Finite Group Databasebeta

← D3×#4762 #11865610

Subgroups — D3×#4762 #11865610

Order 1152.

1232 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#940C211yesmaximal, characteristic
2C2×D3×#214C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4D3×#887C211yesmaximal, characteristic, complemented
5#10592461C211yesmaximal, characteristic, complemented
6C3×D3×#102C211yesmaximal, characteristic, complemented
7C3×#4762C211yesmaximal, characteristic, complemented
8#10591444C211yesmaximal, characteristic, complemented
9#10591439C211yesmaximal, characteristic, complemented
10#10590879C211yesmaximal, characteristic, complemented
11#10590876C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590553C211yesmaximal, characteristic, complemented
15#10590549C211yesmaximal, characteristic, complemented
16D3×#460—31nomaximal
17C2×#4762—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic
23#64149C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25C2×#3744C2211yescharacteristic, complemented
26#64096C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic, complemented
30C2×C3×D3×C8C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×#887C2211yescharacteristic, complemented
33#63979—21no—
34#63979—21no—
35D3×#214—24no—
36#63914C2211yescharacteristic
37#63911C2211yescharacteristic
38D3×Dic3⋊C4—21no—
39C4×D3×Dic3—21no—
40C4×D3×Dic3C2211yescharacteristic
41#63844C2211yescharacteristic, complemented
42#63843C2211yescharacteristic, complemented
43#63838—21no—
44#63837—21no—
45C2×#3717C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×#204—24no—
51C32×#102C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#940—31no—
64C22×#214—31no—
65C2×D3×SD16—31no—
66C2×D3×SD16—31no—
67C22×#204—31no—
68D3×#127—31no—
69C4×D3×Q8—31no—
70C2×#887—31no—
71C3×#460—31no—
72C2×C3×#102—31no—
73#5163—31no—
74#5163—31no—
75C2×Dic3⋊C8—31no—
76#5075—31no—
77#5027—31no—
78C2×#809—31no—
79#4848—31no—
80D3×C4⋊C8—31no—
81D3×#102—31no—
82D3×#102D311yescharacteristic, complemented
83#4762—31no—
84#4762—31no—
85#4762—31no—
86#4762—31no—
87#4762—31no—
88#4762—31no—
89#4762—31no—
90#4762—31no—
91#4762—31no—
92#4762—61no—
93#4762D311yescharacteristic, direct product factor
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C3×D3×D4—22no—
105C3×D3×D4—22no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111D3×#67—44no—
112D3×#67—44no—
113C2×#627—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×D3×Dic3—21no—
120C2×D3×Dic3D411yescharacteristic
121C2×D3×Dic3D411yescharacteristic
122D3×D12—22no—
123D3×D12—22no—
124D3×Dic6—22no—
125D3×Dic6D414yescomplemented
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3754—22no—
129#3750—21no—
130C4×C3⋊Dic3—21no—
131C4×C3⋊Dic3C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3744—22no—
134C3×#214—22no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×#204—22no—
143C3×D3×C8—22no—
144#3724—21no—
145Dic3⋊Dic3—21no—
146Dic32—21no—
147Dic32—21no—
148Dic32D411yescharacteristic
149Dic32D411yescharacteristic
150#3717—22no—
151#3716—22no—
152#3716—22no—
153#3715—22no—
154D3×C3⋊C8—22no—
155C2×#460—91noSylow
156C22×C3×D4—31no—
157C22×#67—61no—
158C22×#67—61no—
159C2×D3×Q8—31no—
160C2×D3×D4—31no—
161C2×D3×D4—61no—
162C2×D3×D4—61no—
163C2×D3×D4C2×D311yescharacteristic
164C22×D12—31no—
165C22×Dic6—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C22×C3×C8—31no—
169C3×#127—31no—
170C3×C4×Q8—31no—
171C2×C3×C4⋊C4—31no—
172Q8×Dic3—31no—
173C2×#215—31no—
174C2×#215—31no—
175#940—31no—
176#940—31no—
177#940—31no—
178#940—31no—
179#940—31no—
180#940—61no—
181#940—61no—
182#940—61no—
183#940—61no—
184#940—61no—
185#940C2×D311yescharacteristic
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—61no—
192C2×#214—64no—
193C2×#214C2×D311yescharacteristic, complemented
194C2×Dic3⋊C4—61no—
195C2×C4×Dic3—31no—
196C2×C4×Dic3—61no—
197C22×C3⋊C8—31no—
198D3×SD16—64no—
199D3×SD16—64no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—61no—
206C2×#204—64no—
207C2×#204C2×D311yescharacteristic, complemented
208C2×D3×C8—31no—
209C2×D3×C8C2×D311yescharacteristic
210D3×C4⋊C4—61no—
211D3×C4⋊C4C2×D311yescharacteristic
212#887—31no—
213#887—31no—
214#887—31no—
215#887—31no—
216#887—61no—
217#887—61no—
218#887—61no—
219#887—61no—
220#887C2×D311yescharacteristic, complemented
221#874—31no—
222C42×D3—31no—
223C42×D3—61no—
224C4×Dic6—31no—
225C4×Dic6—61no—
226C3×C4⋊C8—31no—
227C3×#102—21no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#102C2×D311yescharacteristic, complemented
233C3×#102C2×D311yescharacteristic, complemented
234#832—31no—
235#832C2×D311yescharacteristic, complemented
236#821—31no—
237#821C2×D311yescharacteristic, complemented
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—61no—
244Dic3⋊C8C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#809C2×D311yescharacteristic, complemented
251#809C2×D311yescharacteristic, complemented
252C4⋊(C3⋊C8)—31no—
253C23×C32—21no—
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C32×D4—21no—
265C32×D4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269#638—42no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275#634—21no—
276#634C2×D412yescomplemented
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×C4×D3—42no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292C3×Dic6—21no—
293C3×Dic6C2×D412yescomplemented
294#627—24no—
295#626—42no—
296#626—42no—
297#626—42no—
298#625—42no—
299#625—42no—
300D3×Dic3—24no—
301D3×Dic3—22no—
302D3×Dic3SD1614yescomplemented
303C32×C8—21no—
304C3⋊(C3⋊C8)—21no—
305C3×C3⋊C8—21no—
306C3×C3⋊C8—21no—
307C22×SD16—91no—
308C22×SD16—91no—
309C2×#127—91no—
310C2×C4×Q8—91no—
311#460—31no—
312#460—91no—
313#460—91no—
314#460—91no—
315#460—91no—
316#460—91no—
317#460—91no—
318#460—91no—
319C2×C4⋊C8—91no—
320C2×#102—31no—
321C2×#102—91no—
322C24×C3—61no—
323C23×D3—21no—
324C23×D3—61no—
325C23×D3—61no—
326C2×C3×Q8—31no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—62no—
331C2×C3×D4—62no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—121no—
354C2×#67—121no—
355C2×#67—124no—
356C2×#67—124no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—61no—
360D3×Q8—34no—
361D3×Q8—62no—
362D3×D4—22no—
363D3×D4—22no—
364D3×D4—62no—
365D3×D4—62no—
366D3×D4—124no—
367D3×D4—124no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—21no—
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—61no—
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—34no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6C22×D311yescharacteristic
391C3×SD16—62no—
392C3×SD16—62no—
393C2×C3×C8—21no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C2×C3×C8—62no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C3×C4⋊C4—21no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C42—31no—
406C3×C42—61no—
407#215—62no—
408#215—62no—
409#214—22no—
410#214—62no—
411#214—62no—
412#214—62no—
413#214—62no—
414#214—62no—
415#214—122no—
416C4⋊Dic3—61no—
417C4⋊Dic3C22×D311yescharacteristic
418Dic3⋊C4—21no—
419Dic3⋊C4—21no—
420Dic3⋊C4—61no—
421Dic3⋊C4—61no—
422Dic3⋊C4—61no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—121no—
426C4×Dic3—21no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—61no—
434C4×Dic3—61no—
435C4×Dic3—61no—
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3—61no—
439C4×Dic3—61no—
440C4×Dic3—121no—
441C4×Dic3C22×D311yescharacteristic
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—62no—
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D311yescharacteristic
448#204—22no—
449#204—62no—
450#204—62no—
451#204—62no—
452#204—62no—
453#204—62no—
454#204—122no—
455D3×C8—22no—
456D3×C8—62no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—84no—
471C2×C3×D3#12112yes—
472C2×C3×D3C2×SD1612yes—
473C2×C3×D3AGL(1,ℤ/8)12yes—
474D32—84no—
475C32×C4—41no—
476C32×C4C22×D411yescharacteristic
477C32×C4C2×#4111yescharacteristic
478C3⋊Dic3—22no—
479C3⋊Dic3—21no—
480C3⋊Dic3C2×SD1612yescomplemented
481C3×Dic3—22no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3#12112yes—
485C3×Dic3C2×SD1612yescomplemented
486C22×Q8—91no—
487C22×D4—31no—
488C22×D4—91no—
489C22×D4—181no—
490C22×D4—181no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×SD16—184no—
500C2×SD16—184no—
501C22×C8—31no—
502C22×C8—91no—
503#127—31no—
504#127—91no—
505#127—91no—
506#127—91no—
507#127—181no—
508#127—181no—
509C4×Q8—31no—
510C4×Q8—91no—
511C4×Q8—91no—
512C4×Q8—91no—
513C4×Q8—181no—
514C4×Q8—181no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—181no—
517C2×C42—91no—
518C2×C42—181no—
519C4⋊C8—31no—
520C4⋊C8—91no—
521C4⋊C8—91no—
522C4⋊C8—91no—
523#102—31no—
524#102—31no—
525#102—31no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102—91no—
530#102D3211yescharacteristic, complemented
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—31no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—122no—
538C23×C3—122no—
539C23×C3—122no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—42no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3D3×D411yescharacteristic
555C3×Q8—32no—
556C3×Q8—61no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—122no—
568C3×D4—122no—
569C3×D4—122no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—31no—
578C2×C3×C4—41no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—42no—
585#67—42no—
586#67—42no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—242no—
599#67—242no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—34no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—64no—
610C2×Dic3—62no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—121no—
614C2×Dic3D3×D411yescharacteristic
615C2×Dic3D3×D411yescharacteristic
616C2×Dic3D3×D411yescharacteristic
617D12—21no—
618D12—21no—
619D12—21no—
620D12—21no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—121no—
626D12—121no—
627D12—122no—
628D12—122no—
629D12—122no—
630C4×D3—34no—
631C4×D3—42no—
632C4×D3—64no—
633C4×D3—62no—
634C4×D3#23512yes—
635C4×D3D3×D412yes—
636Dic6—21no—
637Dic6—32no—
638Dic6—32no—
639Dic6—62no—
640Dic6—64no—
641Dic6—61no—
642Dic6—61no—
643Dic6—64no—
644Dic6—121no—
645Dic6D3×D412yescomplemented
646C3×C8—21no—
647C3×C8—21no—
648C3×C8—41no—
649C3×C8—61no—
650C3×C8—61no—
651C3⋊C8—21no—
652C3⋊C8—21no—
653C3⋊C8—61no—
654C3⋊C8—61no—
655C3⋊C8—121no—
656C2×C32—81no—
657C2×C32C2×#12111yescharacteristic
658C2×C32C22×SD1611yescharacteristic
659C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
660C3⋊D3—81no—
661C3×D3—81no—
662C3×D3—81no—
663C3×D3#46014yescomplemented
664C24—61no—
665C24—181no—
666C2×Q8—31no—
667C2×Q8—94no—
668C2×Q8—91no—
669C2×Q8—181no—
670C2×Q8—182no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—62no—
674C2×D4—62no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—91no—
679C2×D4—182no—
680C2×D4—182no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—364no—
689C2×D4—364no—
690C2×D4C2×D3211yescharacteristic
691C22×C4—31no—
692C22×C4—61no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—181no—
696SD16—62no—
697SD16—62no—
698SD16—182no—
699SD16—182no—
700SD16—182no—
701SD16—182no—
702SD16—182no—
703SD16—182no—
704C2×C8—31no—
705C2×C8—31no—
706C2×C8—62no—
707C2×C8—91no—
708C2×C8—182no—
709C2×C8C2×D3211yescharacteristic
710C4⋊C4—31no—
711C4⋊C4—61no—
712C4⋊C4—61no—
713C4⋊C4—181no—
714C4⋊C4—181no—
715C4⋊C4—181no—
716C4⋊C4C2×D3211yescharacteristic
717C42—31no—
718C42—61no—
719C42—91no—
720C42—91no—
721C42—91no—
722C42—181no—
723C42—181no—
724C42—181no—
725C22×C3—21no—
726C22×C3—32no—
727C22×C3—32no—
728C22×C3—32no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—244no—
745C22×C3C2×D3×D411yescharacteristic
746C22×C3C2×D3×D411yescharacteristic
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—84no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—241no—
761C2×D3—241no—
762C2×D3—241no—
763C2×D3—244no—
764C2×D3—244no—
765C2×D3#88412yes—
766C2×D3#91112yes—
767C2×D3D3×SD1612yes—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—32no—
771C3×C4—32no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—62no—
775C3×C4—61no—
776C3×C4—81no—
777C3×C4—121no—
778C3×C4C2×#23511yescharacteristic
779C3×C4C2×D3×D411yescharacteristic
780C3×C4C2×D3×D411yescharacteristic
781C3×C4D3×#4111yescharacteristic
782Dic3—21no—
783Dic3—22no—
784Dic3—32no—
785Dic3—32no—
786Dic3—41no—
787Dic3—62no—
788Dic3—62no—
789Dic3—61no—
790Dic3—61no—
791Dic3—62no—
792Dic3—122no—
793Dic3—121no—
794Dic3#88412yes—
795Dic3D3×SD1612yescomplemented
796C32C2×#46011yescharacteristic, complemented, Sylow
797C23—21no—
798C23—31no—
799C23—61no—
800C23—61no—
801C23—122no—
802C23—122no—
803C23—122no—
804C23—181no—
805C23—362no—
806C23—362no—
807C23—362no—
808Q8—32no—
809Q8—61no—
810Q8—92no—
811Q8—184no—
812Q8—181no—
813D4—21no—
814D4—21no—
815D4—61no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—122no—
820D4—122no—
821D4—122no—
822D4—181no—
823D4—181no—
824D4—362no—
825D4—362no—
826D4—362no—
827D4—362no—
828D4—362no—
829D4—362no—
830D4—362no—
831C2×C4—21no—
832C2×C4—31no—
833C2×C4—31no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—31no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—94no—
840C2×C4—91no—
841C2×C4—91no—
842C2×C4—122no—
843C2×C4—182no—
844C2×C4—184no—
845C2×C4—181no—
846C2×C4C22×D3211yescharacteristic
847C8—21no—
848C8—61no—
849C8—61no—
850C8—181no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—34no—
855C2×C3—81no—
856C2×C3—81no—
857C2×C3—161no—
858C2×C3—241no—
859C2×C3—241no—
860C2×C3C2×#88411yescharacteristic
861C2×C3D3×#12111yescharacteristic
862C2×C3C2×#91111yescharacteristic
863C2×C3C2×D3×SD1611yescharacteristic
864C2×C3C2×D3×SD1611yescharacteristic
865C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
866D3—81no—
867D3—81no—
868D3—241no—
869D3—241no—
870D3—481no—
871D3#476214yesdirect product factor
872C22—32no—
873C22—32no—
874C22—32no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—121no—
879C22—121no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—244no—
885C22—361no—
886C22—361no—
887C22—361no—
888C22—724no—
889C22D32×D411yescharacteristic
890C4—32no—
891C4—32no—
892C4—41no—
893C4—61no—
894C4—62no—
895C4—92no—
896C4—121no—
897C4—181no—
898C4—182no—
899C4D3×#23511yescharacteristic
900C4D32×D411yescharacteristic
901C3—21no—
902C3C2×#476211yescharacteristic, complemented
903C3D3×#46011yescharacteristic, complemented
904C2—34no—
905C2—81no—
906C2—241no—
907C2—241no—
908C2—721no—
909C2D3×#88411yescharacteristic
910C2D3×#91111yescharacteristic
911C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD3×#940C2
hypercenter#102D32
hypocenterC32C2×#460
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×D3×#214C2semidirect
3. C2×D3×#204C2semidirect
4. D3×#887C2semidirect
5. #10592461C2semidirect
6. C3×D3×#102C2semidirect
7. C3×#4762C2semidirect
8. #10591444C2semidirect
9. #10591439C2semidirect
10. #10590879C2semidirect
11. #10590876C2semidirect
12. D3×Dic3⋊C8C2semidirect
13. D3×#809C2semidirect
14. #10590553C2semidirect
15. #10590549C2semidirect
24. C2×#3754C22semidirect
25. C2×#3744C22semidirect
26. #64096C22semidirect
28. C2×C3×#214C22semidirect
29. C2×C3×#204C22semidirect
32. C3×#887C22semidirect
41. #63844C22semidirect
42. #63843C22semidirect
45. C2×#3717C22semidirect
46. C2×#3716C22semidirect
47. C2×#3716C22semidirect
48. C2×#3715C22semidirect
51. C32×#102C22semidirect
52. #63641C22semidirect
53. #63636C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
82. D3×#102D3semidirect
93. #4762D3direct (N × H)
125. D3×Dic6D4semidirect
193. C2×#214C2×D3semidirect
207. C2×#204C2×D3semidirect
220. #887C2×D3semidirect
232. C3×#102C2×D3semidirect
233. C3×#102C2×D3semidirect
235. #832C2×D3semidirect
237. #821C2×D3semidirect
244. Dic3⋊C8C2×D3semidirect
250. #809C2×D3semidirect
251. #809C2×D3semidirect
276. #634C2×D4semidirect
293. C3×Dic6C2×D4semidirect
302. D3×Dic3SD16semidirect
480. C3⋊Dic3C2×SD16semidirect
485. C3×Dic3C2×SD16semidirect
530. #102D32semidirect
645. Dic6D3×D4semidirect
663. C3×D3#460semidirect
795. Dic3D3×SD16semidirect
796. C32C2×#460semidirect
871. D3#4762direct (N × H)
902. C3C2×#4762semidirect
903. C3D3×#460semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
C2×D3×#2142
C2×D3×#2042
D3×#8872
#105924612
C3×D3×#1022
C3×#47622
#105914442
#105914392
#105908792
#105908762
D3×Dic3⋊C82
D3×#8092
#105905532
#105905492
D3×#4603
C2×#47623