Finite Group Databasebeta

← #13140359

Subgroups — #13140359

Order 1728.

830 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×C3×#3673C211yesmaximal, characteristic, complemented
3#11721007C211yesmaximal, characteristic, complemented
4C2×#88417C211yesmaximal, characteristic, complemented
5C9×#832C211yesmaximal, characteristic, complemented
6#11720282C211yesmaximal, characteristic, complemented
7#11720267C211yesmaximal, characteristic, complemented
8#10591456—31nomaximal
9#10588453—31nomaximal
10C23×C3⋊D9—21no—
11C2×C3×D4×C9C2211yescharacteristic
12C2×#6233—21no—
13D4×C3⋊D9—22no—
14D4×C3⋊D9—22no—
15C2×C4⋊(C3⋊D9)C2211yescharacteristic
16C2×C4×C3⋊D9C2211yescharacteristic
17C2×C3×D36C2211yescharacteristic, complemented
18C2×#6192—21no—
19C3×#3673—22no—
20C9×C4⋊Dic3C2211yescharacteristic, complemented
21C2×C9×C3⋊C8C2211yescharacteristic, complemented
22C2×C3×C9⋊C8C2211yescharacteristic, complemented
23(C2×D9)⋊Dic3—21no—
24#88417—22no—
25C2×D4×C3⋊D3—31no—
26C2×C3×#213—31no—
27#63916—31no—
28C2×#3714—31no—
29C2×D4×D9—31no—
30C2×D4×D9—61no—
31C3×#832D311yescharacteristic
32#63564—31no—
33#63557—31no—
34C2×#3673D311yescharacteristic, complemented
35C2×D72—31no—
36#63457—31no—
37C9×#102—31no—
38(C2×D9)⋊C8—31no—
39#63369—31no—
40C23×C3×C9—21no—
41C22×C3⋊D9—24no—
42C22×C3⋊D9—21no—
43C22×C3⋊D9—42no—
44C22×C3⋊D9—42no—
45C22×C3⋊D9D411yescharacteristic
46C22×C3×D9—21no—
47C3×D4×C9—21no—
48C3×D4×C9D412yescomplemented
49C2×C3×C4×C9C2311yescharacteristic
50#6233—24no—
51C2×C3⋊Dic9D411yescharacteristic
52C4⋊(C3⋊D9)—21no—
53C4⋊(C3⋊D9)D412yescomplemented
54C4×C3⋊D9—21no—
55C4×C3⋊D9—21no—
56C2×C9×Dic3—21no—
57C3×D36—21no—
58C3×D36—21no—
59#6192—42no—
60C9×C3⋊C8—21no—
61C3×C9⋊C8—21no—
62#5156—91no—
63#4773—91no—
64C23×C3⋊D3—61no—
65C2×C32×D4C2×D311yescharacteristic
66C2×#638—61no—
67D4×C3⋊D3—62no—
68D4×C3⋊D3—62no—
69C2×C4⋊(C3⋊D3)—31no—
70C2×C4×C3⋊D3—31no—
71C2×C3×D12—31no—
72C2×#626—61no—
73C23×D9—61no—
74C23×D9—62no—
75C3×#213—62no—
76C3×C4⋊Dic3C2×D311yescharacteristic
77C2×C3×C3⋊C8—31no—
78C2×C3×C3⋊C8C2×D311yescharacteristic
79(C2×D3)⋊Dic3—61no—
80#3714—62no—
81C2×D4×C9—21no—
82C2×D4×C9C2×D311yescharacteristic
83C2×#611—61no—
84C2×#611—62no—
85D4×D9—62no—
86D4×D9—64no—
87D4×D9—64no—
88D4×D9—62no—
89C2×D36—31no—
90C2×D36—61no—
91C2×D36—61no—
92C2×D36C2×D311yescharacteristic, complemented
93C2×C4×D9—31no—
94C2×C4×D9—61no—
95C2×C8×C9—31no—
96C9×C4⋊C4—31no—
97#3673—22no—
98(C2×D9)⋊C4—61no—
99C2×C9⋊C8C2×D311yescharacteristic, complemented
100D72—62no—
101C22×C3×C9—22no—
102C22×C3×C9—41no—
103C22×C3×C9—41no—
104C22×C3×C9C2×D411yescharacteristic
105C2×C3⋊D9—21no—
106C2×C3⋊D9—21no—
107C2×C3⋊D9—22no—
108C2×C3⋊D9—48no—
109C2×C3⋊D9—41no—
110C2×C3⋊D9—41no—
111C2×C3⋊D9D812yescomplemented
112C2×C3×D9—41no—
113C2×C3×D9—41no—
114C2×C3×D9—41no—
115C3×C4×C9C2×D411yescharacteristic
116C3×C4×C9C2×D411yescharacteristic
117C3⋊Dic9—21no—
118C9×Dic3—41no—
119C2×D3×D4—91no—
120C2×D3×D4—91no—
121C2×D3×D4—181no—
122C2×C3×D8—91no—
123#938—91no—
124C2×#213—31no—
125C2×#213—91no—
126C2×D24—91no—
127#895—91no—
128C3×#102—31no—
129#832D911yescharacteristic, complemented
130#821—91no—
131(C2×D3)⋊C8—91no—
132(C2×D3)⋊C8—91no—
133#809—91no—
134C23×C32—21no—
135C22×C3⋊D3—31no—
136C22×C3⋊D3—64no—
137C22×C3⋊D3—61no—
138C22×C3⋊D3—122no—
139C22×C3⋊D3—122no—
140C22×C3×D3—61no—
141C32×D4—21no—
142C32×D4D1212yes—
143C2×C32×C4C22×D311yescharacteristic
144#638—64no—
145C2×C3⋊Dic3—31no—
146C4⋊(C3⋊D3)—32no—
147C4⋊(C3⋊D3)—61no—
148C4×C3⋊D3—61no—
149C4×C3⋊D3—61no—
150C2×C3×Dic3—21no—
151C3×D12—61no—
152C3×D12—61no—
153#626—122no—
154C23×C9—22no—
155C23×C9—21no—
156C22×D9—21no—
157C22×D9—31no—
158C22×D9—61no—
159C22×D9—62no—
160C22×D9—68no—
161C22×D9—64no—
162C22×D9—61no—
163C22×D9—122no—
164C22×D9—124no—
165C22×D9—124no—
166C22×D9—122no—
167C3×C3⋊C8—21no—
168C3×C3⋊C8—61no—
169D4×C9—22no—
170D4×C9—21no—
171D4×C9—22no—
172D4×C9#6712yescomplemented
173C2×C4×C9—21no—
174C2×C4×C9—61no—
175C2×C4×C9C22×D311yescharacteristic
176#611—68no—
177#611—64no—
178C2×Dic9—31no—
179C2×Dic9—61no—
180D36—21no—
181D36—21no—
182D36—32no—
183D36—62no—
184D36—62no—
185D36—61no—
186D36—122no—
187C4×D9—62no—
188C4×D9—62no—
189C4×D9—61no—
190C4×D9—61no—
191C8×C9—61no—
192C9⋊C8—21no—
193#447—271noSylow
194C2×C3×C9—42no—
195C2×C3×C9#12011yescharacteristic
196C2×C3×C9C2×D811yescharacteristic
197C2×C3×C9AGL(1,ℤ/8)11yescharacteristic
198C3⋊D9—22no—
199C3⋊D9—42no—
200C3×D9—81no—
201C23×D3—181no—
202C23×D3—181no—
203C23×D3—182no—
204C2×C3×D4—21no—
205C2×C3×D4—91no—
206C2×C3×D4C2×D911yescharacteristic
207C2×C3×D4D3211yescharacteristic
208C2×#67—181no—
209C2×#67—181no—
210C2×#67—181no—
211C2×#67—182no—
212D3×D4—182no—
213D3×D4—182no—
214D3×D4—184no—
215D3×D4—184no—
216D3×D4—182no—
217D3×D4—182no—
218C2×D12—31no—
219C2×D12—91no—
220C2×D12—91no—
221C2×D12—181no—
222C2×D12—181no—
223C2×C4×D3—91no—
224C2×C4×D3—91no—
225C2×C4×D3—181no—
226C3×D8—182no—
227C2×C3×C8—31no—
228C2×C3×C8—91no—
229C3×C4⋊C4—31no—
230#217—181no—
231#213—62no—
232#213—182no—
233(C2×D3)⋊C4—181no—
234C4⋊Dic3C2×D911yescharacteristic, complemented
235C2×C3⋊C8—31no—
236C2×C3⋊C8C2×D911yescharacteristic, complemented
237D24—182no—
238C22×C32—22no—
239C22×C32—41no—
240C22×C32—41no—
241C22×C32D3×D411yescharacteristic
242C2×C3⋊D3—32no—
243C2×C3⋊D3—61no—
244C2×C3⋊D3—61no—
245C2×C3⋊D3—62no—
246C2×C3⋊D3—128no—
247C2×C3⋊D3—121no—
248C2×C3⋊D3—121no—
249C2×C3×D3—121no—
250C2×C3×D3—121no—
251C2×C3×D3—121no—
252C32×C4C2×D1211yescharacteristic
253C32×C4D3×D411yescharacteristic
254C3⋊Dic3—61no—
255C3×Dic3—41no—
256C22×C9—24no—
257C22×C9—22no—
258C22×C9—21no—
259C22×C9—42no—
260C22×C9—42no—
261C22×C9—41no—
262C22×C9—41no—
263C22×C9D3×D411yescharacteristic
264C2×D9—32no—
265C2×D9—41no—
266C2×D9—41no—
267C2×D9—41no—
268C2×D9—62no—
269C2×D9—62no—
270C2×D9—62no—
271C2×D9—61no—
272C2×D9—61no—
273C2×D9—64no—
274C2×D9—62no—
275C2×D9—1216no—
276C2×D9—128no—
277C2×D9—122no—
278C2×D9—122no—
279C2×D9—121no—
280C2×D9—121no—
281C4×C9—21no—
282C4×C9—21no—
283C4×C9—121no—
284C4×C9D3×D411yescharacteristic
285C4×C9C2×#6711yescharacteristic
286Dic9—62no—
287Dic9—61no—
288C22×D4—271no—
289C2×D8—91no—
290C2×D8—271no—
291#121—271no—
292#102—31no—
293#102—271no—
294C22⋊C8—271no—
295C3×C9#44711yescharacteristic, complemented, Sylow
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—181no—
300C22×D3—61no—
301C22×D3—91no—
302C22×D3—91no—
303C22×D3—181no—
304C22×D3—184no—
305C22×D3—182no—
306C22×D3—188no—
307C22×D3—184no—
308C22×D3—181no—
309C22×D3—181no—
310C22×D3—362no—
311C22×D3—362no—
312C22×D3—362no—
313C22×D3—364no—
314C22×D3—364no—
315C22×D3—362no—
316C3×D4—22no—
317C3×D4—21no—
318C3×D4—21no—
319C3×D4—22no—
320C3×D4—181no—
321C3×D4—181no—
322C3×D4D3612yescomplemented
323C3×D4#62612yes—
324C2×C3×C4—21no—
325C2×C3×C4—61no—
326C2×C3×C4C22×D911yescharacteristic
327C2×C3×C4C2×D3211yescharacteristic
328#67—184no—
329#67—188no—
330#67—184no—
331#67—362no—
332C2×Dic3—21no—
333C2×Dic3—91no—
334C2×Dic3—91no—
335C2×Dic3—181no—
336D12—61no—
337D12—61no—
338D12—92no—
339D12—92no—
340D12—182no—
341D12—182no—
342D12—181no—
343D12—181no—
344D12—362no—
345C4×D3—182no—
346C4×D3—182no—
347C4×D3—181no—
348C4×D3—181no—
349C4×D3—181no—
350C4×D3—181no—
351C3×C8—61no—
352C3×C8—181no—
353C3⋊C8—21no—
354C3⋊C8—61no—
355C2×C32—42no—
356C2×C32#88211yescharacteristic
357C2×C32D3×D811yescharacteristic
358C2×C32#91411yescharacteristic
359C3⋊D3—62no—
360C3⋊D3—122no—
361C3×D3—241no—
362C2×C9—21no—
363C2×C9—21no—
364C2×C9—21no—
365C2×C9—44no—
366C2×C9—42no—
367C2×C9D3×D811yescharacteristic
368C2×C9#91111yescharacteristic
369C2×C9#93711yescharacteristic
370D9—64no—
371D9—62no—
372D9—81no—
373D9—124no—
374D9—122no—
375C24—541no—
376C2×D4—91no—
377C2×D4—271no—
378C2×D4—541no—
379C2×D4—541no—
380C2×D4—542no—
381C2×D4—542no—
382C2×D4D3×D911yescharacteristic
383C22×C4—271no—
384D8—182no—
385D8—542no—
386C2×C8—31no—
387C2×C8—91no—
388C4⋊C4—31no—
389C22⋊C4—541no—
390C22×C3—24no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—21no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—361no—
401C22×C3—361no—
402C22×C3—361no—
403C22×C3D4×D911yescharacteristic
404C22×C3#381111yescharacteristic
405C2×D3—92no—
406C2×D3—92no—
407C2×D3—121no—
408C2×D3—121no—
409C2×D3—121no—
410C2×D3—182no—
411C2×D3—182no—
412C2×D3—182no—
413C2×D3—181no—
414C2×D3—181no—
415C2×D3—181no—
416C2×D3—181no—
417C2×D3—184no—
418C2×D3—182no—
419C2×D3—182no—
420C2×D3—368no—
421C2×D3—3616no—
422C2×D3—368no—
423C2×D3—362no—
424C2×D3—362no—
425C2×D3—361no—
426C2×D3—361no—
427C2×D3—361no—
428C2×D3—361no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—121no—
432C3×C4C2×D3611yescharacteristic
433C3×C4D4×D911yescharacteristic
434C3×C4C2×#62611yescharacteristic
435C3×C4#381111yescharacteristic
436Dic3—41no—
437Dic3—182no—
438Dic3—181no—
439Dic3—181no—
440C32#477311yescharacteristic
441C9—21no—
442C9#515611yescharacteristic, complemented
443C23—21no—
444C23—181no—
445C23—271no—
446C23—544no—
447C23—541no—
448C23—1082no—
449C23—1082no—
450D4—21no—
451D4—181no—
452D4—181no—
453D4—272no—
454D4—544no—
455D4—541no—
456D4—1082no—
457D4#619212yescomplemented
458C2×C4—61no—
459C2×C4—271no—
460C2×C4—541no—
461C2×C4—541no—
462C2×C4C2×D3×D911yescharacteristic
463C8—61no—
464C8—181no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—44no—
469C2×C3—42no—
470C2×C3—42no—
471C2×C3—721no—
472C2×C3#6344411yescharacteristic
473C2×C3D8×D911yescharacteristic
474C2×C3#6347611yescharacteristic
475C2×C3#6392611yescharacteristic
476C2×C3#6393711yescharacteristic
477C2×C3#6398111yescharacteristic
478D3—184no—
479D3—182no—
480D3—182no—
481D3—241no—
482D3—364no—
483D3—362no—
484D3—362no—
485C22—22no—
486C22—41no—
487C22—41no—
488C22—272no—
489C22—361no—
490C22—361no—
491C22—361no—
492C22—541no—
493C22—541no—
494C22—542no—
495C22—1088no—
496C22—1081no—
497C22—1081no—
498C22#8866811yescharacteristic
499C4—121no—
500C4—541no—
501C4C2×#619211yescharacteristic
502C4#8866811yescharacteristic
503C3—21no—
504C3#1058845311yescharacteristic, complemented
505C3#1059145611yescharacteristic
506C2—42no—
507C2—542no—
508C2—721no—
509C2—1082no—
510C2#1172117411yescharacteristic
511C2#1172118711yescharacteristic
512C2#1172127811yescharacteristic
subgroupG/H
centerC22#88668
commutator, cosocleC2×C3×C4×C9C23
FrattiniC2×C3×C4C2×D32
FittingC2×C3×D4×C9C22
socleC22×C32D3×D4
hypercenterC2×D4D3×D9
hypocenterC3×C9#447
LCSG ▷ C2×C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊D9C2semidirect
2. C2×C3×#3673C2semidirect
3. #11721007C2semidirect
4. C2×#88417C2semidirect
5. C9×#832C2semidirect
6. #11720282C2semidirect
7. #11720267C2semidirect
17. C2×C3×D36C22semidirect
20. C9×C4⋊Dic3C22semidirect
21. C2×C9×C3⋊C8C22semidirect
22. C2×C3×C9⋊C8C22semidirect
34. C2×#3673D3semidirect
48. C3×D4×C9D4semidirect
53. C4⋊(C3⋊D9)D4semidirect
92. C2×D36C2×D3semidirect
99. C2×C9⋊C8C2×D3semidirect
111. C2×C3⋊D9D8semidirect
129. #832D9semidirect
172. D4×C9#67semidirect
234. C4⋊Dic3C2×D9semidirect
236. C2×C3⋊C8C2×D9semidirect
295. C3×C9#447semidirect
322. C3×D4D36semidirect
442. C9#5156semidirect
457. D4#6192semidirect
504. C3#10588453semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊D92
C2×C3×#36732
#117210072
C2×#884172
C9×#8322
#117202822
#117202672
#105914563
#105884533