Finite Group Databasebeta

← #13139863

Subgroups — #13139863

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C3⋊D9)⋊C4C211yesmaximal, characteristic
2C2×#88536C211yesmaximal, characteristic
3C2×C9×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C2×#88445C211yesmaximal, characteristic
5C2×Dic3⋊Dic9C211yesmaximal, characteristic, complemented
6C3×C9⋊#95C211yesmaximal, characteristic, complemented
7#11720331C211yesmaximal, characteristic, complemented
8#10591367—31nomaximal
9#10588667—31nomaximal
10C23×C3⋊D9C2211yescharacteristic
11C22×C3×C4×C9C2211yescharacteristic
12C22×C3⋊Dic9C2211yescharacteristic
13C22×C9×Dic3C2211yescharacteristic
14C22×C9×Dic3C2211yescharacteristic
15C22×C3×Dic9C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C2×(C3⋊D9)⋊C4—22no—
18C2×(C3⋊D9)⋊C4—22no—
19C2×(C3⋊D9)⋊C4C414yescomplemented
20#88536—22no—
21C9×Dic3⋊C4—22no—
22#88445—22no—
23Dic3⋊Dic9—22no—
24C22×#624—31no—
25C2×#3752—31no—
26C2×C3×Dic3⋊C4D311yescharacteristic
27C2×Dic3⋊Dic3—31no—
28C2×#3722—31no—
29C22×C4×D9—31no—
30C3×C3⋊#95—31no—
31#63579—31no—
32C2×C9×C4⋊C4—31no—
33C2×(C2×D9)⋊C4—31no—
34C2×(C2×D9)⋊C4—31no—
35C2×(C2×D9)⋊C4—61no—
36C2×C4⋊Dic9—31no—
37C9⋊#95—31no—
38C9⋊#95D311yescharacteristic, complemented
39C23×C3×C9C2311yescharacteristic
40C22×C3⋊D9—21no—
41C22×C3⋊D9—21no—
42C22×C3⋊D9—21no—
43C22×C3⋊D9—21no—
44C22×C3⋊D9C2×C412yes—
45C22×C3⋊D9D412yes—
46C22×C3⋊D9Q812yes—
47C2×C3×C4×C9—21no—
48C2×C3×C4×C9—21no—
49C2×C3×C4×C9—21no—
50C2×C3⋊Dic9—21no—
51C2×C3⋊Dic9—21no—
52C2×C3⋊Dic9—21no—
53C2×C9×Dic3—21no—
54C2×C9×Dic3—21no—
55C2×C9×Dic3—21no—
56C2×C9×Dic3C2×C412yes—
57C2×C9×Dic3D412yes—
58C2×C9×Dic3D412yes—
59C2×C3×Dic9—21no—
60C2×C3×Dic9—21no—
61C2×C3×Dic9—21no—
62C2×C3×Dic9—21no—
63C2×C3×Dic9—21no—
64C2×C3×Dic9C2×C412yes—
65(C3⋊D9)⋊C4—28no—
66#4987—91no—
67#4667—91no—
68C23×C3⋊D3—31no—
69C22×C32×C4C2×D311yescharacteristic
70C22×C3⋊Dic3—31no—
71C22×C3×Dic3—31no—
72C22×C3×Dic3—31no—
73C22×C3×Dic3C2×D311yescharacteristic
74C22×C3×Dic3C2×D311yescharacteristic
75C2×#624—34no—
76C2×#624—62no—
77C2×#624—62no—
78C23×D9—31no—
79C23×D9—61no—
80#3752—62no—
81C3×Dic3⋊C4—22no—
82Dic3⋊Dic3—62no—
83#3722—62no—
84C22×C4×C9—21no—
85C22×C4×C9—31no—
86C22×C4×C9—31no—
87C22×C4×C9C2×D311yescharacteristic
88C22×Dic9—31no—
89C22×Dic9—61no—
90C22×Dic9C2×D311yescharacteristic
91C22×Dic9C2×D311yescharacteristic
92C2×C4×D9—34no—
93C2×C4×D9—62no—
94C2×C4×D9—62no—
95C9×C4⋊C4—62no—
96(C2×D9)⋊C4—62no—
97(C2×D9)⋊C4—62no—
98(C2×D9)⋊C4—64no—
99C4⋊Dic9—62no—
100C22×C3×C9C22×C411yescharacteristic
101C22×C3×C9C2×D411yescharacteristic
102C22×C3×C9C2×D411yescharacteristic
103C22×C3×C9C2×D411yescharacteristic
104C22×C3×C9C2×Q811yescharacteristic
105C22×C3×C9#4111yescharacteristic
106C22×C3×C9#4111yescharacteristic
107C2×C3⋊D9—22no—
108C2×C3⋊D9—22no—
109C2×C3⋊D9—22no—
110C2×C3⋊D9—22no—
111C2×C3⋊D9—22no—
112C2×C3⋊D9—22no—
113C2×C3⋊D9C4⋊C414yescomplemented
114C3×C4×C9—41no—
115C3⋊Dic9—41no—
116C9×Dic3—41no—
117C9×Dic3C22⋊C414yescomplemented
118C3×Dic9—22no—
119C3×Dic9—41no—
120C22×C4×D3—91no—
121C22×C4×D3—91no—
122C2×C3×C4⋊C4—31no—
123C2×(C2×D3)⋊C4—91no—
124C2×(C2×D3)⋊C4—91no—
125C2×(C2×D3)⋊C4—91no—
126C2×(C2×D3)⋊C4—91no—
127C2×(C2×D3)⋊C4—181no—
128C2×C4⋊Dic3—91no—
129C2×Dic3⋊C4—91no—
130C2×Dic3⋊C4D911yescharacteristic, complemented
131C3×#95—91no—
132C3⋊#95—31no—
133C3⋊#95—91no—
134C3⋊#95—91no—
135C23×C32C22×D311yescharacteristic
136C22×C3⋊D3—32no—
137C22×C3⋊D3—32no—
138C22×C3⋊D3—32no—
139C22×C3⋊D3—61no—
140C22×C3⋊D3—61no—
141C22×C3⋊D3—61no—
142C22×C3⋊D3—61no—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C3⋊Dic3—61no—
147C2×C3⋊Dic3—61no—
148C2×C3⋊Dic3—61no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—32no—
153C2×C3×Dic3—61no—
154C2×C3×Dic3—61no—
155C2×C3×Dic3—61no—
156C2×C3×Dic3—61no—
157C2×C3×Dic3—61no—
158C2×C3×Dic3C4×D312yes—
159C2×C3×Dic3D1212yes—
160C2×C3×Dic3#6712yes—
161#624—68no—
162C23×C9—21no—
163C23×C9C22×D311yescharacteristic
164C22×D9—32no—
165C22×D9—32no—
166C22×D9—32no—
167C22×D9—62no—
168C22×D9—62no—
169C22×D9—62no—
170C22×D9—61no—
171C22×D9—61no—
172C22×D9—61no—
173C22×D9—61no—
174C22×D9—121no—
175C22×D9—121no—
176C22×D9—121no—
177C22×D9—121no—
178C2×C4×C9—22no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—32no—
183C2×C4×C9—32no—
184C2×C4×C9—32no—
185C2×C4×C9—41no—
186C2×C4×C9—41no—
187C2×C4×C9—61no—
188C2×C4×C9—61no—
189C2×C4×C9—61no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—62no—
196C2×Dic9—61no—
197C2×Dic9—61no—
198C2×Dic9—61no—
199C2×Dic9—121no—
200C2×Dic9—121no—
201C2×Dic9C4×D312yes—
202C4×D9—68no—
203#380—271noSylow
204C2×C3×C9C2×C22⋊C411yescharacteristic
205C2×C3×C9C2×C4⋊C411yescharacteristic
206C2×C3×C9#11711yescharacteristic
207C2×C3×C9#12111yescharacteristic
208C2×C3×C9#12111yescharacteristic
209C2×C3×C9C22⋊Q811yescharacteristic
210C2×C3×C9C22⋊Q811yescharacteristic
211C3⋊D9—24no—
212C23×D3—91no—
213C23×D3—91no—
214C23×D3—181no—
215C22×C3×C4—21no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—91no—
219C22×C3×C4—91no—
220C22×C3×C4C2×D911yescharacteristic
221C22×C3×C4D3211yescharacteristic
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—91no—
225C22×Dic3—91no—
226C22×Dic3—181no—
227C22×Dic3C2×D911yescharacteristic
228C22×Dic3C2×D911yescharacteristic
229C2×C4×D3—94no—
230C2×C4×D3—94no—
231C2×C4×D3—182no—
232C2×C4×D3—182no—
233C2×C4×D3—182no—
234C2×C4×D3—182no—
235C3×C4⋊C4—62no—
236(C2×D3)⋊C4—182no—
237(C2×D3)⋊C4—182no—
238(C2×D3)⋊C4—182no—
239(C2×D3)⋊C4—182no—
240(C2×D3)⋊C4—184no—
241C4⋊Dic3—182no—
242Dic3⋊C4—22no—
243Dic3⋊C4—182no—
244C22×C32C2×C4×D311yescharacteristic
245C22×C32C2×D1211yescharacteristic
246C22×C32D3×D411yescharacteristic
247C22×C32#23711yescharacteristic
248C22×C32D3×Q811yescharacteristic
249C22×C32#23911yescharacteristic
250C22×C32C2×#6711yescharacteristic
251C2×C3⋊D3—34no—
252C2×C3⋊D3—62no—
253C2×C3⋊D3—62no—
254C2×C3⋊D3—62no—
255C2×C3⋊D3—62no—
256C2×C3⋊D3—62no—
257C2×C3⋊D3—62no—
258C32×C4—41no—
259C3⋊Dic3—121no—
260C3×Dic3—41no—
261C3×Dic3—62no—
262C3×Dic3—121no—
263C3×Dic3(C2×D3)⋊C414yes—
264C22×C9—21no—
265C22×C9—21no—
266C22×C9—21no—
267C22×C9—21no—
268C22×C9—21no—
269C22×C9—21no—
270C22×C9—21no—
271C22×C9C2×C4×D311yescharacteristic
272C22×C9#23511yescharacteristic
273C22×C9#23511yescharacteristic
274C22×C9D3×D411yescharacteristic
275C22×C9D3×D411yescharacteristic
276C22×C9D3×D411yescharacteristic
277C22×C9D3×Q811yescharacteristic
278C2×D9—34no—
279C2×D9—64no—
280C2×D9—62no—
281C2×D9—62no—
282C2×D9—62no—
283C2×D9—62no—
284C2×D9—62no—
285C2×D9—62no—
286C2×D9—122no—
287C2×D9—122no—
288C2×D9—122no—
289C2×D9—122no—
290C2×D9—122no—
291C2×D9—122no—
292C4×C9—34no—
293C4×C9—42no—
294C4×C9—41no—
295C4×C9—121no—
296Dic9—22no—
297Dic9—41no—
298Dic9—122no—
299Dic9—121no—
300C23×C4—271no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—271no—
303C2×C22⋊C4—271no—
304C2×C22⋊C4—271no—
305#95—91no—
306#95—271no—
307C3×C9#38011yescharacteristic, complemented, Sylow
308C23×C3—21no—
309C23×C3C22×D911yescharacteristic
310C23×C3C2×D3211yescharacteristic
311C22×D3—92no—
312C22×D3—92no—
313C22×D3—92no—
314C22×D3—92no—
315C22×D3—92no—
316C22×D3—92no—
317C22×D3—182no—
318C22×D3—182no—
319C22×D3—182no—
320C22×D3—181no—
321C22×D3—181no—
322C22×D3—181no—
323C22×D3—181no—
324C22×D3—181no—
325C22×D3—181no—
326C22×D3—181no—
327C22×D3—181no—
328C22×D3—361no—
329C22×D3—361no—
330C22×D3—361no—
331C22×D3—361no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—92no—
348C2×C3×C4—181no—
349C2×C3×C4—181no—
350C2×C3×C4—181no—
351C2×C3×C4—181no—
352C2×C3×C4—181no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—32no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—182no—
363C2×Dic3—181no—
364C2×Dic3—181no—
365C2×Dic3—181no—
366C2×Dic3—181no—
367C2×Dic3—181no—
368C2×Dic3—181no—
369C2×Dic3—361no—
370C2×Dic3—361no—
371C2×Dic3C4×D912yes—
372C2×Dic3D3612yes—
373C2×Dic3#61112yes—
374C4×D3—188no—
375C4×D3—188no—
376C2×C32D3×C4⋊C411yescharacteristic
377C2×C32#89211yescharacteristic
378C2×C32#89511yescharacteristic
379C2×C32#89711yescharacteristic
380C2×C32C2×(C2×D3)⋊C411yescharacteristic
381C2×C32#93811yescharacteristic
382C2×C32#94611yescharacteristic
383C3⋊D3—64no—
384C2×C9—21no—
385C2×C9—21no—
386C2×C9—21no—
387C2×C9—21no—
388C2×C9—21no—
389C2×C9—21no—
390C2×C9—21no—
391C2×C9#87211yescharacteristic
392C2×C9D3×C22⋊C411yescharacteristic
393C2×C9#88411yescharacteristic
394C2×C9#88411yescharacteristic
395C2×C9D3×C4⋊C411yescharacteristic
396C2×C9#89611yescharacteristic
397C2×C9#89611yescharacteristic
398D9—64no—
399D9—124no—
400C24—271no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—91no—
404C22×C4—91no—
405C22×C4—274no—
406C22×C4—271no—
407C22×C4—542no—
408C22×C4—542no—
409C22×C4D3×D911yescharacteristic
410C4⋊C4—62no—
411C4⋊C4—542no—
412C22⋊C4—542no—
413C22⋊C4—542no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3C2×C4×D911yescharacteristic
422C22×C3C2×D3611yescharacteristic
423C22×C3D4×D911yescharacteristic
424C22×C3#369911yescharacteristic
425C22×C3Q8×D911yescharacteristic
426C22×C3#370111yescharacteristic
427C22×C3C2×#61111yescharacteristic
428C22×C3#379711yescharacteristic
429C22×C3#379911yescharacteristic
430C22×C3C4×D3211yescharacteristic
431C22×C3D3×D1211yescharacteristic
432C22×C3#380411yescharacteristic
433C22×C3D3×#6711yescharacteristic
434C22×C3#381111yescharacteristic
435C2×D3—94no—
436C2×D3—94no—
437C2×D3—184no—
438C2×D3—182no—
439C2×D3—182no—
440C2×D3—182no—
441C2×D3—182no—
442C2×D3—182no—
443C2×D3—182no—
444C2×D3—182no—
445C2×D3—182no—
446C2×D3—182no—
447C2×D3—182no—
448C2×D3—182no—
449C2×D3—182no—
450C2×D3—362no—
451C2×D3—362no—
452C2×D3—362no—
453C2×D3—362no—
454C2×D3—362no—
455C2×D3—362no—
456C3×C4—34no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—121no—
461C3×C4—182no—
462C3×C4—361no—
463Dic3—41no—
464Dic3—62no—
465Dic3—121no—
466Dic3—362no—
467Dic3—361no—
468Dic3—361no—
469Dic3(C2×D9)⋊C414yescomplemented
470C32#498711yescharacteristic
471C9—21no—
472C9#466711yescharacteristic, complemented
473C23—272no—
474C23—272no—
475C23—272no—
476C23—541no—
477C23—541no—
478C23—541no—
479C23—541no—
480C23C2×D3×D911yescharacteristic
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—92no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—548no—
497C2×C4—541no—
498C2×C4—541no—
499C2×C4—541no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3C4⋊C4×D911yescharacteristic
508C2×C3#6345411yescharacteristic
509C2×C3#6345711yescharacteristic
510C2×C3#6345911yescharacteristic
511C2×C3C2×(C2×D9)⋊C411yescharacteristic
512C2×C3#6350011yescharacteristic
513C2×C3#6350811yescharacteristic
514C2×C3#6383611yescharacteristic
515C2×C3#6388311yescharacteristic
516C2×C3#6388811yescharacteristic
517C2×C3#6389511yescharacteristic
518C2×C3#6391011yescharacteristic
519C2×C3D3×(C2×D3)⋊C411yescharacteristic
520C2×C3#6395811yescharacteristic
521D3—184no—
522D3—184no—
523D3—364no—
524C22—274no—
525C22—542no—
526C22—542no—
527C22—542no—
528C22—542no—
529C22—542no—
530C22—542no—
531C22#8863511yescharacteristic
532C22(C3⋊D9)⋊Q811yescharacteristic
533C22C4×D3×D911yescharacteristic
534C22D3×D3611yescharacteristic
535C22#8866211yescharacteristic
536C22D3×#61111yescharacteristic
537C22#8866811yescharacteristic
538C4—34no—
539C4—41no—
540C4—121no—
541C4—182no—
542C4—361no—
543C4—1081no—
544C3—21no—
545C3#1058866711yescharacteristic, complemented
546C3#1059136711yescharacteristic
547C2—544no—
548C2#1172089911yescharacteristic
549C2#1172098011yescharacteristic
550C2#1172098611yescharacteristic
551C2#1172099511yescharacteristic
552C2#1172100511yescharacteristic
553C2D3×(C2×D9)⋊C411yescharacteristic
554C2#1172126211yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC23×C3⋊D9C22
cosocleC23×C3×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9#380
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×C9×Dic3⋊C4C2semidirect
5. C2×Dic3⋊Dic9C2semidirect
6. C3×C9⋊#95C2semidirect
7. #11720331C2semidirect
19. C2×(C3⋊D9)⋊C4C4semidirect
38. C9⋊#95D3semidirect
113. C2×C3⋊D9C4⋊C4semidirect
117. C9×Dic3C22⋊C4semidirect
130. C2×Dic3⋊C4D9semidirect
307. C3×C9#380semidirect
469. Dic3(C2×D9)⋊C4semidirect
472. C9#4667semidirect
545. C3#10588667semidirect

Maximal subgroups

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

subgroupindex
C22×(C3⋊D9)⋊C42
C2×#885362
C2×C9×Dic3⋊C42
C2×#884452
C2×Dic3⋊Dic92
C3×C9⋊#952
#117203312
#105913673
#105886673