Finite Group Databasebeta

← #13168277

Subgroups — #13168277

Order 1728.

1454 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3796C211yesmaximal, characteristic, complemented
2C2×C3×#3795C211yesmaximal, characteristic, complemented
3#11723674C211yesmaximal, characteristic, complemented
4C4×#6290C211yesmaximal, characteristic, complemented
5#11723499C211yesmaximal, characteristic, complemented
6#11723451C211yesmaximal, characteristic, complemented
7C3×#63856C211yesmaximal, characteristic, complemented
8#11722986C212yesmaximal, complemented
9#11722985C212yesmaximal, complemented
10#11722954C212yesmaximal, complemented
11D3×#3724C212yesmaximal, complemented
12#10595357—31nomaximal
13#10595252—31nomaximal
14#10594890—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6290C2211yescharacteristic
21C2×D3×C3⋊Dic3C2212yes—
22C2×C3×#626C2212yes—
23C2×C3×#625C2212yes—
24C2×C3×D3×Dic3C2212yes—
25C2×C3×D3×Dic3C2212yes—
26C3×#3796—24no—
27C3×#3795—24no—
28C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30#88815C2212yes—
31#88814C2212yes—
32#88806C2211yescharacteristic
33#88806C2212yes—
34#88806C2212yes—
35#88803C2211yescharacteristic
36(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
37(C2×D3)⋊(C3⋊Dic3)C2212yes—
38C3×#3724C2212yes—
39C3×(C2×D3)⋊Dic3C2212yes—
40C2×C3×#239—31no—
41C2×C3×#237—31no—
42C2×C3×#237—31no—
43C2×C3×#235—31no—
44C2×#3796D311yescharacteristic, complemented
45C2×#3795D311yescharacteristic, complemented
46#64153—31no—
47D4×C3⋊Dic3—31no—
48C4×#638—31no—
49C3×#946—31no—
50C3×#924—31no—
51#63980—32no—
52#63971—32no—
53#63969—32no—
54C2×#3724—32no—
55#63961—32no—
56#63961—32no—
57#63905—32no—
58C4×#625—31no—
59C4×#625—31no—
60C4×#625—61no—
61#63898—31no—
62#63898—31no—
63#63898—61no—
64#63885—32no—
65#63884—32no—
66D3×Dic3⋊C4—32no—
67D3×Dic3⋊C4—32no—
68#63873—31no—
69#63873—31no—
70#63873—61no—
71#63871—31no—
72#63857—31no—
73#63856—31no—
74#63856D311yescharacteristic, complemented
75#63850—32no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C22×C32×D3C2312yes—
79C2×C33×C4C2311yescharacteristic
80C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
81C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C3×C4×C3⋊D3—22no—
86C3×#634—22no—
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C32×D12D414yescomplemented
90C32×C4×D3—22no—
91C32×Dic6—22no—
92#6290—22no—
93D3×C3⋊Dic3—24no—
94C3×#626—24no—
95C3×#625—24no—
96C3×D3×Dic3—24no—
97C3×D3×Dic3—24no—
98#5824—91no—
99#5824—91no—
100#5631—91no—
101C2×C32×Q8—31no—
102C2×C32×D4—31no—
103C22×C32×C4—31no—
104C2×#638—31no—
105C22×C3⋊Dic3—32no—
106C2×C4×C3⋊D3C2×D311yescharacteristic
107C2×#634C2×D311yescharacteristic
108C2×C3×#67—32no—
109C2×C3×#67—32no—
110C2×C3×#67—32no—
111C22×C3×Dic3—32no—
112C22×C3×Dic3—32no—
113C3×#239—64no—
114C3×#237—64no—
115C3×#237—64no—
116C3×#235—64no—
117C2×C3×D12—21no—
118C2×C3×D12—32no—
119C2×C3×D12C2×D311yescharacteristic
120C2×C3×D12C2×D311yescharacteristic
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—32no—
123C2×C3×C4×D3—32no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—61no—
127C2×C3×C4×D3C2×D311yescharacteristic
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×Dic6—21no—
130C2×C3×Dic6—31no—
131C2×C3×Dic6—31no—
132C2×C3×Dic6—61no—
133C2×C3×Dic6C2×D311yescharacteristic
134C2×C3×Dic6C2×D311yescharacteristic
135C2×#626C2×D312yes—
136C2×#625—31no—
137C2×#625—31no—
138C2×#625—61no—
139C2×#625C2×D312yes—
140C2×D3×Dic3—32no—
141C2×D3×Dic3—32no—
142C2×D3×Dic3—62no—
143C2×D3×Dic3C2×D312yes—
144C2×D3×Dic3C2×D312yes—
145#3796—24no—
146#3795—24no—
147#3757—31no—
148#3757—32no—
149#3752—31no—
150C4⋊(C3⋊Dic3)C2×D311yescharacteristic
151#3750—31no—
152#3750—32no—
153#3750—32no—
154C4×C3⋊Dic3—31no—
155C4×C3⋊Dic3—31no—
156C4×C3⋊Dic3—31no—
157C4×C3⋊Dic3—61no—
158C4×C3⋊Dic3—61no—
159C4×C3⋊Dic3—61no—
160C4×C3⋊Dic3—121no—
161C3×#217—32no—
162C3×(C2×D3)⋊C4—32no—
163C3×C4⋊Dic3—31no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—61no—
166C3×Dic3⋊C4—32no—
167C3×Dic3⋊C4—32no—
168#3724—32no—
169#3724—32no—
170#3724—32no—
171#3724—32no—
172#3724—32no—
173#3724—31no—
174#3724—31no—
175#3724—62no—
176#3724—62no—
177#3724—61no—
178#3724C2×D312yes—
179Dic3⋊Dic3—32no—
180Dic3⋊Dic3—32no—
181#3722—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—31no—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—61no—
191(C2×D3)⋊Dic3—62no—
192(C2×D3)⋊Dic3—61no—
193(C2×D3)⋊Dic3C2×D312yes—
194C22×C33C2411yescharacteristic
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3—21no—
198C2×C32×D3—22no—
199C2×C32×D3—22no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C2×C32×D3C2×D414yes—
204C33×C4C2×D412yes—
205C3⋊(C3⋊Dic3)—21no—
206C3⋊(C3⋊Dic3)#4112yescomplemented
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3—22no—
209C3×C3⋊Dic3—22no—
210C32×Dic3—21no—
211C32×Dic3—22no—
212C2×C3×#41—91no—
213C2×C3×#41—91no—
214C2×#239—31no—
215C2×#237—31no—
216C2×#237—31no—
217C2×#235—31no—
218C3×C22⋊Q8—91no—
219#946—31no—
220#946—91no—
221#944—91no—
222#944—91no—
223#944—91no—
224#944—181no—
225#939—92no—
226#939—92no—
227#935—92no—
228#935—92no—
229D4×Dic3—91no—
230D4×Dic3—91no—
231D4×Dic3—181no—
232#929—92no—
233#929—92no—
234C4×#67—91no—
235C4×#67—91no—
236C4×#67—91no—
237C4×#67—181no—
238#924—31no—
239#924—91no—
240C2×Dic3⋊C4—92no—
241C2×Dic3⋊C4—92no—
242#897—91no—
243#894—92no—
244#893—91no—
245D3×C4⋊C4—92no—
246#884—92no—
247#883—92no—
248C23×C32—32no—
249C23×C32—31no—
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3×D3—22no—
252C22×C3×D3—21no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—61no—
256C22×C3×D3C22×D311yescharacteristic
257C22×C3×D3C22×D311yescharacteristic
258C22×C3×D3C22×D312yes—
259C22×C3×D3C22×D312yes—
260C32×Q8—62no—
261C32×D4—34no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—31no—
266C2×C32×C4—32no—
267C2×C32×C4—41no—
268C2×C32×C4—62no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272#638—62no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—31no—
279C2×C3⋊Dic3—61no—
280C2×C3⋊Dic3—61no—
281C2×C3⋊Dic3—61no—
282C2×C3⋊Dic3—61no—
283C2×C3⋊Dic3—61no—
284C2×C3⋊Dic3—61no—
285C2×C3⋊Dic3—64no—
286C2×C3⋊Dic3—121no—
287C2×C3⋊Dic3—121no—
288C2×C3⋊Dic3C22×D312yes—
289C2×C3⋊Dic3C22×D312yes—
290C2×C3⋊Dic3C22×D311yescharacteristic
291C4×C3⋊D3—22no—
292#634—22no—
293C3×#67—64no—
294C3×#67—64no—
295C3×#67—64no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—32no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—32no—
304C2×C3×Dic3—61no—
305C2×C3×Dic3—62no—
306C2×C3×Dic3—62no—
307C2×C3×Dic3—64no—
308C2×C3×Dic3—64no—
309C2×C3×Dic3C22×D311yescharacteristic
310C2×C3×Dic3C22×D311yescharacteristic
311C2×C3×Dic3C22×D312yes—
312C2×C3×Dic3C22×D312yes—
313C3×D12—24no—
314C3×D12—64no—
315C3×D12#6714yescomplemented
316C3×D12#6714yescomplemented
317C3×C4×D3—22no—
318C3×C4×D3—22no—
319C3×C4×D3—42no—
320C3×C4×D3—64no—
321C3×C4×D3—64no—
322C3×C4×D3—62no—
323C3×C4×D3—62no—
324C3×C4×D3—122no—
325C3×Dic6—22no—
326C3×Dic6—22no—
327C3×Dic6—42no—
328C3×Dic6—62no—
329C3×Dic6—62no—
330C3×Dic6—122no—
331#626—24no—
332#625—24no—
333#625—62no—
334#625—62no—
335#625—64no—
336D3×Dic3—24no—
337D3×Dic3—24no—
338D3×Dic3—64no—
339D3×Dic3—64no—
340D3×Dic3—124no—
341#547—271noSylow
342C2×C33C22×D411yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C2×C332−1+411yescharacteristic
345C3×C3⋊D3—41no—
346C32×D3—24no—
347C32×D3—41no—
348C3×#41—184no—
349C3×#41—184no—
350C2×C3×Q8—31no—
351C2×C3×Q8—31no—
352C2×C3×Q8—61no—
353C2×C3×Q8—91no—
354C2×C3×D4—31no—
355C2×C3×D4—31no—
356C2×C3×D4—61no—
357C2×C3×D4—92no—
358C2×C3×D4—92no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—61no—
362C22×C3×C4—92no—
363C22×C3×C4—92no—
364C22×C3×C4—91no—
365C2×#67—32no—
366C2×#67—32no—
367C2×#67—32no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—181no—
372C22×Dic3—32no—
373C22×Dic3—32no—
374C22×Dic3—92no—
375C22×Dic3—92no—
376C22×Dic3—182no—
377#239—64no—
378#237—64no—
379#237—64no—
380#235—64no—
381C2×D12—32no—
382C2×D12D3211yescharacteristic
383C2×C4×D3—32no—
384C2×C4×D3—32no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—61no—
388C2×C4×D3—92no—
389C2×C4×D3D3211yescharacteristic
390C2×Dic6—31no—
391C2×Dic6—31no—
392C2×Dic6—61no—
393C2×Dic6D3211yescharacteristic
394C3×C4⋊C4—92no—
395C3×C4⋊C4—91no—
396C3×C22⋊C4—92no—
397#217—32no—
398#217—92no—
399#217—91no—
400#217—91no—
401#217—92no—
402#217—92no—
403#217—91no—
404#217—181no—
405#217—182no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—92no—
408(C2×D3)⋊C4—92no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—92no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—181no—
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416C4⋊Dic3—61no—
417C4⋊Dic3—92no—
418Dic3⋊C4—32no—
419Dic3⋊C4—32no—
420Dic3⋊C4—92no—
421Dic3⋊C4—92no—
422Dic3⋊C4—92no—
423Dic3⋊C4—92no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—92no—
427Dic3⋊C4—92no—
428Dic3⋊C4—91no—
429Dic3⋊C4—92no—
430Dic3⋊C4—92no—
431Dic3⋊C4—181no—
432Dic3⋊C4—182no—
433Dic3⋊C4—182no—
434C4×Dic3—91no—
435C4×Dic3—91no—
436C4×Dic3—91no—
437C4×Dic3—181no—
438C4×Dic3—181no—
439C4×Dic3—181no—
440C4×Dic3—361no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—34no—
445C22×C32—41no—
446C22×C32—61no—
447C22×C32—62no—
448C22×C32—62no—
449C22×C32—61no—
450C22×C32—61no—
451C22×C32C23×D311yescharacteristic
452C22×C32C23×D311yescharacteristic
453C22×C32C23×D311yescharacteristic
454C2×C3⋊D3—21no—
455C2×C3⋊D3—21no—
456C2×C3⋊D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—24no—
469C2×C3×D3—42no—
470C2×C3×D3—41no—
471C2×C3×D3—42no—
472C2×C3×D3—41no—
473C2×C3×D3—62no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3—121no—
481C2×C3×D3—121no—
482C2×C3×D3C2×#6714yes—
483C2×C3×D3C2×#6714yes—
484C32×C4—22no—
485C32×C4—22no—
486C32×C4—22no—
487C32×C4—42no—
488C32×C4—61no—
489C32×C4—62no—
490C32×C4D3×D412yes—
491C32×C4C2×#6712yes—
492C32×C4C2×#6712yes—
493C3⋊Dic3—22no—
494C3⋊Dic3—21no—
495C3⋊Dic3—22no—
496C3⋊Dic3—32no—
497C3⋊Dic3—32no—
498C3⋊Dic3—32no—
499C3⋊Dic3—62no—
500C3⋊Dic3—62no—
501C3⋊Dic3—62no—
502C3⋊Dic3—61no—
503C3⋊Dic3—62no—
504C3⋊Dic3—61no—
505C3⋊Dic3—61no—
506C3⋊Dic3—122no—
507C3⋊Dic3—121no—
508C3⋊Dic3—121no—
509C3⋊Dic3—122no—
510C3×Dic3—22no—
511C3×Dic3—21no—
512C3×Dic3—21no—
513C3×Dic3—22no—
514C3×Dic3—42no—
515C3×Dic3—41no—
516C3×Dic3—62no—
517C3×Dic3—61no—
518C3×Dic3—62no—
519C3×Dic3—62no—
520C3×Dic3—62no—
521C3×Dic3—61no—
522C3×Dic3—122no—
523C3×Dic3—122no—
524C3×Dic3—121no—
525C2×#41—91no—
526C2×#41—91no—
527C4⋊Q8—271no—
528#123—272no—
529#123—272no—
530C22⋊Q8—91no—
531C22⋊Q8—271no—
532#121—272no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C4⋊C4—272no—
536C33#54711yescharacteristic, complemented, Sylow
537C23×C3—32no—
538C23×C3—32no—
539C23×C3—31no—
540C23×C3—31no—
541C23×C3—62no—
542C23×C3—61no—
543C23×C3—91no—
544C22×D3—31no—
545C22×D3—31no—
546C22×D3—61no—
547C22×D3C2×D3211yescharacteristic
548C22×D3C2×D3212yes—
549C3×Q8—62no—
550C3×Q8—62no—
551C3×Q8—122no—
552C3×Q8—182no—
553C3×D4—34no—
554C3×D4—34no—
555C3×D4—64no—
556C3×D4—184no—
557C3×D4—184no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—62no—
567C2×C3×C4—61no—
568C2×C3×C4—62no—
569C2×C3×C4—62no—
570C2×C3×C4—91no—
571C2×C3×C4—92no—
572C2×C3×C4—92no—
573C2×C3×C4—122no—
574C2×C3×C4—184no—
575C2×C3×C4—184no—
576C2×C3×C4—182no—
577C2×C3×C4C2×D3211yescharacteristic
578C2×C3×C4C2×D3211yescharacteristic
579C2×C3×C4C2×D3211yescharacteristic
580#67—64no—
581#67—64no—
582#67—64no—
583#67—182no—
584#67—182no—
585#67—182no—
586#67—184no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—31no—
591C2×Dic3—32no—
592C2×Dic3—31no—
593C2×Dic3—62no—
594C2×Dic3—61no—
595C2×Dic3—62no—
596C2×Dic3—64no—
597C2×Dic3—64no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—91no—
603C2×Dic3—91no—
604C2×Dic3—181no—
605C2×Dic3—181no—
606C2×Dic3—181no—
607C2×Dic3—181no—
608C2×Dic3—181no—
609C2×Dic3—181no—
610C2×Dic3—184no—
611C2×Dic3—184no—
612C2×Dic3—361no—
613C2×Dic3—361no—
614C2×Dic3—364no—
615C2×Dic3C2×D3211yescharacteristic
616C2×Dic3C2×D3212yes—
617D12—64no—
618D12#62514yescomplemented
619C4×D3—22no—
620C4×D3—64no—
621C4×D3—64no—
622C4×D3—62no—
623C4×D3—62no—
624C4×D3—122no—
625C4×D3—184no—
626Dic6—22no—
627Dic6—62no—
628Dic6—62no—
629Dic6—122no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32—41no—
642C2×C32—64no—
643C2×C32—121no—
644C2×C32C2×D3×D411yescharacteristic
645C2×C32#100711yescharacteristic
646C2×C32D3×#4111yescharacteristic
647C2×C32D3×#4111yescharacteristic
648C2×C32D3×#4111yescharacteristic
649C2×C32#101011yescharacteristic
650C2×C32#101011yescharacteristic
651C2×C32C22×#6711yescharacteristic
652C2×C32C22×#6711yescharacteristic
653C3⋊D3—41no—
654C3×D3—24no—
655C3×D3—24no—
656C3×D3—44no—
657C3×D3—42no—
658C3×D3—41no—
659C3×D3—41no—
660C3×D3—122no—
661C3×D3—121no—
662C3×D3—121no—
663#41—184no—
664#41—184no—
665C2×Q8—31no—
666C2×Q8—91no—
667C2×D4—31no—
668C2×D4—92no—
669C2×D4—92no—
670C2×D4—271no—
671C22×C4—31no—
672C22×C4—92no—
673C22×C4—92no—
674C22×C4—91no—
675C22×C4—272no—
676C4⋊C4—92no—
677C4⋊C4—91no—
678C4⋊C4—271no—
679C4⋊C4—272no—
680C4⋊C4—272no—
681C4⋊C4—272no—
682C22⋊C4—92no—
683C22⋊C4—271no—
684C22⋊C4—272no—
685C22⋊C4—272no—
686C22⋊C4—271no—
687C42—271no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—34no—
692C22×C3—34no—
693C22×C3—41no—
694C22×C3—64no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—62no—
699C22×C3—62no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—122no—
707C22×C3—121no—
708C22×C3—122no—
709C22×C3—121no—
710C22×C3—181no—
711C22×C3—181no—
712C22×C3—181no—
713C22×C3C22×D3211yescharacteristic
714C22×C3C22×D3211yescharacteristic
715C22×C3C22×D3211yescharacteristic
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—62no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3C2×#62514yes—
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—42no—
735C3×C4—61no—
736C3×C4—62no—
737C3×C4—61no—
738C3×C4—62no—
739C3×C4—121no—
740C3×C4—122no—
741C3×C4—182no—
742C3×C4—181no—
743C3×C4—182no—
744C3×C4C2×#62512yes—
745C3×C4D3×#6712yes—
746C3×C4D3×#6712yes—
747Dic3—22no—
748Dic3—21no—
749Dic3—62no—
750Dic3—62no—
751Dic3—62no—
752Dic3—61no—
753Dic3—62no—
754Dic3—61no—
755Dic3—92no—
756Dic3—92no—
757Dic3—92no—
758Dic3—122no—
759Dic3—121no—
760Dic3—122no—
761Dic3—182no—
762Dic3—182no—
763Dic3—182no—
764Dic3—182no—
765Dic3—181no—
766Dic3—181no—
767Dic3—181no—
768Dic3—362no—
769Dic3—361no—
770Dic3—361no—
771Dic3—362no—
772C32—21no—
773C32—21no—
774C32—21no—
775C32—41no—
776C32#563111yescharacteristic, complemented
777C32#582411yescharacteristic, complemented
778C32#582411yescharacteristic, complemented
779C23—32no—
780C23—31no—
781C23—91no—
782Q8—62no—
783Q8—182no—
784D4—34no—
785D4—184no—
786D4—184no—
787D4—542no—
788C2×C4—32no—
789C2×C4—31no—
790C2×C4—62no—
791C2×C4—92no—
792C2×C4—91no—
793C2×C4—92no—
794C2×C4—184no—
795C2×C4—184no—
796C2×C4—182no—
797C2×C4—271no—
798C2×C4—271no—
799C2×C4—544no—
800C2×C4D3311yescharacteristic
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—41no—
811C2×C3—41no—
812C2×C3—41no—
813C2×C3—64no—
814C2×C3—64no—
815C2×C3—124no—
816C2×C3—122no—
817C2×C3—121no—
818C2×C3—121no—
819C2×C3—361no—
820C2×C3#6429711yescharacteristic
821C2×C3#6430611yescharacteristic
822C2×C3#6430911yescharacteristic
823C2×C3#6431211yescharacteristic
824C2×C3#6431511yescharacteristic
825C2×C3#6431911yescharacteristic
826C2×C3C22×#62511yescharacteristic
827C2×C3C2×D3×#6711yescharacteristic
828C2×C3C2×D3×#6711yescharacteristic
829D3—24no—
830D3—41no—
831D3—122no—
832D3—121no—
833D3—121no—
834C22—34no—
835C22—62no—
836C22—62no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—181no—
841C22—181no—
842C22—181no—
843C22C2×D3311yescharacteristic
844C4—61no—
845C4—62no—
846C4—182no—
847C4—181no—
848C4—182no—
849C4—272no—
850C4—541no—
851C4D3×#62512yes—
852C3—21no—
853C3—21no—
854C3—21no—
855C3—41no—
856C3#1059489011yescharacteristic, complemented
857C3#1059525211yescharacteristic, complemented
858C3#1059535711yescharacteristic, complemented
859C2—64no—
860C2—121no—
861C2—361no—
862C2#1172437611yescharacteristic
863C2#1172439311yescharacteristic
864C2C2×D3×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#547
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×#3796C2semidirect
2. C2×C3×#3795C2semidirect
3. #11723674C2semidirect
4. C4×#6290C2semidirect
5. #11723499C2semidirect
6. #11723451C2semidirect
7. C3×#63856C2semidirect
8. #11722986C2semidirect
9. #11722985C2semidirect
10. #11722954C2semidirect
11. D3×#3724C2semidirect
44. C2×#3796D3semidirect
45. C2×#3795D3semidirect
74. #63856D3semidirect
89. C32×D12D4semidirect
206. C3⋊(C3⋊Dic3)#41semidirect
315. C3×D12#67semidirect
316. C3×D12#67semidirect
536. C33#547semidirect
618. D12#625semidirect
776. C32#5631semidirect
777. C32#5824semidirect
778. C32#5824semidirect
856. C3#10594890semidirect
857. C3#10595252semidirect
858. C3#10595357semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37962
C2×C3×#37952
#117236742
C4×#62902
#117234992
#117234512
C3×#638562
#117229862
#117229852
#117229542
D3×#37242
#105953573
#105952523
#105948903