Finite Group Databasebeta

← #13172304

Subgroups — #13172304

Order 1728.

2014 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6291C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C211yesmaximal, characteristic, complemented
3#11723720C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723638C211yesmaximal, characteristic, complemented
6C3×D3×#217C211yesmaximal, characteristic, complemented
7C3×#63962C211yesmaximal, characteristic, complemented
8#11722987C212yesmaximal, complemented
9#11722959C212yesmaximal, complemented
10#11722958C212yesmaximal, complemented
11#11722948C212yesmaximal, complemented
12#10595519—31nomaximal
13#10595234—31nomaximal
14#10594291—31nomaximal
15C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
16C23×C32×D3C2211yescharacteristic
17C22×C3×D32C2211yescharacteristic, complemented
18C2×C3×#638C2211yescharacteristic
19C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×C32×#67C2211yescharacteristic
21C2×#6292C2212yescomplemented
22C2×#6291—24no—
23C2×#6291C2212yes—
24C2×#6291C2212yescomplemented
25C2×#6291C2212yescomplemented
26C3×D3×#67—24no—
27C2×C3×#626C2211yescharacteristic, complemented
28C2×C3×#625C2211yescharacteristic, complemented
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30C2×C3×D3×Dic3C2212yescomplemented
31C3×#3757C2211yescharacteristic, complemented
32C32×#217C2211yescharacteristic, complemented
33#88815C2212yescomplemented
34#88814C2212yescomplemented
35#88804C2212yescomplemented
36#88804C2212yescomplemented
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×#638—31no—
41C22×C3×#67—31no—
42C2×C3×D3×D4—31no—
43C2×D3×#67D311yescharacteristic, complemented
44C22×#626—31no—
45C22×#626—31no—
46C22×#626—61no—
47#64146—31no—
48#64091—31no—
49C2×C3×#217—31no—
50C3×#935—31no—
51C3×#886—31no—
52C3×D3×C22⋊C4—31no—
53#63981—31no—
54#63981—31no—
55#63981—31no—
56#63981—31no—
57#63981—61no—
58#63981—61no—
59#63978—32no—
60#63978—32no—
61#63977—32no—
62#63977—32no—
63#63971—32no—
64D3×#217D311yescharacteristic, complemented
65#63966—31no—
66#63966—32no—
67#63962—31no—
68#63962D311yescharacteristic, complemented
69#63961—31no—
70#63923—32no—
71#63909—32no—
72#63906—32no—
73#63890—32no—
74#63886—32no—
75#63850—32no—
76C23×C33C2311yescharacteristic
77C22×C3⋊(C3⋊D3)—22no—
78C22×C3⋊(C3⋊D3)—42no—
79C22×C3⋊(C3⋊D3)C2312yes—
80C22×C3×C3⋊D3C2311yescharacteristic
81C22×C32×D3—42no—
82C22×C32×D3D414yescomplemented
83C22×C32×D3C2311yescharacteristic
84C22×C32×D3C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C3×D32—22no—
87C2×C3×D32—42no—
88C3×#638—22no—
89C2×C3×C3⋊Dic3—22no—
90C2×C3×C3⋊Dic3C2312yes—
91C2×C3×C3⋊Dic3C2311yescharacteristic
92C2×C3×C3⋊Dic3C2312yes—
93C32×#67—22no—
94C2×C32×Dic3C2312yes—
95C2×C32×Dic3C2311yescharacteristic
96#6292—42no—
97#6291—24no—
98#6291—24no—
99#6291—42no—
100C3×#626—22no—
101C3×#625—22no—
102C3×D3×Dic3—22no—
103C3×D3×Dic3—42no—
104#5804—91no—
105#5653—91no—
106#5493—91no—
107C24×C32—31no—
108C23×C3⋊D3—31no—
109C23×C3⋊D3—31no—
110C23×C3⋊D3—31no—
111C23×C3⋊D3—61no—
112C23×C3⋊D3—61no—
113C23×C3⋊D3—61no—
114C23×C3⋊D3—121no—
115C23×C3×D3—21no—
116C23×C3×D3—31no—
117C23×C3×D3—31no—
118C23×C3×D3C2×D311yescharacteristic
119C23×C3×D3C2×D311yescharacteristic
120C22×D32C2×D311yescharacteristic, complemented
121C2×C32×D4—31no—
122C2×#638—32no—
123C2×#638—32no—
124C2×#638—32no—
125C2×#638—64no—
126C2×#638C2×D311yescharacteristic
127C22×C3⋊Dic3C2×D311yescharacteristic, complemented
128C2×C4⋊(C3⋊D3)—32no—
129C2×C3×#67—21no—
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67—64no—
136C2×C3×#67—61no—
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×#67C2×D311yescharacteristic
139C22×C3×Dic3—31no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—32no—
143C22×C3×Dic3—61no—
144C3×D3×D4—64no—
145C2×C3×D12—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—32no—
148D3×#67—24no—
149C2×#626—32no—
150C2×#626—32no—
151C2×#626—32no—
152C2×#626—32no—
153C2×#626—32no—
154C2×#626—32no—
155C2×#626—32no—
156C2×#626—32no—
157C2×#626—62no—
158C2×#626—62no—
159C2×#626—68no—
160C2×#626—64no—
161C2×#626—64no—
162C2×#626—62no—
163C2×#626—62no—
164C2×#626C2×D311yescharacteristic, complemented
165C2×#625C2×D311yescharacteristic, complemented
166C2×D3×Dic3C2×D311yescharacteristic, complemented
167C2×D3×Dic3C2×D312yescomplemented
168C32×C22⋊C4—31no—
169#3757C2×D311yescharacteristic, complemented
170#3752—32no—
171#3752—32no—
172C3×#217—21no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—32no—
176C3×#217—32no—
177C3×#217—61no—
178C3×#217C2×D311yescharacteristic, complemented
179C3×#217C2×D311yescharacteristic, complemented
180C3×(C2×D3)⋊C4—32no—
181C3×(C2×D3)⋊C4—32no—
182C3×C4⋊Dic3—32no—
183C3×Dic3⋊C4—32no—
184#3724—32no—
185Dic3⋊Dic3—32no—
186Dic3⋊Dic3—32no—
187Dic3⋊Dic3C2×D312yescomplemented
188#3722—32no—
189#3722—32no—
190#3722—32no—
191#3722—32no—
192#3722—32no—
193#3722—62no—
194#3722—62no—
195(C2×D3)⋊Dic3—32no—
196(C2×D3)⋊Dic3—32no—
197(C2×D3)⋊Dic3C2×D312yescomplemented
198(C2×D3)⋊Dic3C2×D312yescomplemented
199C22×C33—22no—
200C22×C33C2×D412yes—
201C22×C33C2411yescharacteristic
202C2×C3⋊(C3⋊D3)—22no—
203C2×C3⋊(C3⋊D3)—22no—
204C2×C3⋊(C3⋊D3)—22no—
205C2×C3⋊(C3⋊D3)—44no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—22no—
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—181no—
226C2×D3×D4—31no—
227C22×D12—91no—
228C3×#123—91no—
229C2×C3×C22⋊C4—91no—
230#953—92no—
231C2×#217—31no—
232#939—92no—
233#939—92no—
234#937—91no—
235#937—91no—
236#937—91no—
237#937—181no—
238#935—31no—
239#935—91no—
240#930—92no—
241#930—92no—
242#929—92no—
243#929—91no—
244#895—92no—
245#894—92no—
246#886—31no—
247#886—92no—
248#886—91no—
249#884—92no—
250#882—92no—
251#882—92no—
252#882—91no—
253#882—91no—
254#882—91no—
255#882—181no—
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—32no—
270C22×C3⋊D3—32no—
271C22×C3⋊D3—32no—
272C22×C3⋊D3—62no—
273C22×C3⋊D3—62no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3—62no—
276C22×C3⋊D3—64no—
277C22×C3⋊D3—62no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—122no—
280C22×C3⋊D3—122no—
281C22×C3⋊D3—122no—
282C22×C3⋊D3—124no—
283C22×C3⋊D3—122no—
284C22×C3⋊D3—122no—
285C22×C3⋊D3—122no—
286C22×C3⋊D3—124no—
287C22×C3⋊D3—124no—
288C22×C3⋊D3—124no—
289C22×C3⋊D3—128no—
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—24no—
292C22×C3×D3—21no—
293C22×C3×D3—21no—
294C22×C3×D3—21no—
295C22×C3×D3—31no—
296C22×C3×D3—31no—
297C22×C3×D3—42no—
298C22×C3×D3—42no—
299C22×C3×D3—44no—
300C22×C3×D3—61no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C22×C3×D3—122no—
304C22×C3×D3—122no—
305C22×C3×D3D1214yescomplemented
306C22×C3×D3#6714yescomplemented
307C22×C3×D3C22×D311yescharacteristic
308C22×C3×D3C22×D311yescharacteristic
309C22×C3×D3C22×D311yescharacteristic
310C22×C3×D3C22×D311yescharacteristic
311C22×C3×D3C22×D311yescharacteristic
312C22×C3×D3C22×D311yescharacteristic
313C2×D32—22no—
314C2×D32—42no—
315C32×D4—62no—
316C2×C32×C4—31no—
317C2×C32×C4—32no—
318#638—22no—
319#638—64no—
320#638—64no—
321#638—122no—
322C2×C3⋊Dic3—22no—
323C2×C3⋊Dic3C22×D312yes—
324C2×C3⋊Dic3C22×D312yes—
325C2×C3⋊Dic3C22×D311yescharacteristic
326C4⋊(C3⋊D3)—122no—
327C3×#67—22no—
328C3×#67—22no—
329C3×#67—42no—
330C3×#67—62no—
331C3×#67—62no—
332C3×#67—62no—
333C3×#67—62no—
334C3×#67—62no—
335C3×#67—122no—
336C2×C3×Dic3—21no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—32no—
339C2×C3×Dic3—32no—
340C2×C3×Dic3—31no—
341C2×C3×Dic3—32no—
342C2×C3×Dic3—31no—
343C2×C3×Dic3—32no—
344C2×C3×Dic3—62no—
345C2×C3×Dic3—61no—
346C2×C3×Dic3—62no—
347C2×C3×Dic3—62no—
348C2×C3×Dic3—64no—
349C2×C3×Dic3—62no—
350C2×C3×Dic3—62no—
351C2×C3×Dic3—122no—
352C2×C3×Dic3C22×D312yes—
353C2×C3×Dic3C22×D312yes—
354C2×C3×Dic3C22×D311yescharacteristic
355C2×C3×Dic3C22×D311yescharacteristic
356C3×D12—62no—
357C3×C4×D3—62no—
358C3×C4×D3—122no—
359#626—22no—
360#626—68no—
361#626—68no—
362#626—64no—
363#626—64no—
364#626—64no—
365#626—64no—
366#626—122no—
367#626—122no—
368#626—124no—
369#626—122no—
370#626—122no—
371#626—124no—
372#625—22no—
373D3×Dic3—22no—
374D3×Dic3—42no—
375#534—271noSylow
376C2×C33—22no—
377C2×C33C22×D411yescharacteristic
378C2×C33H(5,𝔽2)12yes—
379C3⋊(C3⋊D3)—42no—
380C3×C3⋊D3—41no—
381C32×D3—22no—
382C32×D3—22no—
383C32×D3—41no—
384C24×C3—31no—
385C24×C3—31no—
386C24×C3—61no—
387C24×C3—91no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—91no—
391C23×D3—91no—
392C23×D3—91no—
393C23×D3—181no—
394C23×D3—181no—
395C23×D3—181no—
396C23×D3—361no—
397C23×D3D3211yescharacteristic
398C2×C3×D4—31no—
399C2×C3×D4—31no—
400C2×C3×D4—61no—
401C2×C3×D4—91no—
402C2×C3×D4—91no—
403C2×C3×D4—91no—
404C2×C3×D4—184no—
405C22×C3×C4—91no—
406C22×C3×C4—92no—
407C22×C3×C4—91no—
408C2×#67—31no—
409C2×#67—31no—
410C2×#67—31no—
411C2×#67—31no—
412C2×#67—31no—
413C2×#67—61no—
414C2×#67—64no—
415C2×#67—92no—
416C2×#67—92no—
417C2×#67—92no—
418C2×#67—92no—
419C2×#67—92no—
420C2×#67—92no—
421C2×#67—92no—
422C2×#67—182no—
423C2×#67—182no—
424C2×#67—182no—
425C2×#67—184no—
426C2×#67—184no—
427C2×#67—188no—
428C2×#67D3211yescharacteristic
429C22×Dic3—31no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—32no—
433C22×Dic3—61no—
434D3×D4—64no—
435C2×D12—31no—
436C2×D12—92no—
437C2×D12—92no—
438C2×D12—92no—
439C2×D12—92no—
440C2×D12—92no—
441C2×D12—182no—
442C2×D12—184no—
443C2×C4×D3—31no—
444C2×C4×D3—32no—
445C3×C4⋊C4—92no—
446C3×C22⋊C4—31no—
447C3×C22⋊C4—31no—
448C3×C22⋊C4—61no—
449C3×C22⋊C4—92no—
450C3×C22⋊C4—92no—
451C3×C22⋊C4—91no—
452#217—31no—
453#217—31no—
454#217—32no—
455#217—32no—
456#217—61no—
457#217—92no—
458#217D3211yescharacteristic, complemented
459(C2×D3)⋊C4—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—92no—
462(C2×D3)⋊C4—92no—
463(C2×D3)⋊C4—92no—
464(C2×D3)⋊C4—92no—
465(C2×D3)⋊C4—92no—
466(C2×D3)⋊C4—92no—
467(C2×D3)⋊C4—92no—
468(C2×D3)⋊C4—92no—
469(C2×D3)⋊C4—182no—
470(C2×D3)⋊C4—182no—
471C4⋊Dic3—32no—
472C4⋊Dic3—92no—
473Dic3⋊C4—32no—
474Dic3⋊C4—92no—
475Dic3⋊C4—92no—
476C22×C32—22no—
477C22×C32—24no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—21no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—32no—
487C22×C32—32no—
488C22×C32—42no—
489C22×C32—41no—
490C22×C32—42no—
491C22×C32—42no—
492C22×C32—44no—
493C22×C32—62no—
494C22×C32—62no—
495C22×C32—61no—
496C22×C32—62no—
497C22×C32—124no—
498C22×C32C2×D1212yes—
499C22×C32D3×D412yes—
500C22×C32C2×#6712yes—
501C22×C32C23×D311yescharacteristic
502C22×C32C23×D311yescharacteristic
503C22×C32C23×D311yescharacteristic
504C2×C3⋊D3—22no—
505C2×C3⋊D3—21no—
506C2×C3⋊D3—62no—
507C2×C3⋊D3—62no—
508C2×C3⋊D3—62no—
509C2×C3⋊D3—64no—
510C2×C3⋊D3—64no—
511C2×C3⋊D3—64no—
512C2×C3⋊D3—62no—
513C2×C3⋊D3—62no—
514C2×C3⋊D3—62no—
515C2×C3⋊D3—62no—
516C2×C3⋊D3—62no—
517C2×C3⋊D3—62no—
518C2×C3⋊D3—122no—
519C2×C3⋊D3—122no—
520C2×C3⋊D3—122no—
521C2×C3⋊D3—122no—
522C2×C3⋊D3—122no—
523C2×C3⋊D3—122no—
524C2×C3⋊D3—124no—
525C2×C3⋊D3—124no—
526C2×C3⋊D3—124no—
527C2×C3⋊D3—124no—
528C2×C3⋊D3—128no—
529C2×C3⋊D3—124no—
530C2×C3⋊D3—124no—
531C2×C3⋊D3—128no—
532C2×C3⋊D3—128no—
533C2×C3⋊D3—1216no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—21no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—21no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—42no—
545C2×C3×D3—42no—
546C2×C3×D3—42no—
547C2×C3×D3—41no—
548C2×C3×D3—44no—
549C2×C3×D3—44no—
550C2×C3×D3—48no—
551C2×C3×D3—61no—
552C2×C3×D3—61no—
553C2×C3×D3—62no—
554C2×C3×D3—62no—
555C2×C3×D3—122no—
556C2×C3×D3—121no—
557C2×C3×D3—124no—
558C2×C3×D3—124no—
559C2×C3×D3C2×D1212yes—
560C2×C3×D3C2×D1212yes—
561C2×C3×D3C2×#6712yes—
562C2×C3×D3C2×#6712yes—
563D32—44no—
564C32×C4—61no—
565C32×C4—62no—
566C3⋊Dic3—22no—
567C3⋊Dic3—22no—
568C3⋊Dic3—21no—
569C3×Dic3—21no—
570C3×Dic3—22no—
571C3×Dic3—22no—
572C3×Dic3—21no—
573C3×Dic3—42no—
574C3×Dic3—41no—
575C3×Dic3—64no—
576C3×Dic3—62no—
577C3×Dic3—61no—
578C3×Dic3—61no—
579C3×Dic3—62no—
580C3×Dic3—62no—
581C3×Dic3—62no—
582C3×Dic3—122no—
583C3×Dic3—121no—
584C22×D4—91no—
585C22×D4—271no—
586#123—91no—
587#123—272no—
588#123—271no—
589#121—272no—
590#121—272no—
591#120—271no—
592#120—272no—
593#120—271no—
594C2×C22⋊C4—91no—
595C33#53411yescharacteristic, complemented, Sylow
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—31no—
602C23×C3—31no—
603C23×C3—34no—
604C23×C3—34no—
605C23×C3—31no—
606C23×C3—31no—
607C23×C3—41no—
608C23×C3—61no—
609C23×C3—61no—
610C23×C3—64no—
611C23×C3—61no—
612C23×C3—91no—
613C23×C3—122no—
614C23×C3—122no—
615C23×C3—124no—
616C23×C3—182no—
617C23×C3—362no—
618C23×C3C2×D3211yescharacteristic
619C23×C3C2×D3211yescharacteristic
620C23×C3C2×D3211yescharacteristic
621C22×D3—31no—
622C22×D3—31no—
623C22×D3—42no—
624C22×D3—61no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—92no—
628C22×D3—92no—
629C22×D3—92no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—182no—
633C22×D3—182no—
634C22×D3—182no—
635C22×D3—184no—
636C22×D3—182no—
637C22×D3—182no—
638C22×D3—182no—
639C22×D3—362no—
640C22×D3—362no—
641C22×D3—362no—
642C22×D3—364no—
643C22×D3—362no—
644C22×D3—362no—
645C22×D3—362no—
646C22×D3—364no—
647C22×D3—364no—
648C22×D3—364no—
649C22×D3—368no—
650C22×D3#62614yescomplemented
651C22×D3C2×D3211yescharacteristic
652C22×D3C2×D3211yescharacteristic
653C22×D3C2×D3211yescharacteristic
654C3×D4—62no—
655C3×D4—62no—
656C3×D4—122no—
657C3×D4—182no—
658C3×D4—182no—
659C3×D4—182no—
660C2×C3×C4—31no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—31no—
664C2×C3×C4—61no—
665C2×C3×C4—62no—
666C2×C3×C4—91no—
667C2×C3×C4—92no—
668C2×C3×C4—92no—
669C2×C3×C4—182no—
670C2×C3×C4—182no—
671C2×C3×C4—362no—
672#67—22no—
673#67—62no—
674#67—62no—
675#67—62no—
676#67—62no—
677#67—62no—
678#67—122no—
679#67—184no—
680#67—184no—
681#67—184no—
682#67—184no—
683#67—188no—
684#67—188no—
685#67—362no—
686#67—362no—
687#67—362no—
688#67—364no—
689C2×Dic3—32no—
690C2×Dic3—31no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—31no—
695C2×Dic3—62no—
696C2×Dic3—61no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—64no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—122no—
703C2×Dic3C2×D3212yes—
704C2×Dic3C2×D3211yescharacteristic
705D12—62no—
706D12—184no—
707D12—184no—
708D12—362no—
709D12—362no—
710D12—364no—
711D12—362no—
712C4×D3—62no—
713C4×D3—122no—
714C2×C32—22no—
715C2×C32—24no—
716C2×C32—22no—
717C2×C32—22no—
718C2×C32—21no—
719C2×C32—22no—
720C2×C32—22no—
721C2×C32—21no—
722C2×C32—21no—
723C2×C32—22no—
724C2×C32—41no—
725C2×C32—42no—
726C2×C32—42no—
727C2×C32—42no—
728C2×C32—44no—
729C2×C32—62no—
730C2×C32—62no—
731C2×C32—121no—
732C2×C32C22×D1211yescharacteristic
733C2×C32C2×D3×D411yescharacteristic
734C2×C32#100412yes—
735C2×C32#100412yes—
736C2×C32#100912yes—
737C2×C32C22×#6711yescharacteristic
738C3⋊D3—41no—
739C3⋊D3—124no—
740C3⋊D3—124no—
741C3⋊D3—124no—
742C3⋊D3—128no—
743C3⋊D3—122no—
744C3⋊D3—122no—
745C3⋊D3—122no—
746C3×D3—22no—
747C3×D3—22no—
748C3×D3—22no—
749C3×D3—22no—
750C3×D3—42no—
751C3×D3—42no—
752C3×D3—41no—
753C3×D3—41no—
754C3×D3—81no—
755C3×D3—121no—
756C3×D3—121no—
757C3×D3—241no—
758C24—31no—
759C24—91no—
760C24—271no—
761C2×D4—31no—
762C2×D4—91no—
763C2×D4—91no—
764C2×D4—91no—
765C2×D4—184no—
766C2×D4—272no—
767C2×D4—272no—
768C2×D4—272no—
769C2×D4—272no—
770C2×D4—544no—
771C22×C4—91no—
772C22×C4—92no—
773C22×C4—91no—
774C4⋊C4—92no—
775C4⋊C4—272no—
776C22⋊C4—31no—
777C22⋊C4—92no—
778C22⋊C4—92no—
779C22⋊C4—91no—
780C22⋊C4—272no—
781C22⋊C4—272no—
782C22⋊C4—272no—
783C22×C3—24no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—32no—
794C22×C3—32no—
795C22×C3—32no—
796C22×C3—32no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—44no—
800C22×C3—41no—
801C22×C3—42no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—61no—
809C22×C3—62no—
810C22×C3—61no—
811C22×C3—62no—
812C22×C3—122no—
813C22×C3—122no—
814C22×C3—122no—
815C22×C3—121no—
816C22×C3—124no—
817C22×C3—124no—
818C22×C3—128no—
819C22×C3—181no—
820C22×C3—182no—
821C22×C3—364no—
822C22×C3D3×D1212yes—
823C22×C3C2×#62612yes—
824C22×C3D3×#6712yes—
825C22×C3C22×D3211yescharacteristic
826C22×C3C22×D3211yescharacteristic
827C22×C3C22×D3211yescharacteristic
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—21no—
832C2×D3—44no—
833C2×D3—62no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—62no—
837C2×D3—122no—
838C2×D3—121no—
839C2×D3—124no—
840C2×D3—124no—
841C2×D3—184no—
842C2×D3—184no—
843C2×D3—184no—
844C2×D3—182no—
845C2×D3—182no—
846C2×D3—182no—
847C2×D3—182no—
848C2×D3—182no—
849C2×D3—182no—
850C2×D3—182no—
851C2×D3—182no—
852C2×D3—182no—
853C2×D3—362no—
854C2×D3—362no—
855C2×D3—362no—
856C2×D3—362no—
857C2×D3—362no—
858C2×D3—362no—
859C2×D3—364no—
860C2×D3—364no—
861C2×D3—364no—
862C2×D3—368no—
863C2×D3—364no—
864C2×D3—364no—
865C2×D3—364no—
866C2×D3—368no—
867C2×D3—368no—
868C2×D3—3616no—
869C2×D3C2×#62612yes—
870C2×D3C2×#62612yes—
871C3×C4—61no—
872C3×C4—62no—
873C3×C4—61no—
874C3×C4—62no—
875C3×C4—122no—
876C3×C4—121no—
877C3×C4—181no—
878C3×C4—182no—
879C3×C4—182no—
880Dic3—22no—
881Dic3—21no—
882Dic3—64no—
883Dic3—62no—
884Dic3—62no—
885Dic3—61no—
886Dic3—61no—
887Dic3—62no—
888Dic3—62no—
889Dic3—121no—
890Dic3—122no—
891C32—21no—
892C32—21no—
893C32—21no—
894C32—41no—
895C32#549311yescharacteristic, complemented
896C32#565311yescharacteristic, complemented
897C32#580411yescharacteristic, complemented
898C23—31no—
899C23—31no—
900C23—34no—
901C23—31no—
902C23—91no—
903C23—122no—
904C23—182no—
905C23—272no—
906C23—362no—
907C23—542no—
908C23—1082no—
909C23D3311yescharacteristic
910D4—62no—
911D4—182no—
912D4—182no—
913D4—182no—
914D4—544no—
915D4—544no—
916D4—1082no—
917D4—1082no—
918C2×C4—32no—
919C2×C4—31no—
920C2×C4—92no—
921C2×C4—92no—
922C2×C4—91no—
923C2×C4—182no—
924C2×C4—182no—
925C2×C4—362no—
926C2×C3—24no—
927C2×C3—22no—
928C2×C3—22no—
929C2×C3—22no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—22no—
934C2×C3—22no—
935C2×C3—22no—
936C2×C3—42no—
937C2×C3—42no—
938C2×C3—44no—
939C2×C3—41no—
940C2×C3—42no—
941C2×C3—62no—
942C2×C3—62no—
943C2×C3—62no—
944C2×C3—62no—
945C2×C3—122no—
946C2×C3—122no—
947C2×C3—121no—
948C2×C3—121no—
949C2×C3—241no—
950C2×C3—361no—
951C2×C3C2×D3×D1211yescharacteristic
952C2×C3#6431412yes—
953C2×C3#6431412yes—
954C2×C3C22×#62611yescharacteristic
955C2×C3C2×D3×#6711yescharacteristic
956C2×C3#6433012yes—
957D3—22no—
958D3—22no—
959D3—41no—
960D3—121no—
961D3—121no—
962D3—241no—
963D3—364no—
964D3—364no—
965D3—364no—
966D3—368no—
967D3—362no—
968D3—362no—
969D3—362no—
970C22—22no—
971C22—32no—
972C22—32no—
973C22—62no—
974C22—62no—
975C22—61no—
976C22—62no—
977C22—124no—
978C22—181no—
979C22—182no—
980C22—364no—
981C22—542no—
982C22—542no—
983C22—542no—
984C22—1084no—
985C22D3×#62612yes—
986C22C2×D3311yescharacteristic
987C4—61no—
988C4—62no—
989C4—181no—
990C4—182no—
991C4—182no—
992C3—21no—
993C3—21no—
994C3—21no—
995C3—41no—
996C3#1059429111yescharacteristic, complemented
997C3#1059523411yescharacteristic, complemented
998C3#1059551911yescharacteristic, complemented
999C2—22no—
1000C2—62no—
1001C2—62no—
1002C2—121no—
1003C2—361no—
1004C2—1082no—
1005C2C2×D3×#62611yescharacteristic
1006C2#1172441912yes—
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×#6291C2semidirect
2. C2×C3×D3×#67C2semidirect
3. #11723720C2semidirect
4. #11723639C2semidirect
5. #11723638C2semidirect
6. C3×D3×#217C2semidirect
7. C3×#63962C2semidirect
8. #11722987C2semidirect
9. #11722959C2semidirect
10. #11722958C2semidirect
11. #11722948C2semidirect
15. C23×C3⋊(C3⋊D3)C22semidirect
17. C22×C3×D32C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
21. C2×#6292C22semidirect
24. C2×#6291C22semidirect
25. C2×#6291C22semidirect
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. #88815C22semidirect
34. #88814C22semidirect
35. #88804C22semidirect
36. #88804C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
43. C2×D3×#67D3semidirect
64. D3×#217D3semidirect
68. #63962D3semidirect
82. C22×C32×D3D4semidirect
120. C22×D32C2×D3semidirect
127. C22×C3⋊Dic3C2×D3semidirect
164. C2×#626C2×D3semidirect
165. C2×#625C2×D3semidirect
166. C2×D3×Dic3C2×D3semidirect
167. C2×D3×Dic3C2×D3semidirect
169. #3757C2×D3semidirect
178. C3×#217C2×D3semidirect
179. C3×#217C2×D3semidirect
187. Dic3⋊Dic3C2×D3semidirect
197. (C2×D3)⋊Dic3C2×D3semidirect
198. (C2×D3)⋊Dic3C2×D3semidirect
305. C22×C3×D3D12semidirect
306. C22×C3×D3#67semidirect
458. #217D32semidirect
595. C33#534semidirect
650. C22×D3#626semidirect
895. C32#5493semidirect
896. C32#5653semidirect
897. C32#5804semidirect
996. C3#10594291semidirect
997. C3#10595234semidirect
998. C3#10595519semidirect

Maximal subgroups

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

subgroupindex
C22×#62912
C2×C3×D3×#672
#117237202
#117236392
#117236382
C3×D3×#2172
C3×#639622
#117229872
#117229592
#117229582
#117229482
#105955193
#105952343
#105942913