Finite Group Databasebeta

← #67×#638 #13178103

Subgroups — #67×#638 #13178103

Order 1728.

3088 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic, complemented
2C22×C32×#67C211yesmaximal, characteristic, complemented
3C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
4C2×D3×#638C211yesmaximal, characteristic, complemented
5#11723994C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723635C211yesmaximal, characteristic, complemented
8#11723634C211yesmaximal, characteristic, complemented
9#11723633C211yesmaximal, characteristic, complemented
10#11723632C211yesmaximal, characteristic, complemented
11#11723631C211yesmaximal, characteristic, complemented
12#11723629C211yesmaximal, characteristic, complemented
13#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
14Dic3×#638C211yesmaximal, characteristic, complemented
15#11723615C211yesmaximal, characteristic, complemented
16D4×#638—31nomaximal
17#672—34nomaximal
18C24×C33C2211yescharacteristic, complemented
19C23×C3×C3⋊D3C2211yescharacteristic, complemented
20C23×C32×D3C2211yescharacteristic, complemented
21C22×D3×C3⋊D3C2211yescharacteristic, complemented
22C2×#6312C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic, complemented
24C2×#6312C2211yescharacteristic, complemented
25C2×C3×#638—24no—
26C2×C3×#638C2211yescharacteristic
27C2×C3×#638C2211yescharacteristic, complemented
28C2×C3×#638C2211yescharacteristic, complemented
29C2×C3×#638C2211yescharacteristic, complemented
30C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
31C2×C32×#67—24no—
32C2×C32×#67C2211yescharacteristic
33C2×C32×#67C2211yescharacteristic, complemented
34C2×C32×#67C2211yescharacteristic, complemented
35C2×C32×#67C2211yescharacteristic, complemented
36C22×C32×Dic3C2211yescharacteristic, complemented
37C3⋊D3×#67—24no—
38D3×#638—24no—
39C2×#6292C2211yescharacteristic, complemented
40C2×#6291C2211yescharacteristic, complemented
41C2×#6290C2211yescharacteristic, complemented
42C2×#6290C2211yescharacteristic, complemented
43C2×#6290C2211yescharacteristic, complemented
44C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
45C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
46#88864C2211yescharacteristic, complemented
47#88864C2211yescharacteristic, complemented
48#88864C2211yescharacteristic, complemented
49#88807C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
56Dic3×C3⋊Dic3C2211yescharacteristic, complemented
57C22×C32×D4—31no—
58C22×#638—31no—
59C22×#638D311yescharacteristic, complemented
60C2×D4×C3⋊D3—31no—
61C22×C3×#67—34no—
62C22×C3×#67D314yescomplemented
63C2×D3×#67—34no—
64C2×D3×#67—34no—
65#64162—31no—
66#64162—31no—
67#64162—34no—
68#64162—64no—
69#64149—31no—
70#64148—31no—
71#64148—31no—
72#64147—31no—
73#64146—31no—
74#64146—31no—
75D4×C3⋊Dic3—31no—
76#64139—31no—
77C4×#638—31no—
78#63983—34no—
79#63979—34no—
80#63978—34no—
81#63978—34no—
82#63976—34no—
83#63976—34no—
84Dic3×#67—34no—
85Dic3×#67—34no—
86#63970—34no—
87#63970—34no—
88C23×C33—22no—
89C23×C33—22no—
90C23×C33—41no—
91C23×C33C2311yescharacteristic
92C23×C33C2311yescharacteristic
93C23×C33C2311yescharacteristic
94C22×C3⋊(C3⋊D3)C2311yescharacteristic
95C22×C3×C3⋊D3—22no—
96C22×C3×C3⋊D3—22no—
97C22×C3×C3⋊D3—41no—
98C22×C3×C3⋊D3C2311yescharacteristic
99C22×C3×C3⋊D3C2311yescharacteristic
100C22×C32×D3—22no—
101C22×C32×D3—22no—
102C22×C32×D3—41no—
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×D3×C3⋊D3—22no—
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—41no—
108#6312—22no—
109#6312—22no—
110#6312—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C3×#638—22no—
115C3×#638—22no—
116C3×#638—22no—
117C3×#638D414yescomplemented
118C2×C3×C3⋊Dic3—22no—
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C32×#67—22no—
122C32×#67—22no—
123C32×#67—22no—
124C32×#67D414yescomplemented
125C2×C32×Dic3—22no—
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128#6292—22no—
129#6291—22no—
130#6290—22no—
131#6290—22no—
132#6290—41no—
133Dic3×C3⋊D3—22no—
134D3×C3⋊Dic3—22no—
135D4×#67—94no—
136D4×#67—91no—
137C24×C32—24no—
138C24×C32—31no—
139C24×C32C2×D314yescomplemented
140C24×C32C2×D311yescharacteristic, complemented
141C23×C3⋊D3—31no—
142C23×C3⋊D3C2×D311yescharacteristic, complemented
143C23×C3×D3—34no—
144C23×C3×D3C2×D314yescomplemented
145C22×D32—34no—
146C2×C32×D4—31no—
147C2×C32×D4—31no—
148C2×C32×D4—31no—
149C2×C32×D4—31no—
150C2×C32×D4—64no—
151C22×C32×C4—31no—
152C2×#638—24no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—34no—
156C2×#638—34no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—34no—
161C2×#638—31no—
162C2×#638—31no—
163C2×#638—64no—
164C2×#638—64no—
165C2×#638—64no—
166C2×#638—64no—
167C2×#638C2×D311yescharacteristic
168C2×#638C2×D311yescharacteristic, complemented
169C2×#638C2×D311yescharacteristic, complemented
170C2×#638C2×D311yescharacteristic, complemented
171C22×C3⋊Dic3—31no—
172C22×C3⋊Dic3C2×D311yescharacteristic, complemented
173D4×C3⋊D3—64no—
174C2×C4⋊(C3⋊D3)—31no—
175C2×C4×C3⋊D3—31no—
176C2×C3×#67—216no—
177C2×C3×#67—34no—
178C2×C3×#67—34no—
179C2×C3×#67—34no—
180C2×C3×#67—34no—
181C2×C3×#67—616no—
182C2×C3×#67C2×D314yes—
183C2×C3×#67C2×D314yescomplemented
184C2×C3×#67C2×D314yescomplemented
185C2×C3×#67C2×D314yescomplemented
186C22×C3×Dic3—34no—
187C22×C3×Dic3C2×D314yescomplemented
188D3×#67—616no—
189D3×#67—616no—
190C2×#626—34no—
191C2×#626—34no—
192C2×#625—34no—
193C2×#625—34no—
194C2×#625—34no—
195C2×D3×Dic3—34no—
196C2×D3×Dic3—34no—
197#3757—31no—
198#3757—31no—
199#3757—31no—
200#3757—34no—
201#3757—34no—
202#3757—34no—
203#3757—31no—
204#3757—31no—
205#3757—64no—
206#3757—64no—
207#3757—64no—
208#3752—31no—
209#3752—31no—
210#3752—31no—
211C4⋊(C3⋊Dic3)—31no—
212#3750—31no—
213C4×C3⋊Dic3—31no—
214Dic3⋊Dic3—34no—
215Dic3⋊Dic3—34no—
216#3722—34no—
217(C2×D3)⋊Dic3—34no—
218(C2×D3)⋊Dic3—34no—
219(C2×D3)⋊Dic3—34no—
220(C2×D3)⋊Dic3—34no—
221Dic32—34no—
222C22×C33—21no—
223C22×C33—21no—
224C22×C33—21no—
225C22×C33—21no—
226C22×C33—21no—
227C22×C33—21no—
228C22×C33—21no—
229C22×C33—44no—
230C22×C33C2×D412yescomplemented
231C22×C33C2×D412yescomplemented
232C22×C33C2411yescharacteristic
233C2×C3⋊(C3⋊D3)—21no—
234C2×C3⋊(C3⋊D3)—21no—
235C2×C3⋊(C3⋊D3)—21no—
236C2×C3×C3⋊D3—21no—
237C2×C3×C3⋊D3—21no—
238C2×C3×C3⋊D3—21no—
239C2×C3×C3⋊D3—21no—
240C2×C3×C3⋊D3—21no—
241C2×C3×C3⋊D3—44no—
242C2×C3×C3⋊D3C2×D412yescomplemented
243C2×C32×D3—21no—
244C2×C32×D3—21no—
245C2×C32×D3—21no—
246C2×C32×D3—21no—
247C2×C32×D3—21no—
248C2×C32×D3—44no—
249C2×C32×D3C2×D412yescomplemented
250D3×C3⋊D3—44no—
251C3⋊(C3⋊Dic3)—21no—
252C3⋊(C3⋊Dic3)—21no—
253C3⋊(C3⋊Dic3)—21no—
254C3×C3⋊Dic3—21no—
255C3×C3⋊Dic3C2×D412yescomplemented
256C32×Dic3—21no—
257C32×Dic3C2×D412yescomplemented
258C22×C3×D4—34no—
259C22×C3×D4—91no—
260C22×#67—34no—
261C22×#67—94no—
262C22×#67—91no—
263C22×#67C3⋊D311yescharacteristic, complemented
264C2×D3×D4—94no—
265C2×D3×D4—91no—
266#953—94no—
267#953—94no—
268#953—91no—
269#953—91no—
270#953—184no—
271#940—94no—
272#940—91no—
273#939—94no—
274#939—94no—
275#939—91no—
276#939—91no—
277#938—94no—
278#938—91no—
279#937—94no—
280#937—94no—
281#937—91no—
282#937—91no—
283D4×Dic3—94no—
284D4×Dic3—91no—
285#930—94no—
286#930—91no—
287C4×#67—94no—
288C4×#67—91no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32—24no—
292C23×C32—24no—
293C23×C32—24no—
294C23×C32—28no—
295C23×C32—28no—
296C23×C32—31no—
297C23×C32—31no—
298C23×C32—48no—
299C23×C32—48no—
300C23×C32—41no—
301C23×C32—44no—
302C23×C32—48no—
303C23×C32—62no—
304C23×C32—62no—
305C23×C32—121no—
306C23×C32C22×D314yes—
307C23×C32C22×D314yes—
308C23×C32C22×D314yes—
309C23×C32C22×D311yescharacteristic
310C23×C32C22×D311yescharacteristic
311C23×C32C22×D311yescharacteristic
312C22×C3⋊D3—22no—
313C22×C3⋊D3—22no—
314C22×C3⋊D3—31no—
315C22×C3⋊D3—34no—
316C22×C3⋊D3—41no—
317C22×C3⋊D3—64no—
318C22×C3⋊D3—62no—
319C22×C3⋊D3—62no—
320C22×C3⋊D3—121no—
321C22×C3⋊D3C22×D311yescharacteristic
322C22×C3⋊D3C22×D311yescharacteristic
323C22×C3×D3—28no—
324C22×C3×D3—28no—
325C22×C3×D3—34no—
326C22×C3×D3—34no—
327C22×C3×D3—44no—
328C22×C3×D3—68no—
329C22×C3×D3—68no—
330C22×C3×D3—124no—
331C22×C3×D3C22×D314yes—
332C22×C3×D3C22×D314yes—
333C2×D32—68no—
334C2×D32—68no—
335C2×D32—124no—
336C32×D4—34no—
337C32×D4—62no—
338C32×D4—62no—
339C32×D4—62no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—62no—
343#638—22no—
344#638—22no—
345#638—22no—
346#638—62no—
347#638—62no—
348#638—62no—
349#638—62no—
350#638—62no—
351#638—68no—
352#638—68no—
353#638—128no—
354#638—128no—
355#638—121no—
356#638—121no—
357#638—124no—
358#638—128no—
359#638#6714yesdirect product factor
360C2×C3⋊Dic3—22no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—34no—
365C2×C3⋊Dic3—34no—
366C2×C3⋊Dic3—34no—
367C2×C3⋊Dic3—64no—
368C2×C3⋊Dic3—64no—
369C2×C3⋊Dic3—64no—
370C2×C3⋊Dic3—62no—
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C4⋊(C3⋊D3)—62no—
374C4×C3⋊D3—62no—
375C3×#67—28no—
376C3×#67—28no—
377C3×#67—28no—
378C3×#67—316no—
379C3×#67—68no—
380C3×#67—68no—
381C3×#67—68no—
382C3×#67#67116yescomplemented
383C2×C3×Dic3—28no—
384C2×C3×Dic3—34no—
385C2×C3×Dic3—34no—
386C2×C3×Dic3—68no—
387C2×C3×Dic3C22×D314yes—
388C2×C3×Dic3C22×D314yes—
389#626—68no—
390#626—68no—
391#625—68no—
392#625—68no—
393#625—124no—
394D3×Dic3—68no—
395D3×Dic3—68no—
396D42—271noSylow
397C2×C33—22no—
398C2×C33—22no—
399C2×C33—41no—
400C2×C33C22×D411yescharacteristic
401C2×C33C22×D411yescharacteristic
402C2×C33H(5,𝔽2)11yescharacteristic
403C3⋊(C3⋊D3)—41no—
404C3×C3⋊D3—22no—
405C3×C3⋊D3—41no—
406C32×D3—22no—
407C32×D3—41no—
408C24×C3—24no—
409C24×C3—34no—
410C24×C3—91no—
411C24×C3D3214yescomplemented
412C24×C3C2×C3⋊D311yescharacteristic, complemented
413C23×D3—34no—
414C23×D3—94no—
415C23×D3—91no—
416C23×D3C2×C3⋊D311yescharacteristic, complemented
417C2×C3×D4—34no—
418C2×C3×D4—34no—
419C2×C3×D4—34no—
420C2×C3×D4—34no—
421C2×C3×D4—616no—
422C2×C3×D4—91no—
423C2×C3×D4—91no—
424C2×C3×D4—91no—
425C2×C3×D4—91no—
426C2×C3×D4—184no—
427C22×C3×C4—34no—
428C22×C3×C4—91no—
429C2×#67—24no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—616no—
435C2×#67—94no—
436C2×#67—94no—
437C2×#67—94no—
438C2×#67—94no—
439C2×#67—94no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C2×#67—91no—
444C2×#67—94no—
445C2×#67—94no—
446C2×#67—91no—
447C2×#67—91no—
448C2×#67—91no—
449C2×#67—184no—
450C2×#67—184no—
451C2×#67—184no—
452C2×#67—1816no—
453C2×#67—184no—
454C2×#67C2×C3⋊D311yescharacteristic
455C2×#67C2×C3⋊D311yescharacteristic, complemented
456C2×#67C2×C3⋊D311yescharacteristic, complemented
457C2×#67C2×C3⋊D311yescharacteristic, complemented
458C22×Dic3—34no—
459C22×Dic3—94no—
460C22×Dic3—91no—
461C22×Dic3C2×C3⋊D311yescharacteristic, complemented
462D3×D4—1816no—
463D3×D4—184no—
464C2×D12—94no—
465C2×D12—91no—
466C2×C4×D3—94no—
467C2×C4×D3—91no—
468#217—94no—
469#217—94no—
470#217—94no—
471#217—94no—
472#217—94no—
473#217—91no—
474#217—91no—
475#217—91no—
476#217—91no—
477#217—91no—
478#217—184no—
479#217—184no—
480#217—184no—
481(C2×D3)⋊C4—94no—
482(C2×D3)⋊C4—94no—
483(C2×D3)⋊C4—94no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487C4⋊Dic3—94no—
488C4⋊Dic3—91no—
489Dic3⋊C4—94no—
490Dic3⋊C4—91no—
491C4×Dic3—94no—
492C4×Dic3—91no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—21no—
497C22×C32—28no—
498C22×C32—21no—
499C22×C32—24no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—24no—
503C22×C32—28no—
504C22×C32—28no—
505C22×C32—24no—
506C22×C32—24no—
507C22×C32—24no—
508C22×C32—24no—
509C22×C32—24no—
510C22×C32—24no—
511C22×C32—32no—
512C22×C32—44no—
513C22×C32—44no—
514C22×C32—44no—
515C22×C32—44no—
516C22×C32—44no—
517C22×C32—44no—
518C22×C32—44no—
519C22×C32—416no—
520C22×C32—432no—
521C22×C32—61no—
522C22×C32—61no—
523C22×C32—61no—
524C22×C32—61no—
525C22×C32—61no—
526C22×C32—124no—
527C22×C32D3×D418yescomplemented
528C22×C32D3×D412yescomplemented
529C22×C32C2×#6718yescomplemented
530C22×C32C2×#6712yescomplemented
531C22×C32C23×D314yes—
532C22×C32C23×D311yescharacteristic
533C2×C3⋊D3—21no—
534C2×C3⋊D3—21no—
535C2×C3⋊D3—21no—
536C2×C3⋊D3—21no—
537C2×C3⋊D3—21no—
538C2×C3⋊D3—44no—
539C2×C3⋊D3—61no—
540C2×C3⋊D3—61no—
541C2×C3⋊D3—61no—
542C2×C3⋊D3—64no—
543C2×C3⋊D3—64no—
544C2×C3⋊D3—64no—
545C2×C3⋊D3—124no—
546C2×C3⋊D3—124no—
547C2×C3⋊D3—124no—
548C2×C3⋊D3—124no—
549C2×C3⋊D3C2×#6712yescomplemented
550C2×C3×D3—24no—
551C2×C3×D3—24no—
552C2×C3×D3—24no—
553C2×C3×D3—24no—
554C2×C3×D3—24no—
555C2×C3×D3—38no—
556C2×C3×D3—416no—
557C2×C3×D3—64no—
558C2×C3×D3—64no—
559C2×C3×D3—64no—
560C2×C3×D3—64no—
561C2×C3×D3—64no—
562C2×C3×D3—1216no—
563C2×C3×D3C2×#6718yescomplemented
564D32—1216no—
565C32×C4—32no—
566C32×C4—61no—
567C3⋊Dic3—21no—
568C3⋊Dic3—61no—
569C3⋊Dic3—61no—
570C3⋊Dic3—61no—
571C3⋊Dic3—64no—
572C3⋊Dic3—64no—
573C3⋊Dic3—64no—
574C3⋊Dic3—124no—
575C3⋊Dic3—124no—
576C3⋊Dic3—124no—
577C3⋊Dic3C2×#6712yescomplemented
578C3×Dic3—24no—
579C3×Dic3—38no—
580C3×Dic3—64no—
581C3×Dic3C2×#6718yescomplemented
582C22×D4—31no—
583C22×D4—91no—
584C22×D4—271no—
585C22×D4—271no—
586#127—271no—
587#121—271no—
588#121—271no—
589#121—271no—
590#121—271no—
591#120—271no—
592#120—271no—
593#120—271no—
594#120—271no—
595C4×D4—271no—
596C4×D4—271no—
597C33D4211yescharacteristic, complemented, Sylow
598C23×C3—28no—
599C23×C3—28no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—24no—
603C23×C3—24no—
604C23×C3—24no—
605C23×C3—34no—
606C23×C3—34no—
607C23×C3—48no—
608C23×C3—48no—
609C23×C3—44no—
610C23×C3—41no—
611C23×C3—48no—
612C23×C3—68no—
613C23×C3—68no—
614C23×C3—91no—
615C23×C3—91no—
616C23×C3—124no—
617C23×C3—182no—
618C23×C3—182no—
619C23×C3—361no—
620C23×C3C2×D3214yes—
621C23×C3C2×D3214yes—
622C23×C3C2×D3214yes—
623C23×C3C22×C3⋊D311yescharacteristic
624C23×C3C22×C3⋊D311yescharacteristic
625C23×C3C22×C3⋊D311yescharacteristic
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—34no—
629C22×D3—34no—
630C22×D3—41no—
631C22×D3—68no—
632C22×D3—68no—
633C22×D3—94no—
634C22×D3—91no—
635C22×D3—124no—
636C22×D3—184no—
637C22×D3—182no—
638C22×D3—188no—
639C22×D3—188no—
640C22×D3—182no—
641C22×D3—361no—
642C22×D3—364no—
643C22×D3C22×C3⋊D311yescharacteristic
644C22×D3C22×C3⋊D311yescharacteristic
645C3×D4—316no—
646C3×D4—68no—
647C3×D4—68no—
648C3×D4—68no—
649C3×D4—94no—
650C3×D4—182no—
651C3×D4—182no—
652C3×D4—182no—
653C2×C3×C4—34no—
654C2×C3×C4—34no—
655C2×C3×C4—68no—
656C2×C3×C4—91no—
657C2×C3×C4—91no—
658C2×C3×C4—182no—
659#67—22no—
660#67—22no—
661#67—22no—
662#67—316no—
663#67—68no—
664#67—68no—
665#67—68no—
666#67—188no—
667#67—182no—
668#67—188no—
669#67—188no—
670#67—188no—
671#67—188no—
672#67—182no—
673#67—182no—
674#67—182no—
675#67—182no—
676#67—368no—
677#67—368no—
678#67—361no—
679#67—364no—
680#67—364no—
681#67—361no—
682#67—368no—
683#67#63814yesdirect product factor
684C2×Dic3—22no—
685C2×Dic3—34no—
686C2×Dic3—34no—
687C2×Dic3—68no—
688C2×Dic3—94no—
689C2×Dic3—94no—
690C2×Dic3—94no—
691C2×Dic3—91no—
692C2×Dic3—91no—
693C2×Dic3—91no—
694C2×Dic3—184no—
695C2×Dic3—184no—
696C2×Dic3—184no—
697C2×Dic3—188no—
698C2×Dic3—182no—
699C2×Dic3C22×C3⋊D311yescharacteristic
700C2×Dic3C22×C3⋊D311yescharacteristic
701D12—188no—
702D12—182no—
703C4×D3—188no—
704C4×D3—182no—
705C2×C32—22no—
706C2×C32—22no—
707C2×C32—24no—
708C2×C32—24no—
709C2×C32—24no—
710C2×C32—28no—
711C2×C32—28no—
712C2×C32—48no—
713C2×C32—48no—
714C2×C32—48no—
715C2×C32—44no—
716C2×C32—41no—
717C2×C32—62no—
718C2×C32—121no—
719C2×C32C2×D3×D414yes—
720C2×C32C2×D3×D411yescharacteristic
721C2×C32#100414yes—
722C2×C32#100411yescharacteristic
723C2×C32C22×#6714yes—
724C2×C32C22×#6711yescharacteristic
725C3⋊D3—22no—
726C3⋊D3—41no—
727C3⋊D3—121no—
728C3⋊D3—124no—
729C3⋊D3—244no—
730C3×D3—28no—
731C3×D3—44no—
732C3×D3—68no—
733C3×D3—124no—
734C24—31no—
735C24—91no—
736C24—271no—
737C24D3×C3⋊D311yescharacteristic, complemented
738C2×D4—31no—
739C2×D4—31no—
740C2×D4—31no—
741C2×D4—31no—
742C2×D4—64no—
743C2×D4—91no—
744C2×D4—91no—
745C2×D4—91no—
746C2×D4—91no—
747C2×D4—184no—
748C2×D4—271no—
749C2×D4—271no—
750C2×D4—271no—
751C2×D4—271no—
752C2×D4—271no—
753C2×D4—271no—
754C2×D4—271no—
755C2×D4—271no—
756C2×D4—544no—
757C2×D4—544no—
758C22×C4—31no—
759C22×C4—91no—
760C22×C4—271no—
761C22×C4—271no—
762C4⋊C4—271no—
763C4⋊C4—271no—
764C22⋊C4—271no—
765C22⋊C4—271no—
766C22⋊C4—271no—
767C22⋊C4—271no—
768C22⋊C4—271no—
769C22⋊C4—271no—
770C22⋊C4—271no—
771C22⋊C4—271no—
772C42—271no—
773C22×C3—24no—
774C22×C3—24no—
775C22×C3—24no—
776C22×C3—24no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—28no—
782C22×C3—24no—
783C22×C3—24no—
784C22×C3—24no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—24no—
789C22×C3—28no—
790C22×C3—28no—
791C22×C3—38no—
792C22×C3—44no—
793C22×C3—44no—
794C22×C3—44no—
795C22×C3—44no—
796C22×C3—44no—
797C22×C3—44no—
798C22×C3—44no—
799C22×C3—416no—
800C22×C3—432no—
801C22×C3—64no—
802C22×C3—64no—
803C22×C3—64no—
804C22×C3—64no—
805C22×C3—64no—
806C22×C3—92no—
807C22×C3—1216no—
808C22×C3—181no—
809C22×C3—181no—
810C22×C3—181no—
811C22×C3—181no—
812C22×C3—181no—
813C22×C3—364no—
814C22×C3D3×#6718yescomplemented
815C22×C3D3×#6718yescomplemented
816C22×C3D4×C3⋊D312yescomplemented
817C22×C3C2×#63812yescomplemented
818C22×C3C22×D3214yes—
819C22×C3C23×C3⋊D311yescharacteristic
820C2×D3—21no—
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—38no—
826C2×D3—44no—
827C2×D3—64no—
828C2×D3—64no—
829C2×D3—64no—
830C2×D3—64no—
831C2×D3—64no—
832C2×D3—1216no—
833C2×D3—184no—
834C2×D3—184no—
835C2×D3—184no—
836C2×D3—181no—
837C2×D3—181no—
838C2×D3—181no—
839C2×D3—364no—
840C2×D3—364no—
841C2×D3—364no—
842C2×D3—364no—
843C2×D3—3616no—
844C2×D3C2×#63812yescomplemented
845C3×C4—38no—
846C3×C4—64no—
847C3×C4—92no—
848C3×C4—181no—
849Dic3—21no—
850Dic3—38no—
851Dic3—64no—
852Dic3—184no—
853Dic3—184no—
854Dic3—184no—
855Dic3—181no—
856Dic3—181no—
857Dic3—181no—
858Dic3—364no—
859Dic3—364no—
860Dic3—364no—
861Dic3C2×#63812yescomplemented
862C32—24no—
863C32D4×#6714yescomplemented
864C32D4×#6711yescharacteristic, complemented
865C23—22no—
866C23—22no—
867C23—31no—
868C23—31no—
869C23—41no—
870C23—62no—
871C23—62no—
872C23—91no—
873C23—91no—
874C23—121no—
875C23—182no—
876C23—182no—
877C23—271no—
878C23—361no—
879C23—542no—
880C23—542no—
881C23—1081no—
882C23C2×D3×C3⋊D311yescharacteristic
883C23C2×D3×C3⋊D311yescharacteristic
884C23C2×D3×C3⋊D311yescharacteristic
885D4—34no—
886D4—62no—
887D4—62no—
888D4—62no—
889D4—94no—
890D4—182no—
891D4—182no—
892D4—182no—
893D4—542no—
894D4—542no—
895D4—542no—
896D4—542no—
897D4—542no—
898D4—542no—
899D4—1081no—
900D4—1081no—
901C2×C4—31no—
902C2×C4—31no—
903C2×C4—62no—
904C2×C4—91no—
905C2×C4—91no—
906C2×C4—182no—
907C2×C4—271no—
908C2×C4—271no—
909C2×C4—271no—
910C2×C4—542no—
911C2×C4—542no—
912C2×C3—22no—
913C2×C3—22no—
914C2×C3—28no—
915C2×C3—28no—
916C2×C3—24no—
917C2×C3—24no—
918C2×C3—24no—
919C2×C3—48no—
920C2×C3—48no—
921C2×C3—48no—
922C2×C3—41no—
923C2×C3—44no—
924C2×C3—68no—
925C2×C3—124no—
926C2×C3—182no—
927C2×C3—361no—
928C2×C3C2×D3×#6714yes—
929C2×C3C2×D3×#6714yes—
930C2×C3#6433014yes—
931C2×C3C2×D4×C3⋊D311yescharacteristic
932C2×C3#6436111yescharacteristic
933C2×C3C22×#63811yescharacteristic
934D3—22no—
935D3—41no—
936D3—68no—
937D3—124no—
938D3—361no—
939D3—364no—
940D3—724no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—32no—
949C22—44no—
950C22—61no—
951C22—61no—
952C22—61no—
953C22—61no—
954C22—61no—
955C22—92no—
956C22—124no—
957C22—181no—
958C22—181no—
959C22—181no—
960C22—181no—
961C22—181no—
962C22—364no—
963C22—541no—
964C22—541no—
965C22—541no—
966C22—1084no—
967C22D3×#63812yescomplemented
968C22C3⋊D3×#6712yescomplemented
969C22C22×D3×C3⋊D311yescharacteristic
970C4—32no—
971C4—61no—
972C4—92no—
973C4—181no—
974C4—541no—
975C4—541no—
976C4—541no—
977C3—24no—
978C3#67214yescomplemented
979C3D4×#63811yescharacteristic, complemented
980C2—22no—
981C2—22no—
982C2—41no—
983C2—62no—
984C2—121no—
985C2—182no—
986C2—361no—
987C2—1081no—
988C2C2×D3×#63811yescharacteristic
989C2C2×C3⋊D3×#6711yescharacteristic
990C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
hypercenterC24D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C3×#638C2semidirect
2. C22×C32×#67C2semidirect
3. C2×C3⋊D3×#67C2semidirect
4. C2×D3×#638C2semidirect
5. #11723994C2semidirect
6. #11723643C2semidirect
7. #11723635C2semidirect
8. #11723634C2semidirect
9. #11723633C2semidirect
10. #11723632C2semidirect
11. #11723631C2semidirect
12. #11723629C2semidirect
13. #67×C3⋊Dic3C2semidirect
14. Dic3×#638C2semidirect
15. #11723615C2semidirect
18. C24×C33C22semidirect
19. C23×C3×C3⋊D3C22semidirect
20. C23×C32×D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
22. C2×#6312C22semidirect
23. C2×#6312C22semidirect
24. C2×#6312C22semidirect
27. C2×C3×#638C22semidirect
28. C2×C3×#638C22semidirect
29. C2×C3×#638C22semidirect
30. C22×C3×C3⋊Dic3C22semidirect
33. C2×C32×#67C22semidirect
34. C2×C32×#67C22semidirect
35. C2×C32×#67C22semidirect
36. C22×C32×Dic3C22semidirect
39. C2×#6292C22semidirect
40. C2×#6291C22semidirect
41. C2×#6290C22semidirect
42. C2×#6290C22semidirect
43. C2×#6290C22semidirect
44. C2×Dic3×C3⋊D3C22semidirect
45. C2×D3×C3⋊Dic3C22semidirect
46. #88864C22semidirect
47. #88864C22semidirect
48. #88864C22semidirect
49. #88807C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
55. (C2×D3)⋊(C3⋊Dic3)C22semidirect
56. Dic3×C3⋊Dic3C22semidirect
59. C22×#638D3semidirect
62. C22×C3×#67D3semidirect
117. C3×#638D4semidirect
124. C32×#67D4semidirect
139. C24×C32C2×D3semidirect
140. C24×C32C2×D3semidirect
142. C23×C3⋊D3C2×D3semidirect
144. C23×C3×D3C2×D3semidirect
168. C2×#638C2×D3semidirect
169. C2×#638C2×D3semidirect
170. C2×#638C2×D3semidirect
172. C22×C3⋊Dic3C2×D3semidirect
183. C2×C3×#67C2×D3semidirect
184. C2×C3×#67C2×D3semidirect
185. C2×C3×#67C2×D3semidirect
187. C22×C3×Dic3C2×D3semidirect
230. C22×C33C2×D4semidirect
231. C22×C33C2×D4semidirect
242. C2×C3×C3⋊D3C2×D4semidirect
249. C2×C32×D3C2×D4semidirect
255. C3×C3⋊Dic3C2×D4semidirect
257. C32×Dic3C2×D4semidirect
263. C22×#67C3⋊D3semidirect
359. #638#67direct (N × H)
382. C3×#67#67semidirect
411. C24×C3D32semidirect
412. C24×C3C2×C3⋊D3semidirect
416. C23×D3C2×C3⋊D3semidirect
455. C2×#67C2×C3⋊D3semidirect
456. C2×#67C2×C3⋊D3semidirect
457. C2×#67C2×C3⋊D3semidirect
461. C22×Dic3C2×C3⋊D3semidirect
527. C22×C32D3×D4semidirect
528. C22×C32D3×D4semidirect
529. C22×C32C2×#67semidirect
530. C22×C32C2×#67semidirect
549. C2×C3⋊D3C2×#67semidirect
563. C2×C3×D3C2×#67semidirect
577. C3⋊Dic3C2×#67semidirect
581. C3×Dic3C2×#67semidirect
597. C33D42semidirect
683. #67#638direct (N × H)
737. C24D3×C3⋊D3semidirect
814. C22×C3D3×#67semidirect
815. C22×C3D3×#67semidirect
816. C22×C3D4×C3⋊D3semidirect
817. C22×C3C2×#638semidirect
844. C2×D3C2×#638semidirect
861. Dic3C2×#638semidirect
863. C32D4×#67semidirect
864. C32D4×#67semidirect
967. C22D3×#638semidirect
968. C22C3⋊D3×#67semidirect
978. C3#672semidirect
979. C3D4×#638semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C22×C32×#672
C2×C3⋊D3×#672
C2×D3×#6382
#117239942
#117236432
#117236352
#117236342
#117236332
#117236322
#117236312
#117236292
#67×C3⋊Dic32
Dic3×#6382
#117236152
D4×#6383
#6723