Finite Group Databasebeta

← Dic3×#3799 #13168692

Subgroups — Dic3×#3799 #13168692

Order 1728.

1506 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3799C211yesmaximal, characteristic
2#11723691C211yesmaximal, characteristic, complemented
3Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#11723424C211yesmaximal, characteristic, complemented
5Dic6×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×C4×D3×Dic3C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11722927C212yesmaximal, complemented
9Dic3×#626C212yesmaximal, complemented
10#11722915C212yesmaximal, complemented
11Dic3×#624C212yesmaximal, complemented
12Dic3×#239—31nomaximal
13Dic3×#235—31nomaximal
14C4×#3799—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6294C2212yes—
19C2×Dic3×C3⋊D3C2212yes—
20C2×C3×#626C2212yes—
21C2×C3×#624C2212yes—
22C2×C3×D3×Dic3C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C3×#3799C418yescomplemented
25C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29#88814C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31#88803C2212yes—
32(C2×D3)⋊(C3⋊Dic3)C2212yes—
33Dic3×C3⋊Dic3C2212yes—
34Dic3×C3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic32C2211yescharacteristic
37C3×Dic32C2212yes—
38C3×Dic32C2211yescharacteristic
39C2×C3×#239—31no—
40C2×C3×#235—31no—
41C2×#3799D311yescharacteristic
42Q8×C3⋊Dic3—31no—
43#64135—31no—
44C4×C4⋊(C3⋊D3)—31no—
45C3×Q8×Dic3—31no—
46C2×C3×C4×Dic3—31no—
47C3×C42×D3—31no—
48C3×C4×Dic6—31no—
49Dic3×#67—32no—
50Dic3×#67—32no—
51#63904—32no—
52C4×#626—32no—
53#63898—32no—
54#63898—31no—
55#63894—31no—
56Dic3×D12—32no—
57Dic3×D12—31no—
58Dic3×D12—31no—
59Dic3×D12—31no—
60Dic3×D12—61no—
61C4×#624—32no—
62C4×D3×Dic3—32no—
63C4×D3×Dic3—32no—
64C4×D3×Dic3D311yescharacteristic, complemented
65#63855—32no—
66Dic3×Dic6—31no—
67Dic3×Dic6—31no—
68Dic3×Dic6—61no—
69Dic3×Dic6D311yescharacteristic, complemented
70#63841—31no—
71#63841—31no—
72#63841—32no—
73#63841—61no—
74#63836—32no—
75C22×C3×C3⋊D3C2312yes—
76C22×C32×D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4⋊(C3⋊D3)C2×C414yescomplemented
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3C2×C414yescomplemented
88C32×Dic6C2×C414yescomplemented
89#6294—24no—
90Dic3×C3⋊D3—24no—
91C3×#626C2×C418yescomplemented
92C3×#624C2×C418yescomplemented
93C3×D3×Dic3—22no—
94C3×D3×Dic3—22no—
95Dic3×#41—91no—
96C4×#239—91no—
97C4×#235—91no—
98C2×C32×Q8—31no—
99C22×C32×C4—31no—
100C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
101C2×C4×C3⋊D3—32no—
102C2×C3×#67—32no—
103C22×C3×Dic3—31no—
104C22×C3×Dic3—31no—
105C3×#239—38no—
106C3×#235—38no—
107C2×C3×D12—32no—
108C2×C3×D12—31no—
109C2×C3×D12—31no—
110C2×C3×D12—61no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3C2×D311yescharacteristic
117C2×C3×C4×D3C2×D311yescharacteristic
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2×D311yescharacteristic
120C2×C3×Dic6C2×D311yescharacteristic
121C2×#626C2×D312yes—
122C2×#624—32no—
123C2×#624C2×D312yes—
124C2×D3×Dic3—32no—
125C2×D3×Dic3—32no—
126C2×D3×Dic3—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—62no—
129C2×D3×Dic3C2×D311yescharacteristic
130C2×D3×Dic3C2×D311yescharacteristic
131#3799Dic318yesdirect product factor
132C32×C42—31no—
133#3757—32no—
134#3752—32no—
135C4⋊(C3⋊Dic3)—31no—
136C4⋊(C3⋊Dic3)—31no—
137C4⋊(C3⋊Dic3)—31no—
138C4⋊(C3⋊Dic3)—32no—
139C4⋊(C3⋊Dic3)—61no—
140C4⋊(C3⋊Dic3)—61no—
141C4⋊(C3⋊Dic3)—61no—
142C4⋊(C3⋊Dic3)—121no—
143C4⋊(C3⋊Dic3)C2×D311yescharacteristic
144C4×C3⋊Dic3—32no—
145C4×C3⋊Dic3—32no—
146C4×C3⋊Dic3C2×D311yescharacteristic
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—32no—
150C3×C4⋊Dic3—61no—
151C3×Dic3⋊C4—32no—
152C3×C4×Dic3—21no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—31no—
156C3×C4×Dic3—31no—
157C3×C4×Dic3—32no—
158C3×C4×Dic3—31no—
159C3×C4×Dic3—31no—
160C3×C4×Dic3—32no—
161C3×C4×Dic3—61no—
162C3×C4×Dic3C2×D311yescharacteristic
163C3×C4×Dic3C2×D311yescharacteristic
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—62no—
167Dic3⋊Dic3C2×D312yes—
168#3722—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—62no—
176(C2×D3)⋊Dic3—62no—
177Dic32—32no—
178Dic32—32no—
179Dic32—32no—
180Dic32—32no—
181Dic32—62no—
182Dic32—62no—
183Dic32C2×D311yescharacteristic
184Dic32C2×D312yes—
185Dic32C2×D311yescharacteristic
186C22×C33C2411yescharacteristic
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—22no—
189C2×C3×C3⋊D3C22×C414yes—
190C2×C32×D3—21no—
191C2×C32×D3—21no—
192C2×C32×D3C22×C412yes—
193C33×C4C22×C412yes—
194C3⋊(C3⋊Dic3)—22no—
195C3×C3⋊Dic3—21no—
196C3×C3⋊Dic3—22no—
197C3×C3⋊Dic3#4112yescomplemented
198C32×Dic3—21no—
199C32×Dic3C22×C412yes—
200C32×Dic3C22×C414yes—
201C32×Dic3#4112yescomplemented
202C2×C3×#41—91no—
203C2×#239—31no—
204C2×#235—31no—
205C3×C4×Q8—91no—
206C2×C3×C42—91no—
207Q8×Dic3—31no—
208Q8×Dic3—91no—
209Q8×Dic3—91no—
210Q8×Dic3—181no—
211D4×Dic3—91no—
212D4×Dic3—92no—
213D4×Dic3—92no—
214D4×Dic3—91no—
215C4×#67—92no—
216C4×#67—92no—
217#926—92no—
218#926—91no—
219#926—91no—
220#926—181no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—92no—
223#893—91no—
224#893—92no—
225#892—92no—
226#892—91no—
227C4×D12—91no—
228C4×D12—91no—
229C4×D12—91no—
230C4×D12—92no—
231C4×D12—181no—
232#872—92no—
233C42×D3—31no—
234C42×D3—92no—
235C42×D3—92no—
236C4×Dic6—31no—
237C4×Dic6—91no—
238C23×C32—31no—
239C22×C3⋊D3C22×D312yes—
240C22×C3×D3—21no—
241C22×C3×D3—32no—
242C22×C3×D3—32no—
243C22×C3×D3—62no—
244C22×C3×D3C22×D311yescharacteristic
245C22×C3×D3C22×D311yescharacteristic
246C32×Q8—34no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—31no—
251C2×C32×C4—31no—
252C2×C32×C4—32no—
253C2×C32×C4—34no—
254C2×C32×C4—31no—
255C2×C32×C4—41no—
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C3⋊Dic3—32no—
260C2×C3⋊Dic3—32no—
261C2×C3⋊Dic3—32no—
262C2×C3⋊Dic3—62no—
263C2×C3⋊Dic3—62no—
264C2×C3⋊Dic3—62no—
265C2×C3⋊Dic3—122no—
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D312yes—
268C2×C3⋊Dic3C22×D311yescharacteristic
269C4⋊(C3⋊D3)C2×Dic314yescomplemented
270C4×C3⋊D3—64no—
271C3×#67—38no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D312yes—
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D312yes—
295C3×D12—38no—
296C3×D12—34no—
297C3×D12—34no—
298C3×D12—64no—
299C3×C4×D3—24no—
300C3×C4×D3—38no—
301C3×C4×D3—38no—
302C3×C4×D3—62no—
303C3×C4×D3—62no—
304C3×C4×D3C4×D314yescomplemented
305C3×C4×D3C2×Dic314yescomplemented
306C3×Dic6—24no—
307C3×Dic6C4×D314yescomplemented
308C3×Dic6C2×Dic314yescomplemented
309#626C2×Dic318yescomplemented
310#624—64no—
311#624C2×Dic318yescomplemented
312D3×Dic3—22no—
313D3×Dic3—22no—
314D3×Dic3—64no—
315D3×Dic3—64no—
316D3×Dic3—64no—
317D3×Dic3—64no—
318D3×Dic3—124no—
319C4×#41—271noSylow
320C2×C33C23×C411yescharacteristic
321C2×C33C2×#4111yescharacteristic
322C2×C33C2×#4111yescharacteristic
323C3×C3⋊D3—24no—
324C32×D3—22no—
325C3×#41—98no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8—61no—
329C2×C3×D4—92no—
330C2×C3×D4—91no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4—92no—
335C22×C3×C4—91no—
336C22×C3×C4—91no—
337C2×#67—32no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—92no—
341C22×Dic3—92no—
342#239—38no—
343#235—38no—
344C2×D12—32no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—61no—
348C2×C4×D3—32no—
349C2×C4×D3—32no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—92no—
353C2×C4×D3—92no—
354C2×C4×D3—92no—
355C2×C4×D3—92no—
356C2×C4×D3—182no—
357C2×C4×D3D3211yescharacteristic
358C2×Dic6D3211yescharacteristic
359C3×C4⋊C4—92no—
360C3×C4⋊C4—91no—
361C3×C42—31no—
362C3×C42—31no—
363C3×C42—61no—
364C3×C42—91no—
365C3×C42—92no—
366C3×C42—91no—
367C3×C42—91no—
368#217—92no—
369#217—92no—
370#217—92no—
371#217—92no—
372#217—182no—
373(C2×D3)⋊C4—92no—
374(C2×D3)⋊C4—92no—
375(C2×D3)⋊C4—92no—
376(C2×D3)⋊C4—92no—
377(C2×D3)⋊C4—92no—
378(C2×D3)⋊C4—182no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—32no—
382C4⋊Dic3—61no—
383C4⋊Dic3—92no—
384C4⋊Dic3—92no—
385C4⋊Dic3—91no—
386C4⋊Dic3—91no—
387C4⋊Dic3—91no—
388C4⋊Dic3—182no—
389C4⋊Dic3—181no—
390C4⋊Dic3—181no—
391C4⋊Dic3—181no—
392C4⋊Dic3—361no—
393Dic3⋊C4—32no—
394Dic3⋊C4—92no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—32no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—32no—
403C4×Dic3—61no—
404C4×Dic3—92no—
405C4×Dic3—92no—
406C4×Dic3—92no—
407C4×Dic3—92no—
408C4×Dic3—92no—
409C4×Dic3—92no—
410C4×Dic3—182no—
411C4×Dic3—182no—
412C4×Dic3D3211yescharacteristic
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—32no—
417C22×C32—41no—
418C22×C32—61no—
419C22×C32—61no—
420C22×C32C23×D311yescharacteristic
421C22×C32C23×D311yescharacteristic
422C22×C32C23×D311yescharacteristic
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3C22×Dic314yes—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—22no—
431C2×C3×D3—34no—
432C2×C3×D3—34no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—64no—
436C2×C3×D3—62no—
437C2×C3×D3—62no—
438C2×C3×D3—62no—
439C2×C3×D3—62no—
440C2×C3×D3—122no—
441C2×C3×D3—122no—
442C2×C3×D3C2×C4×D312yes—
443C2×C3×D3C22×Dic312yes—
444C32×C4—22no—
445C32×C4—22no—
446C32×C4—22no—
447C32×C4—32no—
448C32×C4—34no—
449C32×C4—32no—
450C32×C4—42no—
451C32×C4—61no—
452C32×C4C2×C4×D312yes—
453C32×C4C2×C4×D312yes—
454C32×C4C22×Dic312yes—
455C3⋊Dic3—21no—
456C3⋊Dic3—22no—
457C3⋊Dic3—62no—
458C3⋊Dic3—62no—
459C3⋊Dic3—62no—
460C3⋊Dic3—122no—
461C3⋊Dic3—122no—
462C3⋊Dic3—122no—
463C3⋊Dic3—242no—
464C3⋊Dic3#23512yescomplemented
465C3×Dic3—21no—
466C3×Dic3—21no—
467C3×Dic3—22no—
468C3×Dic3—24no—
469C3×Dic3—22no—
470C3×Dic3—32no—
471C3×Dic3—32no—
472C3×Dic3—41no—
473C3×Dic3—62no—
474C3×Dic3—62no—
475C3×Dic3—61no—
476C3×Dic3—62no—
477C3×Dic3—61no—
478C3×Dic3—122no—
479C3×Dic3—121no—
480C3×Dic3C2×C4×D314yes—
481C3×Dic3C2×C4×D312yes—
482C3×Dic3#23512yescomplemented
483C3×Dic3#23912yescomplemented
484C3×Dic3C22×Dic312yes—
485C3×Dic3C22×Dic314yes—
486C2×#41—91no—
487C4×Q8—91no—
488C4×Q8—271no—
489C4×D4—271no—
490C4×D4—271no—
491C4×D4—272no—
492C4×D4—272no—
493#117—272no—
494#117—271no—
495C2×C42—91no—
496C2×C42—272no—
497C33C4×#4111yescharacteristic, complemented, Sylow
498C23×C3—31no—
499C23×C3—31no—
500C23×C3—61no—
501C23×C3—92no—
502C22×D3—32no—
503C22×D3—32no—
504C22×D3—62no—
505C22×D3C2×D3211yescharacteristic
506C3×Q8—34no—
507C3×Q8—34no—
508C3×Q8—64no—
509C3×D4—98no—
510C3×D4—94no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—32no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—32no—
520C2×C3×C4—34no—
521C2×C3×C4—34no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—64no—
526C2×C3×C4—61no—
527C2×C3×C4—62no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—98no—
531C2×C3×C4—91no—
532C2×C3×C4—92no—
533C2×C3×C4—91no—
534C2×C3×C4—182no—
535C2×C3×C4—182no—
536C2×C3×C4C2×D3211yescharacteristic
537C2×C3×C4C2×D3211yescharacteristic
538C2×C3×C4C2×D3211yescharacteristic
539#67—38no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—62no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—92no—
552C2×Dic3—92no—
553C2×Dic3—92no—
554C2×Dic3—182no—
555C2×Dic3—182no—
556C2×Dic3—182no—
557C2×Dic3—184no—
558C2×Dic3—184no—
559C2×Dic3—362no—
560C2×Dic3C2×D3211yescharacteristic
561C2×Dic3C2×D3211yescharacteristic
562C2×Dic3C2×D3211yescharacteristic
563C2×Dic3C2×D3212yes—
564D12—38no—
565D12—34no—
566D12—34no—
567D12—64no—
568C4×D3—38no—
569C4×D3—38no—
570C4×D3—62no—
571C4×D3—62no—
572C4×D3—184no—
573C4×D3—184no—
574C4×D3—184no—
575C4×D3—184no—
576C4×D3—364no—
577C4×D3D3×Dic314yescomplemented
578Dic6D3×Dic314yescomplemented
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—41no—
589C2×C32—41no—
590C2×C32—41no—
591C2×C32—62no—
592C2×C32C22×C4×D311yescharacteristic
593C2×C32C22×C4×D311yescharacteristic
594C2×C32C2×#23511yescharacteristic
595C2×C32C2×#23511yescharacteristic
596C2×C32C2×#23911yescharacteristic
597C2×C32D3×#4111yescharacteristic
598C2×C32D3×#4111yescharacteristic
599C2×C32D3×#4111yescharacteristic
600C2×C32C23×Dic311yescharacteristic
601C3⋊D3—24no—
602C3×D3—22no—
603C3×D3—22no—
604C3×D3—42no—
605C3×D3—64no—
606C3×D3—64no—
607C3×D3—124no—
608#41—98no—
609C2×Q8—31no—
610C2×D4—92no—
611C2×D4—91no—
612C22×C4—31no—
613C22×C4—92no—
614C22×C4—91no—
615C22×C4—91no—
616C22×C4—272no—
617C22×C4—272no—
618C4⋊C4—92no—
619C4⋊C4—91no—
620C4⋊C4—272no—
621C4⋊C4—271no—
622C22⋊C4—272no—
623C22⋊C4—272no—
624C22⋊C4—272no—
625C42—31no—
626C42—91no—
627C42—91no—
628C42—92no—
629C42—91no—
630C42—272no—
631C42—272no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—32no—
637C22×C3—41no—
638C22×C3—62no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—94no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—182no—
647C22×C3—182no—
648C22×C3C22×D3211yescharacteristic
649C22×C3C22×D3211yescharacteristic
650C22×C3C22×D3211yescharacteristic
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—34no—
654C2×D3—34no—
655C2×D3—64no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—122no—
661C2×D3—122no—
662C2×D3C2×D3×Dic312yes—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—32no—
667C3×C4—34no—
668C3×C4—32no—
669C3×C4—32no—
670C3×C4—32no—
671C3×C4—34no—
672C3×C4—42no—
673C3×C4—62no—
674C3×C4—62no—
675C3×C4—64no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—92no—
679C3×C4—121no—
680C3×C4—182no—
681C3×C4—181no—
682C3×C4C4×D3212yes—
683C3×C4C2×D3×Dic312yes—
684C3×C4C2×D3×Dic312yes—
685Dic3—21no—
686Dic3—32no—
687Dic3—32no—
688Dic3—62no—
689Dic3—61no—
690Dic3—61no—
691Dic3—62no—
692Dic3—62no—
693Dic3—121no—
694Dic3—122no—
695Dic3—182no—
696Dic3—182no—
697Dic3—182no—
698Dic3—362no—
699Dic3—362no—
700Dic3—362no—
701Dic3—722no—
702Dic3#379912yesdirect product factor
703Dic3C2×D3×Dic314yes—
704Dic3C2×D3×Dic312yes—
705C32—21no—
706C32—21no—
707C32—21no—
708C32—41no—
709C32C4×#23511yescharacteristic, complemented
710C32C4×#23911yescharacteristic, complemented
711C32Dic3×#4111yescharacteristic, complemented
712C23—31no—
713C23—92no—
714Q8—34no—
715D4—98no—
716D4—94no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—32no—
720C2×C4—34no—
721C2×C4—31no—
722C2×C4—98no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—92no—
726C2×C4—182no—
727C2×C4—182no—
728C2×C4—272no—
729C2×C4—544no—
730C2×C4—544no—
731C2×C4D3311yescharacteristic
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—41no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—62no—
745C2×C3—62no—
746C2×C3—122no—
747C2×C3—184no—
748C2×C3C2×#379911yescharacteristic
749C2×C3C2×C4×D3211yescharacteristic
750C2×C3D3×#23511yescharacteristic
751C2×C3D3×#23511yescharacteristic
752C2×C3D3×#23511yescharacteristic
753C2×C3D3×#23911yescharacteristic
754C2×C3#6431911yescharacteristic
755C2×C3C22×D3×Dic311yescharacteristic
756C2×C3C22×D3×Dic311yescharacteristic
757D3—22no—
758D3—64no—
759D3—64no—
760D3—124no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—94no—
765C22—182no—
766C22—182no—
767C22C2×D3311yescharacteristic
768C4—32no—
769C4—32no—
770C4—34no—
771C4—61no—
772C4—92no—
773C4—181no—
774C4—182no—
775C4—542no—
776C4D32×Dic312yes—
777C3—21no—
778C3—21no—
779C3—21no—
780C3—41no—
781C3C4×#379911yescharacteristic, complemented
782C3Dic3×#23511yescharacteristic, complemented
783C3Dic3×#23911yescharacteristic, complemented
784C2—62no—
785C2—184no—
786C2D3×#379911yescharacteristic
787C2#1172438911yescharacteristic
788C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3799C2
hypercenterC2×C4D33
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723691C2semidirect
3. Dic3×C4⋊(C3⋊D3)C2semidirect
4. #11723424C2semidirect
5. Dic6×C3⋊Dic3C2semidirect
6. C3×C4×D3×Dic3C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11722927C2semidirect
9. Dic3×#626C2semidirect
10. #11722915C2semidirect
11. Dic3×#624C2semidirect
24. C3×#3799C4semidirect
64. C4×D3×Dic3D3semidirect
69. Dic3×Dic6D3semidirect
82. C3×C4⋊(C3⋊D3)C2×C4semidirect
87. C32×C4×D3C2×C4semidirect
88. C32×Dic6C2×C4semidirect
91. C3×#626C2×C4semidirect
92. C3×#624C2×C4semidirect
131. #3799Dic3direct (N × H)
197. C3×C3⋊Dic3#41semidirect
201. C32×Dic3#41semidirect
269. C4⋊(C3⋊D3)C2×Dic3semidirect
304. C3×C4×D3C4×D3semidirect
305. C3×C4×D3C2×Dic3semidirect
307. C3×Dic6C4×D3semidirect
308. C3×Dic6C2×Dic3semidirect
309. #626C2×Dic3semidirect
311. #624C2×Dic3semidirect
464. C3⋊Dic3#235semidirect
482. C3×Dic3#235semidirect
483. C3×Dic3#239semidirect
497. C33C4×#41semidirect
577. C4×D3D3×Dic3semidirect
578. Dic6D3×Dic3semidirect
702. Dic3#3799direct (N × H)
709. C32C4×#235semidirect
710. C32C4×#239semidirect
711. C32Dic3×#41semidirect
781. C3C4×#3799semidirect
782. C3Dic3×#235semidirect
783. C3Dic3×#239semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37992
#117236912
Dic3×C4⋊(C3⋊D3)2
#117234242
Dic6×C3⋊Dic32
C3×C4×D3×Dic32
C3×Dic3×Dic62
#117229272
Dic3×#6262
#117229152
Dic3×#6242
Dic3×#2393
Dic3×#2353
C4×#37993