Finite Group Databasebeta

← #13176534

Subgroups — #13176534

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×D12C211yesmaximal, characteristic, complemented
2C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3#11723936C211yesmaximal, characteristic, complemented
4C3×#64103C211yesmaximal, characteristic, complemented
5C32×#894C211yesmaximal, characteristic, complemented
6#11723542C211yesmaximal, characteristic, complemented
7#11723542C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9#11723540C211yesmaximal, characteristic, complemented
10#11723539C211yesmaximal, characteristic, complemented
11#11723527C211yesmaximal, characteristic, complemented
12#11723525C211yesmaximal, characteristic, complemented
13#11723486C211yesmaximal, characteristic, complemented
14#11723417C211yesmaximal, characteristic, complemented
15#11723414C211yesmaximal, characteristic, complemented
16#10596124—31nomaximal
17#10594610—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic, complemented
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
24C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C32×D12C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic
30C2×#6292C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic, complemented
32C2×#6291C2211yescharacteristic
33C2×#6291C2211yescharacteristic, complemented
34C2×#6291C2211yescharacteristic, complemented
35C2×#6290C2211yescharacteristic, complemented
36C2×#6289C2211yescharacteristic, complemented
37C3⋊D3×D12—24no—
38D3×C4⋊(C3⋊D3)—24no—
39C33×C4⋊C4C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3750C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50#88806C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C22×C4⋊(C3⋊D3)—31no—
57C2×D3×D12—34no—
58C2×D3×D12—34no—
59C32×#123—31no—
60#64146—31no—
61#64138—31no—
62#64104—31no—
63#64104—31no—
64#64104—34no—
65#64104—64no—
66#64103—31no—
67#64103D311yescharacteristic, complemented
68#64093—31no—
69#64093—31no—
70#64091—31no—
71#64091—31no—
72#64091—31no—
73C22⋊C4×C3⋊D3—31no—
74C3×#894—34no—
75C3×#894D314yescomplemented
76#63923—34no—
77#63923—34no—
78#63922—34no—
79#63922—34no—
80#63921—34no—
81#63912—34no—
82#63910—34no—
83#63910—34no—
84#63850—34no—
85#63850—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
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
106C4⋊(C3⋊(C3⋊D3))—22no—
107C4⋊(C3⋊(C3⋊D3))—22no—
108C4⋊(C3⋊(C3⋊D3))—41no—
109C4×C3⋊(C3⋊D3)—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4⋊(C3⋊D3)—22no—
113C3×C4×C3⋊D3—22no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C32×D12—22no—
117C32×C4×D3—22no—
118#6292—22no—
119#6292—22no—
120#6292—41no—
121#6291—22no—
122#6291—22no—
123#6291—41no—
124#6290—41no—
125#6289—41no—
126#5653—94no—
127#5653—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)—31no—
145C2×C4⋊(C3⋊D3)—34no—
146C2×C4⋊(C3⋊D3)—34no—
147C2×C4⋊(C3⋊D3)—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—34no—
150C2×C4⋊(C3⋊D3)—64no—
151C2×C4⋊(C3⋊D3)—64no—
152C2×C4⋊(C3⋊D3)—64no—
153C2×C4⋊(C3⋊D3)—64no—
154C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—34no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—64no—
159C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
160C2×C3×D12—34no—
161C2×C3×D12C2×D314yes—
162C2×C3×C4×D3—34no—
163C2×C3×C4×D3C2×D314yescomplemented
164C2×#626—34no—
165C2×#626—34no—
166C2×#626—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#625—34no—
171C2×#624—34no—
172D3×D12—616no—
173D3×D12—616no—
174C32×C4⋊C4—24no—
175C32×C4⋊C4—31no—
176C32×C4⋊C4C2×D314yescomplemented
177C32×C4⋊C4C2×D311yescharacteristic, complemented
178C32×C22⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181#3757—31no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—34no—
186#3752—34no—
187#3752—31no—
188#3752—31no—
189#3752—64no—
190#3752—64no—
191#3752C2×D311yescharacteristic, complemented
192#3752C2×D311yescharacteristic, complemented
193#3752C2×D311yescharacteristic, complemented
194#3750—31no—
195#3750C2×D311yescharacteristic, complemented
196C3×(C2×D3)⋊C4—34no—
197C3×(C2×D3)⋊C4—34no—
198C3×(C2×D3)⋊C4—34no—
199C3×(C2×D3)⋊C4C2×D314yescomplemented
200C3×(C2×D3)⋊C4C2×D314yescomplemented
201C3×(C2×D3)⋊C4C2×D314yescomplemented
202C3×Dic3⋊C4—34no—
203C3×Dic3⋊C4C2×D314yescomplemented
204#3724—34no—
205#3722—34no—
206#3722—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)—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⋊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—
244C22×D12—94no—
245C22×D12—91no—
246C3×#123—34no—
247C3×#123—91no—
248#937—94no—
249#937—91no—
250#929—94no—
251#929—91no—
252#895—94no—
253#895—94no—
254#895—91no—
255#895—91no—
256#895—184no—
257#894—34no—
258#894—94no—
259#894—91no—
260#894C3⋊D311yescharacteristic, complemented
261#884—94no—
262#884—94no—
263#884—91no—
264#884—91no—
265#882—94no—
266#882—94no—
267#882—94no—
268#882—91no—
269#882—91no—
270#882—91no—
271D3×C22⋊C4—94no—
272D3×C22⋊C4—91no—
273C23×C32—31no—
274C23×C32—31no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—34no—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—31no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—34no—
281C22×C3⋊D3—34no—
282C22×C3⋊D3—64no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—64no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—121no—
288C22×C3⋊D3—121no—
289C22×C3⋊D3—121no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3—121no—
293C22×C3⋊D3C22×D311yescharacteristic
294C22×C3⋊D3C22×D311yescharacteristic
295C22×C3×D3—34no—
296C22×C3×D3—34no—
297C22×C3×D3C22×D314yes—
298C22×C3×D3C22×D314yes—
299C2×D32—316no—
300C2×D32—68no—
301C2×D32—68no—
302C2×D32—124no—
303C2×D32—124no—
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—24no—
312C2×C32×C4—31no—
313C2×C32×C4—31no—
314C2×C32×C4—62no—
315C2×C32×C4C22×D314yes—
316C2×C32×C4C22×D314yes—
317C2×C32×C4C22×D314yes—
318C2×C32×C4C22×D311yescharacteristic
319C2×C32×C4C22×D311yescharacteristic
320C2×C32×C4C22×D311yescharacteristic
321#638—62no—
322#638—62no—
323#638—121no—
324#638—121no—
325C2×C3⋊Dic3—31no—
326C2×C3⋊Dic3—34no—
327C2×C3⋊Dic3—64no—
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4⋊(C3⋊D3)—22no—
331C4⋊(C3⋊D3)—62no—
332C4⋊(C3⋊D3)—62no—
333C4⋊(C3⋊D3)—62no—
334C4⋊(C3⋊D3)—62no—
335C4⋊(C3⋊D3)—68no—
336C4⋊(C3⋊D3)—68no—
337C4⋊(C3⋊D3)—128no—
338C4⋊(C3⋊D3)—128no—
339C4⋊(C3⋊D3)—121no—
340C4⋊(C3⋊D3)—124no—
341C4⋊(C3⋊D3)—128no—
342C4⋊(C3⋊D3)—121no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3—121no—
345C4×C3⋊D3—121no—
346C4×C3⋊D3—124no—
347C4×C3⋊D3—128no—
348C2×C3×Dic3—34no—
349C2×C3×Dic3—34no—
350C2×C3×Dic3C22×D314yes—
351C2×C3×Dic3C22×D314yes—
352C3×D12—28no—
353C3×D12—68no—
354C3×C4×D3—28no—
355C3×C4×D3—68no—
356#626—68no—
357#626—68no—
358#626—68no—
359#626—68no—
360#626—124no—
361#626—124no—
362#625—124no—
363#624—124no—
364#534—271noSylow
365C2×C33C22×D411yescharacteristic
366C2×C33H(5,𝔽2)11yescharacteristic
367C2×C33H(5,𝔽2)11yescharacteristic
368C3⋊(C3⋊D3)—22no—
369C3⋊(C3⋊D3)—41no—
370C3⋊(C3⋊D3)—41no—
371C3×C3⋊D3—22no—
372C3×C3⋊D3—41no—
373C32×D3—22no—
374C32×D3—41no—
375C23×D3—94no—
376C23×D3—94no—
377C23×D3—94no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—91no—
381C2×C3×D4—34no—
382C2×C3×D4—91no—
383C22×C3×C4—34no—
384C22×C3×C4—91no—
385C2×#67—94no—
386C2×#67—94no—
387C2×#67—94no—
388C2×#67—94no—
389C2×#67—91no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—91no—
393D3×D4—184no—
394D3×D4—1816no—
395C2×D12—34no—
396C2×D12—94no—
397C2×D12—94no—
398C2×D12—91no—
399C2×D12—91no—
400C2×D12—94no—
401C2×D12—94no—
402C2×D12—91no—
403C2×D12—91no—
404C2×D12—94no—
405C2×D12—91no—
406C2×D12—94no—
407C2×D12—91no—
408C2×D12—184no—
409C2×D12—184no—
410C2×D12—184no—
411C2×D12—184no—
412C2×D12—1816no—
413C2×D12C2×C3⋊D311yescharacteristic
414C2×C4×D3—34no—
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—24no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—91no—
424C3×C4⋊C4D3214yescomplemented
425C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
426C3×C22⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—91no—
432#217—94no—
433#217—91no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—94no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—94no—
442(C2×D3)⋊C4—94no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—184no—
448(C2×D3)⋊C4—184no—
449(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
450(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
451(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
452Dic3⋊C4—34no—
453Dic3⋊C4—94no—
454Dic3⋊C4—91no—
455Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
456C22×C32—24no—
457C22×C32—32no—
458C22×C32—61no—
459C22×C32—61no—
460C22×C32—61no—
461C22×C32—61no—
462C22×C32—61no—
463C22×C32C23×D314yes—
464C22×C32C23×D311yescharacteristic
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—32no—
471C2×C3⋊D3—38no—
472C2×C3⋊D3—68no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—61no—
475C2×C3⋊D3—61no—
476C2×C3⋊D3—61no—
477C2×C3⋊D3—61no—
478C2×C3⋊D3—61no—
479C2×C3⋊D3—61no—
480C2×C3⋊D3—61no—
481C2×C3⋊D3—64no—
482C2×C3⋊D3—64no—
483C2×C3⋊D3—64no—
484C2×C3⋊D3—64no—
485C2×C3⋊D3—64no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—64no—
488C2×C3⋊D3—64no—
489C2×C3⋊D3—124no—
490C2×C3⋊D3—124no—
491C2×C3⋊D3—124no—
492C2×C3⋊D3—124no—
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—24no—
504C2×C3×D3—24no—
505C2×C3×D3—24no—
506C2×C3×D3—38no—
507C2×C3×D3—64no—
508C2×C3×D3—64no—
509C2×C3×D3—64no—
510C2×C3×D3—64no—
511C2×C3×D3—64no—
512C2×C3×D3D3×D418yes—
513D32—1216no—
514D32—1216no—
515D32—1216no—
516C32×C4—28no—
517C32×C4—21no—
518C32×C4—21no—
519C32×C4—24no—
520C32×C4—21no—
521C32×C4—24no—
522C32×C4—24no—
523C32×C4—44no—
524C32×C4—44no—
525C32×C4—61no—
526C32×C4—61no—
527C3⋊Dic3—21no—
528C3⋊Dic3—21no—
529C3⋊Dic3—61no—
530C3⋊Dic3—64no—
531C3⋊Dic3—124no—
532C3×Dic3—24no—
533C3×Dic3—24no—
534C3×Dic3—64no—
535C3×Dic3—64no—
536C22×D4—271no—
537C22×D4—271no—
538#123—31no—
539#123—91no—
540#123—271no—
541#123—271no—
542#121—271no—
543#121—271no—
544#121—271no—
545#121—271no—
546#120—271no—
547#120—271no—
548#120—271no—
549#120—271no—
550C2×C22⋊C4—271no—
551C33#53411yescharacteristic, complemented, Sylow
552C23×C3—34no—
553C23×C3—34no—
554C23×C3—91no—
555C23×C3—91no—
556C22×D3—34no—
557C22×D3—34no—
558C22×D3—916no—
559C22×D3—94no—
560C22×D3—91no—
561C22×D3—94no—
562C22×D3—94no—
563C22×D3—94no—
564C22×D3—91no—
565C22×D3—91no—
566C22×D3—184no—
567C22×D3—184no—
568C22×D3—184no—
569C22×D3—182no—
570C22×D3—188no—
571C22×D3—188no—
572C22×D3—182no—
573C22×D3—361no—
574C22×D3—361no—
575C22×D3—361no—
576C22×D3—361no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—364no—
580C22×D3—364no—
581C22×D3—364no—
582C22×D3—364no—
583C22×D3—364no—
584C22×D3—364no—
585C22×D3C22×C3⋊D311yescharacteristic
586C22×D3C22×C3⋊D311yescharacteristic
587C3×D4—68no—
588C3×D4—182no—
589C2×C3×C4—24no—
590C2×C3×C4—24no—
591C2×C3×C4—24no—
592C2×C3×C4—34no—
593C2×C3×C4—34no—
594C2×C3×C4—68no—
595C2×C3×C4—91no—
596C2×C3×C4—91no—
597C2×C3×C4—182no—
598C2×C3×C4C2×D3214yes—
599C2×C3×C4C2×D3214yes—
600C2×C3×C4C2×D3214yes—
601C2×C3×C4C22×C3⋊D311yescharacteristic
602C2×C3×C4C22×C3⋊D311yescharacteristic
603C2×C3×C4C22×C3⋊D311yescharacteristic
604#67—182no—
605#67—182no—
606#67—188no—
607#67—188no—
608#67—361no—
609#67—364no—
610#67—361no—
611#67—364no—
612C2×Dic3—34no—
613C2×Dic3—34no—
614C2×Dic3—94no—
615C2×Dic3—91no—
616C2×Dic3—184no—
617C2×Dic3C22×C3⋊D311yescharacteristic
618C2×Dic3C22×C3⋊D311yescharacteristic
619D12—22no—
620D12—68no—
621D12—182no—
622D12—182no—
623D12—188no—
624D12—188no—
625D12—188no—
626D12—188no—
627D12—182no—
628D12—182no—
629D12—368no—
630D12—368no—
631D12—364no—
632D12—361no—
633D12—368no—
634D12—364no—
635D12—361no—
636C4×D3—22no—
637C4×D3—68no—
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—62no—
647C2×C32—121no—
648C2×C32C2×D3×D414yes—
649C2×C32C2×D3×D411yescharacteristic
650C2×C32#100914yes—
651C2×C32#100914yes—
652C2×C32#100911yescharacteristic
653C2×C32#100911yescharacteristic
654C3⋊D3—22no—
655C3⋊D3—41no—
656C3⋊D3—62no—
657C3⋊D3—68no—
658C3⋊D3—128no—
659C3⋊D3—121no—
660C3⋊D3—121no—
661C3⋊D3—124no—
662C3⋊D3—124no—
663C3⋊D3—244no—
664C3⋊D3—244no—
665C3×D3—28no—
666C3×D3—44no—
667C3×D3—68no—
668C3×D3—124no—
669C24—271no—
670C24—271no—
671C24—271no—
672C2×D4—31no—
673C2×D4—91no—
674C2×D4—271no—
675C2×D4—271no—
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—91no—
688C22×C4—271no—
689C22×C4—271no—
690C4⋊C4—31no—
691C4⋊C4—91no—
692C4⋊C4—271no—
693C4⋊C4D3×C3⋊D311yescharacteristic, complemented
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—31no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—91no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22×C3—24no—
707C22×C3—38no—
708C22×C3—64no—
709C22×C3—64no—
710C22×C3—64no—
711C22×C3—64no—
712C22×C3—64no—
713C22×C3—92no—
714C22×C3—181no—
715C22×C3—181no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3C22×D3214yes—
720C22×C3C23×C3⋊D311yescharacteristic
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—38no—
727C2×D3—64no—
728C2×D3—64no—
729C2×D3—64no—
730C2×D3—64no—
731C2×D3—64no—
732C2×D3—98no—
733C2×D3—92no—
734C2×D3—188no—
735C2×D3—184no—
736C2×D3—184no—
737C2×D3—181no—
738C2×D3—181no—
739C2×D3—184no—
740C2×D3—184no—
741C2×D3—184no—
742C2×D3—184no—
743C2×D3—184no—
744C2×D3—184no—
745C2×D3—181no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—364no—
752C2×D3—364no—
753C2×D3—364no—
754C2×D3—364no—
755C2×D3—364no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—364no—
759C2×D3—364no—
760C2×D3—364no—
761C2×D3—364no—
762C2×D3—3616no—
763C2×D3—3616no—
764C2×D3—3616no—
765C2×D3D4×C3⋊D312yes—
766C3×C4—28no—
767C3×C4—24no—
768C3×C4—24no—
769C3×C4—24no—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—44no—
774C3×C4—44no—
775C3×C4—64no—
776C3×C4—64no—
777C3×C4—181no—
778C3×C4—181no—
779Dic3—21no—
780Dic3—21no—
781Dic3—64no—
782Dic3—64no—
783Dic3—184no—
784Dic3—181no—
785Dic3—364no—
786C32—24no—
787C32#565314yescomplemented
788C32#565311yescharacteristic, complemented
789C23—31no—
790C23—31no—
791C23—91no—
792C23—91no—
793C23—274no—
794C23—271no—
795C23—271no—
796C23—271no—
797C23—542no—
798C23—542no—
799C23—1081no—
800C23—1081no—
801C23—1081no—
802C23—1081no—
803C23—1081no—
804C23—1081no—
805D4—62no—
806D4—182no—
807D4—542no—
808D4—542no—
809D4—542no—
810D4—542no—
811D4—542no—
812D4—542no—
813D4—1081no—
814D4—1081no—
815D4—1081no—
816D4—1081no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—62no—
820C2×C4—91no—
821C2×C4—91no—
822C2×C4—182no—
823C2×C4—271no—
824C2×C4—1081no—
825C2×C4—1081no—
826C2×C4C2×D3×C3⋊D311yescharacteristic
827C2×C4C2×D3×C3⋊D311yescharacteristic
828C2×C4C2×D3×C3⋊D311yescharacteristic
829C2×C3—24no—
830C2×C3—24no—
831C2×C3—24no—
832C2×C3—68no—
833C2×C3—124no—
834C2×C3—182no—
835C2×C3—361no—
836C2×C3#6430814yes—
837C2×C3D32×D414yes—
838C2×C3#6432014yes—
839C2×C3C2×D4×C3⋊D311yescharacteristic
840C2×C3#6436611yescharacteristic
841C2×C3#6436611yescharacteristic
842D3—22no—
843D3—41no—
844D3—68no—
845D3—124no—
846D3—182no—
847D3—188no—
848D3—368no—
849D3—361no—
850D3—361no—
851D3—364no—
852D3—364no—
853D3—724no—
854D3—724no—
855C22—32no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—92no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—272no—
868C22—541no—
869C22—541no—
870C22—541no—
871C22—541no—
872C22—541no—
873C22—541no—
874C22—541no—
875C22—541no—
876C22—1084no—
877C22—1084no—
878C22—1084no—
879C22C22×D3×C3⋊D311yescharacteristic
880C4—21no—
881C4—21no—
882C4—21no—
883C4—61no—
884C4—61no—
885C4—181no—
886C4—181no—
887C4—541no—
888C3—24no—
889C3#1059461014yescomplemented
890C3#1059612411yescharacteristic, complemented
891C2—62no—
892C2—121no—
893C2—182no—
894C2—361no—
895C2—542no—
896C2—1081no—
897C2—1081no—
898C2#1172458111yescharacteristic
899C2D3×D4×C3⋊D311yescharacteristic
900C2#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×C3⋊D3×D12C2semidirect
2. C2×D3×C4⋊(C3⋊D3)C2semidirect
3. #11723936C2semidirect
4. C3×#64103C2semidirect
5. C32×#894C2semidirect
6. #11723542C2semidirect
7. #11723542C2semidirect
8. #11723541C2semidirect
9. #11723540C2semidirect
10. #11723539C2semidirect
11. #11723527C2semidirect
12. #11723525C2semidirect
13. #11723486C2semidirect
14. #11723417C2semidirect
15. #11723414C2semidirect
19. C22×D3×C3⋊D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
21. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
22. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C2×C4×C3⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C32×C4×D3C22semidirect
30. C2×#6292C22semidirect
31. C2×#6292C22semidirect
33. C2×#6291C22semidirect
34. C2×#6291C22semidirect
35. C2×#6290C22semidirect
36. C2×#6289C22semidirect
39. C33×C4⋊C4C22semidirect
40. #88859C22semidirect
41. #88859C22semidirect
42. C3×#3752C22semidirect
43. C3×#3752C22semidirect
44. C3×#3752C22semidirect
45. C3×#3750C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. #88806C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
67. #64103D3semidirect
75. C3×#894D3semidirect
101. C2×D3×C3⋊D3D4semidirect
159. C2×C4×C3⋊D3C2×D3semidirect
163. C2×C3×C4×D3C2×D3semidirect
176. C32×C4⋊C4C2×D3semidirect
177. C32×C4⋊C4C2×D3semidirect
191. #3752C2×D3semidirect
192. #3752C2×D3semidirect
193. #3752C2×D3semidirect
195. #3750C2×D3semidirect
199. C3×(C2×D3)⋊C4C2×D3semidirect
200. C3×(C2×D3)⋊C4C2×D3semidirect
201. C3×(C2×D3)⋊C4C2×D3semidirect
203. C3×Dic3⋊C4C2×D3semidirect
260. #894C3⋊D3semidirect
420. C2×C4×D3C2×C3⋊D3semidirect
424. C3×C4⋊C4D32semidirect
425. C3×C4⋊C4C2×C3⋊D3semidirect
449. (C2×D3)⋊C4C2×C3⋊D3semidirect
450. (C2×D3)⋊C4C2×C3⋊D3semidirect
451. (C2×D3)⋊C4C2×C3⋊D3semidirect
455. Dic3⋊C4C2×C3⋊D3semidirect
551. C33#534semidirect
693. C4⋊C4D3×C3⋊D3semidirect
787. C32#5653semidirect
788. C32#5653semidirect
889. C3#10594610semidirect
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×D122
C2×D3×C4⋊(C3⋊D3)2
#117239362
C3×#641032
C32×#8942
#117235422
#117235412
#117235402
#117235392
#117235272
#117235252
#117234862
#117234172
#117234142
#105961243
#105946103