Finite Group Databasebeta

← D3×#5726 #11902565

Subgroups — D3×#5726 #11902565

Order 1152.

3410 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C212yesmaximal, complemented
2#10596197C211yesmaximal, characteristic, complemented
3C3×#5726C211yesmaximal, characteristic, complemented
4C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
5D3×#946C212yesmaximal, complemented
6#10595358C212yesmaximal, complemented
7#10595341C212yesmaximal, complemented
8D3×#895C212yesmaximal, complemented
9D3×#894C214yesmaximal, complemented
10D32×C4⋊C4C212yesmaximal, complemented
11#10594517C212yesmaximal, complemented
12#10594373C212yesmaximal, complemented
13#10594372C214yesmaximal, complemented
14C4×D3×D12C211yesmaximal, characteristic, complemented
15C4×D3×D12C211yesmaximal, characteristic, complemented
16#10593896C211yesmaximal, characteristic, complemented
17#10593869C211yesmaximal, characteristic, complemented
18D3×#547—31nomaximal
19C2×#5726—31nomaximal
20C2×#3832C2212yescomplemented
21C2×C3×#239C2212yescomplemented
22C2×C3×D3×Q8C2212yes—
23D3×#239—216no—
24C2×D3×D12C2214yes—
25C2×D3×D12C2211yescharacteristic
26C2×D3×D12C2211yescharacteristic
27C2×C4×D32C2214yes—
28C2×C4×D32C2212yes—
29C2×C4×D32C2212yes—
30C2×#3799C2212yescomplemented
31C2×#3799C2214yescomplemented
32C2×#3796C2212yescomplemented
33C2×#3796C2214yescomplemented
34C32×C4⋊Q8C2211yescharacteristic, complemented
35#64155C2212yescomplemented
36#64104C2212yescomplemented
37#64103C2214yescomplemented
38C4⋊C4×C3⋊D3C2212yescomplemented
39C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
40C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
41C3×#946C2212yescomplemented
42C3×#944C2212yescomplemented
43C3×#895C2212yescomplemented
44C3×#894C2214yescomplemented
45C3×D3×C4⋊C4C2212yes—
46C3×D3×C4⋊C4C2212yes—
47C3×D3×C4⋊C4C2212yescomplemented
48C3×#888C2212yescomplemented
49C3×#888C2212yescomplemented
50C3×C4×D12C2211yescharacteristic, complemented
51C3×C4×D12C2211yescharacteristic, complemented
52C3×C42×D3C2211yescharacteristic
53C3×#869C2211yescharacteristic, complemented
54D3×(C2×D3)⋊C4C2212yes—
55D3×(C2×D3)⋊C4C2212yes—
56D3×(C2×D3)⋊C4C2214yes—
57#63916C2212yescomplemented
58#63910C2214yescomplemented
59#63909C2212yescomplemented
60C4×#626C2212yescomplemented
61C4×#626C2212yescomplemented
62#63900C2212yescomplemented
63#63897C2214yescomplemented
64#63894C2211yescharacteristic, complemented
65#63894C2211yescharacteristic, complemented
66Dic3×D12C2211yescharacteristic, complemented
67Dic3×D12C2211yescharacteristic, complemented
68#63890C2214yescomplemented
69D3×C4⋊Dic3C2211yescharacteristic
70D3×C4⋊Dic3C2211yescharacteristic
71D3×C4⋊Dic3C2212yescomplemented
72#63888C2214yescomplemented
73#63887C2214yescomplemented
74#63886C2214yescomplemented
75#63884C2214yescomplemented
76#63883C2214yescomplemented
77#63880C2212yescomplemented
78#63880C2212yescomplemented
79D3×Dic3⋊C4C2214yes—
80D3×Dic3⋊C4C2214yescomplemented
81#63871C2212yescomplemented
82#63856C2212yescomplemented
83#63854C2214yescomplemented
84#63853C2214yescomplemented
85#63850C2214yescomplemented
86C2×D3×#41—32no—
87C22×#239—32no—
88C3×#547—31no—
89C2×C3×C4⋊Q8—31no—
90#5824—32no—
91C2×#946—32no—
92#5726—32no—
93#5726—31no—
94#5726—31no—
95#5726—32no—
96#5726—32no—
97#5726—34no—
98#5726—32no—
99#5726—31no—
100#5726—31no—
101#5726—61no—
102#5726D311yescharacteristic, direct product factor
103D3×C4⋊Q8D311yescharacteristic, complemented
104#5655—34no—
105D3×#123—34no—
106#5631—32no—
107D3×C22⋊Q8—32no—
108#5611—32no—
109D3×#121—32no—
110#5555—31no—
111#5551—31no—
112C4×D3×D4—31no—
113C4×D3×D4—31no—
114#5507—32no—
115C2×#895—32no—
116C2×#894—34no—
117C2×D3×C4⋊C4—32no—
118C2×D3×C4⋊C4—32no—
119C2×C4×D12—31no—
120C2×C4×D12—31no—
121C22×D32C2312yes—
122C22×D32C2312yes—
123C2×C32×Q8C2312yes—
124#3832—28no—
125C2×C4⋊(C3⋊D3)C2314yes—
126C2×C4⋊(C3⋊D3)C2311yescharacteristic
127C2×C4⋊(C3⋊D3)C2311yescharacteristic
128C2×C4×C3⋊D3C2312yes—
129C2×C4×C3⋊D3C2314yes—
130C2×C4×C3⋊D3C2312yes—
131C3×#239—28no—
132C3×D3×Q8—28no—
133C2×C3×D12C2314yes—
134C2×C3×D12C2311yescharacteristic
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3C2314yes—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2314yes—
139C2×C3×C4×D3C2312yes—
140C2×C3×C4×D3C2312yes—
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×Dic6C2314yes—
144C2×C3×Dic6C2312yes—
145C2×#626C2314yes—
146C2×#626C2314yes—
147C2×#626C2312yes—
148C2×#626C2312yes—
149C2×#624C2314yes—
150C2×#624C2312yes—
151C2×#624C2312yes—
152C2×D3×Dic3C2314yes—
153C2×D3×Dic3C2312yes—
154C2×D3×Dic3C2312yes—
155C2×D3×Dic3C2312yes—
156C2×D3×Dic3C2312yes—
157D3×D12—216no—
158D3×D12—24no—
159D3×D12D418yescomplemented
160C4×D32—216no—
161C4×D32—28no—
162C4×D32—28no—
163#3799—28no—
164#3799—216no—
165#3796—28no—
166#3796—216no—
167C32×C4⋊C4C2312yes—
168C32×C4⋊C4C2312yes—
169C32×C42C2311yescharacteristic
170#3752C2312yes—
171#3752C2312yes—
172#3752C2314yes—
173C4⋊(C3⋊Dic3)C2311yescharacteristic
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175#3750C2314yes—
176C3×(C2×D3)⋊C4C2312yes—
177C3×(C2×D3)⋊C4C2312yes—
178C3×(C2×D3)⋊C4C2314yes—
179C3×C4⋊Dic3C2312yes—
180C3×C4⋊Dic3C2312yes—
181C3×C4⋊Dic3C2311yescharacteristic
182C3×C4⋊Dic3C2311yescharacteristic
183C3×Dic3⋊C4C2314yes—
184C3×Dic3⋊C4C2314yes—
185C3×Dic3⋊C4C2314yes—
186C3×C4×Dic3C2311yescharacteristic
187C3×C4×Dic3C2311yescharacteristic
188C3×C4×Dic3C2311yescharacteristic
189#3724C2314yes—
190Dic3⋊Dic3C2314yes—
191Dic3⋊Dic3C2312yes—
192Dic3⋊Dic3C2312yes—
193#3722C2312yes—
194#3722C2312yes—
195#3722C2314yes—
196(C2×D3)⋊Dic3C2312yes—
197(C2×D3)⋊Dic3C2312yes—
198(C2×D3)⋊Dic3C2314yes—
199C2×#547—91noSylow
200C2×C3×#41—32no—
201C22×C3×Q8—32no—
202D3×#41—616no—
203C2×#239—32no—
204C2×#239—32no—
205C2×#239—34no—
206C2×#239—32no—
207C2×#239—34no—
208C2×#239—32no—
209C2×#239—62no—
210C2×#239—616no—
211C2×#239C2×D312yescomplemented
212C2×D3×Q8C2×D312yes—
213C2×#237—34no—
214C2×#237—32no—
215C2×D3×D4—31no—
216C2×D3×D4—34no—
217C2×D3×D4—31no—
218C2×#235—34no—
219C2×#235—32no—
220C22×D12—31no—
221C22×D12—34no—
222C22×D12—31no—
223C22×C4×D3—34no—
224C22×C4×D3—32no—
225C22×C4×D3—34no—
226C22×C4×D3—32no—
227C22×C4×D3—32no—
228C22×C4×D3—32no—
229C3×C4⋊Q8—21no—
230C3×C4⋊Q8—32no—
231C3×C4⋊Q8—32no—
232C3×C4⋊Q8—32no—
233C3×C4⋊Q8—31no—
234C3×C4⋊Q8C2×D311yescharacteristic, complemented
235C3×C4⋊Q8C2×D311yescharacteristic, complemented
236C3×#123—34no—
237C3×C22⋊Q8—32no—
238C3×#121—32no—
239C3×C4×D4—31no—
240C3×C4×D4—31no—
241C2×C3×C4⋊C4—32no—
242C2×C3×C4⋊C4—32no—
243C2×C3×C4⋊C4—32no—
244C2×C3×C42—31no—
245#946—32no—
246#946—32no—
247#946—32no—
248#946—34no—
249#946—32no—
250#946—34no—
251#946—62no—
252#946C2×D312yescomplemented
253#944C2×D312yescomplemented
254#939—34no—
255#938—32no—
256#935—34no—
257D4×Dic3—31no—
258D4×Dic3—31no—
259#930—32no—
260#929—34no—
261C4×#67—32no—
262C4×#67—32no—
263C2×(C2×D3)⋊C4—32no—
264C2×(C2×D3)⋊C4—32no—
265C2×(C2×D3)⋊C4—34no—
266C2×C4⋊Dic3—31no—
267C2×C4⋊Dic3—31no—
268C2×C4⋊Dic3—32no—
269#924—32no—
270C2×Dic3⋊C4—34no—
271C2×Dic3⋊C4—34no—
272#897—32no—
273#896—34no—
274#895—34no—
275#895—32no—
276#895—32no—
277#895—32no—
278#895—32no—
279#895—34no—
280#895—62no—
281#895C2×D312yescomplemented
282#894—34no—
283#894—34no—
284#894—34no—
285#894—34no—
286#894—34no—
287#894—34no—
288#894—34no—
289#894—34no—
290#894—34no—
291#894—64no—
292#894C2×D314yescomplemented
293#893—31no—
294#893—31no—
295D3×C4⋊C4—34no—
296D3×C4⋊C4—34no—
297D3×C4⋊C4—32no—
298D3×C4⋊C4—31no—
299D3×C4⋊C4—31no—
300D3×C4⋊C4—32no—
301D3×C4⋊C4—32no—
302D3×C4⋊C4—32no—
303D3×C4⋊C4—32no—
304D3×C4⋊C4—34no—
305D3×C4⋊C4—34no—
306D3×C4⋊C4—62no—
307D3×C4⋊C4C2×D312yes—
308D3×C4⋊C4C2×D312yes—
309D3×C4⋊C4C2×D312yescomplemented
310#888C2×D312yescomplemented
311#888C2×D312yescomplemented
312#886—34no—
313#884—34no—
314#883—34no—
315#883—34no—
316#67⋊C4—32no—
317#67⋊C4—32no—
318D3×C22⋊C4—32no—
319D3×C22⋊C4—32no—
320D3×C22⋊C4—34no—
321#878—34no—
322C4×D12—31no—
323C4×D12—31no—
324C4×D12—32no—
325C4×D12—32no—
326C4×D12—31no—
327C4×D12—31no—
328C4×D12—31no—
329C4×D12—31no—
330C4×D12—32no—
331C4×D12—32no—
332C4×D12—31no—
333C4×D12—31no—
334C4×D12—61no—
335C4×D12—61no—
336C4×D12C2×D311yescharacteristic, complemented
337C4×D12C2×D311yescharacteristic, complemented
338C42×D3C2×D311yescharacteristic
339#869C2×D311yescharacteristic, complemented
340C22×C3⋊D3C2412yes—
341C22×C3⋊D3C2412yes—
342C22×C3×D3C2412yes—
343C22×C3×D3C2412yes—
344C22×C3×D3C2411yescharacteristic
345C2×D32—24no—
346C2×D32—24no—
347C2×D32—24no—
348C2×D32—24no—
349C2×D32—24no—
350C2×D32C2×D418yes—
351C32×Q8—24no—
352C2×C32×C4C2411yescharacteristic
353C2×C32×C4C2414yes—
354C2×C32×C4C2411yescharacteristic
355C2×C32×C4C2411yescharacteristic
356C2×C3⋊Dic3C2412yes—
357C2×C3⋊Dic3C2412yes—
358C4⋊(C3⋊D3)—28no—
359C4⋊(C3⋊D3)—22no—
360C4⋊(C3⋊D3)C2×D414yescomplemented
361C4×C3⋊D3—28no—
362C4×C3⋊D3—24no—
363C4×C3⋊D3—24no—
364C2×C3×Dic3C2411yescharacteristic
365C2×C3×Dic3C2414yes—
366C2×C3×Dic3C2412yes—
367C2×C3×Dic3C2412yes—
368C2×C3×Dic3C2411yescharacteristic
369C2×C3×Dic3C2411yescharacteristic
370C3×D12—28no—
371C3×D12—22no—
372C3×D12C2×D414yescomplemented
373C3×C4×D3—28no—
374C3×C4×D3—28no—
375C3×C4×D3—22no—
376C3×C4×D3—24no—
377C3×C4×D3—24no—
378C3×C4×D3C2×D414yes—
379C3×C4×D3#4114yescomplemented
380C3×Dic6—24no—
381C3×Dic6—28no—
382#626—28no—
383#626—28no—
384#626—24no—
385#626C2×D418yescomplemented
386#624—28no—
387#624—24no—
388#624—24no—
389D3×Dic3—28no—
390D3×Dic3—24no—
391D3×Dic3—24no—
392D3×Dic3—24no—
393D3×Dic3—24no—
394C22×#41—92no—
395#547—31no—
396#547—92no—
397#547—91no—
398#547—91no—
399#547—92no—
400#547—92no—
401#547—94no—
402#547—92no—
403#547—91no—
404C2×C4⋊Q8—31no—
405C2×#123—94no—
406C2×C22⋊Q8—92no—
407C2×#121—92no—
408C2×C4×D4—91no—
409C2×C4×D4—91no—
410C22×C4⋊C4—92no—
411C23×D3—32no—
412C23×D3—32no—
413C23×D3—32no—
414C23×D3—32no—
415C3×#41—68no—
416C2×C3×Q8—22no—
417C2×C3×Q8—34no—
418C2×C3×Q8—32no—
419C2×C3×Q8—68no—
420C2×C3×Q8C22×D312yes—
421C2×C3×Q8C22×D312yes—
422C2×C3×D4—31no—
423C2×C3×D4—31no—
424C2×C3×D4—34no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—34no—
428C22×C3×C4—34no—
429C22×C3×C4—32no—
430C22×C3×C4—32no—
431C22×C3×C4—31no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—34no—
435C2×#67—34no—
436C22×Dic3—32no—
437C22×Dic3—32no—
438C22×Dic3—34no—
439C22×Dic3—32no—
440C22×Dic3—32no—
441#239—28no—
442#239—616no—
443#239—68no—
444#239—616no—
445#239—68no—
446#239—68no—
447#239—68no—
448#239—128no—
449D3×Q8—28no—
450#237—616no—
451#237—68no—
452D3×D4—38no—
453D3×D4—616no—
454D3×D4—64no—
455#235—68no—
456#235—616no—
457C2×D12—32no—
458C2×D12—31no—
459C2×D12—31no—
460C2×D12—38no—
461C2×D12—32no—
462C2×D12—34no—
463C2×D12—34no—
464C2×D12—31no—
465C2×D12—31no—
466C2×D12—34no—
467C2×D12—34no—
468C2×D12—61no—
469C2×D12—61no—
470C2×D12—64no—
471C2×D12—64no—
472C2×D12—616no—
473C2×D12C22×D311yescharacteristic
474C2×D12C22×D314yes—
475C2×D12C22×D311yescharacteristic
476C2×C4×D3—32no—
477C2×C4×D3—32no—
478C2×C4×D3—32no—
479C2×C4×D3—32no—
480C2×C4×D3—34no—
481C2×C4×D3—32no—
482C2×C4×D3—32no—
483C2×C4×D3—32no—
484C2×C4×D3—32no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—32no—
488C2×C4×D3—32no—
489C2×C4×D3—32no—
490C2×C4×D3—32no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—62no—
494C2×C4×D3—62no—
495C2×C4×D3—64no—
496C2×C4×D3—68no—
497C2×C4×D3—68no—
498C2×C4×D3—616no—
499C2×C4×D3—616no—
500C2×C4×D3—68no—
501C2×C4×D3—68no—
502C2×C4×D3C22×D311yescharacteristic
503C2×C4×D3C22×D312yes—
504C2×C4×D3C22×D312yes—
505C2×C4×D3C22×D314yes—
506C2×C4×D3C22×D314yes—
507C2×C4×D3C22×D311yescharacteristic
508C2×C4×D3C22×D311yescharacteristic
509C2×Dic6C22×D312yes—
510C2×Dic6C22×D314yes—
511C3×C4⋊C4—22no—
512C3×C4⋊C4—22no—
513C3×C4⋊C4—31no—
514C3×C4⋊C4—34no—
515C3×C4⋊C4—34no—
516C3×C4⋊C4—32no—
517C3×C4⋊C4—31no—
518C3×C4⋊C4—34no—
519C3×C4⋊C4—32no—
520C3×C4⋊C4C22×D312yes—
521C3×C4⋊C4C22×D312yes—
522C3×C4⋊C4C22×D312yes—
523C3×C4⋊C4C22×D312yes—
524C3×C22⋊C4—34no—
525C3×C22⋊C4—32no—
526C3×C22⋊C4—32no—
527C3×C42—21no—
528C3×C42—31no—
529C3×C42—31no—
530C3×C42—31no—
531C3×C42C22×D311yescharacteristic
532C3×C42C22×D311yescharacteristic
533#217—34no—
534#217—32no—
535#217—32no—
536(C2×D3)⋊C4—32no—
537(C2×D3)⋊C4—32no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—32no—
540(C2×D3)⋊C4—32no—
541(C2×D3)⋊C4—32no—
542(C2×D3)⋊C4—32no—
543(C2×D3)⋊C4—34no—
544(C2×D3)⋊C4—34no—
545(C2×D3)⋊C4—32no—
546(C2×D3)⋊C4—32no—
547(C2×D3)⋊C4—32no—
548(C2×D3)⋊C4—34no—
549(C2×D3)⋊C4—32no—
550(C2×D3)⋊C4—34no—
551(C2×D3)⋊C4—62no—
552(C2×D3)⋊C4—62no—
553(C2×D3)⋊C4—64no—
554(C2×D3)⋊C4C22×D312yes—
555(C2×D3)⋊C4C22×D312yes—
556(C2×D3)⋊C4C22×D314yes—
557C4⋊Dic3—31no—
558C4⋊Dic3—31no—
559C4⋊Dic3—31no—
560C4⋊Dic3—31no—
561C4⋊Dic3—32no—
562C4⋊Dic3—32no—
563C4⋊Dic3—34no—
564C4⋊Dic3—61no—
565C4⋊Dic3—61no—
566C4⋊Dic3C22×D312yes—
567C4⋊Dic3C22×D312yes—
568C4⋊Dic3C22×D311yescharacteristic
569C4⋊Dic3C22×D311yescharacteristic
570Dic3⋊C4—34no—
571Dic3⋊C4—34no—
572Dic3⋊C4—32no—
573Dic3⋊C4—32no—
574Dic3⋊C4—34no—
575Dic3⋊C4—34no—
576Dic3⋊C4—34no—
577Dic3⋊C4—64no—
578Dic3⋊C4C22×D314yes—
579Dic3⋊C4C22×D314yes—
580Dic3⋊C4C22×D314yes—
581C4×Dic3C22×D311yescharacteristic
582C4×Dic3C22×D311yescharacteristic
583C4×Dic3C22×D311yescharacteristic
584C22×C32C2511yescharacteristic
585C2×C3⋊D3—22no—
586C2×C3⋊D3—22no—
587C2×C3⋊D3—22no—
588C2×C3⋊D3—22no—
589C2×C3⋊D3—22no—
590C2×C3⋊D3C22×D414yes—
591C2×C3×D3—22no—
592C2×C3×D3—22no—
593C2×C3×D3—22no—
594C2×C3×D3—22no—
595C2×C3×D3—22no—
596C2×C3×D3C22×D414yes—
597C2×C3×D3C22×D412yes—
598C2×C3×D3C2×#4112yes—
599C2×C3×D32−1+412yes—
600D32—216no—
601D32—48no—
602C32×C4—24no—
603C32×C4—21no—
604C32×C4C22×D412yes—
605C32×C4C2×#4112yescomplemented
606C3⋊Dic3—22no—
607C3⋊Dic3—22no—
608C3×Dic3—22no—
609C3×Dic3—24no—
610C3×Dic3—22no—
611C3×Dic3—21no—
612C3×Dic3C22×D412yes—
613C3×Dic3C2×#4112yescomplemented
614C2×#41—32no—
615C2×#41—94no—
616C2×#41—92no—
617C2×#41—92no—
618C2×#41—94no—
619C2×#41—92no—
620C2×#41—1816no—
621C22×Q8—32no—
622C22×D4—91no—
623C22×D4—91no—
624C22×D4—94no—
625C23×C4—92no—
626C23×C4—94no—
627C23×C4—92no—
628C4⋊Q8—32no—
629C4⋊Q8—32no—
630C4⋊Q8—32no—
631C4⋊Q8—31no—
632C4⋊Q8D3211yescharacteristic, complemented
633#123—34no—
634#123—94no—
635#123—94no—
636#123—94no—
637#123—94no—
638#123—94no—
639#123—94no—
640#123—94no—
641C22⋊Q8—32no—
642C22⋊Q8—94no—
643C22⋊Q8—94no—
644C22⋊Q8—92no—
645C22⋊Q8—92no—
646C22⋊Q8—92no—
647#121—32no—
648#121—94no—
649#121—92no—
650#121—92no—
651#121—94no—
652#121—92no—
653C4×D4—31no—
654C4×D4—31no—
655C4×D4—92no—
656C4×D4—92no—
657C4×D4—91no—
658C4×D4—91no—
659C4×D4—92no—
660C4×D4—92no—
661C4×D4—91no—
662C4×D4—91no—
663C4×D4—91no—
664C4×D4—91no—
665C2×C4⋊C4—32no—
666C2×C4⋊C4—32no—
667C2×C4⋊C4—32no—
668C2×C4⋊C4—92no—
669C2×C4⋊C4—94no—
670C2×C4⋊C4—91no—
671C2×C4⋊C4—94no—
672C2×C4⋊C4—94no—
673C2×C4⋊C4—92no—
674C2×C4⋊C4—91no—
675C2×C4⋊C4—92no—
676C2×C22⋊C4—92no—
677C2×C22⋊C4—92no—
678C2×C22⋊C4—94no—
679C2×C42—31no—
680C23×C3—31no—
681C23×C3—32no—
682C23×C3—32no—
683C22×D3—32no—
684C22×D3—32no—
685C22×D3—38no—
686C22×D3—38no—
687C22×D3—32no—
688C22×D3—32no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—64no—
692C22×D3—64no—
693C22×D3—64no—
694C22×D3—64no—
695C22×D3—64no—
696C22×D3—64no—
697C22×D3—64no—
698C22×D3—64no—
699C22×D3—64no—
700C22×D3—64no—
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D311yescharacteristic
704C3×Q8—24no—
705C3×Q8—24no—
706C3×Q8—44no—
707C3×Q8—68no—
708C3×Q8—64no—
709C3×D4—34no—
710C3×D4—68no—
711C3×D4—62no—
712C2×C3×C4—21no—
713C2×C3×C4—21no—
714C2×C3×C4—24no—
715C2×C3×C4—21no—
716C2×C3×C4—31no—
717C2×C3×C4—31no—
718C2×C3×C4—34no—
719C2×C3×C4—34no—
720C2×C3×C4—32no—
721C2×C3×C4—34no—
722C2×C3×C4—32no—
723C2×C3×C4—31no—
724C2×C3×C4—68no—
725C2×C3×C4—68no—
726C2×C3×C4—62no—
727C2×C3×C4—64no—
728C2×C3×C4—64no—
729C2×C3×C4C23×D311yescharacteristic
730C2×C3×C4C23×D314yes—
731C2×C3×C4C23×D314yes—
732C2×C3×C4C23×D311yescharacteristic
733C2×C3×C4C23×D311yescharacteristic
734C2×C3×C4C23×D311yescharacteristic
735C2×C3×C4C23×D311yescharacteristic
736C2×C3×C4C23×D311yescharacteristic
737#67—38no—
738#67—68no—
739#67—68no—
740#67—64no—
741C2×Dic3—32no—
742C2×Dic3—32no—
743C2×Dic3—32no—
744C2×Dic3—32no—
745C2×Dic3—62no—
746C2×Dic3—62no—
747C2×Dic3—64no—
748C2×Dic3—68no—
749C2×Dic3—64no—
750C2×Dic3—64no—
751C2×Dic3—64no—
752C2×Dic3C23×D311yescharacteristic
753C2×Dic3C23×D312yes—
754C2×Dic3C23×D312yes—
755C2×Dic3C23×D314yes—
756C2×Dic3C23×D311yescharacteristic
757C2×Dic3C23×D311yescharacteristic
758D12—28no—
759D12—22no—
760D12—38no—
761D12—34no—
762D12—34no—
763D12—64no—
764D12—68no—
765D12—68no—
766D12—64no—
767D12—68no—
768D12—68no—
769D12—62no—
770D12—62no—
771D12—122no—
772D12—128no—
773D12D3×D414yescomplemented
774C4×D3—28no—
775C4×D3—28no—
776C4×D3—22no—
777C4×D3—24no—
778C4×D3—24no—
779C4×D3—64no—
780C4×D3—64no—
781C4×D3—68no—
782C4×D3—68no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—64no—
786C4×D3—64no—
787C4×D3—64no—
788C4×D3—68no—
789C4×D3—64no—
790C4×D3—64no—
791C4×D3—64no—
792C4×D3—64no—
793C4×D3—64no—
794C4×D3—64no—
795C4×D3—64no—
796C4×D3—124no—
797C4×D3—124no—
798C4×D3—128no—
799C4×D3D3×D414yes—
800C4×D3#23914yescomplemented
801Dic6—24no—
802Dic6—28no—
803C2×C32C23×D411yescharacteristic
804C2×C32C22×#4111yescharacteristic
805C2×C32C2×2−1+411yescharacteristic
806C3⋊D3—24no—
807C3⋊D3—42no—
808C3×D3—24no—
809C3×D3—42no—
810C3×D3#54714yescomplemented
811C24—92no—
812C24—92no—
813#41—68no—
814#41—1816no—
815#41—188no—
816#41—188no—
817#41—1816no—
818#41—188no—
819C2×Q8—34no—
820C2×Q8—32no—
821C2×Q8—68no—
822C2×Q8C2×D3212yes—
823C2×D4—31no—
824C2×D4—31no—
825C2×D4—34no—
826C2×D4—98no—
827C2×D4—92no—
828C2×D4—92no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—91no—
832C2×D4—91no—
833C2×D4—94no—
834C2×D4—184no—
835C2×D4—1816no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—31no—
839C22×C4—34no—
840C22×C4—32no—
841C22×C4—34no—
842C22×C4—32no—
843C22×C4—92no—
844C22×C4—94no—
845C22×C4—92no—
846C22×C4—92no—
847C22×C4—92no—
848C22×C4—92no—
849C22×C4—94no—
850C22×C4—92no—
851C22×C4—92no—
852C22×C4—94no—
853C22×C4—92no—
854C22×C4—188no—
855C22×C4—188no—
856C22×C4—1816no—
857C4⋊C4—31no—
858C4⋊C4—34no—
859C4⋊C4—32no—
860C4⋊C4—34no—
861C4⋊C4—34no—
862C4⋊C4—32no—
863C4⋊C4—31no—
864C4⋊C4—92no—
865C4⋊C4—94no—
866C4⋊C4—94no—
867C4⋊C4—92no—
868C4⋊C4—91no—
869C4⋊C4—94no—
870C4⋊C4—91no—
871C4⋊C4C2×D3212yes—
872C4⋊C4C2×D3212yes—
873C22⋊C4—32no—
874C22⋊C4—32no—
875C22⋊C4—34no—
876C22⋊C4—92no—
877C22⋊C4—92no—
878C22⋊C4—94no—
879C22⋊C4—92no—
880C22⋊C4—92no—
881C22⋊C4—94no—
882C22⋊C4—92no—
883C22⋊C4—92no—
884C22⋊C4—94no—
885C42—31no—
886C42—31no—
887C42—31no—
888C42C2×D3211yescharacteristic
889C22×C3—21no—
890C22×C3—32no—
891C22×C3—32no—
892C22×C3—32no—
893C22×C3—34no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3C24×D311yescharacteristic
900C22×C3C24×D311yescharacteristic
901C2×D3—22no—
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—34no—
907C2×D3—34no—
908C2×D3—64no—
909C2×D3—616no—
910C2×D3—62no—
911C2×D3—62no—
912C2×D3—62no—
913C2×D3—62no—
914C2×D3—616no—
915C2×D3—62no—
916C2×D3—62no—
917C2×D3—62no—
918C2×D3—62no—
919C2×D3—62no—
920C2×D3—62no—
921C2×D3—122no—
922C2×D3—122no—
923C2×D3—122no—
924C2×D3—122no—
925C2×D3—122no—
926C2×D3—128no—
927C2×D3—128no—
928C2×D3C2×D3×D414yes—
929C2×D3C2×D3×D412yes—
930C2×D3C2×#23912yes—
931C2×D3#100712yes—
932C3×C4—24no—
933C3×C4—24no—
934C3×C4—21no—
935C3×C4—21no—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—32no—
939C3×C4—32no—
940C3×C4—44no—
941C3×C4—41no—
942C3×C4—62no—
943C3×C4—64no—
944C3×C4—62no—
945C3×C4—61no—
946C3×C4C2×D3×D412yes—
947C3×C4C2×D3×D412yes—
948C3×C4C2×#23912yescomplemented
949C3×C4D3×#4112yescomplemented
950Dic3—24no—
951Dic3—22no—
952Dic3—21no—
953Dic3—22no—
954Dic3—62no—
955Dic3—62no—
956Dic3—62no—
957Dic3—62no—
958Dic3—122no—
959Dic3—122no—
960Dic3C2×D3×D412yes—
961Dic3C2×#23912yescomplemented
962C32C2×#54711yescharacteristic, complemented, Sylow
963C23—31no—
964C23—32no—
965C23—32no—
966C23—98no—
967C23—92no—
968C23—92no—
969C23—184no—
970C23—184no—
971C23—184no—
972C23—184no—
973C23—184no—
974Q8—24no—
975Q8—68no—
976Q8—64no—
977D4—34no—
978D4—68no—
979D4—62no—
980D4—98no—
981D4—94no—
982D4—188no—
983D4—184no—
984D4—188no—
985D4—188no—
986D4—182no—
987C2×C4—31no—
988C2×C4—31no—
989C2×C4—34no—
990C2×C4—34no—
991C2×C4—31no—
992C2×C4—32no—
993C2×C4—32no—
994C2×C4—34no—
995C2×C4—68no—
996C2×C4—68no—
997C2×C4—62no—
998C2×C4—64no—
999C2×C4—64no—
1000C2×C4—92no—
1001C2×C4—92no—
1002C2×C4—188no—
1003C2×C4—184no—
1004C2×C4—184no—
1005C2×C4—184no—
1006C2×C4—184no—
1007C2×C4—188no—
1008C2×C4—184no—
1009C2×C4—188no—
1010C2×C4—184no—
1011C2×C4—184no—
1012C2×C4—184no—
1013C2×C4C22×D3211yescharacteristic
1014C2×C4C22×D3214yes—
1015C2×C4C22×D3211yescharacteristic
1016C2×C4C22×D3211yescharacteristic
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—34no—
1021C2×C3—64no—
1022C2×C3—122no—
1023C2×C3C22×D3×D411yescharacteristic
1024C2×C3C22×D3×D411yescharacteristic
1025C2×C3C22×#23911yescharacteristic
1026C2×C3C2×#100711yescharacteristic
1027C2×C3C2×D3×#4111yescharacteristic
1028C2×C3D3×2−1+411yescharacteristic
1029D3—24no—
1030D3—42no—
1031D3—64no—
1032D3—64no—
1033D3—124no—
1034D3—122no—
1035D3—122no—
1036D3—242no—
1037D3#572614yesdirect product factor
1038C22—32no—
1039C22—32no—
1040C22—32no—
1041C22—34no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—62no—
1047C22—94no—
1048C22—1816no—
1049C22—182no—
1050C22—182no—
1051C22—182no—
1052C22—182no—
1053C22—182no—
1054C22—368no—
1055C22C23×D3211yescharacteristic
1056C4—24no—
1057C4—21no—
1058C4—32no—
1059C4—32no—
1060C4—62no—
1061C4—64no—
1062C4—62no—
1063C4—61no—
1064C4—182no—
1065C4—182no—
1066C4D32×D412yes—
1067C4D3×#23912yescomplemented
1068C3—21no—
1069C3C2×#572611yescharacteristic, complemented
1070C3D3×#54711yescharacteristic, complemented
1071C2—34no—
1072C2—64no—
1073C2—122no—
1074C2—184no—
1075C2—362no—
1076C2C2×D32×D411yescharacteristic
1077C2C2×D3×#23911yescharacteristic
1078C2D3×#100711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. #10596197C2semidirect
3. C3×#5726C2semidirect
4. C3×D3×C4⋊Q8C2semidirect
5. D3×#946C2semidirect
6. #10595358C2semidirect
7. #10595341C2semidirect
8. D3×#895C2semidirect
9. D3×#894C2semidirect
10. D32×C4⋊C4C2semidirect
11. #10594517C2semidirect
12. #10594373C2semidirect
13. #10594372C2semidirect
14. C4×D3×D12C2semidirect
15. C4×D3×D12C2semidirect
16. #10593896C2semidirect
17. #10593869C2semidirect
20. C2×#3832C22semidirect
21. C2×C3×#239C22semidirect
30. C2×#3799C22semidirect
31. C2×#3799C22semidirect
32. C2×#3796C22semidirect
33. C2×#3796C22semidirect
34. C32×C4⋊Q8C22semidirect
35. #64155C22semidirect
36. #64104C22semidirect
37. #64103C22semidirect
38. C4⋊C4×C3⋊D3C22semidirect
39. C4×C4⋊(C3⋊D3)C22semidirect
40. C4×C4⋊(C3⋊D3)C22semidirect
41. C3×#946C22semidirect
42. C3×#944C22semidirect
43. C3×#895C22semidirect
44. C3×#894C22semidirect
47. C3×D3×C4⋊C4C22semidirect
48. C3×#888C22semidirect
49. C3×#888C22semidirect
50. C3×C4×D12C22semidirect
51. C3×C4×D12C22semidirect
53. C3×#869C22semidirect
57. #63916C22semidirect
58. #63910C22semidirect
59. #63909C22semidirect
60. C4×#626C22semidirect
61. C4×#626C22semidirect
62. #63900C22semidirect
63. #63897C22semidirect
64. #63894C22semidirect
65. #63894C22semidirect
66. Dic3×D12C22semidirect
67. Dic3×D12C22semidirect
68. #63890C22semidirect
71. D3×C4⋊Dic3C22semidirect
72. #63888C22semidirect
73. #63887C22semidirect
74. #63886C22semidirect
75. #63884C22semidirect
76. #63883C22semidirect
77. #63880C22semidirect
78. #63880C22semidirect
80. D3×Dic3⋊C4C22semidirect
81. #63871C22semidirect
82. #63856C22semidirect
83. #63854C22semidirect
84. #63853C22semidirect
85. #63850C22semidirect
102. #5726D3direct (N × H)
103. D3×C4⋊Q8D3semidirect
159. D3×D12D4semidirect
211. C2×#239C2×D3semidirect
234. C3×C4⋊Q8C2×D3semidirect
235. C3×C4⋊Q8C2×D3semidirect
252. #946C2×D3semidirect
253. #944C2×D3semidirect
281. #895C2×D3semidirect
292. #894C2×D3semidirect
309. D3×C4⋊C4C2×D3semidirect
310. #888C2×D3semidirect
311. #888C2×D3semidirect
336. C4×D12C2×D3semidirect
337. C4×D12C2×D3semidirect
339. #869C2×D3semidirect
360. C4⋊(C3⋊D3)C2×D4semidirect
372. C3×D12C2×D4semidirect
379. C3×C4×D3#41semidirect
385. #626C2×D4semidirect
605. C32×C4C2×#41semidirect
613. C3×Dic3C2×#41semidirect
632. C4⋊Q8D32semidirect
773. D12D3×D4semidirect
800. C4×D3#239semidirect
810. C3×D3#547semidirect
948. C3×C4C2×#239semidirect
949. C3×C4D3×#41semidirect
961. Dic3C2×#239semidirect
962. C32C2×#547semidirect
1037. D3#5726direct (N × H)
1067. C4D3×#239semidirect
1069. C3C2×#5726semidirect
1070. C3D3×#547semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
#105961972
C3×#57262
C3×D3×C4⋊Q82
D3×#9462
#105953582
#105953412
D3×#8952
D3×#8942
D32×C4⋊C42
#105945172
#105943732
#105943722
C4×D3×D122
#105938962
#105938692
D3×#5473
C2×#57263