Finite Group Databasebeta

← Dic6×#626 #13168716

Subgroups — Dic6×#626 #13168716

Order 1728.

1456 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4#11723443C211yesmaximal, characteristic, complemented
5#11723426C211yesmaximal, characteristic, complemented
6C3×C4×#626C211yesmaximal, characteristic
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11723033C212yesmaximal, complemented
9#11722974C212yesmaximal, complemented
10#11722971C212yesmaximal, complemented
11Dic3×#626C212yesmaximal
12Q8×#626—31nomaximal
13Dic6×#67—31nomaximal
14Dic6×D12—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6293C2212yes—
21C2×Dic3×C3⋊D3C2212yes—
22C3⋊D3×Dic6—24no—
23C2×C3×#627C2212yes—
24C2×C3×#626C2211yescharacteristic
25C2×C3×D3×Dic3C2212yes—
26C3×D3×Dic6—24no—
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29#88815C2212yes—
30#88814C2212yes—
31#88807C2212yes—
32Dic3⋊(C3⋊Dic3)C2212yes—
33Dic3⋊(C3⋊Dic3)C2212yes—
34(C2×D3)⋊(C3⋊Dic3)C2212yes—
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×Dic3⋊Dic3C2212yes—
37C3×#3722C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C3×Dic32C2212yes—
40C2×Q8×C3⋊D3—31no—
41C2×C3×D3×Q8—31no—
42C22×C3×Dic6—31no—
43C2×D3×Dic6—31no—
44C2×D3×Dic6—31no—
45C2×D3×Dic6—61no—
46C2×D3×Dic6D311yescharacteristic, complemented
47#64133—31no—
48#64078—31no—
49C3×Q8×Dic3—31no—
50C3×C4×#67—31no—
51C3×C4×D12—31no—
52C3×C4×Dic6—31no—
53Dic3×#67—32no—
54#63964—32no—
55#63918—32no—
56C4×#626—32no—
57C4×#626D311yescharacteristic
58#63893—32no—
59#63893—32no—
60Dic3×D12—32no—
61#63887—32no—
62#63871—31no—
63#63871—32no—
64#63866—31no—
65#63866—31no—
66#63866—32no—
67#63866—61no—
68#63857—31no—
69#63857—31no—
70#63857—31no—
71#63857—32no—
72#63857—61no—
73#63856—31no—
74Dic3×Dic6D311yescharacteristic, complemented
75#63839—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2312yes—
80#6308—22no—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4×C3⋊D3—22no—
85C3×#634—22no—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2311yescharacteristic
90C32×C4×D3—22no—
91C32×Dic6D414yescomplemented
92#6293—24no—
93Dic3×C3⋊D3—24no—
94C3×#627—24no—
95C3×#626Q814yescomplemented
96C3×D3×Dic3—24no—
97Q8×#67—91no—
98Q8×D12—91no—
99D4×Dic6—91no—
100C2×C32×Q8—31no—
101C22×C32×C4—31no—
102Q8×C3⋊D3—64no—
103C2×C4×C3⋊D3—32no—
104C2×C4×C3⋊D3C2×D311yescharacteristic
105C2×#634—31no—
106C2×#634—31no—
107C2×#634—31no—
108C2×#634—32no—
109C2×#634—61no—
110C2×#634—61no—
111C2×#634—61no—
112C2×#634—121no—
113C2×#634C2×D311yescharacteristic
114C2×C3×#67—31no—
115C22×C3×Dic3—32no—
116C3×D3×Q8—64no—
117C2×C3×D12—31no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—32no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—61no—
123C2×C3×C4×D3C2×D311yescharacteristic
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×C3×Dic6—21no—
126C2×C3×Dic6—31no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6—32no—
129C2×C3×Dic6—32no—
130C2×C3×Dic6—64no—
131C2×C3×Dic6—61no—
132C2×C3×Dic6C2×D311yescharacteristic
133C2×C3×Dic6C2×D311yescharacteristic
134C2×#627—32no—
135C2×#627—32no—
136C2×#627—62no—
137C2×#627C2×D312yes—
138C2×#626C2×D311yescharacteristic
139C2×D3×Dic3—32no—
140C2×D3×Dic3—32no—
141C2×D3×Dic3—62no—
142C2×D3×Dic3C2×D312yes—
143D3×Dic6—24no—
144D3×Dic6—68no—
145D3×Dic6—64no—
146D3×Dic6—64no—
147C32×C42—31no—
148#3757—32no—
149C4⋊(C3⋊Dic3)—32no—
150C4⋊(C3⋊Dic3)—32no—
151C4⋊(C3⋊Dic3)C2×D311yescharacteristic
152#3750—32no—
153C3×#217—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—31no—
159C3×C4⋊Dic3—32no—
160C3×C4⋊Dic3—31no—
161C3×C4⋊Dic3—61no—
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—32no—
164C3×C4×Dic3—21no—
165C3×C4×Dic3—32no—
166C3×C4×Dic3—32no—
167C3×C4×Dic3C2×D311yescharacteristic
168C3×C4×Dic3C2×D311yescharacteristic
169#3724—32no—
170Dic3⋊Dic3—32no—
171Dic3⋊Dic3—32no—
172Dic3⋊Dic3—32no—
173Dic3⋊Dic3—32no—
174Dic3⋊Dic3—32no—
175Dic3⋊Dic3—32no—
176Dic3⋊Dic3—32no—
177Dic3⋊Dic3—32no—
178Dic3⋊Dic3—62no—
179Dic3⋊Dic3—62no—
180Dic3⋊Dic3—62no—
181Dic3⋊Dic3C2×D312yes—
182Dic3⋊Dic3C2×D311yescharacteristic
183#3722—32no—
184#3722C2×D311yescharacteristic
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—62no—
190(C2×D3)⋊Dic3C2×D311yescharacteristic
191Dic32C2×D312yes—
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3C2×Q812yescomplemented
196C2×C32×D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3C2×Q812yescomplemented
199C33×C4C2×D412yes—
200C3⋊(C3⋊Dic3)—22no—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3—22no—
203C3×C3⋊Dic3—22no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3C2×D414yes—
207C32×Dic3C2×Q812yescomplemented
208C22×C3×Q8—91no—
209C2×D3×Q8—31no—
210C2×D3×Q8—91no—
211C2×D3×Q8—91no—
212C2×D3×Q8—181no—
213C22×Dic6—31no—
214C22×Dic6—91no—
215C3×C4×Q8—91no—
216C3×C4×D4—91no—
217#946—92no—
218#946—91no—
219Q8×Dic3—31no—
220#944—92no—
221#944—91no—
222D4×Dic3—92no—
223C4×#67—31no—
224C4×#67—92no—
225#924—92no—
226#924—91no—
227#924—91no—
228#924—91no—
229#924—181no—
230#897—92no—
231#897—92no—
232#897—91no—
233#897—91no—
234#888—92no—
235#878—92no—
236#878—92no—
237C4×D12—31no—
238C4×D12—92no—
239#869—92no—
240#869—91no—
241#869—91no—
242#869—181no—
243C4×Dic6—31no—
244C23×C32—31no—
245C22×C3⋊D3C22×D311yescharacteristic
246C22×C3×D3—21no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—61no—
250C22×C3×D3C22×D311yescharacteristic
251C22×C3×D3C22×D311yescharacteristic
252C32×Q8—34no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—31no—
257C2×C32×C4—32no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—41no—
261C2×C32×C4—62no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C3⋊Dic3—32no—
266C2×C3⋊Dic3—32no—
267C2×C3⋊Dic3—32no—
268C2×C3⋊Dic3—62no—
269C2×C3⋊Dic3—62no—
270C2×C3⋊Dic3—62no—
271C2×C3⋊Dic3—122no—
272C2×C3⋊Dic3C22×D312yes—
273C2×C3⋊Dic3C22×D312yes—
274C2×C3⋊Dic3C22×D311yescharacteristic
275C4×C3⋊D3—22no—
276C4×C3⋊D3—64no—
277#634—22no—
278#634—64no—
279#634—62no—
280#634—64no—
281#634—62no—
282#634—62no—
283#634—122no—
284#634—122no—
285#634—124no—
286C3×#67—34no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—32no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—32no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—64no—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C2×C3×Dic3C22×D311yescharacteristic
304C2×C3×Dic3C22×D311yescharacteristic
305C2×C3×Dic3C22×D311yescharacteristic
306C2×C3×Dic3C22×D312yes—
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D312yes—
309C3×D12—34no—
310C3×C4×D3—22no—
311C3×C4×D3—22no—
312C3×C4×D3—42no—
313C3×C4×D3—64no—
314C3×C4×D3—64no—
315C3×C4×D3—62no—
316C3×C4×D3—62no—
317C3×Dic6—24no—
318C3×Dic6—64no—
319C3×Dic6—62no—
320C3×Dic6—62no—
321C3×Dic6—64no—
322C3×Dic6—122no—
323C3×Dic6D1214yescomplemented
324C3×Dic6#6714yescomplemented
325#627—24no—
326#627—68no—
327#627—64no—
328#627—64no—
329#626Dic614yesdirect product factor
330D3×Dic3—24no—
331D3×Dic3—68no—
332D3×Dic3—64no—
333D3×Dic3—64no—
334D4×Q8—271noSylow
335C2×C33C22×D411yescharacteristic
336C2×C33C22×Q811yescharacteristic
337C2×C332−1+411yescharacteristic
338C3×C3⋊D3—22no—
339C32×D3—22no—
340C2×C3×Q8—31no—
341C2×C3×Q8—31no—
342C2×C3×Q8—61no—
343C2×C3×Q8—92no—
344C2×C3×Q8—91no—
345C2×C3×Q8—184no—
346C2×C3×D4—91no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—61no—
350C22×C3×C4—92no—
351C22×C3×C4—91no—
352C2×#67—31no—
353C22×Dic3—32no—
354C22×Dic3—92no—
355D3×Q8—64no—
356D3×Q8—184no—
357D3×Q8—184no—
358D3×Q8—188no—
359C2×D12—31no—
360C2×C4×D3—32no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—61no—
364C2×C4×D3—92no—
365C2×C4×D3—92no—
366C2×C4×D3—182no—
367C2×C4×D3D3211yescharacteristic
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—32no—
371C2×Dic6—32no—
372C2×Dic6—61no—
373C2×Dic6—64no—
374C2×Dic6—92no—
375C2×Dic6—92no—
376C2×Dic6—91no—
377C2×Dic6—91no—
378C2×Dic6—91no—
379C2×Dic6—92no—
380C2×Dic6—182no—
381C2×Dic6—181no—
382C2×Dic6—181no—
383C2×Dic6—181no—
384C2×Dic6—184no—
385C2×Dic6—361no—
386C2×Dic6D3211yescharacteristic
387C3×C4⋊C4—91no—
388C3×C4⋊C4—92no—
389C3×C4⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C42—31no—
393C3×C42—31no—
394C3×C42—61no—
395C3×C42—92no—
396#217—31no—
397#217—92no—
398#217—92no—
399#217—92no—
400#217—182no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—92no—
405(C2×D3)⋊C4—92no—
406(C2×D3)⋊C4—92no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—32no—
411C4⋊Dic3—61no—
412C4⋊Dic3—92no—
413C4⋊Dic3—92no—
414C4⋊Dic3—92no—
415C4⋊Dic3—92no—
416C4⋊Dic3—92no—
417C4⋊Dic3—92no—
418C4⋊Dic3—182no—
419C4⋊Dic3—182no—
420Dic3⋊C4—32no—
421Dic3⋊C4—31no—
422Dic3⋊C4—92no—
423Dic3⋊C4—92no—
424Dic3⋊C4—92no—
425Dic3⋊C4—92no—
426Dic3⋊C4—92no—
427Dic3⋊C4—92no—
428Dic3⋊C4—182no—
429C4×Dic3—32no—
430C4×Dic3—32no—
431C4×Dic3D3211yescharacteristic
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—32no—
436C22×C32—41no—
437C22×C32—61no—
438C22×C32—61no—
439C22×C32C23×D311yescharacteristic
440C22×C32C23×D311yescharacteristic
441C22×C32C23×D311yescharacteristic
442C2×C3⋊D3—21no—
443C2×C3⋊D3—21no—
444C2×C3⋊D3C2×Dic612yescomplemented
445C2×C3×D3—21no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3—22no—
450C2×C3×D3—32no—
451C2×C3×D3—32no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—62no—
455C2×C3×D3—62no—
456C2×C3×D3—62no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3C2×Dic612yescomplemented
462C2×C3×D3D3×Q812yescomplemented
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—34no—
467C32×C4—32no—
468C32×C4—42no—
469C32×C4—61no—
470C32×C4—61no—
471C32×C4C2×D1212yes—
472C32×C4D3×D412yes—
473C32×C4C2×#6712yes—
474C3⋊Dic3—21no—
475C3⋊Dic3—22no—
476C3⋊Dic3—22no—
477C3⋊Dic3—62no—
478C3⋊Dic3—64no—
479C3⋊Dic3—62no—
480C3⋊Dic3—62no—
481C3⋊Dic3—122no—
482C3⋊Dic3—122no—
483C3⋊Dic3—124no—
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—22no—
490C3×Dic3—24no—
491C3×Dic3—41no—
492C3×Dic3—62no—
493C3×Dic3—61no—
494C3×Dic3—62no—
495C3×Dic3—62no—
496C3×Dic3—62no—
497C3×Dic3—62no—
498C3×Dic3—61no—
499C3×Dic3—122no—
500C3×Dic3—122no—
501C3×Dic3C2×Dic612yescomplemented
502C3×Dic3C2×D1214yes—
503C3×Dic3D3×Q812yescomplemented
504C3×Dic3C2×#6714yes—
505C22×Q8—91no—
506C22×Q8—271no—
507C4⋊Q8—271no—
508C4⋊Q8—272no—
509C22⋊Q8—272no—
510C22⋊Q8—272no—
511C22⋊Q8—271no—
512C22⋊Q8—271no—
513C4×Q8—91no—
514C4×D4—91no—
515C4×D4—272no—
516C33D4×Q811yescharacteristic, complemented, Sylow
517C23×C3—31no—
518C23×C3—31no—
519C23×C3—61no—
520C23×C3—91no—
521C22×D3—31no—
522C22×D3—31no—
523C22×D3—61no—
524C22×D3C2×D3211yescharacteristic
525C3×Q8—34no—
526C3×Q8—34no—
527C3×Q8—64no—
528C3×Q8—184no—
529C3×Q8—182no—
530C3×D4—94no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—32no—
536C2×C3×C4—31no—
537C2×C3×C4—32no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—41no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—62no—
546C2×C3×C4—61no—
547C2×C3×C4—62no—
548C2×C3×C4—62no—
549C2×C3×C4—92no—
550C2×C3×C4—91no—
551C2×C3×C4—92no—
552C2×C3×C4—122no—
553C2×C3×C4—184no—
554C2×C3×C4—182no—
555C2×C3×C4C2×D3211yescharacteristic
556C2×C3×C4C2×D3211yescharacteristic
557C2×C3×C4C2×D3211yescharacteristic
558#67—34no—
559C2×Dic3—32no—
560C2×Dic3—32no—
561C2×Dic3—31no—
562C2×Dic3—32no—
563C2×Dic3—31no—
564C2×Dic3—32no—
565C2×Dic3—61no—
566C2×Dic3—62no—
567C2×Dic3—62no—
568C2×Dic3—64no—
569C2×Dic3—92no—
570C2×Dic3—92no—
571C2×Dic3—92no—
572C2×Dic3—182no—
573C2×Dic3—182no—
574C2×Dic3—182no—
575C2×Dic3—184no—
576C2×Dic3—362no—
577C2×Dic3C2×D3211yescharacteristic
578C2×Dic3C2×D3211yescharacteristic
579C2×Dic3C2×D3211yescharacteristic
580C2×Dic3C2×D3212yes—
581D12—34no—
582C4×D3—22no—
583C4×D3—64no—
584C4×D3—64no—
585C4×D3—62no—
586C4×D3—62no—
587C4×D3—184no—
588C4×D3—184no—
589C4×D3—188no—
590Dic6—64no—
591Dic6—62no—
592Dic6—62no—
593Dic6—64no—
594Dic6—122no—
595Dic6—184no—
596Dic6—184no—
597Dic6—188no—
598Dic6—184no—
599Dic6—182no—
600Dic6—182no—
601Dic6—182no—
602Dic6—184no—
603Dic6—362no—
604Dic6—362no—
605Dic6—364no—
606Dic6#62614yesdirect product factor
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—41no—
619C2×C32—62no—
620C2×C32C22×Dic611yescharacteristic
621C2×C32C22×D1211yescharacteristic
622C2×C32C2×D3×D411yescharacteristic
623C2×C32C2×D3×Q811yescharacteristic
624C2×C32C2×D3×Q811yescharacteristic
625C2×C32#100711yescharacteristic
626C2×C32#101011yescharacteristic
627C2×C32#101011yescharacteristic
628C2×C32C22×#6711yescharacteristic
629C3⋊D3—22no—
630C3×D3—22no—
631C3×D3—22no—
632C3×D3—42no—
633C3×D3—64no—
634C3×D3—62no—
635C3×D3—62no—
636C2×Q8—31no—
637C2×Q8—92no—
638C2×Q8—91no—
639C2×Q8—184no—
640C2×Q8—272no—
641C2×Q8—271no—
642C2×Q8—544no—
643C2×D4—91no—
644C22×C4—31no—
645C22×C4—92no—
646C22×C4—91no—
647C22×C4—272no—
648C4⋊C4—91no—
649C4⋊C4—92no—
650C4⋊C4—91no—
651C4⋊C4—272no—
652C4⋊C4—272no—
653C4⋊C4—272no—
654C4⋊C4—272no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4—272no—
658C22⋊C4—272no—
659C42—31no—
660C42—92no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—32no—
665C22×C3—32no—
666C22×C3—41no—
667C22×C3—62no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—92no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—181no—
676C22×C3—181no—
677C22×C3C22×D3211yescharacteristic
678C22×C3C22×D3211yescharacteristic
679C22×C3C22×D3211yescharacteristic
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—32no—
683C2×D3—32no—
684C2×D3—62no—
685C2×D3—62no—
686C2×D3—62no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3D3×Dic612yescomplemented
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—32no—
696C3×C4—34no—
697C3×C4—32no—
698C3×C4—34no—
699C3×C4—42no—
700C3×C4—64no—
701C3×C4—62no—
702C3×C4—62no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—121no—
708C3×C4—182no—
709C3×C4—182no—
710C3×C4—181no—
711C3×C4D3×D1212yes—
712C3×C4C2×#62612yes—
713C3×C4D3×#6712yes—
714Dic3—21no—
715Dic3—21no—
716Dic3—62no—
717Dic3—62no—
718Dic3—61no—
719Dic3—62no—
720Dic3—62no—
721Dic3—62no—
722Dic3—61no—
723Dic3—122no—
724Dic3—122no—
725Dic3—184no—
726Dic3—182no—
727Dic3—182no—
728Dic3—182no—
729Dic3—362no—
730Dic3—362no—
731Dic3—364no—
732Dic3D3×Dic612yescomplemented
733Dic3C2×#62614yes—
734C32—21no—
735C32—21no—
736C32—21no—
737C32—41no—
738C32D4×Dic611yescharacteristic, complemented
739C32Q8×D1211yescharacteristic, complemented
740C32Q8×#6711yescharacteristic, complemented
741C23—31no—
742C23—91no—
743Q8—34no—
744Q8—184no—
745Q8—182no—
746Q8—544no—
747Q8—542no—
748D4—94no—
749C2×C4—31no—
750C2×C4—32no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—62no—
754C2×C4—92no—
755C2×C4—91no—
756C2×C4—92no—
757C2×C4—184no—
758C2×C4—182no—
759C2×C4—272no—
760C2×C4—544no—
761C2×C4D3311yescharacteristic
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—62no—
775C2×C3—62no—
776C2×C3—122no—
777C2×C3—182no—
778C2×C3C2×D3×Dic611yescharacteristic
779C2×C3C2×D3×Dic611yescharacteristic
780C2×C3#6429711yescharacteristic
781C2×C3#6429811yescharacteristic
782C2×C3C2×D3×D1211yescharacteristic
783C2×C3#6431511yescharacteristic
784C2×C3D32×Q811yescharacteristic
785C2×C3C22×#62611yescharacteristic
786C2×C3C2×D3×#6711yescharacteristic
787D3—22no—
788D3—64no—
789D3—62no—
790D3—62no—
791C22—32no—
792C22—61no—
793C22—61no—
794C22—92no—
795C22—181no—
796C22—181no—
797C22C2×D3311yescharacteristic
798C4—32no—
799C4—34no—
800C4—61no—
801C4—61no—
802C4—182no—
803C4—182no—
804C4—181no—
805C4—542no—
806C4D3×#62612yes—
807C3—21no—
808C3—21no—
809C3—21no—
810C3—41no—
811C3Dic6×D1211yescharacteristic, complemented
812C3Dic6×#6711yescharacteristic, complemented
813C3Q8×#62611yescharacteristic, complemented
814C2—62no—
815C2—182no—
816C2D32×Dic611yescharacteristic
817C2#1172439611yescharacteristic
818C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×C3×#626C22
hypercenterC2×C4D33
hypocenterC33D4×Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×Dic6C2semidirect
2. C2×C3×D3×Dic6C2semidirect
3. #11723674C2semidirect
4. #11723443C2semidirect
5. #11723426C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11723033C2semidirect
9. #11722974C2semidirect
10. #11722971C2semidirect
46. C2×D3×Dic6D3semidirect
74. Dic3×Dic6D3semidirect
91. C32×Dic6D4semidirect
95. C3×#626Q8semidirect
195. C2×C3×C3⋊D3C2×Q8semidirect
198. C2×C32×D3C2×Q8semidirect
207. C32×Dic3C2×Q8semidirect
323. C3×Dic6D12semidirect
324. C3×Dic6#67semidirect
329. #626Dic6direct (N × H)
444. C2×C3⋊D3C2×Dic6semidirect
461. C2×C3×D3C2×Dic6semidirect
462. C2×C3×D3D3×Q8semidirect
501. C3×Dic3C2×Dic6semidirect
503. C3×Dic3D3×Q8semidirect
516. C33D4×Q8semidirect
606. Dic6#626direct (N × H)
691. C2×D3D3×Dic6semidirect
732. Dic3D3×Dic6semidirect
738. C32D4×Dic6semidirect
739. C32Q8×D12semidirect
740. C32Q8×#67semidirect
811. C3Dic6×D12semidirect
812. C3Dic6×#67semidirect
813. C3Q8×#626semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×Dic62
C2×C3×D3×Dic62
#117236742
#117234432
#117234262
C3×C4×#6262
C3×Dic3×Dic62
#117230332
#117229742
#117229712
Dic3×#6262
Q8×#6263
Dic6×#673
Dic6×D123