Finite Group Databasebeta

← D3×#64148 #13177366

Subgroups — D3×#64148 #13177366

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×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×D3×#638C211yesmaximal, characteristic, complemented
3C2×D3×#638C211yesmaximal, characteristic, complemented
4C22×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#11723980C211yesmaximal, characteristic, complemented
6C3×#64148C211yesmaximal, characteristic, complemented
7#11723637C211yesmaximal, characteristic, complemented
8#11723635C211yesmaximal, characteristic, complemented
9#11723616C211yesmaximal, characteristic, complemented
10#11723615C211yesmaximal, characteristic, complemented
11D3×#3757C211yesmaximal, characteristic, complemented
12D3×#3752C211yesmaximal, characteristic, complemented
13#11723475C211yesmaximal, characteristic, complemented
14#11723474C211yesmaximal, characteristic, complemented
15D3×#3750C211yesmaximal, characteristic, complemented
16C2×#64148—31nomaximal
17D3×#939—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C23×C32×D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic, complemented
24C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic, complemented
27C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic, complemented
30C32×D3×D4—24no—
31C2×C32×D12C2211yescharacteristic, complemented
32C2×C32×C4×D3C2211yescharacteristic
33D3×#638—24no—
34D3×#638—24no—
35C2×#6291C2211yescharacteristic, complemented
36C2×#6291C2211yescharacteristic, complemented
37C2×#6290C2211yescharacteristic, complemented
38C2×#6290C2211yescharacteristic, complemented
39C2×D3×C3⋊Dic3—24no—
40C2×D3×C3⋊Dic3C2211yescharacteristic
41C2×D3×C3⋊Dic3C2211yescharacteristic
42C2×D3×C3⋊Dic3C2211yescharacteristic
43C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
44C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
45#88864C2211yescharacteristic, complemented
46#88859C2211yescharacteristic, complemented
47#88857C2211yescharacteristic, complemented
48C3×#3757C2211yescharacteristic, complemented
49C3×#3752C2211yescharacteristic, complemented
50C3×#3750C2211yescharacteristic, complemented
51#88807C2211yescharacteristic, complemented
52#88806C2211yescharacteristic, complemented
53#88804C2211yescharacteristic, complemented
54#88803C2211yescharacteristic, complemented
55(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
56(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
57C22×C32×D4—31no—
58C22×#638—31no—
59C22×#638—31no—
60C23×C3⋊Dic3—31no—
61C2×C3×D3×D4D314yescomplemented
62C2×D3×#67—34no—
63C2×D3×#67—34no—
64C22×D3×Dic3—34no—
65C2×#3757—31no—
66#64148—31no—
67#64148—31no—
68#64148—31no—
69#64148—31no—
70#64148—31no—
71#64148—34no—
72#64148—31no—
73#64148—31no—
74#64148—64no—
75#64148D311yescharacteristic, direct product factor
76C2×#3752—31no—
77C2×#3750—31no—
78C3×#939—34no—
79#63980—34no—
80#63978—34no—
81#63971—34no—
82#63970—34no—
83D3×#217—34no—
84D3×(C2×D3)⋊C4—34no—
85#63886—34no—
86#63885—34no—
87D3×Dic3⋊C4—34no—
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C32×D3—22no—
93C22×C32×D3—22no—
94C22×C32×D3—22no—
95C22×C32×D3—22no—
96C22×C32×D3—22no—
97C22×C32×D3D414yescomplemented
98C22×C32×D3C2311yescharacteristic
99C22×C32×D3C2311yescharacteristic
100C22×C32×D3C2311yescharacteristic
101C2×D3×C3⋊D3—22no—
102C2×D3×C3⋊D3—22no—
103C2×D3×C3⋊D3—22no—
104C33×D4—22no—
105C2×C33×C4C2311yescharacteristic
106#6312—22no—
107#6312—22no—
108C2×C3⋊(C3⋊Dic3)—22no—
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—22no—
113C3×#638—22no—
114C2×C3×C3⋊Dic3—22no—
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—22no—
119C32×#67—22no—
120C2×C32×Dic3C2311yescharacteristic
121C32×D12—22no—
122C32×C4×D3—22no—
123#6291—22no—
124#6291—22no—
125#6290—22no—
126#6290—22no—
127D3×C3⋊Dic3—22no—
128D3×C3⋊Dic3—22no—
129D3×C3⋊Dic3—22no—
130D3×C3⋊Dic3—22no—
131D3×C3⋊Dic3D414yescomplemented
132C2×#939—94no—
133D3×#121—91no—
134C24×C32—31no—
135C24×C32—31no—
136C23×C3⋊D3—31no—
137C23×C3×D3C2×D314yes—
138C23×C3×D3C2×D314yes—
139C22×D32—34no—
140C2×C32×D4—24no—
141C2×C32×D4—31no—
142C2×C32×D4—31no—
143C2×C32×D4—31no—
144C2×C32×D4—64no—
145C2×C32×D4C2×D314yescomplemented
146C2×C32×D4C2×D311yescharacteristic, complemented
147C22×C32×C4—31no—
148C2×#638—31no—
149C2×#638—31no—
150C2×#638—34no—
151C2×#638—34no—
152C2×#638—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—64no—
157C2×#638—64no—
158C2×#638—64no—
159C2×#638—64no—
160C2×#638C2×D311yescharacteristic, complemented
161C2×#638C2×D311yescharacteristic, complemented
162C22×C3⋊Dic3—31no—
163C22×C3⋊Dic3—31no—
164C22×C3⋊Dic3—34no—
165C22×C3⋊Dic3—31no—
166C22×C3⋊Dic3—31no—
167C22×C3⋊Dic3—31no—
168C22×C3⋊Dic3—31no—
169C22×C3⋊Dic3—64no—
170C22×C3⋊Dic3—64no—
171C22×C3⋊Dic3C2×D311yescharacteristic, complemented
172C2×C3×#67—34no—
173C2×C3×#67—34no—
174C2×C3×#67C2×D314yescomplemented
175C2×C3×#67C2×D314yescomplemented
176C22×C3×Dic3—34no—
177C3×D3×D4—216no—
178C2×C3×D12C2×D314yescomplemented
179C2×C3×C4×D3C2×D314yes—
180D3×#67—616no—
181D3×#67—616no—
182C2×#626—34no—
183C2×#626—34no—
184C2×#625—34no—
185C2×#625—34no—
186C2×D3×Dic3—34no—
187C2×D3×Dic3—34no—
188C2×D3×Dic3—34no—
189C2×D3×Dic3—34no—
190C2×D3×Dic3—34no—
191C2×D3×Dic3—616no—
192#3757—31no—
193#3757—34no—
194#3757—31no—
195#3757—31no—
196#3757—64no—
197#3757C2×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×#217—34no—
211C3×(C2×D3)⋊C4—34no—
212C3×Dic3⋊C4—34no—
213#3724—34no—
214Dic3⋊Dic3—34no—
215#3722—34no—
216(C2×D3)⋊Dic3—34no—
217(C2×D3)⋊Dic3—34no—
218(C2×D3)⋊Dic3—34no—
219C22×C33—21no—
220C22×C33—21no—
221C22×C33—21no—
222C22×C33—21no—
223C22×C33—21no—
224C22×C33C2×D412yescomplemented
225C22×C33C2411yescharacteristic
226C2×C3⋊(C3⋊D3)—21no—
227C2×C3⋊(C3⋊D3)—21no—
228C2×C3⋊(C3⋊D3)—21no—
229C2×C3×C3⋊D3—21no—
230C2×C3×C3⋊D3—21no—
231C2×C3×C3⋊D3—21no—
232C2×C32×D3—21no—
233C2×C32×D3—21no—
234C2×C32×D3—28no—
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×D3C2×D412yescomplemented
242C2×C32×D3#4112yes—
243D3×C3⋊D3—44no—
244C33×C4—21no—
245C3⋊(C3⋊Dic3)—21no—
246C3⋊(C3⋊Dic3)—21no—
247C3⋊(C3⋊Dic3)C2×D412yescomplemented
248C3×C3⋊Dic3—21no—
249C3×C3⋊Dic3—21no—
250C3×C3⋊Dic3C2×D412yescomplemented
251C32×Dic3—21no—
252C22×C3×D4—34no—
253C22×#67—94no—
254C22×#67—94no—
255C23×Dic3—94no—
256C2×D3×D4—91no—
257C2×D3×D4—91no—
258C2×D3×D4C3⋊D311yescharacteristic, complemented
259C22×C4×D3—91no—
260C3×#121—91no—
261C2×#217—94no—
262#939—34no—
263#939—94no—
264#939—94no—
265#939—94no—
266#939—94no—
267#939—94no—
268#939—94no—
269#939—94no—
270#939—91no—
271#939—91no—
272#939—184no—
273#938—91no—
274#930—91no—
275C2×(C2×D3)⋊C4—94no—
276C2×Dic3⋊C4—94no—
277#895—91no—
278D3×C4⋊C4—91no—
279#884—91no—
280#884—91no—
281D3×C22⋊C4—91no—
282D3×C22⋊C4—91no—
283C23×C32—24no—
284C23×C32—24no—
285C23×C32—31no—
286C23×C32—34no—
287C23×C32—31no—
288C23×C32—31no—
289C23×C32—62no—
290C23×C32—62no—
291C23×C32—62no—
292C23×C32—62no—
293C23×C32—62no—
294C23×C32C22×D314yes—
295C23×C32C22×D314yes—
296C23×C32C22×D311yescharacteristic
297C23×C32C22×D311yescharacteristic
298C22×C3⋊D3—31no—
299C22×C3⋊D3—34no—
300C22×C3⋊D3—64no—
301C22×C3⋊D3—62no—
302C22×C3⋊D3—62no—
303C22×C3⋊D3—62no—
304C22×C3⋊D3C22×D311yescharacteristic
305C22×C3×D3—28no—
306C22×C3×D3—28no—
307C22×C3×D3—28no—
308C22×C3×D3—28no—
309C22×C3×D3—28no—
310C22×C3×D3—34no—
311C22×C3×D3#67116yescomplemented
312C22×C3×D3C22×D314yes—
313C22×C3×D3C22×D314yes—
314C22×C3×D3C22×D314yes—
315C2×D32—68no—
316C2×D32—68no—
317C2×D32—68no—
318C32×D4—22no—
319C32×D4—28no—
320C32×D4—48no—
321C32×D4—62no—
322C32×D4—62no—
323C32×D4—62no—
324C2×C32×C4—24no—
325C2×C32×C4—31no—
326C2×C32×C4—62no—
327C2×C32×C4C22×D314yes—
328C2×C32×C4C22×D311yescharacteristic
329#638—22no—
330#638—22no—
331#638—62no—
332#638—62no—
333#638—62no—
334#638—62no—
335#638—62no—
336#638—62no—
337#638—68no—
338#638—68no—
339#638—128no—
340#638—128no—
341C2×C3⋊Dic3—22no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—34no—
344C2×C3⋊Dic3—31no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—34no—
347C2×C3⋊Dic3—34no—
348C2×C3⋊Dic3—34no—
349C2×C3⋊Dic3—64no—
350C2×C3⋊Dic3—64no—
351C2×C3⋊Dic3—64no—
352C2×C3⋊Dic3—62no—
353C2×C3⋊Dic3—62no—
354C2×C3⋊Dic3—62no—
355C2×C3⋊Dic3—62no—
356C2×C3⋊Dic3—62no—
357C2×C3⋊Dic3—68no—
358C2×C3⋊Dic3—128no—
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C3×#67—28no—
363C3×#67—28no—
364C3×#67—68no—
365C3×#67—68no—
366C2×C3×Dic3—34no—
367C2×C3×Dic3—34no—
368C2×C3×Dic3—34no—
369C2×C3×Dic3—68no—
370C2×C3×Dic3C22×D314yes—
371C3×D12—28no—
372C3×C4×D3—28no—
373#626—68no—
374#626—68no—
375#625—68no—
376#625—68no—
377D3×Dic3—316no—
378D3×Dic3—68no—
379D3×Dic3—68no—
380D3×Dic3—68no—
381D3×Dic3—68no—
382C2×#121—271noSylow
383C2×C33—22no—
384C2×C33—41no—
385C2×C33C22×D411yescharacteristic
386C2×C33C22×D411yescharacteristic
387C2×C33C2×#4111yescharacteristic
388C3⋊(C3⋊D3)—41no—
389C3×C3⋊D3—41no—
390C32×D3—22no—
391C32×D3—41no—
392C32×D3#12114yescomplemented
393C24×C3—34no—
394C24×C3—34no—
395C23×D3—94no—
396C23×D3—91no—
397C23×D3C2×C3⋊D311yescharacteristic
398C23×D3C2×C3⋊D311yescharacteristic
399C2×C3×D4—24no—
400C2×C3×D4—34no—
401C2×C3×D4—34no—
402C2×C3×D4—34no—
403C2×C3×D4—616no—
404C2×C3×D4—91no—
405C2×C3×D4—91no—
406C2×C3×D4D3214yescomplemented
407C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
408C22×C3×C4—34no—
409C22×C3×C4—91no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—94no—
413C2×#67—94no—
414C2×#67—94no—
415C2×#67—94no—
416C2×#67—94no—
417C2×#67—94no—
418C2×#67—91no—
419C2×#67—91no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—184no—
423C2×#67—184no—
424C2×#67—1816no—
425C2×#67—1816no—
426C2×#67C2×C3⋊D311yescharacteristic, complemented
427C2×#67C2×C3⋊D311yescharacteristic, complemented
428C22×Dic3—34no—
429C22×Dic3—94no—
430C22×Dic3—94no—
431C22×Dic3—94no—
432C22×Dic3—94no—
433C22×Dic3—94no—
434C22×Dic3—94no—
435C22×Dic3—91no—
436C22×Dic3—184no—
437C22×Dic3—1816no—
438D3×D4—24no—
439D3×D4—184no—
440D3×D4—184no—
441C2×D12—91no—
442C2×D12—91no—
443C2×D12C2×C3⋊D311yescharacteristic, complemented
444C2×C4×D3—91no—
445C2×C4×D3—91no—
446C2×C4×D3—91no—
447C2×C4×D3—91no—
448C2×C4×D3—91no—
449C2×C4×D3—184no—
450C2×C4×D3C2×C3⋊D311yescharacteristic
451C3×C4⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454#217—34no—
455#217—94no—
456#217—94no—
457#217—94no—
458#217—91no—
459#217—91no—
460#217—184no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—94no—
463(C2×D3)⋊C4—94no—
464(C2×D3)⋊C4—91no—
465(C2×D3)⋊C4—91no—
466(C2×D3)⋊C4—94no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—184no—
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—21no—
482C22×C32—21no—
483C22×C32—24no—
484C22×C32—28no—
485C22×C32—24no—
486C22×C32—24no—
487C22×C32—24no—
488C22×C32—24no—
489C22×C32—24no—
490C22×C32—32no—
491C22×C32—32no—
492C22×C32—32no—
493C22×C32—32no—
494C22×C32—44no—
495C22×C32—44no—
496C22×C32—44no—
497C22×C32—44no—
498C22×C32—44no—
499C22×C32—68no—
500C22×C32—61no—
501C22×C32—61no—
502C22×C32—61no—
503C22×C32—61no—
504C22×C32—61no—
505C22×C32—124no—
506C22×C32D3×D412yescomplemented
507C22×C32C2×#6718yescomplemented
508C22×C32C23×D314yes—
509C22×C32C23×D311yescharacteristic
510C2×C3⋊D3—21no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—61no—
514C2×C3⋊D3—61no—
515C2×C3⋊D3—61no—
516C2×C3⋊D3—64no—
517C2×C3⋊D3—64no—
518C2×C3⋊D3—64no—
519C2×C3⋊D3—124no—
520C2×C3⋊D3—124no—
521C2×C3⋊D3—124no—
522C2×C3⋊D3—124no—
523C2×C3×D3—24no—
524C2×C3×D3—24no—
525C2×C3×D3—232no—
526C2×C3×D3—24no—
527C2×C3×D3—24no—
528C2×C3×D3—24no—
529C2×C3×D3—416no—
530C2×C3×D3—64no—
531C2×C3×D3—64no—
532C2×C3×D3—64no—
533C2×C3×D3D3×D418yes—
534C2×C3×D3#23718yes—
535C2×C3×D3C2×#6718yes—
536C2×C3×D3C2×#6718yescomplemented
537D32—1216no—
538C32×C4—21no—
539C32×C4—24no—
540C32×C4—44no—
541C32×C4—61no—
542C3⋊Dic3—21no—
543C3⋊Dic3—21no—
544C3⋊Dic3—32no—
545C3⋊Dic3—38no—
546C3⋊Dic3—68no—
547C3⋊Dic3—61no—
548C3⋊Dic3—61no—
549C3⋊Dic3—64no—
550C3⋊Dic3—64no—
551C3⋊Dic3—124no—
552C3⋊Dic3—124no—
553C3⋊Dic3D3×D412yescomplemented
554C3×Dic3—24no—
555C3×Dic3—38no—
556C3×Dic3—64no—
557C3×Dic3—64no—
558C22×D4—31no—
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—271no—
572C2×C22⋊C4—271no—
573C33C2×#12111yescharacteristic, complemented, Sylow
574C23×C3—24no—
575C23×C3—24no—
576C23×C3—34no—
577C23×C3—34no—
578C23×C3—316no—
579C23×C3—34no—
580C23×C3—68no—
581C23×C3—68no—
582C23×C3—68no—
583C23×C3—68no—
584C23×C3—68no—
585C23×C3—91no—
586C23×C3C2×D3214yes—
587C23×C3C2×D3214yes—
588C23×C3C22×C3⋊D311yescharacteristic
589C23×C3C22×C3⋊D311yescharacteristic
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—34no—
596C22×D3—94no—
597C22×D3—91no—
598C22×D3—184no—
599C22×D3—188no—
600C22×D3—188no—
601C22×D3—188no—
602C22×D3—182no—
603C22×D3—182no—
604C22×D3—182no—
605C22×D3#63814yescomplemented
606C22×D3C22×C3⋊D311yescharacteristic
607C22×D3C22×C3⋊D311yescharacteristic
608C22×D3C22×C3⋊D311yescharacteristic
609C3×D4—28no—
610C3×D4—22no—
611C3×D4—48no—
612C3×D4—68no—
613C3×D4—68no—
614C3×D4—68no—
615C3×D4—182no—
616C3×D4—182no—
617C2×C3×C4—24no—
618C2×C3×C4—34no—
619C2×C3×C4—68no—
620C2×C3×C4—91no—
621C2×C3×C4—91no—
622C2×C3×C4—91no—
623C2×C3×C4—182no—
624C2×C3×C4C2×D3214yes—
625C2×C3×C4C22×C3⋊D311yescharacteristic
626#67—22no—
627#67—22no—
628#67—68no—
629#67—68no—
630#67—188no—
631#67—188no—
632#67—182no—
633#67—188no—
634#67—182no—
635#67—188no—
636#67—188no—
637#67—188no—
638#67—182no—
639#67—182no—
640#67—368no—
641#67—368no—
642C2×Dic3—34no—
643C2×Dic3—34no—
644C2×Dic3—34no—
645C2×Dic3—68no—
646C2×Dic3—916no—
647C2×Dic3—94no—
648C2×Dic3—91no—
649C2×Dic3—94no—
650C2×Dic3—94no—
651C2×Dic3—91no—
652C2×Dic3—91no—
653C2×Dic3—184no—
654C2×Dic3—184no—
655C2×Dic3—184no—
656C2×Dic3—188no—
657C2×Dic3—188no—
658C2×Dic3—188no—
659C2×Dic3—188no—
660C2×Dic3—182no—
661C2×Dic3—188no—
662C2×Dic3—368no—
663C2×Dic3C22×C3⋊D311yescharacteristic
664D12—22no—
665D12—182no—
666D12—182no—
667C4×D3—22no—
668C4×D3—94no—
669C4×D3—182no—
670C4×D3—182no—
671C4×D3—182no—
672C4×D3—182no—
673C2×C32—22no—
674C2×C32—24no—
675C2×C32—24no—
676C2×C32—24no—
677C2×C32—28no—
678C2×C32—34no—
679C2×C32—48no—
680C2×C32—41no—
681C2×C32—44no—
682C2×C32—62no—
683C2×C32—84no—
684C2×C32—121no—
685C2×C32C2×D3×D414yes—
686C2×C32C2×D3×D411yescharacteristic
687C2×C32C2×D3×D411yescharacteristic
688C2×C32C2×#23714yes—
689C2×C32D3×#4111yescharacteristic
690C2×C32C22×#6714yes—
691C3⋊D3—41no—
692C3⋊D3—121no—
693C3⋊D3—124no—
694C3⋊D3—244no—
695C3×D3—28no—
696C3×D3—44no—
697C3×D3—124no—
698C3×D3#939116yescomplemented
699C24—31no—
700C24—31no—
701C24—271no—
702C2×D4—31no—
703C2×D4—31no—
704C2×D4—31no—
705C2×D4—64no—
706C2×D4—91no—
707C2×D4—91no—
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×D4D3×C3⋊D311yescharacteristic, complemented
717C22×C4—31no—
718C22×C4—91no—
719C22×C4—271no—
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—91no—
731C22⋊C4—91no—
732C22⋊C4—271no—
733C22⋊C4—271no—
734C22⋊C4—271no—
735C22⋊C4—271no—
736C22⋊C4—271no—
737C22⋊C4—271no—
738C22×C3—24no—
739C22×C3—24no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—24no—
743C22×C3—24no—
744C22×C3—24no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—24no—
749C22×C3—28no—
750C22×C3—38no—
751C22×C3—38no—
752C22×C3—38no—
753C22×C3—38no—
754C22×C3—44no—
755C22×C3—44no—
756C22×C3—44no—
757C22×C3—44no—
758C22×C3—44no—
759C22×C3—632no—
760C22×C3—64no—
761C22×C3—64no—
762C22×C3—64no—
763C22×C3—64no—
764C22×C3—64no—
765C22×C3—1216no—
766C22×C3—181no—
767C22×C3—181no—
768C22×C3—181no—
769C22×C3D3×#6718yescomplemented
770C22×C3C2×#63812yescomplemented
771C22×C3C22×D3214yes—
772C22×C3C23×C3⋊D311yescharacteristic
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—28no—
776C2×D3—21no—
777C2×D3—21no—
778C2×D3—21no—
779C2×D3—44no—
780C2×D3—64no—
781C2×D3—64no—
782C2×D3—64no—
783C2×D3—184no—
784C2×D3—184no—
785C2×D3—184no—
786C2×D3—181no—
787C2×D3—181no—
788C2×D3—181no—
789C2×D3—364no—
790C2×D3—364no—
791C2×D3—364no—
792C2×D3—3616no—
793C2×D3—364no—
794C2×D3D4×C3⋊D312yes—
795C2×D3#383012yes—
796C2×D3C2×#63812yes—
797C2×D3C2×#63812yescomplemented
798C3×C4—24no—
799C3×C4—21no—
800C3×C4—44no—
801C3×C4—64no—
802C3×C4—92no—
803C3×C4—181no—
804C3×C4—181no—
805Dic3—21no—
806Dic3—38no—
807Dic3—64no—
808Dic3—64no—
809Dic3—98no—
810Dic3—92no—
811Dic3—188no—
812Dic3—184no—
813Dic3—184no—
814Dic3—181no—
815Dic3—181no—
816Dic3—364no—
817Dic3—364no—
818C32—24no—
819C32D3×#12111yescharacteristic, complemented
820C32C2×#93914yescomplemented
821C23—31no—
822C23—31no—
823C23—34no—
824C23—31no—
825C23—62no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—62no—
830C23—91no—
831C23—271no—
832C23—542no—
833C23—542no—
834C23—542no—
835C23C2×D3×C3⋊D311yescharacteristic
836C23C2×D3×C3⋊D311yescharacteristic
837D4—22no—
838D4—62no—
839D4—62no—
840D4—62no—
841D4—182no—
842D4—182no—
843D4—542no—
844D4—542no—
845D4—542no—
846D4—542no—
847D4—542no—
848D4—542no—
849C2×C4—31no—
850C2×C4—62no—
851C2×C4—91no—
852C2×C4—91no—
853C2×C4—91no—
854C2×C4—182no—
855C2×C4—274no—
856C2×C4—271no—
857C2×C4—271no—
858C2×C4—271no—
859C2×C4—542no—
860C2×C4—542no—
861C2×C4—542no—
862C2×C4—542no—
863C2×C4—542no—
864C2×C4C2×D3×C3⋊D311yescharacteristic
865C2×C3—22no—
866C2×C3—28no—
867C2×C3—24no—
868C2×C3—24no—
869C2×C3—24no—
870C2×C3—316no—
871C2×C3—48no—
872C2×C3—41no—
873C2×C3—44no—
874C2×C3—68no—
875C2×C3—84no—
876C2×C3—124no—
877C2×C3—361no—
878C2×C3D32×D414yes—
879C2×C3D3×#23714yes—
880C2×C3C2×D3×#6714yes—
881C2×C3C2×D4×C3⋊D311yescharacteristic
882C2×C3C2×#383011yescharacteristic
883C2×C3C22×#63811yescharacteristic
884D3—22no—
885D3—41no—
886D3—124no—
887D3—361no—
888D3—364no—
889D3—724no—
890D3#6414814yesdirect product factor
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—32no—
897C22—32no—
898C22—32no—
899C22—32no—
900C22—68no—
901C22—61no—
902C22—61no—
903C22—61no—
904C22—61no—
905C22—61no—
906C22—124no—
907C22—181no—
908C22—181no—
909C22—181no—
910C22—541no—
911C22—541no—
912C22—541no—
913C22—1084no—
914C22D3×#63812yescomplemented
915C22C22×D3×C3⋊D311yescharacteristic
916C4—21no—
917C4—61no—
918C4—92no—
919C4—181no—
920C4—181no—
921C4—272no—
922C4—541no—
923C4—541no—
924C3—24no—
925C3D3×#93914yescomplemented
926C3C2×#6414811yescharacteristic, complemented
927C2—22no—
928C2—34no—
929C2—41no—
930C2—62no—
931C2—121no—
932C2—361no—
933C2—1081no—
934C2D3×D4×C3⋊D311yescharacteristic
935C2D3×#383011yescharacteristic
936C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C2×D3×#638C2semidirect
3. C2×D3×#638C2semidirect
4. C22×D3×C3⋊Dic3C2semidirect
5. #11723980C2semidirect
6. C3×#64148C2semidirect
7. #11723637C2semidirect
8. #11723635C2semidirect
9. #11723616C2semidirect
10. #11723615C2semidirect
11. D3×#3757C2semidirect
12. D3×#3752C2semidirect
13. #11723475C2semidirect
14. #11723474C2semidirect
15. D3×#3750C2semidirect
21. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
23. C2×#6312C22semidirect
24. C22×C3⋊(C3⋊Dic3)C22semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×#638C22semidirect
27. C22×C3×C3⋊Dic3C22semidirect
28. C2×C32×#67C22semidirect
29. C2×C32×#67C22semidirect
31. C2×C32×D12C22semidirect
35. C2×#6291C22semidirect
36. C2×#6291C22semidirect
37. C2×#6290C22semidirect
38. C2×#6290C22semidirect
43. C2×D3×C3⋊Dic3C22semidirect
44. C2×D3×C3⋊Dic3C22semidirect
45. #88864C22semidirect
46. #88859C22semidirect
47. #88857C22semidirect
48. C3×#3757C22semidirect
49. C3×#3752C22semidirect
50. C3×#3750C22semidirect
51. #88807C22semidirect
52. #88806C22semidirect
53. #88804C22semidirect
54. #88803C22semidirect
55. (C2×D3)⋊(C3⋊Dic3)C22semidirect
56. (C2×D3)⋊(C3⋊Dic3)C22semidirect
61. C2×C3×D3×D4D3semidirect
75. #64148D3direct (N × H)
97. C22×C32×D3D4semidirect
131. D3×C3⋊Dic3D4semidirect
145. C2×C32×D4C2×D3semidirect
146. C2×C32×D4C2×D3semidirect
160. C2×#638C2×D3semidirect
161. C2×#638C2×D3semidirect
171. C22×C3⋊Dic3C2×D3semidirect
174. C2×C3×#67C2×D3semidirect
175. C2×C3×#67C2×D3semidirect
178. C2×C3×D12C2×D3semidirect
197. #3757C2×D3semidirect
203. #3752C2×D3semidirect
209. #3750C2×D3semidirect
224. C22×C33C2×D4semidirect
241. C2×C32×D3C2×D4semidirect
247. C3⋊(C3⋊Dic3)C2×D4semidirect
250. C3×C3⋊Dic3C2×D4semidirect
258. C2×D3×D4C3⋊D3semidirect
311. C22×C3×D3#67semidirect
392. C32×D3#121semidirect
406. C2×C3×D4D32semidirect
407. C2×C3×D4C2×C3⋊D3semidirect
426. C2×#67C2×C3⋊D3semidirect
427. C2×#67C2×C3⋊D3semidirect
443. C2×D12C2×C3⋊D3semidirect
506. C22×C32D3×D4semidirect
507. C22×C32C2×#67semidirect
536. C2×C3×D3C2×#67semidirect
553. C3⋊Dic3D3×D4semidirect
573. C33C2×#121semidirect
605. C22×D3#638semidirect
698. C3×D3#939semidirect
716. C2×D4D3×C3⋊D3semidirect
769. C22×C3D3×#67semidirect
770. C22×C3C2×#638semidirect
797. C2×D3C2×#638semidirect
819. C32D3×#121semidirect
820. C32C2×#939semidirect
890. D3#64148direct (N × H)
914. C22D3×#638semidirect
925. C3D3×#939semidirect
926. C3C2×#64148semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×D3×#6382
C22×D3×C3⋊Dic32
#117239802
C3×#641482
#117236372
#117236352
#117236162
#117236152
D3×#37572
D3×#37522
#117234752
#117234742
D3×#37502
C2×#641483
D3×#9393