Finite Group Databasebeta

← #13172725

Subgroups — #13172725

Order 1728.

2182 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C22×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C3×#3811C211yesmaximal, characteristic, complemented
4C2×#88953C211yesmaximal, characteristic, complemented
5#11723637C212yesmaximal, complemented
6C3×#63978C212yesmaximal, complemented
7#11722967C212yesmaximal, complemented
8#11722962C212yesmaximal, complemented
9#11722911C211yesmaximal, characteristic, complemented
10#11722905C211yesmaximal, characteristic, complemented
11#11722902C211yesmaximal, characteristic, complemented
12D3×#939—32nomaximal
13#10595081—31nomaximal
14C23×C3×C3⋊D3C2211yescharacteristic
15C22×#1113C2211yescharacteristic
16C22×C3×D32C2211yescharacteristic
17C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
18C2×C3×#638C2212yescomplemented
19C2×C32×#67C2212yescomplemented
20C22×C32×Dic3C2211yescharacteristic, complemented
21#89049—24no—
22C2×#6295C2212yescomplemented
23C2×#6294C2211yescharacteristic
24C2×#6290C2212yescomplemented
25C2×Dic3×C3⋊D3—24no—
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
29C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
30C3×#3811—24no—
31C2×C3×#626C2212yescomplemented
32C2×C3×#626C2212yescomplemented
33C2×C3×#624C2211yescharacteristic
34#88953—24no—
35#88806C2212yescomplemented
36#88803C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38C3×Dic3⋊Dic3C2212yescomplemented
39C3×#3722C2212yescomplemented
40C3×(C2×D3)⋊Dic3C2212yescomplemented
41C22×C4×C3⋊D3—31no—
42C2×C3×D3×D4—32no—
43C2×#3811—31no—
44C2×#3811D311yescharacteristic, complemented
45C2×D3×#67—32no—
46C2×D3×#67—32no—
47C22×D3×Dic3—32no—
48C22×D3×Dic3—61no—
49C2×#3802—31no—
50#64148—32no—
51C3×#939—32no—
52C3×#930—32no—
53#63980—32no—
54#63980—32no—
55#63980—62no—
56#63978D312yescomplemented
57#63971—32no—
58#63970—32no—
59D3×#217—32no—
60#63921—31no—
61#63921—31no—
62D3×(C2×D3)⋊C4—32no—
63#63916—32no—
64#63912—32no—
65#63900—31no—
66#63886—32no—
67#63885—32no—
68D3×Dic3⋊C4—32no—
69C23×C33C2311yescharacteristic
70C22×C3×C3⋊D3—22no—
71C22×C3×C3⋊D3—22no—
72C22×C3×C3⋊D3D414yescomplemented
73C22×C3×C3⋊D3C2312yes—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C32×D3C2312yes—
77C2×#1113—22no—
78C2×#1113—22no—
79C2×#1113—22no—
80C2×C3×D32—22no—
81C2×C3×D32—22no—
82C2×C3×D32—22no—
83C2×C3⋊(C3⋊Dic3)—22no—
84C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
85C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
86C3×#638—24no—
87C2×C3×C3⋊Dic3C2312yes—
88C32×#67—24no—
89C2×C32×Dic3—22no—
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93#6295—24no—
94#6294—22no—
95#6290—24no—
96Dic3×C3⋊D3—22no—
97Dic3×C3⋊D3—22no—
98Dic3×C3⋊D3—22no—
99Dic3×C3⋊D3D414yescomplemented
100C3×#626—24no—
101C3×#626—24no—
102C3×#624—22no—
103C2×#939—91no—
104D3×#121—92no—
105C23×C3⋊D3C2×D311yescharacteristic
106C23×C3×D3—32no—
107C23×C3×D3—32no—
108C23×C3×D3—61no—
109C22×D32—31no—
110C22×D32—32no—
111C22×D32C2×D311yescharacteristic
112C2×C32×D4—32no—
113C22×C32×C4—31no—
114C2×#638—32no—
115C2×#638C2×D312yescomplemented
116C22×C3⋊Dic3—32no—
117C22×C3⋊Dic3—31no—
118C22×C3⋊Dic3—61no—
119C22×C3⋊Dic3—62no—
120C22×C3⋊Dic3—121no—
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3—31no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—64no—
126C2×C3×#67—22no—
127C2×C3×#67—32no—
128C2×C3×#67—32no—
129C2×C3×#67—32no—
130C2×C3×#67—32no—
131C2×C3×#67—62no—
132C2×C3×#67C2×D312yescomplemented
133C2×C3×#67C2×D312yescomplemented
134C22×C3×Dic3—21no—
135C22×C3×Dic3C2×D312yescomplemented
136C3×D3×D4—68no—
137C2×C3×D12—32no—
138C2×C3×D12—32no—
139C2×C3×C4×D3—32no—
140#3811—24no—
141#3811—64no—
142D3×#67—68no—
143D3×#67—68no—
144C2×#626—32no—
145C2×#626—32no—
146C2×#626C2×D312yescomplemented
147C2×#626C2×D312yescomplemented
148C2×#625—32no—
149C2×#625—32no—
150C2×#625—32no—
151C2×#625—62no—
152C2×#624—31no—
153C2×#624C2×D311yescharacteristic
154C2×D3×Dic3—32no—
155C2×D3×Dic3—32no—
156C2×D3×Dic3—32no—
157C2×D3×Dic3—32no—
158C2×D3×Dic3—32no—
159C2×D3×Dic3—68no—
160C2×D3×Dic3—61no—
161C2×D3×Dic3—61no—
162C2×D3×Dic3—61no—
163C2×D3×Dic3—61no—
164C2×D3×Dic3—68no—
165#3802—64no—
166#3757—32no—
167#3752—32no—
168#3750—32no—
169C3×#217—32no—
170C3×(C2×D3)⋊C4—32no—
171C3×(C2×D3)⋊C4—32no—
172C3×(C2×D3)⋊C4—32no—
173C3×C4⋊Dic3—32no—
174C3×Dic3⋊C4—32no—
175#3724—32no—
176#3724—32no—
177#3724—62no—
178Dic3⋊Dic3C2×D312yescomplemented
179#3722C2×D312yescomplemented
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—62no—
185(C2×D3)⋊Dic3—62no—
186(C2×D3)⋊Dic3C2×D312yescomplemented
187C22×C33—21no—
188C22×C33—21no—
189C22×C33C2×D412yescomplemented
190C22×C33C2411yescharacteristic
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—21no—
193C2×C3×C3⋊D3—28no—
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3—22no—
196C2×C3×C3⋊D3—22no—
197C2×C3×C3⋊D3C2×D412yes—
198C2×C3×C3⋊D3C2×D412yes—
199C2×C3×C3⋊D3C2×D412yescomplemented
200C2×C3×C3⋊D3#4112yes—
201C2×C32×D3—22no—
202C2×C32×D3—22no—
203C2×C32×D3—22no—
204#1113—44no—
205C3×D32—44no—
206C3⋊(C3⋊Dic3)—21no—
207C3⋊(C3⋊Dic3)C2×D412yescomplemented
208C3×C3⋊Dic3—22no—
209C32×Dic3—21no—
210C32×Dic3—22no—
211C32×Dic3C2×D412yescomplemented
212C22×C3×D4—91no—
213C22×#67—91no—
214C22×#67—91no—
215C23×Dic3—91no—
216C2×D3×D4—32no—
217C2×D3×D4—92no—
218C2×D3×D4—92no—
219C22×C4×D3—92no—
220C22×C4×D3—181no—
221C3×#121—92no—
222C2×#217—91no—
223#939—32no—
224#939—92no—
225#939—92no—
226#939—92no—
227#939—92no—
228#939—92no—
229#939—182no—
230#938—92no—
231#930—32no—
232C2×(C2×D3)⋊C4—91no—
233C2×Dic3⋊C4—91no—
234#895—92no—
235D3×C4⋊C4—92no—
236#884—92no—
237#884—92no—
238D3×C22⋊C4—92no—
239D3×C22⋊C4—92no—
240C23×C32—21no—
241C23×C32—22no—
242C23×C32—32no—
243C23×C32—41no—
244C23×C32C22×D312yes—
245C23×C32C22×D311yescharacteristic
246C22×C3⋊D3—22no—
247C22×C3⋊D3—22no—
248C22×C3⋊D3#6714yescomplemented
249C22×C3⋊D3C22×D312yes—
250C22×C3⋊D3C22×D311yescharacteristic
251C22×C3⋊D3C22×D311yescharacteristic
252C22×C3×D3—22no—
253C22×C3×D3—32no—
254C22×C3×D3—38no—
255C22×C3×D3—32no—
256C22×C3×D3—32no—
257C22×C3×D3—32no—
258C22×C3×D3—64no—
259C22×C3×D3—61no—
260C22×C3×D3—61no—
261C22×C3×D3—62no—
262C22×C3×D3—64no—
263C22×C3×D3—64no—
264C22×C3×D3—64no—
265C22×C3×D3—64no—
266C22×C3×D3—64no—
267C22×C3×D3—64no—
268C22×C3×D3—64no—
269C22×C3×D3C22×D312yes—
270C22×C3×D3C22×D312yes—
271C2×D32—22no—
272C2×D32—22no—
273C2×D32—22no—
274C2×D32—64no—
275C2×D32—64no—
276C2×D32—64no—
277C2×D32—62no—
278C2×D32—62no—
279C2×D32—62no—
280C32×D4—64no—
281C2×C32×C4—31no—
282C2×C32×C4—32no—
283C2×C32×C4—31no—
284C2×C32×C4—62no—
285#638—24no—
286#638—64no—
287C2×C3⋊Dic3—31no—
288C2×C3⋊Dic3—32no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—32no—
291C2×C3⋊Dic3—62no—
292C2×C3⋊Dic3—61no—
293C2×C3⋊Dic3—61no—
294C2×C3⋊Dic3—62no—
295C2×C3⋊Dic3—62no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3—64no—
298C2×C3⋊Dic3—121no—
299C2×C3⋊Dic3—121no—
300C2×C3⋊Dic3—124no—
301C2×C3⋊Dic3—124no—
302C2×C3⋊Dic3C22×D312yes—
303C4×C3⋊D3—34no—
304C4×C3⋊D3—62no—
305C4×C3⋊D3—62no—
306C4×C3⋊D3—62no—
307C3×#67—24no—
308C3×#67—24no—
309C3×#67—44no—
310C3×#67—64no—
311C3×#67—64no—
312C3×#67—64no—
313C3×#67—64no—
314C3×#67—124no—
315C2×C3×Dic3—24no—
316C2×C3×Dic3—24no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—32no—
321C2×C3×Dic3—32no—
322C2×C3×Dic3—62no—
323C2×C3×Dic3C22×D312yes—
324C2×C3×Dic3C22×D312yes—
325C2×C3×Dic3C22×D312yes—
326C2×C3×Dic3C22×D312yes—
327C3×D12—64no—
328C3×D12—64no—
329C3×C4×D3—64no—
330#626—24no—
331#626—24no—
332#626—64no—
333#626—64no—
334#625—64no—
335#625—64no—
336#625—64no—
337#625—124no—
338#624—22no—
339#624—62no—
340D3×Dic3—38no—
341D3×Dic3—64no—
342D3×Dic3—64no—
343D3×Dic3—64no—
344D3×Dic3—64no—
345D3×Dic3—64no—
346D3×Dic3—64no—
347D3×Dic3—64no—
348D3×Dic3—64no—
349C2×#121—271noSylow
350C2×C33—22no—
351C2×C33C22×D411yescharacteristic
352C2×C33C22×D411yescharacteristic
353C2×C33C2×#4111yescharacteristic
354C3×C3⋊D3—22no—
355C3×C3⋊D3—42no—
356C3×C3⋊D3#12114yescomplemented
357C32×D3—42no—
358C24×C3—91no—
359C24×C3—91no—
360C23×D3—32no—
361C23×D3—32no—
362C23×D3—61no—
363C23×D3—92no—
364C23×D3—91no—
365C2×C3×D4—32no—
366C2×C3×D4—32no—
367C2×C3×D4—62no—
368C2×C3×D4—92no—
369C2×C3×D4—92no—
370C2×C3×D4—92no—
371C2×C3×D4—184no—
372C22×C3×C4—32no—
373C22×C3×C4—61no—
374C22×C3×C4—91no—
375C2×#67—32no—
376C2×#67—32no—
377C2×#67—32no—
378C2×#67—32no—
379C2×#67—62no—
380C2×#67—92no—
381C2×#67—92no—
382C2×#67—92no—
383C2×#67—92no—
384C2×#67—92no—
385C2×#67—182no—
386C2×#67—184no—
387C2×#67—184no—
388C2×#67D3212yescomplemented
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—92no—
392C22×Dic3—91no—
393C22×Dic3—91no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3—181no—
397C22×Dic3—182no—
398C22×Dic3—184no—
399C22×Dic3—361no—
400C22×Dic3D3211yescharacteristic, complemented
401D3×D4—68no—
402D3×D4—188no—
403D3×D4—188no—
404C2×D12—32no—
405C2×D12—32no—
406C2×D12—92no—
407C2×C4×D3—32no—
408C2×C4×D3—92no—
409C2×C4×D3—92no—
410C2×C4×D3—92no—
411C2×C4×D3—92no—
412C2×C4×D3—92no—
413C2×C4×D3—181no—
414C2×C4×D3—181no—
415C2×C4×D3—181no—
416C2×C4×D3—181no—
417C2×C4×D3—188no—
418C2×C4×D3—188no—
419C3×C4⋊C4—92no—
420C3×C22⋊C4—92no—
421C3×C22⋊C4—92no—
422#217—32no—
423#217—92no—
424#217—92no—
425#217—92no—
426#217—182no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—32no—
429(C2×D3)⋊C4—32no—
430(C2×D3)⋊C4—92no—
431(C2×D3)⋊C4—92no—
432(C2×D3)⋊C4—92no—
433(C2×D3)⋊C4—182no—
434C4⋊Dic3—32no—
435Dic3⋊C4—32no—
436Dic3⋊C4—92no—
437Dic3⋊C4—92no—
438Dic3⋊C4—92no—
439Dic3⋊C4—182no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—21no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—24no—
450C22×C32—42no—
451C22×C32—41no—
452C22×C32—42no—
453C22×C32—42no—
454C22×C32—42no—
455C22×C32—42no—
456C22×C32—62no—
457C22×C32—62no—
458C22×C32—62no—
459C22×C32D3×D414yescomplemented
460C22×C32C2×#6712yescomplemented
461C22×C32C23×D312yes—
462C22×C32C23×D311yescharacteristic
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—28no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3D3×D412yes—
470C2×C3⋊D3#23712yes—
471C2×C3⋊D3C2×#6712yes—
472C2×C3⋊D3C2×#6712yescomplemented
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—34no—
480C2×C3×D3—34no—
481C2×C3×D3—34no—
482C2×C3×D3—34no—
483C2×C3×D3—42no—
484C2×C3×D3—42no—
485C2×C3×D3—42no—
486C2×C3×D3—62no—
487C2×C3×D3—62no—
488C2×C3×D3—62no—
489C2×C3×D3—62no—
490C2×C3×D3—616no—
491C2×C3×D3—62no—
492C2×C3×D3—616no—
493C2×C3×D3—62no—
494C2×C3×D3—62no—
495C2×C3×D3—62no—
496C2×C3×D3—62no—
497C2×C3×D3—62no—
498C2×C3×D3—62no—
499C2×C3×D3—62no—
500C2×C3×D3—62no—
501C2×C3×D3—62no—
502C2×C3×D3—122no—
503C2×C3×D3—122no—
504C2×C3×D3—122no—
505C2×C3×D3—128no—
506D32—44no—
507D32—128no—
508D32—124no—
509C32×C4—32no—
510C32×C4—61no—
511C32×C4—62no—
512C3⋊Dic3—22no—
513C3⋊Dic3—34no—
514C3⋊Dic3—32no—
515C3⋊Dic3—62no—
516C3⋊Dic3—64no—
517C3⋊Dic3—61no—
518C3⋊Dic3—62no—
519C3⋊Dic3—62no—
520C3⋊Dic3—122no—
521C3⋊Dic3—122no—
522C3⋊Dic3—122no—
523C3×Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—42no—
529C3×Dic3—62no—
530C3×Dic3—62no—
531C3×Dic3—122no—
532C3×Dic3D3×D414yescomplemented
533C22×D4—91no—
534C22×D4—271no—
535C22×D4—271no—
536C23×C4—271no—
537#121—92no—
538#121—272no—
539#121—272no—
540#121—272no—
541C2×C4⋊C4—271no—
542C2×C22⋊C4—271no—
543C2×C22⋊C4—271no—
544C33C2×#12111yescharacteristic, complemented, Sylow
545C23×C3—21no—
546C23×C3—22no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—41no—
550C23×C3—62no—
551C23×C3—91no—
552C23×C3—91no—
553C23×C3—94no—
554C23×C3—92no—
555C23×C3—182no—
556C23×C3—182no—
557C23×C3—182no—
558C23×C3—182no—
559C23×C3—182no—
560C23×C3C2×D3211yescharacteristic
561C23×C3C2×D3212yes—
562C22×D3—32no—
563C22×D3—32no—
564C22×D3—38no—
565C22×D3—32no—
566C22×D3—32no—
567C22×D3—64no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—62no—
571C22×D3—64no—
572C22×D3—64no—
573C22×D3—64no—
574C22×D3—64no—
575C22×D3—64no—
576C22×D3—64no—
577C22×D3—64no—
578C22×D3—184no—
579C22×D3—184no—
580C22×D3—184no—
581C22×D3—182no—
582C22×D3—182no—
583C22×D3—182no—
584C22×D3C2×D3212yes—
585C3×D4—64no—
586C3×D4—64no—
587C3×D4—124no—
588C3×D4—184no—
589C3×D4—184no—
590C3×D4—184no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—62no—
598C2×C3×C4—64no—
599C2×C3×C4—64no—
600C2×C3×C4—92no—
601C2×C3×C4—182no—
602#67—24no—
603#67—64no—
604#67—64no—
605#67—64no—
606#67—64no—
607#67—124no—
608#67—184no—
609#67—184no—
610#67—184no—
611#67—184no—
612#67—184no—
613#67—364no—
614C2×Dic3—22no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—62no—
618C2×Dic3—92no—
619C2×Dic3—91no—
620C2×Dic3—94no—
621C2×Dic3—92no—
622C2×Dic3—91no—
623C2×Dic3—182no—
624C2×Dic3—181no—
625C2×Dic3—181no—
626C2×Dic3—182no—
627C2×Dic3—182no—
628C2×Dic3—182no—
629C2×Dic3—182no—
630C2×Dic3—182no—
631C2×Dic3—184no—
632C2×Dic3—184no—
633C2×Dic3—182no—
634C2×Dic3—361no—
635C2×Dic3—361no—
636C2×Dic3—364no—
637C2×Dic3—364no—
638C2×Dic3C2×D3212yes—
639C2×Dic3C2×D3211yescharacteristic
640C2×Dic3C2×D3211yescharacteristic
641D12—64no—
642D12—64no—
643D12—184no—
644C4×D3—64no—
645C4×D3—98no—
646C4×D3—184no—
647C4×D3—184no—
648C4×D3—184no—
649C4×D3—184no—
650C4×D3—184no—
651C4×D3—184no—
652C4×D3—184no—
653C4×D3—184no—
654C2×C32—22no—
655C2×C32—24no—
656C2×C32—24no—
657C2×C32—21no—
658C2×C32—21no—
659C2×C32—22no—
660C2×C32—22no—
661C2×C32—22no—
662C2×C32—21no—
663C2×C32—41no—
664C2×C32—41no—
665C2×C32—41no—
666C2×C32—44no—
667C2×C32—44no—
668C2×C32—122no—
669C2×C32C2×D3×D412yes—
670C2×C32C2×D3×D411yescharacteristic
671C2×C32C2×D3×D412yes—
672C2×C32C2×#23711yescharacteristic
673C2×C32D3×#4112yes—
674C2×C32C22×#6711yescharacteristic
675C3⋊D3—22no—
676C3⋊D3—42no—
677C3⋊D3#93914yescomplemented
678C3×D3—38no—
679C3×D3—42no—
680C3×D3—42no—
681C3×D3—64no—
682C3×D3—64no—
683C3×D3—64no—
684C3×D3—82no—
685C3×D3—122no—
686C3×D3—122no—
687C3×D3—242no—
688C24—91no—
689C24—91no—
690C24—271no—
691C2×D4—32no—
692C2×D4—92no—
693C2×D4—92no—
694C2×D4—92no—
695C2×D4—184no—
696C2×D4—272no—
697C2×D4—272no—
698C2×D4—544no—
699C2×D4—544no—
700C22×C4—31no—
701C22×C4—91no—
702C22×C4—271no—
703C22×C4—271no—
704C22×C4—271no—
705C22×C4—271no—
706C22×C4—271no—
707C22×C4—271no—
708C22×C4—544no—
709C4⋊C4—92no—
710C4⋊C4—272no—
711C22⋊C4—92no—
712C22⋊C4—92no—
713C22⋊C4—272no—
714C22⋊C4—272no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—22no—
724C22×C3—24no—
725C22×C3—42no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—41no—
730C22×C3—42no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—92no—
738C22×C3—92no—
739C22×C3—92no—
740C22×C3—92no—
741C22×C3—122no—
742C22×C3—122no—
743C22×C3—122no—
744C22×C3—188no—
745C22×C3—181no—
746C22×C3—181no—
747C22×C3—182no—
748C22×C3—182no—
749C22×C3—182no—
750C22×C3—364no—
751C22×C3#380212yescomplemented
752C22×C3D3×#6714yescomplemented
753C22×C3C22×D3211yescharacteristic
754C22×C3C22×D3212yes—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—34no—
759C2×D3—34no—
760C2×D3—34no—
761C2×D3—34no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3—616no—
767C2×D3—62no—
768C2×D3—616no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—122no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—128no—
782C2×D3—368no—
783C2×D3—364no—
784C3×C4—34no—
785C3×C4—62no—
786C3×C4—62no—
787C3×C4—62no—
788C3×C4—62no—
789C3×C4—62no—
790C3×C4—122no—
791C3×C4—182no—
792Dic3—22no—
793Dic3—21no—
794Dic3—62no—
795Dic3—62no—
796Dic3—94no—
797Dic3—92no—
798Dic3—122no—
799Dic3—182no—
800Dic3—184no—
801Dic3—182no—
802Dic3—182no—
803Dic3—181no—
804Dic3—362no—
805Dic3—362no—
806Dic3—362no—
807Dic3#381112yescomplemented
808C32—21no—
809C32—22no—
810C32—41no—
811C32D3×#12112yescomplemented
812C32C2×#93911yescharacteristic, complemented
813C23—32no—
814C23—91no—
815C23—91no—
816C23—94no—
817C23—92no—
818C23—182no—
819C23—182no—
820C23—182no—
821C23—182no—
822C23—182no—
823C23—542no—
824C23—542no—
825C23—542no—
826C23D3311yescharacteristic
827D4—64no—
828D4—184no—
829D4—184no—
830D4—184no—
831D4—544no—
832D4—544no—
833C2×C4—31no—
834C2×C4—31no—
835C2×C4—32no—
836C2×C4—62no—
837C2×C4—92no—
838C2×C4—182no—
839C2×C4—274no—
840C2×C4—271no—
841C2×C4—271no—
842C2×C4—542no—
843C2×C4—542no—
844C2×C4—542no—
845C2×C4—542no—
846C2×C4—542no—
847C2×C3—24no—
848C2×C3—22no—
849C2×C3—24no—
850C2×C3—21no—
851C2×C3—22no—
852C2×C3—22no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—22no—
856C2×C3—44no—
857C2×C3—44no—
858C2×C3—41no—
859C2×C3—41no—
860C2×C3—41no—
861C2×C3—94no—
862C2×C3—122no—
863C2×C3—122no—
864C2×C3—182no—
865C2×C3—242no—
866C2×C3—362no—
867C2×C3C2×#380211yescharacteristic
868C2×C3#6430611yescharacteristic
869C2×C3D32×D412yes—
870C2×C3D3×#23712yes—
871C2×C3C2×D3×#6712yes—
872C2×C3C2×#381111yescharacteristic
873D3—38no—
874D3—42no—
875D3—64no—
876D3—64no—
877D3—64no—
878D3—122no—
879D3—122no—
880D3—242no—
881C22—21no—
882C22—21no—
883C22—62no—
884C22—62no—
885C22—62no—
886C22—92no—
887C22—92no—
888C22—92no—
889C22—92no—
890C22—188no—
891C22—181no—
892C22—181no—
893C22—182no—
894C22—182no—
895C22—182no—
896C22—364no—
897C22—1084no—
898C22#8895312yescomplemented
899C22C2×D3311yescharacteristic
900C4—32no—
901C4—62no—
902C4—61no—
903C4—182no—
904C4—272no—
905C4—541no—
906C3—21no—
907C3—22no—
908C3—41no—
909C3#1059508111yescharacteristic, complemented
910C3D3×#93912yescomplemented
911C2—22no—
912C2—94no—
913C2—122no—
914C2—182no—
915C2—362no—
916C2#1172440711yescharacteristic
917C2C2×#8895311yescharacteristic
918C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C22×Dic3×C3⋊D3C2semidirect
3. C2×C3×#3811C2semidirect
4. C2×#88953C2semidirect
5. #11723637C2semidirect
6. C3×#63978C2semidirect
7. #11722967C2semidirect
8. #11722962C2semidirect
9. #11722911C2semidirect
10. #11722905C2semidirect
11. #11722902C2semidirect
17. C22×C3⋊(C3⋊Dic3)C22semidirect
18. C2×C3×#638C22semidirect
19. C2×C32×#67C22semidirect
20. C22×C32×Dic3C22semidirect
22. C2×#6295C22semidirect
24. C2×#6290C22semidirect
28. C2×Dic3×C3⋊D3C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
31. C2×C3×#626C22semidirect
32. C2×C3×#626C22semidirect
35. #88806C22semidirect
36. #88803C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. C3×Dic3⋊Dic3C22semidirect
39. C3×#3722C22semidirect
40. C3×(C2×D3)⋊Dic3C22semidirect
44. C2×#3811D3semidirect
56. #63978D3semidirect
72. C22×C3×C3⋊D3D4semidirect
99. Dic3×C3⋊D3D4semidirect
115. C2×#638C2×D3semidirect
132. C2×C3×#67C2×D3semidirect
133. C2×C3×#67C2×D3semidirect
135. C22×C3×Dic3C2×D3semidirect
146. C2×#626C2×D3semidirect
147. C2×#626C2×D3semidirect
178. Dic3⋊Dic3C2×D3semidirect
179. #3722C2×D3semidirect
186. (C2×D3)⋊Dic3C2×D3semidirect
189. C22×C33C2×D4semidirect
199. C2×C3×C3⋊D3C2×D4semidirect
207. C3⋊(C3⋊Dic3)C2×D4semidirect
211. C32×Dic3C2×D4semidirect
248. C22×C3⋊D3#67semidirect
356. C3×C3⋊D3#121semidirect
388. C2×#67D32semidirect
400. C22×Dic3D32semidirect
459. C22×C32D3×D4semidirect
460. C22×C32C2×#67semidirect
472. C2×C3⋊D3C2×#67semidirect
532. C3×Dic3D3×D4semidirect
544. C33C2×#121semidirect
677. C3⋊D3#939semidirect
751. C22×C3#3802semidirect
752. C22×C3D3×#67semidirect
807. Dic3#3811semidirect
811. C32D3×#121semidirect
812. C32C2×#939semidirect
898. C22#88953semidirect
909. C3#10595081semidirect
910. C3D3×#939semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C22×Dic3×C3⋊D32
C2×C3×#38112
C2×#889532
#117236372
C3×#639782
#117229672
#117229622
#117229112
#117229052
#117229022
D3×#9393
#105950813