Finite Group Databasebeta

← #13177515

Subgroups — #13177515

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
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic, complemented
3C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
4C22×#6292C211yesmaximal, characteristic, complemented
5#11723978C211yesmaximal, characteristic, complemented
6C32×#939C211yesmaximal, characteristic, complemented
7#11723636C211yesmaximal, characteristic, complemented
8#11723634C211yesmaximal, characteristic, complemented
9#11723633C211yesmaximal, characteristic, complemented
10#11723623C211yesmaximal, characteristic, complemented
11Dic3×#638C211yesmaximal, characteristic, complemented
12#11723541C211yesmaximal, characteristic, complemented
13#11723520C211yesmaximal, characteristic, complemented
14#11723512C211yesmaximal, characteristic, complemented
15#11723482C211yesmaximal, characteristic, complemented
16#10596080—31nomaximal
17#10595291—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
19C23×C3×C3⋊D3C2211yescharacteristic, complemented
20C23×C3×C3⋊D3C2211yescharacteristic, complemented
21C22×D3×C3⋊D3C2211yescharacteristic, complemented
22C2×C33×D4C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic, complemented
24C2×#6312C2211yescharacteristic, complemented
25C2×C3×#638C2211yescharacteristic
26C2×C3×#638C2211yescharacteristic, complemented
27C3×D4×C3⋊D3—24no—
28C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
29C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
30C2×C32×#67C2211yescharacteristic, complemented
31C2×C32×#67C2211yescharacteristic, complemented
32C22×C32×Dic3C2211yescharacteristic, complemented
33#89039—24no—
34C3⋊D3×#67—24no—
35C2×#6292—24no—
36C2×#6292C2211yescharacteristic
37C2×#6292C2211yescharacteristic, complemented
38C2×#6292C2211yescharacteristic, complemented
39C2×#6292C2211yescharacteristic, complemented
40C2×#6292C2211yescharacteristic, complemented
41C2×#6291C2211yescharacteristic, complemented
42C2×#6290C2211yescharacteristic, complemented
43C2×#6290C2211yescharacteristic, complemented
44C2×#6289C2211yescharacteristic, complemented
45C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
46#88864C2211yescharacteristic, complemented
47#88859C2211yescharacteristic, complemented
48#88859C2211yescharacteristic, complemented
49C32×#217C2211yescharacteristic, complemented
50C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C32×Dic3⋊C4C2211yescharacteristic, complemented
52#88807C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54#88803C2211yescharacteristic, complemented
55#88803C2211yescharacteristic, complemented
56Dic3×C3⋊Dic3C2211yescharacteristic, complemented
57C2×D4×C3⋊D3—31no—
58C2×D4×C3⋊D3—31no—
59C2×D4×C3⋊D3D311yescharacteristic, complemented
60C22×C4⋊(C3⋊D3)—31no—
61C2×C3×D3×D4—34no—
62C2×#3811—34no—
63C2×D3×#67—34no—
64C22×#626—34no—
65C32×#121—31no—
66#64149—31no—
67#64146—31no—
68#64146—34no—
69#64146—31no—
70#64146—64no—
71C4×#638—31no—
72#64104—31no—
73#64102—31no—
74#64093—31no—
75#64093—31no—
76#64091—31no—
77#64091—31no—
78C3×#939D314yescomplemented
79#63979—34no—
80#63977—34no—
81#63976—34no—
82Dic3×#67—34no—
83#63958—34no—
84#63922—34no—
85#63906—34no—
86#63904—34no—
87#63886—34no—
88C23×C33C2311yescharacteristic
89C23×C33C2311yescharacteristic
90C22×C3⋊(C3⋊D3)—22no—
91C22×C3⋊(C3⋊D3)—22no—
92C22×C3⋊(C3⋊D3)—41no—
93C22×C3⋊(C3⋊D3)C2311yescharacteristic
94C22×C3⋊(C3⋊D3)C2311yescharacteristic
95C22×C3×C3⋊D3—22no—
96C22×C3×C3⋊D3—22no—
97C22×C3×C3⋊D3—22no—
98C22×C3×C3⋊D3—22no—
99C22×C3×C3⋊D3—41no—
100C22×C3×C3⋊D3—41no—
101C22×C3×C3⋊D3C2311yescharacteristic
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊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#6312—41no—
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
114C3×#638—22no—
115C3×#638D414yescomplemented
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4⋊(C3⋊D3)—22no—
118C3×C4×C3⋊D3—22no—
119C32×#67—22no—
120C32×#67—22no—
121C2×C32×Dic3—22no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6292—22no—
126#6292—22no—
127#6292—22no—
128#6292—22no—
129#6292D414yescomplemented
130#6291—22no—
131#6290—22no—
132#6290—41no—
133#6289—22no—
134Dic3×C3⋊D3—22no—
135D4×#67—91no—
136#5609—94no—
137C23×C3⋊D3—31no—
138C23×C3⋊D3—34no—
139C23×C3⋊D3—31no—
140C23×C3⋊D3—64no—
141C23×C3⋊D3C2×D311yescharacteristic, complemented
142C23×C3⋊D3C2×D311yescharacteristic, complemented
143C23×C3×D3—34no—
144C23×C3×D3—34no—
145C22×D32—34no—
146C2×C32×D4—24no—
147C2×C32×D4—31no—
148C2×C32×D4—31no—
149C2×C32×D4C2×D314yescomplemented
150C2×C32×D4C2×D311yescharacteristic, complemented
151C22×C32×C4—31no—
152C2×#638—31no—
153C2×#638—34no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—34no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—64no—
160C2×#638—64no—
161C2×#638C2×D311yescharacteristic
162C2×#638C2×D311yescharacteristic, complemented
163D4×C3⋊D3—24no—
164D4×C3⋊D3—64no—
165D4×C3⋊D3—64no—
166C2×C4⋊(C3⋊D3)—31no—
167C2×C4⋊(C3⋊D3)—31no—
168C2×C4⋊(C3⋊D3)—31no—
169C2×C4⋊(C3⋊D3)—31no—
170C2×C4⋊(C3⋊D3)—31no—
171C2×C4⋊(C3⋊D3)—64no—
172C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
173C2×C4×C3⋊D3—31no—
174C2×C4×C3⋊D3—31no—
175C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
176C2×C3×#67—34no—
177C2×C3×#67—34no—
178C2×C3×#67C2×D314yescomplemented
179C2×C3×#67C2×D314yescomplemented
180C22×C3×Dic3C2×D314yescomplemented
181C3×D3×D4—616no—
182C2×C3×D12—34no—
183C2×C3×C4×D3—34no—
184#3811—616no—
185D3×#67—616no—
186C2×#626—34no—
187C2×#626—34no—
188C2×#626—34no—
189C2×#626—34no—
190C2×#626—34no—
191C2×#626—34no—
192C2×#626—616no—
193C2×#625—34no—
194C2×#625—34no—
195C2×#624—34no—
196C2×D3×Dic3—34no—
197C32×C4⋊C4—31no—
198C32×C22⋊C4—31no—
199C32×C22⋊C4—31no—
200#3757—31no—
201#3757—34no—
202#3757—64no—
203#3752—31no—
204#3752—31no—
205#3752—31no—
206#3752—31no—
207#3752—31no—
208#3752—34no—
209#3752—34no—
210#3752—64no—
211#3752—64no—
212#3750—31no—
213C4×C3⋊Dic3—31no—
214C3×#217C2×D314yescomplemented
215C3×(C2×D3)⋊C4C2×D314yescomplemented
216C3×Dic3⋊C4C2×D314yescomplemented
217Dic3⋊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×C33C2×D412yescomplemented
228C22×C33C2411yescharacteristic
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⋊D3)—44no—
235C2×C3⋊(C3⋊D3)C2×D412yescomplemented
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—21no—
242C2×C3×C3⋊D3—21no—
243C2×C3×C3⋊D3—44no—
244C2×C3×C3⋊D3—44no—
245C2×C3×C3⋊D3C2×D412yescomplemented
246C2×C3×C3⋊D3C2×D412yescomplemented
247C2×C32×D3—21no—
248C2×C32×D3—21no—
249C2×C32×D3—21no—
250D3×C3⋊D3—44no—
251C33×C4—21no—
252C3⋊(C3⋊Dic3)—21no—
253C3⋊(C3⋊Dic3)—21no—
254C3×C3⋊Dic3C2×D412yescomplemented
255C32×Dic3—21no—
256C32×Dic3—21no—
257C32×Dic3C2×D412yescomplemented
258C22×C3×D4—91no—
259C22×#67—91no—
260C22×#67—91no—
261C2×D3×D4—34no—
262C2×D3×D4—94no—
263C2×D3×D4—94no—
264C2×D3×D4—91no—
265C22×D12—94no—
266C3×#121—34no—
267#953—91no—
268#953—91no—
269#940—94no—
270#940—91no—
271#939—91no—
272#939C3⋊D311yescharacteristic, complemented
273#938—91no—
274#937—94no—
275#937—94no—
276#937—91no—
277#937—91no—
278#937—184no—
279D4×Dic3—91no—
280#930—91no—
281C4×#67—94no—
282C4×#67—91no—
283#895—94no—
284#893—94no—
285#884—94no—
286#884—94no—
287#882—94no—
288#882—94no—
289C23×C32—24no—
290C23×C32—24no—
291C23×C32—31no—
292C23×C32C22×D314yes—
293C23×C32C22×D314yes—
294C23×C32C22×D311yescharacteristic
295C23×C32C22×D311yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—31no—
301C22×C3⋊D3—31no—
302C22×C3⋊D3—34no—
303C22×C3⋊D3—34no—
304C22×C3⋊D3—41no—
305C22×C3⋊D3—41no—
306C22×C3⋊D3—64no—
307C22×C3⋊D3—64no—
308C22×C3⋊D3—62no—
309C22×C3⋊D3—62no—
310C22×C3⋊D3—62no—
311C22×C3⋊D3—62no—
312C22×C3⋊D3—68no—
313C22×C3⋊D3—68no—
314C22×C3⋊D3—128no—
315C22×C3⋊D3—128no—
316C22×C3⋊D3—121no—
317C22×C3⋊D3—121no—
318C22×C3⋊D3—124no—
319C22×C3⋊D3—128no—
320C22×C3⋊D3C22×D311yescharacteristic
321C22×C3⋊D3C22×D311yescharacteristic
322C22×C3⋊D3C22×D311yescharacteristic
323C22×C3×D3—34no—
324C22×C3×D3—34no—
325C22×C3×D3—34no—
326C22×C3×D3—68no—
327C22×C3×D3—68no—
328C22×C3×D3—68no—
329C22×C3×D3—68no—
330C22×C3×D3—124no—
331C22×C3×D3—124no—
332C22×C3×D3C22×D314yes—
333C2×D32—68no—
334C2×D32—68no—
335C2×D32—124no—
336C32×D4—22no—
337C32×D4—28no—
338C32×D4—48no—
339C32×D4—62no—
340C32×D4—62no—
341C2×C32×C4—24no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—62no—
346C2×C32×C4C22×D314yes—
347C2×C32×C4C22×D311yescharacteristic
348#638—22no—
349#638—62no—
350#638—62no—
351#638—62no—
352#638—68no—
353#638—128no—
354#638—121no—
355#638—121no—
356#638—124no—
357#638—128no—
358#638#6714yescomplemented
359C2×C3⋊Dic3—31no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—34no—
362C2×C3⋊Dic3—34no—
363C2×C3⋊Dic3—64no—
364C2×C3⋊Dic3—64no—
365C2×C3⋊Dic3C22×D311yescharacteristic
366C4⋊(C3⋊D3)—22no—
367C4⋊(C3⋊D3)—34no—
368C4⋊(C3⋊D3)—62no—
369C4⋊(C3⋊D3)—62no—
370C4⋊(C3⋊D3)—62no—
371C4⋊(C3⋊D3)—62no—
372C4×C3⋊D3—22no—
373C4×C3⋊D3—62no—
374C4×C3⋊D3—62no—
375C3×#67—28no—
376C3×#67—28no—
377C3×#67—316no—
378C3×#67—68no—
379C2×C3×Dic3—28no—
380C2×C3×Dic3—34no—
381C2×C3×Dic3C22×D314yes—
382C2×C3×Dic3C22×D314yes—
383C2×C3×Dic3C22×D314yes—
384C3×D12—68no—
385C3×C4×D3—68no—
386#626—316no—
387#626—68no—
388#626—68no—
389#626—68no—
390#626—68no—
391#626—68no—
392#625—68no—
393#625—124no—
394#624—68no—
395D3×Dic3—68no—
396D42—271noSylow
397C2×C33—22no—
398C2×C33—41no—
399C2×C33C22×D411yescharacteristic
400C2×C33C22×D411yescharacteristic
401C2×C33H(5,𝔽2)11yescharacteristic
402C3⋊(C3⋊D3)—22no—
403C3⋊(C3⋊D3)—41no—
404C3×C3⋊D3—22no—
405C3×C3⋊D3—22no—
406C3×C3⋊D3—41no—
407C32×D3—41no—
408C24×C3—91no—
409C24×C3—91no—
410C23×D3—34no—
411C23×D3—34no—
412C23×D3—94no—
413C23×D3—94no—
414C23×D3—91no—
415C23×D3—91no—
416C23×D3—184no—
417C2×C3×D4—24no—
418C2×C3×D4—34no—
419C2×C3×D4—34no—
420C2×C3×D4—91no—
421C2×C3×D4—91no—
422C2×C3×D4—91no—
423C2×C3×D4—184no—
424C2×C3×D4D3214yescomplemented
425C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
426C22×C3×C4—34no—
427C22×C3×C4—91no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—94no—
431C2×#67—94no—
432C2×#67—94no—
433C2×#67—91no—
434C2×#67—91no—
435C2×#67—94no—
436C2×#67—94no—
437C2×#67—91no—
438C2×#67—91no—
439C2×#67—91no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C2×#67—91no—
444C2×#67—184no—
445C2×#67—184no—
446C2×#67—184no—
447C2×#67—184no—
448C2×#67C2×C3⋊D311yescharacteristic, complemented
449C2×#67C2×C3⋊D311yescharacteristic, complemented
450C22×Dic3—91no—
451C22×Dic3C2×C3⋊D311yescharacteristic, complemented
452D3×D4—616no—
453D3×D4—1816no—
454D3×D4—184no—
455D3×D4—1816no—
456C2×D12—34no—
457C2×D12—94no—
458C2×D12—94no—
459C2×D12—94no—
460C2×D12—94no—
461C2×D12—94no—
462C2×D12—91no—
463C2×D12—1816no—
464C2×C4×D3—34no—
465C2×C4×D3—94no—
466C2×C4×D3—94no—
467C2×C4×D3—91no—
468C3×C4⋊C4—34no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471#217—94no—
472#217—91no—
473#217—91no—
474#217—91no—
475#217—91no—
476#217—184no—
477#217C2×C3⋊D311yescharacteristic, complemented
478(C2×D3)⋊C4—94no—
479(C2×D3)⋊C4—94no—
480(C2×D3)⋊C4—94no—
481(C2×D3)⋊C4—94no—
482(C2×D3)⋊C4—94no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—184no—
486(C2×D3)⋊C4—184no—
487(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
488C4⋊Dic3—91no—
489Dic3⋊C4—94no—
490Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
491C4×Dic3—94no—
492C4×Dic3—91no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—21no—
497C22×C32—21no—
498C22×C32—24no—
499C22×C32—28no—
500C22×C32—24no—
501C22×C32—24no—
502C22×C32—24no—
503C22×C32—24no—
504C22×C32—24no—
505C22×C32—44no—
506C22×C32—44no—
507C22×C32—44no—
508C22×C32—44no—
509C22×C32—44no—
510C22×C32—61no—
511C22×C32—61no—
512C22×C32—61no—
513C22×C32D3×D418yescomplemented
514C22×C32C2×#6712yescomplemented
515C22×C32C23×D314yes—
516C22×C32C23×D311yescharacteristic
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—21no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3—21no—
522C2×C3⋊D3—21no—
523C2×C3⋊D3—21no—
524C2×C3⋊D3—32no—
525C2×C3⋊D3—38no—
526C2×C3⋊D3—44no—
527C2×C3⋊D3—44no—
528C2×C3⋊D3—68no—
529C2×C3⋊D3—61no—
530C2×C3⋊D3—61no—
531C2×C3⋊D3—68no—
532C2×C3⋊D3—61no—
533C2×C3⋊D3—61no—
534C2×C3⋊D3—64no—
535C2×C3⋊D3—61no—
536C2×C3⋊D3—64no—
537C2×C3⋊D3—64no—
538C2×C3⋊D3—64no—
539C2×C3⋊D3—64no—
540C2×C3⋊D3—124no—
541C2×C3⋊D3—124no—
542C2×C3⋊D3—124no—
543C2×C3⋊D3—124no—
544C2×C3⋊D3—124no—
545C2×C3⋊D3—124no—
546C2×C3⋊D3—1216no—
547C2×C3⋊D3—1232no—
548C2×C3⋊D3D3×D412yescomplemented
549C2×C3⋊D3C2×#6712yescomplemented
550C2×C3×D3—24no—
551C2×C3×D3—24no—
552C2×C3×D3—24no—
553C2×C3×D3—38no—
554C2×C3×D3—38no—
555C2×C3×D3—64no—
556C2×C3×D3—64no—
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×D3—1216no—
564D32—1216no—
565C32×C4—21no—
566C32×C4—24no—
567C32×C4—32no—
568C32×C4—44no—
569C32×C4—61no—
570C32×C4—61no—
571C3⋊Dic3—61no—
572C3⋊Dic3—61no—
573C3⋊Dic3—64no—
574C3⋊Dic3—64no—
575C3⋊Dic3—124no—
576C3⋊Dic3—124no—
577C3⋊Dic3C2×#6712yescomplemented
578C3×Dic3—24no—
579C3×Dic3—24no—
580C3×Dic3—38no—
581C3×Dic3D3×D418yescomplemented
582C22×D4—91no—
583C22×D4—271no—
584C22×D4—271no—
585C22×D4—271no—
586#127—271no—
587#121—31no—
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—24no—
599C23×C3—24no—
600C23×C3—34no—
601C23×C3—91no—
602C23×C3—91no—
603C23×C3—91no—
604C23×C3—182no—
605C23×C3—182no—
606C23×C3—182no—
607C23×C3—182no—
608C23×C3—361no—
609C23×C3—361no—
610C23×C3C2×D3214yes—
611C23×C3C2×D3214yes—
612C23×C3C22×C3⋊D311yescharacteristic
613C23×C3C22×C3⋊D311yescharacteristic
614C22×D3—34no—
615C22×D3—34no—
616C22×D3—34no—
617C22×D3—68no—
618C22×D3—68no—
619C22×D3—68no—
620C22×D3—68no—
621C22×D3—94no—
622C22×D3—91no—
623C22×D3—94no—
624C22×D3—91no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3—184no—
628C22×D3—184no—
629C22×D3—182no—
630C22×D3—182no—
631C22×D3—188no—
632C22×D3—188no—
633C22×D3—182no—
634C22×D3—188no—
635C22×D3—188no—
636C22×D3—182no—
637C22×D3—368no—
638C22×D3—368no—
639C22×D3—361no—
640C22×D3—364no—
641C22×D3—364no—
642C22×D3—361no—
643C22×D3—368no—
644C22×D3C22×C3⋊D311yescharacteristic
645C3×D4—28no—
646C3×D4—22no—
647C3×D4—48no—
648C3×D4—68no—
649C3×D4—68no—
650C3×D4—94no—
651C3×D4—182no—
652C3×D4—182no—
653C2×C3×C4—24no—
654C2×C3×C4—34no—
655C2×C3×C4—34no—
656C2×C3×C4—34no—
657C2×C3×C4—68no—
658C2×C3×C4—91no—
659C2×C3×C4—182no—
660C2×C3×C4C2×D3214yes—
661C2×C3×C4C22×C3⋊D311yescharacteristic
662#67—22no—
663#67—22no—
664#67—316no—
665#67—68no—
666#67—94no—
667#67—182no—
668#67—182no—
669#67—182no—
670#67—188no—
671#67—182no—
672#67—188no—
673#67—182no—
674#67—188no—
675#67—182no—
676#67—368no—
677#67—361no—
678#67—364no—
679#67—364no—
680#67—361no—
681#67—368no—
682C2×Dic3—22no—
683C2×Dic3—34no—
684C2×Dic3—94no—
685C2×Dic3—94no—
686C2×Dic3—91no—
687C2×Dic3—91no—
688C2×Dic3—184no—
689C2×Dic3—184no—
690C2×Dic3—182no—
691C2×Dic3C22×C3⋊D311yescharacteristic
692C2×Dic3C22×C3⋊D311yescharacteristic
693C2×Dic3C22×C3⋊D311yescharacteristic
694D12—68no—
695D12—916no—
696D12—188no—
697D12—188no—
698D12—188no—
699D12—188no—
700D12—182no—
701C4×D3—68no—
702C4×D3—182no—
703C4×D3—188no—
704C4×D3—188no—
705C2×C32—22no—
706C2×C32—24no—
707C2×C32—24no—
708C2×C32—24no—
709C2×C32—28no—
710C2×C32—48no—
711C2×C32—41no—
712C2×C32—44no—
713C2×C32—84no—
714C2×C32—121no—
715C2×C32C2×D3×D414yes—
716C2×C32C2×D3×D414yes—
717C2×C32C2×D3×D411yescharacteristic
718C2×C32#100411yescharacteristic
719C2×C32#100914yes—
720C2×C32C22×#6711yescharacteristic
721C3⋊D3—22no—
722C3⋊D3—22no—
723C3⋊D3—41no—
724C3⋊D3—62no—
725C3⋊D3—68no—
726C3⋊D3—128no—
727C3⋊D3—128no—
728C3⋊D3—121no—
729C3⋊D3—124no—
730C3×D3—44no—
731C3×D3—68no—
732C3×D3—68no—
733C3×D3—124no—
734C24—91no—
735C24—91no—
736C24—271no—
737C24—271no—
738C2×D4—31no—
739C2×D4—31no—
740C2×D4—91no—
741C2×D4—91no—
742C2×D4—91no—
743C2×D4—184no—
744C2×D4—271no—
745C2×D4—271no—
746C2×D4—271no—
747C2×D4—271no—
748C2×D4—271no—
749C2×D4—271no—
750C2×D4—271no—
751C2×D4—271no—
752C2×D4—271no—
753C2×D4—271no—
754C2×D4—544no—
755C2×D4—544no—
756C2×D4—544no—
757C2×D4D3×C3⋊D311yescharacteristic, complemented
758C22×C4—31no—
759C22×C4—91no—
760C22×C4—271no—
761C22×C4—271no—
762C4⋊C4—31no—
763C4⋊C4—271no—
764C22⋊C4—31no—
765C22⋊C4—31no—
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—21no—
776C22×C3—21no—
777C22×C3—24no—
778C22×C3—24no—
779C22×C3—24no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—24no—
784C22×C3—28no—
785C22×C3—44no—
786C22×C3—44no—
787C22×C3—44no—
788C22×C3—44no—
789C22×C3—44no—
790C22×C3—64no—
791C22×C3—64no—
792C22×C3—64no—
793C22×C3—92no—
794C22×C3—92no—
795C22×C3—181no—
796C22×C3—181no—
797C22×C3—181no—
798C22×C3—181no—
799C22×C3—181no—
800C22×C3—181no—
801C22×C3—181no—
802C22×C3—364no—
803C22×C3—364no—
804C22×C3D3×#6718yescomplemented
805C22×C3D4×C3⋊D312yescomplemented
806C22×C3C22×D3214yes—
807C22×C3C23×C3⋊D311yescharacteristic
808C2×D3—21no—
809C2×D3—21no—
810C2×D3—21no—
811C2×D3—38no—
812C2×D3—38no—
813C2×D3—64no—
814C2×D3—64no—
815C2×D3—64no—
816C2×D3—64no—
817C2×D3—64no—
818C2×D3—64no—
819C2×D3—64no—
820C2×D3—98no—
821C2×D3—92no—
822C2×D3—1216no—
823C2×D3—1216no—
824C2×D3—188no—
825C2×D3—184no—
826C2×D3—184no—
827C2×D3—181no—
828C2×D3—181no—
829C2×D3—188no—
830C2×D3—184no—
831C2×D3—184no—
832C2×D3—184no—
833C2×D3—181no—
834C2×D3—181no—
835C2×D3—181no—
836C2×D3—364no—
837C2×D3—364no—
838C2×D3—364no—
839C2×D3—364no—
840C2×D3—364no—
841C2×D3—3616no—
842C2×D3—3616no—
843C2×D3—364no—
844C2×D3—3632no—
845C3×C4—24no—
846C3×C4—21no—
847C3×C4—38no—
848C3×C4—44no—
849C3×C4—64no—
850C3×C4—64no—
851C3×C4—92no—
852Dic3—21no—
853Dic3—21no—
854Dic3—38no—
855Dic3—184no—
856Dic3—184no—
857Dic3—181no—
858Dic3—181no—
859Dic3—364no—
860Dic3—364no—
861Dic3D4×C3⋊D312yescomplemented
862C32—24no—
863C32#560914yescomplemented
864C32D4×#6711yescharacteristic, complemented
865C23—31no—
866C23—91no—
867C23—91no—
868C23—91no—
869C23—182no—
870C23—182no—
871C23—182no—
872C23—182no—
873C23—271no—
874C23—271no—
875C23—361no—
876C23—361no—
877C23—542no—
878C23—542no—
879C23—542no—
880C23—542no—
881C23—1081no—
882C23—1081no—
883C23C2×D3×C3⋊D311yescharacteristic
884C23C2×D3×C3⋊D311yescharacteristic
885D4—22no—
886D4—62no—
887D4—62no—
888D4—94no—
889D4—182no—
890D4—182no—
891D4—274no—
892D4—542no—
893D4—542no—
894D4—542no—
895D4—542no—
896D4—542no—
897D4—542no—
898D4—542no—
899D4—1081no—
900D4—1081no—
901C2×C4—31no—
902C2×C4—31no—
903C2×C4—31no—
904C2×C4—62no—
905C2×C4—91no—
906C2×C4—182no—
907C2×C4—271no—
908C2×C4—271no—
909C2×C4—542no—
910C2×C4—542no—
911C2×C4C2×D3×C3⋊D311yescharacteristic
912C2×C3—28no—
913C2×C3—22no—
914C2×C3—24no—
915C2×C3—24no—
916C2×C3—24no—
917C2×C3—48no—
918C2×C3—44no—
919C2×C3—41no—
920C2×C3—84no—
921C2×C3—124no—
922C2×C3—182no—
923C2×C3—182no—
924C2×C3—361no—
925C2×C3D32×D414yes—
926C2×C3#6431414yes—
927C2×C3C2×D3×#6714yes—
928C2×C3C2×D4×C3⋊D311yescharacteristic
929C2×C3C2×D4×C3⋊D311yescharacteristic
930C2×C3#6436611yescharacteristic
931D3—41no—
932D3—68no—
933D3—68no—
934D3—124no—
935D3—188no—
936D3—182no—
937D3—368no—
938D3—368no—
939D3—364no—
940D3—361no—
941C22—21no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—21no—
946C22—61no—
947C22—61no—
948C22—61no—
949C22—92no—
950C22—92no—
951C22—181no—
952C22—181no—
953C22—181no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22—181no—
958C22—272no—
959C22—364no—
960C22—364no—
961C22—541no—
962C22—541no—
963C22—541no—
964C22—541no—
965C22—541no—
966C22—1084no—
967C22—1084no—
968C22C3⋊D3×#6712yescomplemented
969C22C22×D3×C3⋊D311yescharacteristic
970C4—21no—
971C4—32no—
972C4—61no—
973C4—61no—
974C4—92no—
975C4—541no—
976C4—541no—
977C3—24no—
978C3#1059529114yescomplemented
979C3#1059608011yescharacteristic, complemented
980C2—22no—
981C2—41no—
982C2—121no—
983C2—182no—
984C2—182no—
985C2—361no—
986C2—542no—
987C2—1081no—
988C2D3×D4×C3⋊D311yescharacteristic
989C2#1172458911yescharacteristic
990C2C2×C3⋊D3×#6711yescharacteristic
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×C3×D4×C3⋊D3C2semidirect
2. C2×#89039C2semidirect
3. C2×C3⋊D3×#67C2semidirect
4. C22×#6292C2semidirect
5. #11723978C2semidirect
6. C32×#939C2semidirect
7. #11723636C2semidirect
8. #11723634C2semidirect
9. #11723633C2semidirect
10. #11723623C2semidirect
11. Dic3×#638C2semidirect
12. #11723541C2semidirect
13. #11723520C2semidirect
14. #11723512C2semidirect
15. #11723482C2semidirect
18. C23×C3⋊(C3⋊D3)C22semidirect
19. C23×C3×C3⋊D3C22semidirect
20. C23×C3×C3⋊D3C22semidirect
21. C22×D3×C3⋊D3C22semidirect
22. C2×C33×D4C22semidirect
23. C2×#6312C22semidirect
24. C2×#6312C22semidirect
26. C2×C3×#638C22semidirect
28. C2×C3×C4⋊(C3⋊D3)C22semidirect
29. C2×C3×C4×C3⋊D3C22semidirect
30. C2×C32×#67C22semidirect
31. C2×C32×#67C22semidirect
32. C22×C32×Dic3C22semidirect
37. C2×#6292C22semidirect
38. C2×#6292C22semidirect
39. C2×#6292C22semidirect
40. C2×#6292C22semidirect
41. C2×#6291C22semidirect
42. C2×#6290C22semidirect
43. C2×#6290C22semidirect
44. C2×#6289C22semidirect
45. C2×Dic3×C3⋊D3C22semidirect
46. #88864C22semidirect
47. #88859C22semidirect
48. #88859C22semidirect
49. C32×#217C22semidirect
50. C32×(C2×D3)⋊C4C22semidirect
51. C32×Dic3⋊C4C22semidirect
52. #88807C22semidirect
53. #88803C22semidirect
54. #88803C22semidirect
55. #88803C22semidirect
56. Dic3×C3⋊Dic3C22semidirect
59. C2×D4×C3⋊D3D3semidirect
78. C3×#939D3semidirect
115. C3×#638D4semidirect
129. #6292D4semidirect
141. C23×C3⋊D3C2×D3semidirect
142. C23×C3⋊D3C2×D3semidirect
149. C2×C32×D4C2×D3semidirect
150. C2×C32×D4C2×D3semidirect
162. C2×#638C2×D3semidirect
172. C2×C4⋊(C3⋊D3)C2×D3semidirect
175. C2×C4×C3⋊D3C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
179. C2×C3×#67C2×D3semidirect
180. C22×C3×Dic3C2×D3semidirect
214. C3×#217C2×D3semidirect
215. C3×(C2×D3)⋊C4C2×D3semidirect
216. C3×Dic3⋊C4C2×D3semidirect
227. C22×C33C2×D4semidirect
235. C2×C3⋊(C3⋊D3)C2×D4semidirect
245. C2×C3×C3⋊D3C2×D4semidirect
246. C2×C3×C3⋊D3C2×D4semidirect
254. C3×C3⋊Dic3C2×D4semidirect
257. C32×Dic3C2×D4semidirect
272. #939C3⋊D3semidirect
358. #638#67semidirect
424. C2×C3×D4D32semidirect
425. C2×C3×D4C2×C3⋊D3semidirect
448. C2×#67C2×C3⋊D3semidirect
449. C2×#67C2×C3⋊D3semidirect
451. C22×Dic3C2×C3⋊D3semidirect
477. #217C2×C3⋊D3semidirect
487. (C2×D3)⋊C4C2×C3⋊D3semidirect
490. Dic3⋊C4C2×C3⋊D3semidirect
513. C22×C32D3×D4semidirect
514. C22×C32C2×#67semidirect
548. C2×C3⋊D3D3×D4semidirect
549. C2×C3⋊D3C2×#67semidirect
577. C3⋊Dic3C2×#67semidirect
581. C3×Dic3D3×D4semidirect
597. C33D42semidirect
757. C2×D4D3×C3⋊D3semidirect
804. C22×C3D3×#67semidirect
805. C22×C3D4×C3⋊D3semidirect
861. Dic3D4×C3⋊D3semidirect
863. C32#5609semidirect
864. C32D4×#67semidirect
968. C22C3⋊D3×#67semidirect
978. C3#10595291semidirect
979. C3#10596080semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×#890392
C2×C3⋊D3×#672
C22×#62922
#117239782
C32×#9392
#117236362
#117236342
#117236332
#117236232
Dic3×#6382
#117235412
#117235202
#117235122
#117234822
#105960803
#105952913