Finite Group Databasebeta

← #13177323

Subgroups — #13177323

Order 1728.

2532 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic, complemented
3C2×#88859C211yesmaximal, characteristic, complemented
4C3×#64138C211yesmaximal, characteristic, complemented
5#11723638C211yesmaximal, characteristic, complemented
6#11723637C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#11723540C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10#11723514C211yesmaximal, characteristic, complemented
11#11723510C211yesmaximal, characteristic, complemented
12#11723477C211yesmaximal, characteristic, complemented
13#11723475C211yesmaximal, characteristic, complemented
14#11723414C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596300—31nomaximal
17#10595068—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C32×#235—24no—
26C2×C32×D12C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28C2×C32×C4×D3C2211yescharacteristic, complemented
29C2×C32×Dic6C2211yescharacteristic, complemented
30#89039—24no—
31C2×#6292C2211yescharacteristic
32C2×#6291C2211yescharacteristic
33C2×#6291C2211yescharacteristic
34C2×#6291C2211yescharacteristic, complemented
35C2×#6290C2211yescharacteristic, complemented
36C2×#6289C2211yescharacteristic
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88859C2211yescharacteristic
39#88859C2211yescharacteristic
40#88859C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3750C2211yescharacteristic, complemented
46C3×#3750C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×C32×#41—31no—
56C2×D4×C3⋊D3—31no—
57C2×C3×#235D314yescomplemented
58C2×#3811—34no—
59#64156—31no—
60#64155—31no—
61#64148—31no—
62#64148—31no—
63#64146—31no—
64#64146—31no—
65D4×C3⋊Dic3—31no—
66#64139—31no—
67#64138—31no—
68#64138D311yescharacteristic, complemented
69C4×#638—31no—
70C2×#3752—31no—
71C2×#3752—31no—
72C2×#3752—34no—
73C2×#3752—64no—
74C3×#929—34no—
75#63981—34no—
76#63980—34no—
77#67⋊Dic3—34no—
78#63922—34no—
79D3×(C2×D3)⋊C4—34no—
80#63907—34no—
81#63906—34no—
82#63904—34no—
83#63888—34no—
84#63886—34no—
85#63850—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—41no—
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)—41no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C3×#638—22no—
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C32×#67—22no—
109C32×#67D414yescomplemented
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C32×D12—22no—
113C32×C4×D3—22no—
114C32×C4×D3—22no—
115C32×Dic6—22no—
116#6292—22no—
117#6291—22no—
118#6291—22no—
119#6291—41no—
120#6290—41no—
121#6289—22no—
122D3×C3⋊Dic3—41no—
123#5829—94no—
124#5654—91no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3—34no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3—64no—
129C22×D32—34no—
130C32×#41—64no—
131C2×C32×Q8—31no—
132C2×C32×D4—31no—
133C2×C32×D4—31no—
134C2×C32×D4—31no—
135C22×C32×C4—24no—
136C22×C32×C4—31no—
137C22×C32×C4—31no—
138C22×C32×C4C2×D314yescomplemented
139C22×C32×C4C2×D311yescharacteristic, complemented
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638C2×D311yescharacteristic
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—34no—
147C22×C3⋊Dic3—31no—
148C22×C3⋊Dic3—64no—
149D4×C3⋊D3—64no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4×C3⋊D3—31no—
152C2×C3×#67—34no—
153C2×C3×#67C2×D314yes—
154C2×C3×#67C2×D314yescomplemented
155C3×#235—216no—
156C2×C3×D12C2×D314yescomplemented
157C2×C3×C4×D3C2×D314yescomplemented
158C2×C3×C4×D3C2×D314yescomplemented
159C2×C3×Dic6C2×D314yescomplemented
160#3811—616no—
161C2×#626—34no—
162C2×#626—34no—
163C2×#626—34no—
164C2×#626—34no—
165C2×#625—34no—
166C2×#624—34no—
167C2×D3×Dic3—34no—
168#3757—31no—
169#3757—31no—
170#3757C2×D311yescharacteristic, complemented
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—34no—
177#3752—34no—
178#3752—34no—
179#3752—34no—
180#3752—31no—
181#3752—31no—
182#3752—64no—
183#3752—64no—
184#3752—64no—
185#3752—64no—
186#3752C2×D311yescharacteristic, complemented
187#3752C2×D311yescharacteristic, complemented
188C4⋊(C3⋊Dic3)—31no—
189#3750—31no—
190#3750C2×D311yescharacteristic, complemented
191#3750C2×D311yescharacteristic, complemented
192C4×C3⋊Dic3—31no—
193C3×#217—34no—
194C3×(C2×D3)⋊C4—34no—
195C3×(C2×D3)⋊C4—34no—
196C3×Dic3⋊C4—34no—
197C3×Dic3⋊C4—34no—
198#3724—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201#3722—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—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)—21no—
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—44no—
216C2×C3⋊(C3⋊D3)#4112yescomplemented
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—21no—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3C2×D412yes—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3C2×D412yes—
236C2×C3×#41—34no—
237C2×D3×D4—94no—
238C2×D3×D4—91no—
239C2×#235C3⋊D311yescharacteristic, complemented
240C3×#123—91no—
241#947—94no—
242#946—94no—
243#939—94no—
244#939—94no—
245#939—91no—
246#937—94no—
247#937—94no—
248D4×Dic3—94no—
249#930—94no—
250#929—34no—
251#929—94no—
252C4×#67—94no—
253C2×(C2×D3)⋊C4—94no—
254C2×(C2×D3)⋊C4—94no—
255C2×(C2×D3)⋊C4—91no—
256C2×(C2×D3)⋊C4—184no—
257#896—91no—
258#895—91no—
259#894—91no—
260#893—91no—
261#885—91no—
262#884—91no—
263#882—91no—
264#882—91no—
265#67⋊C4—91no—
266D3×C22⋊C4—91no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32—31no—
270C23×C32C22×D314yes—
271C23×C32C22×D311yescharacteristic
272C22×C3⋊D3—31no—
273C22×C3⋊D3—31no—
274C22×C3⋊D3—34no—
275C22×C3⋊D3—34no—
276C22×C3⋊D3—64no—
277C22×C3⋊D3—64no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—62no—
280C22×C3⋊D3—62no—
281C22×C3⋊D3—68no—
282C22×C3⋊D3—616no—
283C22×C3⋊D3—62no—
284C22×C3⋊D3—68no—
285C22×C3⋊D3—128no—
286C22×C3⋊D3—121no—
287C22×C3⋊D3—121no—
288C22×C3⋊D3—124no—
289C22×C3⋊D3—128no—
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—34no—
292C22×C3×D3C22×D314yes—
293C22×C3×D3C22×D314yes—
294C2×D32—68no—
295C2×D32—68no—
296C2×D32—124no—
297C32×Q8—62no—
298C32×D4—34no—
299C32×D4—62no—
300C32×D4—62no—
301C2×C32×C4—22no—
302C2×C32×C4—24no—
303C2×C32×C4—24no—
304C2×C32×C4—28no—
305C2×C32×C4—31no—
306C2×C32×C4—31no—
307C2×C32×C4—48no—
308C2×C32×C4—62no—
309C2×C32×C4—62no—
310C2×C32×C4C22×D314yes—
311C2×C32×C4C22×D314yes—
312C2×C32×C4C22×D311yescharacteristic
313C2×C32×C4C22×D311yescharacteristic
314#638—22no—
315#638—62no—
316#638—62no—
317#638—121no—
318#638—121no—
319C2×C3⋊Dic3—31no—
320C2×C3⋊Dic3—31no—
321C2×C3⋊Dic3—34no—
322C2×C3⋊Dic3—34no—
323C2×C3⋊Dic3—64no—
324C2×C3⋊Dic3—64no—
325C2×C3⋊Dic3—121no—
326C2×C3⋊Dic3—121no—
327C2×C3⋊Dic3—124no—
328C2×C3⋊Dic3—128no—
329C2×C3⋊Dic3C22×D311yescharacteristic
330C2×C3⋊Dic3C22×D311yescharacteristic
331C2×C3⋊Dic3C22×D311yescharacteristic
332C4⋊(C3⋊D3)—62no—
333C4×C3⋊D3—62no—
334C3×#67—28no—
335C3×#67—68no—
336C3×#67#67116yescomplemented
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3C22×D314yes—
341C2×C3×Dic3C22×D314yes—
342C3×D12—28no—
343C3×C4×D3—28no—
344C3×C4×D3—28no—
345C3×Dic6—28no—
346#626—68no—
347#626—68no—
348#626—68no—
349#626—124no—
350#625—124no—
351#624—68no—
352D3×Dic3—124no—
353#546—271noSylow
354C2×C33—22no—
355C2×C33C22×D411yescharacteristic
356C2×C33C2×#4111yescharacteristic
357C2×C33H(5,𝔽2)11yescharacteristic
358C3⋊(C3⋊D3)—22no—
359C3⋊(C3⋊D3)—41no—
360C3×C3⋊D3—41no—
361C32×D3—22no—
362C32×D3—41no—
363C23×D3—94no—
364C23×D3—94no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—184no—
368C3×#41—616no—
369C2×C3×Q8—34no—
370C2×C3×D4—34no—
371C2×C3×D4—34no—
372C2×C3×D4—34no—
373C2×C3×D4—91no—
374C22×C3×C4—24no—
375C22×C3×C4—34no—
376C22×C3×C4—34no—
377C22×C3×C4D3214yescomplemented
378C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
379C2×#67—34no—
380C2×#67—94no—
381C2×#67—94no—
382C2×#67—94no—
383C2×#67—94no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67C2×C3⋊D311yescharacteristic
387C2×#67C2×C3⋊D311yescharacteristic, complemented
388C22×Dic3—94no—
389C22×Dic3—94no—
390C22×Dic3—91no—
391C22×Dic3—184no—
392D3×D4—1816no—
393D3×D4—184no—
394#235—24no—
395C2×D12—94no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12—91no—
399C2×D12C2×C3⋊D311yescharacteristic, complemented
400C2×C4×D3—94no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
404C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
405C2×Dic6C2×C3⋊D311yescharacteristic, complemented
406C3×C4⋊C4—91no—
407C3×C4⋊C4—91no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411#217—34no—
412#217—94no—
413#217—94no—
414#217—91no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—94no—
418(C2×D3)⋊C4—94no—
419(C2×D3)⋊C4—94no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
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—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—184no—
433(C2×D3)⋊C4—184no—
434(C2×D3)⋊C4—184no—
435(C2×D3)⋊C4—184no—
436C4⋊Dic3—94no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—94no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442C4×Dic3—94no—
443C4×Dic3—91no—
444C22×C32—28no—
445C22×C32—28no—
446C22×C32—24no—
447C22×C32—21no—
448C22×C32—24no—
449C22×C32—21no—
450C22×C32—24no—
451C22×C32—28no—
452C22×C32—32no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32—61no—
457C22×C32—61no—
458C22×C32D3×D412yes—
459C22×C32C2×#6718yes—
460C22×C32C23×D314yes—
461C22×C32C23×D311yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—32no—
466C2×C3⋊D3—38no—
467C2×C3⋊D3—68no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—61no—
470C2×C3⋊D3—68no—
471C2×C3⋊D3—61no—
472C2×C3⋊D3—64no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—61no—
475C2×C3⋊D3—64no—
476C2×C3⋊D3—64no—
477C2×C3⋊D3—64no—
478C2×C3⋊D3—64no—
479C2×C3⋊D3—124no—
480C2×C3⋊D3—124no—
481C2×C3⋊D3—124no—
482C2×C3⋊D3—124no—
483C2×C3⋊D3—124no—
484C2×C3⋊D3—124no—
485C2×C3⋊D3—1216no—
486C2×C3⋊D3—1232no—
487C2×C3×D3—24no—
488C2×C3×D3—24no—
489C2×C3×D3—24no—
490C2×C3×D3—24no—
491C2×C3×D3—24no—
492C2×C3×D3—64no—
493C2×C3×D3—64no—
494C2×C3×D3—64no—
495C2×C3×D3C2×#6718yes—
496D32—1216no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—24no—
500C32×C4—24no—
501C32×C4—32no—
502C32×C4—44no—
503C32×C4—44no—
504C32×C4—61no—
505C3⋊Dic3—21no—
506C3⋊Dic3—21no—
507C3⋊Dic3—21no—
508C3⋊Dic3—61no—
509C3⋊Dic3—61no—
510C3⋊Dic3—64no—
511C3⋊Dic3—64no—
512C3⋊Dic3—124no—
513C3⋊Dic3—124no—
514C3×Dic3—24no—
515C3×Dic3—64no—
516C3×Dic3—64no—
517C3×Dic3—64no—
518C3×Dic3C2×#6718yes—
519C2×#41—31no—
520C22×D4—271no—
521#124—271no—
522#123—91no—
523#123—271no—
524C22⋊Q8—271no—
525#121—271no—
526#121—271no—
527#121—271no—
528#120—271no—
529#120—271no—
530C4×D4—271no—
531C4×D4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C33#54611yescharacteristic, complemented, Sylow
535C23×C3—24no—
536C23×C3—34no—
537C23×C3—34no—
538C23×C3—91no—
539C23×C3C2×D3214yes—
540C23×C3C22×C3⋊D311yescharacteristic
541C22×D3—34no—
542C22×D3—94no—
543C22×D3—91no—
544C22×D3—94no—
545C22×D3—91no—
546C22×D3—184no—
547C22×D3—184no—
548C22×D3—182no—
549C22×D3—188no—
550C22×D3—188no—
551C22×D3—188no—
552C22×D3—182no—
553C22×D3—1816no—
554C22×D3—188no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—368no—
558C22×D3—361no—
559C22×D3—364no—
560C22×D3—364no—
561C22×D3—361no—
562C22×D3—368no—
563C22×D3C22×C3⋊D311yescharacteristic
564C22×D3C22×C3⋊D311yescharacteristic
565C3×Q8—68no—
566C3×D4—316no—
567C3×D4—68no—
568C3×D4—68no—
569C3×D4—182no—
570C2×C3×C4—28no—
571C2×C3×C4—22no—
572C2×C3×C4—24no—
573C2×C3×C4—24no—
574C2×C3×C4—34no—
575C2×C3×C4—34no—
576C2×C3×C4—48no—
577C2×C3×C4—68no—
578C2×C3×C4—68no—
579C2×C3×C4—91no—
580C2×C3×C4—91no—
581C2×C3×C4—91no—
582C2×C3×C4C2×D3214yes—
583C2×C3×C4C2×D3214yes—
584C2×C3×C4C22×C3⋊D311yescharacteristic
585C2×C3×C4C22×C3⋊D311yescharacteristic
586#67—22no—
587#67—68no—
588#67—188no—
589#67—188no—
590#67—182no—
591#67—364no—
592#67—361no—
593#67—364no—
594#67#63814yescomplemented
595C2×Dic3—34no—
596C2×Dic3—34no—
597C2×Dic3—34no—
598C2×Dic3—94no—
599C2×Dic3—94no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—184no—
603C2×Dic3—184no—
604C2×Dic3—364no—
605C2×Dic3—364no—
606C2×Dic3—361no—
607C2×Dic3—368no—
608C2×Dic3C22×C3⋊D311yescharacteristic
609C2×Dic3C22×C3⋊D311yescharacteristic
610D12—22no—
611D12—188no—
612D12—182no—
613D12—182no—
614D12—361no—
615C4×D3—22no—
616C4×D3—22no—
617C4×D3—188no—
618C4×D3—182no—
619C4×D3—361no—
620Dic6—22no—
621C2×C32—216no—
622C2×C32—22no—
623C2×C32—28no—
624C2×C32—24no—
625C2×C32—24no—
626C2×C32—24no—
627C2×C32—62no—
628C2×C32—121no—
629C2×C32C2×D3×D411yescharacteristic
630C2×C32D3×#4114yes—
631C2×C32D3×#4111yescharacteristic
632C2×C32#100914yes—
633C2×C32#100911yescharacteristic
634C2×C32C22×#6714yes—
635C3⋊D3—41no—
636C3⋊D3—62no—
637C3⋊D3—68no—
638C3⋊D3—128no—
639C3⋊D3—128no—
640C3⋊D3—121no—
641C3⋊D3—124no—
642C3×D3—28no—
643C3×D3—44no—
644C3×D3—124no—
645C24—271no—
646C24—271no—
647#41—64no—
648C2×Q8—31no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—91no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—271no—
656C2×D4—271no—
657C2×D4—271no—
658C2×D4—544no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4D3×C3⋊D311yescharacteristic, complemented
665C4⋊C4—91no—
666C4⋊C4—91no—
667C4⋊C4—271no—
668C4⋊C4—271no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C42—271no—
682C22×C3—28no—
683C22×C3—28no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—24no—
689C22×C3—28no—
690C22×C3—38no—
691C22×C3—64no—
692C22×C3—64no—
693C22×C3—64no—
694C22×C3—64no—
695C22×C3—64no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3D3×#6718yes—
700C22×C3C2×#63812yes—
701C22×C3C22×D3214yes—
702C22×C3C23×C3⋊D311yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—64no—
709C2×D3—64no—
710C2×D3—64no—
711C2×D3—98no—
712C2×D3—92no—
713C2×D3—188no—
714C2×D3—184no—
715C2×D3—184no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—188no—
719C2×D3—184no—
720C2×D3—184no—
721C2×D3—184no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—364no—
726C2×D3—364no—
727C2×D3—364no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3—3616no—
731C2×D3—364no—
732C2×D3—3616no—
733C2×D3—3632no—
734C2×D3C2×#63812yes—
735C3×C4—24no—
736C3×C4—24no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—38no—
740C3×C4—44no—
741C3×C4—44no—
742C3×C4—64no—
743C3×C4—181no—
744C3×C4—181no—
745C3×C4—181no—
746Dic3—21no—
747Dic3—64no—
748Dic3—64no—
749Dic3—64no—
750Dic3—184no—
751Dic3—184no—
752Dic3—181no—
753Dic3—181no—
754Dic3—364no—
755Dic3—364no—
756Dic3C2×#63812yes—
757C32—24no—
758C32#565411yescharacteristic, complemented
759C32#582914yescomplemented
760C23—31no—
761C23—31no—
762C23—91no—
763C23—271no—
764C23—271no—
765C23—542no—
766C23—542no—
767C23—542no—
768C23—542no—
769C23—1081no—
770C23—1081no—
771C23C2×D3×C3⋊D311yescharacteristic
772Q8—62no—
773D4—34no—
774D4—62no—
775D4—62no—
776D4—182no—
777D4—542no—
778D4—542no—
779D4—542no—
780D4—1081no—
781D4—1081no—
782C2×C4—22no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—91no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—271no—
791C2×C4—271no—
792C2×C4—542no—
793C2×C4—1081no—
794C2×C4—1081no—
795C2×C4C2×D3×C3⋊D311yescharacteristic
796C2×C4C2×D3×C3⋊D311yescharacteristic
797C2×C3—216no—
798C2×C3—22no—
799C2×C3—28no—
800C2×C3—24no—
801C2×C3—24no—
802C2×C3—24no—
803C2×C3—68no—
804C2×C3—124no—
805C2×C3—361no—
806C2×C3#6430614yes—
807C2×C3#6430814yes—
808C2×C3C2×D3×#6714yes—
809C2×C3#41×C3⋊D311yescharacteristic
810C2×C3#6436611yescharacteristic
811C2×C3C22×#63811yescharacteristic
812D3—22no—
813D3—41no—
814D3—124no—
815D3—182no—
816D3—188no—
817D3—368no—
818D3—368no—
819D3—361no—
820D3—364no—
821C22—21no—
822C22—21no—
823C22—32no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—61no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—272no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22—541no—
837C22—541no—
838C22—1084no—
839C22—1084no—
840C22D3×#63812yes—
841C22C22×D3×C3⋊D311yescharacteristic
842C4—21no—
843C4—21no—
844C4—32no—
845C4—61no—
846C4—181no—
847C4—181no—
848C4—181no—
849C4—541no—
850C4—541no—
851C3—24no—
852C3#1059506814yescomplemented
853C3#1059630011yescharacteristic, complemented
854C2—22no—
855C2—62no—
856C2—121no—
857C2—361no—
858C2—542no—
859C2—1081no—
860C2#1172457811yescharacteristic
861C2#1172458111yescharacteristic
862C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×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×C32×#235C2semidirect
2. C2×#89039C2semidirect
3. C2×#88859C2semidirect
4. C3×#64138C2semidirect
5. #11723638C2semidirect
6. #11723637C2semidirect
7. #67⋊(C3⋊Dic3)C2semidirect
8. #11723540C2semidirect
9. D3×#3752C2semidirect
10. #11723514C2semidirect
11. #11723510C2semidirect
12. #11723477C2semidirect
13. #11723475C2semidirect
14. #11723414C2semidirect
15. #11723392C2semidirect
20. C22×C33×C4C22semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
24. C2×C32×#67C22semidirect
26. C2×C32×D12C22semidirect
27. C2×C32×C4×D3C22semidirect
28. C2×C32×C4×D3C22semidirect
29. C2×C32×Dic6C22semidirect
34. C2×#6291C22semidirect
35. C2×#6290C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
40. #88859C22semidirect
41. #88859C22semidirect
42. C3×#3757C22semidirect
43. C3×#3752C22semidirect
44. C3×#3752C22semidirect
45. C3×#3750C22semidirect
46. C3×#3750C22semidirect
47. #88806C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
50. #88804C22semidirect
51. #88803C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
57. C2×C3×#235D3semidirect
68. #64138D3semidirect
109. C32×#67D4semidirect
138. C22×C32×C4C2×D3semidirect
139. C22×C32×C4C2×D3semidirect
154. C2×C3×#67C2×D3semidirect
156. C2×C3×D12C2×D3semidirect
157. C2×C3×C4×D3C2×D3semidirect
158. C2×C3×C4×D3C2×D3semidirect
159. C2×C3×Dic6C2×D3semidirect
170. #3757C2×D3semidirect
186. #3752C2×D3semidirect
187. #3752C2×D3semidirect
190. #3750C2×D3semidirect
191. #3750C2×D3semidirect
216. C2×C3⋊(C3⋊D3)#41semidirect
239. C2×#235C3⋊D3semidirect
336. C3×#67#67semidirect
377. C22×C3×C4D32semidirect
378. C22×C3×C4C2×C3⋊D3semidirect
387. C2×#67C2×C3⋊D3semidirect
399. C2×D12C2×C3⋊D3semidirect
403. C2×C4×D3C2×C3⋊D3semidirect
404. C2×C4×D3C2×C3⋊D3semidirect
405. C2×Dic6C2×C3⋊D3semidirect
534. C33#546semidirect
594. #67#638semidirect
664. C22×C4D3×C3⋊D3semidirect
758. C32#5654semidirect
759. C32#5829semidirect
852. C3#10595068semidirect
853. C3#10596300semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C2×#890392
C2×#888592
C3×#641382
#117236382
#117236372
#67⋊(C3⋊Dic3)2
#117235402
D3×#37522
#117235142
#117235102
#117234772
#117234752
#117234142
#117233922
#105963003
#105950683