Finite Group Databasebeta

← #13176537

Subgroups — #13176537

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×#89026C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3#11723935C211yesmaximal, characteristic, complemented
4C3×#64104C211yesmaximal, characteristic, complemented
5C32×#894C211yesmaximal, characteristic, complemented
6#11723542C211yesmaximal, characteristic, complemented
7#11723541C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9#11723540C211yesmaximal, characteristic, complemented
10C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11723520C211yesmaximal, characteristic, complemented
12#11723519C211yesmaximal, characteristic, complemented
13#11723513C211yesmaximal, characteristic, complemented
14#11723482C211yesmaximal, characteristic, complemented
15#11723421C211yesmaximal, characteristic, complemented
16#10596124—31nomaximal
17#10594611—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic, complemented
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C32×D12C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic
30C2×#6292C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic, complemented
32C2×#6291C2211yescharacteristic, complemented
33C2×#6290C2211yescharacteristic
34C2×#6290C2211yescharacteristic, complemented
35C2×#6290C2211yescharacteristic, complemented
36C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
37#89026—24no—
38D3×C4⋊(C3⋊D3)—24no—
39C33×C4⋊C4C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42#88859C2211yescharacteristic, complemented
43#88857C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50#88807C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, 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×#3802—34no—
58C2×D3×D12—34no—
59C32×#123—31no—
60#64146—31no—
61#64138—31no—
62#64104—31no—
63#64104D311yescharacteristic, complemented
64#64103—31no—
65#64103—31no—
66#64103—34no—
67#64103—64no—
68#64093—31no—
69#64093—31no—
70#64091—31no—
71#64091—31no—
72#64091—31no—
73C22⋊C4×C3⋊D3—31no—
74C3×#895—34no—
75C3×#894D314yescomplemented
76#63923—34no—
77#63922—34no—
78#63922—34no—
79#63922—34no—
80D3×(C2×D3)⋊C4—34no—
81#63906—34no—
82#63905—34no—
83#63886—34no—
84#63885—34no—
85#63853—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C3×C3⋊D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C22×C32×D3C2311yescharacteristic
93C2×D3×C3⋊D3—22no—
94C2×D3×C3⋊D3—22no—
95C2×D3×C3⋊D3—41no—
96C2×D3×C3⋊D3—41no—
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
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊(C3⋊D3))—22no—
108C4×C3⋊(C3⋊D3)—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C3×C4⋊(C3⋊D3)—22no—
111C3×C4⋊(C3⋊D3)—22no—
112C3×C4⋊(C3⋊D3)—41no—
113C3×C4×C3⋊D3—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C32×D12—22no—
117C32×C4×D3—22no—
118#6292—22no—
119#6292—22no—
120#6292—41no—
121#6291—41no—
122#6290—22no—
123#6290—22no—
124#6290—41no—
125Dic3×C3⋊D3—41no—
126#5653—94no—
127#5605—91no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3—31no—
130C23×C3⋊D3—31no—
131C22×D32—34no—
132C22×D32—34no—
133C22×D32—34no—
134C2×C32×D4—31no—
135C22×C32×C4—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—31no—
140D4×C3⋊D3—64no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4⋊(C3⋊D3)—34no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)—64no—
147C2×C4⋊(C3⋊D3)—64no—
148C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
149C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
150C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—34no—
153C2×C4×C3⋊D3—31no—
154C2×C4×C3⋊D3—64no—
155C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
156C2×C3×D12—34no—
157C2×C3×D12—34no—
158C2×C3×D12—34no—
159C2×C3×D12C2×D314yes—
160C2×C3×C4×D3—34no—
161C2×C3×C4×D3C2×D314yescomplemented
162C2×#626—34no—
163C2×#626—34no—
164C2×#626—34no—
165C2×#626—34no—
166C2×#625—34no—
167C2×#625—34no—
168C2×#625—34no—
169C2×D3×Dic3—34no—
170#3802—616no—
171D3×D12—616no—
172C32×C4⋊C4—24no—
173C32×C4⋊C4—31no—
174C32×C4⋊C4C2×D314yescomplemented
175C32×C4⋊C4C2×D311yescharacteristic, complemented
176C32×C22⋊C4—31no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179#3757—31no—
180#3752—31no—
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—34no—
186#3752—34no—
187#3752—34no—
188#3752—31no—
189#3752—64no—
190#3752—64no—
191#3752—64no—
192#3752C2×D311yescharacteristic, complemented
193#3752C2×D311yescharacteristic, complemented
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×(C2×D3)⋊C4C2×D314yescomplemented
202C3×(C2×D3)⋊C4C2×D314yescomplemented
203C3×Dic3⋊C4C2×D314yescomplemented
204Dic3⋊Dic3—34no—
205#3722—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208(C2×D3)⋊Dic3—34no—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
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⋊D3C2×D412yes—
225C2×C32×D3—21no—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C2×C32×D3—21no—
229C2×C32×D3—21no—
230C2×C32×D3C2×D412yes—
231D3×C3⋊D3—44no—
232D3×C3⋊D3—44no—
233D3×C3⋊D3—44no—
234C33×C4—21no—
235C33×C4—21no—
236C33×C4—21no—
237C3⋊(C3⋊Dic3)—21no—
238C3⋊(C3⋊Dic3)—21no—
239C3×C3⋊Dic3—21no—
240C32×Dic3—21no—
241C32×Dic3—21no—
242C2×D3×D4—94no—
243C2×D3×D4—91no—
244C2×D3×D4—91no—
245C22×D12—94no—
246C3×#123—34no—
247C3×#121—91no—
248#939—91no—
249#939—91no—
250#937—94no—
251#937—91no—
252#937—91no—
253#930—91no—
254#929—94no—
255C2×(C2×D3)⋊C4—91no—
256#895—34no—
257#895—94no—
258#894—94no—
259#894—94no—
260#894—91no—
261#894—184no—
262#894C3⋊D311yescharacteristic, complemented
263#884—94no—
264#884—94no—
265#883—91no—
266#883—91no—
267#882—94no—
268#882—94no—
269#882—94no—
270#882—91no—
271#882—91no—
272D3×C22⋊C4—94no—
273C23×C32—31no—
274C23×C32—31no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—34no—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—64no—
281C22×C3⋊D3—64no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—62no—
284C22×C3⋊D3—121no—
285C22×C3⋊D3—121no—
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×D3C22×D314yes—
297C22×C3×D3C22×D314yes—
298C2×D32—316no—
299C2×D32—68no—
300C2×D32—68no—
301C2×D32—124no—
302C2×D32—124no—
303C2×D32—124no—
304C2×D32—124no—
305C2×D32—124no—
306C2×D32—124no—
307C32×D4—62no—
308C2×C32×C4—24no—
309C2×C32×C4—24no—
310C2×C32×C4—24no—
311C2×C32×C4—31no—
312C2×C32×C4—31no—
313C2×C32×C4—62no—
314C2×C32×C4C22×D314yes—
315C2×C32×C4C22×D314yes—
316C2×C32×C4C22×D314yes—
317C2×C32×C4C22×D311yescharacteristic
318C2×C32×C4C22×D311yescharacteristic
319C2×C32×C4C22×D311yescharacteristic
320#638—62no—
321#638—62no—
322#638—121no—
323#638—121no—
324C2×C3⋊Dic3—31no—
325C2×C3⋊Dic3—31no—
326C2×C3⋊Dic3—34no—
327C2×C3⋊Dic3—34no—
328C2×C3⋊Dic3—64no—
329C2×C3⋊Dic3—64no—
330C2×C3⋊Dic3C22×D311yescharacteristic
331C4⋊(C3⋊D3)—22no—
332C4⋊(C3⋊D3)—22no—
333C4⋊(C3⋊D3)—41no—
334C4⋊(C3⋊D3)—62no—
335C4⋊(C3⋊D3)—62no—
336C4⋊(C3⋊D3)—62no—
337C4⋊(C3⋊D3)—68no—
338C4⋊(C3⋊D3)—128no—
339C4⋊(C3⋊D3)—121no—
340C4×C3⋊D3—41no—
341C4×C3⋊D3—62no—
342C4×C3⋊D3—68no—
343C4×C3⋊D3—128no—
344C4×C3⋊D3—121no—
345C2×C3×Dic3—34no—
346C2×C3×Dic3C22×D314yes—
347C2×C3×Dic3C22×D314yes—
348C3×D12—28no—
349C3×D12—68no—
350C3×D12—68no—
351C3×D12—124no—
352C3×C4×D3—28no—
353C3×C4×D3—124no—
354#626—68no—
355#626—68no—
356#626—124no—
357#626—124no—
358#625—68no—
359#625—68no—
360#625—124no—
361D3×Dic3—124no—
362#534—271noSylow
363C2×C33C22×D411yescharacteristic
364C2×C33H(5,𝔽2)11yescharacteristic
365C2×C33H(5,𝔽2)11yescharacteristic
366C3⋊(C3⋊D3)—22no—
367C3⋊(C3⋊D3)—41no—
368C3×C3⋊D3—22no—
369C3×C3⋊D3—41no—
370C3×C3⋊D3—41no—
371C32×D3—22no—
372C32×D3—41no—
373C23×D3—94no—
374C23×D3—94no—
375C23×D3—94no—
376C23×D3—91no—
377C23×D3—91no—
378C23×D3—91no—
379C2×C3×D4—34no—
380C2×C3×D4—91no—
381C2×C3×D4—91no—
382C2×C3×D4—91no—
383C22×C3×C4—34no—
384C22×C3×C4—91no—
385C2×#67—94no—
386C2×#67—94no—
387C2×#67—94no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—94no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C22×Dic3—91no—
396D3×D4—184no—
397D3×D4—184no—
398D3×D4—1816no—
399C2×D12—34no—
400C2×D12—34no—
401C2×D12—34no—
402C2×D12—94no—
403C2×D12—94no—
404C2×D12—94no—
405C2×D12—91no—
406C2×D12—94no—
407C2×D12—91no—
408C2×D12—184no—
409C2×D12—1816no—
410C2×D12C2×C3⋊D311yescharacteristic
411C2×C4×D3—34no—
412C2×C4×D3—94no—
413C2×C4×D3—91no—
414C2×C4×D3—94no—
415C2×C4×D3—184no—
416C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
417C3×C4⋊C4—24no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4D3214yescomplemented
420C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
421C3×C22⋊C4—34no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4—34no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4—91no—
426#217—94no—
427#217—91no—
428#217—91no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—94no—
432(C2×D3)⋊C4—94no—
433(C2×D3)⋊C4—94no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—94no—
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—184no—
443(C2×D3)⋊C4—184no—
444(C2×D3)⋊C4—184no—
445(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
446(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
447(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
448C4⋊Dic3—91no—
449Dic3⋊C4—94no—
450Dic3⋊C4—94no—
451Dic3⋊C4—91no—
452Dic3⋊C4—184no—
453Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
454C22×C32—24no—
455C22×C32—32no—
456C22×C32—61no—
457C22×C32—61no—
458C22×C32—61no—
459C22×C32—61no—
460C22×C32—61no—
461C22×C32C23×D314yes—
462C22×C32C23×D311yescharacteristic
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—32no—
472C2×C3⋊D3—38no—
473C2×C3⋊D3—68no—
474C2×C3⋊D3—61no—
475C2×C3⋊D3—61no—
476C2×C3⋊D3—61no—
477C2×C3⋊D3—61no—
478C2×C3⋊D3—61no—
479C2×C3⋊D3—64no—
480C2×C3⋊D3—64no—
481C2×C3⋊D3—64no—
482C2×C3⋊D3—64no—
483C2×C3⋊D3—64no—
484C2×C3⋊D3—124no—
485C2×C3⋊D3—124no—
486C2×C3⋊D3—124no—
487C2×C3⋊D3—124no—
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×D3D3×D418yes—
508D32—1216no—
509D32—1216no—
510D32—1216no—
511C32×C4—21no—
512C32×C4—21no—
513C32×C4—21no—
514C32×C4—24no—
515C32×C4—24no—
516C32×C4—24no—
517C32×C4—44no—
518C32×C4—44no—
519C32×C4—44no—
520C32×C4—61no—
521C32×C4—61no—
522C3⋊Dic3—21no—
523C3⋊Dic3—61no—
524C3⋊Dic3—61no—
525C3⋊Dic3—64no—
526C3⋊Dic3—64no—
527C3⋊Dic3—124no—
528C3⋊Dic3—124no—
529C3×Dic3—24no—
530C3×Dic3—24no—
531C3×Dic3—64no—
532C22×D4—271no—
533C22×D4—271no—
534#123—31no—
535#123—271no—
536#123—271no—
537#123—271no—
538#121—91no—
539#121—271no—
540#121—271no—
541#121—271no—
542#120—271no—
543#120—271no—
544#120—271no—
545#120—271no—
546C2×C22⋊C4—271no—
547C33#53411yescharacteristic, complemented, Sylow
548C23×C3—34no—
549C23×C3—34no—
550C23×C3—91no—
551C23×C3—91no—
552C23×C3—91no—
553C22×D3—34no—
554C22×D3—34no—
555C22×D3—34no—
556C22×D3—916no—
557C22×D3—94no—
558C22×D3—91no—
559C22×D3—94no—
560C22×D3—94no—
561C22×D3—91no—
562C22×D3—184no—
563C22×D3—184no—
564C22×D3—182no—
565C22×D3—188no—
566C22×D3—188no—
567C22×D3—182no—
568C22×D3—361no—
569C22×D3—361no—
570C22×D3—361no—
571C22×D3—361no—
572C22×D3—361no—
573C22×D3—361no—
574C22×D3—364no—
575C22×D3—364no—
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—182no—
584C3×D4—182no—
585C3×D4—361no—
586C2×C3×C4—24no—
587C2×C3×C4—24no—
588C2×C3×C4—24no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—68no—
592C2×C3×C4—91no—
593C2×C3×C4—361no—
594C2×C3×C4C2×D3214yes—
595C2×C3×C4C2×D3214yes—
596C2×C3×C4C2×D3214yes—
597C2×C3×C4C22×C3⋊D311yescharacteristic
598C2×C3×C4C22×C3⋊D311yescharacteristic
599C2×C3×C4C22×C3⋊D311yescharacteristic
600#67—182no—
601#67—182no—
602#67—182no—
603#67—188no—
604#67—188no—
605#67—182no—
606#67—361no—
607#67—364no—
608#67—361no—
609#67—364no—
610C2×Dic3—34no—
611C2×Dic3—94no—
612C2×Dic3—94no—
613C2×Dic3—91no—
614C2×Dic3—91no—
615C2×Dic3—184no—
616C2×Dic3—184no—
617C2×Dic3—361no—
618C2×Dic3C22×C3⋊D311yescharacteristic
619C2×Dic3C22×C3⋊D311yescharacteristic
620D12—22no—
621D12—68no—
622D12—68no—
623D12—124no—
624D12—182no—
625D12—188no—
626D12—188no—
627D12—188no—
628D12—368no—
629D12—364no—
630D12—361no—
631C4×D3—22no—
632C4×D3—124no—
633C4×D3—182no—
634C4×D3—188no—
635C4×D3—368no—
636C4×D3—364no—
637C2×C32—24no—
638C2×C32—24no—
639C2×C32—24no—
640C2×C32—62no—
641C2×C32—121no—
642C2×C32C2×D3×D414yes—
643C2×C32C2×D3×D411yescharacteristic
644C2×C32#100411yescharacteristic
645C2×C32#100914yes—
646C2×C32#100914yes—
647C2×C32#100911yescharacteristic
648C3⋊D3—22no—
649C3⋊D3—41no—
650C3⋊D3—41no—
651C3⋊D3—62no—
652C3⋊D3—68no—
653C3⋊D3—128no—
654C3⋊D3—121no—
655C3⋊D3—124no—
656C3⋊D3—244no—
657C3×D3—28no—
658C3×D3—44no—
659C3×D3—68no—
660C3×D3—124no—
661C3×D3—124no—
662C24—271no—
663C24—271no—
664C24—271no—
665C2×D4—31no—
666C2×D4—91no—
667C2×D4—91no—
668C2×D4—91no—
669C2×D4—271no—
670C2×D4—271no—
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—91no—
681C22×C4—271no—
682C22×C4—271no—
683C4⋊C4—31no—
684C4⋊C4—271no—
685C4⋊C4—271no—
686C4⋊C4D3×C3⋊D311yescharacteristic, complemented
687C22⋊C4—31no—
688C22⋊C4—31no—
689C22⋊C4—31no—
690C22⋊C4—91no—
691C22⋊C4—91no—
692C22⋊C4—271no—
693C22⋊C4—271no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22×C3—24no—
700C22×C3—38no—
701C22×C3—64no—
702C22×C3—64no—
703C22×C3—64no—
704C22×C3—64no—
705C22×C3—64no—
706C22×C3—92no—
707C22×C3—181no—
708C22×C3—181no—
709C22×C3—181no—
710C22×C3—181no—
711C22×C3—181no—
712C22×C3—181no—
713C22×C3—181no—
714C22×C3—181no—
715C22×C3C22×D3214yes—
716C22×C3C23×C3⋊D311yescharacteristic
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—38no—
723C2×D3—64no—
724C2×D3—64no—
725C2×D3—64no—
726C2×D3—64no—
727C2×D3—64no—
728C2×D3—64no—
729C2×D3—64no—
730C2×D3—64no—
731C2×D3—98no—
732C2×D3—92no—
733C2×D3—188no—
734C2×D3—184no—
735C2×D3—184no—
736C2×D3—181no—
737C2×D3—181no—
738C2×D3—184no—
739C2×D3—184no—
740C2×D3—184no—
741C2×D3—181no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—364no—
745C2×D3—364no—
746C2×D3—364no—
747C2×D3—364no—
748C2×D3—364no—
749C2×D3—364no—
750C2×D3—364no—
751C2×D3—364no—
752C2×D3—3616no—
753C2×D3—3616no—
754C2×D3—3616no—
755C2×D3D4×C3⋊D312yes—
756C3×C4—24no—
757C3×C4—24no—
758C3×C4—24no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—44no—
763C3×C4—44no—
764C3×C4—44no—
765C3×C4—64no—
766C3×C4—64no—
767C3×C4—181no—
768Dic3—21no—
769Dic3—21no—
770Dic3—64no—
771Dic3—184no—
772Dic3—184no—
773Dic3—181no—
774Dic3—181no—
775Dic3—364no—
776Dic3—364no—
777C32—24no—
778C32#560511yescharacteristic, complemented
779C32#565314yescomplemented
780C23—31no—
781C23—31no—
782C23—91no—
783C23—91no—
784C23—91no—
785C23—274no—
786C23—271no—
787C23—271no—
788C23—542no—
789C23—542no—
790C23—1081no—
791C23—1081no—
792C23—1081no—
793C23—1081no—
794C23—1081no—
795C23—1081no—
796D4—62no—
797D4—182no—
798D4—182no—
799D4—361no—
800D4—542no—
801D4—542no—
802D4—542no—
803D4—542no—
804D4—542no—
805D4—1081no—
806D4—1081no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—62no—
811C2×C4—91no—
812C2×C4—271no—
813C2×C4—271no—
814C2×C4—361no—
815C2×C4—542no—
816C2×C4—1081no—
817C2×C4C2×D3×C3⋊D311yescharacteristic
818C2×C4C2×D3×C3⋊D311yescharacteristic
819C2×C4C2×D3×C3⋊D311yescharacteristic
820C2×C3—24no—
821C2×C3—24no—
822C2×C3—24no—
823C2×C3—68no—
824C2×C3—124no—
825C2×C3—182no—
826C2×C3—361no—
827C2×C3—361no—
828C2×C3#6430714yes—
829C2×C3D32×D414yes—
830C2×C3#6432014yes—
831C2×C3C2×D4×C3⋊D311yescharacteristic
832C2×C3#6436611yescharacteristic
833C2×C3#6436611yescharacteristic
834D3—22no—
835D3—41no—
836D3—68no—
837D3—124no—
838D3—124no—
839D3—182no—
840D3—188no—
841D3—368no—
842D3—361no—
843D3—364no—
844D3—724no—
845C22—32no—
846C22—61no—
847C22—61no—
848C22—61no—
849C22—61no—
850C22—61no—
851C22—92no—
852C22—181no—
853C22—181no—
854C22—181no—
855C22—181no—
856C22—181no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—272no—
861C22—541no—
862C22—541no—
863C22—541no—
864C22—541no—
865C22—541no—
866C22—1084no—
867C22—1084no—
868C22—1084no—
869C22C22×D3×C3⋊D311yescharacteristic
870C4—21no—
871C4—21no—
872C4—21no—
873C4—61no—
874C4—61no—
875C4—181no—
876C4—541no—
877C4—541no—
878C3—24no—
879C3#1059461114yescomplemented
880C3#1059612411yescharacteristic, complemented
881C2—62no—
882C2—121no—
883C2—182no—
884C2—361no—
885C2—361no—
886C2—542no—
887C2—1081no—
888C2#1172458011yescharacteristic
889C2D3×D4×C3⋊D311yescharacteristic
890C2#1172459711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89026C2semidirect
2. C2×D3×C4⋊(C3⋊D3)C2semidirect
3. #11723935C2semidirect
4. C3×#64104C2semidirect
5. C32×#894C2semidirect
6. #11723542C2semidirect
7. #11723541C2semidirect
8. #11723541C2semidirect
9. #11723540C2semidirect
10. C3⋊D3×(C2×D3)⋊C4C2semidirect
11. #11723520C2semidirect
12. #11723519C2semidirect
13. #11723513C2semidirect
14. #11723482C2semidirect
15. #11723421C2semidirect
19. C22×D3×C3⋊D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×C4⋊(C3⋊D3)C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C32×C4×D3C22semidirect
30. C2×#6292C22semidirect
31. C2×#6292C22semidirect
32. C2×#6291C22semidirect
34. C2×#6290C22semidirect
35. C2×#6290C22semidirect
36. C2×Dic3×C3⋊D3C22semidirect
39. C33×C4⋊C4C22semidirect
40. #88859C22semidirect
41. #88859C22semidirect
42. #88859C22semidirect
43. #88857C22semidirect
44. C3×#3752C22semidirect
45. C3×#3752C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. #88807C22semidirect
51. #88804C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
63. #64104D3semidirect
75. C3×#894D3semidirect
101. C2×D3×C3⋊D3D4semidirect
148. C2×C4⋊(C3⋊D3)C2×D3semidirect
149. C2×C4⋊(C3⋊D3)C2×D3semidirect
150. C2×C4⋊(C3⋊D3)C2×D3semidirect
155. C2×C4×C3⋊D3C2×D3semidirect
161. C2×C3×C4×D3C2×D3semidirect
174. C32×C4⋊C4C2×D3semidirect
175. C32×C4⋊C4C2×D3semidirect
192. #3752C2×D3semidirect
193. #3752C2×D3semidirect
200. C3×(C2×D3)⋊C4C2×D3semidirect
201. C3×(C2×D3)⋊C4C2×D3semidirect
202. C3×(C2×D3)⋊C4C2×D3semidirect
203. C3×Dic3⋊C4C2×D3semidirect
262. #894C3⋊D3semidirect
416. C2×C4×D3C2×C3⋊D3semidirect
419. C3×C4⋊C4D32semidirect
420. C3×C4⋊C4C2×C3⋊D3semidirect
445. (C2×D3)⋊C4C2×C3⋊D3semidirect
446. (C2×D3)⋊C4C2×C3⋊D3semidirect
447. (C2×D3)⋊C4C2×C3⋊D3semidirect
453. Dic3⋊C4C2×C3⋊D3semidirect
547. C33#534semidirect
686. C4⋊C4D3×C3⋊D3semidirect
778. C32#5605semidirect
779. C32#5653semidirect
879. C3#10594611semidirect
880. C3#10596124semidirect

Maximal subgroups

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

subgroupindex
C2×#890262
C2×D3×C4⋊(C3⋊D3)2
#117239352
C3×#641042
C32×#8942
#117235422
#117235412
#117235402
C3⋊D3×(C2×D3)⋊C42
#117235202
#117235192
#117235132
#117234822
#117234212
#105961243
#105946113