Finite Group Databasebeta

← #13168694

Subgroups — #13168694

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×#3799C211yesmaximal, characteristic
2#11723691C211yesmaximal, characteristic, complemented
3Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5Dic6×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63855C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11722929C212yesmaximal, complemented
9#11722928C212yesmaximal, complemented
10#11722915C212yesmaximal, complemented
11#11722908C212yesmaximal, complemented
12#10595394—31nomaximal
13#10594992—31nomaximal
14#10593890—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6294C2212yes—
19C2×Dic3×C3⋊D3C2212yes—
20C2×D3×C3⋊Dic3C2212yes—
21C2×C3×#626C2212yes—
22C2×C3×#624C2212yes—
23C3×#3799C418yescomplemented
24C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88814C2212yes—
29Dic3⋊(C3⋊Dic3)C2212yes—
30Dic3⋊(C3⋊Dic3)C2212yes—
31#88803C2212yes—
32Dic3×C3⋊Dic3C2212yes—
33C3×Dic3⋊Dic3C2211yescharacteristic
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×Dic32C2212yes—
39C2×C3×#239—31no—
40C2×C3×#235—31no—
41C2×#3799D311yescharacteristic
42Q8×C3⋊Dic3—31no—
43C2×C4⋊(C3⋊Dic3)—31no—
44C4×C4⋊(C3⋊D3)—31no—
45C3×Q8×Dic3—31no—
46C3×#926—31no—
47C3×#872—31no—
48C3×C4×Dic6—31no—
49#67⋊Dic3—32no—
50#67⋊Dic3—32no—
51#63898—31no—
52#63898—32no—
53#63894—31no—
54Dic3×D12—31no—
55Dic3×D12—31no—
56Dic3×D12—31no—
57Dic3×D12—32no—
58Dic3×D12—61no—
59D3×C4⋊Dic3—31no—
60D3×C4⋊Dic3—31no—
61D3×C4⋊Dic3—32no—
62D3×C4⋊Dic3—32no—
63D3×C4⋊Dic3—61no—
64#63883—32no—
65#63881—32no—
66#63880—32no—
67#63855—32no—
68#63855D311yescharacteristic, complemented
69Dic3×Dic6—31no—
70Dic3×Dic6—31no—
71Dic3×Dic6—61no—
72Dic3×Dic6D311yescharacteristic, complemented
73#63841—32no—
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⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C3×C4⋊(C3⋊D3)C2×C414yescomplemented
83C2×C32×Dic3C2311yescharacteristic
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C32×C4×D3C2×C414yescomplemented
88C32×Dic6C2×C414yescomplemented
89#6294—42no—
90Dic3×C3⋊D3—42no—
91D3×C3⋊Dic3—42no—
92C3×#626C2×C418yescomplemented
93C3×#624C2×C418yescomplemented
94#5827—91no—
95#5574—91no—
96#5523—91no—
97C2×C32×Q8—31no—
98C22×C32×C4—31no—
99C22×C3⋊Dic3—32no—
100C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
101C2×C4×C3⋊D3—32no—
102C2×C3×#67—32no—
103C3×#239—38no—
104C3×#235—38no—
105C2×C3×D12—32no—
106C2×C3×D12—31no—
107C2×C3×D12—31no—
108C2×C3×D12—61no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3C2×D311yescharacteristic
113C2×C3×C4×D3C2×D311yescharacteristic
114C2×C3×Dic6—21no—
115C2×C3×Dic6C2×D311yescharacteristic
116C2×C3×Dic6C2×D311yescharacteristic
117C2×#626C2×D312yes—
118C2×#624—32no—
119C2×#624C2×D312yes—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—32no—
125C2×D3×Dic3—32no—
126C2×D3×Dic3—62no—
127C2×D3×Dic3—62no—
128#3799Dic318yescomplemented
129C32×C42—31no—
130#3752—32no—
131C4⋊(C3⋊Dic3)—31no—
132C4⋊(C3⋊Dic3)—31no—
133C4⋊(C3⋊Dic3)—31no—
134C4⋊(C3⋊Dic3)—32no—
135C4⋊(C3⋊Dic3)—32no—
136C4⋊(C3⋊Dic3)—61no—
137C4⋊(C3⋊Dic3)—61no—
138C4⋊(C3⋊Dic3)—61no—
139C4⋊(C3⋊Dic3)—121no—
140C4⋊(C3⋊Dic3)C2×D311yescharacteristic
141C4×C3⋊Dic3—32no—
142C4×C3⋊Dic3C2×D311yescharacteristic
143C3×#217—31no—
144C3×#217—31no—
145C3×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4—31no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—32no—
152C3×C4⋊Dic3—61no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—31no—
156C3×C4×Dic3—21no—
157C3×C4×Dic3—31no—
158C3×C4×Dic3—31no—
159C3×C4×Dic3—32no—
160C3×C4×Dic3—32no—
161C3×C4×Dic3—61no—
162C3×C4×Dic3C2×D311yescharacteristic
163C3×C4×Dic3C2×D311yescharacteristic
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—62no—
169Dic3⋊Dic3—62no—
170Dic3⋊Dic3C2×D312yes—
171Dic3⋊Dic3C2×D311yescharacteristic
172Dic3⋊Dic3C2×D311yescharacteristic
173#3722—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—62no—
179(C2×D3)⋊Dic3C2×D311yescharacteristic
180(C2×D3)⋊Dic3C2×D311yescharacteristic
181Dic32—32no—
182Dic32—32no—
183Dic32—62no—
184Dic32C2×D312yes—
185C22×C33C2411yescharacteristic
186C2×C3×C3⋊D3—22no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3C22×C414yes—
189C2×C32×D3—21no—
190C2×C32×D3—21no—
191C2×C32×D3C22×C412yes—
192C33×C4C22×C412yes—
193C3⋊(C3⋊Dic3)—22no—
194C3×C3⋊Dic3—22no—
195C3×C3⋊Dic3—21no—
196C3×C3⋊Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3—21no—
199C32×Dic3C22×C412yes—
200C32×Dic3C22×C414yes—
201C2×C3×#41—91no—
202C2×#239—31no—
203C2×#235—31no—
204C3×C4×Q8—91no—
205C3×#117—91no—
206Q8×Dic3—31no—
207Q8×Dic3—91no—
208Q8×Dic3—91no—
209Q8×Dic3—181no—
210D4×Dic3—91no—
211D4×Dic3—92no—
212D4×Dic3—92no—
213D4×Dic3—91no—
214#926—31no—
215#926—92no—
216C2×C4⋊Dic3—92no—
217C2×C4⋊Dic3—91no—
218C2×C4⋊Dic3—91no—
219C2×C4⋊Dic3—181no—
220#893—91no—
221#893—92no—
222#892—92no—
223D3×C4⋊C4—92no—
224D3×C4⋊C4—92no—
225D3×C4⋊C4—91no—
226#67⋊C4—92no—
227#67⋊C4—92no—
228C4×D12—91no—
229C4×D12—92no—
230C4×D12—91no—
231C4×D12—91no—
232C4×D12—181no—
233#872—31no—
234#872—92no—
235C4×Dic6—31no—
236C4×Dic6—91no—
237C23×C32—31no—
238C22×C3⋊D3C22×D312yes—
239C22×C3×D3—21no—
240C22×C3×D3—32no—
241C22×C3×D3—32no—
242C22×C3×D3—62no—
243C22×C3×D3C22×D311yescharacteristic
244C22×C3×D3C22×D311yescharacteristic
245C32×Q8—34no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—32no—
250C2×C32×C4—31no—
251C2×C32×C4—34no—
252C2×C32×C4—31no—
253C2×C32×C4—31no—
254C2×C32×C4—41no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C3⋊Dic3—32no—
259C2×C3⋊Dic3—32no—
260C2×C3⋊Dic3—32no—
261C2×C3⋊Dic3—62no—
262C2×C3⋊Dic3—62no—
263C2×C3⋊Dic3—62no—
264C2×C3⋊Dic3—122no—
265C2×C3⋊Dic3—122no—
266C2×C3⋊Dic3C22×D312yes—
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D311yescharacteristic
269C4⋊(C3⋊D3)C2×Dic314yescomplemented
270C4×C3⋊D3—122no—
271C3×#67—38no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—21no—
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—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D311yescharacteristic
293C3×D12—38no—
294C3×D12—34no—
295C3×D12—34no—
296C3×D12—64no—
297C3×C4×D3—24no—
298C3×C4×D3—38no—
299C3×C4×D3—38no—
300C3×C4×D3C4×D314yescomplemented
301C3×C4×D3C2×Dic314yescomplemented
302C3×Dic6—24no—
303C3×Dic6C4×D314yescomplemented
304C3×Dic6C2×Dic314yescomplemented
305#626C2×Dic318yescomplemented
306#624—122no—
307#624C2×Dic318yescomplemented
308D3×Dic3—122no—
309D3×Dic3—122no—
310D3×Dic3—124no—
311D3×Dic3—122no—
312D3×Dic3—122no—
313D3×Dic3—122no—
314D3×Dic3—122no—
315D3×Dic3—124no—
316#520—271noSylow
317C2×C33C23×C411yescharacteristic
318C2×C33H(5,𝔽2)11yescharacteristic
319C2×C332−1+411yescharacteristic
320C3×C3⋊D3—24no—
321C32×D3—22no—
322C3×#41—98no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—61no—
326C2×C3×D4—92no—
327C2×C3×D4—91no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C22×C3×C4—92no—
332C2×#67—32no—
333C22×Dic3—92no—
334C22×Dic3—92no—
335C22×Dic3—92no—
336C22×Dic3—92no—
337C22×Dic3—182no—
338#239—38no—
339#235—38no—
340C2×D12—32no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—61no—
344C2×C4×D3—32no—
345C2×C4×D3—32no—
346C2×C4×D3—92no—
347C2×C4×D3—92no—
348C2×C4×D3—92no—
349C2×C4×D3—92no—
350C2×C4×D3—92no—
351C2×C4×D3—182no—
352C2×C4×D3D3211yescharacteristic
353C2×Dic6D3211yescharacteristic
354C3×C4⋊C4—91no—
355C3×C4⋊C4—92no—
356C3×C4⋊C4—91no—
357C3×C4⋊C4—91no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4—91no—
360C3×C42—31no—
361C3×C42—31no—
362C3×C42—61no—
363C3×C42—92no—
364C3×C42—91no—
365#217—31no—
366#217—31no—
367#217—92no—
368#217—92no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—92no—
372(C2×D3)⋊C4—92no—
373(C2×D3)⋊C4—92no—
374(C2×D3)⋊C4—92no—
375(C2×D3)⋊C4—182no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—32no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—92no—
383C4⋊Dic3—92no—
384C4⋊Dic3—92no—
385C4⋊Dic3—92no—
386C4⋊Dic3—91no—
387C4⋊Dic3—91no—
388C4⋊Dic3—91no—
389C4⋊Dic3—182no—
390C4⋊Dic3—182no—
391C4⋊Dic3—181no—
392C4⋊Dic3—181no—
393C4⋊Dic3—181no—
394C4⋊Dic3—361no—
395Dic3⋊C4—32no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—92no—
399Dic3⋊C4—92no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—32no—
403C4×Dic3—32no—
404C4×Dic3—61no—
405C4×Dic3—92no—
406C4×Dic3—92no—
407C4×Dic3—92no—
408C4×Dic3—182no—
409C4×Dic3D3211yescharacteristic
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—32no—
414C22×C32—41no—
415C22×C32—61no—
416C22×C32—61no—
417C22×C32C23×D311yescharacteristic
418C22×C32C23×D311yescharacteristic
419C22×C32C23×D311yescharacteristic
420C2×C3⋊D3—22no—
421C2×C3⋊D3—22no—
422C2×C3⋊D3C22×Dic314yes—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—22no—
430C2×C3×D3—34no—
431C2×C3×D3—34no—
432C2×C3×D3—64no—
433C2×C3×D3—62no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—122no—
438C2×C3×D3—122no—
439C2×C3×D3C2×C4×D312yes—
440C2×C3×D3C22×Dic312yes—
441C32×C4—22no—
442C32×C4—22no—
443C32×C4—22no—
444C32×C4—32no—
445C32×C4—34no—
446C32×C4—42no—
447C32×C4—61no—
448C32×C4—61no—
449C32×C4C2×C4×D312yes—
450C32×C4C2×C4×D312yes—
451C32×C4C22×Dic312yes—
452C3⋊Dic3—21no—
453C3⋊Dic3—21no—
454C3⋊Dic3—22no—
455C3⋊Dic3—62no—
456C3⋊Dic3—62no—
457C3⋊Dic3—62no—
458C3⋊Dic3—122no—
459C3⋊Dic3—122no—
460C3⋊Dic3—122no—
461C3⋊Dic3—242no—
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—21no—
467C3×Dic3—24no—
468C3×Dic3—22no—
469C3×Dic3—41no—
470C3×Dic3—62no—
471C3×Dic3—61no—
472C3×Dic3—62no—
473C3×Dic3—61no—
474C3×Dic3—62no—
475C3×Dic3—61no—
476C3×Dic3—61no—
477C3×Dic3—122no—
478C3×Dic3—121no—
479C3×Dic3C2×C4×D314yes—
480C3×Dic3C2×C4×D312yes—
481C3×Dic3C22×Dic312yes—
482C3×Dic3C22×Dic314yes—
483C2×#41—91no—
484C4×Q8—91no—
485C4×Q8—271no—
486C4×D4—271no—
487C4×D4—272no—
488C4×D4—271no—
489C4×D4—272no—
490#117—91no—
491#117—272no—
492C2×C4⋊C4—272no—
493C2×C4⋊C4—271no—
494C33#52011yescharacteristic, complemented, Sylow
495C23×C3—31no—
496C23×C3—31no—
497C23×C3—61no—
498C23×C3—92no—
499C22×D3—32no—
500C22×D3—32no—
501C22×D3—62no—
502C22×D3C2×D3211yescharacteristic
503C3×Q8—34no—
504C3×Q8—34no—
505C3×Q8—64no—
506C3×D4—98no—
507C3×D4—94no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—34no—
516C2×C3×C4—34no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—64no—
523C2×C3×C4—62no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—98no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—92no—
531C2×C3×C4C2×D3211yescharacteristic
532C2×C3×C4C2×D3211yescharacteristic
533C2×C3×C4C2×D3211yescharacteristic
534#67—38no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—32no—
538C2×Dic3—31no—
539C2×Dic3—32no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—62no—
544C2×Dic3—92no—
545C2×Dic3—92no—
546C2×Dic3—92no—
547C2×Dic3—182no—
548C2×Dic3—182no—
549C2×Dic3—182no—
550C2×Dic3—362no—
551C2×Dic3—362no—
552C2×Dic3—362no—
553C2×Dic3—362no—
554C2×Dic3—362no—
555C2×Dic3—364no—
556C2×Dic3C2×D3211yescharacteristic
557C2×Dic3C2×D3211yescharacteristic
558C2×Dic3C2×D3212yes—
559C2×Dic3C2×D3211yescharacteristic
560D12—38no—
561D12—34no—
562D12—34no—
563D12—64no—
564C4×D3—38no—
565C4×D3—38no—
566C4×D3—362no—
567C4×D3—362no—
568C4×D3—362no—
569C4×D3—362no—
570C4×D3—362no—
571C4×D3—364no—
572C4×D3D3×Dic314yescomplemented
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—62no—
587C2×C32C22×C4×D311yescharacteristic
588C2×C32C22×C4×D311yescharacteristic
589C2×C32#100711yescharacteristic
590C2×C32#100911yescharacteristic
591C2×C32#100911yescharacteristic
592C2×C32#100911yescharacteristic
593C2×C32#101011yescharacteristic
594C2×C32#101011yescharacteristic
595C2×C32C23×Dic311yescharacteristic
596C3⋊D3—24no—
597C3×D3—24no—
598C3×D3—22no—
599C3×D3—22no—
600C3×D3—64no—
601C3×D3—64no—
602C3×D3—124no—
603#41—98no—
604C2×Q8—31no—
605C2×D4—92no—
606C2×D4—91no—
607C22×C4—31no—
608C22×C4—92no—
609C22×C4—272no—
610C22×C4—272no—
611C22×C4—272no—
612C4⋊C4—91no—
613C4⋊C4—92no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—272no—
617C4⋊C4—272no—
618C4⋊C4—271no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—272no—
622C22⋊C4—272no—
623C42—31no—
624C42—92no—
625C42—91no—
626C42—272no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—32no—
631C22×C3—32no—
632C22×C3—41no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—94no—
641C22×C3—182no—
642C22×C3—182no—
643C22×C3C22×D3211yescharacteristic
644C22×C3C22×D3211yescharacteristic
645C22×C3C22×D3211yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—34no—
649C2×D3—34no—
650C2×D3—64no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—122no—
656C2×D3—122no—
657C2×D3C2×D3×Dic312yes—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—32no—
662C3×C4—34no—
663C3×C4—32no—
664C3×C4—34no—
665C3×C4—42no—
666C3×C4—62no—
667C3×C4—64no—
668C3×C4—62no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—121no—
674C3×C4—182no—
675C3×C4—181no—
676C3×C4—181no—
677C3×C4C4×D3212yes—
678C3×C4C2×D3×Dic312yes—
679C3×C4C2×D3×Dic312yes—
680Dic3—21no—
681Dic3—21no—
682Dic3—62no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—62no—
687Dic3—61no—
688Dic3—62no—
689Dic3—122no—
690Dic3—121no—
691Dic3—182no—
692Dic3—182no—
693Dic3—182no—
694Dic3—362no—
695Dic3—362no—
696Dic3—362no—
697Dic3—722no—
698Dic3C2×D3×Dic314yes—
699Dic3C2×D3×Dic312yes—
700C32—21no—
701C32—21no—
702C32—21no—
703C32—41no—
704C32#552311yescharacteristic, complemented
705C32#557411yescharacteristic, complemented
706C32#582711yescharacteristic, complemented
707C23—31no—
708C23—92no—
709Q8—34no—
710D4—98no—
711D4—94no—
712C2×C4—32no—
713C2×C4—31no—
714C2×C4—34no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—98no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—92no—
721C2×C4—272no—
722C2×C4—1082no—
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—62no—
740C2×C3—62no—
741C2×C3—184no—
742C2×C3#6429711yescharacteristic
743C2×C3#6429811yescharacteristic
744C2×C3C2×C4×D3211yescharacteristic
745C2×C3#6430811yescharacteristic
746C2×C3#6430811yescharacteristic
747C2×C3#6431511yescharacteristic
748C2×C3#6432011yescharacteristic
749C2×C3C22×D3×Dic311yescharacteristic
750C2×C3C22×D3×Dic311yescharacteristic
751D3—22no—
752D3—64no—
753D3—64no—
754D3—124no—
755C22—32no—
756C22—61no—
757C22—61no—
758C22—94no—
759C22—182no—
760C22—182no—
761C22C2×D3311yescharacteristic
762C4—32no—
763C4—34no—
764C4—61no—
765C4—61no—
766C4—181no—
767C4—182no—
768C4—181no—
769C4—542no—
770C4D32×Dic312yes—
771C3—21no—
772C3—21no—
773C3—21no—
774C3—41no—
775C3#1059389011yescharacteristic, complemented
776C3#1059499211yescharacteristic, complemented
777C3#1059539411yescharacteristic, complemented
778C2—62no—
779C2—184no—
780C2#1172439011yescharacteristic
781C2#1172439611yescharacteristic
782C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3799C2
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. #11723691C2semidirect
3. Dic3×C4⋊(C3⋊D3)C2semidirect
4. D3×C4⋊(C3⋊Dic3)C2semidirect
5. Dic6×C3⋊Dic3C2semidirect
6. C3×#63855C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11722929C2semidirect
9. #11722928C2semidirect
10. #11722915C2semidirect
11. #11722908C2semidirect
23. C3×#3799C4semidirect
68. #63855D3semidirect
72. Dic3×Dic6D3semidirect
82. C3×C4⋊(C3⋊D3)C2×C4semidirect
87. C32×C4×D3C2×C4semidirect
88. C32×Dic6C2×C4semidirect
92. C3×#626C2×C4semidirect
93. C3×#624C2×C4semidirect
128. #3799Dic3semidirect
269. C4⋊(C3⋊D3)C2×Dic3semidirect
300. C3×C4×D3C4×D3semidirect
301. C3×C4×D3C2×Dic3semidirect
303. C3×Dic6C4×D3semidirect
304. C3×Dic6C2×Dic3semidirect
305. #626C2×Dic3semidirect
307. #624C2×Dic3semidirect
494. C33#520semidirect
572. C4×D3D3×Dic3semidirect
573. Dic6D3×Dic3semidirect
704. C32#5523semidirect
705. C32#5574semidirect
706. C32#5827semidirect
775. C3#10593890semidirect
776. C3#10594992semidirect
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×#37992
#117236912
Dic3×C4⋊(C3⋊D3)2
D3×C4⋊(C3⋊Dic3)2
Dic6×C3⋊Dic32
C3×#638552
C3×Dic3×Dic62
#117229292
#117229282
#117229152
#117229082
#105953943
#105949923
#105938903