Finite Group Databasebeta

← #13178107

Subgroups — #13178107

Order 1728.

3512 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6312C211yesmaximal, characteristic, complemented
2C22×C32×#67C211yesmaximal, characteristic, complemented
3C2×#89039C211yesmaximal, characteristic, complemented
4C2×D3×#638C211yesmaximal, characteristic, complemented
5C3×#64162C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723638C211yesmaximal, characteristic, complemented
8#11723637C211yesmaximal, characteristic, complemented
9#11723633C211yesmaximal, characteristic, complemented
10#11723632C211yesmaximal, characteristic, complemented
11#11723630C211yesmaximal, characteristic, complemented
12#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
13#11723618C211yesmaximal, characteristic, complemented
14#11723616C211yesmaximal, characteristic, complemented
15#11723599C211yesmaximal, characteristic, complemented
16D4×#638—31nomaximal
17#10595526—34nomaximal
18C24×C33C2211yescharacteristic, complemented
19C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
20C23×C32×D3C2211yescharacteristic, complemented
21C22×D3×C3⋊D3C2211yescharacteristic, complemented
22C2×#6312—24no—
23C2×#6312C2211yescharacteristic
24C2×#6312C2211yescharacteristic, complemented
25C2×#6312C2211yescharacteristic, complemented
26C2×#6312C2211yescharacteristic, complemented
27C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
28C2×C3×#638C2211yescharacteristic, complemented
29C2×C3×#638C2211yescharacteristic, complemented
30C2×C3×#638C2211yescharacteristic, complemented
31C2×C32×#67—24no—
32C2×C32×#67C2211yescharacteristic
33C2×C32×#67C2211yescharacteristic, complemented
34C2×C32×#67C2211yescharacteristic, complemented
35C2×C32×#67C2211yescharacteristic, complemented
36C22×C32×Dic3C2211yescharacteristic, complemented
37#89039—24no—
38D3×#638—24no—
39C2×#6292C2211yescharacteristic, complemented
40C2×#6291C2211yescharacteristic, complemented
41C2×#6291C2211yescharacteristic, complemented
42C2×#6291C2211yescharacteristic, complemented
43C2×#6290C2211yescharacteristic, complemented
44C2×#6289C2211yescharacteristic, complemented
45C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3757C2211yescharacteristic, complemented
47C3×#3757C2211yescharacteristic, complemented
48C3×#3757C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
56Dic3×C3⋊Dic3C2211yescharacteristic, complemented
57C22×C32×D4—31no—
58C22×#638—31no—
59C22×#638—31no—
60C22×#638—34no—
61C22×#638—64no—
62C2×D4×C3⋊D3—31no—
63C22×C3×#67D314yescomplemented
64C2×#3811—34no—
65C2×D3×#67—34no—
66#64162—31no—
67#64162D311yescharacteristic, complemented
68#64149—31no—
69#64148—31no—
70#64148—31no—
71#64147—31no—
72#64146—31no—
73#64146—31no—
74D4×C3⋊Dic3—31no—
75#64139—31no—
76C4×#638—31no—
77C3×#953—34no—
78#63983—34no—
79#63981—34no—
80#63980—34no—
81#63979—34no—
82#63978—34no—
83#63977—34no—
84#67⋊Dic3—34no—
85#63971—34no—
86#63958—34no—
87#63952—34no—
88C23×C33—22no—
89C23×C33—22no—
90C23×C33—41no—
91C23×C33C2311yescharacteristic
92C23×C33C2311yescharacteristic
93C23×C33C2311yescharacteristic
94C22×C3⋊(C3⋊D3)—22no—
95C22×C3⋊(C3⋊D3)—22no—
96C22×C3⋊(C3⋊D3)—41no—
97C22×C3⋊(C3⋊D3)C2311yescharacteristic
98C22×C3⋊(C3⋊D3)C2311yescharacteristic
99C22×C3×C3⋊D3C2311yescharacteristic
100C22×C32×D3—22no—
101C22×C32×D3—22no—
102C22×C32×D3—41no—
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×D3×C3⋊D3—22no—
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—41no—
108#6312—22no—
109#6312—22no—
110#6312—22no—
111#6312D414yescomplemented
112C2×C3⋊(C3⋊Dic3)—22no—
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115C3×#638—22no—
116C3×#638—22no—
117C3×#638—41no—
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C32×#67—22no—
122C32×#67—22no—
123C32×#67—22no—
124C32×#67D414yescomplemented
125C2×C32×Dic3—22no—
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6292—22no—
129#6291—22no—
130#6291—22no—
131#6291—41no—
132#6290—22no—
133#6289—22no—
134D3×C3⋊Dic3—22no—
135D4×#67—94no—
136#5590—91no—
137C24×C32—24no—
138C24×C32—31no—
139C24×C32C2×D314yescomplemented
140C24×C32C2×D311yescharacteristic, complemented
141C23×C3⋊D3—31no—
142C23×C3⋊D3—34no—
143C23×C3⋊D3—31no—
144C23×C3⋊D3—64no—
145C23×C3×D3C2×D314yescomplemented
146C22×D32—34no—
147C2×C32×D4—31no—
148C2×C32×D4—31no—
149C2×C32×D4—31no—
150C2×C32×D4—31no—
151C2×C32×D4—64no—
152C22×C32×C4—31no—
153C2×#638—31no—
154C2×#638—34no—
155C2×#638—31no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—34no—
159C2×#638—34no—
160C2×#638—34no—
161C2×#638—31no—
162C2×#638—31no—
163C2×#638—31no—
164C2×#638—31no—
165C2×#638—64no—
166C2×#638—64no—
167C2×#638—616no—
168C2×#638—64no—
169C2×#638—64no—
170C2×#638—64no—
171C2×#638—64no—
172C2×#638—632no—
173C2×#638C2×D311yescharacteristic, complemented
174C2×#638C2×D311yescharacteristic, complemented
175C2×#638C2×D311yescharacteristic, complemented
176C22×C3⋊Dic3—31no—
177C22×C3⋊Dic3—34no—
178C22×C3⋊Dic3—31no—
179C22×C3⋊Dic3—64no—
180D4×C3⋊D3—64no—
181C2×C4⋊(C3⋊D3)—31no—
182C2×C4×C3⋊D3—31no—
183C2×C3×#67—216no—
184C2×C3×#67—34no—
185C2×C3×#67—34no—
186C2×C3×#67—34no—
187C2×C3×#67C2×D314yes—
188C2×C3×#67C2×D314yescomplemented
189C2×C3×#67C2×D314yescomplemented
190C2×C3×#67C2×D314yescomplemented
191C22×C3×Dic3C2×D314yescomplemented
192#3811—616no—
193D3×#67—616no—
194C2×#626—34no—
195C2×#626—34no—
196C2×#626—34no—
197C2×#626—34no—
198C2×#625—34no—
199C2×#624—34no—
200C2×D3×Dic3—34no—
201#3757—31no—
202#3757—31no—
203#3757C2×D311yescharacteristic, complemented
204#3757C2×D311yescharacteristic, complemented
205#3757C2×D311yescharacteristic, complemented
206#3752—31no—
207#3752—31no—
208#3752—31no—
209C4⋊(C3⋊Dic3)—31no—
210#3750—31no—
211C4×C3⋊Dic3—31no—
212C3×#217—34no—
213C3×#217—34no—
214C3×#217—34no—
215#3724—34no—
216Dic3⋊Dic3—34no—
217#3722—34no—
218#3722—34no—
219(C2×D3)⋊Dic3—34no—
220(C2×D3)⋊Dic3—34no—
221(C2×D3)⋊Dic3—34no—
222Dic32—34no—
223C22×C33—21no—
224C22×C33—21no—
225C22×C33—21no—
226C22×C33—21no—
227C22×C33—21no—
228C22×C33—21no—
229C22×C33—21no—
230C22×C33—44no—
231C22×C33C2×D412yescomplemented
232C22×C33C2×D412yescomplemented
233C22×C33C2411yescharacteristic
234C2×C3⋊(C3⋊D3)—21no—
235C2×C3⋊(C3⋊D3)—21no—
236C2×C3⋊(C3⋊D3)—21no—
237C2×C3⋊(C3⋊D3)—21no—
238C2×C3⋊(C3⋊D3)—21no—
239C2×C3⋊(C3⋊D3)—44no—
240C2×C3⋊(C3⋊D3)C2×D412yescomplemented
241C2×C3×C3⋊D3—21no—
242C2×C3×C3⋊D3—21no—
243C2×C3×C3⋊D3—21no—
244C2×C32×D3—21no—
245C2×C32×D3—21no—
246C2×C32×D3—21no—
247C2×C32×D3—21no—
248C2×C32×D3—21no—
249C2×C32×D3—44no—
250C2×C32×D3C2×D412yescomplemented
251D3×C3⋊D3—44no—
252C3⋊(C3⋊Dic3)—21no—
253C3⋊(C3⋊Dic3)C2×D412yescomplemented
254C3×C3⋊Dic3—21no—
255C3×C3⋊Dic3—21no—
256C3×C3⋊Dic3—21no—
257C32×Dic3—21no—
258C32×Dic3C2×D412yescomplemented
259C22×C3×D4—34no—
260C22×#67—94no—
261C22×#67—94no—
262C22×#67—91no—
263C22×#67—184no—
264C22×#67C3⋊D311yescharacteristic, complemented
265C2×D3×D4—94no—
266C2×D3×D4—91no—
267C2×D3×D4—91no—
268C3×#120—91no—
269#953—34no—
270#953—94no—
271#940—94no—
272#940—91no—
273#939—94no—
274#939—94no—
275#939—91no—
276#939—91no—
277#938—94no—
278#937—94no—
279#937—94no—
280#937—91no—
281D4×Dic3—94no—
282#930—94no—
283C4×#67—94no—
284#884—91no—
285#884—91no—
286#882—91no—
287#882—91no—
288#67⋊C4—91no—
289#67⋊C4—91no—
290C23×C32—216no—
291C23×C32—28no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—24no—
295C23×C32—24no—
296C23×C32—24no—
297C23×C32—28no—
298C23×C32—31no—
299C23×C32—31no—
300C23×C32—48no—
301C23×C32—41no—
302C23×C32—44no—
303C23×C32—48no—
304C23×C32—62no—
305C23×C32—62no—
306C23×C32—121no—
307C23×C32C22×D314yes—
308C23×C32C22×D314yes—
309C23×C32C22×D314yes—
310C23×C32C22×D311yescharacteristic
311C23×C32C22×D311yescharacteristic
312C23×C32C22×D311yescharacteristic
313C22×C3⋊D3—31no—
314C22×C3⋊D3—31no—
315C22×C3⋊D3—34no—
316C22×C3⋊D3—34no—
317C22×C3⋊D3—64no—
318C22×C3⋊D3—64no—
319C22×C3⋊D3—62no—
320C22×C3⋊D3—62no—
321C22×C3⋊D3—62no—
322C22×C3⋊D3—68no—
323C22×C3⋊D3—616no—
324C22×C3⋊D3—62no—
325C22×C3⋊D3—68no—
326C22×C3⋊D3—128no—
327C22×C3⋊D3—121no—
328C22×C3⋊D3—121no—
329C22×C3⋊D3—124no—
330C22×C3⋊D3—128no—
331C22×C3⋊D3C22×D311yescharacteristic
332C22×C3×D3—28no—
333C22×C3×D3—28no—
334C22×C3×D3—34no—
335C22×C3×D3—44no—
336C22×C3×D3C22×D314yes—
337C22×C3×D3C22×D314yes—
338C2×D32—68no—
339C2×D32—68no—
340C2×D32—124no—
341C32×D4—34no—
342C32×D4—62no—
343C32×D4—62no—
344C32×D4—62no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—62no—
348#638—22no—
349#638—22no—
350#638—34no—
351#638—316no—
352#638—41no—
353#638—616no—
354#638—62no—
355#638—62no—
356#638—62no—
357#638—62no—
358#638—68no—
359#638—62no—
360#638—68no—
361#638—616no—
362#638—616no—
363#638—616no—
364#638—68no—
365#638—62no—
366#638—121no—
367C2×C3⋊Dic3—31no—
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—34no—
370C2×C3⋊Dic3—34no—
371C2×C3⋊Dic3—64no—
372C2×C3⋊Dic3—64no—
373C2×C3⋊Dic3—62no—
374C2×C3⋊Dic3—62no—
375C2×C3⋊Dic3—68no—
376C2×C3⋊Dic3—616no—
377C2×C3⋊Dic3C22×D311yescharacteristic
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C4⋊(C3⋊D3)—62no—
381C4×C3⋊D3—62no—
382C3×#67—28no—
383C3×#67—28no—
384C3×#67—28no—
385C3×#67—68no—
386C3×#67—68no—
387C3×#67—124no—
388C3×#67#67116yescomplemented
389C2×C3×Dic3—28no—
390C2×C3×Dic3—34no—
391C2×C3×Dic3—34no—
392C2×C3×Dic3—34no—
393C2×C3×Dic3C22×D314yes—
394C2×C3×Dic3C22×D314yes—
395#626—68no—
396#626—68no—
397#626—68no—
398#626—124no—
399#625—68no—
400#624—68no—
401D3×Dic3—68no—
402D42—271noSylow
403C2×C33—22no—
404C2×C33—22no—
405C2×C33—41no—
406C2×C33C22×D411yescharacteristic
407C2×C33C22×D411yescharacteristic
408C2×C33H(5,𝔽2)11yescharacteristic
409C3⋊(C3⋊D3)—22no—
410C3⋊(C3⋊D3)—41no—
411C3×C3⋊D3—41no—
412C32×D3—22no—
413C32×D3—41no—
414C24×C3—24no—
415C24×C3—34no—
416C24×C3D3214yescomplemented
417C24×C3C2×C3⋊D311yescharacteristic, complemented
418C23×D3—94no—
419C23×D3—94no—
420C23×D3—91no—
421C23×D3—91no—
422C23×D3—184no—
423C23×D3C2×C3⋊D311yescharacteristic, complemented
424C2×C3×D4—34no—
425C2×C3×D4—34no—
426C2×C3×D4—34no—
427C2×C3×D4—34no—
428C2×C3×D4—616no—
429C2×C3×D4—91no—
430C2×C3×D4—91no—
431C2×C3×D4—91no—
432C22×C3×C4—34no—
433C2×#67—24no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—94no—
438C2×#67—94no—
439C2×#67—94no—
440C2×#67—94no—
441C2×#67—91no—
442C2×#67—94no—
443C2×#67—94no—
444C2×#67—94no—
445C2×#67—94no—
446C2×#67—91no—
447C2×#67—91no—
448C2×#67—91no—
449C2×#67—91no—
450C2×#67—91no—
451C2×#67—184no—
452C2×#67—184no—
453C2×#67—184no—
454C2×#67—184no—
455C2×#67—1816no—
456C2×#67—1816no—
457C2×#67—184no—
458C2×#67—1832no—
459C2×#67C2×C3⋊D311yescharacteristic
460C2×#67C2×C3⋊D311yescharacteristic, complemented
461C2×#67C2×C3⋊D311yescharacteristic, complemented
462C2×#67C2×C3⋊D311yescharacteristic, complemented
463C22×Dic3—94no—
464C22×Dic3—94no—
465C22×Dic3—91no—
466C22×Dic3—184no—
467C22×Dic3C2×C3⋊D311yescharacteristic, complemented
468D3×D4—1816no—
469D3×D4—184no—
470D3×D4—184no—
471C2×D12—94no—
472C2×D12—91no—
473C2×D12—91no—
474C2×D12—91no—
475C2×C4×D3—94no—
476C2×C4×D3—91no—
477C2×C4×D3—91no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481#217—34no—
482#217—34no—
483#217—34no—
484#217—94no—
485#217—94no—
486#217—91no—
487(C2×D3)⋊C4—94no—
488(C2×D3)⋊C4—94no—
489(C2×D3)⋊C4—94no—
490(C2×D3)⋊C4—91no—
491(C2×D3)⋊C4—91no—
492(C2×D3)⋊C4—91no—
493(C2×D3)⋊C4—91no—
494C4⋊Dic3—94no—
495Dic3⋊C4—94no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498C4×Dic3—94no—
499C4×Dic3—91no—
500C22×C32—28no—
501C22×C32—28no—
502C22×C32—24no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—24no—
506C22×C32—21no—
507C22×C32—21no—
508C22×C32—28no—
509C22×C32—24no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—24no—
514C22×C32—28no—
515C22×C32—28no—
516C22×C32—24no—
517C22×C32—24no—
518C22×C32—24no—
519C22×C32—24no—
520C22×C32—32no—
521C22×C32—44no—
522C22×C32—44no—
523C22×C32—44no—
524C22×C32—44no—
525C22×C32—44no—
526C22×C32—416no—
527C22×C32—432no—
528C22×C32—61no—
529C22×C32—61no—
530C22×C32—61no—
531C22×C32—61no—
532C22×C32—61no—
533C22×C32—124no—
534C22×C32D3×D418yescomplemented
535C22×C32D3×D412yescomplemented
536C22×C32D3×D412yescomplemented
537C22×C32C2×#6718yescomplemented
538C22×C32C23×D314yes—
539C22×C32C23×D311yescharacteristic
540C2×C3⋊D3—21no—
541C2×C3⋊D3—21no—
542C2×C3⋊D3—21no—
543C2×C3⋊D3—32no—
544C2×C3⋊D3—38no—
545C2×C3⋊D3—68no—
546C2×C3⋊D3—61no—
547C2×C3⋊D3—61no—
548C2×C3⋊D3—68no—
549C2×C3⋊D3—61no—
550C2×C3⋊D3—64no—
551C2×C3⋊D3—61no—
552C2×C3⋊D3—61no—
553C2×C3⋊D3—64no—
554C2×C3⋊D3—64no—
555C2×C3⋊D3—64no—
556C2×C3⋊D3—64no—
557C2×C3⋊D3—124no—
558C2×C3⋊D3—124no—
559C2×C3⋊D3—124no—
560C2×C3⋊D3—124no—
561C2×C3⋊D3—124no—
562C2×C3⋊D3—124no—
563C2×C3⋊D3—1216no—
564C2×C3⋊D3—1232no—
565C2×C3×D3—24no—
566C2×C3×D3—24no—
567C2×C3×D3—24no—
568C2×C3×D3—24no—
569C2×C3×D3—24no—
570C2×C3×D3—416no—
571C2×C3×D3—64no—
572C2×C3×D3—64no—
573C2×C3×D3—64no—
574C2×C3×D3C2×#6718yescomplemented
575D32—1216no—
576C32×C4—32no—
577C32×C4—61no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—21no—
581C3⋊Dic3—32no—
582C3⋊Dic3—38no—
583C3⋊Dic3—68no—
584C3⋊Dic3—68no—
585C3⋊Dic3—64no—
586C3⋊Dic3—61no—
587C3×Dic3—24no—
588C3×Dic3—64no—
589C3×Dic3—64no—
590C3×Dic3—64no—
591C3×Dic3C2×#6718yescomplemented
592C22×D4—31no—
593C22×D4—271no—
594C22×D4—271no—
595C22×D4—271no—
596#127—271no—
597#121—271no—
598#121—271no—
599#121—271no—
600#121—271no—
601#120—91no—
602#120—271no—
603#120—271no—
604#120—271no—
605C4×D4—271no—
606C4×D4—271no—
607C33D4211yescharacteristic, complemented, Sylow
608C23×C3—216no—
609C23×C3—28no—
610C23×C3—28no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—24no—
614C23×C3—24no—
615C23×C3—24no—
616C23×C3—34no—
617C23×C3—34no—
618C23×C3—48no—
619C23×C3—44no—
620C23×C3—41no—
621C23×C3—48no—
622C23×C3—68no—
623C23×C3—68no—
624C23×C3—91no—
625C23×C3—124no—
626C23×C3C2×D3214yes—
627C23×C3C2×D3214yes—
628C23×C3C2×D3214yes—
629C23×C3C22×C3⋊D311yescharacteristic
630C23×C3C22×C3⋊D311yescharacteristic
631C23×C3C22×C3⋊D311yescharacteristic
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—34no—
635C22×D3—41no—
636C22×D3—94no—
637C22×D3—91no—
638C22×D3—94no—
639C22×D3—91no—
640C22×D3—184no—
641C22×D3—184no—
642C22×D3—182no—
643C22×D3—188no—
644C22×D3—188no—
645C22×D3—188no—
646C22×D3—182no—
647C22×D3—1816no—
648C22×D3—188no—
649C22×D3—182no—
650C22×D3—182no—
651C22×D3—368no—
652C22×D3—361no—
653C22×D3—364no—
654C22×D3—364no—
655C22×D3—361no—
656C22×D3—368no—
657C22×D3C22×C3⋊D311yescharacteristic
658C22×D3C22×C3⋊D311yescharacteristic
659C3×D4—316no—
660C3×D4—68no—
661C3×D4—68no—
662C3×D4—68no—
663C3×D4—182no—
664C3×D4—182no—
665C3×D4—361no—
666C2×C3×C4—34no—
667C2×C3×C4—34no—
668C2×C3×C4—68no—
669C2×C3×C4—91no—
670C2×C3×C4—91no—
671C2×C3×C4—91no—
672#67—22no—
673#67—22no—
674#67—22no—
675#67—68no—
676#67—68no—
677#67—916no—
678#67—94no—
679#67—124no—
680#67—1816no—
681#67—188no—
682#67—188no—
683#67—182no—
684#67—188no—
685#67—188no—
686#67—182no—
687#67—188no—
688#67—182no—
689#67—1816no—
690#67—1816no—
691#67—1816no—
692#67—188no—
693#67—182no—
694#67—182no—
695#67—364no—
696#67#63814yescomplemented
697C2×Dic3—22no—
698C2×Dic3—34no—
699C2×Dic3—34no—
700C2×Dic3—34no—
701C2×Dic3—94no—
702C2×Dic3—91no—
703C2×Dic3—94no—
704C2×Dic3—91no—
705C2×Dic3—184no—
706C2×Dic3—184no—
707C2×Dic3—188no—
708C2×Dic3—188no—
709C2×Dic3—182no—
710C2×Dic3—1816no—
711C2×Dic3C22×C3⋊D311yescharacteristic
712C2×Dic3C22×C3⋊D311yescharacteristic
713D12—188no—
714D12—182no—
715D12—182no—
716D12—361no—
717C4×D3—188no—
718C4×D3—182no—
719C4×D3—182no—
720C2×C32—216no—
721C2×C32—28no—
722C2×C32—22no—
723C2×C32—22no—
724C2×C32—24no—
725C2×C32—24no—
726C2×C32—24no—
727C2×C32—28no—
728C2×C32—48no—
729C2×C32—48no—
730C2×C32—44no—
731C2×C32—41no—
732C2×C32—62no—
733C2×C32—121no—
734C2×C32C2×D3×D414yes—
735C2×C32C2×D3×D411yescharacteristic
736C2×C32C2×D3×D411yescharacteristic
737C2×C32#100414yes—
738C2×C32#100411yescharacteristic
739C2×C32C22×#6714yes—
740C3⋊D3—41no—
741C3⋊D3—62no—
742C3⋊D3—68no—
743C3⋊D3—128no—
744C3⋊D3—128no—
745C3⋊D3—124no—
746C3⋊D3—121no—
747C3×D3—28no—
748C3×D3—44no—
749C3×D3—124no—
750C24—31no—
751C24—271no—
752C24—271no—
753C24D3×C3⋊D311yescharacteristic, complemented
754C2×D4—31no—
755C2×D4—31no—
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—64no—
759C2×D4—91no—
760C2×D4—91no—
761C2×D4—91no—
762C2×D4—271no—
763C2×D4—271no—
764C2×D4—271no—
765C2×D4—271no—
766C2×D4—271no—
767C2×D4—271no—
768C2×D4—271no—
769C2×D4—271no—
770C2×D4—271no—
771C2×D4—544no—
772C2×D4—544no—
773C2×D4—544no—
774C22×C4—31no—
775C22×C4—271no—
776C22×C4—271no—
777C22×C4—271no—
778C4⋊C4—271no—
779C4⋊C4—271no—
780C22⋊C4—91no—
781C22⋊C4—91no—
782C22⋊C4—91no—
783C22⋊C4—271no—
784C22⋊C4—271no—
785C22⋊C4—271no—
786C22⋊C4—271no—
787C22⋊C4—271no—
788C42—271no—
789C22×C3—28no—
790C22×C3—28no—
791C22×C3—24no—
792C22×C3—24no—
793C22×C3—24no—
794C22×C3—24no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—28no—
800C22×C3—24no—
801C22×C3—24no—
802C22×C3—24no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—24no—
807C22×C3—28no—
808C22×C3—28no—
809C22×C3—38no—
810C22×C3—44no—
811C22×C3—44no—
812C22×C3—44no—
813C22×C3—44no—
814C22×C3—44no—
815C22×C3—416no—
816C22×C3—432no—
817C22×C3—64no—
818C22×C3—64no—
819C22×C3—64no—
820C22×C3—64no—
821C22×C3—64no—
822C22×C3—1216no—
823C22×C3—181no—
824C22×C3—181no—
825C22×C3—181no—
826C22×C3D3×#6718yescomplemented
827C22×C3#381118yescomplemented
828C22×C3D4×C3⋊D312yescomplemented
829C22×C3C2×#63812yescomplemented
830C22×C3C22×D3214yes—
831C22×C3C23×C3⋊D311yescharacteristic
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—44no—
838C2×D3—64no—
839C2×D3—64no—
840C2×D3—64no—
841C2×D3—98no—
842C2×D3—92no—
843C2×D3—188no—
844C2×D3—184no—
845C2×D3—184no—
846C2×D3—181no—
847C2×D3—181no—
848C2×D3—188no—
849C2×D3—184no—
850C2×D3—184no—
851C2×D3—184no—
852C2×D3—181no—
853C2×D3—181no—
854C2×D3—181no—
855C2×D3—364no—
856C2×D3—364no—
857C2×D3—364no—
858C2×D3—364no—
859C2×D3—364no—
860C2×D3—3616no—
861C2×D3—364no—
862C2×D3—3616no—
863C2×D3—3632no—
864C2×D3C2×#63812yescomplemented
865C3×C4—38no—
866C3×C4—64no—
867C3×C4—181no—
868C3×C4—181no—
869C3×C4—181no—
870Dic3—21no—
871Dic3—64no—
872Dic3—64no—
873Dic3—64no—
874Dic3—98no—
875Dic3—92no—
876Dic3—188no—
877Dic3—188no—
878Dic3—184no—
879Dic3—181no—
880Dic3C2×#63812yescomplemented
881C32—24no—
882C32#559011yescharacteristic, complemented
883C32D4×#6714yescomplemented
884C23—22no—
885C23—22no—
886C23—31no—
887C23—31no—
888C23—41no—
889C23—62no—
890C23—62no—
891C23—91no—
892C23—121no—
893C23—271no—
894C23—271no—
895C23—542no—
896C23—542no—
897C23—542no—
898C23—542no—
899C23—1081no—
900C23—1081no—
901C23C2×D3×C3⋊D311yescharacteristic
902C23C2×D3×C3⋊D311yescharacteristic
903C23C2×D3×C3⋊D311yescharacteristic
904D4—34no—
905D4—62no—
906D4—62no—
907D4—62no—
908D4—182no—
909D4—182no—
910D4—274no—
911D4—361no—
912D4—542no—
913D4—542no—
914D4—542no—
915D4—542no—
916D4—542no—
917D4—542no—
918D4—542no—
919D4—1081no—
920C2×C4—31no—
921C2×C4—31no—
922C2×C4—62no—
923C2×C4—91no—
924C2×C4—91no—
925C2×C4—91no—
926C2×C4—271no—
927C2×C4—271no—
928C2×C4—542no—
929C2×C4—542no—
930C2×C4—542no—
931C2×C3—216no—
932C2×C3—22no—
933C2×C3—22no—
934C2×C3—28no—
935C2×C3—28no—
936C2×C3—24no—
937C2×C3—24no—
938C2×C3—24no—
939C2×C3—48no—
940C2×C3—48no—
941C2×C3—41no—
942C2×C3—44no—
943C2×C3—68no—
944C2×C3—124no—
945C2×C3—361no—
946C2×C3C2×D3×#6714yes—
947C2×C3C2×#381114yes—
948C2×C3#6433014yes—
949C2×C3C2×D4×C3⋊D311yescharacteristic
950C2×C3#6436111yescharacteristic
951C2×C3C22×#63811yescharacteristic
952D3—22no—
953D3—41no—
954D3—124no—
955D3—182no—
956D3—188no—
957D3—368no—
958D3—368no—
959D3—361no—
960D3—364no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—21no—
968C22—32no—
969C22—44no—
970C22—61no—
971C22—61no—
972C22—61no—
973C22—61no—
974C22—61no—
975C22—124no—
976C22—181no—
977C22—181no—
978C22—181no—
979C22—272no—
980C22—541no—
981C22—541no—
982C22—541no—
983C22—541no—
984C22—541no—
985C22—1084no—
986C22—1084no—
987C22D3×#63812yescomplemented
988C22#8903912yescomplemented
989C22C22×D3×C3⋊D311yescharacteristic
990C4—32no—
991C4—61no—
992C4—181no—
993C4—181no—
994C4—181no—
995C4—272no—
996C4—541no—
997C3—24no—
998C3#1059552614yescomplemented
999C3D4×#63811yescharacteristic, complemented
1000C2—22no—
1001C2—22no—
1002C2—41no—
1003C2—62no—
1004C2—121no—
1005C2—361no—
1006C2—542no—
1007C2—1081no—
1008C2C2×D3×#63811yescharacteristic
1009C2C2×#8903911yescharacteristic
1010C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
hypercenterC24D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×#6312C2semidirect
2. C22×C32×#67C2semidirect
3. C2×#89039C2semidirect
4. C2×D3×#638C2semidirect
5. C3×#64162C2semidirect
6. #11723643C2semidirect
7. #11723638C2semidirect
8. #11723637C2semidirect
9. #11723633C2semidirect
10. #11723632C2semidirect
11. #11723630C2semidirect
12. #67⋊(C3⋊Dic3)C2semidirect
13. #11723618C2semidirect
14. #11723616C2semidirect
15. #11723599C2semidirect
18. C24×C33C22semidirect
19. C23×C3⋊(C3⋊D3)C22semidirect
20. C23×C32×D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
24. C2×#6312C22semidirect
25. C2×#6312C22semidirect
26. C2×#6312C22semidirect
27. C22×C3⋊(C3⋊Dic3)C22semidirect
28. C2×C3×#638C22semidirect
29. C2×C3×#638C22semidirect
30. C2×C3×#638C22semidirect
33. C2×C32×#67C22semidirect
34. C2×C32×#67C22semidirect
35. C2×C32×#67C22semidirect
36. C22×C32×Dic3C22semidirect
39. C2×#6292C22semidirect
40. C2×#6291C22semidirect
41. C2×#6291C22semidirect
42. C2×#6291C22semidirect
43. C2×#6290C22semidirect
44. C2×#6289C22semidirect
45. C2×D3×C3⋊Dic3C22semidirect
46. C3×#3757C22semidirect
47. C3×#3757C22semidirect
48. C3×#3757C22semidirect
49. #88806C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
55. (C2×D3)⋊(C3⋊Dic3)C22semidirect
56. Dic3×C3⋊Dic3C22semidirect
63. C22×C3×#67D3semidirect
67. #64162D3semidirect
111. #6312D4semidirect
124. C32×#67D4semidirect
139. C24×C32C2×D3semidirect
140. C24×C32C2×D3semidirect
145. C23×C3×D3C2×D3semidirect
173. C2×#638C2×D3semidirect
174. C2×#638C2×D3semidirect
175. C2×#638C2×D3semidirect
188. C2×C3×#67C2×D3semidirect
189. C2×C3×#67C2×D3semidirect
190. C2×C3×#67C2×D3semidirect
191. C22×C3×Dic3C2×D3semidirect
203. #3757C2×D3semidirect
204. #3757C2×D3semidirect
205. #3757C2×D3semidirect
231. C22×C33C2×D4semidirect
232. C22×C33C2×D4semidirect
240. C2×C3⋊(C3⋊D3)C2×D4semidirect
250. C2×C32×D3C2×D4semidirect
253. C3⋊(C3⋊Dic3)C2×D4semidirect
258. C32×Dic3C2×D4semidirect
264. C22×#67C3⋊D3semidirect
388. C3×#67#67semidirect
416. C24×C3D32semidirect
417. C24×C3C2×C3⋊D3semidirect
423. C23×D3C2×C3⋊D3semidirect
460. C2×#67C2×C3⋊D3semidirect
461. C2×#67C2×C3⋊D3semidirect
462. C2×#67C2×C3⋊D3semidirect
467. C22×Dic3C2×C3⋊D3semidirect
534. C22×C32D3×D4semidirect
535. C22×C32D3×D4semidirect
536. C22×C32D3×D4semidirect
537. C22×C32C2×#67semidirect
574. C2×C3×D3C2×#67semidirect
591. C3×Dic3C2×#67semidirect
607. C33D42semidirect
696. #67#638semidirect
753. C24D3×C3⋊D3semidirect
826. C22×C3D3×#67semidirect
827. C22×C3#3811semidirect
828. C22×C3D4×C3⋊D3semidirect
829. C22×C3C2×#638semidirect
864. C2×D3C2×#638semidirect
880. Dic3C2×#638semidirect
882. C32#5590semidirect
883. C32D4×#67semidirect
987. C22D3×#638semidirect
988. C22#89039semidirect
998. C3#10595526semidirect
999. C3D4×#638semidirect

Maximal subgroups

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

subgroupindex
C22×#63122
C22×C32×#672
C2×#890392
C2×D3×#6382
C3×#641622
#117236432
#117236382
#117236372
#117236332
#117236322
#117236302
#67⋊(C3⋊Dic3)2
#117236182
#117236162
#117235992
D4×#6383
#105955263