Finite Group Databasebeta

← C3⋊D3×#884 #13175920

Subgroups — C3⋊D3×#884 #13175920

Order 1728.

2932 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
3C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
4C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
5#11723925C211yesmaximal, characteristic, complemented
6C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
7C32×#884C211yesmaximal, characteristic, complemented
8#11723616C211yesmaximal, characteristic, complemented
9#11723599C211yesmaximal, characteristic, complemented
10C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11723527C211yesmaximal, characteristic, complemented
12#11723514C211yesmaximal, characteristic, complemented
13#11723486C211yesmaximal, characteristic, complemented
14#11723474C211yesmaximal, characteristic, complemented
15C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16C3⋊D3×#121—31nomaximal
17D3×#884—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
24C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic, complemented
29C2×C32×D12C2211yescharacteristic, complemented
30C2×C32×C4×D3C2211yescharacteristic, complemented
31C3⋊D3×#67—24no—
32C3⋊D3×#67—24no—
33C2×#6292C2211yescharacteristic, complemented
34C2×#6292C2211yescharacteristic, complemented
35C2×#6291C2211yescharacteristic, complemented
36C2×#6291C2211yescharacteristic, complemented
37C2×#6290C2211yescharacteristic, complemented
38C2×#6290C2211yescharacteristic, complemented
39C2×#6289C2211yescharacteristic, complemented
40C2×Dic3×C3⋊D3C2211yescharacteristic
41C2×Dic3×C3⋊D3C2211yescharacteristic
42C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
43C3⋊D3×D12—24no—
44C4×D3×C3⋊D3—24no—
45C33×C22⋊C4C2211yescharacteristic, complemented
46#88859C2211yescharacteristic, complemented
47#88857C2211yescharacteristic, complemented
48C3×#3757C2211yescharacteristic, complemented
49C3×#3752C2211yescharacteristic, complemented
50C3×#3752C2211yescharacteristic, complemented
51C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C32×Dic3⋊C4C2211yescharacteristic, complemented
53#88806C2211yescharacteristic, complemented
54Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55#88804C2211yescharacteristic, complemented
56(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
57C2×D4×C3⋊D3—31no—
58C2×D4×C3⋊D3—31no—
59C2×D4×C3⋊D3—31no—
60C22×C4×C3⋊D3—31no—
61C2×D3×#67—34no—
62C2×D3×#67—34no—
63C2×D3×D12—34no—
64C2×C4×D32—34no—
65C32×#121—31no—
66#64148—31no—
67#64148—31no—
68#64147—31no—
69#64139—31no—
70#64104—31no—
71C4⋊C4×C3⋊D3—31no—
72#64093—31no—
73#64093—31no—
74#64093—34no—
75#64093—64no—
76C22⋊C4×C3⋊D3—31no—
77C22⋊C4×C3⋊D3D311yescharacteristic, complemented
78C3×#884D314yescomplemented
79C3×D3×C22⋊C4—34no—
80#63971—34no—
81#63958—34no—
82D3×(C2×D3)⋊C4—34no—
83#63912—34no—
84#63910—34no—
85#63906—34no—
86#63885—34no—
87D3×Dic3⋊C4—34no—
88C23×C33C2311yescharacteristic
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3—22no—
92C22×C3×C3⋊D3—22no—
93C22×C3×C3⋊D3—22no—
94C22×C3×C3⋊D3C2311yescharacteristic
95C22×C3×C3⋊D3C2311yescharacteristic
96C22×C32×D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C2×D3×C3⋊D3—22no—
99C2×D3×C3⋊D3—22no—
100C2×D3×C3⋊D3—22no—
101C2×D3×C3⋊D3—22no—
102C2×D3×C3⋊D3—22no—
103C2×D3×C3⋊D3D414yescomplemented
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106#6312—22no—
107#6312—22no—
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊(C3⋊D3))—22no—
111C4×C3⋊(C3⋊D3)—22no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C3×C4×C3⋊D3—22no—
115C3×C4×C3⋊D3—22no—
116C32×#67—22no—
117C32×#67—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×D12—22no—
121C32×C4×D3—22no—
122#6292—22no—
123#6292—22no—
124#6291—22no—
125#6291—22no—
126#6290—22no—
127#6290—22no—
128#6289—22no—
129Dic3×C3⋊D3—22no—
130Dic3×C3⋊D3D414yescomplemented
131D3×C3⋊Dic3—22no—
132D3×#121—94no—
133C2×#884—91no—
134C23×C3⋊D3—31no—
135C23×C3⋊D3—31no—
136C23×C3⋊D3C2×D311yescharacteristic
137C23×C3×D3—34no—
138C22×D32—34no—
139C22×D32—34no—
140C2×C32×D4—31no—
141C2×C32×D4—31no—
142C2×C32×D4—31no—
143C22×C32×C4—31no—
144C2×#638—31no—
145C2×#638—31no—
146C2×#638—34no—
147C2×#638—34no—
148C2×#638—31no—
149C2×#638—31no—
150C2×#638—31no—
151C2×#638—31no—
152C2×#638—64no—
153C2×#638—64no—
154C22×C3⋊Dic3—31no—
155D4×C3⋊D3—64no—
156D4×C3⋊D3—64no—
157D4×C3⋊D3—64no—
158C2×C4⋊(C3⋊D3)—31no—
159C2×C4⋊(C3⋊D3)—31no—
160C2×C4⋊(C3⋊D3)—31no—
161C2×C4⋊(C3⋊D3)—34no—
162C2×C4⋊(C3⋊D3)—64no—
163C2×C4×C3⋊D3—31no—
164C2×C4×C3⋊D3—31no—
165C2×C4×C3⋊D3—31no—
166C2×C4×C3⋊D3—34no—
167C2×C4×C3⋊D3—31no—
168C2×C4×C3⋊D3—64no—
169C2×C4×C3⋊D3—64no—
170C2×C4×C3⋊D3C2×D311yescharacteristic
171C2×C4×C3⋊D3C2×D311yescharacteristic
172C2×C3×#67C2×D314yescomplemented
173C2×C3×#67C2×D314yescomplemented
174C2×C3×D12C2×D314yescomplemented
175C2×C3×C4×D3—34no—
176C2×C3×C4×D3—34no—
177C2×C3×C4×D3C2×D314yescomplemented
178D3×#67—616no—
179D3×#67—616no—
180C2×#626—34no—
181C2×#626—34no—
182C2×#626—34no—
183C2×#626—34no—
184C2×#625—34no—
185C2×#625—34no—
186C2×#624—34no—
187C2×D3×Dic3—34no—
188C2×D3×Dic3—34no—
189C2×D3×Dic3—34no—
190D3×D12—616no—
191C4×D32—616no—
192C32×C4⋊C4—31no—
193C32×C22⋊C4—24no—
194C32×C22⋊C4—31no—
195C32×C22⋊C4C2×D314yescomplemented
196C32×C22⋊C4C2×D311yescharacteristic, complemented
197#3757—31no—
198#3757C2×D311yescharacteristic, complemented
199#3752—31no—
200#3752—34no—
201#3752—31no—
202#3752—64no—
203#3752C2×D311yescharacteristic, complemented
204#3752C2×D311yescharacteristic, complemented
205C4⋊(C3⋊Dic3)—31no—
206#3750—31no—
207#3750—34no—
208#3750—31no—
209#3750—64no—
210C3×#217—34no—
211C3×(C2×D3)⋊C4—34no—
212C3×(C2×D3)⋊C4—34no—
213C3×(C2×D3)⋊C4C2×D314yescomplemented
214C3×Dic3⋊C4C2×D314yescomplemented
215#3724—34no—
216Dic3⋊Dic3—34no—
217#3722—34no—
218(C2×D3)⋊Dic3—34no—
219C22×C33—21no—
220C22×C33—21no—
221C22×C33—21no—
222C22×C33C2411yescharacteristic
223C2×C3⋊(C3⋊D3)—21no—
224C2×C3⋊(C3⋊D3)—21no—
225C2×C3⋊(C3⋊D3)—21no—
226C2×C3⋊(C3⋊D3)—21no—
227C2×C3⋊(C3⋊D3)—21no—
228C2×C3⋊(C3⋊D3)C2×D412yescomplemented
229C2×C3×C3⋊D3—21no—
230C2×C3×C3⋊D3—21no—
231C2×C3×C3⋊D3—21no—
232C2×C3×C3⋊D3—44no—
233C2×C3×C3⋊D3C2×D412yes—
234C2×C3×C3⋊D3C2×D412yes—
235C2×C3×C3⋊D3#4112yes—
236C2×C32×D3—21no—
237C2×C32×D3—21no—
238C2×C32×D3—21no—
239C2×C32×D3—21no—
240C2×C32×D3—21no—
241C2×C32×D3C2×D412yescomplemented
242D3×C3⋊D3—28no—
243D3×C3⋊D3—44no—
244C33×C4—21no—
245C33×C4—21no—
246C3⋊(C3⋊Dic3)—21no—
247C3⋊(C3⋊Dic3)C2×D412yescomplemented
248C3×C3⋊Dic3—21no—
249C3×C3⋊Dic3—21no—
250C32×Dic3—21no—
251C32×Dic3C2×D412yescomplemented
252C22×#67—91no—
253C22×#67—91no—
254C2×D3×D4—94no—
255C2×D3×D4—94no—
256C2×D3×D4—94no—
257C22×D12—91no—
258C22×C4×D3—94no—
259C22×C4×D3—91no—
260C3×#121—34no—
261C2×C3×C22⋊C4—91no—
262#939—94no—
263#939—94no—
264#938—94no—
265#930—94no—
266C2×(C2×D3)⋊C4—91no—
267C2×Dic3⋊C4—91no—
268#895—94no—
269D3×C4⋊C4—94no—
270#884—94no—
271#884—91no—
272#884—91no—
273#884—91no—
274#884—91no—
275#884—94no—
276#884—91no—
277#884—91no—
278#884—91no—
279#884—184no—
280#884C3⋊D311yescharacteristic, direct product factor
281D3×C22⋊C4—34no—
282D3×C22⋊C4—94no—
283C23×C32—24no—
284C23×C32—31no—
285C23×C32—31no—
286C23×C32C22×D314yes—
287C23×C32C22×D311yescharacteristic
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3—22no—
291C22×C3⋊D3—31no—
292C22×C3⋊D3—34no—
293C22×C3⋊D3—31no—
294C22×C3⋊D3—34no—
295C22×C3⋊D3—34no—
296C22×C3⋊D3—64no—
297C22×C3⋊D3—64no—
298C22×C3⋊D3—62no—
299C22×C3⋊D3—62no—
300C22×C3⋊D3—62no—
301C22×C3⋊D3—62no—
302C22×C3⋊D3—62no—
303C22×C3⋊D3C22×D311yescharacteristic
304C22×C3⋊D3C22×D311yescharacteristic
305C22×C3×D3—34no—
306C22×C3×D3—34no—
307C22×C3×D3—68no—
308C22×C3×D3—68no—
309C22×C3×D3—68no—
310C22×C3×D3C22×D314yes—
311C22×C3×D3C22×D314yes—
312C2×D32—316no—
313C2×D32—68no—
314C2×D32—68no—
315C2×D32—68no—
316C2×D32—68no—
317C2×D32—68no—
318C32×D4—62no—
319C32×D4—62no—
320C32×D4—62no—
321C2×C32×C4—24no—
322C2×C32×C4—24no—
323C2×C32×C4—31no—
324C2×C32×C4—31no—
325C2×C32×C4—62no—
326C2×C32×C4C22×D314yes—
327C2×C32×C4C22×D314yes—
328C2×C32×C4C22×D311yescharacteristic
329C2×C32×C4C22×D311yescharacteristic
330#638—62no—
331#638—62no—
332#638—62no—
333#638—62no—
334#638—62no—
335#638—62no—
336#638—68no—
337#638—68no—
338#638—128no—
339#638—128no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—34no—
343C2×C3⋊Dic3—34no—
344C2×C3⋊Dic3—64no—
345C2×C3⋊Dic3—64no—
346C2×C3⋊Dic3—62no—
347C2×C3⋊Dic3C22×D311yescharacteristic
348C2×C3⋊Dic3C22×D311yescharacteristic
349C4⋊(C3⋊D3)—62no—
350C4⋊(C3⋊D3)—62no—
351C4⋊(C3⋊D3)—62no—
352C4⋊(C3⋊D3)—68no—
353C4⋊(C3⋊D3)—128no—
354C4×C3⋊D3—22no—
355C4×C3⋊D3—22no—
356C4×C3⋊D3—34no—
357C4×C3⋊D3—62no—
358C4×C3⋊D3—62no—
359C4×C3⋊D3—62no—
360C4×C3⋊D3—68no—
361C4×C3⋊D3—128no—
362C3×#67—28no—
363C3×#67—28no—
364C2×C3×Dic3—34no—
365C2×C3×Dic3—34no—
366C2×C3×Dic3C22×D314yes—
367C2×C3×Dic3C22×D314yes—
368C3×D12—28no—
369C3×C4×D3—28no—
370C3×C4×D3—68no—
371C3×C4×D3—68no—
372#626—68no—
373#626—68no—
374#626—68no—
375#626—68no—
376#625—68no—
377#625—68no—
378#624—68no—
379D3×Dic3—316no—
380D3×Dic3—68no—
381D3×Dic3—68no—
382C2×#121—271noSylow
383C2×C33—41no—
384C2×C33C22×D411yescharacteristic
385C2×C33C22×D411yescharacteristic
386C2×C33C2×#4111yescharacteristic
387C3⋊(C3⋊D3)—22no—
388C3⋊(C3⋊D3)—41no—
389C3×C3⋊D3—41no—
390C3×C3⋊D3#12114yescomplemented
391C32×D3—22no—
392C32×D3—41no—
393C24×C3—91no—
394C23×D3—34no—
395C23×D3—94no—
396C23×D3—94no—
397C23×D3—91no—
398C23×D3—91no—
399C2×C3×D4—34no—
400C2×C3×D4—34no—
401C2×C3×D4—34no—
402C22×C3×C4—34no—
403C22×C3×C4—91no—
404C22×C3×C4—91no—
405C2×#67—94no—
406C2×#67—94no—
407C2×#67—94no—
408C2×#67—94no—
409C2×#67—94no—
410C2×#67—94no—
411C2×#67—91no—
412C2×#67—91no—
413C2×#67—91no—
414C2×#67—91no—
415C2×#67—91no—
416C2×#67—91no—
417C2×#67—184no—
418C2×#67—184no—
419C2×#67—184no—
420C2×#67—184no—
421C2×#67C2×C3⋊D311yescharacteristic, complemented
422C2×#67C2×C3⋊D311yescharacteristic, complemented
423C22×Dic3—94no—
424C22×Dic3—91no—
425C22×Dic3—91no—
426D3×D4—1816no—
427D3×D4—1816no—
428D3×D4—1816no—
429C2×D12—94no—
430C2×D12—94no—
431C2×D12—91no—
432C2×D12—91no—
433C2×D12—94no—
434C2×D12—91no—
435C2×D12—184no—
436C2×D12—184no—
437C2×D12C2×C3⋊D311yescharacteristic, complemented
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—94no—
441C2×C4×D3—94no—
442C2×C4×D3—94no—
443C2×C4×D3—91no—
444C2×C4×D3—94no—
445C2×C4×D3—91no—
446C2×C4×D3—91no—
447C2×C4×D3—184no—
448C2×C4×D3—184no—
449C2×C4×D3—1816no—
450C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
451C3×C4⋊C4—34no—
452C3×C22⋊C4—24no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4D3214yescomplemented
458C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
459#217—34no—
460#217—94no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—94no—
464(C2×D3)⋊C4—91no—
465(C2×D3)⋊C4—94no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—184no—
469(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
470C4⋊Dic3—94no—
471Dic3⋊C4—94no—
472Dic3⋊C4—94no—
473Dic3⋊C4—91no—
474Dic3⋊C4—91no—
475Dic3⋊C4—91no—
476Dic3⋊C4—184no—
477Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32—24no—
482C22×C32—24no—
483C22×C32—24no—
484C22×C32—24no—
485C22×C32—32no—
486C22×C32—44no—
487C22×C32—44no—
488C22×C32—44no—
489C22×C32—61no—
490C22×C32—61no—
491C22×C32—61no—
492C22×C32—61no—
493C22×C32—61no—
494C22×C32C23×D314yes—
495C22×C32C23×D311yescharacteristic
496C2×C3⋊D3—21no—
497C2×C3⋊D3—21no—
498C2×C3⋊D3—21no—
499C2×C3⋊D3—32no—
500C2×C3⋊D3—38no—
501C2×C3⋊D3—44no—
502C2×C3⋊D3—68no—
503C2×C3⋊D3—61no—
504C2×C3⋊D3—61no—
505C2×C3⋊D3—68no—
506C2×C3⋊D3—61no—
507C2×C3⋊D3—61no—
508C2×C3⋊D3—61no—
509C2×C3⋊D3—64no—
510C2×C3⋊D3—64no—
511C2×C3⋊D3—64no—
512C2×C3⋊D3—64no—
513C2×C3⋊D3—64no—
514C2×C3⋊D3—124no—
515C2×C3⋊D3—124no—
516C2×C3⋊D3—124no—
517C2×C3⋊D3—124no—
518C2×C3⋊D3—124no—
519C2×C3⋊D3—124no—
520C2×C3⋊D3#23512yes—
521C2×C3⋊D3D3×D412yes—
522C2×C3⋊D3D3×D412yes—
523C2×C3×D3—24no—
524C2×C3×D3—24no—
525C2×C3×D3—24no—
526C2×C3×D3—24no—
527C2×C3×D3—24no—
528C2×C3×D3—38no—
529C2×C3×D3—38no—
530C2×C3×D3—38no—
531C2×C3×D3—64no—
532C2×C3×D3—64no—
533C2×C3×D3—64no—
534C2×C3×D3—1216no—
535C2×C3×D3D3×D418yescomplemented
536D32—632no—
537D32—1216no—
538C32×C4—21no—
539C32×C4—21no—
540C32×C4—24no—
541C32×C4—24no—
542C32×C4—32no—
543C32×C4—44no—
544C32×C4—44no—
545C32×C4—61no—
546C3⋊Dic3—21no—
547C3⋊Dic3—21no—
548C3⋊Dic3—32no—
549C3⋊Dic3—38no—
550C3⋊Dic3—68no—
551C3⋊Dic3—61no—
552C3⋊Dic3—64no—
553C3⋊Dic3—124no—
554C3×Dic3—24no—
555C3×Dic3—64no—
556C3×Dic3—64no—
557C3×Dic3D3×D418yescomplemented
558C22×D4—271no—
559C22×D4—271no—
560C22×D4—271no—
561C23×C4—271no—
562#121—31no—
563#121—271no—
564#121—271no—
565#121—271no—
566#121—271no—
567#121—271no—
568#121—271no—
569#121—271no—
570C2×C4⋊C4—271no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—271no—
573C33C2×#12111yescharacteristic, complemented, Sylow
574C23×C3—24no—
575C23×C3—34no—
576C23×C3—34no—
577C23×C3—91no—
578C23×C3—91no—
579C23×C3—182no—
580C23×C3—182no—
581C23×C3—182no—
582C23×C3C2×D3214yes—
583C23×C3C22×C3⋊D311yescharacteristic
584C22×D3—34no—
585C22×D3—34no—
586C22×D3—68no—
587C22×D3—68no—
588C22×D3—68no—
589C22×D3—916no—
590C22×D3—94no—
591C22×D3—91no—
592C22×D3—94no—
593C22×D3—94no—
594C22×D3—91no—
595C22×D3—184no—
596C22×D3—184no—
597C22×D3—182no—
598C22×D3—182no—
599C22×D3—182no—
600C22×D3—182no—
601C22×D3—182no—
602C22×D3—188no—
603C22×D3—188no—
604C22×D3—188no—
605C22×D3—188no—
606C22×D3—188no—
607C22×D3C22×C3⋊D311yescharacteristic
608C22×D3C22×C3⋊D311yescharacteristic
609C3×D4—68no—
610C3×D4—68no—
611C3×D4—68no—
612C2×C3×C4—24no—
613C2×C3×C4—24no—
614C2×C3×C4—34no—
615C2×C3×C4—34no—
616C2×C3×C4—68no—
617C2×C3×C4—91no—
618C2×C3×C4—91no—
619C2×C3×C4—182no—
620C2×C3×C4—182no—
621C2×C3×C4C2×D3214yes—
622C2×C3×C4C2×D3214yes—
623C2×C3×C4C22×C3⋊D311yescharacteristic
624C2×C3×C4C22×C3⋊D311yescharacteristic
625#67—22no—
626#67—22no—
627#67—182no—
628#67—188no—
629#67—188no—
630#67—182no—
631#67—188no—
632#67—182no—
633#67—188no—
634#67—188no—
635#67—182no—
636#67—188no—
637#67—182no—
638#67—182no—
639#67—368no—
640#67—368no—
641C2×Dic3—34no—
642C2×Dic3—34no—
643C2×Dic3—94no—
644C2×Dic3—91no—
645C2×Dic3—94no—
646C2×Dic3—94no—
647C2×Dic3—91no—
648C2×Dic3—184no—
649C2×Dic3—184no—
650C2×Dic3—182no—
651C2×Dic3—188no—
652C2×Dic3C22×C3⋊D311yescharacteristic
653C2×Dic3C22×C3⋊D311yescharacteristic
654D12—22no—
655D12—182no—
656D12—188no—
657D12—188no—
658D12—188no—
659D12—182no—
660D12—182no—
661D12—368no—
662C4×D3—22no—
663C4×D3—68no—
664C4×D3—68no—
665C4×D3—916no—
666C4×D3—188no—
667C4×D3—182no—
668C4×D3—188no—
669C4×D3—182no—
670C4×D3—188no—
671C4×D3—182no—
672C4×D3—368no—
673C2×C32—24no—
674C2×C32—24no—
675C2×C32—24no—
676C2×C32—41no—
677C2×C32—44no—
678C2×C32—62no—
679C2×C32—84no—
680C2×C32—121no—
681C2×C32C2×#23511yescharacteristic
682C2×C32C2×D3×D414yes—
683C2×C32C2×D3×D414yes—
684C2×C32C2×D3×D411yescharacteristic
685C2×C32C2×D3×D411yescharacteristic
686C2×C32D3×#4114yes—
687C3⋊D3—41no—
688C3⋊D3—62no—
689C3⋊D3—68no—
690C3⋊D3—128no—
691C3⋊D3—121no—
692C3⋊D3—124no—
693C3⋊D3—244no—
694C3⋊D3#88414yesdirect product factor
695C3×D3—28no—
696C3×D3—316no—
697C3×D3—44no—
698C3×D3—124no—
699C24—91no—
700C24—271no—
701C24—271no—
702C2×D4—31no—
703C2×D4—31no—
704C2×D4—31no—
705C2×D4—271no—
706C2×D4—271no—
707C2×D4—271no—
708C2×D4—271no—
709C2×D4—271no—
710C2×D4—271no—
711C2×D4—271no—
712C2×D4—271no—
713C2×D4—271no—
714C2×D4—544no—
715C2×D4—544no—
716C2×D4—544no—
717C22×C4—31no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—271no—
721C22×C4—271no—
722C22×C4—271no—
723C22×C4—271no—
724C22×C4—271no—
725C22×C4—544no—
726C4⋊C4—31no—
727C4⋊C4—271no—
728C4⋊C4—271no—
729C4⋊C4—271no—
730C22⋊C4—31no—
731C22⋊C4—91no—
732C22⋊C4—91no—
733C22⋊C4—91no—
734C22⋊C4—271no—
735C22⋊C4—271no—
736C22⋊C4—271no—
737C22⋊C4D3×C3⋊D311yescharacteristic, complemented
738C22×C3—24no—
739C22×C3—24no—
740C22×C3—24no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—24no—
745C22×C3—38no—
746C22×C3—44no—
747C22×C3—44no—
748C22×C3—44no—
749C22×C3—64no—
750C22×C3—64no—
751C22×C3—64no—
752C22×C3—64no—
753C22×C3—64no—
754C22×C3—92no—
755C22×C3—92no—
756C22×C3—92no—
757C22×C3—181no—
758C22×C3—181no—
759C22×C3—181no—
760C22×C3—364no—
761C22×C3C22×D3214yes—
762C22×C3C23×C3⋊D311yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—38no—
769C2×D3—38no—
770C2×D3—38no—
771C2×D3—64no—
772C2×D3—64no—
773C2×D3—64no—
774C2×D3—98no—
775C2×D3—92no—
776C2×D3—1216no—
777C2×D3—188no—
778C2×D3—188no—
779C2×D3—1832no—
780C2×D3—184no—
781C2×D3—184no—
782C2×D3—181no—
783C2×D3—181no—
784C2×D3—184no—
785C2×D3—184no—
786C2×D3—184no—
787C2×D3—181no—
788C2×D3—181no—
789C2×D3—181no—
790C2×D3—364no—
791C2×D3—364no—
792C2×D3—364no—
793C2×D3—364no—
794C2×D3—364no—
795C2×D3—3616no—
796C2×D3—364no—
797C2×D3D4×C3⋊D312yescomplemented
798C3×C4—24no—
799C3×C4—24no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—38no—
803C3×C4—44no—
804C3×C4—44no—
805C3×C4—64no—
806C3×C4—181no—
807C3×C4—181no—
808Dic3—21no—
809Dic3—64no—
810Dic3—64no—
811Dic3—98no—
812Dic3—92no—
813Dic3—188no—
814Dic3—184no—
815Dic3—181no—
816Dic3—364no—
817Dic3D4×C3⋊D312yescomplemented
818C32—24no—
819C32C2×#88411yescharacteristic, complemented
820C32D3×#12114yescomplemented
821C23—31no—
822C23—31no—
823C23—91no—
824C23—91no—
825C23—182no—
826C23—182no—
827C23—182no—
828C23—274no—
829C23—271no—
830C23—271no—
831C23—542no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23—542no—
836C23C2×D3×C3⋊D311yescharacteristic
837D4—62no—
838D4—62no—
839D4—62no—
840D4—542no—
841D4—542no—
842D4—542no—
843D4—542no—
844D4—542no—
845D4—542no—
846D4—542no—
847D4—542no—
848D4—542no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—62no—
852C2×C4—91no—
853C2×C4—91no—
854C2×C4—182no—
855C2×C4—182no—
856C2×C4—274no—
857C2×C4—271no—
858C2×C4—271no—
859C2×C4—542no—
860C2×C4—542no—
861C2×C4—542no—
862C2×C4—542no—
863C2×C4C2×D3×C3⋊D311yescharacteristic
864C2×C4C2×D3×C3⋊D311yescharacteristic
865C2×C3—24no—
866C2×C3—24no—
867C2×C3—24no—
868C2×C3—44no—
869C2×C3—41no—
870C2×C3—68no—
871C2×C3—84no—
872C2×C3—94no—
873C2×C3—124no—
874C2×C3—361no—
875C2×C3D3×#23514yes—
876C2×C3D32×D414yes—
877C2×C3D32×D414yes—
878C2×C3C2×D4×C3⋊D311yescharacteristic
879C2×C3C2×D4×C3⋊D311yescharacteristic
880C2×C3#41×C3⋊D311yescharacteristic
881D3—22no—
882D3—316no—
883D3—41no—
884D3—124no—
885D3—188no—
886D3—182no—
887D3—368no—
888D3—364no—
889D3—361no—
890D3—724no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—32no—
895C22—61no—
896C22—61no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—92no—
901C22—92no—
902C22—92no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—272no—
907C22—364no—
908C22—548no—
909C22—541no—
910C22—541no—
911C22—541no—
912C22—541no—
913C22—541no—
914C22—1084no—
915C22C22×D3×C3⋊D311yescharacteristic
916C4—21no—
917C4—21no—
918C4—32no—
919C4—61no—
920C4—181no—
921C4—181no—
922C4—272no—
923C4—541no—
924C3—24no—
925C3D3×#88414yescomplemented
926C3C3⋊D3×#12111yescharacteristic, complemented
927C2—41no—
928C2—62no—
929C2—94no—
930C2—121no—
931C2—361no—
932C2—542no—
933C2—1081no—
934C2C3⋊D3×#23511yescharacteristic
935C2D3×D4×C3⋊D311yescharacteristic
936C2D3×D4×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33C2×#121
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×C3⋊D3×#67C2semidirect
3. C2×C3⋊D3×D12C2semidirect
4. C2×C4×D3×C3⋊D3C2semidirect
5. #11723925C2semidirect
6. C3×C22⋊C4×C3⋊D3C2semidirect
7. C32×#884C2semidirect
8. #11723616C2semidirect
9. #11723599C2semidirect
10. C3⋊D3×(C2×D3)⋊C4C2semidirect
11. #11723527C2semidirect
12. #11723514C2semidirect
13. #11723486C2semidirect
14. #11723474C2semidirect
15. C3⋊D3×Dic3⋊C4C2semidirect
21. C2×#6312C22semidirect
22. C2×#6312C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C2×C4×C3⋊(C3⋊D3)C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×#67C22semidirect
29. C2×C32×D12C22semidirect
30. C2×C32×C4×D3C22semidirect
33. C2×#6292C22semidirect
34. C2×#6292C22semidirect
35. C2×#6291C22semidirect
36. C2×#6291C22semidirect
37. C2×#6290C22semidirect
38. C2×#6290C22semidirect
39. C2×#6289C22semidirect
42. C2×D3×C3⋊Dic3C22semidirect
45. C33×C22⋊C4C22semidirect
46. #88859C22semidirect
47. #88857C22semidirect
48. C3×#3757C22semidirect
49. C3×#3752C22semidirect
50. C3×#3752C22semidirect
51. C32×(C2×D3)⋊C4C22semidirect
52. C32×Dic3⋊C4C22semidirect
53. #88806C22semidirect
54. Dic3⋊(C3⋊Dic3)C22semidirect
55. #88804C22semidirect
56. (C2×D3)⋊(C3⋊Dic3)C22semidirect
77. C22⋊C4×C3⋊D3D3semidirect
78. C3×#884D3semidirect
103. C2×D3×C3⋊D3D4semidirect
130. Dic3×C3⋊D3D4semidirect
172. C2×C3×#67C2×D3semidirect
173. C2×C3×#67C2×D3semidirect
174. C2×C3×D12C2×D3semidirect
177. C2×C3×C4×D3C2×D3semidirect
195. C32×C22⋊C4C2×D3semidirect
196. C32×C22⋊C4C2×D3semidirect
198. #3757C2×D3semidirect
203. #3752C2×D3semidirect
204. #3752C2×D3semidirect
213. C3×(C2×D3)⋊C4C2×D3semidirect
214. C3×Dic3⋊C4C2×D3semidirect
228. C2×C3⋊(C3⋊D3)C2×D4semidirect
241. C2×C32×D3C2×D4semidirect
247. C3⋊(C3⋊Dic3)C2×D4semidirect
251. C32×Dic3C2×D4semidirect
280. #884C3⋊D3direct (N × H)
390. C3×C3⋊D3#121semidirect
421. C2×#67C2×C3⋊D3semidirect
422. C2×#67C2×C3⋊D3semidirect
437. C2×D12C2×C3⋊D3semidirect
450. C2×C4×D3C2×C3⋊D3semidirect
457. C3×C22⋊C4D32semidirect
458. C3×C22⋊C4C2×C3⋊D3semidirect
469. (C2×D3)⋊C4C2×C3⋊D3semidirect
477. Dic3⋊C4C2×C3⋊D3semidirect
535. C2×C3×D3D3×D4semidirect
557. C3×Dic3D3×D4semidirect
573. C33C2×#121semidirect
694. C3⋊D3#884direct (N × H)
737. C22⋊C4D3×C3⋊D3semidirect
797. C2×D3D4×C3⋊D3semidirect
817. Dic3D4×C3⋊D3semidirect
819. C32C2×#884semidirect
820. C32D3×#121semidirect
925. C3D3×#884semidirect
926. C3C3⋊D3×#121semidirect

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×C3⋊D3×D122
C2×C4×D3×C3⋊D32
#117239252
C3×C22⋊C4×C3⋊D32
C32×#8842
#117236162
#117235992
C3⋊D3×(C2×D3)⋊C42
#117235272
#117235142
#117234862
#117234742
C3⋊D3×Dic3⋊C42
C3⋊D3×#1213
D3×#8843