Finite Group Databasebeta

← #13170731

Subgroups — #13170731

Order 1728.

1642 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88953C211yesmaximal, characteristic
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723700C211yesmaximal, characteristic, complemented
4C3⋊D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#11723480C212yesmaximal, complemented
6C3×#63921C211yesmaximal, characteristic, complemented
7C3×#63890C212yesmaximal, complemented
8#11722990C212yesmaximal, complemented
9#11722988C212yesmaximal, complemented
10#11722908C211yesmaximal, characteristic, complemented
11#11722905C211yesmaximal, characteristic, complemented
12#10594608—31nomaximal
13D3×#886—32nomaximal
14C22×#1113C2211yescharacteristic
15C22×C3×D32C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×#6294C2211yescharacteristic
18C2×#6290C2212yes—
19C2×Dic3×C3⋊D3C2211yescharacteristic
20C2×Dic3×C3⋊D3C2211yescharacteristic
21C2×D3×C3⋊Dic3C2212yescomplemented
22C2×C3×#626C2212yes—
23C2×C3×#624C2211yescharacteristic
24C2×C3×D3×Dic3C2212yescomplemented
25#88953—24no—
26D32×Dic3—24no—
27C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
28C3×#3752C2212yescomplemented
29C32×(C2×D3)⋊C4C2212yescomplemented
30C32×C4⋊Dic3C2211yescharacteristic, complemented
31#88814C2212yescomplemented
32#88807C2211yescharacteristic, complemented
33#88807C2211yescharacteristic, complemented
34Dic3⋊(C3⋊Dic3)C2212yescomplemented
35#88803C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×#3722C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C2×D3×#67—32no—
40C22×D3×Dic3—32no—
41C2×#3802—31no—
42C2×C4×D32—31no—
43C4⋊C4×C3⋊D3—31no—
44#64095—32no—
45C3×#894—32no—
46C3×#886—32no—
47C3×D3×C22⋊C4—32no—
48#63966—32no—
49#63962—32no—
50#63921—31no—
51#63921—31no—
52#63921D311yescharacteristic, complemented
53D3×(C2×D3)⋊C4—32no—
54D3×(C2×D3)⋊C4—32no—
55#63905—32no—
56#63891—32no—
57#63891—32no—
58#63891—32no—
59#63891—62no—
60#63890—32no—
61#63890D312yescomplemented
62D3×C4⋊Dic3—32no—
63D3×C4⋊Dic3—32no—
64D3×C4⋊Dic3—61no—
65#63884—32no—
66#63883—31no—
67C22×C3×C3⋊D3C2312yes—
68C22×C3×C3⋊D3C2311yescharacteristic
69C22×C32×D3C2312yes—
70C2×#1113—22no—
71C2×#1113—22no—
72C2×#1113—22no—
73C2×C3×D32—22no—
74C2×C3×D32—22no—
75C2×C3×D32D414yes—
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4×C3⋊D3—22no—
82C2×C32×Dic3C2311yescharacteristic
83C2×C32×Dic3C2312yes—
84C2×C32×Dic3C2311yescharacteristic
85#6294—22no—
86#6290—24no—
87Dic3×C3⋊D3—22no—
88Dic3×C3⋊D3—22no—
89D3×C3⋊Dic3—24no—
90C3×#626—24no—
91C3×#624—22no—
92C3×D3×Dic3—24no—
93D3×#123—92no—
94C2×#886—91no—
95C23×C3×D3—32no—
96C22×D32—31no—
97C22×D32—32no—
98C22×D32C2×D311yescharacteristic
99C2×#638—32no—
100C22×C3⋊Dic3—32no—
101C2×C4×C3⋊D3—31no—
102C2×C4×C3⋊D3—31no—
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C2×C3×#67—32no—
105C22×C3×Dic3—32no—
106C2×C3×D12—32no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—61no—
111D3×#67—68no—
112C2×#626C2×D312yes—
113C2×#625—32no—
114C2×#625—32no—
115C2×#625—62no—
116C2×#624—31no—
117C2×#624C2×D311yescharacteristic
118C2×D3×Dic3—32no—
119C2×D3×Dic3—32no—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—68no—
124C2×D3×Dic3—61no—
125C2×D3×Dic3—61no—
126C2×D3×Dic3—62no—
127C2×D3×Dic3C2×D312yescomplemented
128#3802—64no—
129C4×D32—64no—
130C32×C4⋊C4—31no—
131C32×C22⋊C4—32no—
132#3752—32no—
133#3752C2×D312yescomplemented
134C4⋊(C3⋊Dic3)—32no—
135C4⋊(C3⋊Dic3)—31no—
136C4⋊(C3⋊Dic3)—32no—
137C4⋊(C3⋊Dic3)—61no—
138C4⋊(C3⋊Dic3)—62no—
139C4⋊(C3⋊Dic3)—121no—
140#3750—31no—
141#3750—31no—
142C3×#217—32no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—32no—
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4—32no—
147C3×(C2×D3)⋊C4—32no—
148C3×(C2×D3)⋊C4—32no—
149C3×(C2×D3)⋊C4—62no—
150C3×(C2×D3)⋊C4C2×D312yescomplemented
151C3×(C2×D3)⋊C4C2×D312yescomplemented
152C3×C4⋊Dic3—21no—
153C3×C4⋊Dic3—32no—
154C3×C4⋊Dic3C2×D312yescomplemented
155C3×Dic3⋊C4—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—62no—
161Dic3⋊Dic3—61no—
162Dic3⋊Dic3—61no—
163Dic3⋊Dic3C2×D312yescomplemented
164#3722—32no—
165#3722C2×D312yescomplemented
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—62no—
171(C2×D3)⋊Dic3C2×D312yescomplemented
172C22×C33C2411yescharacteristic
173C2×C3×C3⋊D3—22no—
174C2×C3×C3⋊D3—22no—
175C2×C3×C3⋊D3—22no—
176C2×C3×C3⋊D3C2×D412yes—
177C2×C3×C3⋊D3#4112yes—
178C2×C3×C3⋊D3#4112yes—
179C2×C32×D3—22no—
180C2×C32×D3—22no—
181C2×C32×D3C2×D414yes—
182#1113—44no—
183C3×D32—28no—
184C33×C4—21no—
185C3⋊(C3⋊Dic3)—21no—
186C3⋊(C3⋊Dic3)—21no—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C32×Dic3—21no—
190C32×Dic3—21no—
191C32×Dic3—22no—
192C22×#67—91no—
193C23×Dic3—91no—
194C2×D3×D4—92no—
195C22×C4×D3—92no—
196C3×#123—92no—
197C2×C3×C22⋊C4—91no—
198#935—92no—
199#929—92no—
200C2×(C2×D3)⋊C4—91no—
201C2×(C2×D3)⋊C4—91no—
202C2×C4⋊Dic3—91no—
203C2×C4⋊Dic3—91no—
204#894—32no—
205#894—92no—
206D3×C4⋊C4—92no—
207D3×C4⋊C4—92no—
208D3×C4⋊C4—181no—
209#886—32no—
210#886—92no—
211#886—92no—
212#886—92no—
213#886—92no—
214#886—182no—
215#883—92no—
216#883—92no—
217D3×C22⋊C4—32no—
218D3×C22⋊C4—92no—
219D3×C22⋊C4—92no—
220C23×C32—32no—
221C22×C3⋊D3C22×D312yes—
222C22×C3⋊D3C22×D311yescharacteristic
223C22×C3×D3—22no—
224C22×C3×D3—32no—
225C22×C3×D3—38no—
226C22×C3×D3—32no—
227C22×C3×D3—32no—
228C22×C3×D3—61no—
229C22×C3×D3—62no—
230C22×C3×D3—64no—
231C22×C3×D3—64no—
232C22×C3×D3C22×D312yes—
233C22×C3×D3C22×D312yes—
234C2×D32—22no—
235C2×D32—22no—
236C2×D32—64no—
237C2×D32—64no—
238C2×D32—64no—
239C2×D32—62no—
240C2×D32—62no—
241C2×D32—62no—
242C2×D32D1214yes—
243C2×C32×C4—21no—
244C2×C32×C4—22no—
245C2×C32×C4—31no—
246C2×C32×C4—32no—
247C2×C32×C4—31no—
248C2×C32×C4—41no—
249C2×C32×C4C22×D312yes—
250C2×C32×C4C22×D311yescharacteristic
251#638—64no—
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—32no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—32no—
256C2×C3⋊Dic3—62no—
257C2×C3⋊Dic3—61no—
258C2×C3⋊Dic3—61no—
259C2×C3⋊Dic3—62no—
260C2×C3⋊Dic3—64no—
261C2×C3⋊Dic3—121no—
262C2×C3⋊Dic3—121no—
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D312yes—
265C4×C3⋊D3—22no—
266C4×C3⋊D3—62no—
267C4×C3⋊D3—62no—
268C3×#67—64no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—62no—
277C2×C3×Dic3—64no—
278C2×C3×Dic3C22×D312yes—
279C2×C3×Dic3C22×D312yes—
280C2×C3×Dic3C22×D312yes—
281C2×C3×Dic3C22×D312yes—
282C3×D12—64no—
283C3×C4×D3—64no—
284C3×C4×D3—64no—
285C3×C4×D3—64no—
286C3×C4×D3—64no—
287#626—24no—
288#625—64no—
289#625—64no—
290#625—124no—
291#624—22no—
292#624—62no—
293D3×Dic3—24no—
294D3×Dic3—64no—
295D3×Dic3—64no—
296D3×Dic3—64no—
297D3×Dic3—64no—
298D3×Dic3—64no—
299D3×Dic3—124no—
300D3×Dic3—122no—
301D3×Dic3—122no—
302C2×#123—271noSylow
303C2×C33C22×D411yescharacteristic
304C2×C33C2×#4111yescharacteristic
305C2×C33C2×#4111yescharacteristic
306C3×C3⋊D3—42no—
307C3×C3⋊D3#12314yescomplemented
308C32×D3—24no—
309C24×C3—91no—
310C23×D3—32no—
311C23×D3—92no—
312C23×D3—91no—
313C2×C3×D4—92no—
314C22×C3×C4—91no—
315C22×C3×C4—92no—
316C22×C3×C4—91no—
317C2×#67—32no—
318C2×#67—92no—
319C2×#67—92no—
320C2×#67—92no—
321C2×#67—182no—
322C2×#67—184no—
323C22×Dic3—32no—
324C22×Dic3—91no—
325C22×Dic3—92no—
326C22×Dic3—92no—
327C22×Dic3—91no—
328C22×Dic3—91no—
329C22×Dic3—182no—
330C22×Dic3—184no—
331D3×D4—188no—
332C2×D12—32no—
333C2×C4×D3—32no—
334C2×C4×D3—32no—
335C2×C4×D3—32no—
336C2×C4×D3—61no—
337C2×C4×D3—92no—
338C2×C4×D3—92no—
339C2×C4×D3—92no—
340C2×C4×D3—92no—
341C2×C4×D3—181no—
342C2×C4×D3—181no—
343C2×C4×D3—188no—
344C3×C4⋊C4—32no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—92no—
347C3×C22⋊C4—32no—
348C3×C22⋊C4—32no—
349C3×C22⋊C4—62no—
350C3×C22⋊C4—92no—
351C3×C22⋊C4—92no—
352C3×C22⋊C4—92no—
353#217—32no—
354#217—92no—
355#217—92no—
356(C2×D3)⋊C4—32no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—32no—
360(C2×D3)⋊C4—32no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—92no—
363(C2×D3)⋊C4—92no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—182no—
367(C2×D3)⋊C4D3212yescomplemented
368C4⋊Dic3—32no—
369C4⋊Dic3—92no—
370C4⋊Dic3—92no—
371C4⋊Dic3—92no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—182no—
376C4⋊Dic3—182no—
377C4⋊Dic3—181no—
378C4⋊Dic3—361no—
379C4⋊Dic3D3211yescharacteristic, complemented
380Dic3⋊C4—32no—
381Dic3⋊C4—92no—
382Dic3⋊C4—92no—
383Dic3⋊C4—92no—
384Dic3⋊C4—181no—
385Dic3⋊C4—181no—
386C22×C32—21no—
387C22×C32—22no—
388C22×C32—34no—
389C22×C32—41no—
390C22×C32—62no—
391C22×C32—62no—
392C22×C32C23×D311yescharacteristic
393C22×C32C23×D312yes—
394C2×C3⋊D3—22no—
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3C2×D1212yes—
398C2×C3⋊D3#23712yes—
399C2×C3⋊D3#23712yes—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—24no—
405C2×C3×D3—34no—
406C2×C3×D3—34no—
407C2×C3×D3—34no—
408C2×C3×D3—42no—
409C2×C3×D3—42no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—62no—
413C2×C3×D3—616no—
414C2×C3×D3—62no—
415C2×C3×D3—62no—
416C2×C3×D3—62no—
417C2×C3×D3—62no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—122no—
421C2×C3×D3—122no—
422C2×C3×D3—122no—
423C2×C3×D3C2×D1214yes—
424C2×C3×D3D3×D414yes—
425D32—28no—
426D32—128no—
427D32—124no—
428C32×C4—21no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—42no—
432C32×C4—42no—
433C32×C4—61no—
434C32×C4—61no—
435C32×C4—62no—
436C3⋊Dic3—21no—
437C3⋊Dic3—22no—
438C3⋊Dic3—61no—
439C3⋊Dic3—61no—
440C3⋊Dic3—62no—
441C3⋊Dic3—62no—
442C3⋊Dic3—122no—
443C3⋊Dic3—121no—
444C3⋊Dic3—121no—
445C3⋊Dic3—122no—
446C3⋊Dic3—241no—
447C3⋊Dic3—241no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—42no—
455C3×Dic3—62no—
456C3×Dic3—62no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3—122no—
460C22×D4—271no—
461C23×C4—271no—
462#123—92no—
463#123—272no—
464#123—272no—
465#123—272no—
466C2×C4⋊C4—271no—
467C2×C4⋊C4—271no—
468C2×C22⋊C4—91no—
469C2×C22⋊C4—271no—
470C2×C22⋊C4—271no—
471C33C2×#12311yescharacteristic, complemented, Sylow
472C23×C3—32no—
473C23×C3—32no—
474C23×C3—62no—
475C23×C3—94no—
476C23×C3—91no—
477C23×C3—92no—
478C23×C3—182no—
479C23×C3—182no—
480C22×D3—32no—
481C22×D3—38no—
482C22×D3—32no—
483C22×D3—32no—
484C22×D3—61no—
485C22×D3—62no—
486C22×D3—64no—
487C22×D3—64no—
488C22×D3—184no—
489C22×D3—184no—
490C22×D3—184no—
491C22×D3—182no—
492C22×D3—182no—
493C22×D3—182no—
494C22×D3C2×D3212yes—
495C3×D4—184no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—62no—
506C2×C3×C4—92no—
507C2×C3×C4—91no—
508C2×C3×C4—182no—
509C2×C3×C4—182no—
510C2×C3×C4—184no—
511C2×C3×C4C2×D3211yescharacteristic
512C2×C3×C4C2×D3212yes—
513#67—64no—
514#67—184no—
515#67—184no—
516#67—184no—
517#67—364no—
518C2×Dic3—32no—
519C2×Dic3—32no—
520C2×Dic3—32no—
521C2×Dic3—61no—
522C2×Dic3—62no—
523C2×Dic3—64no—
524C2×Dic3—92no—
525C2×Dic3—92no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—181no—
529C2×Dic3—181no—
530C2×Dic3—182no—
531C2×Dic3—182no—
532C2×Dic3—182no—
533C2×Dic3—182no—
534C2×Dic3—182no—
535C2×Dic3—184no—
536C2×Dic3—184no—
537C2×Dic3—361no—
538C2×Dic3—361no—
539C2×Dic3—364no—
540C2×Dic3C2×D3212yes—
541C2×Dic3C2×D3211yescharacteristic
542C2×Dic3C2×D3211yescharacteristic
543D12—64no—
544C4×D3—64no—
545C4×D3—64no—
546C4×D3—64no—
547C4×D3—64no—
548C4×D3—184no—
549C4×D3—184no—
550C4×D3—184no—
551C4×D3—184no—
552C4×D3—362no—
553C4×D3—362no—
554C2×C32—22no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—22no—
558C2×C32—22no—
559C2×C32—21no—
560C2×C32—41no—
561C2×C32—41no—
562C2×C32—41no—
563C2×C32—64no—
564C2×C32C22×D1211yescharacteristic
565C2×C32C2×D3×D412yes—
566C2×C32C2×#23711yescharacteristic
567C2×C32C2×#23711yescharacteristic
568C2×C32D3×#4112yes—
569C2×C32D3×#4112yes—
570C3⋊D3—42no—
571C3⋊D3#88614yescomplemented
572C3×D3—24no—
573C3×D3—24no—
574C3×D3—38no—
575C3×D3—44no—
576C3×D3—64no—
577C3×D3—122no—
578C3×D3—122no—
579C3×D3—242no—
580C24—91no—
581C24—271no—
582C2×D4—92no—
583C2×D4—272no—
584C2×D4—544no—
585C22×C4—91no—
586C22×C4—92no—
587C22×C4—91no—
588C22×C4—271no—
589C22×C4—271no—
590C22×C4—271no—
591C22×C4—272no—
592C22×C4—544no—
593C4⋊C4—31no—
594C4⋊C4—92no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C4⋊C4—272no—
598C4⋊C4—271no—
599C22⋊C4—32no—
600C22⋊C4—92no—
601C22⋊C4—92no—
602C22⋊C4—92no—
603C22⋊C4—272no—
604C22⋊C4—272no—
605C22×C3—21no—
606C22×C3—22no—
607C22×C3—34no—
608C22×C3—34no—
609C22×C3—41no—
610C22×C3—64no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—62no—
615C22×C3—92no—
616C22×C3—92no—
617C22×C3—92no—
618C22×C3—122no—
619C22×C3—122no—
620C22×C3—188no—
621C22×C3—182no—
622C22×C3—182no—
623C22×C3—182no—
624C22×C3C22×D3212yes—
625C22×C3C22×D3211yescharacteristic
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—34no—
629C2×D3—34no—
630C2×D3—34no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—616no—
635C2×D3—62no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—62no—
641C2×D3—122no—
642C2×D3—122no—
643C2×D3—122no—
644C2×D3—368no—
645C2×D3—364no—
646C2×D3D3×D1214yes—
647C3×C4—22no—
648C3×C4—21no—
649C3×C4—22no—
650C3×C4—42no—
651C3×C4—42no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—122no—
659C3×C4—182no—
660C3×C4—181no—
661Dic3—21no—
662Dic3—21no—
663Dic3—22no—
664Dic3—62no—
665Dic3—62no—
666Dic3—62no—
667Dic3—62no—
668Dic3—122no—
669Dic3—182no—
670Dic3—182no—
671Dic3—181no—
672Dic3—181no—
673Dic3—361no—
674Dic3—361no—
675Dic3—362no—
676Dic3—362no—
677Dic3—721no—
678Dic3—721no—
679C32—21no—
680C32—22no—
681C32—41no—
682C32C2×#88611yescharacteristic, complemented
683C32D3×#12312yescomplemented
684C23—32no—
685C23—94no—
686C23—91no—
687C23—92no—
688C23—182no—
689C23—182no—
690C23—542no—
691C23—542no—
692C23—542no—
693D4—184no—
694D4—544no—
695C2×C4—32no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—91no—
699C2×C4—92no—
700C2×C4—182no—
701C2×C4—182no—
702C2×C4—184no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—542no—
706C2×C4—542no—
707C2×C4—542no—
708C2×C4—544no—
709C2×C4D3311yescharacteristic
710C2×C3—22no—
711C2×C3—21no—
712C2×C3—22no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—22no—
716C2×C3—41no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—64no—
720C2×C3—64no—
721C2×C3—94no—
722C2×C3—124no—
723C2×C3—362no—
724C2×C3C2×D3×D1212yes—
725C2×C3#6430611yescharacteristic
726C2×C3D32×D411yescharacteristic
727C2×C3D3×#23712yes—
728C2×C3D3×#23712yes—
729C2×C3#6431911yescharacteristic
730D3—24no—
731D3—38no—
732D3—64no—
733D3—122no—
734D3—122no—
735D3—242no—
736C22—34no—
737C22—62no—
738C22—62no—
739C22—92no—
740C22—92no—
741C22—92no—
742C22—188no—
743C22—182no—
744C22—182no—
745C22—182no—
746C22—1084no—
747C22C2×D3311yescharacteristic
748C4—21no—
749C4—62no—
750C4—61no—
751C4—61no—
752C4—182no—
753C4—181no—
754C4—541no—
755C4—541no—
756C3—21no—
757C3—22no—
758C3—41no—
759C3D3×#88612yescomplemented
760C3#1059460811yescharacteristic, complemented
761C2—64no—
762C2—94no—
763C2—362no—
764C2#1172437411yescharacteristic
765C2D32×D1211yescharacteristic
766C2#1172440711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#88953C2
hypercenterC2×C4D33
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D32×Dic3C2semidirect
3. #11723700C2semidirect
4. C3⋊D3×C4⋊Dic3C2semidirect
5. #11723480C2semidirect
6. C3×#63921C2semidirect
7. C3×#63890C2semidirect
8. #11722990C2semidirect
9. #11722988C2semidirect
10. #11722908C2semidirect
11. #11722905C2semidirect
21. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×D3×Dic3C22semidirect
27. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
28. C3×#3752C22semidirect
29. C32×(C2×D3)⋊C4C22semidirect
30. C32×C4⋊Dic3C22semidirect
31. #88814C22semidirect
32. #88807C22semidirect
33. #88807C22semidirect
34. Dic3⋊(C3⋊Dic3)C22semidirect
35. #88803C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
52. #63921D3semidirect
61. #63890D3semidirect
127. C2×D3×Dic3C2×D3semidirect
133. #3752C2×D3semidirect
150. C3×(C2×D3)⋊C4C2×D3semidirect
151. C3×(C2×D3)⋊C4C2×D3semidirect
154. C3×C4⋊Dic3C2×D3semidirect
163. Dic3⋊Dic3C2×D3semidirect
165. #3722C2×D3semidirect
171. (C2×D3)⋊Dic3C2×D3semidirect
307. C3×C3⋊D3#123semidirect
367. (C2×D3)⋊C4D32semidirect
379. C4⋊Dic3D32semidirect
471. C33C2×#123semidirect
571. C3⋊D3#886semidirect
682. C32C2×#886semidirect
683. C32D3×#123semidirect
759. C3D3×#886semidirect
760. C3#10594608semidirect

Maximal subgroups

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

subgroupindex
C2×#889532
C2×D32×Dic32
#117237002
C3⋊D3×C4⋊Dic32
#117234802
C3×#639212
C3×#638902
#117229902
#117229882
#117229082
#117229052
#105946083
D3×#8863