Finite Group Databasebeta

← D3×#64093 #13175925

Subgroups — D3×#64093 #13175925

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×D3×#638C211yesmaximal, characteristic, complemented
2C2×D3×#638C211yesmaximal, characteristic, complemented
3C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
5#11723925C211yesmaximal, characteristic, complemented
6C3×#64093C211yesmaximal, characteristic, complemented
7C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
8#11723624C211yesmaximal, characteristic, complemented
9#11723623C211yesmaximal, characteristic, complemented
10D3×#3752C211yesmaximal, characteristic, complemented
11#11723527C211yesmaximal, characteristic, complemented
12#11723525C211yesmaximal, characteristic, complemented
13#11723520C211yesmaximal, characteristic, complemented
14#11723519C211yesmaximal, characteristic, complemented
15D3×#3750C211yesmaximal, characteristic, complemented
16C2×#64093—31nomaximal
17D3×#884—34nomaximal
18C23×C32×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×#638C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic, complemented
27C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
28C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
29C2×C32×C4×D3C2211yescharacteristic
30C2×C32×C4×D3C2211yescharacteristic
31D3×#638—24no—
32D3×#638—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, complemented
41C2×D3×C3⋊Dic3C2211yescharacteristic
42C2×D3×C3⋊Dic3C2211yescharacteristic
43D3×C4⋊(C3⋊D3)—24no—
44C4×D3×C3⋊D3—24no—
45C33×C22⋊C4C2211yescharacteristic, complemented
46#88859C2211yescharacteristic, complemented
47#88857C2211yescharacteristic, complemented
48C3×#3752C2211yescharacteristic, complemented
49C3×#3750C2211yescharacteristic, complemented
50C32×#217C2211yescharacteristic, complemented
51C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
53#88807C2211yescharacteristic, complemented
54#88806C2211yescharacteristic, complemented
55#88804C2211yescharacteristic, complemented
56#88803C2211yescharacteristic, complemented
57C22×#638—31no—
58C22×#638—31no—
59C22×C4⋊(C3⋊D3)—31no—
60C22×C4×C3⋊D3—31no—
61C2×D3×#67—34no—
62C2×D3×#67—34no—
63C2×D3×D12—34no—
64C2×C4×D32—34no—
65C2×C32×C22⋊C4—31no—
66C2×#3752—31no—
67C2×#3750—31no—
68#64093—31no—
69#64093—31no—
70#64093—31no—
71#64093—31no—
72#64093—31no—
73#64093—31no—
74#64093—31no—
75#64093—34no—
76#64093—64no—
77#64093D311yescharacteristic, direct product factor
78C3×#884—34no—
79C3×D3×C22⋊C4D314yescomplemented
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⋊D3C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C32×D3—22no—
94C22×C32×D3—22no—
95C22×C32×D3—22no—
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—
112C3×#638—22no—
113C3×#638—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C3×C4⋊(C3⋊D3)—22no—
117C3×C4×C3⋊D3—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×C4×D3—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—
130D3×C3⋊Dic3—22no—
131D3×C3⋊Dic3D414yescomplemented
132D3×#121—91no—
133C2×#884—94no—
134C24×C32—31no—
135C23×C3⋊D3—31no—
136C23×C3⋊D3—31no—
137C23×C3×D3C2×D314yes—
138C22×D32—34no—
139C22×D32—34no—
140C22×C32×C4—31no—
141C22×C32×C4—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—34no—
145C2×#638—34no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149C2×#638—31no—
150C2×#638—64no—
151C2×#638—64no—
152C2×#638—64no—
153C2×#638—64no—
154C2×#638C2×D311yescharacteristic, complemented
155C2×#638C2×D311yescharacteristic, complemented
156C22×C3⋊Dic3—31no—
157C22×C3⋊Dic3—31no—
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)—64no—
164C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
165C2×C4×C3⋊D3—31no—
166C2×C4×C3⋊D3—31no—
167C2×C4×C3⋊D3—34no—
168C2×C4×C3⋊D3—31no—
169C2×C4×C3⋊D3—64no—
170C2×C4×C3⋊D3—64no—
171C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
172C2×C3×#67—34no—
173C2×C3×#67—34no—
174C2×C3×D12—34no—
175C2×C3×C4×D3—34no—
176C2×C3×C4×D3C2×D314yes—
177C2×C3×C4×D3C2×D314yes—
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×C22⋊C4—24no—
193C32×C22⋊C4—31no—
194C32×C22⋊C4—31no—
195C32×C22⋊C4—31no—
196C32×C22⋊C4C2×D314yescomplemented
197C32×C22⋊C4C2×D311yescharacteristic, complemented
198#3752—31no—
199#3752—31no—
200#3752—34no—
201#3752—31no—
202#3752—64no—
203#3752C2×D311yescharacteristic, complemented
204#3750—31no—
205#3750—34no—
206#3750—31no—
207#3750—31no—
208#3750—64no—
209#3750C2×D311yescharacteristic, complemented
210C3×#217C2×D314yescomplemented
211C3×(C2×D3)⋊C4—34no—
212C3×(C2×D3)⋊C4C2×D314yescomplemented
213C3×(C2×D3)⋊C4C2×D314yescomplemented
214C3×Dic3⋊C4—34no—
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—21no—
233C2×C3×C3⋊D3—21no—
234C2×C3×C3⋊D3C2×D412yescomplemented
235C2×C32×D3—21no—
236C2×C32×D3—21no—
237C2×C32×D3—21no—
238C2×C32×D3—44no—
239C2×C32×D3C2×D412yes—
240C2×C32×D3C2×D412yes—
241C2×C32×D3#4112yes—
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⋊Dic3C2×D412yescomplemented
250C32×Dic3—21no—
251C32×Dic3—21no—
252C22×#67—94no—
253C22×#67—94no—
254C2×D3×D4—91no—
255C2×D3×D4—91no—
256C2×D3×D4—91no—
257C22×D12—94no—
258C22×C4×D3—94no—
259C22×C4×D3—91no—
260C3×#121—91no—
261C2×C3×C22⋊C4—34no—
262#939—91no—
263#939—91no—
264#938—91no—
265#930—91no—
266C2×(C2×D3)⋊C4—94no—
267C2×Dic3⋊C4—94no—
268#895—91no—
269D3×C4⋊C4—91no—
270#884—34no—
271#884—94no—
272#884—94no—
273#884—94no—
274#884—94no—
275#884—94no—
276#884—94no—
277#884—94no—
278#884—91no—
279#884—91no—
280#884—184no—
281D3×C22⋊C4—91no—
282D3×C22⋊C4C3⋊D311yescharacteristic, complemented
283C23×C32—24no—
284C23×C32—31no—
285C23×C32—31no—
286C23×C32—62no—
287C23×C32—62no—
288C23×C32—62no—
289C23×C32C22×D314yes—
290C23×C32C22×D311yescharacteristic
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—28no—
306C22×C3×D3—28no—
307C22×C3×D3—28no—
308C22×C3×D3—34no—
309C22×C3×D3—34no—
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—
318C2×C32×C4—24no—
319C2×C32×C4—24no—
320C2×C32×C4—31no—
321C2×C32×C4—31no—
322C2×C32×C4—62no—
323C2×C32×C4—62no—
324C2×C32×C4C22×D314yes—
325C2×C32×C4C22×D314yes—
326C2×C32×C4C22×D311yescharacteristic
327C2×C32×C4C22×D311yescharacteristic
328#638—22no—
329#638—22no—
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—34no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—34no—
344C2×C3⋊Dic3—34no—
345C2×C3⋊Dic3—64no—
346C2×C3⋊Dic3—64no—
347C2×C3⋊Dic3—62no—
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350C4⋊(C3⋊D3)—22no—
351C4⋊(C3⋊D3)—62no—
352C4⋊(C3⋊D3)—62no—
353C4⋊(C3⋊D3)—62no—
354C4⋊(C3⋊D3)—68no—
355C4⋊(C3⋊D3)—128no—
356C4×C3⋊D3—22no—
357C4×C3⋊D3—62no—
358C4×C3⋊D3—62no—
359C4×C3⋊D3—62no—
360C4×C3⋊D3—68no—
361C4×C3⋊D3—128no—
362C3×#67—68no—
363C3×#67—68no—
364C2×C3×Dic3—34no—
365C2×C3×Dic3—34no—
366C2×C3×Dic3C22×D314yes—
367C2×C3×Dic3C22×D314yes—
368C3×D12—68no—
369C3×C4×D3—28no—
370C3×C4×D3—28no—
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—22no—
390C3×C3⋊D3—41no—
391C32×D3—41no—
392C32×D3#12114yescomplemented
393C24×C3—34no—
394C23×D3—94no—
395C23×D3—94no—
396C23×D3—91no—
397C23×D3—91no—
398C23×D3C2×C3⋊D311yescharacteristic
399C2×C3×D4—91no—
400C2×C3×D4—91no—
401C2×C3×D4—91no—
402C22×C3×C4—34no—
403C22×C3×C4—34no—
404C22×C3×C4—91no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—94no—
408C2×#67—94no—
409C2×#67—94no—
410C2×#67—94no—
411C2×#67—94no—
412C2×#67—94no—
413C2×#67—91no—
414C2×#67—91no—
415C2×#67—91no—
416C2×#67—91no—
417C2×#67—91no—
418C2×#67—91no—
419C2×#67—184no—
420C2×#67—184no—
421C2×#67—1816no—
422C2×#67—1816no—
423C22×Dic3—94no—
424C22×Dic3—94no—
425C22×Dic3—91no—
426D3×D4—184no—
427D3×D4—184no—
428D3×D4—184no—
429C2×D12—34no—
430C2×D12—94no—
431C2×D12—94no—
432C2×D12—91no—
433C2×D12—91no—
434C2×D12—94no—
435C2×D12—91no—
436C2×D12—184no—
437C2×D12—1816no—
438C2×C4×D3—34no—
439C2×C4×D3—91no—
440C2×C4×D3—94no—
441C2×C4×D3—94no—
442C2×C4×D3—91no—
443C2×C4×D3—94no—
444C2×C4×D3—91no—
445C2×C4×D3—91no—
446C2×C4×D3—184no—
447C2×C4×D3—184no—
448C2×C4×D3—1816no—
449C2×C4×D3C2×C3⋊D311yescharacteristic
450C2×C4×D3C2×C3⋊D311yescharacteristic
451C3×C4⋊C4—91no—
452C3×C22⋊C4—24no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4D3214yescomplemented
458C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
459#217—91no—
460#217C2×C3⋊D311yescharacteristic, complemented
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—94no—
463(C2×D3)⋊C4—94no—
464(C2×D3)⋊C4—94no—
465(C2×D3)⋊C4—91no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—184no—
468(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
469(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
470C4⋊Dic3—91no—
471Dic3⋊C4—34no—
472Dic3⋊C4—94no—
473Dic3⋊C4—94no—
474Dic3⋊C4—94no—
475Dic3⋊C4—91no—
476Dic3⋊C4—91no—
477Dic3⋊C4—184no—
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—32no—
487C22×C32—32no—
488C22×C32—44no—
489C22×C32—44no—
490C22×C32—44no—
491C22×C32—61no—
492C22×C32—61no—
493C22×C32—61no—
494C22×C32—124no—
495C22×C32C23×D314yes—
496C22×C32C23×D311yescharacteristic
497C2×C3⋊D3—21no—
498C2×C3⋊D3—21no—
499C2×C3⋊D3—21no—
500C2×C3⋊D3—21no—
501C2×C3⋊D3—21no—
502C2×C3⋊D3—32no—
503C2×C3⋊D3—38no—
504C2×C3⋊D3—68no—
505C2×C3⋊D3—68no—
506C2×C3⋊D3—61no—
507C2×C3⋊D3—61no—
508C2×C3⋊D3—61no—
509C2×C3⋊D3—61no—
510C2×C3⋊D3—61no—
511C2×C3⋊D3—64no—
512C2×C3⋊D3—64no—
513C2×C3⋊D3—64no—
514C2×C3⋊D3—64no—
515C2×C3⋊D3—64no—
516C2×C3⋊D3—124no—
517C2×C3⋊D3—124no—
518C2×C3⋊D3—124no—
519C2×C3⋊D3—124no—
520C2×C3⋊D3—124no—
521C2×C3⋊D3—124no—
522C2×C3⋊D3D3×D412yescomplemented
523C2×C3×D3—24no—
524C2×C3×D3—24no—
525C2×C3×D3—24no—
526C2×C3×D3—38no—
527C2×C3×D3—416no—
528C2×C3×D3—64no—
529C2×C3×D3—64no—
530C2×C3×D3—64no—
531C2×C3×D3—64no—
532C2×C3×D3—64no—
533C2×C3×D3#23518yes—
534C2×C3×D3D3×D418yes—
535C2×C3×D3D3×D418yes—
536D32—632no—
537D32—1216no—
538C32×C4—21no—
539C32×C4—21no—
540C32×C4—24no—
541C32×C4—24no—
542C32×C4—44no—
543C32×C4—44no—
544C32×C4—61no—
545C32×C4—61no—
546C3⋊Dic3—21no—
547C3⋊Dic3—32no—
548C3⋊Dic3—38no—
549C3⋊Dic3—68no—
550C3⋊Dic3—61no—
551C3⋊Dic3—64no—
552C3⋊Dic3—124no—
553C3⋊Dic3D3×D412yescomplemented
554C3×Dic3—24no—
555C3×Dic3—24no—
556C3×Dic3—38no—
557C3×Dic3—64no—
558C22×D4—271no—
559C22×D4—271no—
560C22×D4—271no—
561C23×C4—271no—
562#121—91no—
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—31no—
572C2×C22⋊C4—271no—
573C33C2×#12111yescharacteristic, complemented, Sylow
574C23×C3—24no—
575C23×C3—34no—
576C23×C3—34no—
577C23×C3—68no—
578C23×C3—68no—
579C23×C3—68no—
580C23×C3—91no—
581C23×C3—91no—
582C23×C3C2×D3214yes—
583C23×C3C22×C3⋊D311yescharacteristic
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—34no—
588C22×D3—34no—
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—188no—
598C22×D3—188no—
599C22×D3—188no—
600C22×D3—188no—
601C22×D3—188no—
602C22×D3—182no—
603C22×D3—182no—
604C22×D3—182no—
605C22×D3—182no—
606C22×D3—182no—
607C22×D3C22×C3⋊D311yescharacteristic
608C22×D3C22×C3⋊D311yescharacteristic
609C3×D4—182no—
610C3×D4—182no—
611C3×D4—182no—
612C2×C3×C4—24no—
613C2×C3×C4—24no—
614C2×C3×C4—34no—
615C2×C3×C4—34no—
616C2×C3×C4—68no—
617C2×C3×C4—68no—
618C2×C3×C4—91no—
619C2×C3×C4—91no—
620C2×C3×C4—182no—
621C2×C3×C4C2×D3214yes—
622C2×C3×C4C2×D3214yes—
623C2×C3×C4C22×C3⋊D311yescharacteristic
624C2×C3×C4C22×C3⋊D311yescharacteristic
625#67—68no—
626#67—68no—
627#67—182no—
628#67—182no—
629#67—188no—
630#67—188no—
631#67—182no—
632#67—188no—
633#67—182no—
634#67—188no—
635#67—182no—
636#67—188no—
637#67—182no—
638#67—188no—
639#67—368no—
640#67—368no—
641C2×Dic3—34no—
642C2×Dic3—34no—
643C2×Dic3—916no—
644C2×Dic3—94no—
645C2×Dic3—91no—
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—68no—
655D12—182no—
656D12—188no—
657D12—188no—
658D12—188no—
659D12—182no—
660D12—182no—
661D12—368no—
662C4×D3—22no—
663C4×D3—22no—
664C4×D3—68no—
665C4×D3—94no—
666C4×D3—182no—
667C4×D3—188no—
668C4×D3—182no—
669C4×D3—188no—
670C4×D3—188no—
671C4×D3—182no—
672C4×D3—368no—
673C2×C32—24no—
674C2×C32—24no—
675C2×C32—24no—
676C2×C32—34no—
677C2×C32—41no—
678C2×C32—44no—
679C2×C32—84no—
680C2×C32—121no—
681C2×C32C2×#23514yes—
682C2×C32C2×D3×D414yes—
683C2×C32C2×D3×D414yes—
684C2×C32C2×D3×D411yescharacteristic
685C2×C32C2×D3×D411yescharacteristic
686C2×C32D3×#4111yescharacteristic
687C3⋊D3—22no—
688C3⋊D3—41no—
689C3⋊D3—62no—
690C3⋊D3—68no—
691C3⋊D3—128no—
692C3⋊D3—121no—
693C3⋊D3—124no—
694C3⋊D3—244no—
695C3×D3—44no—
696C3×D3—68no—
697C3×D3—124no—
698C3×D3#884116yescomplemented
699C24—31no—
700C24—271no—
701C24—271no—
702C2×D4—91no—
703C2×D4—91no—
704C2×D4—91no—
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—31no—
719C22×C4—91no—
720C22×C4—271no—
721C22×C4—271no—
722C22×C4—271no—
723C22×C4—271no—
724C22×C4—271no—
725C22×C4—544no—
726C4⋊C4—91no—
727C4⋊C4—271no—
728C4⋊C4—271no—
729C4⋊C4—271no—
730C22⋊C4—31no—
731C22⋊C4—31no—
732C22⋊C4—31no—
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—38no—
747C22×C3—38no—
748C22×C3—44no—
749C22×C3—44no—
750C22×C3—44no—
751C22×C3—64no—
752C22×C3—64no—
753C22×C3—64no—
754C22×C3—92no—
755C22×C3—1216no—
756C22×C3—181no—
757C22×C3—181no—
758C22×C3—181no—
759C22×C3—181no—
760C22×C3—181no—
761C22×C3C22×D3214yes—
762C22×C3C23×C3⋊D311yescharacteristic
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—38no—
767C2×D3—44no—
768C2×D3—64no—
769C2×D3—64no—
770C2×D3—64no—
771C2×D3—64no—
772C2×D3—64no—
773C2×D3—98no—
774C2×D3—92no—
775C2×D3—188no—
776C2×D3—1832no—
777C2×D3—184no—
778C2×D3—184no—
779C2×D3—181no—
780C2×D3—181no—
781C2×D3—188no—
782C2×D3—184no—
783C2×D3—184no—
784C2×D3—184no—
785C2×D3—181no—
786C2×D3—181no—
787C2×D3—181no—
788C2×D3—364no—
789C2×D3—364no—
790C2×D3—364no—
791C2×D3—364no—
792C2×D3—364no—
793C2×D3—3616no—
794C2×D3—364no—
795C2×D3#382812yes—
796C2×D3D4×C3⋊D312yes—
797C2×D3D4×C3⋊D312yes—
798C3×C4—24no—
799C3×C4—24no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—44no—
803C3×C4—44no—
804C3×C4—64no—
805C3×C4—64no—
806C3×C4—92no—
807C3×C4—181no—
808Dic3—21no—
809Dic3—21no—
810Dic3—38no—
811Dic3—64no—
812Dic3—98no—
813Dic3—92no—
814Dic3—188no—
815Dic3—184no—
816Dic3—181no—
817Dic3—364no—
818C32—24no—
819C32C2×#88414yescomplemented
820C32D3×#12111yescharacteristic, complemented
821C23—31no—
822C23—31no—
823C23—62no—
824C23—62no—
825C23—62no—
826C23—91no—
827C23—91no—
828C23—274no—
829C23—271no—
830C23—271no—
831C23—542no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23—542no—
836C23C2×D3×C3⋊D311yescharacteristic
837D4—182no—
838D4—182no—
839D4—182no—
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—62no—
853C2×C4—91no—
854C2×C4—91no—
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—316no—
869C2×C3—41no—
870C2×C3—44no—
871C2×C3—84no—
872C2×C3—124no—
873C2×C3—182no—
874C2×C3—361no—
875C2×C3D3×#23514yes—
876C2×C3D32×D414yes—
877C2×C3D32×D414yes—
878C2×C3C2×#382811yescharacteristic
879C2×C3C2×D4×C3⋊D311yescharacteristic
880C2×C3C2×D4×C3⋊D311yescharacteristic
881D3—41no—
882D3—68no—
883D3—124no—
884D3—182no—
885D3—188no—
886D3—368no—
887D3—361no—
888D3—364no—
889D3—724no—
890D3#6409314yesdirect product factor
891C22—21no—
892C22—21no—
893C22—21no—
894C22—32no—
895C22—32no—
896C22—32no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—92no—
901C22—124no—
902C22—181no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—181no—
907C22—272no—
908C22—548no—
909C22—541no—
910C22—541no—
911C22—541no—
912C22—541no—
913C22—541no—
914C22—1084no—
915C22C22×D3×C3⋊D311yescharacteristic
916C4—21no—
917C4—21no—
918C4—61no—
919C4—61no—
920C4—92no—
921C4—181no—
922C4—272no—
923C4—541no—
924C3—24no—
925C3D3×#88414yescomplemented
926C3C2×#6409311yescharacteristic, complemented
927C2—34no—
928C2—41no—
929C2—121no—
930C2—182no—
931C2—361no—
932C2—542no—
933C2—1081no—
934C2D3×#382811yescharacteristic
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×D3×#638C2semidirect
2. C2×D3×#638C2semidirect
3. C2×D3×C4⋊(C3⋊D3)C2semidirect
4. C2×C4×D3×C3⋊D3C2semidirect
5. #11723925C2semidirect
6. C3×#64093C2semidirect
7. C32×D3×C22⋊C4C2semidirect
8. #11723624C2semidirect
9. #11723623C2semidirect
10. D3×#3752C2semidirect
11. #11723527C2semidirect
12. #11723525C2semidirect
13. #11723520C2semidirect
14. #11723519C2semidirect
15. D3×#3750C2semidirect
21. C2×#6312C22semidirect
22. C2×#6312C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
24. C2×C4×C3⋊(C3⋊D3)C22semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×#638C22semidirect
27. C2×C3×C4⋊(C3⋊D3)C22semidirect
28. C2×C3×C4×C3⋊D3C22semidirect
33. C2×#6292C22semidirect
34. C2×#6292C22semidirect
35. C2×#6291C22semidirect
36. C2×#6291C22semidirect
37. C2×#6290C22semidirect
38. C2×#6290C22semidirect
39. C2×#6289C22semidirect
40. C2×Dic3×C3⋊D3C22semidirect
45. C33×C22⋊C4C22semidirect
46. #88859C22semidirect
47. #88857C22semidirect
48. C3×#3752C22semidirect
49. C3×#3750C22semidirect
50. C32×#217C22semidirect
51. C32×(C2×D3)⋊C4C22semidirect
52. C32×(C2×D3)⋊C4C22semidirect
53. #88807C22semidirect
54. #88806C22semidirect
55. #88804C22semidirect
56. #88803C22semidirect
77. #64093D3direct (N × H)
79. C3×D3×C22⋊C4D3semidirect
103. C2×D3×C3⋊D3D4semidirect
131. D3×C3⋊Dic3D4semidirect
154. C2×#638C2×D3semidirect
155. C2×#638C2×D3semidirect
164. C2×C4⋊(C3⋊D3)C2×D3semidirect
171. C2×C4×C3⋊D3C2×D3semidirect
196. C32×C22⋊C4C2×D3semidirect
197. C32×C22⋊C4C2×D3semidirect
203. #3752C2×D3semidirect
209. #3750C2×D3semidirect
210. C3×#217C2×D3semidirect
212. C3×(C2×D3)⋊C4C2×D3semidirect
213. C3×(C2×D3)⋊C4C2×D3semidirect
228. C2×C3⋊(C3⋊D3)C2×D4semidirect
234. C2×C3×C3⋊D3C2×D4semidirect
247. C3⋊(C3⋊Dic3)C2×D4semidirect
249. C3×C3⋊Dic3C2×D4semidirect
282. D3×C22⋊C4C3⋊D3semidirect
392. C32×D3#121semidirect
457. C3×C22⋊C4D32semidirect
458. C3×C22⋊C4C2×C3⋊D3semidirect
460. #217C2×C3⋊D3semidirect
468. (C2×D3)⋊C4C2×C3⋊D3semidirect
469. (C2×D3)⋊C4C2×C3⋊D3semidirect
522. C2×C3⋊D3D3×D4semidirect
553. C3⋊Dic3D3×D4semidirect
573. C33C2×#121semidirect
698. C3×D3#884semidirect
737. C22⋊C4D3×C3⋊D3semidirect
819. C32C2×#884semidirect
820. C32D3×#121semidirect
890. D3#64093direct (N × H)
925. C3D3×#884semidirect
926. C3C2×#64093semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×D3×C4⋊(C3⋊D3)2
C2×C4×D3×C3⋊D32
#117239252
C3×#640932
C32×D3×C22⋊C42
#117236242
#117236232
D3×#37522
#117235272
#117235252
#117235202
#117235192
D3×#37502
C2×#640933
D3×#8843