Finite Group Databasebeta

← #13175922

Subgroups — #13175922

Order 1728.

2388 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#89026C211yesmaximal, characteristic, complemented
3#11723924C211yesmaximal, characteristic, complemented
4C3×#64091C211yesmaximal, characteristic, complemented
5C32×#884C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723634C211yesmaximal, characteristic, complemented
8#11723615C211yesmaximal, characteristic, complemented
9#11723541C211yesmaximal, characteristic, complemented
10D3×#3752C211yesmaximal, characteristic, complemented
11#11723523C211yesmaximal, characteristic, complemented
12#11723515C211yesmaximal, characteristic, complemented
13#11723488C211yesmaximal, characteristic, complemented
14#11723474C211yesmaximal, characteristic, complemented
15#11723421C211yesmaximal, characteristic, complemented
16#10596076—31nomaximal
17#10594263—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic, complemented
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×D12C2211yescharacteristic, complemented
29C2×C32×C4×D3C2211yescharacteristic, complemented
30C3⋊D3×#67—24no—
31C2×#6292C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×#6290C2211yescharacteristic, complemented
34C2×#6290C2211yescharacteristic, complemented
35C2×#6290C2211yescharacteristic, complemented
36C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#89026—24no—
39C33×C22⋊C4C2211yescharacteristic, complemented
40#88864C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
43#88857C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×D4×C3⋊D3—31no—
57C2×D3×#67—34no—
58C2×#3802—34no—
59C32×#121—31no—
60#64148—31no—
61#64148—31no—
62#64146—31no—
63#64146—31no—
64#64139—31no—
65C2×#3752—31no—
66#64103—31no—
67#64103—31no—
68#64092—31no—
69#64092—31no—
70#64092—34no—
71#64092—64no—
72#64091—31no—
73#64091D311yescharacteristic, complemented
74C3×#884D314yescomplemented
75C3×#882—34no—
76#63983—34no—
77#63976—34no—
78#63970—34no—
79#63922—34no—
80D3×(C2×D3)⋊C4—34no—
81#63908—34no—
82#63891—34no—
83#63885—34no—
84#63884—34no—
85#63853—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3—22no—
89C22×C3×C3⋊D3—41no—
90C22×C3×C3⋊D3—41no—
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×D3×C3⋊D3—41no—
99C2×D3×C3⋊D3—41no—
100C2×D3×C3⋊D3—41no—
101C2×D3×C3⋊D3D414yescomplemented
102C2×C33×C4C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104#6312—22no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊(C3⋊D3)—22no—
109C3×#638—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×C4⋊(C3⋊D3)—22no—
112C3×C4⋊(C3⋊D3)—41no—
113C32×#67—22no—
114C32×#67—41no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—22no—
118C32×C4×D3—41no—
119#6292—22no—
120#6290—22no—
121#6290—22no—
122#6290—22no—
123#6290—41no—
124Dic3×C3⋊D3—22no—
125D3×C3⋊Dic3—41no—
126#5605—94no—
127#5589—91no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3—31no—
130C23×C3⋊D3C2×D311yescharacteristic, complemented
131C23×C3×D3—34no—
132C22×D32—34no—
133C22×D32—34no—
134C2×C32×D4—31no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C22×C32×C4—31no—
138C2×#638—31no—
139C2×#638—34no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—64no—
145C2×#638C2×D311yescharacteristic, complemented
146C22×C3⋊Dic3—31no—
147D4×C3⋊D3—64no—
148D4×C3⋊D3—64no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
151C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
152C2×C4×C3⋊D3—31no—
153C2×C4×C3⋊D3—31no—
154C2×C4×C3⋊D3—34no—
155C2×C4×C3⋊D3—64no—
156C2×C3×#67—34no—
157C2×C3×#67C2×D314yescomplemented
158C2×C3×#67C2×D314yescomplemented
159C2×C3×D12—34no—
160C2×C3×D12—34no—
161C2×C3×D12C2×D314yescomplemented
162C2×C3×C4×D3C2×D314yescomplemented
163D3×#67—616no—
164C2×#626—34no—
165C2×#625—34no—
166C2×#625—34no—
167C2×#625—34no—
168C2×#625—34no—
169C2×D3×Dic3—34no—
170C2×D3×Dic3—34no—
171#3802—616no—
172C32×C4⋊C4—31no—
173C32×C22⋊C4—24no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4C2×D314yescomplemented
176C32×C22⋊C4C2×D311yescharacteristic, complemented
177#3757—31no—
178#3757—34no—
179#3757—31no—
180#3757—64no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752—34no—
187#3752—31no—
188#3752—64no—
189#3752C2×D311yescharacteristic, complemented
190#3752C2×D311yescharacteristic, complemented
191C4⋊(C3⋊Dic3)—31no—
192C4⋊(C3⋊Dic3)—34no—
193C4⋊(C3⋊Dic3)—64no—
194#3750—31no—
195#3750—34no—
196#3750—31no—
197#3750—64no—
198C3×(C2×D3)⋊C4—34no—
199C3×(C2×D3)⋊C4—34no—
200C3×(C2×D3)⋊C4C2×D314yescomplemented
201C3×Dic3⋊C4C2×D314yescomplemented
202Dic3⋊Dic3—34no—
203#3722—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208(C2×D3)⋊Dic3—34no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)C2×D412yes—
216C2×C3×C3⋊D3—21no—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—21no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3—21no—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3—44no—
225C2×C3×C3⋊D3C2×D412yes—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C2×C32×D3—21no—
229C2×C32×D3—21no—
230C2×C32×D3—21no—
231C2×C32×D3C2×D412yes—
232D3×C3⋊D3—44no—
233D3×C3⋊D3—44no—
234C33×C4—21no—
235C33×C4—21no—
236C3⋊(C3⋊Dic3)—21no—
237C3⋊(C3⋊Dic3)—21no—
238C3⋊(C3⋊Dic3)—21no—
239C3×C3⋊Dic3—21no—
240C32×Dic3—21no—
241C32×Dic3—21no—
242C22×#67—91no—
243C2×D3×D4—94no—
244C2×D3×D4—94no—
245C2×D3×D4—91no—
246C3×#121—34no—
247C3×#120—91no—
248#953—91no—
249#939—94no—
250#939—94no—
251#938—91no—
252#938—91no—
253#937—94no—
254#937—94no—
255#937—91no—
256#937—91no—
257#935—91no—
258#930—94no—
259C2×(C2×D3)⋊C4—94no—
260#894—94no—
261#894—94no—
262#886—91no—
263#884—91no—
264#884C3⋊D311yescharacteristic, complemented
265#883—94no—
266#883—94no—
267#883—91no—
268#883—91no—
269#883—184no—
270#882—34no—
271#882—94no—
272D3×C22⋊C4—91no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32—31no—
276C23×C32C22×D314yes—
277C23×C32C22×D311yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—31no—
280C22×C3⋊D3—34no—
281C22×C3⋊D3—34no—
282C22×C3⋊D3—41no—
283C22×C3⋊D3—41no—
284C22×C3⋊D3—64no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—121no—
287C22×C3⋊D3—121no—
288C22×C3⋊D3—121no—
289C22×C3⋊D3—121no—
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—34no—
294C22×C3×D3—34no—
295C22×C3×D3—34no—
296C22×C3×D3—68no—
297C22×C3×D3—124no—
298C22×C3×D3—124no—
299C22×C3×D3C22×D314yes—
300C22×C3×D3C22×D314yes—
301C2×D32—316no—
302C2×D32—68no—
303C2×D32—124no—
304C2×D32—124no—
305C2×D32—124no—
306C2×D32—124no—
307C32×D4—62no—
308C32×D4—62no—
309C32×D4—121no—
310C2×C32×C4—24no—
311C2×C32×C4—24no—
312C2×C32×C4—31no—
313C2×C32×C4—31no—
314C2×C32×C4—121no—
315C2×C32×C4C22×D314yes—
316C2×C32×C4C22×D314yes—
317C2×C32×C4C22×D311yescharacteristic
318C2×C32×C4C22×D311yescharacteristic
319#638—41no—
320#638—62no—
321#638—62no—
322#638—62no—
323#638—62no—
324#638—68no—
325#638—128no—
326#638—121no—
327C2×C3⋊Dic3—31no—
328C2×C3⋊Dic3—31no—
329C2×C3⋊Dic3—31no—
330C2×C3⋊Dic3—34no—
331C2×C3⋊Dic3—34no—
332C2×C3⋊Dic3—34no—
333C2×C3⋊Dic3—64no—
334C2×C3⋊Dic3—64no—
335C2×C3⋊Dic3—64no—
336C2×C3⋊Dic3—121no—
337C2×C3⋊Dic3C22×D311yescharacteristic
338C4⋊(C3⋊D3)—22no—
339C4⋊(C3⋊D3)—41no—
340C4⋊(C3⋊D3)—62no—
341C4×C3⋊D3—62no—
342C4×C3⋊D3—62no—
343C4×C3⋊D3—68no—
344C4×C3⋊D3—128no—
345C3×#67—28no—
346C3×#67—44no—
347C3×#67—124no—
348C2×C3×Dic3—34no—
349C2×C3×Dic3C22×D314yes—
350C2×C3×Dic3C22×D314yes—
351C3×D12—28no—
352C3×D12—68no—
353C3×D12—124no—
354C3×C4×D3—44no—
355#626—68no—
356#625—68no—
357#625—68no—
358#625—68no—
359#625—124no—
360D3×Dic3—68no—
361D3×Dic3—124no—
362#534—271noSylow
363C2×C33—41no—
364C2×C33C22×D411yescharacteristic
365C2×C33H(5,𝔽2)11yescharacteristic
366C2×C33H(5,𝔽2)11yescharacteristic
367C3⋊(C3⋊D3)—22no—
368C3×C3⋊D3—22no—
369C3×C3⋊D3—41no—
370C3×C3⋊D3—41no—
371C32×D3—22no—
372C32×D3—41no—
373C24×C3—91no—
374C23×D3—34no—
375C23×D3—94no—
376C23×D3—94no—
377C23×D3—91no—
378C23×D3—91no—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C22×C3×C4—34no—
386C2×#67—34no—
387C2×#67—94no—
388C2×#67—94no—
389C2×#67—94no—
390C2×#67—94no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—94no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—184no—
399C2×#67—184no—
400C2×#67C2×C3⋊D311yescharacteristic, complemented
401C2×#67C2×C3⋊D311yescharacteristic, complemented
402C22×Dic3—94no—
403C22×Dic3—91no—
404D3×D4—184no—
405D3×D4—1816no—
406D3×D4—1816no—
407C2×D12—34no—
408C2×D12—34no—
409C2×D12—94no—
410C2×D12C2×C3⋊D311yescharacteristic, complemented
411C2×C4×D3—94no—
412C2×C4×D3—94no—
413C2×C4×D3—91no—
414C2×C4×D3—91no—
415C2×C4×D3—184no—
416C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
417C3×C4⋊C4—34no—
418C3×C22⋊C4—24no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—91no—
421C3×C22⋊C4—91no—
422C3×C22⋊C4D3214yescomplemented
423C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
424#217—94no—
425#217—94no—
426#217—91no—
427#217—91no—
428#217—91no—
429#217—91no—
430#217—91no—
431#217—184no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—94no—
435(C2×D3)⋊C4—94no—
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—94no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—184no—
444(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
445C4⋊Dic3—94no—
446C4⋊Dic3—91no—
447C4⋊Dic3—91no—
448C4⋊Dic3—184no—
449Dic3⋊C4—94no—
450Dic3⋊C4—94no—
451Dic3⋊C4—91no—
452Dic3⋊C4—184no—
453Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—24no—
458C22×C32—24no—
459C22×C32—24no—
460C22×C32—24no—
461C22×C32—32no—
462C22×C32—44no—
463C22×C32—44no—
464C22×C32—44no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—61no—
468C22×C32—61no—
469C22×C32—61no—
470C22×C32C23×D314yes—
471C22×C32C23×D311yescharacteristic
472C2×C3⋊D3—21no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—32no—
481C2×C3⋊D3—38no—
482C2×C3⋊D3—44no—
483C2×C3⋊D3—68no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—64no—
488C2×C3⋊D3—124no—
489C2×C3⋊D3—124no—
490C2×C3⋊D3—124no—
491C2×C3⋊D3—124no—
492C2×C3⋊D3D3×D412yes—
493C2×C3×D3—24no—
494C2×C3×D3—24no—
495C2×C3×D3—24no—
496C2×C3×D3—24no—
497C2×C3×D3—24no—
498C2×C3×D3—38no—
499C2×C3×D3—64no—
500C2×C3×D3—64no—
501C2×C3×D3—64no—
502C2×C3×D3—64no—
503C2×C3×D3—64no—
504C2×C3×D3—64no—
505C2×C3×D3—64no—
506C2×C3×D3—64no—
507C2×C3×D3—1216no—
508C2×C3×D3D3×D418yes—
509D32—1216no—
510D32—1216no—
511C32×C4—21no—
512C32×C4—21no—
513C32×C4—24no—
514C32×C4—24no—
515C32×C4—44no—
516C32×C4—44no—
517C32×C4—61no—
518C32×C4—61no—
519C3⋊Dic3—21no—
520C3⋊Dic3—61no—
521C3⋊Dic3—61no—
522C3⋊Dic3—61no—
523C3⋊Dic3—64no—
524C3⋊Dic3—64no—
525C3⋊Dic3—64no—
526C3⋊Dic3—124no—
527C3⋊Dic3—124no—
528C3⋊Dic3—124no—
529C3×Dic3—24no—
530C3×Dic3—24no—
531C3×Dic3—64no—
532C22×D4—271no—
533C22×D4—271no—
534#123—271no—
535#123—271no—
536#123—271no—
537#123—271no—
538#121—31no—
539#121—271no—
540#121—271no—
541#121—271no—
542#120—91no—
543#120—271no—
544#120—271no—
545#120—271no—
546C2×C22⋊C4—271no—
547C33#53411yescharacteristic, complemented, Sylow
548C23×C3—24no—
549C23×C3—34no—
550C23×C3—34no—
551C23×C3—91no—
552C23×C3—91no—
553C23×C3—91no—
554C23×C3—182no—
555C23×C3—361no—
556C23×C3—361no—
557C23×C3C2×D3214yes—
558C23×C3C22×C3⋊D311yescharacteristic
559C22×D3—34no—
560C22×D3—34no—
561C22×D3—34no—
562C22×D3—68no—
563C22×D3—916no—
564C22×D3—94no—
565C22×D3—91no—
566C22×D3—94no—
567C22×D3—124no—
568C22×D3—124no—
569C22×D3—184no—
570C22×D3—182no—
571C22×D3—188no—
572C22×D3—361no—
573C22×D3—361no—
574C22×D3—361no—
575C22×D3—361no—
576C22×D3—364no—
577C22×D3—364no—
578C22×D3—364no—
579C22×D3—364no—
580C22×D3C22×C3⋊D311yescharacteristic
581C22×D3C22×C3⋊D311yescharacteristic
582C3×D4—68no—
583C3×D4—68no—
584C3×D4—124no—
585C3×D4—182no—
586C3×D4—361no—
587C3×D4—361no—
588C2×C3×C4—24no—
589C2×C3×C4—24no—
590C2×C3×C4—34no—
591C2×C3×C4—34no—
592C2×C3×C4—91no—
593C2×C3×C4—124no—
594C2×C3×C4C2×D3214yes—
595C2×C3×C4C2×D3214yes—
596C2×C3×C4C22×C3⋊D311yescharacteristic
597C2×C3×C4C22×C3⋊D311yescharacteristic
598#67—22no—
599#67—41no—
600#67—124no—
601#67—182no—
602#67—182no—
603#67—188no—
604#67—188no—
605#67—188no—
606#67—182no—
607#67—188no—
608#67—182no—
609#67—182no—
610#67—368no—
611#67—361no—
612#67—364no—
613C2×Dic3—34no—
614C2×Dic3—94no—
615C2×Dic3—94no—
616C2×Dic3—94no—
617C2×Dic3—91no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—184no—
621C2×Dic3—184no—
622C2×Dic3—184no—
623C2×Dic3—182no—
624C2×Dic3—364no—
625C2×Dic3C22×C3⋊D311yescharacteristic
626C2×Dic3C22×C3⋊D311yescharacteristic
627D12—22no—
628D12—68no—
629D12—124no—
630D12—188no—
631C4×D3—41no—
632C4×D3—182no—
633C4×D3—188no—
634C4×D3—188no—
635C4×D3—368no—
636C4×D3—361no—
637C2×C32—24no—
638C2×C32—24no—
639C2×C32—24no—
640C2×C32—41no—
641C2×C32—44no—
642C2×C32—62no—
643C2×C32—84no—
644C2×C32—121no—
645C2×C32C2×D3×D414yes—
646C2×C32C2×D3×D411yescharacteristic
647C2×C32#100414yes—
648C2×C32#100411yescharacteristic
649C2×C32#100411yescharacteristic
650C2×C32#100914yes—
651C3⋊D3—22no—
652C3⋊D3—41no—
653C3⋊D3—41no—
654C3⋊D3—62no—
655C3⋊D3—68no—
656C3⋊D3—128no—
657C3×D3—28no—
658C3×D3—44no—
659C3×D3—68no—
660C3×D3—124no—
661C3×D3—124no—
662C24—91no—
663C24—271no—
664C24—271no—
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—91no—
669C2×D4—91no—
670C2×D4—91no—
671C2×D4—271no—
672C2×D4—271no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—544no—
678C2×D4—544no—
679C22×C4—31no—
680C22×C4—271no—
681C22×C4—271no—
682C22×C4—271no—
683C4⋊C4—31no—
684C4⋊C4—271no—
685C4⋊C4—271no—
686C4⋊C4—271no—
687C22⋊C4—31no—
688C22⋊C4—91no—
689C22⋊C4—91no—
690C22⋊C4—271no—
691C22⋊C4—271no—
692C22⋊C4—271no—
693C22⋊C4—271no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4D3×C3⋊D311yescharacteristic, complemented
699C22×C3—24no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—24no—
706C22×C3—38no—
707C22×C3—44no—
708C22×C3—44no—
709C22×C3—44no—
710C22×C3—64no—
711C22×C3—64no—
712C22×C3—64no—
713C22×C3—64no—
714C22×C3—64no—
715C22×C3—92no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—364no—
725C22×C3C22×D3214yes—
726C22×C3C23×C3⋊D311yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—38no—
733C2×D3—64no—
734C2×D3—64no—
735C2×D3—64no—
736C2×D3—64no—
737C2×D3—64no—
738C2×D3—64no—
739C2×D3—64no—
740C2×D3—64no—
741C2×D3—98no—
742C2×D3—92no—
743C2×D3—1216no—
744C2×D3—188no—
745C2×D3—184no—
746C2×D3—184no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—364no—
750C2×D3—364no—
751C2×D3—364no—
752C2×D3—364no—
753C2×D3—3616no—
754C2×D3—3616no—
755C2×D3D4×C3⋊D312yes—
756C3×C4—24no—
757C3×C4—24no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—44no—
761C3×C4—44no—
762C3×C4—64no—
763C3×C4—64no—
764C3×C4—181no—
765Dic3—21no—
766Dic3—21no—
767Dic3—64no—
768Dic3—184no—
769Dic3—184no—
770Dic3—184no—
771Dic3—181no—
772Dic3—181no—
773Dic3—181no—
774Dic3—364no—
775Dic3—364no—
776Dic3—364no—
777C32—24no—
778C32#558911yescharacteristic, complemented
779C32#560514yescomplemented
780C23—31no—
781C23—31no—
782C23—91no—
783C23—91no—
784C23—91no—
785C23—182no—
786C23—274no—
787C23—271no—
788C23—361no—
789C23—361no—
790C23—542no—
791C23—1081no—
792C23—1081no—
793C23—1081no—
794C23—1081no—
795C23C2×D3×C3⋊D311yescharacteristic
796D4—62no—
797D4—62no—
798D4—121no—
799D4—182no—
800D4—361no—
801D4—361no—
802D4—542no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—91no—
811C2×C4—121no—
812C2×C4—271no—
813C2×C4—271no—
814C2×C4—271no—
815C2×C4—542no—
816C2×C4—542no—
817C2×C4—1081no—
818C2×C4C2×D3×C3⋊D311yescharacteristic
819C2×C4C2×D3×C3⋊D311yescharacteristic
820C2×C3—24no—
821C2×C3—24no—
822C2×C3—24no—
823C2×C3—44no—
824C2×C3—41no—
825C2×C3—68no—
826C2×C3—84no—
827C2×C3—124no—
828C2×C3—182no—
829C2×C3—361no—
830C2×C3—361no—
831C2×C3#6430714yes—
832C2×C3D32×D414yes—
833C2×C3#6431314yes—
834C2×C3C2×D4×C3⋊D311yescharacteristic
835C2×C3#6436111yescharacteristic
836C2×C3#6436611yescharacteristic
837D3—22no—
838D3—41no—
839D3—68no—
840D3—124no—
841D3—124no—
842D3—188no—
843D3—182no—
844D3—368no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—32no—
849C22—61no—
850C22—61no—
851C22—61no—
852C22—61no—
853C22—61no—
854C22—92no—
855C22—181no—
856C22—181no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—272no—
864C22—364no—
865C22—541no—
866C22—541no—
867C22—1084no—
868C22—1084no—
869C22C22×D3×C3⋊D311yescharacteristic
870C4—21no—
871C4—21no—
872C4—61no—
873C4—61no—
874C4—181no—
875C4—541no—
876C4—541no—
877C4—541no—
878C3—24no—
879C3#1059426314yescomplemented
880C3#1059607611yescharacteristic, complemented
881C2—41no—
882C2—62no—
883C2—121no—
884C2—182no—
885C2—361no—
886C2—361no—
887C2—542no—
888C2#1172458011yescharacteristic
889C2D3×D4×C3⋊D311yescharacteristic
890C2#1172458711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×#89026C2semidirect
3. #11723924C2semidirect
4. C3×#64091C2semidirect
5. C32×#884C2semidirect
6. #11723643C2semidirect
7. #11723634C2semidirect
8. #11723615C2semidirect
9. #11723541C2semidirect
10. D3×#3752C2semidirect
11. #11723523C2semidirect
12. #11723515C2semidirect
13. #11723488C2semidirect
14. #11723474C2semidirect
15. #11723421C2semidirect
18. C23×C3×C3⋊D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×#638C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C32×#67C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×D12C22semidirect
29. C2×C32×C4×D3C22semidirect
33. C2×#6290C22semidirect
34. C2×#6290C22semidirect
35. C2×#6290C22semidirect
36. C2×Dic3×C3⋊D3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
39. C33×C22⋊C4C22semidirect
40. #88864C22semidirect
41. #88859C22semidirect
42. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
43. #88857C22semidirect
44. C3×#3752C22semidirect
45. C3×#3752C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. #88807C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
73. #64091D3semidirect
74. C3×#884D3semidirect
101. C2×D3×C3⋊D3D4semidirect
130. C23×C3⋊D3C2×D3semidirect
145. C2×#638C2×D3semidirect
151. C2×C4⋊(C3⋊D3)C2×D3semidirect
157. C2×C3×#67C2×D3semidirect
158. C2×C3×#67C2×D3semidirect
161. C2×C3×D12C2×D3semidirect
162. C2×C3×C4×D3C2×D3semidirect
175. C32×C22⋊C4C2×D3semidirect
176. C32×C22⋊C4C2×D3semidirect
189. #3752C2×D3semidirect
190. #3752C2×D3semidirect
200. C3×(C2×D3)⋊C4C2×D3semidirect
201. C3×Dic3⋊C4C2×D3semidirect
264. #884C3⋊D3semidirect
400. C2×#67C2×C3⋊D3semidirect
401. C2×#67C2×C3⋊D3semidirect
410. C2×D12C2×C3⋊D3semidirect
416. C2×C4×D3C2×C3⋊D3semidirect
422. C3×C22⋊C4D32semidirect
423. C3×C22⋊C4C2×C3⋊D3semidirect
444. (C2×D3)⋊C4C2×C3⋊D3semidirect
453. Dic3⋊C4C2×C3⋊D3semidirect
547. C33#534semidirect
698. C22⋊C4D3×C3⋊D3semidirect
778. C32#5589semidirect
779. C32#5605semidirect
879. C3#10594263semidirect
880. C3#10596076semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#890262
#117239242
C3×#640912
C32×#8842
#117236432
#117236342
#117236152
#117235412
D3×#37522
#117235232
#117235152
#117234882
#117234742
#117234212
#105960763
#105942633