×D312yes—
408C4⋊Dic3C22×D314yes—
409Dic3⋊C4—34no—
410Dic3⋊C4—34no—
411Dic3⋊C4—34no—
412Dic3⋊C4—32no—
413Dic3⋊C4—32no—
414Dic3⋊C4—34no—
415Dic3⋊C4—34no—
416Dic3⋊C4—34no—
417Dic3⋊C4—34no—
418Dic3⋊C4—32no—
419Dic3⋊C4—34no—
420Dic3⋊C4—34no—
421Dic3⋊C4—32no—
422Dic3⋊C4—32no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—64no—
428Dic3⋊C4—62no—
429Dic3⋊C4—64no—
430Dic3⋊C4C22×D314yes—
431Dic3⋊C4C22×D314yes—
432Dic3⋊C4C22×D312yes—
433Dic3⋊C4C22×D314yes—
434Dic3⋊C4C22×D314yes—
435C4×Dic3—31no—
436C4×Dic3—34no—
437C4×Dic3—31no—
438C4×Dic3—34no—
439C4×Dic3—32no—
440C4×Dic3—34no—
441C4×Dic3—34no—
442C4×Dic3—32no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—61no—
446C4×Dic3—64no—
447C4×Dic3C22×D311yescharacteristic
448C4×Dic3C22×D312yes—
449C4×Dic3C22×D311yescharacteristic
450C4×Dic3C22×D314yes—
451C22×C32C2511yescharacteristic
452C2×C3⋊D3—21no—
453C2×C3⋊D3—22no—
454C2×C3×D3—21no—
455C2×C3×D3—22no—
456C2×C3×D3C2×#4112yes—
457C2×C3×D32−1+414yes—
458D32—44no—
459C32×C4—24no—
460C32×C4—22no—
461C32×C4C2×#4112yes—
462C3⋊Dic3—21no—
463C3⋊Dic3—22no—
464C3⋊Dic3—24no—
465C3×Dic3—21no—
466C3×Dic3—24no—
467C3×Dic3—22no—
468C3×Dic3—24no—
469C3×Dic3—22no—
470C3×Dic3C2×#4112yes—
471C22×Q8—32no—
472C23×C4—91no—
473C4⋊Q8—32no—
474C4⋊Q8—34no—
475C4⋊Q8—31no—
476C4⋊Q8D3211yescharacteristic, complemented
477#126—34no—
478#126—94no—
479#126—94no—
480#126—94no—
481#126—94no—
482#126—94no—
483#126—94no—
484#126—94no—
485#125—34no—
486#125—31no—
487#125—94no—
488#125—94no—
489#125—92no—
490#125—94no—
491#125—94no—
492#125—94no—
493#125—94no—
494#125—94no—
495#125—94no—
496#125—91no—
497C22⋊Q8—32no—
498C22⋊Q8—94no—
499C22⋊Q8—94no—
500C22⋊Q8—92no—
501C22⋊Q8—92no—
502C22⋊Q8—92no—
503C4×Q8—32no—
504C4×Q8—92no—
505C4×Q8—94no—
506C4×Q8—94no—
507C4×Q8—92no—
508C4×Q8—92no—
509#117—31no—
510#117—91no—
511#117—92no—
512#117—92no—
513#117—91no—
514#117—91no—
515C2×C4⋊C4—34no—
516C2×C4⋊C4—92no—
517C2×C4⋊C4—92no—
518C2×C4⋊C4—94no—
519C2×C4⋊C4—94no—
520C2×C4⋊C4—94no—
521C2×C22⋊C4—92no—
522C2×C22⋊C4—94no—
523C2×C42—31no—
524C2×C42—91no—
525C2×C42—94no—
526C23×C3—31no—
527C23×C3—31no—
528C22×D3—31no—
529C22×D3—31no—
530C22×D3—61no—
531C22×D3—62no—
532C22×D3—64no—
533C22×D3—62no—
534C22×D3—64no—
535C22×D3C23×D311yescharacteristic
536C22×D3C23×D311yescharacteristic
537C3×Q8—24no—
538C3×Q8—24no—
539C3×Q8—44no—
540C3×Q8—68no—
541C3×Q8—64no—
542C2×C3×C4—21no—
543C2×C3×C4—24no—
544C2×C3×C4—22no—
545C2×C3×C4—31no—
546C2×C3×C4—34no—
547C2×C3×C4—32no—
548C2×C3×C4—34no—
549C2×C3×C4—34no—
550C2×C3×C4—32no—
551C2×C3×C4—31no—
552C2×C3×C4—64no—
553C2×C3×C4—68no—
554C2×C3×C4—62no—
555C2×C3×C4C23×D314yes—
556C2×C3×C4C23×D314yes—
557C2×C3×C4C23×D312yes—
558C2×C3×C4C23×D312yes—
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×Dic3—32no—
562C2×Dic3—32no—
563C2×Dic3—34no—
564C2×Dic3—34no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—62no—
568C2×Dic3—64no—
569C2×Dic3—61no—
570C2×Dic3—62no—
571C2×Dic3—64no—
572C2×Dic3—68no—
573C2×Dic3—62no—
574C2×Dic3C23×D312yes—
575C2×Dic3C23×D314yes—
576C2×Dic3C23×D314yes—
577C2×Dic3C23×D312yes—
578C2×Dic3C23×D311yescharacteristic
579C2×Dic3C23×D311yescharacteristic
580C4×D3—28no—
581C4×D3—24no—
582C4×D3—22no—
583C4×D3—62no—
584C4×D3—62no—
585C4×D3—62no—
586C4×D3—64no—
587C4×D3—68no—
588C4×D3—62no—
589C4×D3—62no—
590C4×D3—62no—
591C4×D3—122no—
592C4×D3#23714yes—
593Dic6—24no—
594Dic6—28no—
595C2×C32C22×#4111yescharacteristic
596C2×C32C2×2−1+412yes—
597C3⋊D3—41no—
598C3×D3—41no—
599C3×D3#54114yescomplemented
600C24—91no—
601C2×Q8—34no—
602C2×Q8—32no—
603C2×Q8—68no—
604C2×Q8C2×D3212yes—
605C22×C4—31no—
606C22×C4—32no—
607C22×C4—34no—
608C22×C4—31no—
609C22×C4—91no—
610C22×C4—92no—
611C22×C4—94no—
612C22×C4—91no—
613C22×C4—91no—
614C22×C4—91no—
615C22×C4—184no—
616C4⋊C4—34no—
617C4⋊C4—34no—
618C4⋊C4—34no—
619C4⋊C4—32no—
620C4⋊C4—32no—
621C4⋊C4—34no—
622C4⋊C4—34no—
623C4⋊C4—34no—
624C4⋊C4—92no—
625C4⋊C4—92no—
626C4⋊C4—94no—
627C4⋊C4—94no—
628C4⋊C4—94no—
629C4⋊C4—94no—
630C4⋊C4—94no—
631C4⋊C4—94no—
632C4⋊C4—94no—
633C4⋊C4—92no—
634C4⋊C4—92no—
635C4⋊C4—94no—
636C4⋊C4—94no—
637C4⋊C4—94no—
638C4⋊C4C2×D3214yes—
639C22⋊C4—32no—
640C22⋊C4—34no—
641C22⋊C4—92no—
642C22⋊C4—94no—
643C22⋊C4—92no—
644C22⋊C4—94no—
645C22⋊C4—92no—
646C22⋊C4—94no—
647C42—32no—
648C42—31no—
649C42—31no—
650C42—34no—
651C42—92no—
652C42—94no—
653C42—94no—
654C42—91no—
655C42—94no—
656C42C2×D3211yescharacteristic
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—34no—
660C22×C3—61no—
661C22×C3—62no—
662C22×C3C24×D311yescharacteristic
663C22×C3C24×D311yescharacteristic
664C2×D3—21no—
665C2×D3—22no—
666C2×D3—61no—
667C2×D3—62no—
668C2×D3—61no—
669C2×D3—62no—
670C2×D3—121no—
671C2×D3—122no—
672C2×D3—124no—
673C2×D3—124no—
674C2×D3C2×#23712yes—
675C2×D3#100714yes—
676C3×C4—24no—
677C3×C4—22no—
678C3×C4—24no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—32no—
682C3×C4—44no—
683C3×C4—42no—
684C3×C4—61no—
685C3×C4—62no—
686C3×C4—64no—
687C3×C4—64no—
688C3×C4—62no—
689C3×C4C2×#23712yes—
690C3×C4D3×#4112yes—
691Dic3—24no—
692Dic3—22no—
693Dic3—21no—
694Dic3—22no—
695Dic3—24no—
696Dic3—61no—
697Dic3—62no—
698Dic3—64no—
699Dic3—61no—
700Dic3—62no—
701Dic3—64no—
702Dic3—121no—
703Dic3—122no—
704Dic3—124no—
705Dic3C2×#23712yes—
706C32C2×#54111yescharacteristic, complemented, Sylow
707C23—31no—
708C23—31no—
709C23—91no—
710C23—182no—
711C23—184no—
712Q8—24no—
713Q8—68no—
714Q8—64no—
715C2×C4—31no—
716C2×C4—34no—
717C2×C4—32no—
718C2×C4—32no—
719C2×C4—34no—
720C2×C4—34no—
721C2×C4—31no—
722C2×C4—68no—
723C2×C4—64no—
724C2×C4—62no—
725C2×C4—92no—
726C2×C4—94no—
727C2×C4—91no—
728C2×C4—182no—
729C2×C4—182no—
730C2×C4—182no—
731C2×C4—184no—
732C2×C4—188no—
733C2×C4—182no—
734C2×C4C22×D3214yes—
735C2×C4C22×D3212yes—
736C2×C4C22×D3211yescharacteristic
737C2×C3—21no—
738C2×C3—22no—
739C2×C3—34no—
740C2×C3—121no—
741C2×C3C22×#23711yescharacteristic
742C2×C3C2×#100712yes—
743C2×C3C2×D3×#4111yescharacteristic
744C2×C3D3×2−1+412yes—
745D3—41no—
746D3—121no—
747D3—121no—
748D3—241no—
749D3#573114yesdirect product factor
750C22—32no—
751C22—34no—
752C22—61no—
753C22—62no—
754C22—181no—
755C22—182no—
756C22—364no—
757C22C23×D3211yescharacteristic
758C4—24no—
759C4—22no—
760C4—32no—
761C4—61no—
762C4—64no—
763C4—62no—
764C4—62no—
765C4—64no—
766C4—181no—
767C4—182no—
768C4—184no—
769C4D3×#23712yes—
770C3—21no—
771C3C2×#573111yescharacteristic, complemented
772C3D3×#54111yescharacteristic, complemented
773C2—34no—
774C2—121no—
775C2—361no—
776C2C2×D3×#23711yescharacteristic
777C2D3×#100712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC22×D32C23
hypercenterC4⋊Q8D32
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596202C2semidirect
2. C3×#5731C2semidirect
3. C3×D3×C4⋊Q8C2semidirect
5. D3×Q8×Dic3C2semidirect
6. #10595354C2semidirect
7. #10595349C2semidirect
9. #10594446C2semidirect
10. D3×#889C2semidirect
11. #10594316C2semidirect
13. D3×#870C2semidirect
14. #10593867C2semidirect
15. #10593862C2semidirect
20. C32×C4⋊Q8C22semidirect
22. Q8×C3⋊Dic3C22semidirect
24. #64098C22semidirect
26. #64079C22semidirect
28. C3×Q8×Dic3C22semidirect
29. C3×#944C22semidirect
32. C3×#889C22semidirect
33. C3×#888C22semidirect
36. C3×#870C22semidirect
37. C3×#869C22semidirect
52. #63870C22semidirect
53. #63869C22semidirect
55. #63867C22semidirect
56. #63867C22semidirect
64. #63847C22semidirect
65. #63847C22semidirect
66. #63846C22semidirect
67. #63845C22semidirect
68. #63843C22semidirect
69. #63843C22semidirect
70. Dic3×Dic6C22semidirect
71. Dic3×Dic6C22semidirect
86. #5731D3direct (N × H)
87. D3×C4⋊Q8D3semidirect
170. C3×C4⋊Q8C2×D3semidirect
171. C3×C4⋊Q8C2×D3semidirect
195. Q8×Dic3C2×D3semidirect
196. #944C2×D3semidirect
245. #889C2×D3semidirect
246. #888C2×D3semidirect
275. #870C2×D3semidirect
276. #869C2×D3semidirect
476. C4⋊Q8D32semidirect
599. C3×D3#541semidirect
706. C32C2×#541semidirect
749. D3#5731direct (N × H)
771. C3C2×#5731semidirect
772. C3D3×#541semidirect

Maximal subgroups

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

subgroupindex
#105962022
C3×#57312
C3×D3×C4⋊Q82
D3×#9462
D3×Q8×Dic32
#105953542
#105953492
D3×#8982
#105944462
D3×#8892
#105943162
D3×#8722
D3×#8702
#105938672
#105938622
D3×#5413
C2×#57313