Finite Group Databasebeta

← #13168743

Subgroups — #13168743

Order 1728.

1540 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
2C2×D3×#634C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4#11723399C211yesmaximal, characteristic, complemented
5C3×C4×#626C211yesmaximal, characteristic
6C3×#63866C211yesmaximal, characteristic, complemented
7C3×#63856C211yesmaximal, characteristic, complemented
8#11723037C212yesmaximal, complemented
9#11722983C212yesmaximal, complemented
10#11722980C212yesmaximal, complemented
11#11722929C212yesmaximal
12#10595361—31nomaximal
13#10594915—31nomaximal
14#10593904—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6293C2212yes—
21C2×#6293C2212yes—
22C2×Dic3×C3⋊D3C2212yes—
23C2×D3×C3⋊Dic3C2212yes—
24C3⋊D3×Dic6—24no—
25D3×#634—24no—
26C2×C3×#626C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29#88815C2212yes—
30#88814C2212yes—
31#88806C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×#3724C2212yes—
34C3×Dic3⋊Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×#3722C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2212yes—
39C3×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×Q8×C3⋊D3—31no—
41C22×#634—31no—
42C2×D3×Dic6—31no—
43C2×D3×Dic6—31no—
44C2×D3×Dic6—31no—
45C2×D3×Dic6—31no—
46C2×D3×Dic6—61no—
47C2×D3×Dic6—61no—
48C4×#634—31no—
49C3×#946—31no—
50C3×#944—31no—
51C3×C4×#67—31no—
52C3×#924—31no—
53C3×C4×D12—31no—
54C3×#869—31no—
55#63982—32no—
56#67⋊Dic3—32no—
57#63919—32no—
58C4×#626D311yescharacteristic
59#63899—32no—
60#63899—32no—
61#63898—32no—
62#63896—32no—
63#63896—32no—
64#63881—32no—
65#63871—31no—
66#63866D311yescharacteristic, complemented
67#63865—32no—
68#63857—31no—
69#63856—31no—
70#63856D311yescharacteristic, complemented
71#63844—31no—
72#63844—31no—
73#63844—61no—
74#63840—32no—
75#63840—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2312yes—
80#6308D414yescomplemented
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4×C3⋊D3—22no—
85C3×#634—22no—
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2311yescharacteristic
90C32×C4×D3—22no—
91C32×Dic6—22no—
92#6293—24no—
93#6293—24no—
94Dic3×C3⋊D3—24no—
95D3×C3⋊Dic3—24no—
96C3×#626Q814yescomplemented
97#5727—91no—
98#5632—91no—
99D4×Dic6—91no—
100C2×C32×Q8—31no—
101C22×C32×C4—31no—
102C22×C3⋊Dic3—32no—
103Q8×C3⋊D3—64no—
104C2×C4×C3⋊D3—32no—
105C2×C4×C3⋊D3C2×D311yescharacteristic
106C2×#634—31no—
107C2×#634—31no—
108C2×#634—31no—
109C2×#634—32no—
110C2×#634—32no—
111C2×#634—64no—
112C2×#634—61no—
113C2×#634—61no—
114C2×#634—61no—
115C2×#634—121no—
116C2×#634C2×D311yescharacteristic
117C2×C3×#67—31no—
118C2×C3×D12—31no—
119C2×C3×C4×D3—21no—
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—61no—
129C2×C3×Dic6C2×D311yescharacteristic
130C2×C3×Dic6C2×D311yescharacteristic
131C2×#627—32no—
132C2×#627—32no—
133C2×#627—32no—
134C2×#627—32no—
135C2×#627—62no—
136C2×#627—62no—
137C2×#626C2×D311yescharacteristic
138C2×D3×Dic3—32no—
139C2×D3×Dic3—32no—
140C2×D3×Dic3—32no—
141C2×D3×Dic3—32no—
142C2×D3×Dic3—62no—
143C2×D3×Dic3—62no—
144D3×Dic6—64no—
145D3×Dic6—64no—
146D3×Dic6—68no—
147D3×Dic6—64no—
148D3×Dic6—64no—
149D3×Dic6—68no—
150C32×C42—31no—
151C4⋊(C3⋊Dic3)C2×D311yescharacteristic
152#3750—32no—
153C4×C3⋊Dic3—32no—
154C3×#217—32no—
155C3×#217—31no—
156C3×(C2×D3)⋊C4—32no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×C4⋊Dic3—31no—
161C3×C4⋊Dic3—31no—
162C3×C4⋊Dic3—32no—
163C3×C4⋊Dic3—32no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—61no—
166C3×Dic3⋊C4—32no—
167C3×Dic3⋊C4—31no—
168C3×Dic3⋊C4—32no—
169C3×Dic3⋊C4—32no—
170C3×Dic3⋊C4—32no—
171C3×C4×Dic3—21no—
172C3×C4×Dic3C2×D311yescharacteristic
173C3×C4×Dic3C2×D311yescharacteristic
174#3724—32no—
175#3724—32no—
176#3724—32no—
177#3724—62no—
178#3724C2×D312yes—
179Dic3⋊Dic3—32no—
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3C2×D311yescharacteristic
182Dic3⋊Dic3C2×D312yes—
183Dic3⋊Dic3C2×D312yes—
184#3722—32no—
185#3722C2×D311yescharacteristic
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3C2×D312yes—
189(C2×D3)⋊Dic3C2×D311yescharacteristic
190Dic32—32no—
191Dic32—32no—
192Dic32—62no—
193C22×C33C2411yescharacteristic
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3C2×Q812yescomplemented
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3C2×Q812yescomplemented
200C33×C4C2×D412yes—
201C3⋊(C3⋊Dic3)C2×D414yes—
202C3×C3⋊Dic3—22no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3—22no—
205C32×Dic3—22no—
206C32×Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3C2×Q812yescomplemented
209C2×D3×Q8—91no—
210C2×D3×Q8—91no—
211C2×D3×Q8—91no—
212C2×D3×Q8—181no—
213C22×Dic6—91no—
214C22×Dic6—91no—
215C22×Dic6—91no—
216C22×Dic6—181no—
217C3×C4⋊Q8—91no—
218C3×C22⋊Q8—91no—
219C3×C4×D4—91no—
220#946—31no—
221#946—91no—
222#944—31no—
223D4×Dic3—92no—
224C4×#67—31no—
225#924—31no—
226#924—91no—
227#897—91no—
228#896—92no—
229#896—92no—
230#896—92no—
231#893—92no—
232#888—92no—
233#888—92no—
234#888—92no—
235#887—91no—
236#67⋊C4—92no—
237#878—92no—
238#878—92no—
239#878—92no—
240C4×D12—31no—
241#869—31no—
242C4×Dic6—91no—
243C4×Dic6—91no—
244C4×Dic6—181no—
245C23×C32—31no—
246C22×C3⋊D3C22×D311yescharacteristic
247C22×C3×D3—21no—
248C22×C3×D3—31no—
249C22×C3×D3—31no—
250C22×C3×D3—61no—
251C22×C3×D3C22×D311yescharacteristic
252C22×C3×D3C22×D311yescharacteristic
253C32×Q8—62no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—32no—
260C2×C32×C4—31no—
261C2×C32×C4—41no—
262C2×C32×C4—62no—
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C3⋊Dic3—32no—
267C2×C3⋊Dic3—32no—
268C2×C3⋊Dic3—32no—
269C2×C3⋊Dic3—62no—
270C2×C3⋊Dic3—62no—
271C2×C3⋊Dic3—62no—
272C2×C3⋊Dic3—64no—
273C2×C3⋊Dic3—122no—
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D312yes—
276C2×C3⋊Dic3C22×D311yescharacteristic
277C4×C3⋊D3—22no—
278C4×C3⋊D3—64no—
279#634—22no—
280#634—34no—
281#634—34no—
282#634—34no—
283#634—64no—
284#634—64no—
285#634—64no—
286#634—64no—
287#634—64no—
288#634—124no—
289C3×#67—34no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—32no—
295C2×C3×Dic3—32no—
296C2×C3×Dic3—32no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—62no—
301C2×C3×Dic3—61no—
302C2×C3×Dic3—62no—
303C2×C3×Dic3C22×D311yescharacteristic
304C2×C3×Dic3C22×D312yes—
305C2×C3×Dic3C22×D311yescharacteristic
306C2×C3×Dic3C22×D311yescharacteristic
307C2×C3×Dic3C22×D312yes—
308C2×C3×Dic3C22×D311yescharacteristic
309C2×C3×Dic3C22×D311yescharacteristic
310C2×C3×Dic3C22×D311yescharacteristic
311C3×D12—34no—
312C3×C4×D3—24no—
313C3×C4×D3—22no—
314C3×C4×D3—22no—
315C3×C4×D3—64no—
316C3×C4×D3—62no—
317C3×C4×D3—62no—
318C3×Dic6—24no—
319C3×Dic6—22no—
320C3×Dic6—22no—
321C3×Dic6—64no—
322C3×Dic6—62no—
323C3×Dic6—62no—
324#627—64no—
325#627—64no—
326#627—64no—
327#627—64no—
328#627—68no—
329#627—68no—
330#626Dic614yescomplemented
331D3×Dic3—64no—
332D3×Dic3—64no—
333D3×Dic3—68no—
334D3×Dic3—64no—
335D3×Dic3—64no—
336D3×Dic3—68no—
337D4×Q8—271noSylow
338C2×C33C22×D411yescharacteristic
339C2×C33C22×Q811yescharacteristic
340C2×C332−1+411yescharacteristic
341C3×C3⋊D3—22no—
342C32×D3—22no—
343C2×C3×Q8—31no—
344C2×C3×Q8—31no—
345C2×C3×Q8—61no—
346C2×C3×Q8—91no—
347C2×C3×D4—91no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—61no—
351C22×C3×C4—91no—
352C2×#67—31no—
353C22×Dic3—92no—
354C22×Dic3—92no—
355C22×Dic3—92no—
356C22×Dic3—182no—
357D3×Q8—184no—
358D3×Q8—184no—
359D3×Q8—184no—
360D3×Q8—188no—
361C2×D12—31no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—61no—
365C2×C4×D3—92no—
366C2×C4×D3—92no—
367C2×C4×D3—92no—
368C2×C4×D3—182no—
369C2×C4×D3D3211yescharacteristic
370C2×Dic6—31no—
371C2×Dic6—31no—
372C2×Dic6—61no—
373C2×Dic6—91no—
374C2×Dic6—91no—
375C2×Dic6—91no—
376C2×Dic6—92no—
377C2×Dic6—92no—
378C2×Dic6—92no—
379C2×Dic6—92no—
380C2×Dic6—92no—
381C2×Dic6—92no—
382C2×Dic6—182no—
383C2×Dic6—182no—
384C2×Dic6—181no—
385C2×Dic6—181no—
386C2×Dic6—181no—
387C2×Dic6—184no—
388C2×Dic6—184no—
389C2×Dic6—184no—
390C2×Dic6—188no—
391C2×Dic6—361no—
392C2×Dic6D3211yescharacteristic
393C3×C4⋊C4—91no—
394C3×C4⋊C4—92no—
395C3×C4⋊C4—92no—
396C3×C4⋊C4—92no—
397C3×C4⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4—92no—
401C3×C42—31no—
402C3×C42—31no—
403C3×C42—61no—
404#217—31no—
405#217—32no—
406#217—92no—
407(C2×D3)⋊C4—31no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
411(C2×D3)⋊C4—92no—
412(C2×D3)⋊C4—92no—
413C4⋊Dic3—31no—
414C4⋊Dic3—31no—
415C4⋊Dic3—32no—
416C4⋊Dic3—32no—
417C4⋊Dic3—31no—
418C4⋊Dic3—61no—
419C4⋊Dic3—92no—
420Dic3⋊C4—32no—
421Dic3⋊C4—32no—
422Dic3⋊C4—32no—
423Dic3⋊C4—31no—
424Dic3⋊C4—32no—
425Dic3⋊C4—92no—
426Dic3⋊C4—92no—
427Dic3⋊C4—92no—
428Dic3⋊C4—92no—
429Dic3⋊C4—92no—
430Dic3⋊C4—182no—
431C4×Dic3—92no—
432C4×Dic3—92no—
433C4×Dic3—92no—
434C4×Dic3—182no—
435C4×Dic3D3211yescharacteristic
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—32no—
440C22×C32—41no—
441C22×C32—61no—
442C22×C32—61no—
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C22×C32C23×D311yescharacteristic
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3C2×Dic612yescomplemented
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—22no—
456C2×C3×D3—32no—
457C2×C3×D3—32no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—62no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3C2×Dic612yescomplemented
466C2×C3×D3D3×Q812yescomplemented
467C32×C4—22no—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4—32no—
471C32×C4—42no—
472C32×C4—61no—
473C32×C4—62no—
474C32×C4—61no—
475C32×C4D3×D412yes—
476C32×C4D3×D412yes—
477C32×C4D3×D412yes—
478C3⋊Dic3—22no—
479C3⋊Dic3—21no—
480C3⋊Dic3—22no—
481C3⋊Dic3—34no—
482C3⋊Dic3—34no—
483C3⋊Dic3—34no—
484C3⋊Dic3—64no—
485C3⋊Dic3—64no—
486C3⋊Dic3—64no—
487C3⋊Dic3—124no—
488C3×Dic3—24no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—21no—
496C3×Dic3—22no—
497C3×Dic3—41no—
498C3×Dic3—64no—
499C3×Dic3—62no—
500C3×Dic3—62no—
501C3×Dic3—62no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—62no—
505C3×Dic3—62no—
506C3×Dic3—122no—
507C3×Dic3C2×Dic612yescomplemented
508C3×Dic3D3×Q812yescomplemented
509C22×Q8—271no—
510C22×Q8—271no—
511C4⋊Q8—91no—
512C4⋊Q8—272no—
513C22⋊Q8—91no—
514C22⋊Q8—272no—
515C22⋊Q8—272no—
516C22⋊Q8—271no—
517C4×Q8—271no—
518C4×D4—91no—
519C4×D4—272no—
520C33D4×Q811yescharacteristic, complemented, Sylow
521C23×C3—31no—
522C23×C3—31no—
523C23×C3—61no—
524C23×C3—91no—
525C22×D3—31no—
526C22×D3—31no—
527C22×D3—61no—
528C22×D3C2×D3211yescharacteristic
529C3×Q8—64no—
530C3×Q8—62no—
531C3×Q8—62no—
532C3×Q8—182no—
533C3×D4—94no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—32no—
541C2×C3×C4—31no—
542C2×C3×C4—32no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—41no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—62no—
549C2×C3×C4—61no—
550C2×C3×C4—64no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—92no—
554C2×C3×C4—91no—
555C2×C3×C4—92no—
556C2×C3×C4—182no—
557C2×C3×C4C2×D3211yescharacteristic
558C2×C3×C4C2×D3211yescharacteristic
559C2×C3×C4C2×D3211yescharacteristic
560#67—34no—
561C2×Dic3—32no—
562C2×Dic3—32no—
563C2×Dic3—32no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—32no—
567C2×Dic3—62no—
568C2×Dic3—61no—
569C2×Dic3—62no—
570C2×Dic3—92no—
571C2×Dic3—92no—
572C2×Dic3—92no—
573C2×Dic3—182no—
574C2×Dic3—182no—
575C2×Dic3—182no—
576C2×Dic3—184no—
577C2×Dic3—184no—
578C2×Dic3—184no—
579C2×Dic3—188no—
580C2×Dic3—362no—
581C2×Dic3C2×D3211yescharacteristic
582C2×Dic3C2×D3211yescharacteristic
583C2×Dic3C2×D3212yes—
584C2×Dic3C2×D3211yescharacteristic
585D12—34no—
586C4×D3—22no—
587C4×D3—64no—
588C4×D3—62no—
589C4×D3—62no—
590C4×D3—184no—
591C4×D3—184no—
592C4×D3—184no—
593C4×D3—188no—
594Dic6—22no—
595Dic6—64no—
596Dic6—62no—
597Dic6—62no—
598Dic6—94no—
599Dic6—94no—
600Dic6—94no—
601Dic6—184no—
602Dic6—184no—
603Dic6—184no—
604Dic6—184no—
605Dic6—184no—
606Dic6—184no—
607Dic6—184no—
608Dic6—184no—
609Dic6—184no—
610Dic6—188no—
611Dic6—188no—
612Dic6—364no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—41no—
623C2×C32—41no—
624C2×C32—41no—
625C2×C32—62no—
626C2×C32C22×Dic611yescharacteristic
627C2×C32C2×D3×D411yescharacteristic
628C2×C32C2×D3×D411yescharacteristic
629C2×C32C2×D3×D411yescharacteristic
630C2×C32C2×D3×Q811yescharacteristic
631C2×C32C2×D3×Q811yescharacteristic
632C2×C32#100711yescharacteristic
633C2×C32#101011yescharacteristic
634C2×C32#101011yescharacteristic
635C3⋊D3—22no—
636C3×D3—24no—
637C3×D3—22no—
638C3×D3—22no—
639C3×D3—64no—
640C3×D3—62no—
641C3×D3—62no—
642C2×Q8—31no—
643C2×Q8—91no—
644C2×Q8—272no—
645C2×Q8—272no—
646C2×Q8—271no—
647C2×Q8—544no—
648C2×Q8—544no—
649C2×D4—91no—
650C22×C4—31no—
651C22×C4—91no—
652C22×C4—272no—
653C22×C4—272no—
654C4⋊C4—91no—
655C4⋊C4—92no—
656C4⋊C4—92no—
657C4⋊C4—92no—
658C4⋊C4—91no—
659C4⋊C4—272no—
660C4⋊C4—272no—
661C22⋊C4—91no—
662C22⋊C4—91no—
663C22⋊C4—92no—
664C22⋊C4—272no—
665C42—31no—
666C42—272no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—32no—
671C22×C3—32no—
672C22×C3—41no—
673C22×C3—62no—
674C22×C3—62no—
675C22×C3—62no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—92no—
681C22×C3—181no—
682C22×C3—181no—
683C22×C3C22×D3211yescharacteristic
684C22×C3C22×D3211yescharacteristic
685C22×C3C22×D3211yescharacteristic
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—32no—
689C2×D3—32no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3D3×Dic612yescomplemented
698C3×C4—22no—
699C3×C4—22no—
700C3×C4—22no—
701C3×C4—32no—
702C3×C4—32no—
703C3×C4—42no—
704C3×C4—62no—
705C3×C4—62no—
706C3×C4—64no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—62no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—62no—
713C3×C4—121no—
714C3×C4—182no—
715C3×C4—181no—
716C3×C4—182no—
717C3×C4#380212yes—
718C3×C4#381112yes—
719C3×C4#381112yes—
720Dic3—21no—
721Dic3—22no—
722Dic3—21no—
723Dic3—64no—
724Dic3—62no—
725Dic3—62no—
726Dic3—62no—
727Dic3—61no—
728Dic3—62no—
729Dic3—62no—
730Dic3—61no—
731Dic3—94no—
732Dic3—94no—
733Dic3—94no—
734Dic3—122no—
735Dic3—184no—
736Dic3—184no—
737Dic3—184no—
738Dic3—364no—
739Dic3D3×Dic612yescomplemented
740C32—21no—
741C32—21no—
742C32—21no—
743C32—41no—
744C32D4×Dic611yescharacteristic, complemented
745C32#563211yescharacteristic, complemented
746C32#572711yescharacteristic, complemented
747C23—31no—
748C23—91no—
749Q8—62no—
750Q8—182no—
751Q8—274no—
752Q8—544no—
753Q8—544no—
754D4—94no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—32no—
759C2×C4—62no—
760C2×C4—92no—
761C2×C4—91no—
762C2×C4—92no—
763C2×C4—182no—
764C2×C4—272no—
765C2×C4—544no—
766C2×C4—544no—
767C2×C4D3311yescharacteristic
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—41no—
778C2×C3—41no—
779C2×C3—41no—
780C2×C3—64no—
781C2×C3—62no—
782C2×C3—62no—
783C2×C3—182no—
784C2×C3C2×D3×Dic611yescharacteristic
785C2×C3C2×D3×Dic611yescharacteristic
786C2×C3#6429711yescharacteristic
787C2×C3#6429811yescharacteristic
788C2×C3C2×#380211yescharacteristic
789C2×C3#6431511yescharacteristic
790C2×C3D32×Q811yescharacteristic
791C2×C3C2×#381111yescharacteristic
792C2×C3C2×#381111yescharacteristic
793D3—22no—
794D3—64no—
795D3—62no—
796D3—62no—
797C22—32no—
798C22—61no—
799C22—61no—
800C22—92no—
801C22—181no—
802C22—181no—
803C22C2×D3311yescharacteristic
804C4—32no—
805C4—61no—
806C4—61no—
807C4—62no—
808C4—182no—
809C4—181no—
810C4—182no—
811C4—274no—
812C4#8895412yes—
813C3—21no—
814C3—21no—
815C3—21no—
816C3—41no—
817C3#1059390411yescharacteristic, complemented
818C3#1059491511yescharacteristic, complemented
819C3#1059536111yescharacteristic, complemented
820C2—62no—
821C2—182no—
822C2D32×Dic611yescharacteristic
823C2#1172439611yescharacteristic
824C2C2×#8895411yescharacteristic
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×D3×#634C2semidirect
3. #11723674C2semidirect
4. #11723399C2semidirect
6. C3×#63866C2semidirect
7. C3×#63856C2semidirect
8. #11723037C2semidirect
9. #11722983C2semidirect
10. #11722980C2semidirect
66. #63866D3semidirect
70. #63856D3semidirect
80. #6308D4semidirect
96. C3×#626Q8semidirect
196. C2×C3×C3⋊D3C2×Q8semidirect
199. C2×C32×D3C2×Q8semidirect
208. C32×Dic3C2×Q8semidirect
330. #626Dic6semidirect
448. C2×C3⋊D3C2×Dic6semidirect
465. C2×C3×D3C2×Dic6semidirect
466. C2×C3×D3D3×Q8semidirect
507. C3×Dic3C2×Dic6semidirect
508. C3×Dic3D3×Q8semidirect
520. C33D4×Q8semidirect
697. C2×D3D3×Dic6semidirect
739. Dic3D3×Dic6semidirect
744. C32D4×Dic6semidirect
745. C32#5632semidirect
746. C32#5727semidirect
817. C3#10593904semidirect
818. C3#10594915semidirect
819. C3#10595361semidirect

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×D3×#6342
#117236742
#117233992
C3×C4×#6262
C3×#638662
C3×#638562
#117230372
#117229832
#117229802
#117229292
#105953613
#105949153
#105939043