Finite Group Databasebeta

← #13172294

Subgroups — #13172294

Order 1728.

1830 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6290C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C211yesmaximal, characteristic, complemented
3#11723727C211yesmaximal, characteristic, complemented
4#11723609C211yesmaximal, characteristic, complemented
5#11723603C211yesmaximal, characteristic, complemented
6C3×#63981C211yesmaximal, characteristic, complemented
7C3×D3×#217C211yesmaximal, characteristic, complemented
8#11722988C212yesmaximal, complemented
9#11722960C212yesmaximal, complemented
10#11722956C212yesmaximal, complemented
11#11722947C212yesmaximal, complemented
12#10595519—31nomaximal
13#10595230—31nomaximal
14#10594290—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic, complemented
16C23×C32×D3C2211yescharacteristic
17C22×C3×D32C2211yescharacteristic, complemented
18C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C3×#638C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×#6295C2212yescomplemented
22C2×#6290—24no—
23C2×#6290C2212yes—
24C2×#6290C2212yescomplemented
25C3×D3×#67—24no—
26C2×C3×#626C2211yescharacteristic, complemented
27C2×C3×#626C2212yescomplemented
28C2×C3×#625C2211yescharacteristic, complemented
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30C2×C3×D3×Dic3C2212yescomplemented
31C3×#3757C2211yescharacteristic, complemented
32C32×#217C2211yescharacteristic, complemented
33#88814C2212yescomplemented
34#88807C2212yescomplemented
35Dic3⋊(C3⋊Dic3)C2212yescomplemented
36#88803C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38C3×#3722C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×#638—31no—
41C22×C3×#67—31no—
42C2×C3×D3×D4—31no—
43C2×D3×#67D311yescharacteristic, complemented
44C22×#625—31no—
45C22×#625—31no—
46C22×#625—61no—
47#64144—31no—
48#64095—31no—
49C2×C3×#217—31no—
50C3×#937—31no—
51C3×#882—31no—
52C3×D3×C22⋊C4—31no—
53#63981—31no—
54#63981D311yescharacteristic, complemented
55#63978—32no—
56#63978—32no—
57#63977—31no—
58#63977—32no—
59#63976—31no—
60#63976—32no—
61#63970—32no—
62D3×#217D311yescharacteristic, complemented
63#63966—32no—
64#63962—31no—
65#63962—31no—
66#63962—31no—
67#63962—31no—
68#63962—61no—
69#63962—61no—
70#63922—32no—
71#63908—32no—
72#63906—32no—
73#63905—32no—
74#63891—32no—
75#63885—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3—22no—
78C22×C3×C3⋊D3—42no—
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C3×C3⋊D3C2312yes—
81C22×C32×D3—42no—
82C22×C32×D3D414yescomplemented
83C22×C32×D3C2311yescharacteristic
84C22×C32×D3C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C3×D32—22no—
87C2×C3×D32—42no—
88C2×C3⋊(C3⋊Dic3)—22no—
89C2×C3⋊(C3⋊Dic3)C2312yes—
90C3×#638—22no—
91C2×C3×C3⋊Dic3C2312yes—
92C2×C3×C3⋊Dic3C2311yescharacteristic
93C32×#67—22no—
94C2×C32×Dic3C2312yes—
95C2×C32×Dic3C2311yescharacteristic
96#6295—42no—
97#6290—24no—
98#6290—24no—
99C3×#626—22no—
100C3×#626—42no—
101C3×#625—22no—
102C3×D3×Dic3—22no—
103C3×D3×Dic3—42no—
104#5804—91no—
105#5589—91no—
106#5493—91no—
107C24×C32—31no—
108C23×C3⋊D3C2×D311yescharacteristic, complemented
109C23×C3×D3—21no—
110C23×C3×D3—31no—
111C23×C3×D3—31no—
112C23×C3×D3—31no—
113C23×C3×D3—31no—
114C23×C3×D3—61no—
115C23×C3×D3C2×D311yescharacteristic
116C23×C3×D3C2×D311yescharacteristic
117C22×D32C2×D311yescharacteristic, complemented
118C2×C32×D4—31no—
119C2×#638—32no—
120C2×#638—32no—
121C2×#638—64no—
122C2×#638C2×D311yescharacteristic
123C22×C3⋊Dic3—31no—
124C22×C3⋊Dic3—31no—
125C22×C3⋊Dic3—31no—
126C22×C3⋊Dic3—61no—
127C22×C3⋊Dic3—61no—
128C22×C3⋊Dic3—61no—
129C22×C3⋊Dic3—121no—
130C2×C3×#67—21no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C2×C3×#67—32no—
137C2×C3×#67—64no—
138C2×C3×#67—61no—
139C2×C3×#67C2×D311yescharacteristic
140C2×C3×#67C2×D311yescharacteristic
141C22×C3×Dic3—31no—
142C22×C3×Dic3—32no—
143C3×D3×D4—64no—
144C2×C3×D12—31no—
145C2×C3×D12—32no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—32no—
148D3×#67—24no—
149C2×#626—32no—
150C2×#626—32no—
151C2×#626C2×D311yescharacteristic, complemented
152C2×#626C2×D312yescomplemented
153C2×#625—32no—
154C2×#625—32no—
155C2×#625—32no—
156C2×#625—32no—
157C2×#625—32no—
158C2×#625—62no—
159C2×#625—62no—
160C2×#625—68no—
161C2×#625—64no—
162C2×#625—64no—
163C2×#625C2×D311yescharacteristic, complemented
164C2×D3×Dic3C2×D311yescharacteristic, complemented
165C2×D3×Dic3C2×D312yescomplemented
166C32×C22⋊C4—31no—
167#3757—32no—
168#3757C2×D311yescharacteristic, complemented
169#3752—32no—
170C4⋊(C3⋊Dic3)—32no—
171#3750—32no—
172C3×#217—21no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—32no—
176C3×#217—61no—
177C3×#217C2×D311yescharacteristic, complemented
178C3×#217C2×D311yescharacteristic, complemented
179C3×(C2×D3)⋊C4—32no—
180C3×(C2×D3)⋊C4—32no—
181C3×(C2×D3)⋊C4—32no—
182Dic3⋊Dic3—32no—
183Dic3⋊Dic3—32no—
184Dic3⋊Dic3—32no—
185Dic3⋊Dic3—32no—
186Dic3⋊Dic3—62no—
187Dic3⋊Dic3—62no—
188#3722—32no—
189#3722C2×D312yescomplemented
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—32no—
194(C2×D3)⋊Dic3—32no—
195(C2×D3)⋊Dic3—32no—
196(C2×D3)⋊Dic3—62no—
197(C2×D3)⋊Dic3—62no—
198(C2×D3)⋊Dic3C2×D312yescomplemented
199C22×C33—22no—
200C22×C33C2×D412yes—
201C22×C33C2411yescharacteristic
202C2×C3×C3⋊D3—22no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—22no—
205C2×C3×C3⋊D3—22no—
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3—44no—
208C2×C32×D3—22no—
209C2×C32×D3—22no—
210C2×C32×D3—21no—
211C2×C32×D3—22no—
212C2×C32×D3—44no—
213C2×C32×D3C2×D412yes—
214C2×C32×D3C2×D412yes—
215C3×D32—44no—
216C3⋊(C3⋊Dic3)—22no—
217C3×C3⋊Dic3—21no—
218C3×C3⋊Dic3—22no—
219C32×Dic3—21no—
220C32×Dic3—22no—
221C22×C3×D4—91no—
222C22×#67—31no—
223C22×#67—91no—
224C22×#67—91no—
225C22×#67—91no—
226C22×#67—181no—
227C2×D3×D4—31no—
228C3×#120—91no—
229C2×C3×C22⋊C4—91no—
230#953—92no—
231#953—91no—
232C2×#217—31no—
233#939—92no—
234#939—92no—
235#938—92no—
236#937—31no—
237#937—92no—
238#937—91no—
239#935—91no—
240#935—91no—
241#935—91no—
242#935—181no—
243#930—92no—
244#930—92no—
245#929—92no—
246#886—92no—
247#886—91no—
248#886—91no—
249#886—91no—
250#886—181no—
251#884—92no—
252#883—92no—
253#882—31no—
254#882—92no—
255#882—91no—
256D3×C22⋊C4—31no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—21no—
260C23×C32—31no—
261C23×C32—31no—
262C23×C32—34no—
263C23×C32—31no—
264C23×C32—41no—
265C23×C32—122no—
266C23×C32C22×D311yescharacteristic
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C22×C3⋊D3—22no—
270C22×C3⋊D3—42no—
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3⋊D3C22×D312yes—
273C22×C3×D3—24no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—31no—
278C22×C3×D3—31no—
279C22×C3×D3—32no—
280C22×C3×D3—32no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3—44no—
284C22×C3×D3—62no—
285C22×C3×D3—61no—
286C22×C3×D3—62no—
287C22×C3×D3—64no—
288C22×C3×D3—62no—
289C22×C3×D3—62no—
290C22×C3×D3—62no—
291C22×C3×D3—122no—
292C22×C3×D3—122no—
293C22×C3×D3—122no—
294C22×C3×D3—122no—
295C22×C3×D3—124no—
296C22×C3×D3D1214yescomplemented
297C22×C3×D3#6714yescomplemented
298C22×C3×D3C22×D311yescharacteristic
299C22×C3×D3C22×D311yescharacteristic
300C22×C3×D3C22×D311yescharacteristic
301C22×C3×D3C22×D311yescharacteristic
302C22×C3×D3C22×D311yescharacteristic
303C22×C3×D3C22×D311yescharacteristic
304C2×D32—22no—
305C2×D32—42no—
306C32×D4—62no—
307C2×C32×C4—31no—
308C2×C32×C4—32no—
309#638—22no—
310#638—64no—
311#638—64no—
312C2×C3⋊Dic3—32no—
313C2×C3⋊Dic3—32no—
314C2×C3⋊Dic3—32no—
315C2×C3⋊Dic3—62no—
316C2×C3⋊Dic3—62no—
317C2×C3⋊Dic3—62no—
318C2×C3⋊Dic3—62no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—62no—
321C2×C3⋊Dic3—62no—
322C2×C3⋊Dic3—122no—
323C2×C3⋊Dic3—122no—
324C2×C3⋊Dic3—122no—
325C2×C3⋊Dic3—124no—
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D312yes—
328C3×#67—22no—
329C3×#67—22no—
330C3×#67—42no—
331C3×#67—62no—
332C3×#67—62no—
333C3×#67—62no—
334C3×#67—62no—
335C3×#67—62no—
336C3×#67—122no—
337C3×#67—122no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—21no—
340C2×C3×Dic3—31no—
341C2×C3×Dic3—32no—
342C2×C3×Dic3—32no—
343C2×C3×Dic3—31no—
344C2×C3×Dic3—62no—
345C2×C3×Dic3—61no—
346C2×C3×Dic3—62no—
347C2×C3×Dic3—122no—
348C2×C3×Dic3C22×D312yes—
349C2×C3×Dic3C22×D312yes—
350C2×C3×Dic3C22×D311yescharacteristic
351C2×C3×Dic3C22×D311yescharacteristic
352C3×D12—62no—
353C3×D12—122no—
354C3×C4×D3—62no—
355C3×C4×D3—122no—
356#626—22no—
357#626—42no—
358#626—122no—
359#626—122no—
360#625—22no—
361#625—68no—
362#625—68no—
363#625—64no—
364#625—64no—
365#625—64no—
366#625—64no—
367#625—122no—
368D3×Dic3—22no—
369D3×Dic3—42no—
370#534—271noSylow
371C2×C33—22no—
372C2×C33C22×D411yescharacteristic
373C2×C33H(5,𝔽2)12yes—
374C3×C3⋊D3—42no—
375C3×C3⋊D3—41no—
376C32×D3—22no—
377C32×D3—22no—
378C32×D3—41no—
379C24×C3—31no—
380C24×C3—31no—
381C24×C3—61no—
382C24×C3—91no—
383C24×C3—91no—
384C23×D3—31no—
385C23×D3—31no—
386C23×D3—31no—
387C23×D3—31no—
388C23×D3—61no—
389C23×D3D3211yescharacteristic
390C2×C3×D4—31no—
391C2×C3×D4—31no—
392C2×C3×D4—61no—
393C2×C3×D4—91no—
394C2×C3×D4—92no—
395C2×C3×D4—91no—
396C2×C3×D4—91no—
397C2×C3×D4—184no—
398C22×C3×C4—91no—
399C22×C3×C4—92no—
400C2×#67—31no—
401C2×#67—31no—
402C2×#67—31no—
403C2×#67—31no—
404C2×#67—31no—
405C2×#67—32no—
406C2×#67—61no—
407C2×#67—64no—
408C2×#67—92no—
409C2×#67—92no—
410C2×#67—92no—
411C2×#67—92no—
412C2×#67—92no—
413C2×#67—92no—
414C2×#67—92no—
415C2×#67—92no—
416C2×#67—182no—
417C2×#67—182no—
418C2×#67—184no—
419C2×#67—184no—
420C2×#67—188no—
421C2×#67—184no—
422C2×#67D3211yescharacteristic
423C22×Dic3—31no—
424C22×Dic3—32no—
425C22×Dic3—91no—
426C22×Dic3—91no—
427C22×Dic3—91no—
428C22×Dic3—181no—
429C22×Dic3—181no—
430C22×Dic3—181no—
431C22×Dic3—361no—
432D3×D4—64no—
433C2×D12—31no—
434C2×D12—32no—
435C2×D12—92no—
436C2×C4×D3—31no—
437C2×C4×D3—32no—
438C3×C22⋊C4—31no—
439C3×C22⋊C4—31no—
440C3×C22⋊C4—61no—
441C3×C22⋊C4—92no—
442C3×C22⋊C4—92no—
443C3×C22⋊C4—91no—
444#217—31no—
445#217—31no—
446#217—32no—
447#217—61no—
448#217—92no—
449#217—92no—
450#217—92no—
451#217—92no—
452#217—182no—
453#217D3211yescharacteristic, complemented
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—32no—
456(C2×D3)⋊C4—32no—
457(C2×D3)⋊C4—92no—
458(C2×D3)⋊C4—92no—
459(C2×D3)⋊C4—92no—
460(C2×D3)⋊C4—92no—
461(C2×D3)⋊C4—92no—
462(C2×D3)⋊C4—182no—
463C4⋊Dic3—92no—
464C4⋊Dic3—92no—
465C4⋊Dic3—92no—
466C4⋊Dic3—182no—
467Dic3⋊C4—92no—
468Dic3⋊C4—92no—
469Dic3⋊C4—92no—
470Dic3⋊C4—182no—
471C22×C32—22no—
472C22×C32—24no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—32no—
482C22×C32—32no—
483C22×C32—42no—
484C22×C32—41no—
485C22×C32—42no—
486C22×C32—42no—
487C22×C32—44no—
488C22×C32—62no—
489C22×C32—62no—
490C22×C32—61no—
491C22×C32—62no—
492C22×C32—124no—
493C22×C32C2×D1212yes—
494C22×C32D3×D412yes—
495C22×C32C2×#6712yes—
496C22×C32C23×D311yescharacteristic
497C22×C32C23×D311yescharacteristic
498C22×C32C23×D311yescharacteristic
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—21no—
504C2×C3⋊D3—44no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—21no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—21no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—42no—
516C2×C3×D3—42no—
517C2×C3×D3—41no—
518C2×C3×D3—42no—
519C2×C3×D3—44no—
520C2×C3×D3—44no—
521C2×C3×D3—48no—
522C2×C3×D3—64no—
523C2×C3×D3—62no—
524C2×C3×D3—61no—
525C2×C3×D3—61no—
526C2×C3×D3—62no—
527C2×C3×D3—62no—
528C2×C3×D3—62no—
529C2×C3×D3—62no—
530C2×C3×D3—62no—
531C2×C3×D3—62no—
532C2×C3×D3—62no—
533C2×C3×D3—122no—
534C2×C3×D3—122no—
535C2×C3×D3—121no—
536C2×C3×D3—122no—
537C2×C3×D3—124no—
538C2×C3×D3—124no—
539C2×C3×D3—128no—
540C2×C3×D3—124no—
541C2×C3×D3—124no—
542C2×C3×D3C2×D1212yes—
543C2×C3×D3C2×D1212yes—
544C2×C3×D3C2×#6712yes—
545C2×C3×D3C2×#6712yes—
546D32—44no—
547C32×C4—61no—
548C32×C4—62no—
549C3⋊Dic3—22no—
550C3⋊Dic3—21no—
551C3⋊Dic3—62no—
552C3⋊Dic3—64no—
553C3⋊Dic3—62no—
554C3⋊Dic3—62no—
555C3⋊Dic3—122no—
556C3⋊Dic3—122no—
557C3⋊Dic3—124no—
558C3×Dic3—21no—
559C3×Dic3—22no—
560C3×Dic3—22no—
561C3×Dic3—21no—
562C3×Dic3—42no—
563C3×Dic3—41no—
564C3×Dic3—61no—
565C3×Dic3—61no—
566C3×Dic3—62no—
567C3×Dic3—62no—
568C3×Dic3—122no—
569C3×Dic3—121no—
570C22×D4—91no—
571C22×D4—271no—
572#123—271no—
573#123—272no—
574#123—271no—
575#121—272no—
576#121—272no—
577#120—91no—
578#120—272no—
579#120—271no—
580C2×C22⋊C4—91no—
581C33#53411yescharacteristic, complemented, Sylow
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—31no—
589C23×C3—34no—
590C23×C3—34no—
591C23×C3—31no—
592C23×C3—31no—
593C23×C3—41no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—64no—
597C23×C3—61no—
598C23×C3—91no—
599C23×C3—92no—
600C23×C3—122no—
601C23×C3—122no—
602C23×C3—124no—
603C23×C3—182no—
604C23×C3—182no—
605C23×C3—362no—
606C23×C3—362no—
607C23×C3C2×D3211yescharacteristic
608C23×C3C2×D3211yescharacteristic
609C23×C3C2×D3211yescharacteristic
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—31no—
613C22×D3—31no—
614C22×D3—42no—
615C22×D3—62no—
616C22×D3—61no—
617C22×D3—62no—
618C22×D3—64no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—122no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—124no—
627C22×D3#62614yescomplemented
628C22×D3C2×D3211yescharacteristic
629C22×D3C2×D3211yescharacteristic
630C22×D3C2×D3211yescharacteristic
631C3×D4—62no—
632C3×D4—62no—
633C3×D4—122no—
634C3×D4—182no—
635C3×D4—182no—
636C3×D4—182no—
637C3×D4—362no—
638C2×C3×C4—31no—
639C2×C3×C4—31no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—61no—
643C2×C3×C4—62no—
644C2×C3×C4—91no—
645C2×C3×C4—92no—
646C2×C3×C4—182no—
647C2×C3×C4—362no—
648#67—22no—
649#67—62no—
650#67—62no—
651#67—62no—
652#67—62no—
653#67—62no—
654#67—122no—
655#67—122no—
656#67—184no—
657#67—184no—
658#67—184no—
659#67—184no—
660#67—188no—
661#67—188no—
662#67—184no—
663#67—184no—
664#67—362no—
665#67—362no—
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—31no—
669C2×Dic3—31no—
670C2×Dic3—62no—
671C2×Dic3—61no—
672C2×Dic3—62no—
673C2×Dic3—92no—
674C2×Dic3—92no—
675C2×Dic3—92no—
676C2×Dic3—122no—
677C2×Dic3—182no—
678C2×Dic3—182no—
679C2×Dic3—182no—
680C2×Dic3—184no—
681C2×Dic3—182no—
682C2×Dic3—182no—
683C2×Dic3—182no—
684C2×Dic3—362no—
685C2×Dic3—362no—
686C2×Dic3—362no—
687C2×Dic3—364no—
688C2×Dic3C2×D3212yes—
689C2×Dic3C2×D3211yescharacteristic
690D12—62no—
691D12—122no—
692D12—362no—
693C4×D3—62no—
694C4×D3—122no—
695C2×C32—22no—
696C2×C32—24no—
697C2×C32—22no—
698C2×C32—22no—
699C2×C32—21no—
700C2×C32—22no—
701C2×C32—22no—
702C2×C32—21no—
703C2×C32—21no—
704C2×C32—22no—
705C2×C32—41no—
706C2×C32—42no—
707C2×C32—42no—
708C2×C32—42no—
709C2×C32—44no—
710C2×C32—62no—
711C2×C32—62no—
712C2×C32—121no—
713C2×C32C22×D1211yescharacteristic
714C2×C32C2×D3×D411yescharacteristic
715C2×C32#100412yes—
716C2×C32#100412yes—
717C2×C32#100412yes—
718C2×C32C22×#6711yescharacteristic
719C3⋊D3—42no—
720C3⋊D3—41no—
721C3×D3—22no—
722C3×D3—22no—
723C3×D3—22no—
724C3×D3—22no—
725C3×D3—42no—
726C3×D3—42no—
727C3×D3—41no—
728C3×D3—41no—
729C3×D3—81no—
730C3×D3—124no—
731C3×D3—121no—
732C3×D3—122no—
733C3×D3—122no—
734C3×D3—121no—
735C3×D3—241no—
736C24—31no—
737C24—91no—
738C24—91no—
739C2×D4—31no—
740C2×D4—91no—
741C2×D4—92no—
742C2×D4—91no—
743C2×D4—91no—
744C2×D4—184no—
745C2×D4—272no—
746C2×D4—272no—
747C2×D4—272no—
748C2×D4—544no—
749C22×C4—91no—
750C22×C4—92no—
751C22×C4—271no—
752C4⋊C4—272no—
753C4⋊C4—272no—
754C22⋊C4—31no—
755C22⋊C4—92no—
756C22⋊C4—92no—
757C22⋊C4—91no—
758C22⋊C4—272no—
759C22⋊C4—272no—
760C22⋊C4—272no—
761C22×C3—24no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—32no—
772C22×C3—32no—
773C22×C3—32no—
774C22×C3—32no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—44no—
778C22×C3—41no—
779C22×C3—42no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—61no—
787C22×C3—62no—
788C22×C3—61no—
789C22×C3—62no—
790C22×C3—122no—
791C22×C3—122no—
792C22×C3—121no—
793C22×C3—122no—
794C22×C3—124no—
795C22×C3—124no—
796C22×C3—128no—
797C22×C3—181no—
798C22×C3—182no—
799C22×C3—182no—
800C22×C3—182no—
801C22×C3—182no—
802C22×C3—364no—
803C22×C3—364no—
804C22×C3D3×D1212yes—
805C22×C3C2×#62612yes—
806C22×C3D3×#6712yes—
807C22×C3C22×D3211yescharacteristic
808C22×C3C22×D3211yescharacteristic
809C22×C3C22×D3211yescharacteristic
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—21no—
814C2×D3—44no—
815C2×D3—64no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—122no—
827C2×D3—122no—
828C2×D3—121no—
829C2×D3—122no—
830C2×D3—124no—
831C2×D3—124no—
832C2×D3—128no—
833C2×D3—124no—
834C2×D3—124no—
835C2×D3C2×#62612yes—
836C2×D3C2×#62612yes—
837C3×C4—61no—
838C3×C4—62no—
839C3×C4—61no—
840C3×C4—62no—
841C3×C4—121no—
842C3×C4—122no—
843C3×C4—181no—
844C3×C4—182no—
845Dic3—22no—
846Dic3—21no—
847Dic3—62no—
848Dic3—61no—
849Dic3—61no—
850Dic3—62no—
851Dic3—121no—
852Dic3—122no—
853Dic3—184no—
854Dic3—182no—
855Dic3—182no—
856Dic3—182no—
857Dic3—362no—
858Dic3—362no—
859Dic3—364no—
860C32—21no—
861C32—21no—
862C32—21no—
863C32—41no—
864C32#549311yescharacteristic, complemented
865C32#558911yescharacteristic, complemented
866C32#580411yescharacteristic, complemented
867C23—31no—
868C23—31no—
869C23—34no—
870C23—31no—
871C23—92no—
872C23—91no—
873C23—122no—
874C23—182no—
875C23—182no—
876C23—362no—
877C23—362no—
878C23D3311yescharacteristic
879D4—62no—
880D4—182no—
881D4—182no—
882D4—182no—
883D4—362no—
884D4—544no—
885D4—544no—
886D4—1082no—
887C2×C4—32no—
888C2×C4—31no—
889C2×C4—92no—
890C2×C4—91no—
891C2×C4—182no—
892C2×C4—272no—
893C2×C4—362no—
894C2×C4—542no—
895C2×C3—24no—
896C2×C3—22no—
897C2×C3—22no—
898C2×C3—22no—
899C2×C3—22no—
900C2×C3—22no—
901C2×C3—22no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—42no—
906C2×C3—42no—
907C2×C3—44no—
908C2×C3—42no—
909C2×C3—41no—
910C2×C3—62no—
911C2×C3—62no—
912C2×C3—62no—
913C2×C3—62no—
914C2×C3—122no—
915C2×C3—122no—
916C2×C3—121no—
917C2×C3—121no—
918C2×C3—241no—
919C2×C3—362no—
920C2×C3—361no—
921C2×C3C2×D3×D1211yescharacteristic
922C2×C3#6431312yes—
923C2×C3#6431312yes—
924C2×C3C22×#62611yescharacteristic
925C2×C3C2×D3×#6711yescharacteristic
926C2×C3#6433012yes—
927D3—22no—
928D3—22no—
929D3—41no—
930D3—124no—
931D3—122no—
932D3—121no—
933D3—121no—
934D3—122no—
935D3—241no—
936C22—22no—
937C22—32no—
938C22—32no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—61no—
943C22—124no—
944C22—182no—
945C22—182no—
946C22—182no—
947C22—181no—
948C22—182no—
949C22—364no—
950C22—364no—
951C22D3×#62612yes—
952C22C2×D3311yescharacteristic
953C4—62no—
954C4—61no—
955C4—182no—
956C4—181no—
957C4—542no—
958C3—21no—
959C3—21no—
960C3—21no—
961C3—41no—
962C3#1059429011yescharacteristic, complemented
963C3#1059523011yescharacteristic, complemented
964C3#1059551911yescharacteristic, complemented
965C2—22no—
966C2—62no—
967C2—62no—
968C2—121no—
969C2—362no—
970C2—361no—
971C2#1172441512yes—
972C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6290C2semidirect
2. C2×C3×D3×#67C2semidirect
3. #11723727C2semidirect
4. #11723609C2semidirect
5. #11723603C2semidirect
6. C3×#63981C2semidirect
7. C3×D3×#217C2semidirect
8. #11722988C2semidirect
9. #11722960C2semidirect
10. #11722956C2semidirect
11. #11722947C2semidirect
15. C23×C3×C3⋊D3C22semidirect
17. C22×C3×D32C22semidirect
18. C22×C3⋊(C3⋊Dic3)C22semidirect
21. C2×#6295C22semidirect
24. C2×#6290C22semidirect
26. C2×C3×#626C22semidirect
27. C2×C3×#626C22semidirect
28. C2×C3×#625C22semidirect
29. C2×C3×D3×Dic3C22semidirect
30. C2×C3×D3×Dic3C22semidirect
31. C3×#3757C22semidirect
32. C32×#217C22semidirect
33. #88814C22semidirect
34. #88807C22semidirect
35. Dic3⋊(C3⋊Dic3)C22semidirect
36. #88803C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. C3×#3722C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
43. C2×D3×#67D3semidirect
54. #63981D3semidirect
62. D3×#217D3semidirect
82. C22×C32×D3D4semidirect
108. C23×C3⋊D3C2×D3semidirect
117. C22×D32C2×D3semidirect
151. C2×#626C2×D3semidirect
152. C2×#626C2×D3semidirect
163. C2×#625C2×D3semidirect
164. C2×D3×Dic3C2×D3semidirect
165. C2×D3×Dic3C2×D3semidirect
168. #3757C2×D3semidirect
177. C3×#217C2×D3semidirect
178. C3×#217C2×D3semidirect
189. #3722C2×D3semidirect
198. (C2×D3)⋊Dic3C2×D3semidirect
296. C22×C3×D3D12semidirect
297. C22×C3×D3#67semidirect
453. #217D32semidirect
581. C33#534semidirect
627. C22×D3#626semidirect
864. C32#5493semidirect
865. C32#5589semidirect
866. C32#5804semidirect
962. C3#10594290semidirect
963. C3#10595230semidirect
964. C3#10595519semidirect

Maximal subgroups

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

subgroupindex
C22×#62902
C2×C3×D3×#672
#117237272
#117236092
#117236032
C3×#639812
C3×D3×#2172
#117229882
#117229602
#117229562
#117229472
#105955193
#105952303
#105942903