Finite Group Databasebeta

← #13139902

Subgroups — #13139902

Order 1728.

906 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6195C211yesmaximal, characteristic
2C2×#88536C211yesmaximal, characteristic, complemented
3C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×Dic9⋊C4C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
6C2×#88445C211yesmaximal, characteristic, complemented
7C2×Dic3×Dic9C211yesmaximal, characteristic, complemented
8#10591384—31nomaximal
9#10588637—31nomaximal
10C23×C3⋊D9C2211yescharacteristic
11C23×D3×C9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C22×C9×Dic3C2211yescharacteristic
15C22×C3×Dic9C2211yescharacteristic
16C22×C3×Dic9C2211yescharacteristic
17C2×#6195—22no—
18C2×#6195—22no—
19C2×#6195C414yescomplemented
20#88536—22no—
21C9×(C2×D3)⋊C4—22no—
22C3×Dic9⋊C4—22no—
23(C2×D3)⋊Dic9—22no—
24#88445—22no—
25Dic3×Dic9—22no—
26C22×#626—31no—
27C2×#3752—31no—
28C2×C3×(C2×D3)⋊C4D311yescharacteristic
29C2×C3×Dic3⋊C4—31no—
30C2×#3722—31no—
31C2×(C2×D3)⋊Dic3—31no—
32C2×Dic32—31no—
33C22×#611—31no—
34C2×C9×C22⋊C4—31no—
35C2×#3676—31no—
36C2×(C2×D9)⋊C4—31no—
37C2×(C2×D9)⋊C4—31no—
38C2×(C2×D9)⋊C4—61no—
39C2×Dic9⋊C4D311yescharacteristic, complemented
40C2×C4×Dic9—31no—
41C23×C3×C9C2311yescharacteristic
42C22×C3⋊D9—21no—
43C22×C3⋊D9—21no—
44C22×C3⋊D9—21no—
45C22×C3⋊D9—21no—
46C22×C3⋊D9—21no—
47C22×C3⋊D9—21no—
48C22×C3⋊D9C2×C412yes—
49C22×D3×C9—21no—
50C22×D3×C9—21no—
51C22×D3×C9—21no—
52C22×D3×C9—21no—
53C22×D3×C9—21no—
54C22×D3×C9—21no—
55C22×D3×C9C2×C412yes—
56C2×C3×C4×C9—21no—
57C2×C3×C4×C9—21no—
58C2×C3×C4×C9—21no—
59C2×C3⋊Dic9—21no—
60C2×C3⋊Dic9—21no—
61C2×C3⋊Dic9D412yescomplemented
62C2×C9×Dic3—21no—
63C2×C9×Dic3—21no—
64C2×C9×Dic3D412yescomplemented
65C2×C3×Dic9—21no—
66C2×C3×Dic9—21no—
67C2×C3×Dic9—21no—
68C2×C3×Dic9C2×C412yes—
69C2×C3×Dic9D412yes—
70C2×C3×Dic9D412yes—
71#6195—28no—
72#4988—91no—
73#4957—91no—
74C23×C3⋊D3—31no—
75C23×C3×D3C2×D311yescharacteristic
76C22×C32×C4C2×D311yescharacteristic
77C22×C3⋊Dic3—31no—
78C22×C3×Dic3—31no—
79C22×C3×Dic3—31no—
80C22×C3×Dic3C2×D311yescharacteristic
81C2×#626—34no—
82C2×#626—62no—
83C2×#626—62no—
84C24×C9—31no—
85C23×D9—31no—
86C23×D9—61no—
87#3752—62no—
88C3×(C2×D3)⋊C4—22no—
89C3×Dic3⋊C4—62no—
90#3722—62no—
91(C2×D3)⋊Dic3—62no—
92Dic32—62no—
93C22×C4×C9—21no—
94C22×C4×C9—31no—
95C22×C4×C9C2×D311yescharacteristic
96C2×#611—34no—
97C2×#611—62no—
98C2×#611—62no—
99C22×Dic9—31no—
100C22×Dic9—61no—
101C22×Dic9C2×D311yescharacteristic
102C22×Dic9C2×D311yescharacteristic
103C9×C22⋊C4—62no—
104#3676—62no—
105(C2×D9)⋊C4—62no—
106(C2×D9)⋊C4—62no—
107(C2×D9)⋊C4—64no—
108Dic9⋊C4—22no—
109C4×Dic9—62no—
110C22×C3×C9C22×C411yescharacteristic
111C22×C3×C9C2×D411yescharacteristic
112C22×C3×C9C2×D411yescharacteristic
113C22×C3×C9C2×D411yescharacteristic
114C22×C3×C9C2×D411yescharacteristic
115C22×C3×C9#4111yescharacteristic
116C22×C3×C9#4111yescharacteristic
117C2×C3⋊D9—22no—
118C2×C3⋊D9—22no—
119C2×C3⋊D9—22no—
120C2×C3⋊D9—41no—
121C2×C3⋊D9—41no—
122C2×C3⋊D9—41no—
123C2×C3⋊D9—41no—
124C2×D3×C9—22no—
125C2×D3×C9—22no—
126C2×D3×C9—22no—
127C2×D3×C9—41no—
128C2×D3×C9—41no—
129C2×D3×C9—41no—
130C2×D3×C9—41no—
131C3×C4×C9—41no—
132C3⋊Dic9—22no—
133C9×Dic3—22no—
134C3×Dic9—41no—
135C3×Dic9C22⋊C414yescomplemented
136C22×#67—91no—
137C22×D12—91no—
138C2×C3×C4⋊C4—91no—
139C2×C3×C22⋊C4—31no—
140C2×#217—91no—
141C2×(C2×D3)⋊C4—91no—
142C2×(C2×D3)⋊C4—91no—
143C2×(C2×D3)⋊C4—91no—
144C2×(C2×D3)⋊C4—91no—
145C2×(C2×D3)⋊C4—91no—
146C2×(C2×D3)⋊C4—181no—
147C2×(C2×D3)⋊C4D911yescharacteristic, complemented
148C2×Dic3⋊C4—31no—
149C2×C4×Dic3—91no—
150C2×C4×Dic3—91no—
151C23×C32C22×D311yescharacteristic
152C22×C3⋊D3—32no—
153C22×C3⋊D3—61no—
154C22×C3⋊D3—61no—
155C22×C3⋊D3—61no—
156C22×C3⋊D3—61no—
157C22×C3⋊D3—61no—
158C22×C3⋊D3—61no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C22×C3×D3C4×D312yes—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C3⋊Dic3—32no—
170C2×C3⋊Dic3—61no—
171C2×C3⋊Dic3—61no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—32no—
175C2×C3×Dic3—32no—
176C2×C3×Dic3—32no—
177C2×C3×Dic3—61no—
178C2×C3×Dic3—61no—
179C2×C3×Dic3—61no—
180C2×C3×Dic3#6712yes—
181#626—68no—
182C23×C9—21no—
183C23×C9—32no—
184C23×C9—61no—
185C23×C9—61no—
186C23×C9—61no—
187C23×C9—61no—
188C23×C9—61no—
189C23×C9—61no—
190C23×C9C22×D311yescharacteristic
191C22×D9—32no—
192C22×D9—62no—
193C22×D9—62no—
194C22×D9—62no—
195C22×D9—61no—
196C22×D9—61no—
197C22×D9—61no—
198C22×D9—61no—
199C22×D9—61no—
200C22×D9—61no—
201C22×D9—121no—
202C22×D9—121no—
203C22×D9—121no—
204C22×D9—121no—
205C2×C4×C9—22no—
206C2×C4×C9—21no—
207C2×C4×C9—21no—
208C2×C4×C9—21no—
209C2×C4×C9—32no—
210C2×C4×C9—41no—
211C2×C4×C9—41no—
212C2×C4×C9—61no—
213C2×C4×C9—61no—
214#611—68no—
215C2×Dic9—21no—
216C2×Dic9—21no—
217C2×Dic9—21no—
218C2×Dic9—32no—
219C2×Dic9—62no—
220C2×Dic9—61no—
221C2×Dic9—61no—
222C2×Dic9—121no—
223C2×Dic9—121no—
224C2×Dic9C4×D312yes—
225C2×Dic9D1212yes—
226C2×Dic9#6712yes—
227#390—271noSylow
228C2×C3×C9C2×C22⋊C411yescharacteristic
229C2×C3×C9C4×D411yescharacteristic
230C2×C3×C9C4×D411yescharacteristic
231C2×C3×C9#12111yescharacteristic
232C2×C3×C9#12111yescharacteristic
233C2×C3×C9#12411yescharacteristic
234C2×C3×C9#12711yescharacteristic
235C3⋊D9—42no—
236D3×C9—42no—
237C24×C3—31no—
238C23×D3—91no—
239C23×D3—91no—
240C23×D3—181no—
241C23×D3C2×D911yescharacteristic
242C22×C3×C4—21no—
243C22×C3×C4—31no—
244C22×C3×C4—91no—
245C22×C3×C4—91no—
246C22×C3×C4C2×D911yescharacteristic
247C22×C3×C4D3211yescharacteristic
248C2×#67—94no—
249C2×#67—182no—
250C2×#67—182no—
251C22×Dic3—31no—
252C22×Dic3—31no—
253C22×Dic3—91no—
254C22×Dic3—91no—
255C22×Dic3—181no—
256C22×Dic3C2×D911yescharacteristic
257C2×D12—94no—
258C2×D12—182no—
259C2×D12—182no—
260C3×C4⋊C4—182no—
261C3×C22⋊C4—62no—
262#217—182no—
263(C2×D3)⋊C4—22no—
264(C2×D3)⋊C4—182no—
265(C2×D3)⋊C4—182no—
266(C2×D3)⋊C4—182no—
267(C2×D3)⋊C4—182no—
268(C2×D3)⋊C4—184no—
269(C2×D3)⋊C4—182no—
270Dic3⋊C4—62no—
271C4×Dic3—182no—
272C4×Dic3—182no—
273C22×C32C2×C4×D311yescharacteristic
274C22×C32#23511yescharacteristic
275C22×C32D3×D411yescharacteristic
276C22×C32D3×D411yescharacteristic
277C22×C32D3×D411yescharacteristic
278C22×C32#23711yescharacteristic
279C22×C32C2×#6711yescharacteristic
280C2×C3⋊D3—62no—
281C2×C3⋊D3—62no—
282C2×C3⋊D3—62no—
283C2×C3⋊D3—121no—
284C2×C3⋊D3—121no—
285C2×C3⋊D3—121no—
286C2×C3⋊D3—121no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C32×C4—41no—
295C3⋊Dic3—62no—
296C3×Dic3—22no—
297C3×Dic3—34no—
298C3×Dic3—121no—
299C22×C9—21no—
300C22×C9—21no—
301C22×C9—21no—
302C22×C9—21no—
303C22×C9—21no—
304C22×C9—21no—
305C22×C9—21no—
306C22×C9—62no—
307C22×C9—62no—
308C22×C9—62no—
309C22×C9—121no—
310C22×C9—121no—
311C22×C9—121no—
312C22×C9—121no—
313C22×C9C2×C4×D311yescharacteristic
314C22×C9C2×D1211yescharacteristic
315C22×C9D3×D411yescharacteristic
316C22×C9D3×D411yescharacteristic
317C22×C9#23911yescharacteristic
318C22×C9#23911yescharacteristic
319C22×C9C2×#6711yescharacteristic
320C2×D9—64no—
321C2×D9—62no—
322C2×D9—62no—
323C2×D9—62no—
324C2×D9—122no—
325C2×D9—122no—
326C2×D9—122no—
327C2×D9—122no—
328C2×D9—122no—
329C2×D9—122no—
330C2×D9—121no—
331C2×D9—121no—
332C2×D9—121no—
333C2×D9—121no—
334C4×C9—42no—
335C4×C9—41no—
336C4×C9—62no—
337Dic9—41no—
338Dic9—62no—
339Dic9—122no—
340Dic9(C2×D3)⋊C414yescomplemented
341C22×D4—271no—
342C2×C4⋊C4—91no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—271no—
345C2×C22⋊C4—271no—
346C2×C22⋊C4—271no—
347C2×C42—271no—
348C3×C9#39011yescharacteristic, complemented, Sylow
349C23×C3—21no—
350C23×C3—32no—
351C23×C3—61no—
352C23×C3—61no—
353C23×C3—61no—
354C23×C3—61no—
355C23×C3—61no—
356C23×C3—61no—
357C23×C3C22×D911yescharacteristic
358C23×C3C2×D3211yescharacteristic
359C22×D3—21no—
360C22×D3—21no—
361C22×D3—21no—
362C22×D3—21no—
363C22×D3—21no—
364C22×D3—21no—
365C22×D3—92no—
366C22×D3—92no—
367C22×D3—182no—
368C22×D3—182no—
369C22×D3—182no—
370C22×D3—181no—
371C22×D3—181no—
372C22×D3—181no—
373C22×D3—181no—
374C22×D3—181no—
375C22×D3—181no—
376C22×D3—181no—
377C22×D3—181no—
378C22×D3—181no—
379C22×D3—181no—
380C22×D3—181no—
381C22×D3—181no—
382C22×D3—361no—
383C22×D3—361no—
384C22×D3—361no—
385C22×D3—361no—
386C22×D3C4×D912yes—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—32no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—92no—
400C2×C3×C4—92no—
401C2×C3×C4—92no—
402C2×C3×C4—181no—
403C2×C3×C4—181no—
404C2×C3×C4—181no—
405#67—188no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—32no—
409C2×Dic3—32no—
410C2×Dic3—32no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—92no—
415C2×Dic3—92no—
416C2×Dic3—182no—
417C2×Dic3—181no—
418C2×Dic3—181no—
419C2×Dic3—181no—
420C2×Dic3—181no—
421C2×Dic3—361no—
422C2×Dic3—361no—
423C2×Dic3#61112yescomplemented
424D12—188no—
425C2×C32D3×C22⋊C411yescharacteristic
426C2×C32#67⋊C411yescharacteristic
427C2×C32#88411yescharacteristic
428C2×C32#88511yescharacteristic
429C2×C32C4×#6711yescharacteristic
430C2×C32#93911yescharacteristic
431C2×C32#94011yescharacteristic
432C3⋊D3—122no—
433C3×D3—42no—
434C2×C9—21no—
435C2×C9—21no—
436C2×C9—21no—
437C2×C9—21no—
438C2×C9—21no—
439C2×C9—21no—
440C2×C9—21no—
441C2×C9—122no—
442C2×C9#89311yescharacteristic
443C2×C9#89311yescharacteristic
444C2×C9#89511yescharacteristic
445C2×C9#89511yescharacteristic
446C2×C9C2×(C2×D3)⋊C411yescharacteristic
447C2×C9#94011yescharacteristic
448C2×C9#94711yescharacteristic
449D9—124no—
450D9—122no—
451C24—31no—
452C24—271no—
453C2×D4—274no—
454C2×D4—542no—
455C2×D4—542no—
456C22×C4—31no—
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—271no—
460C22×C4D3×D911yescharacteristic
461C4⋊C4—182no—
462C22⋊C4—62no—
463C22⋊C4—542no—
464C22⋊C4—542no—
465C22⋊C4—542no—
466C42—542no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3—121no—
478C22×C3—121no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3C2×C4×D911yescharacteristic
482C22×C3#369711yescharacteristic
483C22×C3D4×D911yescharacteristic
484C22×C3D4×D911yescharacteristic
485C22×C3D4×D911yescharacteristic
486C22×C3#369911yescharacteristic
487C22×C3C2×#61111yescharacteristic
488C22×C3#379611yescharacteristic
489C22×C3#379911yescharacteristic
490C22×C3C4×D3211yescharacteristic
491C22×C3D3×D1211yescharacteristic
492C22×C3D3×#6711yescharacteristic
493C22×C3D3×#6711yescharacteristic
494C22×C3#381111yescharacteristic
495C2×D3—22no—
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—184no—
503C2×D3—182no—
504C2×D3—182no—
505C2×D3—182no—
506C2×D3—182no—
507C2×D3—182no—
508C2×D3—182no—
509C2×D3—362no—
510C2×D3—362no—
511C2×D3—362no—
512C2×D3—362no—
513C2×D3—362no—
514C2×D3—362no—
515C2×D3—361no—
516C2×D3—361no—
517C2×D3—361no—
518C2×D3—361no—
519C2×D3—361no—
520C2×D3—361no—
521C2×D3—361no—
522C2×D3—361no—
523C3×C4—42no—
524C3×C4—41no—
525C3×C4—41no—
526C3×C4—62no—
527C3×C4—94no—
528C3×C4—361no—
529Dic3—22no—
530Dic3—34no—
531Dic3—121no—
532Dic3—182no—
533Dic3—182no—
534Dic3—362no—
535C32#495711yescharacteristic
536C9—21no—
537C9#498811yescharacteristic, complemented
538C23—32no—
539C23—61no—
540C23—61no—
541C23—61no—
542C23—61no—
543C23—61no—
544C23—61no—
545C23—272no—
546C23—541no—
547C23—541no—
548C23—541no—
549C23—541no—
550C23—541no—
551C23—541no—
552C23C2×D3×D911yescharacteristic
553D4—548no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—32no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—92no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—272no—
567C2×C4—541no—
568C2×C4—541no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—122no—
577C2×C3C22⋊C4×D911yescharacteristic
578C2×C3#611⋊C411yescharacteristic
579C2×C3#6344611yescharacteristic
580C2×C3#6344711yescharacteristic
581C2×C3C4×#61111yescharacteristic
582C2×C3#6350111yescharacteristic
583C2×C3#6350211yescharacteristic
584C2×C3#6388111yescharacteristic
585C2×C3#6388611yescharacteristic
586C2×C3#6390411yescharacteristic
587C2×C3#6390711yescharacteristic
588C2×C3#6391011yescharacteristic
589C2×C3D3×(C2×D3)⋊C411yescharacteristic
590C2×C3#6397911yescharacteristic
591D3—42no—
592D3—364no—
593D3—362no—
594D3—362no—
595C22—62no—
596C22—62no—
597C22—62no—
598C22—121no—
599C22—121no—
600C22—121no—
601C22—121no—
602C22—542no—
603C22—542no—
604C22—542no—
605C22—1081no—
606C22—1081no—
607C22—1081no—
608C22—1081no—
609C22#8863911yescharacteristic
610C22#8864211yescharacteristic
611C22C4×D3×D911yescharacteristic
612C22D9×D1211yescharacteristic
613C22D3×#61111yescharacteristic
614C22D9×#6711yescharacteristic
615C22#8866811yescharacteristic
616C4—41no—
617C4—62no—
618C4—94no—
619C4—361no—
620C4—542no—
621C3—21no—
622C3#1058863711yescharacteristic, complemented
623C3#1059138411yescharacteristic
624C2—122no—
625C2—1082no—
626C2#1172101411yescharacteristic
627C2#1172101711yescharacteristic
628C2#1172103011yescharacteristic
629C2#1172103511yescharacteristic
630C2#1172103911yescharacteristic
631C2D9×(C2×D3)⋊C411yescharacteristic
632C2#1172128911yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C2×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC22×#6195C2
cosocleC23×C3×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9#390
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88536C2semidirect
3. C2×C9×(C2×D3)⋊C4C2semidirect
4. C2×C3×Dic9⋊C4C2semidirect
5. C2×(C2×D3)⋊Dic9C2semidirect
6. C2×#88445C2semidirect
7. C2×Dic3×Dic9C2semidirect
19. C2×#6195C4semidirect
39. C2×Dic9⋊C4D3semidirect
61. C2×C3⋊Dic9D4semidirect
64. C2×C9×Dic3D4semidirect
135. C3×Dic9C22⋊C4semidirect
147. C2×(C2×D3)⋊C4D9semidirect
340. Dic9(C2×D3)⋊C4semidirect
348. C3×C9#390semidirect
423. C2×Dic3#611semidirect
537. C9#4988semidirect
622. C3#10588637semidirect

Maximal subgroups

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

subgroupindex
C22×#61952
C2×#885362
C2×C9×(C2×D3)⋊C42
C2×C3×Dic9⋊C42
C2×(C2×D3)⋊Dic92
C2×#884452
C2×Dic3×Dic92
#105913843
#105886373