Finite Group Databasebeta

← #13169242

Subgroups — #13169242

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×#89041C211yesmaximal, characteristic
2C3⋊D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4Dic3×#634C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×#63874C211yesmaximal, characteristic, complemented
7C3×#63844C211yesmaximal, characteristic, complemented
8#11722938C212yesmaximal, complemented
9#11722934C212yesmaximal, complemented
10#11722922C212yesmaximal, complemented
11#11722910C212yesmaximal, complemented
12#10594361—31nomaximal
13#10593890—31nomaximal
14#10593887—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×#6295C2212yes—
19C2×#6294C2212yes—
20#89041C418yescomplemented
21C2×Dic3×C3⋊D3C2212yes—
22C2×Dic3×C3⋊D3C2212yes—
23C2×C3×#624C2212yes—
24C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4×Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88807C2212yes—
29#88807C2212yes—
30#88803C2212yes—
31Dic3×C3⋊Dic3C2212yes—
32C3×#3724C2211yescharacteristic
33C3×#3724C2212yes—
34C3×#3724C2211yescharacteristic
35C3×#3722C2212yes—
36C3×#3722C2211yescharacteristic
37C3×#3722C2211yescharacteristic
38C3×Dic32C2212yes—
39C2×#3799—31no—
40C2×#3796—31no—
41C2×#3795—31no—
42C4⋊C4×C3⋊D3—31no—
43C4×C4⋊(C3⋊D3)—31no—
44C4×#634—31no—
45C3×#893—31no—
46C3×#887—31no—
47C3×C4×D12—31no—
48C3×#872—31no—
49C3×#872—31no—
50C3×C4×Dic6—31no—
51C4×#626—32no—
52#63902—32no—
53#63894D311yescharacteristic, complemented
54Dic3×D12—31no—
55Dic3×D12—31no—
56Dic3×D12—61no—
57D3×C4⋊Dic3—31no—
58D3×C4⋊Dic3—31no—
59D3×C4⋊Dic3—61no—
60#63883—32no—
61#63881—32no—
62#63881—32no—
63#63880—32no—
64#63879—32no—
65#63878—32no—
66#63877—32no—
67D3×Dic3⋊C4—32no—
68D3×Dic3⋊C4—32no—
69#63874D311yescharacteristic, complemented
70#63844D311yescharacteristic, complemented
71Dic3×Dic6—31no—
72Dic3×Dic6—31no—
73Dic3×Dic6—61no—
74#63836—32no—
75C22×C3×C3⋊D3C2312yes—
76C22×C3×C3⋊D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4⋊(C3⋊D3)C2×C414yescomplemented
82C3×C4×C3⋊D3C2×C414yescomplemented
83C3×#634C2×C414yescomplemented
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89#6295C2×C418yescomplemented
90#6294C2×C418yescomplemented
91Dic3×C3⋊D3—42no—
92Dic3×C3⋊D3—42no—
93C3×#624—42no—
94#5574—91no—
95#5546—91no—
96#5523—91no—
97C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
98C2×C4×C3⋊D3—32no—
99C2×C4×C3⋊D3—32no—
100C2×C4×C3⋊D3C2×D311yescharacteristic
101C2×#634C2×D311yescharacteristic
102C2×C3×D12—31no—
103C2×C3×D12—31no—
104C2×C3×D12—61no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—61no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—61no—
113C2×#626—32no—
114C2×#626—32no—
115C2×#625—32no—
116C2×#624—32no—
117C2×#624C2×D312yes—
118C2×D3×Dic3—32no—
119C2×D3×Dic3—32no—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—62no—
125C2×D3×Dic3—62no—
126#3799—38no—
127#3796—38no—
128#3795—38no—
129C32×C4⋊C4—31no—
130C32×C42—31no—
131C32×C42—31no—
132#3752—32no—
133C4⋊(C3⋊Dic3)—31no—
134C4⋊(C3⋊Dic3)—31no—
135C4⋊(C3⋊Dic3)—31no—
136C4⋊(C3⋊Dic3)—61no—
137C4⋊(C3⋊Dic3)—61no—
138C4⋊(C3⋊Dic3)—61no—
139C4⋊(C3⋊Dic3)—121no—
140#3750—32no—
141#3750—32no—
142C4×C3⋊Dic3—32no—
143C3×(C2×D3)⋊C4—32no—
144C3×(C2×D3)⋊C4—32no—
145C3×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×C4⋊Dic3—21no—
150C3×C4⋊Dic3C2×D311yescharacteristic
151C3×C4⋊Dic3C2×D311yescharacteristic
152C3×Dic3⋊C4—32no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4—31no—
156C3×Dic3⋊C4—32no—
157C3×Dic3⋊C4—31no—
158C3×C4×Dic3—21no—
159C3×C4×Dic3—21no—
160C3×C4×Dic3—32no—
161C3×C4×Dic3—32no—
162C3×C4×Dic3C2×D311yescharacteristic
163C3×C4×Dic3C2×D311yescharacteristic
164C3×C4×Dic3C2×D311yescharacteristic
165C3×C4×Dic3C2×D311yescharacteristic
166#3724C2×D312yes—
167#3724C2×D311yescharacteristic
168#3724C2×D311yescharacteristic
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—32no—
171Dic3⋊Dic3—32no—
172Dic3⋊Dic3—32no—
173Dic3⋊Dic3—62no—
174Dic3⋊Dic3—62no—
175#3722C2×D312yes—
176#3722C2×D311yescharacteristic
177#3722C2×D311yescharacteristic
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—62no—
181Dic32—32no—
182Dic32—32no—
183Dic32—62no—
184Dic32C2×D312yes—
185C22×C33C2411yescharacteristic
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—22no—
190C2×C3×C3⋊D3C22×C414yes—
191C2×C3×C3⋊D3C22×C412yes—
192C33×C4C22×C412yes—
193C3⋊(C3⋊Dic3)—22no—
194C3×C3⋊Dic3C22×C412yes—
195C3×C3⋊Dic3C22×C414yes—
196C32×Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3—22no—
199C32×Dic3—21no—
200C32×Dic3—21no—
201C2×#239—91no—
202C2×#237—91no—
203C2×#235—91no—
204C3×C4×Q8—91no—
205C3×C4×D4—91no—
206C3×#117—91no—
207Q8×Dic3—91no—
208D4×Dic3—91no—
209C4×#67—92no—
210C2×C4⋊Dic3—91no—
211C2×Dic3⋊C4—92no—
212#893—31no—
213#893—92no—
214#892—92no—
215D3×C4⋊C4—92no—
216D3×C4⋊C4—92no—
217D3×C4⋊C4—91no—
218D3×C4⋊C4—91no—
219D3×C4⋊C4—181no—
220#887—31no—
221#67⋊C4—92no—
222#67⋊C4—92no—
223#67⋊C4—92no—
224#877—92no—
225C4×D12—31no—
226C4×D12—92no—
227C4×D12—91no—
228C4×D12—91no—
229C4×D12—181no—
230#872—31no—
231#872—31no—
232#872—92no—
233C4×Dic6—31no—
234C4×Dic6—91no—
235C4×Dic6—91no—
236C4×Dic6—181no—
237C22×C3⋊D3C22×D311yescharacteristic
238C22×C3⋊D3C22×D312yes—
239C22×C3×D3—32no—
240C22×C3×D3—32no—
241C22×C3×D3—31no—
242C22×C3×D3—31no—
243C22×C3×D3—61no—
244C22×C3×D3—62no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—31no—
249C2×C32×C4—32no—
250C2×C32×C4—31no—
251C2×C32×C4—31no—
252C2×C32×C4—31no—
253C2×C32×C4—41no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C3⋊Dic3—32no—
258C2×C3⋊Dic3—32no—
259C2×C3⋊Dic3—32no—
260C2×C3⋊Dic3—62no—
261C2×C3⋊Dic3—62no—
262C2×C3⋊Dic3—62no—
263C2×C3⋊Dic3—122no—
264C2×C3⋊Dic3C22×D312yes—
265C2×C3⋊Dic3C22×D311yescharacteristic
266C4⋊(C3⋊D3)C4×D314yescomplemented
267C4×C3⋊D3—122no—
268C4×C3⋊D3—122no—
269C4×C3⋊D3C4×D314yescomplemented
270#634C4×D314yescomplemented
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D311yescharacteristic
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C3×D12—34no—
293C3×D12—34no—
294C3×D12—64no—
295C3×C4×D3—34no—
296C3×C4×D3—34no—
297C3×C4×D3—64no—
298C3×C4×D3—122no—
299C3×C4×D3—122no—
300C3×Dic6—34no—
301C3×Dic6—34no—
302C3×Dic6—64no—
303#626—38no—
304#626—38no—
305#625—38no—
306#624—38no—
307#624—42no—
308D3×Dic3—38no—
309D3×Dic3—38no—
310D3×Dic3—122no—
311D3×Dic3—122no—
312D3×Dic3—122no—
313D3×Dic3—122no—
314D3×Dic3—124no—
315D3×Dic3—124no—
316#520—271noSylow
317C2×C33C23×C411yescharacteristic
318C2×C33H(5,𝔽2)11yescharacteristic
319C2×C332−1+411yescharacteristic
320C3×C3⋊D3—22no—
321C3×C3⋊D3—24no—
322C2×C3×Q8—91no—
323C2×C3×D4—91no—
324C22×C3×C4—92no—
325C22×C3×C4—91no—
326C2×#67—92no—
327C2×#67—92no—
328C22×Dic3—92no—
329C22×Dic3—92no—
330C22×Dic3—92no—
331#239—98no—
332#237—98no—
333#235—98no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—61no—
337C2×D12—92no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—32no—
341C2×C4×D3—32no—
342C2×C4×D3—61no—
343C2×C4×D3—92no—
344C2×C4×D3—92no—
345C2×C4×D3—92no—
346C2×C4×D3—92no—
347C2×C4×D3—92no—
348C2×C4×D3—92no—
349C2×C4×D3—182no—
350C2×C4×D3—182no—
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—61no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—92no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—92no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42—92no—
370#217—92no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—32no—
376(C2×D3)⋊C4—32no—
377(C2×D3)⋊C4—92no—
378(C2×D3)⋊C4—92no—
379(C2×D3)⋊C4—182no—
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382C4⋊Dic3—91no—
383C4⋊Dic3—92no—
384C4⋊Dic3—92no—
385C4⋊Dic3—181no—
386C4⋊Dic3—181no—
387C4⋊Dic3—181no—
388C4⋊Dic3—361no—
389C4⋊Dic3D3211yescharacteristic
390Dic3⋊C4—32no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—32no—
396Dic3⋊C4—92no—
397Dic3⋊C4—92no—
398Dic3⋊C4—92no—
399Dic3⋊C4—92no—
400Dic3⋊C4—182no—
401Dic3⋊C4—182no—
402C4×Dic3—32no—
403C4×Dic3—32no—
404C4×Dic3—92no—
405C4×Dic3—92no—
406C4×Dic3—92no—
407C4×Dic3—182no—
408C4×Dic3D3211yescharacteristic
409C4×Dic3D3211yescharacteristic
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—41no—
414C22×C32C23×D311yescharacteristic
415C22×C32C23×D311yescharacteristic
416C22×C32C23×D311yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—22no—
421C2×C3⋊D3C2×C4×D314yes—
422C2×C3⋊D3C2×C4×D312yes—
423C2×C3×D3—34no—
424C2×C3×D3—34no—
425C2×C3×D3—32no—
426C2×C3×D3—32no—
427C2×C3×D3—62no—
428C2×C3×D3—64no—
429C2×C3×D3—62no—
430C2×C3×D3—62no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—62no—
434C2×C3×D3—61no—
435C2×C3×D3—62no—
436C2×C3×D3—62no—
437C2×C3×D3—62no—
438C2×C3×D3—61no—
439C2×C3×D3—122no—
440C2×C3×D3—122no—
441C32×C4—22no—
442C32×C4—22no—
443C32×C4—22no—
444C32×C4—42no—
445C32×C4—61no—
446C32×C4—61no—
447C32×C4—61no—
448C32×C4—62no—
449C32×C4—61no—
450C32×C4C2×C4×D312yes—
451C32×C4C2×C4×D312yes—
452C32×C4C2×C4×D312yes—
453C3⋊Dic3—62no—
454C3⋊Dic3—62no—
455C3⋊Dic3—62no—
456C3⋊Dic3—122no—
457C3⋊Dic3—122no—
458C3⋊Dic3—122no—
459C3⋊Dic3—242no—
460C3⋊Dic3C2×C4×D312yes—
461C3⋊Dic3C2×C4×D314yes—
462C3×Dic3—22no—
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—21no—
466C3×Dic3—21no—
467C3×Dic3—21no—
468C3×Dic3—21no—
469C3×Dic3—22no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—21no—
474C3×Dic3—32no—
475C3×Dic3—34no—
476C3×Dic3—32no—
477C3×Dic3—34no—
478C3×Dic3—42no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—64no—
482C3×Dic3—62no—
483C2×#41—271no—
484C4×Q8—91no—
485C4×Q8—271no—
486C4×D4—91no—
487C4×D4—271no—
488C4×D4—272no—
489C4×D4—272no—
490#117—91no—
491#117—272no—
492C2×C4⋊C4—271no—
493C2×C4⋊C4—272no—
494C33#52011yescharacteristic, complemented, Sylow
495C23×C3—92no—
496C23×C3—91no—
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—32no—
500C22×D3—32no—
501C22×D3—61no—
502C22×D3—62no—
503C3×Q8—94no—
504C3×D4—94no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—32no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—32no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—62no—
523C2×C3×C4—61no—
524C2×C3×C4—92no—
525C2×C3×C4—91no—
526C2×C3×C4—94no—
527C2×C3×C4—362no—
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C2×D3211yescharacteristic
530C2×C3×C4C2×D3211yescharacteristic
531#67—98no—
532#67—98no—
533C2×Dic3—32no—
534C2×Dic3—32no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—62no—
538C2×Dic3—61no—
539C2×Dic3—98no—
540C2×Dic3—92no—
541C2×Dic3—92no—
542C2×Dic3—92no—
543C2×Dic3—182no—
544C2×Dic3—182no—
545C2×Dic3—182no—
546C2×Dic3—362no—
547C2×Dic3—362no—
548C2×Dic3—362no—
549C2×Dic3C2×D3211yescharacteristic
550C2×Dic3C2×D3212yes—
551C2×Dic3C2×D3211yescharacteristic
552C2×Dic3C2×D3211yescharacteristic
553C2×Dic3C2×D3211yescharacteristic
554D12—34no—
555D12—34no—
556D12—64no—
557D12—98no—
558C4×D3—34no—
559C4×D3—34no—
560C4×D3—64no—
561C4×D3—98no—
562C4×D3—98no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—362no—
566C4×D3—362no—
567C4×D3—362no—
568C4×D3—362no—
569C4×D3—364no—
570C4×D3—364no—
571Dic6—34no—
572Dic6—34no—
573Dic6—64no—
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×C32C22×C4×D311yescharacteristic
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
595C3⋊D3—22no—
596C3⋊D3—24no—
597C3×D3—64no—
598C3×D3—64no—
599C3×D3—62no—
600C3×D3—64no—
601C3×D3—62no—
602C3×D3—124no—
603#41—278no—
604C2×Q8—91no—
605C2×D4—91no—
606C2×D4—272no—
607C22×C4—92no—
608C22×C4—91no—
609C22×C4—272no—
610C22×C4—272no—
611C22×C4—272no—
612C4⋊C4—31no—
613C4⋊C4—91no—
614C4⋊C4—92no—
615C4⋊C4—91no—
616C4⋊C4—272no—
617C4⋊C4—272no—
618C4⋊C4—271no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—92no—
622C22⋊C4—272no—
623C42—31no—
624C42—31no—
625C42—92no—
626C42—272no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—41no—
631C22×C3—94no—
632C22×C3—92no—
633C22×C3—182no—
634C22×C3—182no—
635C22×C3—181no—
636C22×C3—181no—
637C22×C3C22×D3211yescharacteristic
638C22×C3C22×D3211yescharacteristic
639C22×C3C22×D3211yescharacteristic
640C2×D3—32no—
641C2×D3—32no—
642C2×D3—34no—
643C2×D3—34no—
644C2×D3—62no—
645C2×D3—64no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—122no—
657C2×D3—122no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—42no—
662C3×C4—62no—
663C3×C4—62no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—62no—
667C3×C4—61no—
668C3×C4—62no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—92no—
675C3×C4—94no—
676C3×C4—122no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C4×D3212yes—
680C3×C4C4×D3212yes—
681C3×C4C4×D3212yes—
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—22no—
687Dic3—34no—
688Dic3—34no—
689Dic3—32no—
690Dic3—32no—
691Dic3—64no—
692Dic3—62no—
693Dic3—182no—
694Dic3—182no—
695Dic3—182no—
696Dic3—362no—
697Dic3—362no—
698Dic3—362no—
699Dic3—722no—
700C32—21no—
701C32—21no—
702C32—21no—
703C32—41no—
704C32#552311yescharacteristic, complemented
705C32#554611yescharacteristic, complemented
706C32#557411yescharacteristic, complemented
707C23—91no—
708C23—92no—
709Q8—94no—
710D4—94no—
711D4—278no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—32no—
717C2×C4—92no—
718C2×C4—91no—
719C2×C4—94no—
720C2×C4—278no—
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—182no—
739C2×C3—184no—
740C2×C3#6429711yescharacteristic
741C2×C3#6429811yescharacteristic
742C2×C3C2×C4×D3211yescharacteristic
743C2×C3C2×C4×D3211yescharacteristic
744C2×C3C2×C4×D3211yescharacteristic
745C2×C3#6430711yescharacteristic
746C2×C3#6430811yescharacteristic
747C2×C3#6431411yescharacteristic
748C2×C3#6431511yescharacteristic
749D3—64no—
750D3—64no—
751D3—62no—
752D3—64no—
753D3—62no—
754D3—124no—
755C22—92no—
756C22—94no—
757C22—182no—
758C22—181no—
759C22—181no—
760C22—182no—
761C22C2×D3311yescharacteristic
762C4—61no—
763C4—62no—
764C4—61no—
765C4—61no—
766C4—61no—
767C4—92no—
768C4—94no—
769C4—542no—
770C4#8894912yes—
771C3—21no—
772C3—21no—
773C3—21no—
774C3—41no—
775C3#1059388711yescharacteristic, complemented
776C3#1059389011yescharacteristic, complemented
777C3#1059436111yescharacteristic, complemented
778C2—182no—
779C2—184no—
780C2#1172438411yescharacteristic
781C2#1172439611yescharacteristic
782C2C2×#8894911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89041C2
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. C3⋊D3×C4⋊Dic3C2semidirect
3. Dic3×C4⋊(C3⋊D3)C2semidirect
4. Dic3×#634C2semidirect
5. C3×#63894C2semidirect
6. C3×#63874C2semidirect
7. C3×#63844C2semidirect
8. #11722938C2semidirect
9. #11722934C2semidirect
10. #11722922C2semidirect
11. #11722910C2semidirect
20. #89041C4semidirect
53. #63894D3semidirect
69. #63874D3semidirect
70. #63844D3semidirect
81. C3×C4⋊(C3⋊D3)C2×C4semidirect
82. C3×C4×C3⋊D3C2×C4semidirect
83. C3×#634C2×C4semidirect
89. #6295C2×C4semidirect
90. #6294C2×C4semidirect
266. C4⋊(C3⋊D3)C4×D3semidirect
269. C4×C3⋊D3C4×D3semidirect
270. #634C4×D3semidirect
494. C33#520semidirect
704. C32#5523semidirect
705. C32#5546semidirect
706. C32#5574semidirect
775. C3#10593887semidirect
776. C3#10593890semidirect
777. C3#10594361semidirect

Maximal subgroups

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

subgroupindex
C2×#890412
C3⋊D3×C4⋊Dic32
Dic3×C4⋊(C3⋊D3)2
Dic3×#6342
C3×#638942
C3×#638742
C3×#638442
#117229382
#117229342
#117229222
#117229102
#105943613
#105938903
#105938873