Finite Group Databasebeta

← #13175939

Subgroups — #13175939

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723922C211yesmaximal, characteristic, complemented
4C3×#64091C211yesmaximal, characteristic, complemented
5C32×#886C211yesmaximal, characteristic, complemented
6#11723637C211yesmaximal, characteristic, complemented
7C2×#88803C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9#11723539C211yesmaximal, characteristic, complemented
10#11723532C211yesmaximal, characteristic, complemented
11#11723530C211yesmaximal, characteristic, complemented
12#11723519C211yesmaximal, characteristic, complemented
13#11723504C211yesmaximal, characteristic, complemented
14#11723502C211yesmaximal, characteristic, complemented
15#11723501C211yesmaximal, characteristic, complemented
16#10596125—31nomaximal
17#10594294—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic, complemented
28C3⋊D3×#67—24no—
29C2×#6293C2211yescharacteristic, complemented
30C2×#6292C2211yescharacteristic
31C2×#6292C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic
33C2×#6290C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35#89031—24no—
36C2×Dic3×C3⋊D3C2211yescharacteristic
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38C33×C22⋊C4C2211yescharacteristic, complemented
39#88859C2211yescharacteristic, complemented
40#88857C2211yescharacteristic, complemented
41C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic
43C3×#3752C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47C32×C4⋊Dic3C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×#3828—31no—
57C2×D3×#67—34no—
58C2×#3804—34no—
59C32×#123—31no—
60#64148—31no—
61C2×#3752—31no—
62#64105—31no—
63#64104—31no—
64#64103—31no—
65#64102—31no—
66#64094—31no—
67#64093—31no—
68#64091—31no—
69#64091D311yescharacteristic, complemented
70#64090—31no—
71#64090—34no—
72#64090—64no—
73C22⋊C4×C3⋊D3—31no—
74C3×#886D314yescomplemented
75C3×#882—34no—
76#63980—34no—
77C2×(C2×D3)⋊Dic3—34no—
78#63922—34no—
79#63921—34no—
80#63916—34no—
81#63915—34no—
82#63899—34no—
83#63898—34no—
84#63885—34no—
85#63854—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3—22no—
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—41no—
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100#6312D414yescomplemented
101C2×C3⋊(C3⋊Dic3)—41no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4×C3⋊(C3⋊D3)—41no—
106C3×#638—22no—
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C3×C4⋊(C3⋊D3)—22no—
109C3×C4⋊(C3⋊D3)—41no—
110C32×#67—22no—
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115#6293—22no—
116#6292—22no—
117#6292—22no—
118#6290—22no—
119#6290—41no—
120#6289—22no—
121Dic3×C3⋊D3—22no—
122Dic3×C3⋊D3—22no—
123#5654—94no—
124#5591—91no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—34no—
128C22×D32—34no—
129C2×C32×D4—31no—
130C22×C32×C4—31no—
131C2×#638—31no—
132C2×#638—34no—
133C2×#638—31no—
134C2×#638—31no—
135C2×#638—64no—
136C2×#638C2×D311yescharacteristic, complemented
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—34no—
139C22×C3⋊Dic3—64no—
140D4×C3⋊D3—64no—
141#3828—64no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
145C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—34no—
151C2×C4×C3⋊D3—64no—
152C2×#634—31no—
153C2×C3×#67—34no—
154C2×C3×#67C2×D314yes—
155C22×C3×Dic3C2×D314yescomplemented
156C2×C3×D12—34no—
157C2×C3×D12—34no—
158D3×#67—616no—
159C2×#627—34no—
160C2×#626—34no—
161C2×#626—34no—
162C2×#625—34no—
163C2×#625—34no—
164C2×#624—34no—
165#3804—616no—
166C2×D3×Dic3—34no—
167C2×D3×Dic3—34no—
168C32×C4⋊C4—31no—
169C32×C4⋊C4—31no—
170C32×C22⋊C4—24no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173C32×C22⋊C4C2×D314yescomplemented
174C32×C22⋊C4C2×D311yescharacteristic, complemented
175#3757—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—31no—
181#3752—31no—
182#3752—34no—
183#3752—64no—
184#3752C2×D311yescharacteristic
185#3752C2×D311yescharacteristic, complemented
186#3750—31no—
187#3750—34no—
188#3750—31no—
189#3750—64no—
190C4×C3⋊Dic3—31no—
191C4×C3⋊Dic3—34no—
192C4×C3⋊Dic3—64no—
193C3×(C2×D3)⋊C4—34no—
194C3×(C2×D3)⋊C4—34no—
195C3×(C2×D3)⋊C4C2×D314yescomplemented
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×C4⋊Dic3C2×D314yescomplemented
198C3×C4⋊Dic3C2×D314yescomplemented
199#3724—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)C2×D412yes—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C3×C3⋊D3—21no—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—21no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—44no—
222C2×C3×C3⋊D3#4112yescomplemented
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)C2×D412yes—
232C3×C3⋊Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×#67—91no—
237C2×#237—91no—
238C2×D3×D4—94no—
239C2×#235—94no—
240C3×#123—34no—
241C3×#120—91no—
242C2×#217—91no—
243#939—94no—
244#939—91no—
245#939—91no—
246#938—91no—
247#937—91no—
248D4×Dic3—91no—
249C2×(C2×D3)⋊C4—94no—
250#896—94no—
251#895—94no—
252#894—94no—
253#893—94no—
254#886C3⋊D311yescharacteristic, complemented
255#885—94no—
256#885—91no—
257#884—94no—
258#883—91no—
259#882—34no—
260#882—94no—
261#67⋊C4—94no—
262#67⋊C4—91no—
263#67⋊C4—184no—
264D3×C22⋊C4—94no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32C22×D314yes—
270C23×C32C22×D311yescharacteristic
271C22×C3⋊D3—22no—
272C22×C3⋊D3—22no—
273C22×C3⋊D3—31no—
274C22×C3⋊D3—34no—
275C22×C3⋊D3—41no—
276C22×C3⋊D3—64no—
277C22×C3⋊D3—62no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—121no—
280C22×C3⋊D3C22×D311yescharacteristic
281C22×C3⋊D3C22×D311yescharacteristic
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3×D3—34no—
284C22×C3×D3—34no—
285C22×C3×D3—34no—
286C22×C3×D3—68no—
287C22×C3×D3—68no—
288C22×C3×D3—124no—
289C22×C3×D3C22×D314yes—
290C2×D32—68no—
291C2×D32—68no—
292C2×D32—124no—
293C32×D4—62no—
294C2×C32×C4—24no—
295C2×C32×C4—24no—
296C2×C32×C4—31no—
297C2×C32×C4—31no—
298C2×C32×C4—31no—
299C2×C32×C4—62no—
300C2×C32×C4C22×D314yes—
301C2×C32×C4C22×D314yes—
302C2×C32×C4C22×D311yescharacteristic
303C2×C32×C4C22×D311yescharacteristic
304#638—22no—
305#638—34no—
306#638—316no—
307#638—616no—
308#638—62no—
309#638—121no—
310C2×C3⋊Dic3—31no—
311C2×C3⋊Dic3—31no—
312C2×C3⋊Dic3—31no—
313C2×C3⋊Dic3—34no—
314C2×C3⋊Dic3—34no—
315C2×C3⋊Dic3—34no—
316C2×C3⋊Dic3—64no—
317C2×C3⋊Dic3—64no—
318C2×C3⋊Dic3—64no—
319C2×C3⋊Dic3—121no—
320C2×C3⋊Dic3—124no—
321C2×C3⋊Dic3—128no—
322C2×C3⋊Dic3C22×D311yescharacteristic
323C4⋊(C3⋊D3)—22no—
324C4⋊(C3⋊D3)—41no—
325C4⋊(C3⋊D3)—62no—
326C4⋊(C3⋊D3)—62no—
327C4×C3⋊D3—62no—
328C4×C3⋊D3—62no—
329C4×C3⋊D3—62no—
330C4×C3⋊D3—121no—
331C4×C3⋊D3—124no—
332C4×C3⋊D3—128no—
333#634—62no—
334C3×#67—28no—
335C3×#67—68no—
336C2×C3×Dic3—28no—
337C2×C3×Dic3—34no—
338C2×C3×Dic3C22×D314yes—
339C2×C3×Dic3C22×D314yes—
340C2×C3×Dic3C22×D314yes—
341C3×D12—68no—
342C3×D12—124no—
343#627—68no—
344#626—68no—
345#626—68no—
346#625—68no—
347#625—124no—
348#624—68no—
349D3×Dic3—68no—
350D3×Dic3—68no—
351#546—271noSylow
352C2×C33—22no—
353C2×C33C22×D411yescharacteristic
354C2×C33C2×#4111yescharacteristic
355C2×C33H(5,𝔽2)11yescharacteristic
356C3⋊(C3⋊D3)—22no—
357C3×C3⋊D3—22no—
358C3×C3⋊D3—41no—
359C3×C3⋊D3—41no—
360C32×D3—41no—
361C24×C3—91no—
362C23×D3—34no—
363C23×D3—94no—
364C23×D3—91no—
365C2×C3×D4—34no—
366C2×C3×D4—91no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C22×C3×C4—34no—
370C2×#67—34no—
371C2×#67—94no—
372C2×#67—91no—
373C2×#67—94no—
374C2×#67—91no—
375C2×#67—94no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—184no—
380C2×#67—184no—
381C2×#67C2×C3⋊D311yescharacteristic
382C22×Dic3—94no—
383C22×Dic3—91no—
384C22×Dic3—91no—
385C22×Dic3—91no—
386C22×Dic3—184no—
387C22×Dic3C2×C3⋊D311yescharacteristic, complemented
388#237—184no—
389D3×D4—1816no—
390#235—1816no—
391C2×D12—34no—
392C2×D12—34no—
393C2×D12—94no—
394C2×D12—94no—
395C2×C4×D3—94no—
396C2×C4×D3—94no—
397C2×C4×D3—94no—
398C2×C4×D3—91no—
399C2×C4×D3—94no—
400C2×C4×D3—91no—
401C2×C4×D3—184no—
402C2×Dic6—94no—
403C2×Dic6—91no—
404C3×C4⋊C4—34no—
405C3×C4⋊C4—34no—
406C3×C22⋊C4—24no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4D3214yescomplemented
412C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
413#217—94no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—94no—
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—94no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—184no—
430(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
431(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
432C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
433C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
434Dic3⋊C4—94no—
435Dic3⋊C4—94no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—184no—
439C4×Dic3—94no—
440C4×Dic3—91no—
441C4×Dic3—184no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—24no—
445C22×C32—28no—
446C22×C32—24no—
447C22×C32—24no—
448C22×C32—44no—
449C22×C32—44no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32D3×D418yes—
454C22×C32D3×D412yes—
455C22×C32C23×D314yes—
456C22×C32C23×D311yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—32no—
466C2×C3⋊D3—38no—
467C2×C3⋊D3—44no—
468C2×C3⋊D3—68no—
469C2×C3⋊D3—61no—
470C2×C3⋊D3—61no—
471C2×C3⋊D3—64no—
472C2×C3⋊D3—64no—
473C2×C3⋊D3—124no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3—124no—
476C2×C3⋊D3#23712yescomplemented
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C2×C3×D3—38no—
481C2×C3×D3—64no—
482C2×C3×D3—64no—
483C2×C3×D3—64no—
484C2×C3×D3—64no—
485C2×C3×D3—64no—
486C2×C3×D3—64no—
487C2×C3×D3—64no—
488C2×C3×D3—64no—
489C2×C3×D3—1216no—
490D32—1216no—
491C32×C4—21no—
492C32×C4—21no—
493C32×C4—24no—
494C32×C4—24no—
495C32×C4—44no—
496C32×C4—44no—
497C32×C4—61no—
498C32×C4—61no—
499C32×C4—61no—
500C3⋊Dic3—21no—
501C3⋊Dic3—32no—
502C3⋊Dic3—38no—
503C3⋊Dic3—68no—
504C3⋊Dic3—68no—
505C3⋊Dic3—61no—
506C3⋊Dic3—61no—
507C3⋊Dic3—64no—
508C3⋊Dic3—64no—
509C3⋊Dic3—124no—
510C3×Dic3—24no—
511C3×Dic3—24no—
512C3×Dic3—24no—
513C3×Dic3—64no—
514C2×#41—271no—
515C22×D4—271no—
516#124—271no—
517#123—31no—
518#123—271no—
519C22⋊Q8—271no—
520#121—271no—
521#121—271no—
522#121—271no—
523#120—91no—
524#120—271no—
525C4×D4—271no—
526C4×D4—271no—
527C2×C22⋊C4—271no—
528C2×C22⋊C4—271no—
529C33#54611yescharacteristic, complemented, Sylow
530C23×C3—24no—
531C23×C3—34no—
532C23×C3—91no—
533C23×C3—91no—
534C23×C3—91no—
535C23×C3—182no—
536C23×C3—182no—
537C23×C3—361no—
538C23×C3C2×D3214yes—
539C23×C3C22×C3⋊D311yescharacteristic
540C22×D3—34no—
541C22×D3—34no—
542C22×D3—34no—
543C22×D3—68no—
544C22×D3—68no—
545C22×D3—94no—
546C22×D3—91no—
547C22×D3—124no—
548C22×D3—184no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—188no—
552C22×D3—188no—
553C22×D3—361no—
554C22×D3—364no—
555C22×D3C22×C3⋊D311yescharacteristic
556C3×D4—68no—
557C3×D4—182no—
558C3×D4—182no—
559C3×D4—361no—
560C2×C3×C4—24no—
561C2×C3×C4—24no—
562C2×C3×C4—34no—
563C2×C3×C4—34no—
564C2×C3×C4—34no—
565C2×C3×C4—68no—
566C2×C3×C4—91no—
567C2×C3×C4C2×D3214yes—
568C2×C3×C4C2×D3214yes—
569C2×C3×C4C22×C3⋊D311yescharacteristic
570C2×C3×C4C22×C3⋊D311yescharacteristic
571#67—22no—
572#67—68no—
573#67—916no—
574#67—94no—
575#67—1816no—
576#67—182no—
577#67—182no—
578#67—182no—
579#67—188no—
580#67—361no—
581#67—364no—
582C2×Dic3—22no—
583C2×Dic3—34no—
584C2×Dic3—94no—
585C2×Dic3—91no—
586C2×Dic3—94no—
587C2×Dic3—94no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—184no—
591C2×Dic3—184no—
592C2×Dic3—184no—
593C2×Dic3—182no—
594C2×Dic3—182no—
595C2×Dic3—364no—
596C2×Dic3—361no—
597C2×Dic3—368no—
598C2×Dic3C22×C3⋊D311yescharacteristic
599C2×Dic3C22×C3⋊D311yescharacteristic
600C2×Dic3C22×C3⋊D311yescharacteristic
601D12—68no—
602D12—124no—
603D12—188no—
604D12—188no—
605C4×D3—182no—
606C4×D3—188no—
607C4×D3—188no—
608C4×D3—188no—
609C4×D3—364no—
610C4×D3—361no—
611C4×D3—368no—
612Dic6—182no—
613Dic6—188no—
614C2×C32—22no—
615C2×C32—24no—
616C2×C32—24no—
617C2×C32—24no—
618C2×C32—28no—
619C2×C32—48no—
620C2×C32—121no—
621C2×C32C2×D3×D414yes—
622C2×C32C2×D3×D411yescharacteristic
623C2×C32C2×#23711yescharacteristic
624C2×C32#100411yescharacteristic
625C2×C32D3×#4114yes—
626C2×C32#100914yes—
627C3⋊D3—22no—
628C3⋊D3—41no—
629C3⋊D3—41no—
630C3⋊D3—62no—
631C3⋊D3—68no—
632C3⋊D3—128no—
633C3×D3—44no—
634C3×D3—68no—
635C3×D3—124no—
636C3×D3—124no—
637C24—91no—
638C24—271no—
639#41—544no—
640C2×Q8—271no—
641C2×D4—31no—
642C2×D4—91no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
650C2×D4—544no—
651C22×C4—31no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C4⋊C4—31no—
658C4⋊C4—31no—
659C4⋊C4—271no—
660C4⋊C4—271no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—91no—
664C22⋊C4—91no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4D3×C3⋊D311yescharacteristic, complemented
673C42—271no—
674C22×C3—24no—
675C22×C3—24no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—24no—
679C22×C3—28no—
680C22×C3—44no—
681C22×C3—44no—
682C22×C3—64no—
683C22×C3—64no—
684C22×C3—64no—
685C22×C3—92no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—364no—
695C22×C3#380218yes—
696C22×C3D4×C3⋊D312yes—
697C22×C3C22×D3214yes—
698C22×C3C23×C3⋊D311yescharacteristic
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—38no—
703C2×D3—64no—
704C2×D3—64no—
705C2×D3—64no—
706C2×D3—64no—
707C2×D3—64no—
708C2×D3—64no—
709C2×D3—64no—
710C2×D3—64no—
711C2×D3—98no—
712C2×D3—92no—
713C2×D3—1216no—
714C2×D3—188no—
715C2×D3—184no—
716C2×D3—184no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—364no—
720C2×D3—364no—
721C2×D3—364no—
722C2×D3—3616no—
723C3×C4—24no—
724C3×C4—24no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—44no—
728C3×C4—44no—
729C3×C4—64no—
730C3×C4—64no—
731C3×C4—64no—
732C3×C4—181no—
733Dic3—21no—
734Dic3—21no—
735Dic3—21no—
736Dic3—64no—
737Dic3—98no—
738Dic3—92no—
739Dic3—188no—
740Dic3—188no—
741Dic3—184no—
742Dic3—184no—
743Dic3—181no—
744Dic3—181no—
745Dic3—364no—
746C32—24no—
747C32#559111yescharacteristic, complemented
748C32#565414yescomplemented
749C23—31no—
750C23—91no—
751C23—91no—
752C23—91no—
753C23—182no—
754C23—182no—
755C23—271no—
756C23—361no—
757C23—542no—
758C23—542no—
759C23—1081no—
760C23C2×D3×C3⋊D311yescharacteristic
761Q8—542no—
762D4—62no—
763D4—182no—
764D4—182no—
765D4—274no—
766D4—361no—
767D4—542no—
768D4—542no—
769D4—542no—
770D4—1081no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—62no—
775C2×C4—91no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—271no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—1081no—
783C2×C4—1081no—
784C2×C4C2×D3×C3⋊D311yescharacteristic
785C2×C4C2×D3×C3⋊D311yescharacteristic
786C2×C3—22no—
787C2×C3—28no—
788C2×C3—24no—
789C2×C3—24no—
790C2×C3—24no—
791C2×C3—48no—
792C2×C3—124no—
793C2×C3—182no—
794C2×C3—361no—
795C2×C3—361no—
796C2×C3C2×#380214yes—
797C2×C3D3×#23714yes—
798C2×C3#6431414yes—
799C2×C3C2×D4×C3⋊D311yescharacteristic
800C2×C3#41×C3⋊D311yescharacteristic
801C2×C3#6436611yescharacteristic
802D3—41no—
803D3—68no—
804D3—124no—
805D3—124no—
806D3—182no—
807D3—188no—
808D3—368no—
809C22—21no—
810C22—21no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—92no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—181no—
823C22—272no—
824C22—364no—
825C22—541no—
826C22—541no—
827C22—1084no—
828C22#8902612yes—
829C22C22×D3×C3⋊D311yescharacteristic
830C4—21no—
831C4—21no—
832C4—61no—
833C4—61no—
834C4—61no—
835C4—181no—
836C4—272no—
837C4—541no—
838C4—541no—
839C3—24no—
840C3#1059429414yescomplemented
841C3#1059612511yescharacteristic, complemented
842C2—22no—
843C2—121no—
844C2—182no—
845C2—361no—
846C2—361no—
847C2—542no—
848C2C2×#8902611yescharacteristic
849C2C3⋊D3×#23711yescharacteristic
850C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×#89031C2semidirect
3. #11723922C2semidirect
4. C3×#64091C2semidirect
5. C32×#886C2semidirect
6. #11723637C2semidirect
7. C2×#88803C2semidirect
8. #11723541C2semidirect
9. #11723539C2semidirect
10. #11723532C2semidirect
11. #11723530C2semidirect
12. #11723519C2semidirect
13. #11723504C2semidirect
14. #11723502C2semidirect
15. #11723501C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×#638C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
27. C22×C32×Dic3C22semidirect
29. C2×#6293C22semidirect
31. C2×#6292C22semidirect
33. C2×#6290C22semidirect
34. C2×#6289C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
38. C33×C22⋊C4C22semidirect
39. #88859C22semidirect
40. #88857C22semidirect
41. C4×C3⋊(C3⋊Dic3)C22semidirect
43. C3×#3752C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. C32×C4⋊Dic3C22semidirect
48. #88806C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
69. #64091D3semidirect
74. C3×#886D3semidirect
100. #6312D4semidirect
136. C2×#638C2×D3semidirect
145. C2×C4⋊(C3⋊D3)C2×D3semidirect
155. C22×C3×Dic3C2×D3semidirect
173. C32×C22⋊C4C2×D3semidirect
174. C32×C22⋊C4C2×D3semidirect
185. #3752C2×D3semidirect
195. C3×(C2×D3)⋊C4C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
197. C3×C4⋊Dic3C2×D3semidirect
198. C3×C4⋊Dic3C2×D3semidirect
222. C2×C3×C3⋊D3#41semidirect
254. #886C3⋊D3semidirect
387. C22×Dic3C2×C3⋊D3semidirect
411. C3×C22⋊C4D32semidirect
412. C3×C22⋊C4C2×C3⋊D3semidirect
430. (C2×D3)⋊C4C2×C3⋊D3semidirect
431. (C2×D3)⋊C4C2×C3⋊D3semidirect
432. C4⋊Dic3C2×C3⋊D3semidirect
433. C4⋊Dic3C2×C3⋊D3semidirect
476. C2×C3⋊D3#237semidirect
529. C33#546semidirect
672. C22⋊C4D3×C3⋊D3semidirect
747. C32#5591semidirect
748. C32#5654semidirect
840. C3#10594294semidirect
841. C3#10596125semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#890312
#117239222
C3×#640912
C32×#8862
#117236372
C2×#888032
#117235412
#117235392
#117235322
#117235302
#117235192
#117235042
#117235022
#117235012
#105961253
#105942943