Finite Group Databasebeta

← #13168154

Subgroups — #13168154

Order 1728.

1458 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3796C211yesmaximal, characteristic
2#11723673C211yesmaximal, characteristic, complemented
3C3⋊D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4D12×C3⋊Dic3C211yesmaximal, characteristic, complemented
5Dic6×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63898C211yesmaximal, characteristic, complemented
7C3×#63843C211yesmaximal, characteristic, complemented
8#11722929C212yesmaximal, complemented
9Dic3×#626C212yesmaximal, complemented
10#11722913C212yesmaximal, complemented
11D3×Dic3⋊Dic3C212yesmaximal, complemented
12#10595394—31nomaximal
13#10595222—31nomaximal
14#10594361—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C32×D12C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×Dic3×C3⋊D3C2212yes—
19C2×D3×C3⋊Dic3C2212yes—
20C2×C3×#626C2212yes—
21C2×C3×D3×Dic3C2212yes—
22C2×C3×D3×Dic3C2212yes—
23C3×#3796C418yescomplemented
24C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C32×C4⋊Dic3C2211yescharacteristic
28#88815C2211yescharacteristic
29#88815C2211yescharacteristic
30#88814C2211yescharacteristic
31#88814C2211yescharacteristic
32#88807C2212yes—
33Dic3⋊(C3⋊Dic3)C2212yes—
34(C2×D3)⋊(C3⋊Dic3)C2212yes—
35Dic3×C3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×Dic32C2212yes—
39C2×C3×#239—31no—
40C2×C3×#237—31no—
41C2×#3796D311yescharacteristic
42Q8×C3⋊Dic3—31no—
43D4×C3⋊Dic3—31no—
44C4⋊C4×C3⋊D3—31no—
45C3×Q8×Dic3—31no—
46C3×D4×Dic3—31no—
47C3×#893—31no—
48C3×#887—31no—
49#67⋊Dic3—32no—
50Dic3×#67—32no—
51C2×Dic3⋊Dic3—32no—
52#63955—32no—
53C4×#626—32no—
54#63898—32no—
55#63898D311yescharacteristic, complemented
56Dic3×D12—31no—
57Dic3×D12—31no—
58Dic3×D12—32no—
59Dic3×D12—61no—
60D3×C4⋊Dic3—32no—
61D3×C4⋊Dic3—31no—
62D3×C4⋊Dic3—31no—
63D3×C4⋊Dic3—61no—
64#63881—32no—
65#63877—32no—
66D3×Dic3⋊C4—32no—
67#63874—31no—
68#63855—31no—
69#63855—31no—
70#63855—32no—
71#63843D311yescharacteristic, complemented
72Dic3×Dic6—31no—
73Dic3×Dic6—31no—
74Dic3×Dic6—61no—
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C32×D3C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4×C3⋊D3C2×C414yescomplemented
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2312yes—
87C32×D12C2×C414yescomplemented
88C32×Dic6C2×C414yescomplemented
89Dic3×C3⋊D3—42no—
90D3×C3⋊Dic3—42no—
91C3×#626C2×C418yescomplemented
92C3×D3×Dic3—42no—
93C3×D3×Dic3C2×C418yescomplemented
94#5827—91no—
95#5574—91no—
96#5546—91no—
97C2×C32×Q8—31no—
98C2×C32×D4—31no—
99C22×C3⋊Dic3—32no—
100C2×C4×C3⋊D3—32no—
101C2×C4×C3⋊D3C2×D311yescharacteristic
102C2×C3×#67—32no—
103C22×C3×Dic3—32no—
104C22×C3×Dic3—32no—
105C3×#239—38no—
106C3×#237—38no—
107C2×C3×D12—21no—
108C2×C3×D12—32no—
109C2×C3×D12C2×D311yescharacteristic
110C2×C3×D12C2×D311yescharacteristic
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—32no—
115C2×C3×C4×D3—61no—
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2×D311yescharacteristic
118C2×C3×Dic6C2×D311yescharacteristic
119C2×#626C2×D312yes—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—62no—
125C2×D3×Dic3—62no—
126C2×D3×Dic3C2×D312yes—
127C2×D3×Dic3C2×D312yes—
128#3796Dic318yescomplemented
129C32×C4⋊C4—31no—
130#3757—32no—
131C4⋊(C3⋊Dic3)—31no—
132C4⋊(C3⋊Dic3)—31no—
133C4⋊(C3⋊Dic3)—31no—
134C4⋊(C3⋊Dic3)—32no—
135C4⋊(C3⋊Dic3)—61no—
136C4⋊(C3⋊Dic3)—61no—
137C4⋊(C3⋊Dic3)—61no—
138C4⋊(C3⋊Dic3)—121no—
139#3750—32no—
140C4×C3⋊Dic3—32no—
141C4×C3⋊Dic3C2×D311yescharacteristic
142C4×C3⋊Dic3C2×D311yescharacteristic
143C3×#217—32no—
144C3×(C2×D3)⋊C4—32no—
145C3×C4⋊Dic3—21no—
146C3×C4⋊Dic3—32no—
147C3×C4⋊Dic3C2×D311yescharacteristic
148C3×C4⋊Dic3C2×D311yescharacteristic
149C3×Dic3⋊C4—32no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—32no—
155C3×C4×Dic3—32no—
156C3×C4×Dic3—61no—
157C3×C4×Dic3—61no—
158#3724—31no—
159#3724—31no—
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—62no—
169Dic3⋊Dic3—62no—
170Dic3⋊Dic3C2×D312yes—
171#3722—31no—
172#3722—31no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179(C2×D3)⋊Dic3—62no—
180(C2×D3)⋊Dic3C2×D312yes—
181Dic32—32no—
182Dic32—32no—
183Dic32—62no—
184Dic32C2×D312yes—
185C22×C33C2411yescharacteristic
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—21no—
188C2×C3×C3⋊D3C22×C412yes—
189C2×C32×D3—22no—
190C2×C32×D3—22no—
191C2×C32×D3C22×C414yes—
192C33×C4C22×C412yes—
193C3⋊(C3⋊Dic3)—22no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—21no—
196C3×C3⋊Dic3—21no—
197C3×C3⋊Dic3—21no—
198C3×C3⋊Dic3C22×C412yes—
199C32×Dic3—22no—
200C32×Dic3C22×C414yes—
201C2×C3×#41—91no—
202C2×#239—31no—
203C2×#237—31no—
204C3×C4×Q8—91no—
205C3×C4×D4—91no—
206Q8×Dic3—31no—
207Q8×Dic3—91no—
208Q8×Dic3—91no—
209Q8×Dic3—181no—
210D4×Dic3—31no—
211D4×Dic3—92no—
212D4×Dic3—91no—
213D4×Dic3—91no—
214D4×Dic3—92no—
215D4×Dic3—181no—
216C4×#67—92no—
217#926—91no—
218#926—92no—
219C2×C4⋊Dic3—92no—
220C2×C4⋊Dic3—91no—
221C2×Dic3⋊C4—92no—
222#893—31no—
223#893—92no—
224D3×C4⋊C4—91no—
225D3×C4⋊C4—91no—
226D3×C4⋊C4—92no—
227D3×C4⋊C4—181no—
228#887—31no—
229#67⋊C4—92no—
230#877—92no—
231C4×D12—92no—
232C4×D12—91no—
233#872—91no—
234#872—91no—
235#872—92no—
236C4×Dic6—91no—
237C23×C32—32no—
238C22×C3⋊D3C22×D311yescharacteristic
239C22×C3×D3—22no—
240C22×C3×D3—31no—
241C22×C3×D3—31no—
242C22×C3×D3—61no—
243C22×C3×D3C22×D312yes—
244C22×C3×D3C22×D312yes—
245C32×Q8—34no—
246C32×D4—34no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—32no—
251C2×C32×C4—32no—
252C2×C32×C4—41no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C3⋊Dic3—32no—
257C2×C3⋊Dic3—32no—
258C2×C3⋊Dic3—32no—
259C2×C3⋊Dic3—62no—
260C2×C3⋊Dic3—62no—
261C2×C3⋊Dic3—62no—
262C2×C3⋊Dic3—122no—
263C2×C3⋊Dic3—122no—
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D311yescharacteristic
269C4×C3⋊D3—122no—
270C4×C3⋊D3C2×Dic314yescomplemented
271C3×#67—38no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—38no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—122no—
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D312yes—
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D312yes—
295C3×D12—24no—
296C3×D12—38no—
297C3×D12C4×D314yescomplemented
298C3×D12C2×Dic314yescomplemented
299C3×C4×D3—38no—
300C3×C4×D3—34no—
301C3×C4×D3—34no—
302C3×C4×D3—64no—
303C3×C4×D3—122no—
304C3×Dic6—24no—
305C3×Dic6C4×D314yescomplemented
306C3×Dic6C2×Dic314yescomplemented
307#626C2×Dic318yescomplemented
308D3×Dic3—42no—
309D3×Dic3—122no—
310D3×Dic3—122no—
311D3×Dic3—124no—
312D3×Dic3—122no—
313D3×Dic3—122no—
314D3×Dic3—124no—
315D3×Dic3C2×Dic318yescomplemented
316#520—271noSylow
317C2×C33C23×C411yescharacteristic
318C2×C33H(5,𝔽2)11yescharacteristic
319C2×C332−1+411yescharacteristic
320C3×C3⋊D3—22no—
321C32×D3—24no—
322C3×#41—98no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—61no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—92no—
330C22×C3×C4—92no—
331C22×C3×C4—92no—
332C22×C3×C4—91no—
333C2×#67—32no—
334C22×Dic3—32no—
335C22×Dic3—32no—
336C22×Dic3—92no—
337C22×Dic3—92no—
338C22×Dic3—92no—
339C22×Dic3—182no—
340#239—38no—
341#237—38no—
342C2×D12—32no—
343C2×D12D3211yescharacteristic
344C2×C4×D3—32no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—32no—
348C2×C4×D3—61no—
349C2×C4×D3—92no—
350C2×C4×D3—92no—
351C2×C4×D3—92no—
352C2×C4×D3—182no—
353C2×Dic6D3211yescharacteristic
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—92no—
358C3×C22⋊C4—92no—
359C3×C42—92no—
360C3×C42—91no—
361C3×C42—91no—
362#217—32no—
363#217—91no—
364#217—91no—
365#217—92no—
366#217—92no—
367#217—182no—
368(C2×D3)⋊C4—32no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—92no—
374C4⋊Dic3—32no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—92no—
378C4⋊Dic3—92no—
379C4⋊Dic3—91no—
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382C4⋊Dic3—92no—
383C4⋊Dic3—182no—
384C4⋊Dic3—181no—
385C4⋊Dic3—181no—
386C4⋊Dic3—181no—
387C4⋊Dic3—361no—
388C4⋊Dic3D3211yescharacteristic
389Dic3⋊C4—32no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—92no—
395Dic3⋊C4—92no—
396Dic3⋊C4—92no—
397Dic3⋊C4—182no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—32no—
403C4×Dic3—32no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—92no—
407C4×Dic3—92no—
408C4×Dic3—92no—
409C4×Dic3—182no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—34no—
414C22×C32—41no—
415C22×C32—62no—
416C22×C32—62no—
417C22×C32C23×D311yescharacteristic
418C22×C32C23×D311yescharacteristic
419C22×C32C23×D311yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3C22×Dic312yes—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—24no—
428C2×C3×D3—32no—
429C2×C3×D3—32no—
430C2×C3×D3—42no—
431C2×C3×D3—42no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C2×C3×D3C2×C4×D314yes—
440C2×C3×D3C22×Dic314yes—
441C32×C4—22no—
442C32×C4—22no—
443C32×C4—22no—
444C32×C4—34no—
445C32×C4—42no—
446C32×C4—62no—
447C32×C4C2×C4×D312yes—
448C32×C4C2×C4×D312yes—
449C32×C4C22×Dic312yes—
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—21no—
453C3⋊Dic3—21no—
454C3⋊Dic3—62no—
455C3⋊Dic3—62no—
456C3⋊Dic3—62no—
457C3⋊Dic3—122no—
458C3⋊Dic3—122no—
459C3⋊Dic3—122no—
460C3⋊Dic3—242no—
461C3⋊Dic3C22×Dic312yes—
462C3×Dic3—22no—
463C3×Dic3—22no—
464C3×Dic3—24no—
465C3×Dic3—32no—
466C3×Dic3—32no—
467C3×Dic3—42no—
468C3×Dic3—62no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C3×Dic3—61no—
476C3×Dic3—61no—
477C3×Dic3—61no—
478C3×Dic3—61no—
479C3×Dic3—121no—
480C3×Dic3—121no—
481C3×Dic3C2×C4×D314yes—
482C3×Dic3C22×Dic314yes—
483C2×#41—91no—
484C4×Q8—91no—
485C4×Q8—271no—
486C4×D4—91no—
487C4×D4—272no—
488C4×D4—271no—
489C4×D4—272no—
490#117—271no—
491#117—272no—
492C2×C4⋊C4—271no—
493C2×C4⋊C4—272no—
494C33#52011yescharacteristic, complemented, Sylow
495C23×C3—32no—
496C23×C3—32no—
497C23×C3—62no—
498C23×C3—91no—
499C22×D3—31no—
500C22×D3—31no—
501C22×D3—61no—
502C22×D3C2×D3212yes—
503C3×Q8—34no—
504C3×Q8—34no—
505C3×Q8—64no—
506C3×D4—34no—
507C3×D4—34no—
508C3×D4—64no—
509C3×D4—98no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—41no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—98no—
521C2×C3×C4—91no—
522C2×C3×C4—94no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—91no—
526C2×C3×C4—91no—
527C2×C3×C4—362no—
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C2×D3211yescharacteristic
530C2×C3×C4C2×D3211yescharacteristic
531#67—38no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—38no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—92no—
549C2×Dic3—92no—
550C2×Dic3—92no—
551C2×Dic3—122no—
552C2×Dic3—182no—
553C2×Dic3—182no—
554C2×Dic3—182no—
555C2×Dic3—362no—
556C2×Dic3—362no—
557C2×Dic3—362no—
558C2×Dic3—362no—
559C2×Dic3—364no—
560C2×Dic3C2×D3212yes—
561C2×Dic3C2×D3212yes—
562D12—38no—
563D12D3×Dic314yescomplemented
564C4×D3—38no—
565C4×D3—34no—
566C4×D3—34no—
567C4×D3—64no—
568C4×D3—122no—
569C4×D3—362no—
570C4×D3—362no—
571C4×D3—362no—
572C4×D3—364no—
573Dic6D3×Dic314yescomplemented
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32—41no—
586C2×C32—64no—
587C2×C32C22×C4×D311yescharacteristic
588C2×C32C22×C4×D311yescharacteristic
589C2×C32#100411yescharacteristic
590C2×C32#100711yescharacteristic
591C2×C32#100911yescharacteristic
592C2×C32#100911yescharacteristic
593C2×C32#101011yescharacteristic
594C2×C32#101011yescharacteristic
595C2×C32C23×Dic311yescharacteristic
596C3⋊D3—22no—
597C3×D3—24no—
598C3×D3—24no—
599C3×D3—44no—
600C3×D3—64no—
601C3×D3—62no—
602C3×D3—62no—
603#41—98no—
604C2×Q8—31no—
605C2×D4—31no—
606C2×D4—92no—
607C22×C4—92no—
608C22×C4—92no—
609C22×C4—91no—
610C22×C4—272no—
611C22×C4—272no—
612C4⋊C4—31no—
613C4⋊C4—92no—
614C4⋊C4—272no—
615C4⋊C4—272no—
616C4⋊C4—271no—
617C4⋊C4—271no—
618C4⋊C4—271no—
619C22⋊C4—92no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—272no—
623C42—92no—
624C42—91no—
625C42—91no—
626C42—272no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—34no—
631C22×C3—34no—
632C22×C3—41no—
633C22×C3—64no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—92no—
639C22×C3—122no—
640C22×C3—122no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3C22×D3211yescharacteristic
644C22×C3C22×D3211yescharacteristic
645C22×C3C22×D3211yescharacteristic
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—32no—
649C2×D3—32no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3C2×D3×Dic314yes—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—34no—
662C3×C4—34no—
663C3×C4—42no—
664C3×C4—64no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—92no—
668C3×C4—122no—
669C3×C4—181no—
670C3×C4—181no—
671C3×C4—181no—
672C3×C4—181no—
673C3×C4C4×D3212yes—
674C3×C4C2×D3×Dic312yes—
675C3×C4C2×D3×Dic312yes—
676Dic3—22no—
677Dic3—32no—
678Dic3—32no—
679Dic3—62no—
680Dic3—62no—
681Dic3—62no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—121no—
691Dic3—121no—
692Dic3—182no—
693Dic3—182no—
694Dic3—182no—
695Dic3—362no—
696Dic3—362no—
697Dic3—362no—
698Dic3—722no—
699Dic3C2×D3×Dic314yes—
700C32—21no—
701C32—21no—
702C32—21no—
703C32—41no—
704C32#554611yescharacteristic, complemented
705C32#557411yescharacteristic, complemented
706C32#582711yescharacteristic, complemented
707C23—32no—
708C23—91no—
709Q8—34no—
710D4—34no—
711D4—98no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—98no—
715C2×C4—91no—
716C2×C4—94no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—272no—
722C2×C4—362no—
723C2×C4—1082no—
724C2×C4—1082no—
725C2×C4D3311yescharacteristic
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—41no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—64no—
739C2×C3—64no—
740C2×C3—124no—
741C2×C3—182no—
742C2×C3C2×C4×D3211yescharacteristic
743C2×C3#6430911yescharacteristic
744C2×C3#6431411yescharacteristic
745C2×C3#6431411yescharacteristic
746C2×C3#6431511yescharacteristic
747C2×C3#6431511yescharacteristic
748C2×C3#6432011yescharacteristic
749C2×C3C22×D3×Dic311yescharacteristic
750C2×C3C22×D3×Dic311yescharacteristic
751D3—24no—
752D3—64no—
753D3—62no—
754D3—62no—
755C22—34no—
756C22—62no—
757C22—62no—
758C22—92no—
759C22—181no—
760C22—181no—
761C22C2×D3311yescharacteristic
762C4—34no—
763C4—62no—
764C4—92no—
765C4—181no—
766C4—181no—
767C4—181no—
768C4—181no—
769C4—542no—
770C4D32×Dic312yes—
771C3—21no—
772C3—21no—
773C3—21no—
774C3—41no—
775C3#1059436111yescharacteristic, complemented
776C3#1059522211yescharacteristic, complemented
777C3#1059539411yescharacteristic, complemented
778C2—64no—
779C2—182no—
780C2#1172438611yescharacteristic
781C2#1172439411yescharacteristic
782C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3796C2
hypercenterC2×C4D33
hypocenterC33#520
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723673C2semidirect
3. C3⋊D3×C4⋊Dic3C2semidirect
4. D12×C3⋊Dic3C2semidirect
5. Dic6×C3⋊Dic3C2semidirect
6. C3×#63898C2semidirect
7. C3×#63843C2semidirect
8. #11722929C2semidirect
9. Dic3×#626C2semidirect
10. #11722913C2semidirect
11. D3×Dic3⋊Dic3C2semidirect
23. C3×#3796C4semidirect
55. #63898D3semidirect
71. #63843D3semidirect
84. C3×C4×C3⋊D3C2×C4semidirect
87. C32×D12C2×C4semidirect
88. C32×Dic6C2×C4semidirect
91. C3×#626C2×C4semidirect
93. C3×D3×Dic3C2×C4semidirect
128. #3796Dic3semidirect
270. C4×C3⋊D3C2×Dic3semidirect
297. C3×D12C4×D3semidirect
298. C3×D12C2×Dic3semidirect
305. C3×Dic6C4×D3semidirect
306. C3×Dic6C2×Dic3semidirect
307. #626C2×Dic3semidirect
315. D3×Dic3C2×Dic3semidirect
494. C33#520semidirect
563. D12D3×Dic3semidirect
573. Dic6D3×Dic3semidirect
704. C32#5546semidirect
705. C32#5574semidirect
706. C32#5827semidirect
775. C3#10594361semidirect
776. C3#10595222semidirect
777. C3#10595394semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37962
#117236732
C3⋊D3×C4⋊Dic32
D12×C3⋊Dic32
Dic6×C3⋊Dic32
C3×#638982
C3×#638432
#117229292
Dic3×#6262
#117229132
D3×Dic3⋊Dic32
#105953943
#105952223
#105943613