Finite Group Databasebeta

← Dic6×#237 #11903774

Subgroups — Dic6×#237 #11903774

Order 1152.

2250 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic
4#10595272C212yesmaximal, complemented
5Dic3×#237C212yesmaximal
6#10594993C212yesmaximal, complemented
7Dic6×#67C212yesmaximal, complemented
8C2×Dic3×Dic6C212yesmaximal, complemented
9#10594808C212yesmaximal, complemented
10#10594445C212yesmaximal, complemented
11#10594317C212yesmaximal, complemented
12#10594133C214yesmaximal, complemented
13#10594029C214yesmaximal, complemented
14C4×D3×Dic6C211yesmaximal, characteristic, complemented
15#10593861C211yesmaximal, characteristic, complemented
16#10593859C211yesmaximal, characteristic, complemented
17Dic62C211yesmaximal, characteristic, complemented
18Q8×#237—31nomaximal
19#41×Dic6—31nomaximal
20C2×C3×#237C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C2×D3×Dic6C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic
24D4×C3⋊Dic3C2212yes—
25C2×C4⋊(C3⋊Dic3)C2212yes—
26#64133C2212yes—
27#64099C2212yes—
28#64087C2214yes—
29#64078C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×D4×Dic3C2211yescharacteristic
32C3×D4×Dic3C2212yes—
33C3×C4×#67C2212yes—
34C3×#924C2212yes—
35C2×C3×C4×Dic3C2212yes—
36C3×#892C2211yescharacteristic
37C3×#888C2212yes—
38C3×#887C2211yescharacteristic
39C3×#67⋊C4C2212yes—
40C3×#878C2214yes—
41C3×#877C2212yes—
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63982C2214yes—
47#67⋊Dic3C2214yes—
48Dic3×#67C2214yes—
49C2×Dic3⋊Dic3C2214yes—
50#63964C2214yes—
51#63964C2214yes—
52#63955C2214yes—
53C2×Dic32C2214yes—
54#63918C2212yes—
55#63918C2212yes—
56C4×#627C2212yes—
57#63893C2214yes—
58D3×C4⋊Dic3C2211yescharacteristic
59#63887C2214yes—
60D3×Dic3⋊C4C2212yes—
61C4×D3×Dic3C2212yes—
62#63872C2212yes—
63#63869C2212yes—
64#63867C2214yes—
65#63866C2212yes—
66#63857C2212yes—
67#63856C2212yes—
68#63846C2214yes—
69#63845C2214yes—
70#63844C2212yes—
71#63844C2211yescharacteristic
72#63843C2212yes—
73Dic3×Dic6C2211yescharacteristic
74Dic3×Dic6C2214yes—
75Dic3×Dic6C2212yes—
76Dic3×Dic6C2212yes—
77Dic3×Dic6C2212yes—
78Dic3×Dic6C2214yes—
79Dic3×Dic6C2212yes—
80#63841C2212yes—
81#63840C2214yes—
82#63839C2214yes—
83#63837C2212yes—
84#63837C2214yes—
85C3×D4×Q8—31no—
86C3×C4×#41—31no—
87Dic3×#41—32no—
88Q8×#67—32no—
89C2×Q8×Dic3—32no—
90#5728—32no—
91#5728—31no—
92#5721—32no—
93#5721—31no—
94#5635—32no—
95#5635—34no—
96#5622—32no—
97#5622—34no—
98C4×D3×Q8—31no—
99#5570—31no—
100#5569—32no—
101Q8×Dic6—31no—
102Q8×Dic6—31no—
103#5543—31no—
104#5543—31no—
105#5543—32no—
106#5543—32no—
107#5543—61no—
108#5539—32no—
109#5539—34no—
110D4×Dic6—32no—
111D4×Dic6D311yescharacteristic, complemented
112C4×#237—32no—
113C4×#237D311yescharacteristic
114#5517—32no—
115#5517—34no—
116#5470—32no—
117#5470—31no—
118C2×C4×Dic6—32no—
119C2×C4×Dic6—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C22×C3⋊Dic3C2314yes—
123C2×#634C2311yescharacteristic
124C2×#634C2312yes—
125C2×C3×#67C2312yes—
126C22×C3×Dic3C2314yes—
127C22×C3×Dic3C2312yes—
128C22×C3×Dic3C2312yes—
129C3×#237Q818yescomplemented
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×Dic6—28no—
134C2×C3×Dic6C2314yes—
135C2×C3×Dic6C2312yes—
136C2×C3×Dic6C2311yescharacteristic
137C2×C3×Dic6C2311yescharacteristic
138C2×#627C2312yes—
139C2×#627C2314yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142D3×Dic6—24no—
143C32×C4⋊C4C2311yescharacteristic
144C32×C22⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146#3757C2314yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2312yes—
150C4⋊(C3⋊Dic3)C2314yes—
151#3750C2312yes—
152#3750C2314yes—
153C4×C3⋊Dic3C2312yes—
154C3×#217C2312yes—
155C3×#217C2314yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4C2312yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2312yes—
167C3×C4×Dic3C2312yes—
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2312yes—
172#3724C2314yes—
173#3724C2312yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183Dic32C2312yes—
184Dic32C2314yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2314yes—
188Q8×#41—91noSylow
189C2×C3×#41—31no—
190C22×C3×Q8—32no—
191C2×D3×Q8—31no—
192C2×#237C2×D311yescharacteristic
193C22×Dic6—31no—
194C22×Dic6C2×D312yes—
195C3×C4⋊Q8—32no—
196C3×C4⋊Q8—31no—
197C3×C22⋊Q8—32no—
198C3×C22⋊Q8—34no—
199C3×C4×Q8—31no—
200C3×C4×Q8—31no—
201C3×C4×Q8—31no—
202C3×C4×D4—21no—
203C3×C4×D4—32no—
204C3×C4×D4—31no—
205C3×C4×D4—32no—
206C3×C4×D4—32no—
207C3×C4×D4C2×D311yescharacteristic
208C3×C4×D4C2×D311yescharacteristic
209C3×#117—31no—
210C3×#117—32no—
211C2×C3×C42—32no—
212C2×C3×C42—31no—
213#946—32no—
214#946—34no—
215Q8×Dic3—32no—
216Q8×Dic3—34no—
217Q8×Dic3—32no—
218Q8×Dic3—34no—
219Q8×Dic3—32no—
220Q8×Dic3—31no—
221Q8×Dic3—32no—
222Q8×Dic3—32no—
223#944—34no—
224#944—32no—
225D4×Dic3—32no—
226D4×Dic3—32no—
227D4×Dic3—34no—
228D4×Dic3—34no—
229D4×Dic3—62no—
230D4×Dic3C2×D311yescharacteristic
231D4×Dic3C2×D312yes—
232C4×#67—34no—
233C4×#67C2×D312yes—
234#926—34no—
235#926—32no—
236C2×C4⋊Dic3—32no—
237C2×C4⋊Dic3—32no—
238C2×C4⋊Dic3—34no—
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3—62no—
241#924—32no—
242#924—32no—
243#924—32no—
244#924—34no—
245#924—34no—
246#924—32no—
247#924—62no—
248#924C2×D312yes—
249C2×Dic3⋊C4—34no—
250C2×Dic3⋊C4—32no—
251C2×C4×Dic3—34no—
252C2×C4×Dic3—34no—
253C2×C4×Dic3—32no—
254C2×C4×Dic3C2×D312yes—
255#897—32no—
256#897—34no—
257#892—32no—
258#892C2×D311yescharacteristic
259D3×C4⋊C4—32no—
260D3×C4⋊C4—31no—
261#890—32no—
262#890—32no—
263#890—32no—
264#890—34no—
265#890—32no—
266#890—34no—
267#890—32no—
268#890—62no—
269#889—34no—
270#889—34no—
271#889—34no—
272#888—34no—
273#888—34no—
274#888—34no—
275#888—32no—
276#888—32no—
277#888C2×D312yes—
278#887—32no—
279#887—34no—
280#887—32no—
281#887—32no—
282#887—31no—
283#887C2×D311yescharacteristic
284#67⋊C4—34no—
285#67⋊C4C2×D312yes—
286#878—34no—
287#878—34no—
288#878—34no—
289#878—34no—
290#878—34no—
291#878—34no—
292#878—34no—
293#878—34no—
294#878—64no—
295#878C2×D314yes—
296#877—34no—
297#877C2×D312yes—
298C42×D3—32no—
299C42×D3C2×D311yescharacteristic
300#870—32no—
301#870—34no—
302#869—32no—
303#869—31no—
304#869—31no—
305#869—32no—
306#869—32no—
307#869—61no—
308#869C2×D311yescharacteristic
309C4×Dic6—32no—
310C4×Dic6—31no—
311C4×Dic6—32no—
312C4×Dic6—34no—
313C4×Dic6—32no—
314C4×Dic6—34no—
315C4×Dic6—32no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C23×C32C2412yes—
328C22×C3×D3C2411yescharacteristic
329C32×D4C2×Q814yescomplemented
330C2×C32×C4—24no—
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C3⋊Dic3—44no—
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2414yes—
338C2×C3⋊Dic3C2412yes—
339#634—22no—
340#634—42no—
341C3×#67C2×Q818yescomplemented
342C2×C3×Dic3—28no—
343C2×C3×Dic3—42no—
344C2×C3×Dic3C2×Q818yescomplemented
345C2×C3×Dic3C2414yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2411yescharacteristic
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C3×C4×D3—22no—
354C3×C4×D3—41no—
355C3×C4×D3C2×Q814yescomplemented
356C3×Dic6—24no—
357C3×Dic6—28no—
358C3×Dic6C2×Q814yescomplemented
359C3×Dic6#4114yescomplemented
360#627—24no—
361#627—44no—
362D3×Dic3—24no—
363D3×Dic3—42no—
364Q82—91no—
365#557—92no—
366#557—91no—
367#554—92no—
368#554—94no—
369#554—92no—
370#554—91no—
371D4×Q8—31no—
372D4×Q8—92no—
373#533—92no—
374#533—91no—
375#533—94no—
376#533—92no—
377C4×#41—31no—
378C4×#41—92no—
379C2×C4×Q8—91no—
380C2×C4×Q8—92no—
381C3×#41—38no—
382C2×C3×Q8—31no—
383C2×C3×Q8—31no—
384C2×C3×Q8—34no—
385C2×C3×Q8—32no—
386C2×C3×Q8—68no—
387C2×C3×D4—21no—
388C2×C3×D4—32no—
389C2×C3×D4C22×D311yescharacteristic
390C2×C3×D4C22×D311yescharacteristic
391C22×C3×C4—22no—
392C22×C3×C4—32no—
393C22×C3×C4—31no—
394C22×C3×C4—34no—
395C22×C3×C4—32no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4C22×D312yes—
399C22×C3×C4C22×D312yes—
400C2×#67C22×D312yes—
401C22×Dic3—34no—
402C22×Dic3—34no—
403C22×Dic3—32no—
404C22×Dic3—32no—
405C22×Dic3—64no—
406C22×Dic3C22×D314yes—
407C22×Dic3C22×D312yes—
408C22×Dic3C22×D312yes—
409D3×Q8—64no—
410#237Dic618yesdirect product factor
411C2×C4×D3—32no—
412C2×C4×D3—32no—
413C2×C4×D3C22×D311yescharacteristic
414C2×C4×D3C22×D311yescharacteristic
415C2×C4×D3C22×D311yescharacteristic
416C2×Dic6—28no—
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—32no—
420C2×Dic6—32no—
421C2×Dic6—32no—
422C2×Dic6—32no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—61no—
426C2×Dic6—62no—
427C2×Dic6—64no—
428C2×Dic6C22×D312yes—
429C2×Dic6C22×D314yes—
430C2×Dic6C22×D311yescharacteristic
431C2×Dic6C22×D311yescharacteristic
432C3×C4⋊C4—21no—
433C3×C4⋊C4—32no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4—32no—
437C3×C4⋊C4—32no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4C22×D311yescharacteristic
442C3×C4⋊C4C22×D311yescharacteristic
443C3×C22⋊C4—22no—
444C3×C22⋊C4—34no—
445C3×C22⋊C4—32no—
446C3×C22⋊C4—32no—
447C3×C22⋊C4C22×D312yes—
448C3×C22⋊C4C22×D312yes—
449C3×C42—21no—
450C3×C42—31no—
451C3×C42—32no—
452C3×C42—31no—
453C3×C42—32no—
454C3×C42—32no—
455C3×C42—32no—
456C3×C42—31no—
457C3×C42C22×D311yescharacteristic
458C3×C42C22×D311yescharacteristic
459#217—34no—
460#217—34no—
461#217—34no—
462#217—64no—
463#217C22×D312yes—
464#217C22×D314yes—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4C22×D312yes—
467C4⋊Dic3—31no—
468C4⋊Dic3—32no—
469C4⋊Dic3—34no—
470C4⋊Dic3—32no—
471C4⋊Dic3—31no—
472C4⋊Dic3—32no—
473C4⋊Dic3—32no—
474C4⋊Dic3—34no—
475C4⋊Dic3—32no—
476C4⋊Dic3—34no—
477C4⋊Dic3—32no—
478C4⋊Dic3—34no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—61no—
484C4⋊Dic3—62no—
485C4⋊Dic3—62no—
486C4⋊Dic3—64no—
487C4⋊Dic3C22×D311yescharacteristic
488C4⋊Dic3C22×D312yes—
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D312yes—
491Dic3⋊C4—32no—
492Dic3⋊C4—34no—
493Dic3⋊C4—32no—
494Dic3⋊C4—34no—
495Dic3⋊C4—32no—
496Dic3⋊C4—34no—
497Dic3⋊C4—32no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—62no—
508Dic3⋊C4—64no—
509Dic3⋊C4C22×D312yes—
510Dic3⋊C4C22×D314yes—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D312yes—
513C4×Dic3—32no—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—34no—
517C4×Dic3—32no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—34no—
524C4×Dic3—34no—
525C4×Dic3—62no—
526C4×Dic3C22×D311yescharacteristic
527C4×Dic3C22×D312yes—
528C4×Dic3C22×D312yes—
529C4×Dic3C22×D311yescharacteristic
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D312yes—
533C22×C32—22no—
534C22×C32—22no—
535C22×C32C22×Q814yes—
536C22×C32C2511yescharacteristic
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3C22×Q812yes—
540C32×C4—22no—
541C32×C4—21no—
542C32×C4C22×Q812yes—
543C32×C4C2×#4112yes—
544C3⋊Dic3—22no—
545C3⋊Dic3—22no—
546C3⋊Dic3—24no—
547C3×Dic3—21no—
548C3×Dic3—24no—
549C3×Dic3—22no—
550C3×Dic3—22no—
551C3×Dic3—21no—
552C3×Dic3C22×Q814yes—
553C3×Dic3C22×Q812yes—
554C3×Dic3C2×#4114yes—
555C2×#41—31no—
556C22×Q8—32no—
557C22×Q8—91no—
558C4⋊Q8—32no—
559C4⋊Q8—31no—
560C4⋊Q8—92no—
561C4⋊Q8—92no—
562C4⋊Q8—92no—
563C4⋊Q8—94no—
564C4⋊Q8—94no—
565C4⋊Q8—91no—
566#125—94no—
567#125—92no—
568#125—94no—
569#125—94no—
570#125—92no—
571#125—92no—
572C22⋊Q8—32no—
573C22⋊Q8—34no—
574C22⋊Q8—94no—
575C22⋊Q8—94no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—92no—
580C22⋊Q8—92no—
581C22⋊Q8—92no—
582C22⋊Q8—94no—
583C4×Q8—31no—
584C4×Q8—31no—
585C4×Q8—31no—
586C4×Q8—92no—
587C4×Q8—91no—
588C4×Q8—92no—
589C4×Q8—94no—
590C4×Q8—92no—
591C4×Q8—91no—
592C4×Q8—92no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—91no—
600C4×D4—31no—
601C4×D4—32no—
602C4×D4—32no—
603C4×D4—32no—
604C4×D4—94no—
605C4×D4—94no—
606C4×D4—92no—
607C4×D4D3211yescharacteristic
608#117—31no—
609#117—32no—
610#117—94no—
611#117—92no—
612C2×C4⋊C4—92no—
613C2×C4⋊C4—91no—
614C2×C4⋊C4—94no—
615C2×C4⋊C4—92no—
616C2×C42—32no—
617C2×C42—31no—
618C2×C42—92no—
619C2×C42—94no—
620C23×C3—22no—
621C23×C3—31no—
622C23×C3C23×D312yes—
623C23×C3C23×D312yes—
624C22×D3C23×D311yescharacteristic
625C3×Q8—34no—
626C3×Q8—34no—
627C3×Q8—68no—
628C3×Q8—64no—
629C3×D4—24no—
630C3×D4—38no—
631C3×D4C2×Dic614yescomplemented
632C3×D4D3×Q814yescomplemented
633C2×C3×C4—24no—
634C2×C3×C4—24no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—22no—
638C2×C3×C4—21no—
639C2×C3×C4—38no—
640C2×C3×C4—31no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—34no—
644C2×C3×C4—34no—
645C2×C3×C4—32no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—32no—
649C2×C3×C4—44no—
650C2×C3×C4—68no—
651C2×C3×C4—62no—
652C2×C3×C4—121no—
653C2×C3×C4—122no—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D312yes—
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662#67C2×Dic618yescomplemented
663C2×Dic3—28no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—34no—
669C2×Dic3—34no—
670C2×Dic3—42no—
671C2×Dic3—62no—
672C2×Dic3—62no—
673C2×Dic3—64no—
674C2×Dic3—64no—
675C2×Dic3—122no—
676C2×Dic3—124no—
677C2×Dic3—124no—
678C2×Dic3—244no—
679C2×Dic3C2×Dic618yescomplemented
680C2×Dic3C23×D314yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D311yescharacteristic
683C2×Dic3C23×D311yescharacteristic
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D311yescharacteristic
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D312yes—
688C4×D3—22no—
689C4×D3—41no—
690C4×D3—64no—
691C4×D3—122no—
692C4×D3C2×Dic614yescomplemented
693Dic6—24no—
694Dic6—28no—
695Dic6—64no—
696Dic6—62no—
697Dic6—62no—
698Dic6—64no—
699Dic6—122no—
700Dic6—124no—
701Dic6—124no—
702Dic6—122no—
703Dic6—122no—
704Dic6—242no—
705Dic6C2×Dic614yescomplemented
706Dic6#23714yesdirect product factor
707C2×C32—24no—
708C2×C32C23×Q811yescharacteristic
709C2×C32C22×#4111yescharacteristic
710C2×C32#58511yescharacteristic
711C3×D3—22no—
712#41—38no—
713C2×Q8—31no—
714C2×Q8—31no—
715C2×Q8—34no—
716C2×Q8—32no—
717C2×Q8—68no—
718C2×Q8—92no—
719C2×Q8—94no—
720C2×Q8—91no—
721C2×Q8—92no—
722C2×Q8—184no—
723C2×D4—32no—
724C2×D4C2×D3211yescharacteristic
725C22×C4—32no—
726C22×C4—31no—
727C22×C4—34no—
728C22×C4—32no—
729C22×C4—31no—
730C22×C4—31no—
731C22×C4—92no—
732C22×C4—92no—
733C22×C4—94no—
734C22×C4C2×D3212yes—
735C4⋊C4—32no—
736C4⋊C4—31no—
737C4⋊C4—32no—
738C4⋊C4—32no—
739C4⋊C4—31no—
740C4⋊C4—32no—
741C4⋊C4—34no—
742C4⋊C4—32no—
743C4⋊C4—92no—
744C4⋊C4—92no—
745C4⋊C4—94no—
746C4⋊C4—92no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—91no—
754C4⋊C4—92no—
755C4⋊C4—94no—
756C4⋊C4—92no—
757C4⋊C4—92no—
758C4⋊C4—94no—
759C4⋊C4C2×D3211yescharacteristic
760C22⋊C4—32no—
761C22⋊C4—34no—
762C22⋊C4—32no—
763C22⋊C4—94no—
764C22⋊C4—94no—
765C22⋊C4C2×D3212yes—
766C42—31no—
767C42—32no—
768C42—31no—
769C42—32no—
770C42—31no—
771C42—32no—
772C42—32no—
773C42—92no—
774C42—92no—
775C42—94no—
776C42—94no—
777C42—94no—
778C42—92no—
779C42C2×D3211yescharacteristic
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—24no—
785C22×C3—21no—
786C22×C3—32no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—61no—
790C22×C3—61no—
791C22×C3C22×Dic614yes—
792C22×C3C2×D3×Q814yes—
793C22×C3C24×D311yescharacteristic
794C22×C3C24×D311yescharacteristic
795C2×D3—21no—
796C2×D3—21no—
797C2×D3C22×Dic612yes—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—32no—
805C3×C4—34no—
806C3×C4—34no—
807C3×C4—41no—
808C3×C4—42no—
809C3×C4—61no—
810C3×C4—64no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—61no—
814C3×C4C22×Dic612yes—
815C3×C4C2×#23712yes—
816C3×C4C2×D3×Q812yes—
817C3×C4D3×#4112yes—
818Dic3—24no—
819Dic3—21no—
820Dic3—22no—
821Dic3—21no—
822Dic3—22no—
823Dic3—62no—
824Dic3—62no—
825Dic3—64no—
826Dic3—62no—
827Dic3—64no—
828Dic3—62no—
829Dic3—122no—
830Dic3—124no—
831Dic3—122no—
832Dic3C22×Dic614yes—
833Dic3C22×Dic612yes—
834Dic3C2×#23714yes—
835C32Q8×#4111yescharacteristic, complemented, Sylow
836C23—31no—
837C23C22×D3212yes—
838Q8—34no—
839Q8—34no—
840Q8—68no—
841Q8—64no—
842Q8—184no—
843Q8—182no—
844Q8—362no—
845Q8—364no—
846D4—38no—
847D4D3×Dic614yescomplemented
848C2×C4—24no—
849C2×C4—38no—
850C2×C4—31no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—34no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—34no—
859C2×C4—68no—
860C2×C4—62no—
861C2×C4—92no—
862C2×C4—92no—
863C2×C4—94no—
864C2×C4—121no—
865C2×C4—122no—
866C2×C4—184no—
867C2×C4—362no—
868C2×C4—364no—
869C2×C4C22×D3212yes—
870C2×C4C22×D3211yescharacteristic
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—24no—
874C2×C3—24no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—44no—
879C2×C3—62no—
880C2×C3C23×Dic611yescharacteristic
881C2×C3C22×#23711yescharacteristic
882C2×C3C22×D3×Q811yescharacteristic
883C2×C3C2×D3×#4111yescharacteristic
884C2×C3#596411yescharacteristic
885C2×C3#596811yescharacteristic
886D3—22no—
887C22—22no—
888C22—22no—
889C22—32no—
890C22—61no—
891C22—61no—
892C22C2×D3×Dic614yes—
893C22C23×D3211yescharacteristic
894C4—22no—
895C4—21no—
896C4—32no—
897C4—34no—
898C4—34no—
899C4—64no—
900C4—61no—
901C4—61no—
902C4—62no—
903C4—62no—
904C4—182no—
905C4—182no—
906C4—184no—
907C4C2×D3×Dic612yes—
908C4D3×#23712yes—
909C3—21no—
910C3#41×Dic611yescharacteristic, complemented
911C3Q8×#23711yescharacteristic, complemented
912C2—24no—
913C2—62no—
914C2C22×D3×Dic611yescharacteristic
915C2C2×D3×#23711yescharacteristic
916C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×C3×#237C22
hypercenterC4×D4D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596014C2semidirect
2. C3×D4×Dic6C2semidirect
4. #10595272C2semidirect
6. #10594993C2semidirect
7. Dic6×#67C2semidirect
8. C2×Dic3×Dic6C2semidirect
9. #10594808C2semidirect
10. #10594445C2semidirect
11. #10594317C2semidirect
12. #10594133C2semidirect
13. #10594029C2semidirect
14. C4×D3×Dic6C2semidirect
15. #10593861C2semidirect
16. #10593859C2semidirect
17. Dic62C2semidirect
111. D4×Dic6D3semidirect
129. C3×#237Q8semidirect
329. C32×D4C2×Q8semidirect
341. C3×#67C2×Q8semidirect
344. C2×C3×Dic3C2×Q8semidirect
355. C3×C4×D3C2×Q8semidirect
358. C3×Dic6C2×Q8semidirect
359. C3×Dic6#41semidirect
410. #237Dic6direct (N × H)
631. C3×D4C2×Dic6semidirect
632. C3×D4D3×Q8semidirect
662. #67C2×Dic6semidirect
679. C2×Dic3C2×Dic6semidirect
692. C4×D3C2×Dic6semidirect
705. Dic6C2×Dic6semidirect
706. Dic6#237direct (N × H)
835. C32Q8×#41semidirect
847. D4D3×Dic6semidirect
910. C3#41×Dic6semidirect
911. C3Q8×#237semidirect

Maximal subgroups

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

subgroupindex
#105960142
C3×D4×Dic62
C3×C4×#2372
#105952722
Dic3×#2372
#105949932
Dic6×#672
C2×Dic3×Dic62
#105948082
#105944452
#105943172
#105941332
#105940292
C4×D3×Dic62
#105938612
#105938592
Dic622
Q8×#2373
#41×Dic63