Finite Group Databasebeta

← #13169235

Subgroups — #13169235

Order 1728.

1582 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89022C211yesmaximal, characteristic
2#11723668C211yesmaximal, characteristic, complemented
3#11723494C211yesmaximal, characteristic, complemented
4#11723484C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63855C211yesmaximal, characteristic, complemented
7C3×#63844C211yesmaximal, characteristic, complemented
8#11722935C212yesmaximal, complemented
9#11722932C212yesmaximal, complemented
10#11722920C212yesmaximal, complemented
11#11722912C212yesmaximal, complemented
12#10594990—31nomaximal
13#10594327—31nomaximal
14#10593890—31nomaximal
15C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6291C2212yes—
19C2×#6289C2212yes—
20C2×#6289C2212yes—
21C2×#6289C2212yes—
22#89022C418yescomplemented
23C2×C3×D3×Dic3C2212yes—
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C32×C4⋊Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88815C2212yes—
29#88813C2212yes—
30#88804C2212yes—
31#88804C2212yes—
32C3×#3724C2212yes—
33C3×Dic3⋊Dic3C2211yescharacteristic
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×Dic32C2212yes—
39C2×#3828—31no—
40C2×#3799—31no—
41C2×#3799—31no—
42C2×#3799—61no—
43#64102—31no—
44C4×C4⋊(C3⋊D3)—31no—
45C3×#926—31no—
46C2×C3×C4⋊Dic3—31no—
47C3×D3×C4⋊C4—31no—
48C3×#887—31no—
49C3×#872—31no—
50C3×C4×Dic6—31no—
51#63952—32no—
52#63952—32no—
53#63904—32no—
54C4×#626—32no—
55#63900—32no—
56#63894—31no—
57#63894—31no—
58#63894—31no—
59#63894—31no—
60#63894—61no—
61#63894—61no—
62D3×C4⋊Dic3D311yescharacteristic, complemented
63#63883—32no—
64#63883—32no—
65#63881—32no—
66#63880—32no—
67#63855D311yescharacteristic, complemented
68#63849—32no—
69#63844—31no—
70#63844D311yescharacteristic, complemented
71#63843—31no—
72Dic3×Dic6—31no—
73#63836—32no—
74#63836—32no—
75C22×C3⋊(C3⋊D3)C2312yes—
76C22×C32×D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C4⋊(C3⋊(C3⋊D3))C2×C414yescomplemented
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C3×#634C2×C414yescomplemented
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C32×C4×D3C2×C414yescomplemented
89#6291C2×C418yescomplemented
90#6289—42no—
91#6289—42no—
92#6289C2×C418yescomplemented
93C3×D3×Dic3—42no—
94#5574—91no—
95#5523—91no—
96#5504—91no—
97C22×C32×C4—31no—
98C2×#638—32no—
99#3828—38no—
100C2×C4⋊(C3⋊D3)—31no—
101C2×C4⋊(C3⋊D3)—31no—
102C2×C4⋊(C3⋊D3)—31no—
103C2×C4⋊(C3⋊D3)—61no—
104C2×C4⋊(C3⋊D3)—61no—
105C2×C4⋊(C3⋊D3)—61no—
106C2×C4⋊(C3⋊D3)—121no—
107C2×C4×C3⋊D3—32no—
108C2×C4×C3⋊D3—32no—
109C2×C4×C3⋊D3—32no—
110C2×#634C2×D311yescharacteristic
111C22×C3×Dic3—32no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3C2×D311yescharacteristic
115C2×C3×C4×D3C2×D311yescharacteristic
116C2×C3×Dic6—31no—
117C2×C3×Dic6—31no—
118C2×C3×Dic6—61no—
119C2×#626—32no—
120C2×#626—32no—
121C2×#626—62no—
122C2×#624—32no—
123C2×#624—32no—
124C2×#624—32no—
125C2×#624—32no—
126C2×#624—32no—
127C2×#624—32no—
128C2×#624—62no—
129C2×#624—62no—
130C2×#624—62no—
131C2×D3×Dic3C2×D312yes—
132#3799—38no—
133#3799—38no—
134#3799—68no—
135C32×C4⋊C4—31no—
136C32×C42—31no—
137#3752—32no—
138#3752—32no—
139C4⋊(C3⋊Dic3)C2×D311yescharacteristic
140C4×C3⋊Dic3C2×D311yescharacteristic
141C3×#217—31no—
142C3×#217—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4—31no—
145C3×C4⋊Dic3—21no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—32no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—61no—
152C3×C4⋊Dic3C2×D311yescharacteristic
153C3×C4⋊Dic3C2×D311yescharacteristic
154C3×Dic3⋊C4—32no—
155C3×Dic3⋊C4—32no—
156C3×Dic3⋊C4—31no—
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—31no—
159C3×C4×Dic3—21no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—32no—
163C3×C4×Dic3—32no—
164C3×C4×Dic3—61no—
165C3×C4×Dic3C2×D311yescharacteristic
166C3×C4×Dic3C2×D311yescharacteristic
167#3724—32no—
168#3724C2×D312yes—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—32no—
171Dic3⋊Dic3C2×D311yescharacteristic
172Dic3⋊Dic3C2×D312yes—
173Dic3⋊Dic3C2×D311yescharacteristic
174#3722—32no—
175#3722—32no—
176#3722—32no—
177#3722—32no—
178#3722—62no—
179#3722—62no—
180(C2×D3)⋊Dic3C2×D311yescharacteristic
181(C2×D3)⋊Dic3C2×D311yescharacteristic
182Dic32—32no—
183Dic32—32no—
184Dic32—32no—
185Dic32C2×D312yes—
186C22×C33C2411yescharacteristic
187C2×C3⋊(C3⋊D3)—22no—
188C2×C3⋊(C3⋊D3)—22no—
189C2×C3⋊(C3⋊D3)C22×C414yes—
190C2×C32×D3—21no—
191C2×C32×D3—21no—
192C2×C32×D3C22×C412yes—
193C33×C4C22×C412yes—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3—21no—
197C3×C3⋊Dic3C22×C414yes—
198C32×Dic3—21no—
199C32×Dic3—22no—
200C32×Dic3—21no—
201C32×Dic3C22×C412yes—
202C2×#239—91no—
203C2×#235—91no—
204C2×#235—91no—
205C2×#235—181no—
206C3×C4×Q8—91no—
207C3×#117—91no—
208C2×C3×C4⋊C4—91no—
209Q8×Dic3—91no—
210C4×#67—92no—
211C4×#67—92no—
212#926—31no—
213C2×C4⋊Dic3—31no—
214#893—91no—
215#893—91no—
216#893—92no—
217#893—91no—
218#893—181no—
219#892—92no—
220#892—92no—
221D3×C4⋊C4—31no—
222D3×C4⋊C4—92no—
223D3×C4⋊C4—92no—
224D3×C4⋊C4—92no—
225#887—31no—
226#887—91no—
227#67⋊C4—92no—
228#67⋊C4—92no—
229C4×D12—91no—
230C4×D12—91no—
231C4×D12—92no—
232C4×D12—91no—
233C4×D12—181no—
234#872—31no—
235#872—92no—
236C4×Dic6—31no—
237C4×Dic6—91no—
238C23×C32—31no—
239C22×C3⋊D3—32no—
240C22×C3⋊D3—32no—
241C22×C3⋊D3—32no—
242C22×C3⋊D3—62no—
243C22×C3⋊D3—62no—
244C22×C3⋊D3—62no—
245C22×C3⋊D3—122no—
246C22×C3×D3—21no—
247C22×C3×D3C22×D311yescharacteristic
248C22×C3×D3C22×D311yescharacteristic
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—31no—
253C2×C32×C4—34no—
254C2×C32×C4—31no—
255C2×C32×C4—32no—
256C2×C32×C4—31no—
257C2×C32×C4—41no—
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261#638—38no—
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D312yes—
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D312yes—
266C4⋊(C3⋊D3)—34no—
267C4⋊(C3⋊D3)—34no—
268C4⋊(C3⋊D3)—34no—
269C4⋊(C3⋊D3)—64no—
270C4⋊(C3⋊D3)—64no—
271C4⋊(C3⋊D3)—64no—
272C4⋊(C3⋊D3)—124no—
273C4×C3⋊D3—38no—
274C4×C3⋊D3—122no—
275C4×C3⋊D3—122no—
276#634C4×D314yescomplemented
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—62no—
291C2×C3×Dic3—61no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3—122no—
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D312yes—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D312yes—
299C2×C3×Dic3C22×D311yescharacteristic
300C2×C3×Dic3C22×D311yescharacteristic
301C2×C3×Dic3C22×D311yescharacteristic
302C3×C4×D3—24no—
303C3×C4×D3—122no—
304C3×C4×D3C4×D314yescomplemented
305C3×C4×D3C4×D314yescomplemented
306C3×Dic6—34no—
307C3×Dic6—34no—
308C3×Dic6—64no—
309#626—38no—
310#626—38no—
311#626—68no—
312#624—38no—
313#624—38no—
314#624—68no—
315#624—122no—
316#624—122no—
317#624—122no—
318#624—122no—
319#624—124no—
320#624—124no—
321D3×Dic3—42no—
322#520—271noSylow
323C2×C33C23×C411yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C2×C332−1+411yescharacteristic
326C3⋊(C3⋊D3)—24no—
327C32×D3—22no—
328C2×C3×Q8—91no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—92no—
333C2×#67—92no—
334C2×#67—92no—
335C2×#67—182no—
336C22×Dic3—32no—
337#239—98no—
338#235—98no—
339#235—98no—
340#235—188no—
341C2×D12—92no—
342C2×D12—91no—
343C2×D12—91no—
344C2×D12—91no—
345C2×D12—181no—
346C2×D12—181no—
347C2×D12—181no—
348C2×D12—361no—
349C2×C4×D3—32no—
350C2×C4×D3—92no—
351C2×C4×D3—92no—
352C2×C4×D3—92no—
353C2×C4×D3—92no—
354C2×C4×D3—92no—
355C2×C4×D3—92no—
356C2×C4×D3—92no—
357C2×C4×D3—92no—
358C2×C4×D3—92no—
359C2×C4×D3—182no—
360C2×C4×D3—182no—
361C2×C4×D3—182no—
362C2×C4×D3D3211yescharacteristic
363C2×Dic6—31no—
364C2×Dic6—31no—
365C2×Dic6—61no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—92no—
371C3×C4⋊C4—92no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C42—31no—
377C3×C42—31no—
378C3×C42—61no—
379C3×C42—92no—
380C3×C42—91no—
381#217—31no—
382#217—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—92no—
386(C2×D3)⋊C4—92no—
387(C2×D3)⋊C4—92no—
388(C2×D3)⋊C4—92no—
389(C2×D3)⋊C4—92no—
390(C2×D3)⋊C4—92no—
391(C2×D3)⋊C4—182no—
392(C2×D3)⋊C4—182no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—32no—
397C4⋊Dic3—31no—
398C4⋊Dic3—61no—
399C4⋊Dic3—92no—
400C4⋊Dic3D3211yescharacteristic
401Dic3⋊C4—32no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—32no—
405Dic3⋊C4—32no—
406Dic3⋊C4—92no—
407Dic3⋊C4—92no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—32no—
411C4×Dic3—32no—
412C4×Dic3—61no—
413C4×Dic3—92no—
414C4×Dic3—92no—
415C4×Dic3—92no—
416C4×Dic3D3211yescharacteristic
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—32no—
421C22×C32—41no—
422C22×C32—61no—
423C22×C32—61no—
424C22×C32C23×D311yescharacteristic
425C22×C32C23×D311yescharacteristic
426C22×C32C23×D311yescharacteristic
427C2×C3⋊D3—34no—
428C2×C3⋊D3—34no—
429C2×C3⋊D3—34no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—62no—
434C2×C3⋊D3—62no—
435C2×C3⋊D3—62no—
436C2×C3⋊D3—62no—
437C2×C3⋊D3—62no—
438C2×C3⋊D3—62no—
439C2×C3⋊D3—124no—
440C2×C3⋊D3—122no—
441C2×C3⋊D3—122no—
442C2×C3⋊D3—122no—
443C2×C3⋊D3—122no—
444C2×C3⋊D3—122no—
445C2×C3⋊D3—122no—
446C2×C3⋊D3—242no—
447C2×C3⋊D3—242no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—22no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3C2×C4×D312yes—
456C2×C3×D3C2×C4×D312yes—
457C32×C4—22no—
458C32×C4—22no—
459C32×C4—22no—
460C32×C4—32no—
461C32×C4—42no—
462C32×C4—61no—
463C32×C4—61no—
464C32×C4—62no—
465C32×C4C2×C4×D312yes—
466C32×C4C2×C4×D312yes—
467C32×C4C2×C4×D312yes—
468C3⋊Dic3—21no—
469C3⋊Dic3—22no—
470C3⋊Dic3—21no—
471C3⋊Dic3C2×C4×D314yes—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—22no—
478C3×Dic3—21no—
479C3×Dic3—22no—
480C3×Dic3—34no—
481C3×Dic3—34no—
482C3×Dic3—42no—
483C3×Dic3—41no—
484C3×Dic3—64no—
485C3×Dic3—62no—
486C3×Dic3—61no—
487C3×Dic3—61no—
488C3×Dic3—61no—
489C3×Dic3—61no—
490C3×Dic3—62no—
491C3×Dic3—62no—
492C3×Dic3—122no—
493C3×Dic3—121no—
494C3×Dic3C2×C4×D312yes—
495C3×Dic3C2×C4×D312yes—
496C2×#41—271no—
497C4×Q8—91no—
498C4×Q8—271no—
499C4×D4—271no—
500C4×D4—272no—
501C4×D4—271no—
502C4×D4—272no—
503#117—91no—
504#117—272no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—272no—
507C33#52011yescharacteristic, complemented, Sylow
508C23×C3—31no—
509C23×C3—31no—
510C23×C3—61no—
511C22×D3—92no—
512C22×D3—92no—
513C22×D3—92no—
514C22×D3—182no—
515C22×D3—182no—
516C22×D3—182no—
517C22×D3—362no—
518C22×D3C2×D3211yescharacteristic
519C3×Q8—94no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—34no—
526C2×C3×C4—34no—
527C2×C3×C4—31no—
528C2×C3×C4—32no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—32no—
533C2×C3×C4—41no—
534C2×C3×C4—64no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—62no—
539C2×C3×C4—92no—
540C2×C3×C4—91no—
541C2×C3×C4—92no—
542C2×C3×C4—91no—
543C2×C3×C4—362no—
544C2×C3×C4C2×D3211yescharacteristic
545C2×C3×C4C2×D3211yescharacteristic
546C2×C3×C4C2×D3211yescharacteristic
547#67—98no—
548#67—98no—
549#67—188no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—61no—
559C2×Dic3—62no—
560C2×Dic3—61no—
561C2×Dic3—62no—
562C2×Dic3—122no—
563C2×Dic3C2×D3211yescharacteristic
564C2×Dic3C2×D3212yes—
565C2×Dic3C2×D3211yescharacteristic
566C2×Dic3C2×D3211yescharacteristic
567D12—98no—
568D12—94no—
569D12—94no—
570D12—94no—
571D12—184no—
572D12—184no—
573D12—184no—
574D12—364no—
575C4×D3—98no—
576C4×D3—98no—
577C4×D3—98no—
578C4×D3—122no—
579C4×D3—188no—
580C4×D3—362no—
581C4×D3—362no—
582C4×D3—362no—
583C4×D3—362no—
584C4×D3—362no—
585C4×D3—362no—
586C4×D3—364no—
587C4×D3—364no—
588C4×D3#62414yescomplemented
589Dic6—34no—
590Dic6—34no—
591Dic6—64no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—41no—
602C2×C32—41no—
603C2×C32—41no—
604C2×C32—62no—
605C2×C32C22×C4×D311yescharacteristic
606C2×C32C22×C4×D311yescharacteristic
607C2×C32C22×C4×D311yescharacteristic
608C2×C32#100411yescharacteristic
609C2×C32#100711yescharacteristic
610C2×C32#100711yescharacteristic
611C2×C32#100911yescharacteristic
612C2×C32#100911yescharacteristic
613C2×C32#101011yescharacteristic
614C3⋊D3—64no—
615C3⋊D3—64no—
616C3⋊D3—64no—
617C3⋊D3—124no—
618C3⋊D3—124no—
619C3⋊D3—124no—
620C3⋊D3—244no—
621C3×D3—22no—
622C3×D3—22no—
623C3×D3—42no—
624#41—278no—
625C2×Q8—91no—
626C2×D4—272no—
627C2×D4—271no—
628C22×C4—31no—
629C22×C4—92no—
630C22×C4—272no—
631C22×C4—272no—
632C22×C4—272no—
633C4⋊C4—31no—
634C4⋊C4—92no—
635C4⋊C4—91no—
636C4⋊C4—92no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—272no—
640C22⋊C4—91no—
641C22⋊C4—91no—
642C22⋊C4—272no—
643C22⋊C4—272no—
644C42—31no—
645C42—92no—
646C42—91no—
647C42—272no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—32no—
652C22×C3—32no—
653C22×C3—41no—
654C22×C3—62no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C22×D3211yescharacteristic
662C22×C3C22×D3211yescharacteristic
663C22×C3C22×D3211yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—94no—
667C2×D3—94no—
668C2×D3—94no—
669C2×D3—184no—
670C2×D3—184no—
671C2×D3—184no—
672C2×D3—182no—
673C2×D3—182no—
674C2×D3—182no—
675C2×D3—182no—
676C2×D3—182no—
677C2×D3—182no—
678C2×D3—364no—
679C2×D3—362no—
680C2×D3—362no—
681C2×D3—362no—
682C2×D3—362no—
683C2×D3—362no—
684C2×D3—362no—
685C2×D3—722no—
686C2×D3—722no—
687C2×D3C2×#62412yes—
688C3×C4—22no—
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—32no—
692C3×C4—32no—
693C3×C4—42no—
694C3×C4—62no—
695C3×C4—62no—
696C3×C4—61no—
697C3×C4—62no—
698C3×C4—61no—
699C3×C4—62no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—94no—
703C3×C4—122no—
704C3×C4—121no—
705C3×C4—182no—
706C3×C4—181no—
707C3×C4—181no—
708C3×C4C4×D3212yes—
709C3×C4C4×D3212yes—
710C3×C4C2×#62412yes—
711Dic3—21no—
712Dic3—21no—
713Dic3—22no—
714Dic3—34no—
715Dic3—34no—
716Dic3—64no—
717Dic3—62no—
718Dic3—61no—
719Dic3—61no—
720Dic3—62no—
721Dic3—61no—
722Dic3—61no—
723Dic3—62no—
724Dic3—122no—
725Dic3—121no—
726Dic3C2×#62412yes—
727C32—21no—
728C32—21no—
729C32—21no—
730C32—41no—
731C32#550411yescharacteristic, complemented
732C32#552311yescharacteristic, complemented
733C32#557411yescharacteristic, complemented
734C23—31no—
735C23—272no—
736Q8—94no—
737D4—278no—
738D4—274no—
739C2×C4—31no—
740C2×C4—34no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—32no—
744C2×C4—92no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—92no—
748C2×C4—278no—
749C2×C4—362no—
750C2×C4—1082no—
751C2×C4—1082no—
752C2×C4D3311yescharacteristic
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—41no—
763C2×C3—41no—
764C2×C3—41no—
765C2×C3—62no—
766C2×C3—62no—
767C2×C3—122no—
768C2×C3#6429711yescharacteristic
769C2×C3#6429711yescharacteristic
770C2×C3C2×C4×D3211yescharacteristic
771C2×C3C2×C4×D3211yescharacteristic
772C2×C3#6430711yescharacteristic
773C2×C3#6430811yescharacteristic
774C2×C3#6431411yescharacteristic
775C2×C3#6431611yescharacteristic
776C2×C3C22×#62411yescharacteristic
777D3—22no—
778D3—184no—
779D3—184no—
780D3—184no—
781D3—364no—
782D3—364no—
783D3—364no—
784D3—724no—
785C22—32no—
786C22—61no—
787C22—61no—
788C22—274no—
789C22—542no—
790C22—542no—
791C22C2×D3311yescharacteristic
792C4—32no—
793C4—62no—
794C4—61no—
795C4—61no—
796C4—94no—
797C4—182no—
798C4—181no—
799C4—181no—
800C4D3×#62412yes—
801C3—21no—
802C3—21no—
803C3—21no—
804C3—41no—
805C3#1059389011yescharacteristic, complemented
806C3#1059432711yescharacteristic, complemented
807C3#1059499011yescharacteristic, complemented
808C2—62no—
809C2—544no—
810C2#1172438411yescharacteristic
811C2#1172439511yescharacteristic
812C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89022C2
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. #11723668C2semidirect
3. #11723494C2semidirect
4. #11723484C2semidirect
5. C3×D3×C4⋊Dic3C2semidirect
6. C3×#63855C2semidirect
7. C3×#63844C2semidirect
8. #11722935C2semidirect
9. #11722932C2semidirect
10. #11722920C2semidirect
11. #11722912C2semidirect
22. #89022C4semidirect
62. D3×C4⋊Dic3D3semidirect
67. #63855D3semidirect
70. #63844D3semidirect
78. C4⋊(C3⋊(C3⋊D3))C2×C4semidirect
83. C3×#634C2×C4semidirect
88. C32×C4×D3C2×C4semidirect
89. #6291C2×C4semidirect
92. #6289C2×C4semidirect
276. #634C4×D3semidirect
304. C3×C4×D3C4×D3semidirect
305. C3×C4×D3C4×D3semidirect
507. C33#520semidirect
588. C4×D3#624semidirect
731. C32#5504semidirect
732. C32#5523semidirect
733. C32#5574semidirect
805. C3#10593890semidirect
806. C3#10594327semidirect
807. C3#10594990semidirect

Maximal subgroups

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

subgroupindex
C2×#890222
#117236682
#117234942
#117234842
C3×D3×C4⋊Dic32
C3×#638552
C3×#638442
#117229352
#117229322
#117229202
#117229122
#105949903
#105943273
#105938903