Finite Group Databasebeta

← #13175921

Subgroups — #13175921

Order 1728.

2452 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3#11723925C211yesmaximal, characteristic, complemented
4C3×#64091C211yesmaximal, characteristic, complemented
5C32×#883C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723636C211yesmaximal, characteristic, complemented
8#11723623C211yesmaximal, characteristic, complemented
9#11723541C211yesmaximal, characteristic, complemented
10#11723539C211yesmaximal, characteristic, complemented
11#11723532C211yesmaximal, characteristic, complemented
12#11723513C211yesmaximal, characteristic, complemented
13#11723493C211yesmaximal, characteristic, complemented
14#11723488C211yesmaximal, characteristic, complemented
15#11723486C211yesmaximal, characteristic, complemented
16#10596124—31nomaximal
17#10594262—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic, complemented
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
24C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
27C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic, complemented
30C3⋊D3×#67—24no—
31C2×#6292C2211yescharacteristic
32C2×#6292C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6292C2211yescharacteristic, complemented
35C2×#6290C2211yescharacteristic
36C2×#6289C2211yescharacteristic, complemented
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38D3×C4⋊(C3⋊D3)—24no—
39C33×C22⋊C4C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41#88857C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, 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—
56C22×C4⋊(C3⋊D3)—31no—
57C2×D3×#67—34no—
58C2×D3×D12—34no—
59C32×#123—31no—
60#64146—31no—
61#64138—31no—
62#64104—31no—
63#64104—31no—
64#64103—31no—
65#64103—31no—
66#64093—31no—
67#64093—31no—
68#64093—34no—
69#64093—64no—
70#64091—31no—
71#64091—31no—
72#64091D311yescharacteristic, complemented
73C22⋊C4×C3⋊D3—31no—
74C3×#883D314yescomplemented
75C3×#882—34no—
76#63983—34no—
77#63977—34no—
78#63958—34no—
79#63922—34no—
80#63921—34no—
81#63916—34no—
82#63910—34no—
83#63905—34no—
84#63890—34no—
85#63884—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—41no—
91C22×C3×C3⋊D3—41no—
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C3×C3⋊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—
105#6312—41no—
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊(C3⋊D3))—22no—
109C4×C3⋊(C3⋊D3)—41no—
110C3×#638—41no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4⋊(C3⋊D3)—22no—
113C3×C4⋊(C3⋊D3)—41no—
114C32×#67—22no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×C4×D3—22no—
119#6292—22no—
120#6292—22no—
121#6292—22no—
122#6292—41no—
123#6290—22no—
124#6289—41no—
125Dic3×C3⋊D3—22no—
126#5653—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—
135C22×C32×C4—31no—
136C2×#638—31no—
137C2×#638—34no—
138C2×#638—31no—
139C2×#638—31no—
140C2×#638—34no—
141C2×#638—64no—
142C2×#638—64no—
143C2×#638C2×D311yescharacteristic, complemented
144D4×C3⋊D3—64no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—34no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—64no—
152C2×C4⋊(C3⋊D3)—64no—
153C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
154C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—34no—
158C2×C4×C3⋊D3—31no—
159C2×C4×C3⋊D3—64no—
160C2×C3×#67—34no—
161C2×C3×#67C2×D314yes—
162C2×C3×D12—34no—
163C2×C3×D12—34no—
164C2×C3×C4×D3C2×D314yescomplemented
165D3×#67—616no—
166C2×#626—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#625—34no—
171C2×#624—34no—
172C2×D3×Dic3—34no—
173D3×D12—616no—
174C32×C4⋊C4—31no—
175C32×C4⋊C4—31no—
176C32×C22⋊C4—24no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C22⋊C4C2×D314yescomplemented
180C32×C22⋊C4C2×D311yescharacteristic, complemented
181#3757—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752—34no—
188#3752—31no—
189#3752—64no—
190#3752C2×D311yescharacteristic, complemented
191#3752C2×D311yescharacteristic, complemented
192#3750—31no—
193#3750—34no—
194#3750—31no—
195#3750—64no—
196C3×#217C2×D314yescomplemented
197C3×(C2×D3)⋊C4—34no—
198C3×(C2×D3)⋊C4—34no—
199C3×(C2×D3)⋊C4C2×D314yescomplemented
200C3×C4⋊Dic3C2×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)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)C2×D412yes—
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—21no—
225C2×C3×C3⋊D3—21no—
226C2×C3×C3⋊D3—21no—
227C2×C3×C3⋊D3—44no—
228C2×C3×C3⋊D3C2×D412yes—
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—
239C32×Dic3—21no—
240C32×Dic3—21no—
241C32×Dic3—21no—
242C22×#67—91no—
243C2×D3×D4—94no—
244C2×D3×D4—91no—
245C22×D12—94no—
246C3×#123—34no—
247C3×#120—91no—
248#953—91no—
249#938—91no—
250#938—91no—
251#937—94no—
252#937—91no—
253#937—91no—
254#935—91no—
255#929—94no—
256#895—94no—
257#895—94no—
258#894—94no—
259#894—94no—
260#886—91no—
261#884—94no—
262#884—94no—
263#884—91no—
264#884—91no—
265#884—184no—
266#883—91no—
267#883C3⋊D311yescharacteristic, complemented
268#882—34no—
269#882—94no—
270#882—94no—
271D3×C22⋊C4—94no—
272D3×C22⋊C4—91no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32C22×D314yes—
276C23×C32C22×D311yescharacteristic
277C22×C3⋊D3—22no—
278C22×C3⋊D3—31no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—31no—
281C22×C3⋊D3—34no—
282C22×C3⋊D3—34no—
283C22×C3⋊D3—41no—
284C22×C3⋊D3—41no—
285C22×C3⋊D3—64no—
286C22×C3⋊D3—64no—
287C22×C3⋊D3—62no—
288C22×C3⋊D3—121no—
289C22×C3⋊D3—121no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3⋊D3C22×D311yescharacteristic
294C22×C3⋊D3C22×D311yescharacteristic
295C22×C3×D3—34no—
296C22×C3×D3—34no—
297C22×C3×D3—34no—
298C22×C3×D3—68no—
299C22×C3×D3—124no—
300C22×C3×D3—124no—
301C22×C3×D3C22×D314yes—
302C2×D32—316no—
303C2×D32—68no—
304C2×D32—124no—
305C2×D32—124no—
306C2×D32—124no—
307C2×D32—124no—
308C32×D4—62no—
309C2×C32×C4—24no—
310C2×C32×C4—24no—
311C2×C32×C4—31no—
312C2×C32×C4—31no—
313C2×C32×C4—31no—
314C2×C32×C4—62no—
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—68no—
323#638—128no—
324#638—121no—
325#638—124no—
326#638—128no—
327C2×C3⋊Dic3—31no—
328C2×C3⋊Dic3—31no—
329C2×C3⋊Dic3—34no—
330C2×C3⋊Dic3—34no—
331C2×C3⋊Dic3—64no—
332C2×C3⋊Dic3—64no—
333C2×C3⋊Dic3C22×D311yescharacteristic
334C4⋊(C3⋊D3)—22no—
335C4⋊(C3⋊D3)—41no—
336C4⋊(C3⋊D3)—62no—
337C4⋊(C3⋊D3)—62no—
338C4⋊(C3⋊D3)—62no—
339C4⋊(C3⋊D3)—62no—
340C4⋊(C3⋊D3)—68no—
341C4⋊(C3⋊D3)—128no—
342C4⋊(C3⋊D3)—121no—
343C4×C3⋊D3—62no—
344C4×C3⋊D3—121no—
345C4×C3⋊D3—121no—
346C4×C3⋊D3—124no—
347C4×C3⋊D3—128no—
348C3×#67—28no—
349C3×#67—124no—
350C2×C3×Dic3—34no—
351C2×C3×Dic3C22×D314yes—
352C2×C3×Dic3C22×D314yes—
353C2×C3×Dic3C22×D314yes—
354C3×D12—68no—
355C3×D12—124no—
356C3×C4×D3—28no—
357#626—68no—
358#626—68no—
359#626—68no—
360#626—124no—
361#625—68no—
362#624—124no—
363D3×Dic3—68no—
364#534—271noSylow
365C2×C33—41no—
366C2×C33C22×D411yescharacteristic
367C2×C33H(5,𝔽2)11yescharacteristic
368C2×C33H(5,𝔽2)11yescharacteristic
369C3⋊(C3⋊D3)—22no—
370C3⋊(C3⋊D3)—41no—
371C3×C3⋊D3—22no—
372C3×C3⋊D3—41no—
373C3×C3⋊D3—41no—
374C32×D3—22no—
375C24×C3—91no—
376C23×D3—34no—
377C23×D3—94no—
378C23×D3—94no—
379C23×D3—91no—
380C23×D3—91no—
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—91no—
390C2×#67—91no—
391C2×#67—94no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—184no—
398C2×#67—184no—
399C2×#67—184no—
400C2×#67C2×C3⋊D311yescharacteristic
401C22×Dic3—91no—
402D3×D4—184no—
403D3×D4—1816no—
404C2×D12—34no—
405C2×D12—34no—
406C2×D12—94no—
407C2×D12—94no—
408C2×D12—94no—
409C2×D12—94no—
410C2×D12—91no—
411C2×D12—94no—
412C2×D12—184no—
413C2×D12—1816no—
414C2×C4×D3—94no—
415C2×C4×D3—94no—
416C2×C4×D3—94no—
417C2×C4×D3—91no—
418C2×C4×D3—91no—
419C2×C4×D3—184no—
420C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
421C3×C4⋊C4—34no—
422C3×C4⋊C4—34no—
423C3×C22⋊C4—24no—
424C3×C22⋊C4—34no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—91no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4D3214yescomplemented
429C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
430#217—94no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—91no—
435#217C2×C3⋊D311yescharacteristic, complemented
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—94no—
440(C2×D3)⋊C4—94no—
441(C2×D3)⋊C4—94no—
442(C2×D3)⋊C4—94no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—94no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—184no—
448(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
449C4⋊Dic3—91no—
450C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
451Dic3⋊C4—94no—
452Dic3⋊C4—94no—
453Dic3⋊C4—91no—
454Dic3⋊C4—184no—
455Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—24no—
460C22×C32—24no—
461C22×C32—24no—
462C22×C32—24no—
463C22×C32—32no—
464C22×C32—44no—
465C22×C32—44no—
466C22×C32—44no—
467C22×C32—61no—
468C22×C32—61no—
469C22×C32C23×D314yes—
470C22×C32C23×D311yescharacteristic
471C2×C3⋊D3—21no—
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—32no—
480C2×C3⋊D3—38no—
481C2×C3⋊D3—44no—
482C2×C3⋊D3—68no—
483C2×C3⋊D3—61no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—61no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—64no—
489C2×C3⋊D3—64no—
490C2×C3⋊D3—64no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—64no—
493C2×C3⋊D3—124no—
494C2×C3⋊D3—124no—
495C2×C3⋊D3—124no—
496C2×C3⋊D3—124no—
497C2×C3⋊D3—124no—
498C2×C3⋊D3—124no—
499C2×C3⋊D3—124no—
500C2×C3⋊D3D3×D412yes—
501C2×C3×D3—24no—
502C2×C3×D3—24no—
503C2×C3×D3—38no—
504C2×C3×D3—64no—
505C2×C3×D3—64no—
506C2×C3×D3—64no—
507C2×C3×D3—64no—
508C2×C3×D3—64no—
509C2×C3×D3—64no—
510C2×C3×D3—64no—
511C2×C3×D3—64no—
512C2×C3×D3—1216no—
513C2×C3×D3D3×D418yes—
514D32—1216no—
515D32—1216no—
516C32×C4—21no—
517C32×C4—21no—
518C32×C4—24no—
519C32×C4—24no—
520C32×C4—44no—
521C32×C4—44no—
522C32×C4—61no—
523C32×C4—61no—
524C32×C4—61no—
525C3⋊Dic3—21no—
526C3⋊Dic3—68no—
527C3⋊Dic3—61no—
528C3⋊Dic3—61no—
529C3⋊Dic3—64no—
530C3⋊Dic3—64no—
531C3⋊Dic3—124no—
532C3×Dic3—24no—
533C3×Dic3—24no—
534C3×Dic3—24no—
535C3×Dic3—64no—
536C22×D4—271no—
537C22×D4—271no—
538#123—31no—
539#123—271no—
540#123—271no—
541#123—271no—
542#121—271no—
543#121—271no—
544#121—271no—
545#121—271no—
546#120—91no—
547#120—271no—
548#120—271no—
549#120—271no—
550C2×C22⋊C4—271no—
551C33#53411yescharacteristic, complemented, Sylow
552C23×C3—24no—
553C23×C3—34no—
554C23×C3—91no—
555C23×C3—91no—
556C23×C3—91no—
557C23×C3—182no—
558C23×C3—361no—
559C23×C3—361no—
560C23×C3C2×D3214yes—
561C23×C3C22×C3⋊D311yescharacteristic
562C22×D3—34no—
563C22×D3—34no—
564C22×D3—34no—
565C22×D3—68no—
566C22×D3—916no—
567C22×D3—94no—
568C22×D3—91no—
569C22×D3—94no—
570C22×D3—94no—
571C22×D3—91no—
572C22×D3—124no—
573C22×D3—124no—
574C22×D3—184no—
575C22×D3—184no—
576C22×D3—188no—
577C22×D3—182no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—364no—
583C22×D3—364no—
584C22×D3—364no—
585C22×D3—364no—
586C22×D3C22×C3⋊D311yescharacteristic
587C3×D4—68no—
588C3×D4—182no—
589C3×D4—361no—
590C3×D4—361no—
591C2×C3×C4—24no—
592C2×C3×C4—24no—
593C2×C3×C4—34no—
594C2×C3×C4—34no—
595C2×C3×C4—34no—
596C2×C3×C4—68no—
597C2×C3×C4—91no—
598C2×C3×C4C2×D3214yes—
599C2×C3×C4C2×D3214yes—
600C2×C3×C4C22×C3⋊D311yescharacteristic
601C2×C3×C4C22×C3⋊D311yescharacteristic
602#67—22no—
603#67—124no—
604#67—182no—
605#67—182no—
606#67—182no—
607#67—188no—
608#67—182no—
609#67—188no—
610#67—182no—
611#67—368no—
612#67—361no—
613#67—364no—
614#67—361no—
615#67—368no—
616C2×Dic3—34no—
617C2×Dic3—94no—
618C2×Dic3—94no—
619C2×Dic3—91no—
620C2×Dic3—91no—
621C2×Dic3—184no—
622C2×Dic3—184no—
623C2×Dic3—182no—
624C2×Dic3C22×C3⋊D311yescharacteristic
625C2×Dic3C22×C3⋊D311yescharacteristic
626C2×Dic3C22×C3⋊D311yescharacteristic
627D12—68no—
628D12—124no—
629D12—182no—
630D12—188no—
631D12—188no—
632D12—188no—
633D12—188no—
634D12—368no—
635D12—364no—
636C4×D3—22no—
637C4×D3—188no—
638C4×D3—361no—
639C4×D3—364no—
640C4×D3—364no—
641C4×D3—361no—
642C4×D3—368no—
643C2×C32—24no—
644C2×C32—24no—
645C2×C32—24no—
646C2×C32—41no—
647C2×C32—44no—
648C2×C32—62no—
649C2×C32—84no—
650C2×C32C2×D3×D414yes—
651C2×C32C2×D3×D411yescharacteristic
652C2×C32#100411yescharacteristic
653C2×C32#100411yescharacteristic
654C2×C32#100914yes—
655C2×C32#100914yes—
656C3⋊D3—22no—
657C3⋊D3—41no—
658C3⋊D3—41no—
659C3⋊D3—62no—
660C3⋊D3—68no—
661C3⋊D3—128no—
662C3⋊D3—121no—
663C3⋊D3—124no—
664C3⋊D3—244no—
665C3×D3—28no—
666C3×D3—68no—
667C3×D3—124no—
668C3×D3—124no—
669C24—91no—
670C24—271no—
671C24—271no—
672C2×D4—31no—
673C2×D4—91no—
674C2×D4—91no—
675C2×D4—91no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—544no—
685C2×D4—544no—
686C22×C4—31no—
687C22×C4—271no—
688C22×C4—271no—
689C22×C4—271no—
690C4⋊C4—31no—
691C4⋊C4—31no—
692C4⋊C4—271no—
693C4⋊C4—271no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—91no—
697C22⋊C4—91no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4D3×C3⋊D311yescharacteristic, complemented
706C22×C3—24no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—24no—
713C22×C3—38no—
714C22×C3—44no—
715C22×C3—44no—
716C22×C3—44no—
717C22×C3—64no—
718C22×C3—64no—
719C22×C3—92no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3—181no—
727C22×C3—181no—
728C22×C3—364no—
729C22×C3C22×D3214yes—
730C22×C3C23×C3⋊D311yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—38no—
734C2×D3—64no—
735C2×D3—64no—
736C2×D3—64no—
737C2×D3—64no—
738C2×D3—64no—
739C2×D3—64no—
740C2×D3—64no—
741C2×D3—64no—
742C2×D3—98no—
743C2×D3—92no—
744C2×D3—1216no—
745C2×D3—188no—
746C2×D3—184no—
747C2×D3—184no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—184no—
751C2×D3—184no—
752C2×D3—184no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—364no—
759C2×D3—364no—
760C2×D3—364no—
761C2×D3—364no—
762C2×D3—364no—
763C2×D3—3616no—
764C2×D3—3616no—
765C2×D3D4×C3⋊D312yes—
766C3×C4—24no—
767C3×C4—24no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—44no—
771C3×C4—44no—
772C3×C4—64no—
773C3×C4—64no—
774C3×C4—64no—
775C3×C4—181no—
776Dic3—21no—
777Dic3—21no—
778Dic3—21no—
779Dic3—64no—
780Dic3—188no—
781Dic3—184no—
782Dic3—184no—
783Dic3—181no—
784Dic3—181no—
785Dic3—364no—
786C32—24no—
787C32#558911yescharacteristic, complemented
788C32#565314yescomplemented
789C23—31no—
790C23—91no—
791C23—91no—
792C23—91no—
793C23—182no—
794C23—274no—
795C23—271no—
796C23—271no—
797C23—361no—
798C23—361no—
799C23—542no—
800C23—1081no—
801C23—1081no—
802C23—1081no—
803C23—1081no—
804C23C2×D3×C3⋊D311yescharacteristic
805D4—62no—
806D4—182no—
807D4—361no—
808D4—361no—
809D4—542no—
810D4—542no—
811D4—542no—
812D4—542no—
813D4—542no—
814D4—542no—
815D4—1081no—
816D4—1081no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—62no—
821C2×C4—91no—
822C2×C4—271no—
823C2×C4—271no—
824C2×C4—542no—
825C2×C4—1081no—
826C2×C4—1081no—
827C2×C4C2×D3×C3⋊D311yescharacteristic
828C2×C4C2×D3×C3⋊D311yescharacteristic
829C2×C3—24no—
830C2×C3—24no—
831C2×C3—24no—
832C2×C3—41no—
833C2×C3—44no—
834C2×C3—68no—
835C2×C3—84no—
836C2×C3—182no—
837C2×C3—361no—
838C2×C3—361no—
839C2×C3#6430714yes—
840C2×C3D32×D414yes—
841C2×C3#6431414yes—
842C2×C3C2×D4×C3⋊D311yescharacteristic
843C2×C3#6436611yescharacteristic
844C2×C3#6436611yescharacteristic
845D3—22no—
846D3—68no—
847D3—124no—
848D3—124no—
849D3—182no—
850D3—188no—
851D3—368no—
852D3—361no—
853D3—364no—
854D3—724no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—32no—
859C22—61no—
860C22—61no—
861C22—92no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—181no—
868C22—181no—
869C22—181no—
870C22—272no—
871C22—364no—
872C22—541no—
873C22—541no—
874C22—541no—
875C22—541no—
876C22—541no—
877C22—1084no—
878C22—1084no—
879C22C22×D3×C3⋊D311yescharacteristic
880C4—21no—
881C4—21no—
882C4—61no—
883C4—61no—
884C4—61no—
885C4—181no—
886C4—541no—
887C4—541no—
888C3—24no—
889C3#1059426214yescomplemented
890C3#1059612411yescharacteristic, complemented
891C2—41no—
892C2—62no—
893C2—182no—
894C2—361no—
895C2—361no—
896C2—542no—
897C2—1081no—
898C2#1172458011yescharacteristic
899C2D3×D4×C3⋊D311yescharacteristic
900C2#1172458911yescharacteristic
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×D3×C4⋊(C3⋊D3)C2semidirect
3. #11723925C2semidirect
4. C3×#64091C2semidirect
5. C32×#883C2semidirect
6. #11723643C2semidirect
7. #11723636C2semidirect
8. #11723623C2semidirect
9. #11723541C2semidirect
10. #11723539C2semidirect
11. #11723532C2semidirect
12. #11723513C2semidirect
13. #11723493C2semidirect
14. #11723488C2semidirect
15. #11723486C2semidirect
18. C23×C3×C3⋊D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
21. C2×#6312C22semidirect
22. C2×#6312C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C2×C4×C3⋊(C3⋊D3)C22semidirect
25. C2×C3×#638C22semidirect
27. C2×C3×C4⋊(C3⋊D3)C22semidirect
29. C2×C32×C4×D3C22semidirect
32. C2×#6292C22semidirect
33. C2×#6292C22semidirect
34. C2×#6292C22semidirect
36. C2×#6289C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
39. C33×C22⋊C4C22semidirect
40. #88859C22semidirect
41. #88857C22semidirect
42. C3×#3752C22semidirect
43. C3×#3752C22semidirect
44. C32×#217C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. #88807C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
72. #64091D3semidirect
74. C3×#883D3semidirect
101. C2×D3×C3⋊D3D4semidirect
130. C23×C3⋊D3C2×D3semidirect
143. C2×#638C2×D3semidirect
154. C2×C4⋊(C3⋊D3)C2×D3semidirect
164. C2×C3×C4×D3C2×D3semidirect
179. C32×C22⋊C4C2×D3semidirect
180. C32×C22⋊C4C2×D3semidirect
190. #3752C2×D3semidirect
191. #3752C2×D3semidirect
196. C3×#217C2×D3semidirect
199. C3×(C2×D3)⋊C4C2×D3semidirect
200. C3×C4⋊Dic3C2×D3semidirect
201. C3×Dic3⋊C4C2×D3semidirect
267. #883C3⋊D3semidirect
420. C2×C4×D3C2×C3⋊D3semidirect
428. C3×C22⋊C4D32semidirect
429. C3×C22⋊C4C2×C3⋊D3semidirect
435. #217C2×C3⋊D3semidirect
448. (C2×D3)⋊C4C2×C3⋊D3semidirect
450. C4⋊Dic3C2×C3⋊D3semidirect
455. Dic3⋊C4C2×C3⋊D3semidirect
551. C33#534semidirect
705. C22⋊C4D3×C3⋊D3semidirect
787. C32#5589semidirect
788. C32#5653semidirect
889. C3#10594262semidirect
890. C3#10596124semidirect

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×D3×C4⋊(C3⋊D3)2
#117239252
C3×#640912
C32×#8832
#117236432
#117236362
#117236232
#117235412
#117235392
#117235322
#117235132
#117234932
#117234882
#117234862
#105961243
#105942623