Finite Group Databasebeta

← #13172004

Subgroups — #13172004

Order 1728.

1638 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C211yesmaximal, characteristic, complemented
2C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
3#11723720C211yesmaximal, characteristic, complemented
4#11723629C211yesmaximal, characteristic, complemented
5#11723602C211yesmaximal, characteristic, complemented
6#11723594C211yesmaximal, characteristic, complemented
7C3×#63976C211yesmaximal, characteristic, complemented
8#11722969C212yesmaximal, complemented
9#11722956C212yesmaximal, complemented
10#11722930C212yesmaximal, complemented
11Dic3×#625C212yesmaximal, complemented
12#10595498—31nomaximal
13#10595154—31nomaximal
14#10595022—31nomaximal
15C23×C32×D3C2211yescharacteristic
16C2×C3×#638C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C2×C32×#67C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C2×#6290C2212yes—
21C2×C3×#627C2211yescharacteristic, complemented
22C2×C3×#626C2211yescharacteristic, complemented
23C2×C3×#625C2212yes—
24C2×C3×#624C2211yescharacteristic, complemented
25C3×#3804—24no—
26C2×C3×D3×Dic3—24no—
27C2×C3×D3×Dic3C2212yes—
28C2×C3×D3×Dic3C2212yes—
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30#88864C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32#88815C2212yescomplemented
33#88814C2212yescomplemented
34#88806C2212yescomplemented
35Dic3⋊(C3⋊Dic3)C2212yescomplemented
36(C2×D3)⋊(C3⋊Dic3)C2212yes—
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38Dic3×C3⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yes—
40C23×C3×Dic3—31no—
41C2×C3×#237—31no—
42C2×C3×#235—31no—
43C22×C3×C4×D3—31no—
44C2×#3804D311yescharacteristic, complemented
45C22×D3×Dic3D311yescharacteristic, complemented
46#64162—31no—
47#64144—31no—
48#64135—31no—
49C3×#953—31no—
50C3×#937—31no—
51#63978—32no—
52#63976—31no—
53#63976—31no—
54#63976—61no—
55#63976D311yescharacteristic, complemented
56Dic3×#67—32no—
57Dic3×#67—32no—
58#63970—32no—
59#63966—31no—
60#63964—32no—
61#63962—31no—
62#63961—31no—
63#63961—31no—
64#63961—31no—
65#63961—61no—
66#63955—31no—
67#63955—31no—
68#63955—61no—
69#63952—32no—
70#63908—32no—
71C4×#625—32no—
72C4×#625—32no—
73#63887—32no—
74#63879—32no—
75#63856—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3—22no—
79C22×C32×D3—24no—
80C22×C32×D3C2311yescharacteristic
81C22×C32×D3C2312yes—
82C2×C3⋊(C3⋊Dic3)C2312yes—
83C3×#638—22no—
84C2×C3×C3⋊Dic3—22no—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C32×#67—22no—
89C2×C32×Dic3D414yescomplemented
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93#6290—24no—
94C3×#627—22no—
95C3×#626—22no—
96C3×#625—24no—
97C3×#624—22no—
98C3×D3×Dic3—24no—
99C3×D3×Dic3—24no—
100C3×D3×Dic3—22no—
101#5828—91no—
102#5791—91no—
103#5586—91no—
104C24×C32—31no—
105C23×C3×D3—21no—
106C23×C3×D3C2×D311yescharacteristic
107C23×C3×D3C2×D311yescharacteristic
108C2×C32×D4—31no—
109C22×C32×C4—31no—
110C2×#638—32no—
111C2×#638C2×D311yescharacteristic
112C22×C3⋊Dic3C2×D311yescharacteristic
113C2×C3×#67—21no—
114C2×C3×#67—31no—
115C2×C3×#67—31no—
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—31no—
119C2×C3×#67—61no—
120C2×C3×#67C2×D311yescharacteristic
121C2×C3×#67C2×D311yescharacteristic
122C22×C3×Dic3—21no—
123C22×C3×Dic3—31no—
124C22×C3×Dic3—31no—
125C22×C3×Dic3—31no—
126C22×C3×Dic3—32no—
127C22×C3×Dic3—32no—
128C22×C3×Dic3—64no—
129C22×C3×Dic3—61no—
130C22×C3×Dic3C2×D311yescharacteristic
131C22×C3×Dic3C2×D311yescharacteristic
132C3×#237—64no—
133C3×#235—64no—
134C2×C3×D12—31no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—32no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—64no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—31no—
143C2×#627C2×D311yescharacteristic, complemented
144C2×#626C2×D311yescharacteristic, complemented
145C2×#625—32no—
146C2×#625—32no—
147C2×#625—62no—
148C2×#625C2×D312yes—
149C2×#624C2×D311yescharacteristic, complemented
150#3804—24no—
151C2×D3×Dic3—24no—
152C2×D3×Dic3C2×D312yes—
153C2×D3×Dic3C2×D312yes—
154C2×D3×Dic3C2×D311yescharacteristic, complemented
155#3757—31no—
156#3757—31no—
157#3757—31no—
158#3757—32no—
159#3757—32no—
160#3757—61no—
161#3757—61no—
162#3757—61no—
163#3757—121no—
164#3757C2×D311yescharacteristic
165C4⋊(C3⋊Dic3)—32no—
166#3750—32no—
167C4×C3⋊Dic3—32no—
168C3×#217—31no—
169C3×#217—31no—
170C3×#217—32no—
171C3×#217—61no—
172C3×(C2×D3)⋊C4—32no—
173#3724—32no—
174#3724—32no—
175#3724—32no—
176#3724—62no—
177Dic3⋊Dic3—32no—
178Dic3⋊Dic3—32no—
179Dic3⋊Dic3—32no—
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—62no—
182#3722—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
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)⋊Dic3—62no—
191(C2×D3)⋊Dic3C2×D312yes—
192Dic32—32no—
193Dic32—32no—
194Dic32—62no—
195C22×C33—22no—
196C22×C33C2×D412yes—
197C22×C33C2411yescharacteristic
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—22no—
200C2×C32×D3—28no—
201C2×C32×D3—22no—
202C2×C32×D3—22no—
203C2×C32×D3—21no—
204C2×C32×D3—22no—
205C2×C32×D3#4114yescomplemented
206C3⋊(C3⋊Dic3)—22no—
207C3×C3⋊Dic3—22no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3—22no—
210C32×Dic3—21no—
211C32×Dic3C2×D412yes—
212C32×Dic3C2×D412yes—
213C2×C3×#41—91no—
214C23×C3×C4—91no—
215C23×Dic3—31no—
216C2×#237—31no—
217C2×#235—31no—
218C22×C4×D3—31no—
219C3×#120—91no—
220#953—31no—
221#953—91no—
222#953—91no—
223#953—181no—
224#946—92no—
225#939—92no—
226#938—92no—
227#937—31no—
228#937—91no—
229#935—91no—
230#935—91no—
231#935—91no—
232#935—181no—
233D4×Dic3—92no—
234#930—92no—
235#929—91no—
236#929—91no—
237C4×#67—92no—
238C4×#67—92no—
239C4×#67—92no—
240C4×#67—92no—
241#926—91no—
242#926—91no—
243#926—181no—
244#924—92no—
245#886—91no—
246#67⋊C4—92no—
247#878—92no—
248#877—91no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—32no—
253C23×C32—31no—
254C23×C32—41no—
255C23×C32—64no—
256C23×C32—62no—
257C23×C32C22×D311yescharacteristic
258C23×C32C22×D311yescharacteristic
259C23×C32C22×D311yescharacteristic
260C22×C3⋊D3C22×D311yescharacteristic
261C22×C3×D3—22no—
262C22×C3×D3—22no—
263C22×C3×D3—24no—
264C22×C3×D3—24no—
265C22×C3×D3—22no—
266C22×C3×D3—21no—
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—44no—
270C22×C3×D3—42no—
271C22×C3×D3—61no—
272C22×C3×D3C22×D311yescharacteristic
273C22×C3×D3C22×D311yescharacteristic
274C22×C3×D3C22×D312yes—
275C22×C3×D3C22×D312yes—
276C32×D4—62no—
277C2×C32×C4—34no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281#638—22no—
282#638—64no—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3—32no—
285C2×C3⋊Dic3—32no—
286C2×C3⋊Dic3—32no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—62no—
289C2×C3⋊Dic3—62no—
290C2×C3⋊Dic3—122no—
291C2×C3⋊Dic3C22×D312yes—
292C2×C3⋊Dic3C22×D312yes—
293C2×C3⋊Dic3C22×D311yescharacteristic
294C3×#67—22no—
295C3×#67—22no—
296C3×#67—42no—
297C3×#67—64no—
298C3×#67—62no—
299C3×#67—62no—
300C3×#67—64no—
301C3×#67—62no—
302C3×#67—122no—
303C2×C3×Dic3—24no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—32no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—32no—
312C2×C3×Dic3—32no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—62no—
316C2×C3×Dic3—62no—
317C2×C3×Dic3—62no—
318C2×C3×Dic3—62no—
319C2×C3×Dic3—64no—
320C2×C3×Dic3—64no—
321C2×C3×Dic3—122no—
322C2×C3×Dic3#6714yescomplemented
323C2×C3×Dic3#6714yescomplemented
324C2×C3×Dic3C22×D311yescharacteristic
325C2×C3×Dic3C22×D311yescharacteristic
326C2×C3×Dic3C22×D311yescharacteristic
327C2×C3×Dic3C22×D311yescharacteristic
328C2×C3×Dic3C22×D311yescharacteristic
329C2×C3×Dic3C22×D311yescharacteristic
330C3×D12—62no—
331C3×C4×D3—62no—
332C3×C4×D3—64no—
333C3×C4×D3—64no—
334C3×C4×D3—62no—
335C3×C4×D3—62no—
336C3×Dic6—62no—
337C3×Dic6—62no—
338#627—22no—
339#626—22no—
340#625—24no—
341#625—64no—
342#625—64no—
343#625—124no—
344#624—22no—
345D3×Dic3—24no—
346D3×Dic3—24no—
347D3×Dic3—22no—
348#525—271noSylow
349C2×C33—22no—
350C2×C33C22×D411yescharacteristic
351C2×C33C2×#4112yes—
352C3×C3⋊D3—41no—
353C32×D3—24no—
354C32×D3—41no—
355C24×C3—31no—
356C24×C3—31no—
357C24×C3—61no—
358C23×D3D3211yescharacteristic
359C3×#41—184no—
360C2×C3×Q8—91no—
361C2×C3×D4—31no—
362C2×C3×D4—31no—
363C2×C3×D4—61no—
364C2×C3×D4—91no—
365C2×C3×D4—92no—
366C2×C3×D4—91no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—61no—
370C22×C3×C4—91no—
371C22×C3×C4—92no—
372C22×C3×C4—92no—
373C22×C3×C4—91no—
374C22×C3×C4—91no—
375C22×C3×C4—184no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—32no—
379C2×#67—32no—
380C2×#67—31no—
381C2×#67—61no—
382C2×#67—92no—
383C2×#67—92no—
384C2×#67—92no—
385C2×#67—182no—
386C2×#67D3211yescharacteristic
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—32no—
390C22×Dic3—32no—
391C22×Dic3—31no—
392C22×Dic3—61no—
393C22×Dic3—64no—
394C22×Dic3D3211yescharacteristic
395#237—64no—
396#235—64no—
397C2×D12—31no—
398C2×C4×D3—32no—
399C2×C4×D3—31no—
400C2×C4×D3—32no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—64no—
404C2×Dic6—31no—
405C2×Dic6—31no—
406C3×C22⋊C4—92no—
407C3×C22⋊C4—91no—
408#217—31no—
409#217—31no—
410#217—32no—
411#217—61no—
412#217—92no—
413#217—92no—
414#217—92no—
415#217—92no—
416#217—92no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—182no—
421#217—182no—
422#217—181no—
423#217—181no—
424#217—181no—
425#217—361no—
426(C2×D3)⋊C4—32no—
427(C2×D3)⋊C4—92no—
428(C2×D3)⋊C4—92no—
429(C2×D3)⋊C4—92no—
430(C2×D3)⋊C4—92no—
431C4⋊Dic3—92no—
432C4⋊Dic3—92no—
433C4⋊Dic3—92no—
434C4⋊Dic3—182no—
435Dic3⋊C4—92no—
436Dic3⋊C4—92no—
437Dic3⋊C4—92no—
438Dic3⋊C4—92no—
439Dic3⋊C4—92no—
440Dic3⋊C4—92no—
441Dic3⋊C4—182no—
442C4×Dic3—92no—
443C4×Dic3—92no—
444C4×Dic3—92no—
445C4×Dic3—182no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32—22no—
455C22×C32—34no—
456C22×C32—41no—
457C22×C32—42no—
458C22×C32—42no—
459C22×C32—42no—
460C22×C32—42no—
461C22×C32—68no—
462C22×C32—62no—
463C22×C32—62no—
464C22×C32—62no—
465C22×C32—61no—
466C22×C32—82no—
467C22×C32D3×D412yes—
468C22×C32C2×#6712yes—
469C22×C32C2×#6712yes—
470C22×C32C23×D311yescharacteristic
471C22×C32C23×D311yescharacteristic
472C22×C32C23×D311yescharacteristic
473C2×C3⋊D3—22no—
474C2×C3⋊D3—21no—
475C2×C3×D3—28no—
476C2×C3×D3—28no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—21no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—21no—
485C2×C3×D3—24no—
486C2×C3×D3—42no—
487C2×C3×D3—42no—
488C2×C3×D3—48no—
489C2×C3×D3—41no—
490C2×C3×D3—42no—
491C2×C3×D3—62no—
492C2×C3×D3—61no—
493C2×C3×D3—62no—
494C2×C3×D3—61no—
495C2×C3×D3—122no—
496C2×C3×D3—121no—
497C2×C3×D3#23514yescomplemented
498C2×C3×D3#23714yescomplemented
499C32×C4—32no—
500C32×C4—32no—
501C32×C4—61no—
502C3⋊Dic3—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—21no—
505C3⋊Dic3—62no—
506C3⋊Dic3—62no—
507C3⋊Dic3—62no—
508C3⋊Dic3—122no—
509C3⋊Dic3—122no—
510C3⋊Dic3—122no—
511C3⋊Dic3—242no—
512C3×Dic3—21no—
513C3×Dic3—21no—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—41no—
517C3×Dic3—62no—
518C3×Dic3—61no—
519C3×Dic3—62no—
520C3×Dic3—62no—
521C3×Dic3—61no—
522C3×Dic3—62no—
523C3×Dic3—122no—
524C3×Dic3—122no—
525C3×Dic3—121no—
526C3×Dic3C2×#6712yes—
527C3×Dic3C2×#6712yes—
528C3×Dic3C2×#6712yes—
529C3×Dic3C2×#6712yes—
530C2×#41—91no—
531C23×C4—91no—
532#123—271no—
533#123—271no—
534C22⋊Q8—272no—
535#121—272no—
536#120—91no—
537#120—271no—
538C4×D4—272no—
539C4×D4—272no—
540#117—271no—
541C33#52511yescharacteristic, complemented, Sylow
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—31no—
548C23×C3—31no—
549C23×C3—41no—
550C23×C3—62no—
551C23×C3—61no—
552C23×C3—64no—
553C23×C3—64no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3—91no—
557C23×C3—122no—
558C23×C3—124no—
559C23×C3C2×D3211yescharacteristic
560C23×C3C2×D3211yescharacteristic
561C23×C3C2×D3211yescharacteristic
562C22×D3—22no—
563C22×D3—24no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—61no—
567C22×D3C2×D3211yescharacteristic
568C22×D3C2×D3212yes—
569C3×Q8—182no—
570C3×D4—62no—
571C3×D4—62no—
572C3×D4—122no—
573C3×D4—182no—
574C3×D4—184no—
575C3×D4—182no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—34no—
581C2×C3×C4—34no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—64no—
587C2×C3×C4—61no—
588C2×C3×C4—92no—
589C2×C3×C4—92no—
590C2×C3×C4—91no—
591C2×C3×C4—182no—
592C2×C3×C4—184no—
593C2×C3×C4—184no—
594C2×C3×C4—182no—
595C2×C3×C4—182no—
596#67—22no—
597#67—64no—
598#67—62no—
599#67—62no—
600#67—64no—
601#67—62no—
602#67—122no—
603#67—184no—
604#67—184no—
605#67—184no—
606#67—364no—
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—31no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—31no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—61no—
616C2×Dic3—62no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—64no—
620C2×Dic3—64no—
621C2×Dic3—92no—
622C2×Dic3—92no—
623C2×Dic3—92no—
624C2×Dic3—122no—
625C2×Dic3—182no—
626C2×Dic3—182no—
627C2×Dic3—182no—
628C2×Dic3—362no—
629C2×Dic3#62514yescomplemented
630C2×Dic3C2×D3211yescharacteristic
631C2×Dic3C2×D3211yescharacteristic
632C2×Dic3C2×D3211yescharacteristic
633D12—62no—
634C4×D3—62no—
635C4×D3—64no—
636C4×D3—64no—
637C4×D3—62no—
638C4×D3—62no—
639Dic6—62no—
640Dic6—62no—
641C2×C32—22no—
642C2×C32—22no—
643C2×C32—22no—
644C2×C32—22no—
645C2×C32—22no—
646C2×C32—22no—
647C2×C32—21no—
648C2×C32—21no—
649C2×C32—21no—
650C2×C32—41no—
651C2×C32—42no—
652C2×C32—42no—
653C2×C32—42no—
654C2×C32—42no—
655C2×C32—64no—
656C2×C32—82no—
657C2×C32—121no—
658C2×C32C2×#23512yes—
659C2×C32C2×D3×D411yescharacteristic
660C2×C32C2×#23712yes—
661C2×C32D3×#4112yes—
662C2×C32C22×#6711yescharacteristic
663C2×C32C22×#6711yescharacteristic
664C3⋊D3—41no—
665C3×D3—24no—
666C3×D3—24no—
667C3×D3—44no—
668C3×D3—41no—
669C3×D3—41no—
670C3×D3—81no—
671C3×D3—121no—
672C3×D3—121no—
673C3×D3—241no—
674C24—31no—
675#41—184no—
676C2×Q8—91no—
677C2×D4—31no—
678C2×D4—91no—
679C2×D4—92no—
680C2×D4—91no—
681C2×D4—272no—
682C22×C4—31no—
683C22×C4—91no—
684C22×C4—92no—
685C22×C4—91no—
686C22×C4—92no—
687C22×C4—91no—
688C22×C4—184no—
689C4⋊C4—272no—
690C4⋊C4—272no—
691C4⋊C4—272no—
692C22⋊C4—92no—
693C22⋊C4—91no—
694C22⋊C4—272no—
695C22⋊C4—272no—
696C22⋊C4—272no—
697C22⋊C4—271no—
698C42—272no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—34no—
709C22×C3—34no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—41no—
714C22×C3—42no—
715C22×C3—64no—
716C22×C3—68no—
717C22×C3—68no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—82no—
727C22×C3—122no—
728C22×C3—122no—
729C22×C3—121no—
730C22×C3—122no—
731C22×C3—128no—
732C22×C3—182no—
733C22×C3—181no—
734C22×C3C2×#62512yes—
735C22×C3D3×#6712yes—
736C22×C3D3×#6712yes—
737C22×C3C22×D3211yescharacteristic
738C22×C3C22×D3211yescharacteristic
739C22×C3C22×D3211yescharacteristic
740C2×D3—28no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—21no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—121no—
750C2×D3—122no—
751C2×D3#380414yescomplemented
752C3×C4—32no—
753C3×C4—32no—
754C3×C4—32no—
755C3×C4—32no—
756C3×C4—62no—
757C3×C4—62no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—121no—
761C3×C4—182no—
762C3×C4—182no—
763C3×C4—181no—
764Dic3—21no—
765Dic3—62no—
766Dic3—62no—
767Dic3—61no—
768Dic3—62no—
769Dic3—61no—
770Dic3—62no—
771Dic3—122no—
772Dic3—121no—
773Dic3—122no—
774Dic3—182no—
775Dic3—182no—
776Dic3—182no—
777Dic3—362no—
778Dic3—362no—
779Dic3—362no—
780Dic3—722no—
781Dic3C2×#62512yes—
782Dic3C2×#62512yes—
783C32—21no—
784C32—21no—
785C32—21no—
786C32—41no—
787C32#558611yescharacteristic, complemented
788C32#579111yescharacteristic, complemented
789C32#582811yescharacteristic, complemented
790C23—32no—
791C23—31no—
792C23—64no—
793C23—62no—
794C23—91no—
795C23D3311yescharacteristic
796Q8—182no—
797D4—62no—
798D4—182no—
799D4—184no—
800D4—182no—
801D4—544no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—34no—
805C2×C4—31no—
806C2×C4—92no—
807C2×C4—92no—
808C2×C4—91no—
809C2×C4—182no—
810C2×C4—184no—
811C2×C4—184no—
812C2×C4—182no—
813C2×C4—182no—
814C2×C4—272no—
815C2×C3—22no—
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—22no—
819C2×C3—22no—
820C2×C3—22no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—42no—
825C2×C3—42no—
826C2×C3—42no—
827C2×C3—42no—
828C2×C3—41no—
829C2×C3—64no—
830C2×C3—64no—
831C2×C3—82no—
832C2×C3—124no—
833C2×C3—121no—
834C2×C3—121no—
835C2×C3—241no—
836C2×C3—361no—
837C2×C3D3×#23512yes—
838C2×C3D3×#23712yes—
839C2×C3C2×#380412yes—
840C2×C3C22×#62511yescharacteristic
841C2×C3C2×D3×#6711yescharacteristic
842C2×C3C2×D3×#6711yescharacteristic
843D3—24no—
844D3—41no—
845D3—121no—
846D3—121no—
847D3—241no—
848C22—22no—
849C22—34no—
850C22—68no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—61no—
855C22—182no—
856C22—181no—
857C22D3×#62512yes—
858C22C2×D3311yescharacteristic
859C4—32no—
860C4—32no—
861C4—61no—
862C4—182no—
863C4—182no—
864C4—181no—
865C4—542no—
866C3—21no—
867C3—21no—
868C3—21no—
869C3—41no—
870C3#1059502211yescharacteristic, complemented
871C3#1059515411yescharacteristic, complemented
872C3#1059549811yescharacteristic, complemented
873C2—22no—
874C2—64no—
875C2—121no—
876C2—361no—
877C2D3×#380412yes—
878C2C2×D3×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3804C2semidirect
2. C22×C3×D3×Dic3C2semidirect
3. #11723720C2semidirect
4. #11723629C2semidirect
5. #11723602C2semidirect
6. #11723594C2semidirect
7. C3×#63976C2semidirect
8. #11722969C2semidirect
9. #11722956C2semidirect
10. #11722930C2semidirect
11. Dic3×#625C2semidirect
21. C2×C3×#627C22semidirect
22. C2×C3×#626C22semidirect
24. C2×C3×#624C22semidirect
29. C2×C3×D3×Dic3C22semidirect
32. #88815C22semidirect
33. #88814C22semidirect
34. #88806C22semidirect
35. Dic3⋊(C3⋊Dic3)C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. Dic3×C3⋊Dic3C22semidirect
44. C2×#3804D3semidirect
45. C22×D3×Dic3D3semidirect
55. #63976D3semidirect
89. C2×C32×Dic3D4semidirect
143. C2×#627C2×D3semidirect
144. C2×#626C2×D3semidirect
149. C2×#624C2×D3semidirect
154. C2×D3×Dic3C2×D3semidirect
205. C2×C32×D3#41semidirect
322. C2×C3×Dic3#67semidirect
323. C2×C3×Dic3#67semidirect
497. C2×C3×D3#235semidirect
498. C2×C3×D3#237semidirect
541. C33#525semidirect
629. C2×Dic3#625semidirect
751. C2×D3#3804semidirect
787. C32#5586semidirect
788. C32#5791semidirect
789. C32#5828semidirect
870. C3#10595022semidirect
871. C3#10595154semidirect
872. C3#10595498semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C22×C3×D3×Dic32
#117237202
#117236292
#117236022
#117235942
C3×#639762
#117229692
#117229562
#117229302
Dic3×#6252
#105954983
#105951543
#105950223