Finite Group Databasebeta

← #13172034

Subgroups — #13172034

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×#89046C211yesmaximal, characteristic, complemented
2C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
3#11723629C211yesmaximal, characteristic, complemented
4#11723605C211yesmaximal, characteristic, complemented
5#11723595C211yesmaximal, characteristic, complemented
6C3×#63977C211yesmaximal, characteristic, complemented
7C3×#63966C211yesmaximal, characteristic, complemented
8#11722978C212yesmaximal, complemented
9#11722960C212yesmaximal, complemented
10#11722936C212yesmaximal, complemented
11#11722927C212yesmaximal, complemented
12#10595498—31nomaximal
13#10594896—31nomaximal
14#10594082—31nomaximal
15C23×C32×D3C2211yescharacteristic
16C2×C3×#638C2211yescharacteristic
17C2×C3×#638C2211yescharacteristic
18C22×C3×C3⋊Dic3C2211yescharacteristic
19C22×C32×Dic3C2211yescharacteristic
20C2×#6296C2211yescharacteristic, complemented
21C2×#6295C2211yescharacteristic, complemented
22#89046—24no—
23C2×#6294C2211yescharacteristic, complemented
24C2×#6294C2211yescharacteristic, complemented
25C2×#6290C2212yes—
26C2×C3×#626C2212yes—
27C2×C3×D3×Dic3—24no—
28C2×C3×D3×Dic3C2212yes—
29C2×C3×D3×Dic3C2212yes—
30#88864C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88807C2212yescomplemented
33#88806C2212yescomplemented
34#88803C2212yescomplemented
35(C2×D3)⋊(C3⋊Dic3)C2212yes—
36Dic3×C3⋊Dic3C2212yescomplemented
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×#3722C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yes—
40C23×C3×Dic3—31no—
41C22×C3×C4×D3—31no—
42C2×#3805—31no—
43C2×#3804—31no—
44C2×#3804—31no—
45C22×D3×Dic3D311yescharacteristic, complemented
46#64162—31no—
47#64138—31no—
48#64086—31no—
49C3×#953—31no—
50C3×#929—31no—
51C3×#886—31no—
52C3×#882—31no—
53#63978—32no—
54#63977D311yescharacteristic, complemented
55#63976—31no—
56#63976—31no—
57#63976—61no—
58Dic3×#67—32no—
59#63966D311yescharacteristic, complemented
60#63964—32no—
61#63961—31no—
62#63961—31no—
63#63961—61no—
64#63955—31no—
65#63955—31no—
66#63955—61no—
67#63952—32no—
68#63906—32no—
69#63904—32no—
70#63902—32no—
71#63899—32no—
72#63898—32no—
73#63885—32no—
74#63879—32no—
75#63851—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C3×C3⋊D3C2311yescharacteristic
79C22×C32×D3—22no—
80C22×C32×D3—24no—
81C22×C32×D3C2312yes—
82C2×C3⋊(C3⋊Dic3)C2312yes—
83C3×#638—22no—
84C3×#638—22no—
85C2×C3×C3⋊Dic3D414yescomplemented
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊Dic3C2311yescharacteristic
90C2×C32×Dic3—22no—
91C2×C32×Dic3C2312yes—
92C2×C32×Dic3C2312yes—
93#6296—22no—
94#6295—22no—
95#6294—22no—
96#6294—22no—
97#6290—24no—
98C3×#626—24no—
99C3×D3×Dic3—24no—
100C3×D3×Dic3—24no—
101#5791—91no—
102#5656—91no—
103#5586—91no—
104C24×C32—31no—
105C23×C3×D3—21no—
106C23×C3×D3C2×D311yescharacteristic
107C23×C3×D3C2×D311yescharacteristic
108C22×C32×C4—31no—
109C2×#638—32no—
110C2×#638C2×D311yescharacteristic
111C2×#638C2×D311yescharacteristic
112C22×C3⋊Dic3C2×D311yescharacteristic
113C2×C3×#67—31no—
114C2×C3×#67—31no—
115C2×C3×#67—31no—
116C2×C3×#67—31no—
117C2×C3×#67—32no—
118C2×C3×#67—61no—
119C2×C3×#67—61no—
120C22×C3×Dic3—21no—
121C22×C3×Dic3—31no—
122C22×C3×Dic3—31no—
123C22×C3×Dic3—32no—
124C22×C3×Dic3—32no—
125C22×C3×Dic3—64no—
126C22×C3×Dic3—61no—
127C22×C3×Dic3C2×D311yescharacteristic
128C22×C3×Dic3C2×D311yescharacteristic
129C2×C3×D12—32no—
130C2×C3×C4×D3—32no—
131C2×C3×C4×D3—32no—
132C2×C3×C4×D3—64no—
133C2×#627—31no—
134C2×#627—31no—
135C2×#627—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626C2×D312yes—
139C2×#625—32no—
140C2×#625—32no—
141C2×#625—31no—
142C2×#625—62no—
143C2×#624—31no—
144C2×#624—31no—
145#3805—64no—
146#3804—64no—
147#3804—64no—
148C2×D3×Dic3—24no—
149C2×D3×Dic3—31no—
150C2×D3×Dic3—31no—
151C2×D3×Dic3—31no—
152C2×D3×Dic3—31no—
153C2×D3×Dic3C2×D312yes—
154C2×D3×Dic3C2×D312yes—
155C32×C22⋊C4—31no—
156#3757—31no—
157#3757—31no—
158#3757—31no—
159#3757—32no—
160#3757—61no—
161#3757—61no—
162#3757—61no—
163#3757—121no—
164#3752—32no—
165#3750—32no—
166#3750—32no—
167C4×C3⋊Dic3—32no—
168C3×#217—21no—
169C3×#217—32no—
170C3×#217C2×D311yescharacteristic
171C3×#217C2×D311yescharacteristic
172C3×(C2×D3)⋊C4—32no—
173C3×(C2×D3)⋊C4—32no—
174C3×(C2×D3)⋊C4—32no—
175C3×C4⋊Dic3—32no—
176C3×Dic3⋊C4—32no—
177#3724—32no—
178#3724—32no—
179#3724—62no—
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—62no—
183Dic3⋊Dic3C2×D312yescomplemented
184#3722C2×D312yescomplemented
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—21no—
200C2×C3×C3⋊D3—22no—
201C2×C3×C3⋊D3—22no—
202C2×C32×D3—28no—
203C2×C32×D3—22no—
204C2×C32×D3—22no—
205C2×C32×D3#4114yescomplemented
206C3⋊(C3⋊Dic3)—22no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3—21no—
209C3×C3⋊Dic3C2×D412yes—
210C3×C3⋊Dic3C2×D412yes—
211C32×Dic3—22no—
212C32×Dic3—22no—
213C23×C3×C4—91no—
214C23×Dic3—31no—
215C2×#237—91no—
216C2×#237—91no—
217C2×#235—91no—
218C22×C4×D3—31no—
219C3×#123—91no—
220C3×#120—91no—
221#953—31no—
222#953—91no—
223#953—91no—
224#953—181no—
225#939—92no—
226#937—91no—
227#935—91no—
228D4×Dic3—92no—
229#930—92no—
230#929—31no—
231#929—91no—
232#929—91no—
233#929—181no—
234C4×#67—92no—
235C4×#67—92no—
236#926—91no—
237#924—92no—
238#896—92no—
239#893—92no—
240#886—31no—
241#884—92no—
242#882—31no—
243#67⋊C4—92no—
244#67⋊C4—92no—
245#878—92no—
246#877—91no—
247#877—91no—
248#877—181no—
249C23×C32—21no—
250C23×C32—21no—
251C23×C32—21no—
252C23×C32—32no—
253C23×C32—41no—
254C23×C32—64no—
255C23×C32—62no—
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C23×C32C22×D311yescharacteristic
259C22×C3⋊D3C22×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—31no—
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—44no—
271C22×C3×D3—42no—
272C22×C3×D3—61no—
273C22×C3×D3—61no—
274C22×C3×D3C22×D312yes—
275C22×C3×D3C22×D312yes—
276C2×C32×C4—32no—
277C2×C32×C4—32no—
278C2×C32×C4—62no—
279#638—22no—
280#638—22no—
281#638—64no—
282C2×C3⋊Dic3—32no—
283C2×C3⋊Dic3—32no—
284C2×C3⋊Dic3—32no—
285C2×C3⋊Dic3—62no—
286C2×C3⋊Dic3—62no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—122no—
289C2×C3⋊Dic3#6714yescomplemented
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C3×#67—64no—
295C3×#67—62no—
296C3×#67—62no—
297C3×#67—62no—
298C3×#67—62no—
299C3×#67—122no—
300C3×#67—122no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—34no—
306C2×C3×Dic3—34no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—42no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—64no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—64no—
322C2×C3×Dic3—64no—
323C2×C3×Dic3C22×D312yes—
324C2×C3×Dic3C22×D312yes—
325C2×C3×Dic3C22×D312yes—
326C2×C3×Dic3C22×D312yes—
327C3×D12—64no—
328C3×C4×D3—64no—
329C3×C4×D3—64no—
330#627—62no—
331#627—62no—
332#627—62no—
333#626—24no—
334#626—62no—
335#626—62no—
336#625—64no—
337#625—64no—
338#625—62no—
339#625—124no—
340#624—62no—
341#624—62no—
342D3×Dic3—24no—
343D3×Dic3—24no—
344D3×Dic3—62no—
345D3×Dic3—62no—
346D3×Dic3—62no—
347D3×Dic3—62no—
348#525—271noSylow
349C2×C33—22no—
350C2×C33C22×D411yescharacteristic
351C2×C33C2×#4112yes—
352C3×C3⋊D3—41no—
353C3×C3⋊D3—41no—
354C32×D3—24no—
355C24×C3—31no—
356C24×C3—31no—
357C24×C3—61no—
358C23×D3D3211yescharacteristic
359C2×C3×D4—92no—
360C2×C3×D4—91no—
361C2×C3×D4—91no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—61no—
365C22×C3×C4—92no—
366C22×C3×C4—92no—
367C22×C3×C4—91no—
368C22×C3×C4—184no—
369C2×#67—31no—
370C2×#67—31no—
371C2×#67—31no—
372C2×#67—31no—
373C2×#67—32no—
374C2×#67—61no—
375C2×#67—61no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—92no—
379C2×#67—92no—
380C2×#67—92no—
381C2×#67—182no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—32no—
385C22×Dic3—32no—
386C22×Dic3—61no—
387C22×Dic3—64no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3D3211yescharacteristic
391#237—184no—
392#237—184no—
393#235—184no—
394C2×D12—32no—
395C2×D12—91no—
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—64no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×Dic6—91no—
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C4⋊C4—92no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—92no—
411C3×C22⋊C4—92no—
412#217—32no—
413#217—92no—
414#217—92no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—92no—
419#217—182no—
420#217—181no—
421#217—181no—
422#217—181no—
423#217—361no—
424#217D3211yescharacteristic
425(C2×D3)⋊C4—32no—
426(C2×D3)⋊C4—32no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—92no—
429(C2×D3)⋊C4—92no—
430(C2×D3)⋊C4—92no—
431(C2×D3)⋊C4—182no—
432C4⋊Dic3—32no—
433C4⋊Dic3—92no—
434Dic3⋊C4—32no—
435Dic3⋊C4—92no—
436Dic3⋊C4—92no—
437Dic3⋊C4—92no—
438Dic3⋊C4—92no—
439Dic3⋊C4—92no—
440Dic3⋊C4—182no—
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—82no—
465C22×C32D3×D412yes—
466C22×C32D3×D412yes—
467C22×C32C2×#6712yes—
468C22×C32C23×D311yescharacteristic
469C22×C32C23×D311yescharacteristic
470C22×C32C23×D311yescharacteristic
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
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—24no—
482C2×C3×D3—42no—
483C2×C3×D3—42no—
484C2×C3×D3—48no—
485C2×C3×D3—62no—
486C2×C3×D3—62no—
487C2×C3×D3—61no—
488C2×C3×D3—61no—
489C2×C3×D3—62no—
490C2×C3×D3—62no—
491C2×C3×D3—61no—
492C2×C3×D3—61no—
493C2×C3×D3—122no—
494C2×C3×D3—121no—
495C2×C3×D3—121no—
496C2×C3×D3—122no—
497C2×C3×D3#23514yescomplemented
498C2×C3×D3#23714yescomplemented
499C32×C4—62no—
500C32×C4—62no—
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—62no—
504C3⋊Dic3—62no—
505C3⋊Dic3—62no—
506C3⋊Dic3—122no—
507C3⋊Dic3—122no—
508C3⋊Dic3—122no—
509C3⋊Dic3—242no—
510C3⋊Dic3C2×#6712yes—
511C3⋊Dic3C2×#6712yes—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—32no—
517C3×Dic3—32no—
518C3×Dic3—32no—
519C3×Dic3—32no—
520C3×Dic3—42no—
521C3×Dic3—42no—
522C3×Dic3—62no—
523C3×Dic3—62no—
524C3×Dic3—61no—
525C3×Dic3—61no—
526C3×Dic3—61no—
527C3×Dic3—61no—
528C3×Dic3—121no—
529C3×Dic3—121no—
530C2×#41—271no—
531C23×C4—91no—
532#123—91no—
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—41no—
548C23×C3—62no—
549C23×C3—64no—
550C23×C3—64no—
551C23×C3—62no—
552C23×C3—62no—
553C23×C3—91no—
554C23×C3—91no—
555C23×C3—122no—
556C23×C3—124no—
557C23×C3C2×D3211yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C23×C3C2×D3211yescharacteristic
560C22×D3—22no—
561C22×D3—24no—
562C22×D3—31no—
563C22×D3—31no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3C2×D3212yes—
569C3×D4—184no—
570C3×D4—182no—
571C3×D4—182no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—62no—
577C2×C3×C4—62no—
578C2×C3×C4—62no—
579C2×C3×C4—62no—
580C2×C3×C4—91no—
581C2×C3×C4—91no—
582C2×C3×C4—94no—
583C2×C3×C4—91no—
584C2×C3×C4—91no—
585C2×C3×C4—122no—
586C2×C3×C4—184no—
587C2×C3×C4—184no—
588#67—64no—
589#67—62no—
590#67—62no—
591#67—62no—
592#67—62no—
593#67—122no—
594#67—122no—
595#67—182no—
596#67—182no—
597#67—184no—
598#67—184no—
599#67—184no—
600#67—364no—
601C2×Dic3—22no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—34no—
607C2×Dic3—34no—
608C2×Dic3—31no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—64no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—64no—
618C2×Dic3—64no—
619C2×Dic3—92no—
620C2×Dic3—92no—
621C2×Dic3—92no—
622C2×Dic3—182no—
623C2×Dic3—182no—
624C2×Dic3—182no—
625C2×Dic3—182no—
626C2×Dic3—182no—
627C2×Dic3—362no—
628C2×Dic3C2×D3212yes—
629C2×Dic3C2×D3212yes—
630D12—64no—
631D12—182no—
632C4×D3—64no—
633C4×D3—64no—
634C4×D3—182no—
635C4×D3—182no—
636C4×D3—182no—
637C4×D3—182no—
638Dic6—182no—
639Dic6—182no—
640Dic6—182no—
641C2×C32—22no—
642C2×C32—22no—
643C2×C32—22no—
644C2×C32—21no—
645C2×C32—22no—
646C2×C32—22no—
647C2×C32—22no—
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×C32C2×#23512yes—
658C2×C32C2×D3×D411yescharacteristic
659C2×C32C2×D3×D411yescharacteristic
660C2×C32C2×#23712yes—
661C2×C32D3×#4112yes—
662C2×C32C22×#6711yescharacteristic
663C3⋊D3—41no—
664C3⋊D3—41no—
665C3×D3—24no—
666C3×D3—24no—
667C3×D3—44no—
668C3×D3—121no—
669C3×D3—121no—
670C3×D3—121no—
671C3×D3—121no—
672C3×D3—241no—
673C3×D3—241no—
674C24—31no—
675#41—544no—
676C2×Q8—271no—
677C2×D4—92no—
678C2×D4—91no—
679C2×D4—91no—
680C2×D4—271no—
681C2×D4—272no—
682C22×C4—31no—
683C22×C4—92no—
684C22×C4—92no—
685C22×C4—91no—
686C22×C4—184no—
687C22×C4—271no—
688C22×C4—271no—
689C4⋊C4—92no—
690C4⋊C4—272no—
691C4⋊C4—272no—
692C22⋊C4—31no—
693C22⋊C4—92no—
694C22⋊C4—92no—
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—82no—
723C22×C3—122no—
724C22×C3—122no—
725C22×C3—128no—
726C22×C3—182no—
727C22×C3—182no—
728C22×C3—181no—
729C22×C3—181no—
730C22×C3#380212yes—
731C22×C3D3×#6712yes—
732C22×C3D3×#6712yes—
733C22×C3C22×D3211yescharacteristic
734C22×C3C22×D3211yescharacteristic
735C22×C3C22×D3211yescharacteristic
736C2×D3—28no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—122no—
750C2×D3—122no—
751C2×D3#380414yescomplemented
752C3×C4—62no—
753C3×C4—62no—
754C3×C4—62no—
755C3×C4—62no—
756C3×C4—92no—
757C3×C4—92no—
758C3×C4—122no—
759C3×C4—122no—
760C3×C4—181no—
761C3×C4—181no—
762Dic3—22no—
763Dic3—22no—
764Dic3—32no—
765Dic3—32no—
766Dic3—32no—
767Dic3—32no—
768Dic3—62no—
769Dic3—62no—
770Dic3—61no—
771Dic3—61no—
772Dic3—61no—
773Dic3—61no—
774Dic3—121no—
775Dic3—121no—
776Dic3—182no—
777Dic3—182no—
778Dic3—182no—
779Dic3—362no—
780Dic3—362no—
781Dic3—362no—
782Dic3—722no—
783C32—21no—
784C32—21no—
785C32—21no—
786C32—41no—
787C32#558611yescharacteristic, complemented
788C32#565611yescharacteristic, complemented
789C32#579111yescharacteristic, complemented
790C23—32no—
791C23—64no—
792C23—62no—
793C23—91no—
794C23—91no—
795C23D3311yescharacteristic
796Q8—542no—
797D4—184no—
798D4—182no—
799D4—182no—
800D4—542no—
801D4—544no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—62no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—94no—
808C2×C4—91no—
809C2×C4—91no—
810C2×C4—184no—
811C2×C4—184no—
812C2×C4—272no—
813C2×C4—542no—
814C2×C4—542no—
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—361no—
834C2×C3—361no—
835C2×C3C2×#380211yescharacteristic
836C2×C3D3×#23512yes—
837C2×C3D3×#23712yes—
838C2×C3C2×#380412yes—
839C2×C3C2×D3×#6711yescharacteristic
840C2×C3C2×D3×#6711yescharacteristic
841D3—24no—
842D3—121no—
843D3—121no—
844D3—121no—
845D3—121no—
846D3—241no—
847D3—241no—
848C22—22no—
849C22—34no—
850C22—68no—
851C22—62no—
852C22—62no—
853C22—182no—
854C22—182no—
855C22—181no—
856C22—181no—
857C22#8895312yes—
858C22C2×D3311yescharacteristic
859C4—62no—
860C4—62no—
861C4—92no—
862C4—92no—
863C4—181no—
864C4—181no—
865C4—542no—
866C3—21no—
867C3—21no—
868C3—21no—
869C3—41no—
870C3#1059408211yescharacteristic, complemented
871C3#1059489611yescharacteristic, complemented
872C3#1059549811yescharacteristic, complemented
873C2—22no—
874C2—64no—
875C2—361no—
876C2—361no—
877C2D3×#380412yes—
878C2C2×#8895311yescharacteristic
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×#89046C2semidirect
2. C22×C3×D3×Dic3C2semidirect
3. #11723629C2semidirect
4. #11723605C2semidirect
5. #11723595C2semidirect
6. C3×#63977C2semidirect
7. C3×#63966C2semidirect
8. #11722978C2semidirect
9. #11722960C2semidirect
10. #11722936C2semidirect
11. #11722927C2semidirect
20. C2×#6296C22semidirect
21. C2×#6295C22semidirect
23. C2×#6294C22semidirect
24. C2×#6294C22semidirect
32. #88807C22semidirect
33. #88806C22semidirect
34. #88803C22semidirect
36. Dic3×C3⋊Dic3C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
38. C3×#3722C22semidirect
45. C22×D3×Dic3D3semidirect
54. #63977D3semidirect
59. #63966D3semidirect
85. C2×C3×C3⋊Dic3D4semidirect
183. Dic3⋊Dic3C2×D3semidirect
184. #3722C2×D3semidirect
205. C2×C32×D3#41semidirect
289. C2×C3⋊Dic3#67semidirect
497. C2×C3×D3#235semidirect
498. C2×C3×D3#237semidirect
541. C33#525semidirect
751. C2×D3#3804semidirect
787. C32#5586semidirect
788. C32#5656semidirect
789. C32#5791semidirect
870. C3#10594082semidirect
871. C3#10594896semidirect
872. C3#10595498semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C22×C3×D3×Dic32
#117236292
#117236052
#117235952
C3×#639772
C3×#639662
#117229782
#117229602
#117229362
#117229272
#105954983
#105948963
#105940823