Finite Group Databasebeta

← #13177506

Subgroups — #13177506

Order 1728.

2944 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
3C2×D3×#638C211yesmaximal, characteristic, complemented
4C22×#6290C211yesmaximal, characteristic, complemented
5#11723980C211yesmaximal, characteristic, complemented
6C3×#64146C211yesmaximal, characteristic, complemented
7#11723633C211yesmaximal, characteristic, complemented
8#11723631C211yesmaximal, characteristic, complemented
9#11723630C211yesmaximal, characteristic, complemented
10#11723629C211yesmaximal, characteristic, complemented
11#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
12#11723540C211yesmaximal, characteristic, complemented
13#11723514C211yesmaximal, characteristic, complemented
14#11723506C211yesmaximal, characteristic, complemented
15#11723474C211yesmaximal, characteristic, complemented
16D4×#638—31nomaximal
17#10595287—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic, complemented
19C23×C32×D3C2211yescharacteristic, complemented
20C23×C32×D3C2211yescharacteristic, complemented
21C22×D3×C3⋊D3C2211yescharacteristic, complemented
22C2×C33×D4C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic, complemented
24C2×#6312C2211yescharacteristic, complemented
25C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic, complemented
27C2×C3×#638C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic
29C2×C32×#67C2211yescharacteristic, complemented
30C32×D3×D4—24no—
31C2×C32×D12C2211yescharacteristic, complemented
32C2×C32×C4×D3C2211yescharacteristic, complemented
33C3⋊D3×#67—24no—
34D3×#638—24no—
35C2×#6292C2211yescharacteristic, complemented
36C2×#6291C2211yescharacteristic, complemented
37C2×#6291C2211yescharacteristic, complemented
38C2×#6290—24no—
39C2×#6290C2211yescharacteristic
40C2×#6290C2211yescharacteristic, complemented
41C2×#6290C2211yescharacteristic, complemented
42C2×#6290C2211yescharacteristic, complemented
43C2×#6290C2211yescharacteristic, complemented
44C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
45C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
46#88864C2211yescharacteristic, complemented
47#88859C2211yescharacteristic, complemented
48#88857C2211yescharacteristic, complemented
49C3×#3757C2211yescharacteristic, complemented
50C3×#3752C2211yescharacteristic, complemented
51C3×#3752C2211yescharacteristic, complemented
52Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, 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—
60C2×D4×C3⋊D3—31no—
61C2×C3×D3×D4D314yescomplemented
62C2×D3×#67—34no—
63C2×D3×#67—34no—
64C22×#625—34no—
65#64162—31no—
66#64162—31no—
67#64149—31no—
68#64148—31no—
69#64148—34no—
70#64148—31no—
71#64148—64no—
72#64147—31no—
73#64146—31no—
74#64146D311yescharacteristic, complemented
75D4×C3⋊Dic3—31no—
76#64139—31no—
77C4×#638—31no—
78C3×#937—34no—
79#63979—34no—
80#63977—34no—
81#63976—34no—
82#67⋊Dic3—34no—
83#63970—34no—
84#63922—34no—
85#63906—34no—
86#63885—34no—
87#63879—34no—
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3—22no—
92C22×C3×C3⋊D3—22no—
93C22×C3×C3⋊D3—41no—
94C22×C3×C3⋊D3C2311yescharacteristic
95C22×C3×C3⋊D3C2311yescharacteristic
96C22×C32×D3—22no—
97C22×C32×D3—22no—
98C22×C32×D3—22no—
99C22×C32×D3—22no—
100C22×C32×D3—41no—
101C22×C32×D3—41no—
102C22×C32×D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×D3×C3⋊D3—22no—
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—41no—
108C33×D4—22no—
109C2×C33×C4C2311yescharacteristic
110#6312—22no—
111#6312—22no—
112C2×C3⋊(C3⋊Dic3)—22no—
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
116C3×#638—22no—
117C3×#638—41no—
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C32×#67—22no—
121C32×#67D414yescomplemented
122C2×C32×Dic3C2311yescharacteristic
123C32×D12—22no—
124C32×C4×D3—22no—
125#6292—22no—
126#6291—22no—
127#6291—41no—
128#6290—22no—
129#6290—22no—
130#6290—22no—
131#6290—22no—
132#6290D414yescomplemented
133Dic3×C3⋊D3—22no—
134D3×C3⋊Dic3—22no—
135D4×#67—94no—
136#5590—91no—
137C24×C32—31no—
138C24×C32—31no—
139C23×C3⋊D3—31no—
140C23×C3⋊D3C2×D311yescharacteristic, complemented
141C23×C3×D3—34no—
142C23×C3×D3C2×D314yescomplemented
143C23×C3×D3C2×D314yescomplemented
144C22×D32—34no—
145C2×C32×D4—24no—
146C2×C32×D4—31no—
147C2×C32×D4—31no—
148C2×C32×D4—31no—
149C2×C32×D4—64no—
150C2×C32×D4C2×D314yescomplemented
151C2×C32×D4C2×D311yescharacteristic, complemented
152C22×C32×C4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—34no—
157C2×#638—34no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638—31no—
163C2×#638—31no—
164C2×#638—64no—
165C2×#638—64no—
166C2×#638—64no—
167C2×#638—64no—
168C2×#638C2×D311yescharacteristic, complemented
169C2×#638C2×D311yescharacteristic, complemented
170C22×C3⋊Dic3—31no—
171C22×C3⋊Dic3—34no—
172C22×C3⋊Dic3—31no—
173C22×C3⋊Dic3—64no—
174D4×C3⋊D3—64no—
175C2×C4⋊(C3⋊D3)—31no—
176C2×C4×C3⋊D3—31no—
177C2×C3×#67—34no—
178C2×C3×#67—34no—
179C2×C3×#67C2×D314yes—
180C2×C3×#67C2×D314yescomplemented
181C3×D3×D4—216no—
182C2×C3×D12C2×D314yescomplemented
183C2×C3×C4×D3C2×D314yescomplemented
184D3×#67—616no—
185D3×#67—616no—
186C2×#626—34no—
187C2×#626—34no—
188C2×#626—34no—
189C2×#625—34no—
190C2×#625—34no—
191C2×#625—34no—
192C2×#625—34no—
193C2×#625—34no—
194C2×#625—616no—
195C2×D3×Dic3—34no—
196C2×D3×Dic3—34no—
197#3757—31no—
198#3757—34no—
199#3757—31no—
200#3757—31no—
201#3757—31no—
202#3757—64no—
203#3757C2×D311yescharacteristic, complemented
204#3752—31no—
205#3752—34no—
206#3752—64no—
207#3752C2×D311yescharacteristic, complemented
208#3752C2×D311yescharacteristic, complemented
209C4⋊(C3⋊Dic3)—31no—
210#3750—31no—
211#3750—34no—
212#3750—64no—
213C4×C3⋊Dic3—31no—
214C3×#217—34no—
215C3×(C2×D3)⋊C4—34no—
216C3×(C2×D3)⋊C4—34no—
217Dic3⋊Dic3—34no—
218(C2×D3)⋊Dic3—34no—
219(C2×D3)⋊Dic3—34no—
220(C2×D3)⋊Dic3—34no—
221Dic32—34no—
222C22×C33—21no—
223C22×C33—21no—
224C22×C33—21no—
225C22×C33—21no—
226C22×C33—21no—
227C22×C33C2×D412yescomplemented
228C22×C33C2411yescharacteristic
229C2×C3⋊(C3⋊D3)—21no—
230C2×C3⋊(C3⋊D3)—21no—
231C2×C3⋊(C3⋊D3)—21no—
232C2×C3×C3⋊D3—21no—
233C2×C3×C3⋊D3—21no—
234C2×C3×C3⋊D3—21no—
235C2×C3×C3⋊D3—21no—
236C2×C3×C3⋊D3—21no—
237C2×C3×C3⋊D3—44no—
238C2×C3×C3⋊D3C2×D412yescomplemented
239C2×C32×D3—21no—
240C2×C32×D3—21no—
241C2×C32×D3—21no—
242C2×C32×D3—21no—
243C2×C32×D3—21no—
244C2×C32×D3—21no—
245C2×C32×D3—21no—
246C2×C32×D3—44no—
247C2×C32×D3—44no—
248C2×C32×D3C2×D412yescomplemented
249C2×C32×D3C2×D412yescomplemented
250D3×C3⋊D3—44no—
251C33×C4—21no—
252C3⋊(C3⋊Dic3)—21no—
253C3⋊(C3⋊Dic3)—21no—
254C3⋊(C3⋊Dic3)C2×D412yescomplemented
255C3×C3⋊Dic3—21no—
256C3×C3⋊Dic3—21no—
257C32×Dic3C2×D412yescomplemented
258C22×C3×D4—34no—
259C22×#67—94no—
260C22×#67—94no—
261C22×#67—91no—
262C22×#67—91no—
263C2×D3×D4—94no—
264C2×D3×D4—91no—
265C2×D3×D4C3⋊D311yescharacteristic, complemented
266C3×#120—91no—
267#953—94no—
268#953—94no—
269#940—94no—
270#940—91no—
271#939—94no—
272#939—94no—
273#939—91no—
274#939—91no—
275#939—184no—
276#938—94no—
277#937—34no—
278#937—94no—
279#937—91no—
280D4×Dic3—94no—
281#930—94no—
282C4×#67—94no—
283#884—91no—
284#884—91no—
285#882—91no—
286#882—91no—
287#67⋊C4—91no—
288#67⋊C4—91no—
289C23×C32—24no—
290C23×C32—24no—
291C23×C32—31no—
292C23×C32—31no—
293C23×C32—31no—
294C23×C32—62no—
295C23×C32—62no—
296C23×C32—62no—
297C23×C32—62no—
298C23×C32—121no—
299C23×C32—121no—
300C23×C32C22×D314yes—
301C23×C32C22×D314yes—
302C23×C32C22×D311yescharacteristic
303C23×C32C22×D311yescharacteristic
304C22×C3⋊D3—22no—
305C22×C3⋊D3—22no—
306C22×C3⋊D3—31no—
307C22×C3⋊D3—34no—
308C22×C3⋊D3—41no—
309C22×C3⋊D3—64no—
310C22×C3⋊D3—62no—
311C22×C3⋊D3—62no—
312C22×C3⋊D3—121no—
313C22×C3⋊D3C22×D311yescharacteristic
314C22×C3⋊D3C22×D311yescharacteristic
315C22×C3×D3—28no—
316C22×C3×D3—28no—
317C22×C3×D3—28no—
318C22×C3×D3—28no—
319C22×C3×D3—34no—
320C22×C3×D3—34no—
321C22×C3×D3—44no—
322C22×C3×D3—44no—
323C22×C3×D3—68no—
324C22×C3×D3—68no—
325C22×C3×D3—124no—
326C22×C3×D3C22×D314yes—
327C22×C3×D3C22×D314yes—
328C22×C3×D3C22×D314yes—
329C2×D32—68no—
330C2×D32—68no—
331C2×D32—124no—
332C32×D4—22no—
333C32×D4—28no—
334C32×D4—34no—
335C32×D4—48no—
336C32×D4—62no—
337C32×D4—62no—
338C2×C32×C4—24no—
339C2×C32×C4—31no—
340C2×C32×C4—62no—
341C2×C32×C4C22×D314yes—
342C2×C32×C4C22×D311yescharacteristic
343#638—22no—
344#638—34no—
345#638—41no—
346#638—62no—
347#638—62no—
348#638—62no—
349#638—62no—
350#638—62no—
351#638—62no—
352#638—62no—
353#638—68no—
354#638—68no—
355#638—128no—
356#638—128no—
357#638—121no—
358C2×C3⋊Dic3—31no—
359C2×C3⋊Dic3—31no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—34no—
362C2×C3⋊Dic3—34no—
363C2×C3⋊Dic3—34no—
364C2×C3⋊Dic3—64no—
365C2×C3⋊Dic3—64no—
366C2×C3⋊Dic3—64no—
367C2×C3⋊Dic3—62no—
368C2×C3⋊Dic3—62no—
369C2×C3⋊Dic3—68no—
370C2×C3⋊Dic3—128no—
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C4⋊(C3⋊D3)—62no—
374C4×C3⋊D3—62no—
375C3×#67—28no—
376C3×#67—68no—
377C3×#67—124no—
378C3×#67#67116yescomplemented
379C2×C3×Dic3—34no—
380C2×C3×Dic3—34no—
381C2×C3×Dic3C22×D314yes—
382C3×D12—28no—
383C3×C4×D3—28no—
384#626—68no—
385#626—68no—
386#626—124no—
387#625—316no—
388#625—68no—
389#625—68no—
390#625—68no—
391#625—68no—
392D3×Dic3—68no—
393D3×Dic3—68no—
394D42—271noSylow
395C2×C33—22no—
396C2×C33—41no—
397C2×C33C22×D411yescharacteristic
398C2×C33C22×D411yescharacteristic
399C2×C33H(5,𝔽2)11yescharacteristic
400C3⋊(C3⋊D3)—41no—
401C3×C3⋊D3—22no—
402C3×C3⋊D3—41no—
403C32×D3—22no—
404C32×D3—22no—
405C32×D3—41no—
406C24×C3—34no—
407C24×C3—34no—
408C24×C3—91no—
409C23×D3—34no—
410C23×D3—94no—
411C23×D3—91no—
412C23×D3C2×C3⋊D311yescharacteristic, complemented
413C23×D3C2×C3⋊D311yescharacteristic, complemented
414C2×C3×D4—24no—
415C2×C3×D4—34no—
416C2×C3×D4—34no—
417C2×C3×D4—34no—
418C2×C3×D4—616no—
419C2×C3×D4—91no—
420C2×C3×D4—91no—
421C2×C3×D4D3214yescomplemented
422C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
423C22×C3×C4—34no—
424C2×#67—34no—
425C2×#67—34no—
426C2×#67—94no—
427C2×#67—94no—
428C2×#67—94no—
429C2×#67—91no—
430C2×#67—94no—
431C2×#67—94no—
432C2×#67—94no—
433C2×#67—94no—
434C2×#67—94no—
435C2×#67—94no—
436C2×#67—91no—
437C2×#67—91no—
438C2×#67—91no—
439C2×#67—91no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C2×#67—184no—
444C2×#67—184no—
445C2×#67—1816no—
446C2×#67—184no—
447C2×#67—1816no—
448C2×#67—184no—
449C2×#67C2×C3⋊D311yescharacteristic
450C2×#67C2×C3⋊D311yescharacteristic, complemented
451C22×Dic3—94no—
452C22×Dic3—94no—
453C22×Dic3—91no—
454C22×Dic3—91no—
455C22×Dic3—184no—
456D3×D4—24no—
457D3×D4—184no—
458D3×D4—1816no—
459C2×D12—94no—
460C2×D12—91no—
461C2×D12—91no—
462C2×D12C2×C3⋊D311yescharacteristic, complemented
463C2×C4×D3—94no—
464C2×C4×D3—91no—
465C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
466C3×C22⋊C4—91no—
467C3×C22⋊C4—91no—
468C3×C22⋊C4—91no—
469#217—34no—
470#217—94no—
471#217—94no—
472#217—94no—
473#217—94no—
474#217—91no—
475#217—184no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—94no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—184no—
484C4⋊Dic3—94no—
485Dic3⋊C4—94no—
486Dic3⋊C4—91no—
487Dic3⋊C4—91no—
488Dic3⋊C4—184no—
489C4×Dic3—94no—
490C4×Dic3—91no—
491C22×C32—21no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—24no—
497C22×C32—28no—
498C22×C32—24no—
499C22×C32—24no—
500C22×C32—24no—
501C22×C32—24no—
502C22×C32—24no—
503C22×C32—32no—
504C22×C32—32no—
505C22×C32—44no—
506C22×C32—44no—
507C22×C32—44no—
508C22×C32—44no—
509C22×C32—44no—
510C22×C32—61no—
511C22×C32—61no—
512C22×C32—61no—
513C22×C32—61no—
514C22×C32—61no—
515C22×C32—61no—
516C22×C32—61no—
517C22×C32—124no—
518C22×C32—124no—
519C22×C32D3×D412yescomplemented
520C22×C32C2×#6718yescomplemented
521C22×C32C23×D314yes—
522C22×C32C23×D311yescharacteristic
523C2×C3⋊D3—21no—
524C2×C3⋊D3—21no—
525C2×C3⋊D3—21no—
526C2×C3⋊D3—21no—
527C2×C3⋊D3—21no—
528C2×C3⋊D3—44no—
529C2×C3⋊D3—61no—
530C2×C3⋊D3—61no—
531C2×C3⋊D3—61no—
532C2×C3⋊D3—64no—
533C2×C3⋊D3—64no—
534C2×C3⋊D3—64no—
535C2×C3⋊D3—124no—
536C2×C3⋊D3—124no—
537C2×C3⋊D3—124no—
538C2×C3⋊D3—124no—
539C2×C3⋊D3D3×D412yescomplemented
540C2×C3×D3—24no—
541C2×C3×D3—24no—
542C2×C3×D3—24no—
543C2×C3×D3—24no—
544C2×C3×D3—24no—
545C2×C3×D3—24no—
546C2×C3×D3—24no—
547C2×C3×D3—38no—
548C2×C3×D3—416no—
549C2×C3×D3—416no—
550C2×C3×D3—64no—
551C2×C3×D3—64no—
552C2×C3×D3—64no—
553C2×C3×D3—64no—
554C2×C3×D3—64no—
555C2×C3×D3—1216no—
556C2×C3×D3D3×D418yescomplemented
557C2×C3×D3C2×#6718yescomplemented
558D32—1216no—
559C32×C4—21no—
560C32×C4—24no—
561C32×C4—32no—
562C32×C4—44no—
563C3⋊Dic3—21no—
564C3⋊Dic3—21no—
565C3⋊Dic3—32no—
566C3⋊Dic3—38no—
567C3⋊Dic3—68no—
568C3⋊Dic3—61no—
569C3⋊Dic3—61no—
570C3⋊Dic3—64no—
571C3⋊Dic3—64no—
572C3⋊Dic3—124no—
573C3⋊Dic3—124no—
574C3×Dic3—64no—
575C3×Dic3—64no—
576C3×Dic3C2×#6718yescomplemented
577C22×D4—31no—
578C22×D4—271no—
579C22×D4—271no—
580C22×D4—271no—
581#127—271no—
582#121—271no—
583#121—271no—
584#121—271no—
585#121—271no—
586#120—91no—
587#120—271no—
588#120—271no—
589#120—271no—
590C4×D4—271no—
591C4×D4—271no—
592C33D4211yescharacteristic, complemented, Sylow
593C23×C3—24no—
594C23×C3—24no—
595C23×C3—34no—
596C23×C3—34no—
597C23×C3—34no—
598C23×C3—68no—
599C23×C3—68no—
600C23×C3—68no—
601C23×C3—68no—
602C23×C3—91no—
603C23×C3—91no—
604C23×C3—124no—
605C23×C3—124no—
606C23×C3—182no—
607C23×C3—182no—
608C23×C3—361no—
609C23×C3C2×D3214yes—
610C23×C3C2×D3214yes—
611C23×C3C22×C3⋊D311yescharacteristic
612C23×C3C22×C3⋊D311yescharacteristic
613C22×D3—22no—
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—34no—
618C22×D3—34no—
619C22×D3—41no—
620C22×D3—41no—
621C22×D3—68no—
622C22×D3—68no—
623C22×D3—94no—
624C22×D3—91no—
625C22×D3—124no—
626C22×D3—184no—
627C22×D3—182no—
628C22×D3—188no—
629C22×D3—188no—
630C22×D3—182no—
631C22×D3—361no—
632C22×D3—364no—
633C22×D3C22×C3⋊D311yescharacteristic
634C22×D3C22×C3⋊D311yescharacteristic
635C22×D3C22×C3⋊D311yescharacteristic
636C3×D4—28no—
637C3×D4—22no—
638C3×D4—316no—
639C3×D4—48no—
640C3×D4—68no—
641C3×D4—68no—
642C3×D4—182no—
643C3×D4—361no—
644C2×C3×C4—24no—
645C2×C3×C4—34no—
646C2×C3×C4—68no—
647C2×C3×C4—91no—
648C2×C3×C4—91no—
649C2×C3×C4C2×D3214yes—
650C2×C3×C4C22×C3⋊D311yescharacteristic
651#67—22no—
652#67—68no—
653#67—916no—
654#67—94no—
655#67—124no—
656#67—188no—
657#67—182no—
658#67—188no—
659#67—182no—
660#67—188no—
661#67—182no—
662#67—188no—
663#67—188no—
664#67—188no—
665#67—188no—
666#67—182no—
667#67—182no—
668#67—182no—
669#67—182no—
670#67—368no—
671#67—368no—
672#67—364no—
673#67#63814yescomplemented
674C2×Dic3—34no—
675C2×Dic3—34no—
676C2×Dic3—94no—
677C2×Dic3—91no—
678C2×Dic3—94no—
679C2×Dic3—94no—
680C2×Dic3—91no—
681C2×Dic3—91no—
682C2×Dic3—184no—
683C2×Dic3—184no—
684C2×Dic3—184no—
685C2×Dic3—188no—
686C2×Dic3—182no—
687C2×Dic3—188no—
688C2×Dic3—182no—
689C2×Dic3—368no—
690C2×Dic3C22×C3⋊D311yescharacteristic
691D12—22no—
692D12—188no—
693D12—182no—
694D12—361no—
695C4×D3—22no—
696C4×D3—182no—
697C4×D3—188no—
698C2×C32—22no—
699C2×C32—24no—
700C2×C32—24no—
701C2×C32—24no—
702C2×C32—28no—
703C2×C32—48no—
704C2×C32—41no—
705C2×C32—44no—
706C2×C32—62no—
707C2×C32—62no—
708C2×C32—84no—
709C2×C32—121no—
710C2×C32C2×D3×D414yes—
711C2×C32C2×D3×D411yescharacteristic
712C2×C32C2×D3×D411yescharacteristic
713C2×C32#100414yes—
714C2×C32#100411yescharacteristic
715C2×C32C22×#6714yes—
716C3⋊D3—22no—
717C3⋊D3—41no—
718C3⋊D3—121no—
719C3⋊D3—124no—
720C3⋊D3—244no—
721C3×D3—28no—
722C3×D3—28no—
723C3×D3—44no—
724C3×D3—68no—
725C3×D3—124no—
726C24—31no—
727C24—31no—
728C24—91no—
729C24—271no—
730C2×D4—31no—
731C2×D4—31no—
732C2×D4—31no—
733C2×D4—64no—
734C2×D4—91no—
735C2×D4—91no—
736C2×D4—271no—
737C2×D4—271no—
738C2×D4—271no—
739C2×D4—271no—
740C2×D4—271no—
741C2×D4—271no—
742C2×D4—271no—
743C2×D4—271no—
744C2×D4—271no—
745C2×D4—271no—
746C2×D4—544no—
747C2×D4—544no—
748C2×D4—544no—
749C2×D4D3×C3⋊D311yescharacteristic, complemented
750C22×C4—31no—
751C22×C4—271no—
752C22×C4—271no—
753C22×C4—271no—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4—91no—
759C22⋊C4—271no—
760C22⋊C4—271no—
761C22⋊C4—271no—
762C22⋊C4—271no—
763C22⋊C4—271no—
764C42—271no—
765C22×C3—24no—
766C22×C3—24no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—24no—
770C22×C3—24no—
771C22×C3—24no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—24no—
776C22×C3—28no—
777C22×C3—38no—
778C22×C3—38no—
779C22×C3—44no—
780C22×C3—44no—
781C22×C3—44no—
782C22×C3—44no—
783C22×C3—44no—
784C22×C3—64no—
785C22×C3—64no—
786C22×C3—64no—
787C22×C3—64no—
788C22×C3—64no—
789C22×C3—64no—
790C22×C3—64no—
791C22×C3—92no—
792C22×C3—1216no—
793C22×C3—1216no—
794C22×C3—181no—
795C22×C3—181no—
796C22×C3—181no—
797C22×C3—181no—
798C22×C3—181no—
799C22×C3—364no—
800C22×C3D3×#6718yescomplemented
801C22×C3C2×#63812yescomplemented
802C22×C3C22×D3214yes—
803C22×C3C23×C3⋊D311yescharacteristic
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—21no—
807C2×D3—21no—
808C2×D3—21no—
809C2×D3—21no—
810C2×D3—21no—
811C2×D3—38no—
812C2×D3—44no—
813C2×D3—44no—
814C2×D3—64no—
815C2×D3—64no—
816C2×D3—64no—
817C2×D3—64no—
818C2×D3—64no—
819C2×D3—1216no—
820C2×D3—184no—
821C2×D3—184no—
822C2×D3—184no—
823C2×D3—181no—
824C2×D3—181no—
825C2×D3—181no—
826C2×D3—364no—
827C2×D3—364no—
828C2×D3—364no—
829C2×D3—364no—
830C2×D3—3616no—
831C2×D3D4×C3⋊D312yescomplemented
832C2×D3C2×#63812yescomplemented
833C3×C4—24no—
834C3×C4—21no—
835C3×C4—38no—
836C3×C4—44no—
837C3×C4—181no—
838C3×C4—181no—
839Dic3—64no—
840Dic3—64no—
841Dic3—98no—
842Dic3—92no—
843Dic3—188no—
844Dic3—184no—
845Dic3—184no—
846Dic3—181no—
847Dic3—181no—
848Dic3—364no—
849Dic3—364no—
850Dic3C2×#63812yescomplemented
851C32—24no—
852C32#559011yescharacteristic, complemented
853C32D4×#6714yescomplemented
854C23—31no—
855C23—31no—
856C23—31no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—62no—
861C23—91no—
862C23—91no—
863C23—121no—
864C23—121no—
865C23—182no—
866C23—182no—
867C23—271no—
868C23—361no—
869C23—542no—
870C23—542no—
871C23—1081no—
872C23C2×D3×C3⋊D311yescharacteristic
873C23C2×D3×C3⋊D311yescharacteristic
874D4—22no—
875D4—34no—
876D4—62no—
877D4—62no—
878D4—182no—
879D4—274no—
880D4—361no—
881D4—542no—
882D4—542no—
883D4—542no—
884D4—542no—
885D4—542no—
886D4—542no—
887D4—542no—
888D4—542no—
889D4—1081no—
890C2×C4—31no—
891C2×C4—62no—
892C2×C4—91no—
893C2×C4—91no—
894C2×C4—271no—
895C2×C4—271no—
896C2×C4—271no—
897C2×C4—542no—
898C2×C4—542no—
899C2×C4—542no—
900C2×C4C2×D3×C3⋊D311yescharacteristic
901C2×C3—22no—
902C2×C3—28no—
903C2×C3—24no—
904C2×C3—24no—
905C2×C3—24no—
906C2×C3—48no—
907C2×C3—41no—
908C2×C3—44no—
909C2×C3—68no—
910C2×C3—68no—
911C2×C3—84no—
912C2×C3—124no—
913C2×C3—182no—
914C2×C3—361no—
915C2×C3D32×D414yes—
916C2×C3#6431314yes—
917C2×C3C2×D3×#6714yes—
918C2×C3C2×D4×C3⋊D311yescharacteristic
919C2×C3#6436111yescharacteristic
920C2×C3C22×#63811yescharacteristic
921D3—22no—
922D3—22no—
923D3—41no—
924D3—68no—
925D3—124no—
926D3—361no—
927D3—364no—
928D3—724no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—32no—
935C22—32no—
936C22—61no—
937C22—61no—
938C22—61no—
939C22—61no—
940C22—61no—
941C22—61no—
942C22—61no—
943C22—92no—
944C22—124no—
945C22—124no—
946C22—181no—
947C22—181no—
948C22—181no—
949C22—181no—
950C22—181no—
951C22—364no—
952C22—541no—
953C22—541no—
954C22—541no—
955C22—1084no—
956C22D3×#63812yescomplemented
957C22C22×D3×C3⋊D311yescharacteristic
958C4—21no—
959C4—32no—
960C4—181no—
961C4—181no—
962C4—272no—
963C4—541no—
964C4—541no—
965C3—24no—
966C3#1059528714yescomplemented
967C3D4×#63811yescharacteristic, complemented
968C2—22no—
969C2—41no—
970C2—62no—
971C2—62no—
972C2—121no—
973C2—182no—
974C2—361no—
975C2—1081no—
976C2D3×D4×C3⋊D311yescharacteristic
977C2#1172458711yescharacteristic
978C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C2×C3⋊D3×#67C2semidirect
3. C2×D3×#638C2semidirect
4. C22×#6290C2semidirect
5. #11723980C2semidirect
6. C3×#64146C2semidirect
7. #11723633C2semidirect
8. #11723631C2semidirect
9. #11723630C2semidirect
10. #11723629C2semidirect
11. #67⋊(C3⋊Dic3)C2semidirect
12. #11723540C2semidirect
13. #11723514C2semidirect
14. #11723506C2semidirect
15. #11723474C2semidirect
18. C23×C3×C3⋊D3C22semidirect
19. C23×C32×D3C22semidirect
20. C23×C32×D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
22. C2×C33×D4C22semidirect
23. C2×#6312C22semidirect
24. C2×#6312C22semidirect
25. C22×C3⋊(C3⋊Dic3)C22semidirect
26. C2×C3×#638C22semidirect
27. C2×C3×#638C22semidirect
29. C2×C32×#67C22semidirect
31. C2×C32×D12C22semidirect
32. C2×C32×C4×D3C22semidirect
35. C2×#6292C22semidirect
36. C2×#6291C22semidirect
37. C2×#6291C22semidirect
40. C2×#6290C22semidirect
41. C2×#6290C22semidirect
42. C2×#6290C22semidirect
43. C2×#6290C22semidirect
44. C2×Dic3×C3⋊D3C22semidirect
45. C2×D3×C3⋊Dic3C22semidirect
46. #88864C22semidirect
47. #88859C22semidirect
48. #88857C22semidirect
49. C3×#3757C22semidirect
50. C3×#3752C22semidirect
51. C3×#3752C22semidirect
52. Dic3⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
55. (C2×D3)⋊(C3⋊Dic3)C22semidirect
56. Dic3×C3⋊Dic3C22semidirect
61. C2×C3×D3×D4D3semidirect
74. #64146D3semidirect
121. C32×#67D4semidirect
132. #6290D4semidirect
140. C23×C3⋊D3C2×D3semidirect
142. C23×C3×D3C2×D3semidirect
143. C23×C3×D3C2×D3semidirect
150. C2×C32×D4C2×D3semidirect
151. C2×C32×D4C2×D3semidirect
168. C2×#638C2×D3semidirect
169. C2×#638C2×D3semidirect
180. C2×C3×#67C2×D3semidirect
182. C2×C3×D12C2×D3semidirect
183. C2×C3×C4×D3C2×D3semidirect
203. #3757C2×D3semidirect
207. #3752C2×D3semidirect
208. #3752C2×D3semidirect
227. C22×C33C2×D4semidirect
238. C2×C3×C3⋊D3C2×D4semidirect
248. C2×C32×D3C2×D4semidirect
249. C2×C32×D3C2×D4semidirect
254. C3⋊(C3⋊Dic3)C2×D4semidirect
257. C32×Dic3C2×D4semidirect
265. C2×D3×D4C3⋊D3semidirect
378. C3×#67#67semidirect
412. C23×D3C2×C3⋊D3semidirect
413. C23×D3C2×C3⋊D3semidirect
421. C2×C3×D4D32semidirect
422. C2×C3×D4C2×C3⋊D3semidirect
450. C2×#67C2×C3⋊D3semidirect
462. C2×D12C2×C3⋊D3semidirect
465. C2×C4×D3C2×C3⋊D3semidirect
519. C22×C32D3×D4semidirect
520. C22×C32C2×#67semidirect
539. C2×C3⋊D3D3×D4semidirect
556. C2×C3×D3D3×D4semidirect
557. C2×C3×D3C2×#67semidirect
576. C3×Dic3C2×#67semidirect
592. C33D42semidirect
673. #67#638semidirect
749. C2×D4D3×C3⋊D3semidirect
800. C22×C3D3×#67semidirect
801. C22×C3C2×#638semidirect
831. C2×D3D4×C3⋊D3semidirect
832. C2×D3C2×#638semidirect
850. Dic3C2×#638semidirect
852. C32#5590semidirect
853. C32D4×#67semidirect
956. C22D3×#638semidirect
966. C3#10595287semidirect
967. C3D4×#638semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×C3⋊D3×#672
C2×D3×#6382
C22×#62902
#117239802
C3×#641462
#117236332
#117236312
#117236302
#117236292
#67⋊(C3⋊Dic3)2
#117235402
#117235142
#117235062
#117234742
D4×#6383
#105952873