Finite Group Databasebeta

← #13169174

Subgroups — #13169174

Order 1728.

1446 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89041C211yesmaximal, characteristic
2#11723501C211yesmaximal, characteristic, complemented
3#11723437C211yesmaximal, characteristic, complemented
4#11723410C211yesmaximal, characteristic, complemented
5C3×#63900C211yesmaximal, characteristic, complemented
6C3×#63894C211yesmaximal, characteristic, complemented
7C3×#63844C211yesmaximal, characteristic, complemented
8#11722934C212yesmaximal, complemented
9#11722931C212yesmaximal, complemented
10#11722922C212yesmaximal, complemented
11#11722910C212yesmaximal, complemented
12#10594359—31nomaximal
13#10594327—31nomaximal
14#10593889—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×C3×#624C2212yes—
23C2×C3×#624C2212yes—
24C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
25C32×C4⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88807C2212yes—
29#88807C2211yescharacteristic
30#88807C2211yescharacteristic
31#88803C2212yes—
32#88803C2211yescharacteristic
33#88803C2211yescharacteristic
34Dic3×C3⋊Dic3C2212yes—
35C3×#3724C2212yes—
36C3×#3724C2212yes—
37C3×#3722C2212yes—
38C3×Dic32C2212yes—
39C2×#3799—31no—
40C2×#3796—31no—
41C2×#3795—31no—
42#64102—31no—
43#64096—31no—
44#64081—31no—
45C3×#893—31no—
46C3×D3×C4⋊C4—31no—
47C3×D3×C4⋊C4—31no—
48C3×#887—31no—
49C3×C4×D12—31no—
50C3×C4×Dic6—31no—
51#63904—32no—
52#63904—32no—
53C4×#626—32no—
54C4×#625—32no—
55#63900D311yescharacteristic, complemented
56#63898—31no—
57#63898—31no—
58#63898—61no—
59#63894D311yescharacteristic, complemented
60#63883—32no—
61#63880—32no—
62#63879—32no—
63#63878—32no—
64#63877—32no—
65D3×Dic3⋊C4—32no—
66D3×Dic3⋊C4—32no—
67#63855—31no—
68#63855—31no—
69#63855—61no—
70#63844D311yescharacteristic, complemented
71#63843—31no—
72#63843—31no—
73#63843—61no—
74#63836—32no—
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C3×C3⋊D3C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C3×C4⋊(C3⋊D3)C2×C414yescomplemented
83C3×C4×C3⋊D3C2×C414yescomplemented
84C3×#634C2×C414yescomplemented
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2311yescharacteristic
89#6295C2×C418yescomplemented
90#6294C2×C418yescomplemented
91Dic3×C3⋊D3—42no—
92C3×#624—42no—
93C3×#624—42no—
94#5574—91no—
95#5546—91no—
96#5504—91no—
97C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
98C2×C4×C3⋊D3—32no—
99C2×C4×C3⋊D3C2×D311yescharacteristic
100C2×#634C2×D311yescharacteristic
101C2×C3×D12—31no—
102C2×C3×D12—31no—
103C2×C3×D12—61no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—32no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—61no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—31no—
113C2×C3×Dic6—61no—
114C2×#626—32no—
115C2×#626—32no—
116C2×#625—32no—
117C2×#624—32no—
118C2×#624C2×D312yes—
119C2×#624C2×D312yes—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—62no—
125#3799—38no—
126#3796—38no—
127#3795—38no—
128C32×C4⋊C4—31no—
129C32×C4⋊C4—31no—
130C32×C42—31no—
131#3752—31no—
132#3752—31no—
133#3752—32no—
134#3750—31no—
135#3750—31no—
136#3750—32no—
137C4×C3⋊Dic3—31no—
138C4×C3⋊Dic3—31no—
139C4×C3⋊Dic3—31no—
140C4×C3⋊Dic3—32no—
141C4×C3⋊Dic3—61no—
142C4×C3⋊Dic3—61no—
143C4×C3⋊Dic3—61no—
144C4×C3⋊Dic3—121no—
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4—32no—
147C3×C4⋊Dic3—21no—
148C3×C4⋊Dic3—21no—
149C3×C4⋊Dic3C2×D311yescharacteristic
150C3×C4⋊Dic3C2×D311yescharacteristic
151C3×C4⋊Dic3C2×D311yescharacteristic
152C3×C4⋊Dic3C2×D311yescharacteristic
153C3×Dic3⋊C4—32no—
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—32no—
156C3×Dic3⋊C4—32no—
157C3×C4×Dic3—21no—
158C3×C4×Dic3—32no—
159C3×C4×Dic3—32no—
160C3×C4×Dic3C2×D311yescharacteristic
161C3×C4×Dic3C2×D311yescharacteristic
162#3724C2×D312yes—
163#3724C2×D312yes—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—62no—
171Dic3⋊Dic3—61no—
172Dic3⋊Dic3—61no—
173#3722C2×D312yes—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—61no—
181(C2×D3)⋊Dic3—61no—
182(C2×D3)⋊Dic3—62no—
183Dic32—32no—
184Dic32—32no—
185Dic32—62no—
186Dic32C2×D312yes—
187C22×C33C2411yescharacteristic
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—22no—
190C2×C3×C3⋊D3—22no—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3C22×C414yes—
193C2×C3×C3⋊D3C22×C412yes—
194C33×C4C22×C412yes—
195C3⋊(C3⋊Dic3)—21no—
196C3⋊(C3⋊Dic3)—21no—
197C3×C3⋊Dic3C22×C412yes—
198C3×C3⋊Dic3C22×C414yes—
199C32×Dic3—21no—
200C32×Dic3—22no—
201C32×Dic3—22no—
202C32×Dic3—21no—
203C2×#239—91no—
204C2×#237—91no—
205C2×#235—91no—
206C3×C4×Q8—91no—
207C3×C4×D4—91no—
208C2×C3×C4⋊C4—91no—
209Q8×Dic3—91no—
210D4×Dic3—91no—
211C4×#67—92no—
212C4×#67—92no—
213C4×#67—92no—
214#926—91no—
215C2×Dic3⋊C4—92no—
216#893—31no—
217#893—91no—
218#893—91no—
219#893—92no—
220#893—181no—
221#892—92no—
222D3×C4⋊C4—31no—
223D3×C4⋊C4—31no—
224D3×C4⋊C4—92no—
225D3×C4⋊C4—92no—
226#887—31no—
227#887—91no—
228#887—91no—
229#887—181no—
230#67⋊C4—92no—
231#877—92no—
232C4×D12—31no—
233C4×D12—92no—
234#872—92no—
235#872—91no—
236#872—91no—
237#872—181no—
238C4×Dic6—31no—
239C22×C3⋊D3C22×D312yes—
240C22×C3⋊D3C22×D311yescharacteristic
241C22×C3×D3—31no—
242C22×C3×D3—31no—
243C22×C3×D3—32no—
244C22×C3×D3—32no—
245C22×C3×D3—61no—
246C22×C3×D3—62no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—31no—
251C2×C32×C4—32no—
252C2×C32×C4—31no—
253C2×C32×C4—32no—
254C2×C32×C4—41no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—61no—
265C2×C3⋊Dic3—61no—
266C2×C3⋊Dic3—61no—
267C2×C3⋊Dic3—61no—
268C2×C3⋊Dic3—61no—
269C2×C3⋊Dic3—61no—
270C2×C3⋊Dic3—121no—
271C2×C3⋊Dic3—121no—
272C2×C3⋊Dic3C22×D312yes—
273C2×C3⋊Dic3C22×D311yescharacteristic
274C4⋊(C3⋊D3)C4×D314yescomplemented
275C4×C3⋊D3—122no—
276C4×C3⋊D3C4×D314yescomplemented
277#634C4×D314yescomplemented
278C2×C3×Dic3—22no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—62no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D312yes—
296C3×D12—34no—
297C3×D12—34no—
298C3×D12—64no—
299C3×C4×D3—34no—
300C3×C4×D3—34no—
301C3×C4×D3—64no—
302C3×C4×D3—122no—
303C3×C4×D3—122no—
304C3×C4×D3—122no—
305C3×C4×D3—122no—
306C3×Dic6—34no—
307C3×Dic6—34no—
308C3×Dic6—64no—
309#626—38no—
310#626—38no—
311#625—38no—
312#624—38no—
313#624—42no—
314#624—42no—
315D3×Dic3—38no—
316D3×Dic3—38no—
317D3×Dic3—122no—
318D3×Dic3—122no—
319D3×Dic3—124no—
320#520—271noSylow
321C2×C33C23×C411yescharacteristic
322C2×C33H(5,𝔽2)11yescharacteristic
323C2×C332−1+411yescharacteristic
324C3×C3⋊D3—24no—
325C3×C3⋊D3—22no—
326C2×C3×Q8—91no—
327C2×C3×D4—91no—
328C22×C3×C4—92no—
329C22×C3×C4—92no—
330C22×C3×C4—91no—
331C2×#67—92no—
332C2×#67—92no—
333C22×Dic3—92no—
334C22×Dic3—92no—
335#239—98no—
336#237—98no—
337#235—98no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—61no—
341C2×D12—92no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
344C2×C4×D3—32no—
345C2×C4×D3—32no—
346C2×C4×D3—32no—
347C2×C4×D3—32no—
348C2×C4×D3—61no—
349C2×C4×D3—92no—
350C2×C4×D3—92no—
351C2×C4×D3—92no—
352C2×C4×D3—92no—
353C2×C4×D3—182no—
354C2×Dic6—31no—
355C2×Dic6—31no—
356C2×Dic6—61no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—92no—
364C3×C4⋊C4—92no—
365C3×C22⋊C4—92no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—61no—
369C3×C42—92no—
370#217—92no—
371#217—91no—
372#217—91no—
373(C2×D3)⋊C4—32no—
374(C2×D3)⋊C4—32no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—92no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—92no—
381(C2×D3)⋊C4—181no—
382(C2×D3)⋊C4—181no—
383(C2×D3)⋊C4—182no—
384C4⋊Dic3—92no—
385C4⋊Dic3—91no—
386C4⋊Dic3—91no—
387C4⋊Dic3D3211yescharacteristic
388C4⋊Dic3D3211yescharacteristic
389Dic3⋊C4—32no—
390Dic3⋊C4—32no—
391Dic3⋊C4—32no—
392Dic3⋊C4—32no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—92no—
398Dic3⋊C4—92no—
399Dic3⋊C4—181no—
400Dic3⋊C4—181no—
401Dic3⋊C4—182no—
402C4×Dic3—32no—
403C4×Dic3—32no—
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—41no—
420C22×C32C23×D311yescharacteristic
421C22×C32C23×D311yescharacteristic
422C22×C32C23×D311yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3C2×C4×D314yes—
428C2×C3⋊D3C2×C4×D312yes—
429C2×C3×D3—34no—
430C2×C3×D3—34no—
431C2×C3×D3—32no—
432C2×C3×D3—32no—
433C2×C3×D3—62no—
434C2×C3×D3—64no—
435C2×C3×D3—62no—
436C2×C3×D3—61no—
437C2×C3×D3—62no—
438C2×C3×D3—62no—
439C2×C3×D3—61no—
440C2×C3×D3—62no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—122no—
444C2×C3×D3—121no—
445C2×C3×D3—121no—
446C2×C3×D3—122no—
447C32×C4—22no—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—42no—
451C32×C4—61no—
452C32×C4—62no—
453C32×C4—61no—
454C32×C4—62no—
455C32×C4C2×C4×D312yes—
456C32×C4C2×C4×D312yes—
457C32×C4C2×C4×D312yes—
458C3⋊Dic3—61no—
459C3⋊Dic3—61no—
460C3⋊Dic3—62no—
461C3⋊Dic3—62no—
462C3⋊Dic3—61no—
463C3⋊Dic3—61no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—121no—
467C3⋊Dic3—121no—
468C3⋊Dic3—121no—
469C3⋊Dic3—121no—
470C3⋊Dic3—122no—
471C3⋊Dic3—122no—
472C3⋊Dic3C2×C4×D312yes—
473C3⋊Dic3C2×C4×D314yes—
474C3×Dic3—22no—
475C3×Dic3—21no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C3×Dic3—21no—
479C3×Dic3—22no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—32no—
483C3×Dic3—34no—
484C3×Dic3—32no—
485C3×Dic3—34no—
486C3×Dic3—42no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—42no—
490C3×Dic3—64no—
491C3×Dic3—62no—
492C2×#41—271no—
493C4×Q8—91no—
494C4×Q8—271no—
495C4×D4—91no—
496C4×D4—272no—
497C4×D4—271no—
498C4×D4—272no—
499#117—271no—
500#117—272no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—272no—
503C33#52011yescharacteristic, complemented, Sylow
504C23×C3—91no—
505C23×C3—92no—
506C22×D3—32no—
507C22×D3—32no—
508C22×D3—31no—
509C22×D3—31no—
510C22×D3—61no—
511C22×D3—62no—
512C3×Q8—94no—
513C3×D4—94no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—31no—
522C2×C3×C4—32no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—62no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—62no—
530C2×C3×C4—92no—
531C2×C3×C4—91no—
532C2×C3×C4—94no—
533C2×C3×C4—362no—
534C2×C3×C4—362no—
535C2×C3×C4C2×D3211yescharacteristic
536C2×C3×C4C2×D3211yescharacteristic
537C2×C3×C4C2×D3211yescharacteristic
538#67—98no—
539#67—98no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—98no—
547C2×Dic3—91no—
548C2×Dic3—91no—
549C2×Dic3—91no—
550C2×Dic3—91no—
551C2×Dic3—91no—
552C2×Dic3—91no—
553C2×Dic3—181no—
554C2×Dic3—181no—
555C2×Dic3—181no—
556C2×Dic3—181no—
557C2×Dic3—181no—
558C2×Dic3—181no—
559C2×Dic3—361no—
560C2×Dic3—361no—
561C2×Dic3—362no—
562C2×Dic3C2×D3211yescharacteristic
563C2×Dic3C2×D3212yes—
564C2×Dic3C2×D3212yes—
565C2×Dic3C2×D3211yescharacteristic
566D12—34no—
567D12—34no—
568D12—64no—
569D12—98no—
570C4×D3—34no—
571C4×D3—34no—
572C4×D3—64no—
573C4×D3—98no—
574C4×D3—98no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—362no—
580C4×D3—362no—
581C4×D3—364no—
582Dic6—34no—
583Dic6—34no—
584Dic6—64no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—21no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—41no—
595C2×C32—41no—
596C2×C32—41no—
597C2×C32C22×C4×D311yescharacteristic
598C2×C32C22×C4×D311yescharacteristic
599C2×C32C22×C4×D311yescharacteristic
600C2×C32#100411yescharacteristic
601C2×C32#100411yescharacteristic
602C2×C32#100711yescharacteristic
603C2×C32#100711yescharacteristic
604C2×C32#100911yescharacteristic
605C2×C32#101011yescharacteristic
606C3⋊D3—22no—
607C3⋊D3—24no—
608C3×D3—64no—
609C3×D3—62no—
610C3×D3—62no—
611C3×D3—64no—
612C3×D3—124no—
613C3×D3—122no—
614#41—278no—
615C2×Q8—91no—
616C2×D4—91no—
617C2×D4—272no—
618C22×C4—92no—
619C22×C4—92no—
620C22×C4—91no—
621C22×C4—272no—
622C22×C4—272no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—92no—
626C4⋊C4—92no—
627C4⋊C4—271no—
628C4⋊C4—272no—
629C4⋊C4—271no—
630C22⋊C4—92no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—272no—
634C42—31no—
635C42—92no—
636C42—272no—
637C42—271no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—41no—
642C22×C3—94no—
643C22×C3—92no—
644C22×C3—181no—
645C22×C3—181no—
646C22×C3—182no—
647C22×C3—182no—
648C22×C3C22×D3211yescharacteristic
649C22×C3C22×D3211yescharacteristic
650C22×C3C22×D3211yescharacteristic
651C2×D3—32no—
652C2×D3—32no—
653C2×D3—34no—
654C2×D3—34no—
655C2×D3—62no—
656C2×D3—64no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—61no—
660C2×D3—62no—
661C2×D3—61no—
662C2×D3—62no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—122no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—122no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—42no—
673C3×C4—62no—
674C3×C4—62no—
675C3×C4—61no—
676C3×C4—62no—
677C3×C4—62no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—92no—
682C3×C4—94no—
683C3×C4—122no—
684C3×C4—122no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C4×D3212yes—
688C3×C4C4×D3212yes—
689C3×C4C4×D3212yes—
690Dic3—21no—
691Dic3—21no—
692Dic3—22no—
693Dic3—22no—
694Dic3—34no—
695Dic3—34no—
696Dic3—32no—
697Dic3—32no—
698Dic3—64no—
699Dic3—62no—
700Dic3—182no—
701Dic3—182no—
702Dic3—181no—
703Dic3—181no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—181no—
708Dic3—361no—
709Dic3—361no—
710Dic3—361no—
711Dic3—361no—
712Dic3—362no—
713Dic3—362no—
714C32—21no—
715C32—21no—
716C32—21no—
717C32—41no—
718C32#550411yescharacteristic, complemented
719C32#554611yescharacteristic, complemented
720C32#557411yescharacteristic, complemented
721C23—92no—
722C23—91no—
723Q8—94no—
724D4—94no—
725D4—278no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—92no—
731C2×C4—91no—
732C2×C4—94no—
733C2×C4—278no—
734C2×C4—271no—
735C2×C4—271no—
736C2×C4—362no—
737C2×C4—362no—
738C2×C4—1082no—
739C2×C4D3311yescharacteristic
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—41no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—184no—
753C2×C3—182no—
754C2×C3#6429711yescharacteristic
755C2×C3C2×C4×D3211yescharacteristic
756C2×C3C2×C4×D3211yescharacteristic
757C2×C3C2×C4×D3211yescharacteristic
758C2×C3#6430711yescharacteristic
759C2×C3#6431311yescharacteristic
760C2×C3#6431411yescharacteristic
761C2×C3#6431511yescharacteristic
762C2×C3#6431611yescharacteristic
763D3—62no—
764D3—62no—
765D3—64no—
766D3—64no—
767D3—124no—
768D3—122no—
769C22—92no—
770C22—94no—
771C22—181no—
772C22—182no—
773C22—182no—
774C22—181no—
775C22C2×D3311yescharacteristic
776C4—61no—
777C4—62no—
778C4—62no—
779C4—61no—
780C4—92no—
781C4—94no—
782C4—541no—
783C4—541no—
784C4#8894912yes—
785C3—21no—
786C3—21no—
787C3—21no—
788C3—41no—
789C3#1059388911yescharacteristic, complemented
790C3#1059432711yescharacteristic, complemented
791C3#1059435911yescharacteristic, complemented
792C2—182no—
793C2—184no—
794C2#1172438111yescharacteristic
795C2#1172439711yescharacteristic
796C2C2×#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. #11723501C2semidirect
3. #11723437C2semidirect
4. #11723410C2semidirect
5. C3×#63900C2semidirect
6. C3×#63894C2semidirect
7. C3×#63844C2semidirect
8. #11722934C2semidirect
9. #11722931C2semidirect
10. #11722922C2semidirect
11. #11722910C2semidirect
20. #89041C4semidirect
55. #63900D3semidirect
59. #63894D3semidirect
70. #63844D3semidirect
82. C3×C4⋊(C3⋊D3)C2×C4semidirect
83. C3×C4×C3⋊D3C2×C4semidirect
84. C3×#634C2×C4semidirect
89. #6295C2×C4semidirect
90. #6294C2×C4semidirect
274. C4⋊(C3⋊D3)C4×D3semidirect
276. C4×C3⋊D3C4×D3semidirect
277. #634C4×D3semidirect
503. C33#520semidirect
718. C32#5504semidirect
719. C32#5546semidirect
720. C32#5574semidirect
789. C3#10593889semidirect
790. C3#10594327semidirect
791. C3#10594359semidirect

Maximal subgroups

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

subgroupindex
C2×#890412
#117235012
#117234372
#117234102
C3×#639002
C3×#638942
C3×#638442
#117229342
#117229312
#117229222
#117229102
#105943593
#105943273
#105938893