Finite Group Databasebeta

← #13177527

Subgroups — #13177527

Order 1728.

3512 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic, complemented
3C2×D3×#638C211yesmaximal, characteristic, complemented
4C22×#6291C211yesmaximal, characteristic, complemented
5C3×#64148C211yesmaximal, characteristic, complemented
6C32×#937C211yesmaximal, characteristic, complemented
7#11723639C211yesmaximal, characteristic, complemented
8#11723638C211yesmaximal, characteristic, complemented
9#11723633C211yesmaximal, characteristic, complemented
10#11723622C211yesmaximal, characteristic, complemented
11#11723616C211yesmaximal, characteristic, complemented
12#11723542C211yesmaximal, characteristic, complemented
13#11723527C211yesmaximal, characteristic, complemented
14#11723525C211yesmaximal, characteristic, complemented
15#11723462C211yesmaximal, characteristic, complemented
16#10596061—31nomaximal
17#10595292—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
19C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
20C23×C32×D3C2211yescharacteristic, complemented
21C22×D3×C3⋊D3C2211yescharacteristic, complemented
22C2×C33×D4C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic
24C2×#6312C2211yescharacteristic, complemented
25D4×C3⋊(C3⋊D3)—24no—
26C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
27C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
28C2×C3×#638C2211yescharacteristic, complemented
29C2×C3×#638C2211yescharacteristic, complemented
30C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
31C2×C32×#67C2211yescharacteristic, complemented
32C2×C32×#67C2211yescharacteristic, complemented
33#89039—24no—
34D3×#638—24no—
35C2×#6292C2211yescharacteristic, complemented
36C2×#6292C2211yescharacteristic, complemented
37C2×#6291—24no—
38C2×#6291C2211yescharacteristic
39C2×#6291C2211yescharacteristic, complemented
40C2×#6291C2211yescharacteristic, complemented
41C2×#6291C2211yescharacteristic, complemented
42C2×#6291C2211yescharacteristic, complemented
43C2×#6290C2211yescharacteristic, complemented
44C2×#6289C2211yescharacteristic, complemented
45C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×#3757C2211yescharacteristic, complemented
47C3×#3752C2211yescharacteristic, complemented
48C3×#3750C2211yescharacteristic, complemented
49C32×#217C2211yescharacteristic, complemented
50C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
52#88806C2211yescharacteristic, complemented
53#88804C2211yescharacteristic, complemented
54#88804C2211yescharacteristic, complemented
55#88804C2211yescharacteristic, complemented
56Dic3×C3⋊Dic3C2211yescharacteristic, complemented
57C22×#638—31no—
58C22×#638—31no—
59C2×D4×C3⋊D3—31no—
60C2×D4×C3⋊D3—31no—
61C2×D4×C3⋊D3—34no—
62C2×D4×C3⋊D3—64no—
63C2×#3811—34no—
64C2×D3×#67—34no—
65C22×#626—34no—
66C32×#120—31no—
67#64149—31no—
68#64148—31no—
69#64148D311yescharacteristic, complemented
70#64146—31no—
71#64093—31no—
72#64093—31no—
73#64091—31no—
74#64091—31no—
75#64090—31no—
76#64090—31no—
77C3×#939—34no—
78C3×#937D314yescomplemented
79#63981—34no—
80#63981—34no—
81#63979—34no—
82#63971—34no—
83#63952—34no—
84#63923—34no—
85#63912—34no—
86#63910—34no—
87#63881—34no—
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C22×C3⋊(C3⋊D3)—22no—
91C22×C3⋊(C3⋊D3)—22no—
92C22×C3⋊(C3⋊D3)—22no—
93C22×C3⋊(C3⋊D3)—22no—
94C22×C3⋊(C3⋊D3)—41no—
95C22×C3⋊(C3⋊D3)—41no—
96C22×C3⋊(C3⋊D3)C2311yescharacteristic
97C22×C3⋊(C3⋊D3)C2311yescharacteristic
98C22×C3⋊(C3⋊D3)C2311yescharacteristic
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—
108C33×D4—22no—
109C2×C33×C4C2311yescharacteristic
110#6312—22no—
111#6312D414yescomplemented
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊(C3⋊D3))—22no—
114C4×C3⋊(C3⋊D3)—22no—
115C3×#638—22no—
116C3×#638—22no—
117C2×C3×C3⋊Dic3—22no—
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C32×#67—22no—
122C32×#67—41no—
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6292—22no—
126#6292—41no—
127#6291—22no—
128#6291—22no—
129#6291—22no—
130#6291—22no—
131#6291D414yescomplemented
132#6290—22no—
133#6289—22no—
134D3×C3⋊Dic3—22no—
135#5609—91no—
136#5590—94no—
137C24×C32—31no—
138C23×C3⋊D3—31no—
139C23×C3⋊D3—31no—
140C23×C3⋊D3—34no—
141C23×C3⋊D3—34no—
142C23×C3⋊D3—31no—
143C23×C3⋊D3—64no—
144C23×C3⋊D3—64no—
145C23×C3×D3C2×D314yescomplemented
146C22×D32—34no—
147C2×C32×D4—24no—
148C2×C32×D4—31no—
149C2×C32×D4—31no—
150C2×C32×D4C2×D314yescomplemented
151C2×C32×D4C2×D311yescharacteristic, complemented
152C2×#638—31no—
153C2×#638—34no—
154C2×#638—31no—
155C2×#638—34no—
156C2×#638—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638—64no—
163C2×#638—64no—
164C2×#638—64no—
165C2×#638—64no—
166C2×#638C2×D311yescharacteristic, complemented
167C2×#638C2×D311yescharacteristic, complemented
168C22×C3⋊Dic3—31no—
169C22×C3⋊Dic3C2×D311yescharacteristic, complemented
170D4×C3⋊D3—64no—
171D4×C3⋊D3—64no—
172D4×C3⋊D3—616no—
173D4×C3⋊D3—632no—
174C2×C4⋊(C3⋊D3)—31no—
175C2×C4⋊(C3⋊D3)—31no—
176C2×C4⋊(C3⋊D3)—34no—
177C2×C4⋊(C3⋊D3)—31no—
178C2×C4⋊(C3⋊D3)—64no—
179C2×C4×C3⋊D3—31no—
180C2×C4×C3⋊D3—34no—
181C2×C4×C3⋊D3—31no—
182C2×C4×C3⋊D3—64no—
183C2×C3×#67—34no—
184C2×C3×#67—34no—
185C2×C3×#67C2×D314yescomplemented
186C2×C3×#67C2×D314yescomplemented
187C22×C3×Dic3—34no—
188#3811—616no—
189D3×#67—616no—
190C2×#626—34no—
191C2×#626—34no—
192C2×#626—34no—
193C2×#626—34no—
194C2×#626—34no—
195C2×#626—34no—
196C2×#626—34no—
197C2×#626—616no—
198C2×#625—34no—
199C2×#624—34no—
200C2×D3×Dic3—34no—
201C32×C22⋊C4—31no—
202C32×C22⋊C4—31no—
203C32×C22⋊C4—31no—
204#3757C2×D311yescharacteristic, complemented
205#3752—31no—
206#3752—31no—
207#3752—31no—
208#3752C2×D311yescharacteristic, complemented
209#3750—31no—
210#3750C2×D311yescharacteristic, complemented
211C4×C3⋊Dic3—31no—
212C3×#217—34no—
213C3×#217C2×D314yescomplemented
214C3×(C2×D3)⋊C4—34no—
215C3×(C2×D3)⋊C4C2×D314yescomplemented
216C3×(C2×D3)⋊C4C2×D314yescomplemented
217C3×Dic3⋊C4—34no—
218#3724—34no—
219#3722—34no—
220#3722—34no—
221#3722—34no—
222Dic32—34no—
223C22×C33—21no—
224C22×C33—21no—
225C22×C33—21no—
226C22×C33—21no—
227C22×C33—21no—
228C22×C33C2×D412yescomplemented
229C22×C33C2411yescharacteristic
230C2×C3⋊(C3⋊D3)—21no—
231C2×C3⋊(C3⋊D3)—21no—
232C2×C3⋊(C3⋊D3)—21no—
233C2×C3⋊(C3⋊D3)—21no—
234C2×C3⋊(C3⋊D3)—21no—
235C2×C3⋊(C3⋊D3)—21no—
236C2×C3⋊(C3⋊D3)—21no—
237C2×C3⋊(C3⋊D3)—44no—
238C2×C3⋊(C3⋊D3)—44no—
239C2×C3⋊(C3⋊D3)C2×D412yescomplemented
240C2×C3⋊(C3⋊D3)C2×D412yescomplemented
241C2×C3×C3⋊D3—21no—
242C2×C3×C3⋊D3—21no—
243C2×C3×C3⋊D3—21no—
244C2×C32×D3—21no—
245C2×C32×D3—21no—
246C2×C32×D3—21no—
247C2×C32×D3—21no—
248C2×C32×D3—21no—
249C2×C32×D3—44no—
250C2×C32×D3C2×D412yescomplemented
251D3×C3⋊D3—44no—
252C33×C4—21no—
253C3⋊(C3⋊Dic3)C2×D412yescomplemented
254C3×C3⋊Dic3—21no—
255C3×C3⋊Dic3—21no—
256C3×C3⋊Dic3C2×D412yescomplemented
257C32×Dic3—21no—
258C32×Dic3—21no—
259C22×#67—94no—
260C22×#67—94no—
261C2×D3×D4—94no—
262C2×D3×D4—91no—
263C2×D3×D4—94no—
264C2×D3×D4—91no—
265C2×D3×D4—91no—
266C2×D3×D4—184no—
267C22×D12—91no—
268C3×#121—91no—
269C3×#120—34no—
270#940—94no—
271#940—91no—
272#939—34no—
273#939—94no—
274#937—94no—
275#937—91no—
276#937C3⋊D311yescharacteristic, complemented
277C4×#67—91no—
278#895—91no—
279#893—91no—
280#884—94no—
281#884—94no—
282#884—91no—
283#884—91no—
284#882—94no—
285#882—94no—
286#882—91no—
287#882—91no—
288#67⋊C4—94no—
289#67⋊C4—94no—
290C23×C32—24no—
291C23×C32—24no—
292C23×C32—31no—
293C23×C32—31no—
294C23×C32—62no—
295C23×C32—62no—
296C23×C32—121no—
297C23×C32C22×D314yes—
298C23×C32C22×D314yes—
299C23×C32C22×D311yescharacteristic
300C23×C32C22×D311yescharacteristic
301C22×C3⋊D3—31no—
302C22×C3⋊D3—31no—
303C22×C3⋊D3—31no—
304C22×C3⋊D3—34no—
305C22×C3⋊D3—34no—
306C22×C3⋊D3—34no—
307C22×C3⋊D3—64no—
308C22×C3⋊D3—64no—
309C22×C3⋊D3—64no—
310C22×C3⋊D3—62no—
311C22×C3⋊D3—62no—
312C22×C3⋊D3—62no—
313C22×C3⋊D3—68no—
314C22×C3⋊D3—62no—
315C22×C3⋊D3—62no—
316C22×C3⋊D3—616no—
317C22×C3⋊D3—616no—
318C22×C3⋊D3—68no—
319C22×C3⋊D3—62no—
320C22×C3⋊D3—68no—
321C22×C3⋊D3—68no—
322C22×C3⋊D3—128no—
323C22×C3⋊D3—128no—
324C22×C3⋊D3—121no—
325C22×C3⋊D3—121no—
326C22×C3⋊D3—121no—
327C22×C3⋊D3—124no—
328C22×C3⋊D3—124no—
329C22×C3⋊D3—128no—
330C22×C3⋊D3—128no—
331C22×C3⋊D3C22×D311yescharacteristic
332C22×C3×D3—28no—
333C22×C3×D3—28no—
334C22×C3×D3—34no—
335C22×C3×D3—44no—
336C22×C3×D3C22×D314yes—
337C22×C3×D3C22×D314yes—
338C2×D32—68no—
339C2×D32—68no—
340C2×D32—124no—
341C32×D4—216no—
342C32×D4—28no—
343C32×D4—22no—
344C32×D4—62no—
345C32×D4—121no—
346C2×C32×C4—24no—
347C2×C32×C4—31no—
348C2×C32×C4—31no—
349C2×C32×C4C22×D314yes—
350C2×C32×C4C22×D311yescharacteristic
351#638—22no—
352#638—22no—
353#638—34no—
354#638—34no—
355#638—316no—
356#638—616no—
357#638—62no—
358#638—62no—
359#638—62no—
360#638—62no—
361#638—62no—
362#638—68no—
363#638—616no—
364#638—62no—
365C2×C3⋊Dic3—22no—
366C2×C3⋊Dic3—31no—
367C2×C3⋊Dic3—34no—
368C2×C3⋊Dic3—64no—
369C2×C3⋊Dic3—62no—
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C4⋊(C3⋊D3)—62no—
374C4⋊(C3⋊D3)—68no—
375C4⋊(C3⋊D3)—616no—
376C4⋊(C3⋊D3)—62no—
377C4⋊(C3⋊D3)—121no—
378C4×C3⋊D3—62no—
379C4×C3⋊D3—68no—
380C4×C3⋊D3—616no—
381C4×C3⋊D3—62no—
382C3×#67—28no—
383C3×#67—44no—
384C3×#67—68no—
385C3×#67—68no—
386C2×C3×Dic3—34no—
387C2×C3×Dic3—34no—
388C2×C3×Dic3—34no—
389C2×C3×Dic3—68no—
390C2×C3×Dic3C22×D314yes—
391C2×C3×Dic3C22×D314yes—
392#626—316no—
393#626—68no—
394#626—68no—
395#626—68no—
396#626—68no—
397#626—68no—
398#626—124no—
399#625—68no—
400#624—68no—
401D3×Dic3—68no—
402D42—271noSylow
403C2×C33—22no—
404C2×C33—41no—
405C2×C33C22×D411yescharacteristic
406C2×C33C22×D411yescharacteristic
407C2×C33H(5,𝔽2)11yescharacteristic
408C3⋊(C3⋊D3)—22no—
409C3⋊(C3⋊D3)—22no—
410C3⋊(C3⋊D3)—41no—
411C3×C3⋊D3—41no—
412C32×D3—22no—
413C32×D3—41no—
414C24×C3—34no—
415C23×D3—94no—
416C23×D3—94no—
417C23×D3—94no—
418C23×D3—91no—
419C23×D3—91no—
420C23×D3—91no—
421C23×D3—184no—
422C23×D3—184no—
423C23×D3C2×C3⋊D311yescharacteristic, complemented
424C2×C3×D4—24no—
425C2×C3×D4—34no—
426C2×C3×D4—34no—
427C2×C3×D4—91no—
428C2×C3×D4—91no—
429C2×C3×D4D3214yescomplemented
430C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
431C22×C3×C4—91no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—94no—
435C2×#67—94no—
436C2×#67—94no—
437C2×#67—94no—
438C2×#67—94no—
439C2×#67—94no—
440C2×#67—91no—
441C2×#67—94no—
442C2×#67—94no—
443C2×#67—91no—
444C2×#67—91no—
445C2×#67—91no—
446C2×#67—91no—
447C2×#67—184no—
448C2×#67—184no—
449C2×#67—1816no—
450C2×#67—1816no—
451C2×#67C2×C3⋊D311yescharacteristic, complemented
452C2×#67C2×C3⋊D311yescharacteristic, complemented
453C22×Dic3—34no—
454C22×Dic3—94no—
455D3×D4—184no—
456D3×D4—1816no—
457D3×D4—1816no—
458D3×D4—184no—
459D3×D4—184no—
460D3×D4—1832no—
461C2×D12—91no—
462C2×D12—94no—
463C2×D12—91no—
464C2×D12—91no—
465C2×D12—91no—
466C2×D12—91no—
467C2×D12—94no—
468C2×D12—91no—
469C2×D12—94no—
470C2×D12—184no—
471C2×D12—184no—
472C2×C4×D3—94no—
473C2×C4×D3—91no—
474C2×C4×D3—94no—
475C2×C4×D3—91no—
476C2×C4×D3—91no—
477C2×C4×D3—184no—
478C3×C4⋊C4—91no—
479C3×C22⋊C4—34no—
480C3×C22⋊C4—34no—
481C3×C22⋊C4—34no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484#217—34no—
485#217C2×C3⋊D311yescharacteristic, complemented
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—94no—
488(C2×D3)⋊C4—94no—
489(C2×D3)⋊C4—94no—
490(C2×D3)⋊C4—91no—
491(C2×D3)⋊C4—91no—
492(C2×D3)⋊C4—91no—
493(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
494(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
495Dic3⋊C4—34no—
496Dic3⋊C4—94no—
497Dic3⋊C4—91no—
498C4×Dic3—94no—
499C4×Dic3—91no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—28no—
503C22×C32—21no—
504C22×C32—24no—
505C22×C32—21no—
506C22×C32—21no—
507C22×C32—24no—
508C22×C32—28no—
509C22×C32—24no—
510C22×C32—24no—
511C22×C32—24no—
512C22×C32—24no—
513C22×C32—32no—
514C22×C32—44no—
515C22×C32—44no—
516C22×C32—44no—
517C22×C32—44no—
518C22×C32—61no—
519C22×C32—61no—
520C22×C32—61no—
521C22×C32—61no—
522C22×C32—61no—
523C22×C32—124no—
524C22×C32D3×D418yescomplemented
525C22×C32D3×D412yescomplemented
526C22×C32C23×D314yes—
527C22×C32C23×D311yescharacteristic
528C2×C3⋊D3—21no—
529C2×C3⋊D3—21no—
530C2×C3⋊D3—21no—
531C2×C3⋊D3—32no—
532C2×C3⋊D3—32no—
533C2×C3⋊D3—38no—
534C2×C3⋊D3—38no—
535C2×C3⋊D3—68no—
536C2×C3⋊D3—68no—
537C2×C3⋊D3—68no—
538C2×C3⋊D3—68no—
539C2×C3⋊D3—64no—
540C2×C3⋊D3—61no—
541C2×C3⋊D3—61no—
542C2×C3⋊D3—64no—
543C2×C3⋊D3—61no—
544C2×C3⋊D3—61no—
545C2×C3⋊D3—68no—
546C2×C3⋊D3—64no—
547C2×C3⋊D3—61no—
548C2×C3⋊D3—61no—
549C2×C3⋊D3—61no—
550C2×C3⋊D3—64no—
551C2×C3⋊D3—64no—
552C2×C3⋊D3—64no—
553C2×C3⋊D3—64no—
554C2×C3⋊D3—124no—
555C2×C3⋊D3—124no—
556C2×C3⋊D3—124no—
557C2×C3⋊D3—124no—
558C2×C3⋊D3—124no—
559C2×C3⋊D3—124no—
560C2×C3⋊D3—1216no—
561C2×C3⋊D3—124no—
562C2×C3⋊D3—1216no—
563C2×C3⋊D3—1232no—
564C2×C3⋊D3—1232no—
565C2×C3×D3—24no—
566C2×C3×D3—24no—
567C2×C3×D3—24no—
568C2×C3×D3—24no—
569C2×C3×D3—24no—
570C2×C3×D3—416no—
571C2×C3×D3—64no—
572C2×C3×D3—64no—
573C2×C3×D3—64no—
574C2×C3×D3D3×D418yescomplemented
575D32—1216no—
576C32×C4—28no—
577C32×C4—24no—
578C32×C4—21no—
579C32×C4—61no—
580C32×C4—61no—
581C3⋊Dic3—21no—
582C3⋊Dic3—21no—
583C3⋊Dic3—32no—
584C3⋊Dic3—38no—
585C3⋊Dic3—68no—
586C3⋊Dic3D3×D412yescomplemented
587C3×Dic3—24no—
588C3×Dic3—24no—
589C3×Dic3—38no—
590C3×Dic3—64no—
591C3×Dic3—64no—
592C22×D4—271no—
593C22×D4—271no—
594C22×D4—271no—
595C22×D4—271no—
596#127—271no—
597#121—91no—
598#121—271no—
599#121—271no—
600#121—271no—
601#120—31no—
602#120—271no—
603#120—271no—
604#120—271no—
605C4×D4—271no—
606C4×D4—271no—
607C33D4211yescharacteristic, complemented, Sylow
608C23×C3—24no—
609C23×C3—24no—
610C23×C3—34no—
611C23×C3—34no—
612C23×C3—68no—
613C23×C3—68no—
614C23×C3—91no—
615C23×C3—124no—
616C23×C3C2×D3214yes—
617C23×C3C2×D3214yes—
618C23×C3C22×C3⋊D311yescharacteristic
619C23×C3C22×C3⋊D311yescharacteristic
620C22×D3—22no—
621C22×D3—22no—
622C22×D3—34no—
623C22×D3—41no—
624C22×D3—94no—
625C22×D3—94no—
626C22×D3—91no—
627C22×D3—91no—
628C22×D3—94no—
629C22×D3—91no—
630C22×D3—184no—
631C22×D3—184no—
632C22×D3—184no—
633C22×D3—182no—
634C22×D3—188no—
635C22×D3—188no—
636C22×D3—182no—
637C22×D3—188no—
638C22×D3—182no—
639C22×D3—182no—
640C22×D3—188no—
641C22×D3—188no—
642C22×D3—1816no—
643C22×D3—1816no—
644C22×D3—188no—
645C22×D3—182no—
646C22×D3—182no—
647C22×D3—368no—
648C22×D3—368no—
649C22×D3—361no—
650C22×D3—364no—
651C22×D3—364no—
652C22×D3—364no—
653C22×D3—361no—
654C22×D3—361no—
655C22×D3—368no—
656C22×D3—368no—
657C22×D3C22×C3⋊D311yescharacteristic
658C22×D3C22×C3⋊D311yescharacteristic
659C3×D4—216no—
660C3×D4—28no—
661C3×D4—22no—
662C3×D4—68no—
663C3×D4—124no—
664C3×D4—182no—
665C3×D4—182no—
666C2×C3×C4—24no—
667C2×C3×C4—34no—
668C2×C3×C4—34no—
669C2×C3×C4—91no—
670C2×C3×C4—91no—
671C2×C3×C4—91no—
672C2×C3×C4—182no—
673C2×C3×C4C2×D3214yes—
674C2×C3×C4C22×C3⋊D311yescharacteristic
675#67—22no—
676#67—41no—
677#67—68no—
678#67—68no—
679#67—916no—
680#67—916no—
681#67—94no—
682#67—1816no—
683#67—182no—
684#67—188no—
685#67—188no—
686#67—188no—
687#67—188no—
688#67—182no—
689#67—188no—
690#67—188no—
691#67—182no—
692#67—1816no—
693#67—361no—
694C2×Dic3—34no—
695C2×Dic3—34no—
696C2×Dic3—34no—
697C2×Dic3—68no—
698C2×Dic3—94no—
699C2×Dic3—91no—
700C2×Dic3—184no—
701C2×Dic3—188no—
702C2×Dic3C22×C3⋊D311yescharacteristic
703C2×Dic3C22×C3⋊D311yescharacteristic
704D12—94no—
705D12—188no—
706D12—182no—
707D12—1816no—
708D12—188no—
709D12—182no—
710D12—182no—
711D12—182no—
712D12—182no—
713D12—364no—
714C4×D3—182no—
715C4×D3—188no—
716C4×D3—188no—
717C4×D3—182no—
718C4×D3—182no—
719C4×D3—1816no—
720C2×C32—22no—
721C2×C32—24no—
722C2×C32—24no—
723C2×C32—24no—
724C2×C32—28no—
725C2×C32—48no—
726C2×C32—48no—
727C2×C32—44no—
728C2×C32—41no—
729C2×C32—62no—
730C2×C32—121no—
731C2×C32C2×D3×D414yes—
732C2×C32C2×D3×D414yes—
733C2×C32C2×D3×D411yescharacteristic
734C2×C32C2×D3×D411yescharacteristic
735C2×C32#100414yes—
736C2×C32#100911yescharacteristic
737C3⋊D3—41no—
738C3⋊D3—616no—
739C3⋊D3—68no—
740C3⋊D3—62no—
741C3⋊D3—62no—
742C3⋊D3—68no—
743C3⋊D3—128no—
744C3⋊D3—128no—
745C3⋊D3—124no—
746C3⋊D3—121no—
747C3×D3—28no—
748C3×D3—44no—
749C3×D3—124no—
750C24—31no—
751C24—271no—
752C24—271no—
753C24—271no—
754C2×D4—31no—
755C2×D4—31no—
756C2×D4—91no—
757C2×D4—91no—
758C2×D4—271no—
759C2×D4—271no—
760C2×D4—271no—
761C2×D4—271no—
762C2×D4—271no—
763C2×D4—271no—
764C2×D4—271no—
765C2×D4—271no—
766C2×D4—271no—
767C2×D4—271no—
768C2×D4—271no—
769C2×D4—544no—
770C2×D4—544no—
771C2×D4—544no—
772C2×D4—544no—
773C2×D4D3×C3⋊D311yescharacteristic, complemented
774C22×C4—91no—
775C22×C4—271no—
776C22×C4—271no—
777C22×C4—271no—
778C4⋊C4—91no—
779C4⋊C4—271no—
780C22⋊C4—31no—
781C22⋊C4—31no—
782C22⋊C4—31no—
783C22⋊C4—91no—
784C22⋊C4—91no—
785C22⋊C4—271no—
786C22⋊C4—271no—
787C22⋊C4—271no—
788C42—271no—
789C22×C3—24no—
790C22×C3—24no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—28no—
794C22×C3—24no—
795C22×C3—24no—
796C22×C3—24no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—24no—
801C22×C3—28no—
802C22×C3—38no—
803C22×C3—44no—
804C22×C3—44no—
805C22×C3—44no—
806C22×C3—44no—
807C22×C3—64no—
808C22×C3—64no—
809C22×C3—64no—
810C22×C3—64no—
811C22×C3—64no—
812C22×C3—1216no—
813C22×C3—181no—
814C22×C3—181no—
815C22×C3—181no—
816C22×C3#381118yescomplemented
817C22×C3D4×C3⋊D312yescomplemented
818C22×C3C22×D3214yes—
819C22×C3C23×C3⋊D311yescharacteristic
820C2×D3—21no—
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—21no—
824C2×D3—21no—
825C2×D3—44no—
826C2×D3—64no—
827C2×D3—64no—
828C2×D3—64no—
829C2×D3—98no—
830C2×D3—98no—
831C2×D3—92no—
832C2×D3—92no—
833C2×D3—188no—
834C2×D3—188no—
835C2×D3—188no—
836C2×D3—188no—
837C2×D3—184no—
838C2×D3—184no—
839C2×D3—184no—
840C2×D3—184no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—181no—
844C2×D3—181no—
845C2×D3—188no—
846C2×D3—184no—
847C2×D3—184no—
848C2×D3—184no—
849C2×D3—181no—
850C2×D3—181no—
851C2×D3—181no—
852C2×D3—364no—
853C2×D3—364no—
854C2×D3—364no—
855C2×D3—364no—
856C2×D3—364no—
857C2×D3—3616no—
858C2×D3—3616no—
859C2×D3—364no—
860C2×D3—3616no—
861C2×D3—364no—
862C2×D3—3632no—
863C2×D3—3632no—
864C2×D3D4×C3⋊D312yescomplemented
865C3×C4—28no—
866C3×C4—24no—
867C3×C4—21no—
868C3×C4—64no—
869C3×C4—64no—
870C3×C4—92no—
871C3×C4—181no—
872C3×C4—181no—
873Dic3—21no—
874Dic3—21no—
875Dic3—38no—
876Dic3—64no—
877Dic3—64no—
878Dic3—98no—
879Dic3—92no—
880Dic3—188no—
881C32—24no—
882C32#559014yescomplemented
883C32#560911yescharacteristic, complemented
884C23—31no—
885C23—31no—
886C23—62no—
887C23—62no—
888C23—91no—
889C23—121no—
890C23—271no—
891C23—271no—
892C23—271no—
893C23—542no—
894C23—542no—
895C23—542no—
896C23—542no—
897C23—542no—
898C23—542no—
899C23—1081no—
900C23—1081no—
901C23—1081no—
902C23C2×D3×C3⋊D311yescharacteristic
903C23C2×D3×C3⋊D311yescharacteristic
904D4—22no—
905D4—62no—
906D4—121no—
907D4—182no—
908D4—182no—
909D4—274no—
910D4—274no—
911D4—542no—
912D4—542no—
913D4—542no—
914D4—542no—
915D4—542no—
916D4—542no—
917D4—542no—
918D4—542no—
919D4—1081no—
920C2×C4—31no—
921C2×C4—31no—
922C2×C4—91no—
923C2×C4—91no—
924C2×C4—91no—
925C2×C4—182no—
926C2×C4—271no—
927C2×C4—542no—
928C2×C4—542no—
929C2×C4—542no—
930C2×C4C2×D3×C3⋊D311yescharacteristic
931C2×C3—28no—
932C2×C3—22no—
933C2×C3—24no—
934C2×C3—24no—
935C2×C3—24no—
936C2×C3—48no—
937C2×C3—48no—
938C2×C3—44no—
939C2×C3—41no—
940C2×C3—68no—
941C2×C3—124no—
942C2×C3—361no—
943C2×C3D32×D414yes—
944C2×C3#6431414yes—
945C2×C3C2×#381114yes—
946C2×C3C2×D4×C3⋊D311yescharacteristic
947C2×C3C2×D4×C3⋊D311yescharacteristic
948C2×C3#6436111yescharacteristic
949D3—22no—
950D3—41no—
951D3—124no—
952D3—1816no—
953D3—188no—
954D3—188no—
955D3—182no—
956D3—182no—
957D3—368no—
958D3—368no—
959D3—364no—
960D3—361no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—32no—
967C22—61no—
968C22—61no—
969C22—61no—
970C22—61no—
971C22—61no—
972C22—124no—
973C22—181no—
974C22—181no—
975C22—181no—
976C22—272no—
977C22—272no—
978C22—541no—
979C22—541no—
980C22—541no—
981C22—541no—
982C22—541no—
983C22—541no—
984C22—541no—
985C22—1084no—
986C22—1084no—
987C22—1084no—
988C22#8903912yescomplemented
989C22C22×D3×C3⋊D311yescharacteristic
990C4—21no—
991C4—61no—
992C4—61no—
993C4—92no—
994C4—181no—
995C4—181no—
996C4—272no—
997C3—24no—
998C3#1059529214yescomplemented
999C3#1059606111yescharacteristic, complemented
1000C2—22no—
1001C2—41no—
1002C2—62no—
1003C2—121no—
1004C2—361no—
1005C2—542no—
1006C2—542no—
1007C2—1081no—
1008C2D3×D4×C3⋊D311yescharacteristic
1009C2#1172458811yescharacteristic
1010C2C2×#8903911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊(C3⋊D3)C2semidirect
2. C2×#89039C2semidirect
3. C2×D3×#638C2semidirect
4. C22×#6291C2semidirect
5. C3×#64148C2semidirect
6. C32×#937C2semidirect
7. #11723639C2semidirect
8. #11723638C2semidirect
9. #11723633C2semidirect
10. #11723622C2semidirect
11. #11723616C2semidirect
12. #11723542C2semidirect
13. #11723527C2semidirect
14. #11723525C2semidirect
15. #11723462C2semidirect
18. C23×C3⋊(C3⋊D3)C22semidirect
19. C23×C3⋊(C3⋊D3)C22semidirect
20. C23×C32×D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
22. C2×C33×D4C22semidirect
24. C2×#6312C22semidirect
26. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
27. C2×C4×C3⋊(C3⋊D3)C22semidirect
28. C2×C3×#638C22semidirect
29. C2×C3×#638C22semidirect
30. C22×C3×C3⋊Dic3C22semidirect
31. C2×C32×#67C22semidirect
32. C2×C32×#67C22semidirect
35. C2×#6292C22semidirect
36. C2×#6292C22semidirect
39. C2×#6291C22semidirect
40. C2×#6291C22semidirect
41. C2×#6291C22semidirect
42. C2×#6291C22semidirect
43. C2×#6290C22semidirect
44. C2×#6289C22semidirect
45. C2×D3×C3⋊Dic3C22semidirect
46. C3×#3757C22semidirect
47. C3×#3752C22semidirect
48. C3×#3750C22semidirect
49. C32×#217C22semidirect
50. C32×(C2×D3)⋊C4C22semidirect
51. C32×(C2×D3)⋊C4C22semidirect
52. #88806C22semidirect
53. #88804C22semidirect
54. #88804C22semidirect
55. #88804C22semidirect
56. Dic3×C3⋊Dic3C22semidirect
69. #64148D3semidirect
78. C3×#937D3semidirect
111. #6312D4semidirect
131. #6291D4semidirect
145. C23×C3×D3C2×D3semidirect
150. C2×C32×D4C2×D3semidirect
151. C2×C32×D4C2×D3semidirect
166. C2×#638C2×D3semidirect
167. C2×#638C2×D3semidirect
169. C22×C3⋊Dic3C2×D3semidirect
185. C2×C3×#67C2×D3semidirect
186. C2×C3×#67C2×D3semidirect
204. #3757C2×D3semidirect
208. #3752C2×D3semidirect
210. #3750C2×D3semidirect
213. C3×#217C2×D3semidirect
215. C3×(C2×D3)⋊C4C2×D3semidirect
216. C3×(C2×D3)⋊C4C2×D3semidirect
228. C22×C33C2×D4semidirect
239. C2×C3⋊(C3⋊D3)C2×D4semidirect
240. C2×C3⋊(C3⋊D3)C2×D4semidirect
250. C2×C32×D3C2×D4semidirect
253. C3⋊(C3⋊Dic3)C2×D4semidirect
256. C3×C3⋊Dic3C2×D4semidirect
276. #937C3⋊D3semidirect
423. C23×D3C2×C3⋊D3semidirect
429. C2×C3×D4D32semidirect
430. C2×C3×D4C2×C3⋊D3semidirect
451. C2×#67C2×C3⋊D3semidirect
452. C2×#67C2×C3⋊D3semidirect
485. #217C2×C3⋊D3semidirect
493. (C2×D3)⋊C4C2×C3⋊D3semidirect
494. (C2×D3)⋊C4C2×C3⋊D3semidirect
524. C22×C32D3×D4semidirect
525. C22×C32D3×D4semidirect
574. C2×C3×D3D3×D4semidirect
586. C3⋊Dic3D3×D4semidirect
607. C33D42semidirect
773. C2×D4D3×C3⋊D3semidirect
816. C22×C3#3811semidirect
817. C22×C3D4×C3⋊D3semidirect
864. C2×D3D4×C3⋊D3semidirect
882. C32#5590semidirect
883. C32#5609semidirect
988. C22#89039semidirect
998. C3#10595292semidirect
999. C3#10596061semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊(C3⋊D3)2
C2×#890392
C2×D3×#6382
C22×#62912
C3×#641482
C32×#9372
#117236392
#117236382
#117236332
#117236222
#117236162
#117235422
#117235272
#117235252
#117234622
#105960613
#105952923