Finite Group Databasebeta

← #13168688

Subgroups — #13168688

Order 1728.

1530 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3798C211yesmaximal, characteristic
2C4×#6294C211yesmaximal, characteristic, complemented
3C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723437C211yesmaximal, characteristic, complemented
5#11723423C211yesmaximal, characteristic, complemented
6C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
7C3×#63855C211yesmaximal, characteristic, complemented
8#11722940C212yesmaximal, complemented
9#11722928C212yesmaximal, complemented
10#11722927C212yesmaximal, complemented
11#11722924C212yesmaximal, complemented
12#10594958—31nomaximal
13Dic3×#235—31nomaximal
14#10593965—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6294C2212yes—
19C2×D3×C3⋊Dic3C2212yes—
20C2×C3×#627C2211yescharacteristic
21C2×C3×#626C2211yescharacteristic
22C2×C3×#626C2211yescharacteristic
23C2×C3×#625C2211yescharacteristic
24C2×C3×D3×Dic3C2212yes—
25C3×#3798C418yescomplemented
26C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C32×C4×Dic3C2211yescharacteristic
30#88813C2212yes—
31#88807C2212yes—
32Dic3⋊(C3⋊Dic3)C2212yes—
33#88803C2212yes—
34(C2×D3)⋊(C3⋊Dic3)C2212yes—
35Dic3×C3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×Dic32C2212yes—
39C2×C3×#235—31no—
40C2×C3×#235—31no—
41C2×#3798D311yescharacteristic
42#64135—31no—
43C2×C4×C3⋊Dic3—31no—
44#64081—31no—
45C3×#926—31no—
46C2×C3×C4×Dic3—31no—
47C3×#872—31no—
48C3×C42×D3—31no—
49#67⋊Dic3—32no—
50#67⋊Dic3—32no—
51Dic3×#67—32no—
52Dic3×#67—32no—
53#63904—32no—
54#63898—32no—
55Dic3×D12—32no—
56C4×#624—31no—
57#63880—32no—
58#63879—32no—
59C4×D3×Dic3—31no—
60C4×D3×Dic3—31no—
61C4×D3×Dic3—31no—
62C4×D3×Dic3—31no—
63C4×D3×Dic3—61no—
64C4×D3×Dic3D311yescharacteristic, complemented
65#63855—31no—
66#63855—31no—
67#63855—31no—
68#63855—31no—
69#63855—61no—
70#63855—61no—
71#63855D311yescharacteristic, complemented
72#63843—32no—
73Dic3×Dic6—32no—
74#63837—32no—
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C32×D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C2×C33×C4C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2312yes—
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C3×C4×C3⋊D3C2×C414yescomplemented
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3C2×C414yescomplemented
88C32×C4×D3C2×C414yescomplemented
89#6294—24no—
90D3×C3⋊Dic3—24no—
91C3×#627C2×C414yescomplemented
92C3×#626C2×C414yescomplemented
93C3×#626C2×C414yescomplemented
94C3×#625C2×C414yescomplemented
95C3×D3×Dic3—24no—
96Dic3×#41—91no—
97#5522—91no—
98C4×#235—91no—
99C22×C32×C4—31no—
100C22×C32×C4—31no—
101C22×C3⋊Dic3—32no—
102C2×C4×C3⋊D3C2×D311yescharacteristic
103C2×C3×#67—31no—
104C2×C3×#67—31no—
105C2×C3×#67—31no—
106C2×C3×#67—31no—
107C22×C3×Dic3—32no—
108C3×#235—38no—
109C3×#235—38no—
110C2×C3×D12—31no—
111C2×C3×D12—31no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3—61no—
118C2×C3×C4×D3C2×D311yescharacteristic
119C2×C3×C4×D3C2×D311yescharacteristic
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×C3×Dic6—31no—
123C2×C3×Dic6—31no—
124C2×#627C2×D311yescharacteristic
125C2×#626C2×D311yescharacteristic
126C2×#626C2×D311yescharacteristic
127C2×#625C2×D311yescharacteristic
128C2×#624—32no—
129C2×D3×Dic3—32no—
130C2×D3×Dic3—32no—
131C2×D3×Dic3—32no—
132C2×D3×Dic3—32no—
133C2×D3×Dic3—62no—
134C2×D3×Dic3C2×D312yes—
135#3798Dic318yescomplemented
136C32×C42—31no—
137#3757—32no—
138#3752—32no—
139C4⋊(C3⋊Dic3)—32no—
140#3750—32no—
141C4×C3⋊Dic3—31no—
142C4×C3⋊Dic3—31no—
143C4×C3⋊Dic3—31no—
144C4×C3⋊Dic3—32no—
145C4×C3⋊Dic3—61no—
146C4×C3⋊Dic3—61no—
147C4×C3⋊Dic3—61no—
148C4×C3⋊Dic3—121no—
149C4×C3⋊Dic3C2×D311yescharacteristic
150C4×C3⋊Dic3C2×D311yescharacteristic
151C3×#217—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×C4⋊Dic3—32no—
154C3×Dic3⋊C4—32no—
155C3×C4×Dic3—21no—
156C3×C4×Dic3—31no—
157C3×C4×Dic3—31no—
158C3×C4×Dic3—31no—
159C3×C4×Dic3—31no—
160C3×C4×Dic3—32no—
161C3×C4×Dic3—32no—
162C3×C4×Dic3—61no—
163C3×C4×Dic3—61no—
164C3×C4×Dic3C2×D311yescharacteristic
165C3×C4×Dic3C2×D311yescharacteristic
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—62no—
171Dic3⋊Dic3—62no—
172Dic3⋊Dic3C2×D312yes—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—62no—
178(C2×D3)⋊Dic3—62no—
179(C2×D3)⋊Dic3C2×D312yes—
180Dic32—32no—
181Dic32—32no—
182Dic32—32no—
183Dic32—32no—
184Dic32—32no—
185Dic32—62no—
186Dic32C2×D312yes—
187C22×C33C2411yescharacteristic
188C2×C3×C3⋊D3—22no—
189C2×C3×C3⋊D3C22×C412yes—
190C2×C32×D3—22no—
191C2×C32×D3—22no—
192C2×C32×D3C22×C412yes—
193C2×C32×D3C22×C412yes—
194C33×C4C22×C412yes—
195C3⋊(C3⋊Dic3)—22no—
196C3×C3⋊Dic3—22no—
197C3×C3⋊Dic3C22×C412yes—
198C3×C3⋊Dic3#4114yescomplemented
199C32×Dic3—22no—
200C32×Dic3C22×C412yes—
201C32×Dic3C22×C412yes—
202C2×C3×#41—91no—
203C2×#235—31no—
204C2×#235—31no—
205C3×#117—91no—
206C2×C3×C42—91no—
207Q8×Dic3—92no—
208D4×Dic3—92no—
209D4×Dic3—92no—
210D4×Dic3—92no—
211C4×#67—92no—
212C4×#67—92no—
213#926—31no—
214#926—91no—
215#926—91no—
216#926—91no—
217#926—181no—
218C2×C4×Dic3—31no—
219C2×C4×Dic3—91no—
220C2×C4×Dic3—91no—
221C2×C4×Dic3—91no—
222C2×C4×Dic3—181no—
223#893—92no—
224#887—92no—
225#67⋊C4—92no—
226#67⋊C4—92no—
227C4×D12—92no—
228#872—31no—
229#872—91no—
230#872—91no—
231#872—91no—
232#872—181no—
233C42×D3—31no—
234C42×D3—91no—
235C42×D3—91no—
236C42×D3—91no—
237C4×Dic6—92no—
238C23×C32—31no—
239C23×C32—31no—
240C22×C3⋊D3C22×D311yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—31no—
244C22×C3×D3—31no—
245C22×C3×D3—61no—
246C22×C3×D3C22×D311yescharacteristic
247C22×C3×D3C22×D311yescharacteristic
248C22×C3×D3C22×D311yescharacteristic
249C22×C3×D3C22×D311yescharacteristic
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—31no—
254C2×C32×C4—31no—
255C2×C32×C4—34no—
256C2×C32×C4—34no—
257C2×C32×C4—32no—
258C2×C32×C4—41no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—32no—
263C2×C3⋊Dic3—32no—
264C2×C3⋊Dic3—32no—
265C2×C3⋊Dic3—62no—
266C2×C3⋊Dic3—62no—
267C2×C3⋊Dic3—62no—
268C2×C3⋊Dic3—64no—
269C2×C3⋊Dic3—122no—
270C2×C3⋊Dic3C22×D312yes—
271C2×C3⋊Dic3C22×D312yes—
272C2×C3⋊Dic3C22×D311yescharacteristic
273C4×C3⋊D3C2×Dic314yescomplemented
274C3×#67—34no—
275C3×#67—34no—
276C3×#67—34no—
277C3×#67—34no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—62no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3—64no—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C3×D12—34no—
298C3×D12—34no—
299C3×C4×D3—24no—
300C3×C4×D3—24no—
301C3×C4×D3—34no—
302C3×C4×D3—34no—
303C3×C4×D3—64no—
304C3×C4×D3—64no—
305C3×C4×D3C4×D314yescomplemented
306C3×C4×D3C4×D314yescomplemented
307C3×C4×D3C2×Dic314yescomplemented
308C3×C4×D3C2×Dic314yescomplemented
309C3×Dic6—34no—
310C3×Dic6—34no—
311#627C2×Dic314yescomplemented
312#626C2×Dic314yescomplemented
313#626C2×Dic314yescomplemented
314#625C2×Dic314yescomplemented
315#624—64no—
316D3×Dic3—24no—
317D3×Dic3—64no—
318D3×Dic3—64no—
319D3×Dic3—64no—
320D3×Dic3—68no—
321D3×Dic3—64no—
322C4×#41—271noSylow
323C2×C33C23×C411yescharacteristic
324C2×C33C2×#4112yes—
325C3×C3⋊D3—22no—
326C32×D3—22no—
327C32×D3—22no—
328C3×#41—98no—
329C2×C3×Q8—91no—
330C2×C3×D4—91no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—92no—
340C22×C3×C4—91no—
341C2×#67—31no—
342C2×#67—31no—
343C2×#67—31no—
344C2×#67—31no—
345C22×Dic3—32no—
346C22×Dic3—92no—
347C22×Dic3—92no—
348C22×Dic3—92no—
349C22×Dic3—182no—
350#235—38no—
351#235—38no—
352C2×D12—31no—
353C2×D12—31no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—32no—
357C2×C4×D3—61no—
358C2×C4×D3—92no—
359C2×C4×D3—92no—
360C2×C4×D3—92no—
361C2×C4×D3D3211yescharacteristic
362C2×C4×D3D3211yescharacteristic
363C2×Dic6—31no—
364C2×Dic6—31no—
365C3×C4⋊C4—92no—
366C3×C22⋊C4—92no—
367C3×C42—31no—
368C3×C42—31no—
369C3×C42—61no—
370C3×C42—92no—
371C3×C42—91no—
372C3×C42—91no—
373#217—32no—
374#217—92no—
375#217—92no—
376#217—92no—
377#217—182no—
378(C2×D3)⋊C4—32no—
379(C2×D3)⋊C4—92no—
380(C2×D3)⋊C4—92no—
381(C2×D3)⋊C4—92no—
382(C2×D3)⋊C4—182no—
383C4⋊Dic3—32no—
384C4⋊Dic3—92no—
385C4⋊Dic3—92no—
386C4⋊Dic3—92no—
387C4⋊Dic3—182no—
388Dic3⋊C4—32no—
389Dic3⋊C4—92no—
390Dic3⋊C4—92no—
391Dic3⋊C4—92no—
392Dic3⋊C4—182no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—32no—
398C4×Dic3—32no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—92no—
402C4×Dic3—92no—
403C4×Dic3—92no—
404C4×Dic3—92no—
405C4×Dic3—92no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C4×Dic3—91no—
409C4×Dic3—92no—
410C4×Dic3—182no—
411C4×Dic3—181no—
412C4×Dic3—181no—
413C4×Dic3—181no—
414C4×Dic3—361no—
415C4×Dic3D3211yescharacteristic
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—32no—
420C22×C32—32no—
421C22×C32—41no—
422C22×C32—62no—
423C22×C32—62no—
424C22×C32C23×D311yescharacteristic
425C22×C32C23×D311yescharacteristic
426C22×C32C23×D311yescharacteristic
427C2×C3⋊D3—22no—
428C2×C3⋊D3C22×Dic312yes—
429C2×C3×D3—24no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—32no—
437C2×C3×D3—32no—
438C2×C3×D3—42no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—62no—
442C2×C3×D3—122no—
443C2×C3×D3C2×C4×D312yes—
444C2×C3×D3C2×C4×D312yes—
445C2×C3×D3C22×Dic312yes—
446C2×C3×D3C22×Dic312yes—
447C32×C4—22no—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—32no—
451C32×C4—32no—
452C32×C4—42no—
453C32×C4—62no—
454C32×C4C2×C4×D312yes—
455C32×C4C2×C4×D312yes—
456C32×C4C22×Dic312yes—
457C3⋊Dic3—22no—
458C3⋊Dic3—62no—
459C3⋊Dic3—64no—
460C3⋊Dic3—62no—
461C3⋊Dic3—62no—
462C3⋊Dic3—122no—
463C3⋊Dic3—122no—
464C3⋊Dic3—124no—
465C3⋊Dic3#23514yescomplemented
466C3⋊Dic3C22×Dic312yes—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—32no—
472C3×Dic3—32no—
473C3×Dic3—34no—
474C3×Dic3—34no—
475C3×Dic3—42no—
476C3×Dic3—62no—
477C3×Dic3—64no—
478C3×Dic3—62no—
479C3×Dic3—62no—
480C3×Dic3—122no—
481C3×Dic3C2×C4×D312yes—
482C3×Dic3C2×C4×D312yes—
483C3×Dic3C22×Dic312yes—
484C3×Dic3C22×Dic312yes—
485C2×#41—91no—
486C4×Q8—272no—
487C4×D4—272no—
488C4×D4—272no—
489C4×D4—272no—
490#117—91no—
491#117—271no—
492#117—271no—
493C2×C42—91no—
494C2×C42—271no—
495C2×C42—271no—
496C33C4×#4111yescharacteristic, complemented, Sylow
497C23×C3—31no—
498C23×C3—31no—
499C23×C3—31no—
500C23×C3—31no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—91no—
504C22×D3—31no—
505C22×D3—31no—
506C22×D3—61no—
507C22×D3C2×D3211yescharacteristic
508C22×D3C2×D3211yescharacteristic
509C3×Q8—94no—
510C3×D4—94no—
511C3×D4—94no—
512C3×D4—94no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—34no—
521C2×C3×C4—34no—
522C2×C3×C4—34no—
523C2×C3×C4—34no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—41no—
527C2×C3×C4—64no—
528C2×C3×C4—64no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—62no—
532C2×C3×C4—91no—
533C2×C3×C4—92no—
534C2×C3×C4—94no—
535C2×C3×C4—92no—
536C2×C3×C4—184no—
537C2×C3×C4C2×D3211yescharacteristic
538C2×C3×C4C2×D3211yescharacteristic
539C2×C3×C4C2×D3211yescharacteristic
540#67—34no—
541#67—34no—
542#67—34no—
543#67—34no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—32no—
549C2×Dic3—32no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—62no—
553C2×Dic3—64no—
554C2×Dic3—92no—
555C2×Dic3—92no—
556C2×Dic3—92no—
557C2×Dic3—182no—
558C2×Dic3—182no—
559C2×Dic3—182no—
560C2×Dic3—184no—
561C2×Dic3—184no—
562C2×Dic3—184no—
563C2×Dic3—188no—
564C2×Dic3—362no—
565C2×Dic3C2×D3212yes—
566C2×Dic3C2×D3211yescharacteristic
567C2×Dic3C2×D3211yescharacteristic
568D12—34no—
569D12—34no—
570C4×D3—34no—
571C4×D3—34no—
572C4×D3—64no—
573C4×D3—64no—
574C4×D3—184no—
575C4×D3—184no—
576C4×D3—184no—
577C4×D3D3×Dic314yescomplemented
578C4×D3D3×Dic314yescomplemented
579Dic6—34no—
580Dic6—34no—
581C2×C32—21no—
582C2×C32—22no—
583C2×C32—22no—
584C2×C32—22no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—41no—
588C2×C32—42no—
589C2×C32—62no—
590C2×C32—62no—
591C2×C32C22×C4×D311yescharacteristic
592C2×C32C22×C4×D311yescharacteristic
593C2×C32C2×#23512yes—
594C2×C32D3×#4112yes—
595C2×C32D3×#4112yes—
596C2×C32C23×Dic311yescharacteristic
597C3⋊D3—22no—
598C3×D3—24no—
599C3×D3—22no—
600C3×D3—22no—
601C3×D3—22no—
602C3×D3—22no—
603C3×D3—42no—
604C3×D3—62no—
605C3×D3—62no—
606C3×D3—122no—
607#41—98no—
608C2×Q8—91no—
609C2×D4—91no—
610C2×D4—91no—
611C2×D4—91no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—92no—
615C22×C4—91no—
616C22×C4—272no—
617C22×C4—272no—
618C4⋊C4—92no—
619C4⋊C4—272no—
620C4⋊C4—272no—
621C22⋊C4—92no—
622C22⋊C4—272no—
623C22⋊C4—272no—
624C42—31no—
625C42—92no—
626C42—91no—
627C42—91no—
628C42—272no—
629C42—272no—
630C42—271no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—32no—
636C22×C3—32no—
637C22×C3—32no—
638C22×C3—41no—
639C22×C3—62no—
640C22×C3—62no—
641C22×C3—64no—
642C22×C3—62no—
643C22×C3—62no—
644C22×C3—62no—
645C22×C3—62no—
646C22×C3—92no—
647C22×C3—122no—
648C22×C3—182no—
649C22×C3C22×D3211yescharacteristic
650C22×C3C22×D3211yescharacteristic
651C22×C3C22×D3211yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—32no—
655C2×D3—32no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—122no—
660C2×D3C2×D3×Dic312yes—
661C2×D3C2×D3×Dic312yes—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—32no—
666C3×C4—32no—
667C3×C4—32no—
668C3×C4—32no—
669C3×C4—42no—
670C3×C4—62no—
671C3×C4—62no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—92no—
675C3×C4—94no—
676C3×C4—122no—
677C3×C4—182no—
678C3×C4C4×D3212yes—
679C3×C4C2×D3×Dic312yes—
680C3×C4C2×D3×Dic312yes—
681Dic3—22no—
682Dic3—34no—
683Dic3—34no—
684Dic3—32no—
685Dic3—32no—
686Dic3—62no—
687Dic3—64no—
688Dic3—62no—
689Dic3—62no—
690Dic3—122no—
691Dic3—184no—
692Dic3—182no—
693Dic3—182no—
694Dic3—182no—
695Dic3—362no—
696Dic3—362no—
697Dic3—364no—
698Dic3C2×D3×Dic312yes—
699Dic3C2×D3×Dic312yes—
700C32—21no—
701C32—21no—
702C32—21no—
703C32—41no—
704C32C4×#23511yescharacteristic, complemented
705C32#552211yescharacteristic, complemented
706C32Dic3×#4111yescharacteristic, complemented
707C23—31no—
708C23—31no—
709C23—91no—
710Q8—94no—
711D4—94no—
712D4—94no—
713D4—94no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—34no—
717C2×C4—34no—
718C2×C4—32no—
719C2×C4—92no—
720C2×C4—91no—
721C2×C4—94no—
722C2×C4—92no—
723C2×C4—184no—
724C2×C4—272no—
725C2×C4—544no—
726C2×C4—544no—
727C2×C4D3311yescharacteristic
728C2×C3—22no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—42no—
735C2×C3—41no—
736C2×C3—64no—
737C2×C3—62no—
738C2×C3—62no—
739C2×C3—62no—
740C2×C3—62no—
741C2×C3—122no—
742C2×C3—182no—
743C2×C3C2×C4×D3211yescharacteristic
744C2×C3D3×#23512yes—
745C2×C3D3×#23512yes—
746C2×C3#6430612yes—
747C2×C3C22×D3×Dic311yescharacteristic
748C2×C3C22×D3×Dic311yescharacteristic
749D3—22no—
750D3—22no—
751D3—62no—
752D3—62no—
753D3—122no—
754C22—32no—
755C22—32no—
756C22—62no—
757C22—62no—
758C22—92no—
759C22—182no—
760C22C2×D3311yescharacteristic
761C4—32no—
762C4—32no—
763C4—62no—
764C4—94no—
765C4—92no—
766C4—182no—
767C4—542no—
768C4D32×Dic312yes—
769C3—21no—
770C3—21no—
771C3—21no—
772C3—41no—
773C3#1059396511yescharacteristic, complemented
774C3Dic3×#23511yescharacteristic, complemented
775C3#1059495811yescharacteristic, complemented
776C2—62no—
777C2—62no—
778C2—182no—
779C2#1172438712yes—
780C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, hypercenterC2×C4D33
commutatorC2×C33C23×C4
FrattiniC22C2×D33
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3798C2
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6294C2semidirect
3. C4×D3×C3⋊Dic3C2semidirect
4. #11723437C2semidirect
5. #11723423C2semidirect
6. C3×C4×D3×Dic3C2semidirect
7. C3×#63855C2semidirect
8. #11722940C2semidirect
9. #11722928C2semidirect
10. #11722927C2semidirect
11. #11722924C2semidirect
25. C3×#3798C4semidirect
64. C4×D3×Dic3D3semidirect
71. #63855D3semidirect
83. C3×C4×C3⋊D3C2×C4semidirect
87. C32×C4×D3C2×C4semidirect
88. C32×C4×D3C2×C4semidirect
91. C3×#627C2×C4semidirect
92. C3×#626C2×C4semidirect
93. C3×#626C2×C4semidirect
94. C3×#625C2×C4semidirect
135. #3798Dic3semidirect
198. C3×C3⋊Dic3#41semidirect
273. C4×C3⋊D3C2×Dic3semidirect
305. C3×C4×D3C4×D3semidirect
306. C3×C4×D3C4×D3semidirect
307. C3×C4×D3C2×Dic3semidirect
308. C3×C4×D3C2×Dic3semidirect
311. #627C2×Dic3semidirect
312. #626C2×Dic3semidirect
313. #626C2×Dic3semidirect
314. #625C2×Dic3semidirect
465. C3⋊Dic3#235semidirect
496. C33C4×#41semidirect
577. C4×D3D3×Dic3semidirect
578. C4×D3D3×Dic3semidirect
704. C32C4×#235semidirect
705. C32#5522semidirect
706. C32Dic3×#41semidirect
773. C3#10593965semidirect
774. C3Dic3×#235semidirect
775. C3#10594958semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37982
C4×#62942
C4×D3×C3⋊Dic32
#117234372
#117234232
C3×C4×D3×Dic32
C3×#638552
#117229402
#117229282
#117229272
#117229242
#105949583
Dic3×#2353
#105939653