Finite Group Databasebeta

← #13150564

Subgroups — #13150564

Order 1728.

1166 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88736C211yesmaximal, characteristic, complemented
2C2×D9×D12C211yesmaximal, characteristic, complemented
3C9×#930C211yesmaximal, characteristic, complemented
4C3×C4×#611C211yesmaximal, characteristic, complemented
5#11721292C212yesmaximal, complemented
6#11721262C212yesmaximal, complemented
7#11721048C212yesmaximal, complemented
8#11720992C211yesmaximal, characteristic, complemented
9#11720964C211yesmaximal, characteristic, complemented
10#11720957C212yesmaximal, complemented
11#11720945C211yesmaximal, characteristic, complemented
12#10595078—31nomaximal
13#10589714—31nomaximal
14C22×D3×D9C2212yes—
15C22×C3×C4×C9C2211yescharacteristic, complemented
16C2×#6233C2212yescomplemented
17#88736—24no—
18C2×C4⋊(C3⋊D9)C2211yescharacteristic
19C2×C4×C3⋊D9C2212yescomplemented
20C2×#6226C2211yescharacteristic, complemented
21C2×C9×#67C2212yescomplemented
22C2×C3×#611C2211yescharacteristic
23C2×C9×D12C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×#6195C2212yes—
26C2×(C3⋊D9)⋊C4C2212yescomplemented
27D9×D12—24no—
28C3×#3676C2211yescharacteristic, complemented
29C9×(C2×D3)⋊C4C2212yescomplemented
30C3×(C2×D9)⋊C4C2211yescharacteristic
31C9×C4⋊Dic3C2211yescharacteristic, complemented
32C3×Dic9⋊C4C2211yescharacteristic, complemented
33C3×C4×Dic9C2211yescharacteristic, complemented
34(C2×D3)⋊Dic9C2212yescomplemented
35(C2×D3)⋊Dic9C2212yescomplemented
36#88445C2212yescomplemented
37(C2×D9)⋊Dic3C2212yes—
38Dic3⋊Dic9C2212yescomplemented
39C2×#3828—31no—
40C2×D3×D12—31no—
41C3×#930D311yescharacteristic
42C3×C4×#67—31no—
43#63983—32no—
44#63958—32no—
45#63921—32no—
46#63894—31no—
47#63860—31no—
48#63857—31no—
49#63853—32no—
50C2×D4×D9—31no—
51C2×#3697—31no—
52C2×#3697—61no—
53C9×#121—31no—
54#63500—32no—
55#63499—32no—
56#63498—31no—
57C4×#611D311yescharacteristic, complemented
58#63459—31no—
59#63455—31no—
60#63445—32no—
61C22⋊C4×D9—32no—
62C23×C3×C9C2311yescharacteristic
63C22×C3⋊D9C2312yes—
64C22×D3×C9C2312yes—
65C22×C3×D9C2311yescharacteristic
66C2×D3×D9—24no—
67C2×D3×D9—24no—
68C2×D3×D9—42no—
69C2×C3×C4×C9—22no—
70C2×C3×C4×C9C2311yescharacteristic
71C2×C3×C4×C9C2311yescharacteristic
72#6233—24no—
73C2×C3⋊Dic9C2312yes—
74C4⋊(C3⋊D9)D414yescomplemented
75C4×C3⋊D9—24no—
76#6226—22no—
77C9×#67—42no—
78C3×#611—22no—
79C2×C9×Dic3C2312yes—
80C2×C3×Dic9C2311yescharacteristic
81C2×C3×Dic9C2311yescharacteristic
82C2×C3×Dic9C2311yescharacteristic
83C9×D12—22no—
84C3×C4×D9—22no—
85#6195—24no—
86(C3⋊D9)⋊C4—42no—
87#5612—91no—
88#5550—91no—
89C22×D32—32no—
90C22×C32×C4C2×D311yescharacteristic
91C2×#638—32no—
92#3828—64no—
93C2×C4⋊(C3⋊D3)—31no—
94C2×C4×C3⋊D3—32no—
95C2×#634—31no—
96C2×C3×#67—31no—
97C2×C3×#67C2×D312yes—
98C2×C3×D12C2×D311yescharacteristic
99C2×C3×C4×D3—31no—
100C2×#626—32no—
101C2×#624—32no—
102D3×D12—64no—
103C23×D9—32no—
104C3×#217—31no—
105C3×(C2×D3)⋊C4—31no—
106C3×(C2×D3)⋊C4C2×D312yes—
107C3×C4⋊Dic3C2×D311yescharacteristic
108C3×Dic3⋊C4—31no—
109C3×C4×Dic3—31no—
110Dic3⋊Dic3—32no—
111#3722—32no—
112(C2×D3)⋊Dic3—32no—
113(C2×D3)⋊Dic3—32no—
114(C2×D3)⋊Dic3—32no—
115C2×D4×C9—32no—
116C2×D4×C9—31no—
117C22×C4×C9—21no—
118C22×C4×C9C2×D311yescharacteristic, complemented
119C2×#611—32no—
120C2×#611—32no—
121C2×#611—62no—
122C2×#611C2×D311yescharacteristic
123D4×D9—64no—
124#3697—64no—
125#3697—68no—
126C2×D36—31no—
127C2×D36—61no—
128C2×C4×D9—32no—
129C2×C4×D9—32no—
130C2×C4×D9—62no—
131C2×C4×D9C2×D311yescharacteristic
132C2×Dic18—31no—
133C2×Dic18—61no—
134C9×C4⋊C4—31no—
135C9×C22⋊C4—32no—
136#3676—32no—
137#3676—32no—
138#3676C2×D311yescharacteristic, complemented
139(C2×D9)⋊C4—32no—
140(C2×D9)⋊C4—32no—
141(C2×D9)⋊C4C2×D311yescharacteristic
142C4⋊Dic9—32no—
143Dic9⋊C4C2×D311yescharacteristic, complemented
144C4×Dic9C2×D311yescharacteristic, complemented
145C22×C3×C9—21no—
146C22×C3×C9—21no—
147C22×C3×C9—21no—
148C22×C3×C9C2411yescharacteristic
149C2×C3⋊D9—22no—
150C2×C3⋊D9—22no—
151C2×C3⋊D9C2×D414yes—
152C2×D3×C9—22no—
153C2×D3×C9—22no—
154C2×D3×C9—22no—
155C2×C3×D9—21no—
156C2×C3×D9—21no—
157C2×C3×D9#4112yescomplemented
158D3×D9—48no—
159C3×C4×C9—21no—
160C3×C4×C9C2×D412yes—
161C3⋊Dic9—22no—
162C9×Dic3—22no—
163C3×Dic9—21no—
164C3×Dic9—21no—
165C3×Dic9—21no—
166C2×D3×D4—91no—
167C2×#235—91no—
168C2×#235—91no—
169C2×#235—181no—
170C22×D12—91no—
171C3×#121—31no—
172C3×C4×D4—91no—
173#938—92no—
174#937—92no—
175#937—92no—
176#936—91no—
177#930D911yescharacteristic, complemented
178C4×#67—31no—
179#924—91no—
180#897—91no—
181#894—92no—
182#893—91no—
183#884—92no—
184#883—92no—
185D3×C22⋊C4—92no—
186D3×C22⋊C4—92no—
187#875—91no—
188C4×D12—91no—
189C23×C32C22×D311yescharacteristic
190C22×C3⋊D3—32no—
191C22×C3×D3—31no—
192C22×C3×D3C22×D312yes—
193C2×D32—64no—
194C2×D32—64no—
195C2×D32—122no—
196C2×C32×C4—22no—
197C2×C32×C4C22×D311yescharacteristic
198C2×C32×C4C22×D311yescharacteristic
199#638—64no—
200C2×C3⋊Dic3—32no—
201C4⋊(C3⋊D3)—34no—
202C4×C3⋊D3—64no—
203#634—62no—
204C3×#67—42no—
205C3×#67—62no—
206C2×C3×Dic3—31no—
207C2×C3×Dic3—31no—
208C2×C3×Dic3—31no—
209C2×C3×Dic3C22×D312yes—
210C3×D12—22no—
211C3×C4×D3—62no—
212#626—64no—
213#624—122no—
214C23×C9—21no—
215C23×C9—32no—
216C23×C9C22×D311yescharacteristic
217C22×D9—32no—
218C22×D9—62no—
219C22×D9—64no—
220C22×D9—64no—
221C22×D9—122no—
222C22×D9C22×D311yescharacteristic
223D4×C9—62no—
224D4×C9—122no—
225C2×C4×C9—24no—
226C2×C4×C9—22no—
227C2×C4×C9—21no—
228C2×C4×C9—21no—
229C2×C4×C9—32no—
230C2×C4×C9C22×D311yescharacteristic
231C2×C4×C9C22×D311yescharacteristic
232#611—22no—
233#611—64no—
234#611—64no—
235#611—68no—
236C2×Dic9—32no—
237C2×Dic9—62no—
238C2×Dic9C22×D311yescharacteristic
239C2×Dic9C22×D311yescharacteristic
240C2×Dic9C22×D311yescharacteristic
241D36—34no—
242D36—64no—
243C4×D9—22no—
244C4×D9—64no—
245C4×D9—68no—
246C4×D9—122no—
247Dic18—64no—
248Dic18—62no—
249#546—271noSylow
250C2×C3×C9—41no—
251C2×C3×C9C22×D411yescharacteristic
252C2×C3×C9C2×#4111yescharacteristic
253C2×C3×C9H(5,𝔽2)11yescharacteristic
254C3⋊D9—24no—
255D3×C9—42no—
256C3×D9—22no—
257C23×D3—92no—
258C23×D3—92no—
259C2×C3×D4—32no—
260C2×C3×D4—31no—
261C2×C3×D4—91no—
262C22×C3×C4—21no—
263C22×C3×C4—91no—
264C22×C3×C4C2×D911yescharacteristic, complemented
265C22×C3×C4D3211yescharacteristic
266C2×#67—31no—
267C2×#67—92no—
268C2×#67—92no—
269C2×#67—92no—
270C2×#67—182no—
271C2×#67C2×D912yescomplemented
272D3×D4—184no—
273#235—184no—
274#235—184no—
275#235—188no—
276C2×D12—91no—
277C2×D12—91no—
278C2×D12—92no—
279C2×D12—181no—
280C2×D12—184no—
281C2×D12C2×D911yescharacteristic
282C2×C4×D3—31no—
283C2×C4×D3—92no—
284C2×C4×D3—92no—
285C2×C4×D3—92no—
286C2×C4×D3—92no—
287C2×C4×D3—182no—
288C2×Dic6—91no—
289C2×Dic6—91no—
290C2×Dic6—181no—
291C3×C4⋊C4—31no—
292C3×C4⋊C4—91no—
293C3×C22⋊C4—32no—
294C3×C22⋊C4—91no—
295C3×C22⋊C4—91no—
296C3×C42—91no—
297#217—31no—
298#217—92no—
299#217—92no—
300#217—92no—
301(C2×D3)⋊C4—31no—
302(C2×D3)⋊C4—92no—
303(C2×D3)⋊C4—92no—
304(C2×D3)⋊C4—92no—
305(C2×D3)⋊C4—92no—
306(C2×D3)⋊C4—92no—
307(C2×D3)⋊C4C2×D912yescomplemented
308C4⋊Dic3—92no—
309C4⋊Dic3C2×D911yescharacteristic, complemented
310Dic3⋊C4—31no—
311Dic3⋊C4—92no—
312C4×Dic3—31no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32C23×D311yescharacteristic
317C2×C3⋊D3—34no—
318C2×C3⋊D3—62no—
319C2×C3⋊D3—62no—
320C2×C3×D3—22no—
321C2×C3×D3—22no—
322C2×C3×D3—22no—
323C2×C3×D3—32no—
324C2×C3×D3—61no—
325C2×C3×D3—61no—
326D32—128no—
327C32×C4—21no—
328C32×C4D3×D412yes—
329C3⋊Dic3—62no—
330C3×Dic3—22no—
331C3×Dic3—61no—
332C3×Dic3—61no—
333C3×Dic3—61no—
334C22×C9—22no—
335C22×C9—21no—
336C22×C9—21no—
337C22×C9—21no—
338C22×C9—21no—
339C22×C9—41no—
340C22×C9—41no—
341C22×C9—62no—
342C22×C9—62no—
343C22×C9—62no—
344C22×C9C23×D311yescharacteristic
345C2×D9—21no—
346C2×D9—21no—
347C2×D9—34no—
348C2×D9—64no—
349C2×D9—62no—
350C2×D9—62no—
351C2×D9—122no—
352C2×D9—122no—
353C2×D9—128no—
354C2×D9#23512yescomplemented
355C4×C9—22no—
356C4×C9—21no—
357C4×C9—22no—
358C4×C9—62no—
359C4×C9D3×D412yes—
360Dic9—21no—
361Dic9—21no—
362Dic9—21no—
363Dic9—64no—
364Dic9—62no—
365C2×#41—271no—
366C22×D4—271no—
367#124—271no—
368#123—272no—
369C22⋊Q8—271no—
370#121—31no—
371#121—272no—
372#120—272no—
373C4×D4—91no—
374C4×D4—271no—
375C2×C22⋊C4—272no—
376C3×C9#54611yescharacteristic, complemented, Sylow
377C23×C3—21no—
378C23×C3—32no—
379C23×C3—91no—
380C23×C3C22×D911yescharacteristic
381C23×C3C2×D3211yescharacteristic
382C22×D3—31no—
383C22×D3—92no—
384C22×D3—92no—
385C22×D3—182no—
386C22×D3—184no—
387C22×D3—184no—
388C22×D3—184no—
389C22×D3—184no—
390C22×D3—362no—
391C22×D3—362no—
392C22×D3C22×D912yes—
393C3×D4—62no—
394C3×D4—122no—
395C3×D4—182no—
396C2×C3×C4—24no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—32no—
402C2×C3×C4—91no—
403C2×C3×C4—91no—
404C2×C3×C4—91no—
405C2×C3×C4—182no—
406C2×C3×C4C22×D911yescharacteristic
407C2×C3×C4C22×D911yescharacteristic
408C2×C3×C4C2×D3211yescharacteristic
409C2×C3×C4C2×D3211yescharacteristic
410#67—42no—
411#67—62no—
412#67—184no—
413#67—184no—
414#67—184no—
415#67—188no—
416C2×Dic3—31no—
417C2×Dic3—31no—
418C2×Dic3—31no—
419C2×Dic3—92no—
420C2×Dic3—92no—
421C2×Dic3—182no—
422C2×Dic3C22×D912yes—
423D12—22no—
424D12—94no—
425D12—94no—
426D12—184no—
427D12—184no—
428C4×D3—62no—
429C4×D3—184no—
430C4×D3—184no—
431C4×D3—188no—
432C4×D3—362no—
433C4×D3—362no—
434Dic6—184no—
435Dic6—182no—
436Dic6—182no—
437C2×C32—41no—
438C2×C32C2×D3×D411yescharacteristic
439C2×C32#100411yescharacteristic
440C2×C32D3×#4111yescharacteristic
441C3⋊D3—64no—
442C3×D3—42no—
443C3×D3—62no—
444C2×C9—21no—
445C2×C9—21no—
446C2×C9—21no—
447C2×C9—42no—
448C2×C9—41no—
449C2×C9—122no—
450C2×C9C2×#23511yescharacteristic
451C2×C9C2×D3×D411yescharacteristic
452C2×C9#100911yescharacteristic
453D9—22no—
454D9—64no—
455D9—124no—
456C24—272no—
457#41—544no—
458C2×Q8—271no—
459C2×D4—32no—
460C2×D4—31no—
461C2×D4—91no—
462C2×D4—272no—
463C2×D4—272no—
464C2×D4—271no—
465C2×D4—544no—
466C22×C4—91no—
467C22×C4—272no—
468C22×C4—272no—
469C22×C4D3×D911yescharacteristic, complemented
470C4⋊C4—31no—
471C4⋊C4—91no—
472C4⋊C4—272no—
473C22⋊C4—32no—
474C22⋊C4—91no—
475C22⋊C4—91no—
476C22⋊C4—272no—
477C22⋊C4—272no—
478C22⋊C4—272no—
479C22⋊C4—272no—
480C42—91no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—62no—
492C22×C3—62no—
493C22×C3—62no—
494C22×C3—92no—
495C22×C3—181no—
496C22×C3—181no—
497C22×C3C23×D911yescharacteristic
498C22×C3C22×D3211yescharacteristic
499C2×D3—22no—
500C2×D3—22no—
501C2×D3—22no—
502C2×D3—32no—
503C2×D3—61no—
504C2×D3—61no—
505C2×D3—94no—
506C2×D3—94no—
507C2×D3—184no—
508C2×D3—182no—
509C2×D3—182no—
510C2×D3—182no—
511C2×D3—182no—
512C2×D3—362no—
513C2×D3—362no—
514C2×D3—368no—
515C2×D3—368no—
516C3×C4—22no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—22no—
520C3×C4—62no—
521C3×C4—181no—
522C3×C4—181no—
523C3×C4—181no—
524C3×C4D4×D912yes—
525C3×C4#381112yes—
526Dic3—22no—
527Dic3—61no—
528Dic3—61no—
529Dic3—61no—
530Dic3—184no—
531Dic3—182no—
532Dic3—182no—
533C32#561211yescharacteristic
534C9—21no—
535C9#555011yescharacteristic, complemented
536C23—32no—
537C23—91no—
538C23—272no—
539C23—544no—
540C23—544no—
541C23—1082no—
542C23C2×D3×D911yescharacteristic
543Q8—542no—
544D4—62no—
545D4—122no—
546D4—182no—
547D4—274no—
548D4—544no—
549D4—544no—
550C2×C4—22no—
551C2×C4—32no—
552C2×C4—91no—
553C2×C4—91no—
554C2×C4—91no—
555C2×C4—182no—
556C2×C4—272no—
557C2×C4—544no—
558C2×C4—1082no—
559C2×C4C2×D3×D911yescharacteristic
560C2×C4C2×D3×D911yescharacteristic
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—42no—
565C2×C3—41no—
566C2×C3—41no—
567C2×C3—122no—
568C2×C3—182no—
569C2×C3C2×D4×D911yescharacteristic
570C2×C3#6371011yescharacteristic
571C2×C3#41×D911yescharacteristic
572C2×C3D3×#23511yescharacteristic
573C2×C3#6430711yescharacteristic
574C2×C3C2×#381111yescharacteristic
575D3—42no—
576D3—62no—
577D3—184no—
578D3—184no—
579D3—364no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—62no—
584C22—62no—
585C22—62no—
586C22—92no—
587C22—181no—
588C22—181no—
589C22—274no—
590C22—542no—
591C22—542no—
592C22—1088no—
593C22C22×D3×D911yescharacteristic
594C4—21no—
595C4—62no—
596C4—181no—
597C4—181no—
598C4—181no—
599C4—542no—
600C4#8866812yes—
601C3—21no—
602C3#1058971411yescharacteristic, complemented
603C3#1059507811yescharacteristic
604C2—41no—
605C2—122no—
606C2—182no—
607C2—544no—
608C2D9×#23511yescharacteristic
609C2#1172247611yescharacteristic
610C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88736C2semidirect
2. C2×D9×D12C2semidirect
3. C9×#930C2semidirect
4. C3×C4×#611C2semidirect
5. #11721292C2semidirect
6. #11721262C2semidirect
7. #11721048C2semidirect
8. #11720992C2semidirect
9. #11720964C2semidirect
10. #11720957C2semidirect
11. #11720945C2semidirect
15. C22×C3×C4×C9C22semidirect
16. C2×#6233C22semidirect
19. C2×C4×C3⋊D9C22semidirect
20. C2×#6226C22semidirect
21. C2×C9×#67C22semidirect
26. C2×(C3⋊D9)⋊C4C22semidirect
28. C3×#3676C22semidirect
29. C9×(C2×D3)⋊C4C22semidirect
31. C9×C4⋊Dic3C22semidirect
32. C3×Dic9⋊C4C22semidirect
33. C3×C4×Dic9C22semidirect
34. (C2×D3)⋊Dic9C22semidirect
35. (C2×D3)⋊Dic9C22semidirect
36. #88445C22semidirect
38. Dic3⋊Dic9C22semidirect
57. C4×#611D3semidirect
74. C4⋊(C3⋊D9)D4semidirect
118. C22×C4×C9C2×D3semidirect
138. #3676C2×D3semidirect
143. Dic9⋊C4C2×D3semidirect
144. C4×Dic9C2×D3semidirect
157. C2×C3×D9#41semidirect
177. #930D9semidirect
264. C22×C3×C4C2×D9semidirect
271. C2×#67C2×D9semidirect
307. (C2×D3)⋊C4C2×D9semidirect
309. C4⋊Dic3C2×D9semidirect
354. C2×D9#235semidirect
376. C3×C9#546semidirect
469. C22×C4D3×D9semidirect
535. C9#5550semidirect
602. C3#10589714semidirect

Maximal subgroups

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

subgroupindex
C2×#887362
C2×D9×D122
C9×#9302
C3×C4×#6112
#117212922
#117212622
#117210482
#117209922
#117209642
#117209572
#117209452
#105950783
#105897143