Finite Group Databasebeta

← #13172149

Subgroups — #13172149

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
1C22×C3×#624C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723634C211yesmaximal, characteristic, complemented
5#11723605C211yesmaximal, characteristic, complemented
6#11723594C211yesmaximal, characteristic, complemented
7C3×#63961C211yesmaximal, characteristic, complemented
8#11722970C212yesmaximal, complemented
9#11722957C212yesmaximal, complemented
10#11722931C212yesmaximal, complemented
11#11722930C212yesmaximal, complemented
12#10595159—31nomaximal
13#10595022—31nomaximal
14#10594896—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C2×C3×#638C2211yescharacteristic
17C2×C32×#67C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C2×#6295C2212yes—
21C2×#6290C2212yes—
22C2×C3×#627C2211yescharacteristic, complemented
23C2×C3×#626C2211yescharacteristic, complemented
24C2×C3×#624—24no—
25C2×C3×#624C2212yes—
26C2×C3×#624C2212yes—
27C2×C3×#624C2211yescharacteristic, complemented
28C3×#3804—24no—
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30#88864C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32#88814C2212yes—
33#88806C2212yescomplemented
34Dic3⋊(C3⋊Dic3)C2212yescomplemented
35#88803C2212yes—
36#88803C2212yescomplemented
37Dic3×C3⋊Dic3C2212yescomplemented
38C3×#3724C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×C3×#237—31no—
41C2×C3×#235—31no—
42C22×C3×C4×D3—31no—
43C22×C3×C4×D3—31no—
44C22×#624D311yescharacteristic, complemented
45C2×#3804D311yescharacteristic, complemented
46#64146—31no—
47#64138—31no—
48#64135—31no—
49C3×#935—31no—
50C3×#929—31no—
51#63981—31no—
52#63977—31no—
53#63976—31no—
54#63976—31no—
55#63976—31no—
56#63976—61no—
57#63961—31no—
58#63961—31no—
59#63961—61no—
60#63961D311yescharacteristic, complemented
61#63958—32no—
62#63955—31no—
63#63955—31no—
64#63955—61no—
65#63952—32no—
66#63908—32no—
67#63906—32no—
68#63904—32no—
69#63904—32no—
70C4×#625—32no—
71C4×#625—32no—
72#63888—32no—
73#63879—32no—
74#63856—32no—
75#63851—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3—22no—
78C22×C3×C3⋊D3—24no—
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C3×C3⋊D3C2312yes—
81C22×C32×D3C2311yescharacteristic
82C2×C3⋊(C3⋊Dic3)C2312yes—
83C3×#638—22no—
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C32×#67—22no—
87C2×C32×Dic3—22no—
88C2×C32×Dic3D414yescomplemented
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93#6295—24no—
94#6290—24no—
95C3×#627—22no—
96C3×#626—22no—
97C3×#624—22no—
98C3×#624—24no—
99C3×#624—24no—
100C3×D3×Dic3—22no—
101#5828—91no—
102#5791—91no—
103#5656—91no—
104C23×C3⋊D3C2×D311yescharacteristic
105C23×C3×D3—31no—
106C23×C3×D3—31no—
107C23×C3×D3—61no—
108C2×C32×D4—31no—
109C22×C32×C4—31no—
110C22×C32×C4—31no—
111C2×#638—32no—
112C2×#638C2×D311yescharacteristic
113C2×C3×#67—21no—
114C2×C3×#67—31no—
115C2×C3×#67—31no—
116C2×C3×#67—31no—
117C2×C3×#67—61no—
118C2×C3×#67C2×D311yescharacteristic
119C2×C3×#67C2×D311yescharacteristic
120C22×C3×Dic3—21no—
121C22×C3×Dic3—21no—
122C22×C3×Dic3—31no—
123C22×C3×Dic3C2×D311yescharacteristic
124C22×C3×Dic3C2×D311yescharacteristic
125C22×C3×Dic3C2×D311yescharacteristic
126C22×C3×Dic3C2×D311yescharacteristic
127C3×#237—64no—
128C3×#235—64no—
129C2×C3×D12—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—32no—
132C2×C3×C4×D3—32no—
133C2×C3×C4×D3—32no—
134C2×C3×C4×D3—32no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—64no—
138C2×C3×C4×D3—64no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—31no—
141C2×#627C2×D311yescharacteristic, complemented
142C2×#626—32no—
143C2×#626—32no—
144C2×#626C2×D311yescharacteristic, complemented
145C2×#625—32no—
146C2×#625—32no—
147C2×#625—32no—
148C2×#625—62no—
149C2×#624—24no—
150C2×#624C2×D312yes—
151C2×#624C2×D312yes—
152C2×#624C2×D311yescharacteristic, complemented
153#3804—24no—
154C2×D3×Dic3C2×D311yescharacteristic, complemented
155#3757—31no—
156#3757—31no—
157#3757—31no—
158#3757—61no—
159#3757—61no—
160#3757—61no—
161#3757—121no—
162#3757C2×D311yescharacteristic
163#3752—32no—
164#3752—32no—
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—
173C3×Dic3⋊C4—32no—
174C3×Dic3⋊C4—32no—
175#3724—32no—
176#3724—32no—
177#3724—62no—
178#3724C2×D312yescomplemented
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×D312yescomplemented
192Dic32—32no—
193Dic32—32no—
194Dic32—62no—
195C22×C33—22no—
196C22×C33C2×D412yes—
197C22×C33C2411yescharacteristic
198C2×C3×C3⋊D3—28no—
199C2×C3×C3⋊D3—22no—
200C2×C3×C3⋊D3—22no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—22no—
203C2×C3×C3⋊D3#4114yescomplemented
204C2×C32×D3—21no—
205C2×C32×D3—22no—
206C3⋊(C3⋊Dic3)—22no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3—22no—
209C32×Dic3—22no—
210C32×Dic3—21no—
211C32×Dic3C2×D412yes—
212C32×Dic3C2×D412yes—
213C2×C3×#41—91no—
214C23×C3×C4—91no—
215C2×#237—31no—
216C2×#235—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C3×#123—91no—
220#953—91no—
221#953—91no—
222#946—92no—
223#938—92no—
224#937—91no—
225#937—91no—
226#937—91no—
227#937—181no—
228#935—31no—
229#935—91no—
230#930—92no—
231#929—31no—
232#929—91no—
233#929—91no—
234#929—181no—
235C4×#67—92no—
236C4×#67—92no—
237C4×#67—92no—
238C4×#67—92no—
239#926—91no—
240#926—91no—
241#926—181no—
242#924—92no—
243#896—92no—
244#893—92no—
245#884—92no—
246#882—91no—
247#67⋊C4—92no—
248#877—91no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—31no—
253C23×C32—41no—
254C23×C32C22×D311yescharacteristic
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—22no—
258C22×C3⋊D3—24no—
259C22×C3⋊D3C22×D311yescharacteristic
260C22×C3⋊D3C22×D312yes—
261C22×C3×D3—21no—
262C22×C3×D3—32no—
263C22×C3×D3—32no—
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—62no—
267C22×C3×D3—61no—
268C22×C3×D3—64no—
269C22×C3×D3—64no—
270C22×C3×D3—62no—
271C22×C3×D3—62no—
272C22×C3×D3—124no—
273C22×C3×D3—122no—
274C22×C3×D3C22×D311yescharacteristic
275C22×C3×D3C22×D311yescharacteristic
276C32×D4—62no—
277C2×C32×C4—34no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—32no—
282C2×C32×C4—62no—
283#638—22no—
284#638—64no—
285C2×C3⋊Dic3—32no—
286C2×C3⋊Dic3—32no—
287C2×C3⋊Dic3—32no—
288C2×C3⋊Dic3—62no—
289C2×C3⋊Dic3—62no—
290C2×C3⋊Dic3—62no—
291C2×C3⋊Dic3—122no—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D312yes—
294C3×#67—22no—
295C3×#67—22no—
296C3×#67—42no—
297C3×#67—62no—
298C3×#67—62no—
299C3×#67—62no—
300C3×#67—122no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—24no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—32no—
309C2×C3×Dic3—32no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—42no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—62no—
316C2×C3×Dic3#6714yescomplemented
317C2×C3×Dic3#6714yescomplemented
318C2×C3×Dic3C22×D311yescharacteristic
319C2×C3×Dic3C22×D311yescharacteristic
320C2×C3×Dic3C22×D312yes—
321C2×C3×Dic3C22×D312yes—
322C2×C3×Dic3C22×D311yescharacteristic
323C2×C3×Dic3C22×D311yescharacteristic
324C2×C3×Dic3C22×D311yescharacteristic
325C2×C3×Dic3C22×D311yescharacteristic
326C3×D12—62no—
327C3×C4×D3—64no—
328C3×C4×D3—64no—
329C3×C4×D3—62no—
330C3×C4×D3—62no—
331C3×C4×D3—64no—
332C3×C4×D3—64no—
333C3×C4×D3—62no—
334C3×Dic6—62no—
335C3×Dic6—62no—
336#627—22no—
337#626—22no—
338#626—64no—
339#626—64no—
340#625—64no—
341#625—64no—
342#625—64no—
343#625—124no—
344#624—22no—
345#624—24no—
346#624—24no—
347D3×Dic3—22no—
348#525—271noSylow
349C2×C33—22no—
350C2×C33C22×D411yescharacteristic
351C2×C33C2×#4112yes—
352C3×C3⋊D3—24no—
353C3×C3⋊D3—41no—
354C32×D3—41no—
355C24×C3—91no—
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—61no—
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—91no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C22×C3×C4—92no—
373C22×C3×C4—92no—
374C22×C3×C4—91no—
375C22×C3×C4—91no—
376C22×C3×C4—184no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—61no—
381C2×#67—92no—
382C2×#67—92no—
383C2×#67—92no—
384C2×#67—92no—
385C2×#67—92no—
386C2×#67—182no—
387C2×#67D3211yescharacteristic
388C22×Dic3—31no—
389C22×Dic3D3211yescharacteristic
390C22×Dic3D3211yescharacteristic
391#237—64no—
392#235—64no—
393C2×D12—31no—
394C2×D12—92no—
395C2×C4×D3—31no—
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—31no—
399C2×C4×D3—32no—
400C2×C4×D3—31no—
401C2×C4×D3—32no—
402C2×C4×D3—64no—
403C2×C4×D3—64no—
404C2×Dic6—31no—
405C2×Dic6—31no—
406C3×C4⋊C4—92no—
407C3×C22⋊C4—92no—
408C3×C22⋊C4—91no—
409#217—31no—
410#217—31no—
411#217—32no—
412#217—61no—
413#217—92no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—92no—
418#217—92no—
419#217—181no—
420#217—181no—
421#217—181no—
422#217—361no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—92no—
425(C2×D3)⋊C4—92no—
426(C2×D3)⋊C4—92no—
427(C2×D3)⋊C4—92no—
428(C2×D3)⋊C4—92no—
429(C2×D3)⋊C4—92no—
430(C2×D3)⋊C4—182no—
431(C2×D3)⋊C4—182no—
432C4⋊Dic3—92no—
433C4⋊Dic3—92no—
434C4⋊Dic3—182no—
435Dic3⋊C4—32no—
436Dic3⋊C4—32no—
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—41no—
456C22×C32—42no—
457C22×C32—42no—
458C22×C32—42no—
459C22×C32—42no—
460C22×C32—62no—
461C22×C32—61no—
462C22×C32—82no—
463C22×C32D3×D412yes—
464C22×C32C2×#6712yes—
465C22×C32C2×#6712yes—
466C22×C32C23×D311yescharacteristic
467C22×C32C23×D311yescharacteristic
468C22×C32C23×D311yescharacteristic
469C2×C3⋊D3—28no—
470C2×C3⋊D3—22no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3#23514yescomplemented
475C2×C3×D3—21no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—21no—
479C2×C3×D3—34no—
480C2×C3×D3—34no—
481C2×C3×D3—42no—
482C2×C3×D3—41no—
483C2×C3×D3—64no—
484C2×C3×D3—68no—
485C2×C3×D3—68no—
486C2×C3×D3—62no—
487C2×C3×D3—62no—
488C2×C3×D3—62no—
489C2×C3×D3—62no—
490C2×C3×D3—62no—
491C2×C3×D3—61no—
492C2×C3×D3—62no—
493C2×C3×D3—61no—
494C2×C3×D3—122no—
495C2×C3×D3—122no—
496C2×C3×D3—128no—
497C2×C3×D3—121no—
498C2×C3×D3—122no—
499C32×C4—32no—
500C32×C4—32no—
501C32×C4—61no—
502C32×C4—62no—
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—22no—
514C3×Dic3—22no—
515C3×Dic3—21no—
516C3×Dic3—22no—
517C3×Dic3—22no—
518C3×Dic3—42no—
519C3×Dic3—41no—
520C3×Dic3—62no—
521C3×Dic3—61no—
522C3×Dic3—62no—
523C3×Dic3—61no—
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—91no—
533#123—271no—
534C22⋊Q8—272no—
535#121—272no—
536#120—271no—
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—31no—
546C23×C3—31no—
547C23×C3—41no—
548C23×C3—61no—
549C23×C3—92no—
550C23×C3—91no—
551C23×C3—184no—
552C23×C3—182no—
553C23×C3C2×D3211yescharacteristic
554C23×C3C2×D3211yescharacteristic
555C23×C3C2×D3211yescharacteristic
556C22×D3—32no—
557C22×D3—32no—
558C22×D3—31no—
559C22×D3—31no—
560C22×D3—62no—
561C22×D3—61no—
562C22×D3—64no—
563C22×D3—64no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—124no—
567C22×D3—122no—
568C22×D3C2×D3211yescharacteristic
569C3×Q8—182no—
570C3×D4—62no—
571C3×D4—62no—
572C3×D4—122no—
573C3×D4—182no—
574C3×D4—182no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—34no—
580C2×C3×C4—34no—
581C2×C3×C4—31no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—31no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—64no—
588C2×C3×C4—62no—
589C2×C3×C4—61no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—92no—
593C2×C3×C4—91no—
594C2×C3×C4—122no—
595C2×C3×C4—184no—
596C2×C3×C4—184no—
597C2×C3×C4—182no—
598C2×C3×C4—182no—
599#67—22no—
600#67—62no—
601#67—62no—
602#67—62no—
603#67—122no—
604#67—184no—
605#67—184no—
606#67—184no—
607#67—184no—
608#67—184no—
609#67—364no—
610C2×Dic3—22no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—62no—
616C2×Dic3—61no—
617C2×Dic3—62no—
618C2×Dic3—92no—
619C2×Dic3—92no—
620C2×Dic3—92no—
621C2×Dic3—182no—
622C2×Dic3—182no—
623C2×Dic3—182no—
624C2×Dic3—362no—
625C2×Dic3#62514yescomplemented
626C2×Dic3C2×D3211yescharacteristic
627C2×Dic3C2×D3212yes—
628C2×Dic3C2×D3211yescharacteristic
629C2×Dic3C2×D3211yescharacteristic
630D12—62no—
631D12—184no—
632C4×D3—64no—
633C4×D3—64no—
634C4×D3—62no—
635C4×D3—62no—
636C4×D3—64no—
637C4×D3—64no—
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—82no—
656C2×C32—121no—
657C2×C32C2×#23512yes—
658C2×C32C2×D3×D411yescharacteristic
659C2×C32D3×#4112yes—
660C2×C32D3×#4112yes—
661C2×C32C22×#6711yescharacteristic
662C2×C32C22×#6711yescharacteristic
663C3⋊D3—24no—
664C3⋊D3—41no—
665C3×D3—41no—
666C3×D3—41no—
667C3×D3—64no—
668C3×D3—64no—
669C3×D3—81no—
670C3×D3—124no—
671C3×D3—121no—
672C3×D3—121no—
673C3×D3—241no—
674C24—91no—
675#41—184no—
676C2×Q8—91no—
677C2×D4—31no—
678C2×D4—91no—
679C2×D4—91no—
680C2×D4—272no—
681C2×D4—272no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—92no—
685C22×C4—91no—
686C22×C4—92no—
687C22×C4—91no—
688C22×C4—184no—
689C4⋊C4—92no—
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—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—42no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—82no—
718C22×C3—94no—
719C22×C3—122no—
720C22×C3—121no—
721C22×C3—188no—
722C22×C3—182no—
723C22×C3—182no—
724C22×C3—182no—
725C22×C3—181no—
726C22×C3C2×#62512yes—
727C22×C3D3×#6712yes—
728C22×C3D3×#6712yes—
729C22×C3C22×D3211yescharacteristic
730C22×C3C22×D3211yescharacteristic
731C22×C3C22×D3211yescharacteristic
732C2×D3—22no—
733C2×D3—21no—
734C2×D3—34no—
735C2×D3—34no—
736C2×D3—64no—
737C2×D3—68no—
738C2×D3—68no—
739C2×D3—62no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—122no—
748C2×D3—122no—
749C2×D3—128no—
750C2×D3—121no—
751C2×D3—122no—
752C3×C4—32no—
753C3×C4—32no—
754C3×C4—32no—
755C3×C4—32no—
756C3×C4—62no—
757C3×C4—62no—
758C3×C4—61no—
759C3×C4—62no—
760C3×C4—62no—
761C3×C4—61no—
762C3×C4—122no—
763C3×C4—121no—
764C3×C4—182no—
765C3×C4—181no—
766Dic3—21no—
767Dic3—22no—
768Dic3—62no—
769Dic3—62no—
770Dic3—61no—
771Dic3—61no—
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#565611yescharacteristic, complemented
788C32#579111yescharacteristic, complemented
789C32#582811yescharacteristic, complemented
790C23—31no—
791C23—92no—
792C23—91no—
793C23—184no—
794C23—182no—
795C23D3311yescharacteristic
796Q8—182no—
797D4—62no—
798D4—182no—
799D4—182no—
800D4—544no—
801D4—544no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—34no—
805C2×C4—32no—
806C2×C4—31no—
807C2×C4—62no—
808C2×C4—92no—
809C2×C4—91no—
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—82no—
830C2×C3—121no—
831C2×C3—121no—
832C2×C3—184no—
833C2×C3—241no—
834C2×C3—361no—
835C2×C3D3×#23512yes—
836C2×C3D3×#23512yes—
837C2×C3#6431212yes—
838C2×C3C22×#62511yescharacteristic
839C2×C3C2×D3×#6711yescharacteristic
840C2×C3C2×D3×#6711yescharacteristic
841D3—41no—
842D3—64no—
843D3—64no—
844D3—124no—
845D3—121no—
846D3—121no—
847D3—241no—
848C22—22no—
849C22—62no—
850C22—61no—
851C22—94no—
852C22—188no—
853C22—182no—
854C22—182no—
855C22—182no—
856C22—181no—
857C22D3×#62512yes—
858C22C2×D3311yescharacteristic
859C4—32no—
860C4—32no—
861C4—62no—
862C4—61no—
863C4—182no—
864C4—181no—
865C4—542no—
866C3—21no—
867C3—21no—
868C3—21no—
869C3—41no—
870C3#1059489611yescharacteristic, complemented
871C3#1059502211yescharacteristic, complemented
872C3#1059515911yescharacteristic, complemented
873C2—22no—
874C2—121no—
875C2—184no—
876C2—361no—
877C2#1172441012yes—
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. C22×C3×#624C2semidirect
2. C2×C3×#3804C2semidirect
3. #11723727C2semidirect
4. #11723634C2semidirect
5. #11723605C2semidirect
6. #11723594C2semidirect
7. C3×#63961C2semidirect
8. #11722970C2semidirect
9. #11722957C2semidirect
10. #11722931C2semidirect
11. #11722930C2semidirect
22. C2×C3×#627C22semidirect
23. C2×C3×#626C22semidirect
27. C2×C3×#624C22semidirect
29. C2×C3×D3×Dic3C22semidirect
33. #88806C22semidirect
34. Dic3⋊(C3⋊Dic3)C22semidirect
36. #88803C22semidirect
37. Dic3×C3⋊Dic3C22semidirect
38. C3×#3724C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C22×#624D3semidirect
45. C2×#3804D3semidirect
60. #63961D3semidirect
88. C2×C32×Dic3D4semidirect
141. C2×#627C2×D3semidirect
144. C2×#626C2×D3semidirect
152. C2×#624C2×D3semidirect
154. C2×D3×Dic3C2×D3semidirect
178. #3724C2×D3semidirect
191. (C2×D3)⋊Dic3C2×D3semidirect
203. C2×C3×C3⋊D3#41semidirect
316. C2×C3×Dic3#67semidirect
317. C2×C3×Dic3#67semidirect
474. C2×C3⋊D3#235semidirect
541. C33#525semidirect
625. C2×Dic3#625semidirect
787. C32#5656semidirect
788. C32#5791semidirect
789. C32#5828semidirect
870. C3#10594896semidirect
871. C3#10595022semidirect
872. C3#10595159semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6242
C2×C3×#38042
#117237272
#117236342
#117236052
#117235942
C3×#639612
#117229702
#117229572
#117229312
#117229302
#105951593
#105950223
#105948963