Finite Group Databasebeta

← #13178296

Subgroups — #13178296

Order 1728.

882 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64099C211yesmaximal, characteristic
2C3×#64098C212yesmaximal
3#11723680C212yesmaximal
4#11723679C212yesmaximal
5#11723679C211yesmaximal, characteristic
6#11723679C211yesmaximal, characteristic
7#11723669C212yesmaximal
8#11723669C212yesmaximal
9#11723669C212yesmaximal
10#10594354—31nomaximal
11#10594326—32nomaximal
12C33×C4⋊C4C2211yescharacteristic
13C3×C4⋊(C3⋊Dic3)C2212yes—
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C3×C4⋊(C3⋊Dic3)C2212yes—
16C3×#3750C2212yes—
17C3×#3750C2212yes—
18C3×#3750C2212yes—
19C3×#3750C2212yes—
20C3×#3750C2212yes—
21C3×C4×C3⋊Dic3C2212yes—
22C3×C4×C3⋊Dic3C2211yescharacteristic
23#88815C2212yes—
24#88815C2211yescharacteristic
25#88815C2211yescharacteristic
26#88815C2212yes—
27#88815C2212yes—
28#88815C2212yes—
29#88815C2212yes—
30#88815C2211yescharacteristic
31#88815C2211yescharacteristic
32#88813C2212yes—
33#64099D311yescharacteristic
34#64098D312yes—
35C3×#890—32no—
36C3×#890—61no—
37C3×#889—32no—
38C3×#889—32no—
39C3×#889—62no—
40#63872—32no—
41#63870—32no—
42#63870—31no—
43#63870—31no—
44#63869—32no—
45#63869—32no—
46#63867—32no—
47#63867—32no—
48#63867—32no—
49#63867—32no—
50#63847—32no—
51#63847—32no—
52#63847—32no—
53#63846—32no—
54#63846—32no—
55#63846—32no—
56#63845—32no—
57#63845—32no—
58#63845—32no—
59C2×C33×C4C2311yescharacteristic
60C2×C33×C4C2312yes—
61C2×C3×C3⋊Dic3C2312yes—
62C2×C3×C3⋊Dic3C2311yescharacteristic
63C2×C3×C3⋊Dic3C2312yes—
64C2×C3×C3⋊Dic3C2311yescharacteristic
65C2×C3×C3⋊Dic3C2312yes—
66C2×C3×C3⋊Dic3C2312yes—
67C2×C3×C3⋊Dic3C2312yes—
68C3⋊#564—91no—
69C3⋊#564—92no—
70C32×C4⋊C4—22no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—41no—
73C32×C4⋊C4C2×D311yescharacteristic
74C32×C4⋊C4C2×D312yes—
75C4⋊(C3⋊Dic3)C2×D312yes—
76C4⋊(C3⋊Dic3)C2×D311yescharacteristic
77C4⋊(C3⋊Dic3)C2×D312yes—
78#3750C2×D312yes—
79#3750C2×D312yes—
80#3750C2×D312yes—
81#3750C2×D312yes—
82#3750C2×D312yes—
83C4×C3⋊Dic3C2×D312yes—
84C4×C3⋊Dic3C2×D311yescharacteristic
85C3×C4⋊Dic3—32no—
86C3×C4⋊Dic3—32no—
87C3×C4⋊Dic3—32no—
88C3×C4⋊Dic3—32no—
89C3×C4⋊Dic3—32no—
90C3×C4⋊Dic3—62no—
91C3×C4⋊Dic3—62no—
92C3×C4⋊Dic3—61no—
93C3×Dic3⋊C4—32no—
94C3×Dic3⋊C4—32no—
95C3×Dic3⋊C4—32no—
96C3×Dic3⋊C4—32no—
97C3×Dic3⋊C4—32no—
98C3×Dic3⋊C4—32no—
99C3×Dic3⋊C4—32no—
100C3×Dic3⋊C4—32no—
101C3×Dic3⋊C4—32no—
102C3×Dic3⋊C4—32no—
103C3×Dic3⋊C4—62no—
104C3×Dic3⋊C4—62no—
105C3×Dic3⋊C4—62no—
106C3×Dic3⋊C4—62no—
107C3×Dic3⋊C4—62no—
108C3×C4×Dic3—32no—
109C3×C4×Dic3—32no—
110C3×C4×Dic3—32no—
111C3×C4×Dic3—62no—
112C3×C4×Dic3—61no—
113#3724—31no—
114#3724—32no—
115#3724—32no—
116#3724—32no—
117#3724—31no—
118#3724—32no—
119#3724—32no—
120#3724—31no—
121#3724—31no—
122Dic3⋊Dic3—32no—
123Dic3⋊Dic3—32no—
124Dic3⋊Dic3—32no—
125Dic3⋊Dic3—32no—
126Dic3⋊Dic3—32no—
127Dic3⋊Dic3—32no—
128Dic3⋊Dic3—32no—
129Dic3⋊Dic3—32no—
130Dic3⋊Dic3—32no—
131Dic3⋊Dic3—32no—
132Dic3⋊Dic3—32no—
133Dic3⋊Dic3—32no—
134Dic3⋊Dic3—32no—
135Dic3⋊Dic3—32no—
136Dic32—32no—
137Dic32—32no—
138Dic32—32no—
139C22×C33C2411yescharacteristic
140C33×C4—21no—
141C33×C4—22no—
142C3×C3⋊Dic3—22no—
143C3×C3⋊Dic3—21no—
144C3×C3⋊Dic3—22no—
145C3×C3⋊Dic3—22no—
146C3×C3⋊Dic3—22no—
147C3×C3⋊Dic3—21no—
148C3×C3⋊Dic3—22no—
149C3×#125—92no—
150C3×#125—91no—
151#890—32no—
152#890—61no—
153#890—92no—
154#890—92no—
155#890—92no—
156#890—92no—
157#890—92no—
158#889—32no—
159#889—32no—
160#889—62no—
161#889—92no—
162#889—92no—
163#889—92no—
164#889—92no—
165#889—92no—
166#889—92no—
167#889—92no—
168#889—92no—
169#889—92no—
170#889—92no—
171#870—91no—
172#870—91no—
173#870—92no—
174#870—92no—
175C2×C32×C4—21no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—41no—
181C2×C32×C4—42no—
182C2×C32×C4C22×D312yes—
183C2×C32×C4C22×D312yes—
184C2×C32×C4C22×D312yes—
185C2×C32×C4C22×D311yescharacteristic
186C2×C32×C4C22×D312yes—
187C2×C3⋊Dic3C22×D312yes—
188C2×C3⋊Dic3C22×D312yes—
189C2×C3⋊Dic3C22×D312yes—
190C2×C3⋊Dic3C22×D312yes—
191C2×C3⋊Dic3C22×D311yescharacteristic
192C2×C3⋊Dic3C22×D312yes—
193C2×C3⋊Dic3C22×D311yescharacteristic
194C2×C3×Dic3—32no—
195C2×C3×Dic3—32no—
196C2×C3×Dic3—32no—
197C2×C3×Dic3—32no—
198C2×C3×Dic3—32no—
199C2×C3×Dic3—32no—
200C2×C3×Dic3—32no—
201C2×C3×Dic3—32no—
202C2×C3×Dic3—32no—
203C2×C3×Dic3—32no—
204C2×C3×Dic3—32no—
205C2×C3×Dic3—32no—
206C2×C3×Dic3—62no—
207C2×C3×Dic3—61no—
208C2×C3×Dic3—62no—
209C2×C3×Dic3—61no—
210C2×C3×Dic3—62no—
211C2×C3×Dic3—62no—
212C2×C3×Dic3—62no—
213#564—271noSylow
214C2×C332−1+411yescharacteristic
215C2×C332−1+411yescharacteristic
216C2×C332−1+411yescharacteristic
217C3×C4⋊C4—22no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—41no—
220C3×C4⋊C4—92no—
221C3×C4⋊C4—92no—
222C3×C4⋊C4—91no—
223C3×C4⋊C4—92no—
224C3×C4⋊C4—92no—
225C3×C4⋊C4—92no—
226C3×C4⋊C4—92no—
227C3×C4⋊C4—92no—
228C3×C4⋊C4D3211yescharacteristic
229C3×C4⋊C4D3212yes—
230C3×C42—92no—
231C3×C42—91no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—62no—
238C4⋊Dic3—62no—
239C4⋊Dic3—61no—
240C4⋊Dic3—91no—
241C4⋊Dic3—92no—
242C4⋊Dic3—91no—
243C4⋊Dic3—92no—
244C4⋊Dic3—91no—
245C4⋊Dic3—91no—
246C4⋊Dic3—92no—
247C4⋊Dic3—92no—
248C4⋊Dic3—92no—
249Dic3⋊C4—32no—
250Dic3⋊C4—32no—
251Dic3⋊C4—32no—
252Dic3⋊C4—32no—
253Dic3⋊C4—32no—
254Dic3⋊C4—32no—
255Dic3⋊C4—32no—
256Dic3⋊C4—32no—
257Dic3⋊C4—32no—
258Dic3⋊C4—32no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—92no—
265Dic3⋊C4—92no—
266Dic3⋊C4—92no—
267Dic3⋊C4—92no—
268Dic3⋊C4—92no—
269Dic3⋊C4—92no—
270Dic3⋊C4—92no—
271Dic3⋊C4—92no—
272Dic3⋊C4—92no—
273Dic3⋊C4—92no—
274Dic3⋊C4—92no—
275Dic3⋊C4—92no—
276Dic3⋊C4—92no—
277Dic3⋊C4—92no—
278C4×Dic3—32no—
279C4×Dic3—32no—
280C4×Dic3—32no—
281C4×Dic3—62no—
282C4×Dic3—61no—
283C4×Dic3—92no—
284C4×Dic3—92no—
285C4×Dic3—92no—
286C22×C32—22no—
287C22×C32—21no—
288C22×C32—41no—
289C22×C32C23×D311yescharacteristic
290C22×C32C23×D312yes—
291C32×C4—21no—
292C32×C4—22no—
293C32×C4—22no—
294C32×C4—22no—
295C32×C4—22no—
296C32×C4—22no—
297C32×C4—42no—
298C32×C4—42no—
299C32×C4—42no—
300C32×C4—42no—
301C32×C4—42no—
302C32×C4—82no—
303C3⋊Dic3—22no—
304C3⋊Dic3—22no—
305C3⋊Dic3—22no—
306C3⋊Dic3—22no—
307C3⋊Dic3—21no—
308C3⋊Dic3—22no—
309C3⋊Dic3—21no—
310C3×Dic3—64no—
311C3×Dic3—62no—
312C3×Dic3—62no—
313C3×Dic3—62no—
314C3×Dic3—62no—
315C3×Dic3—62no—
316C3×Dic3—62no—
317C3×Dic3—62no—
318C3×Dic3—62no—
319C3×Dic3—62no—
320C3×Dic3—62no—
321C3×Dic3—62no—
322C3×Dic3—62no—
323C3×Dic3—122no—
324C3×Dic3—122no—
325C3×Dic3—121no—
326C3×Dic3—122no—
327C3×Dic3—121no—
328C3×Dic3—122no—
329#125—92no—
330#125—91no—
331#125—272no—
332#125—271no—
333#125—271no—
334#125—272no—
335#125—272no—
336#125—272no—
337#125—272no—
338C33#56411yescharacteristic, complemented, Sylow
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—41no—
345C2×C3×C4—42no—
346C2×C3×C4—92no—
347C2×C3×C4—92no—
348C2×C3×C4—92no—
349C2×C3×C4—92no—
350C2×C3×C4—92no—
351C2×C3×C4—91no—
352C2×C3×C4—91no—
353C2×C3×C4C2×D3212yes—
354C2×C3×C4C2×D3212yes—
355C2×C3×C4C2×D3212yes—
356C2×C3×C4C2×D3211yescharacteristic
357C2×C3×C4C2×D3212yes—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—62no—
371C2×Dic3—61no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×C32—22no—
378C2×C32—21no—
379C2×C32—22no—
380C2×C32—21no—
381C2×C32—22no—
382C2×C32—21no—
383C2×C32—41no—
384C2×C32—41no—
385C2×C32—41no—
386C2×C32#100711yescharacteristic
387C2×C32#100712yes—
388C2×C32#101012yes—
389C2×C32#101011yescharacteristic
390C2×C32#101012yes—
391C2×C32#101011yescharacteristic
392C4⋊C4—92no—
393C4⋊C4—92no—
394C4⋊C4—92no—
395C4⋊C4—92no—
396C4⋊C4—92no—
397C4⋊C4—92no—
398C4⋊C4—92no—
399C4⋊C4—91no—
400C4⋊C4—271no—
401C4⋊C4—271no—
402C4⋊C4—272no—
403C4⋊C4—272no—
404C4⋊C4—272no—
405C4⋊C4—272no—
406C4⋊C4—271no—
407C4⋊C4—271no—
408C4⋊C4—272no—
409C4⋊C4#111311yescharacteristic
410C42—92no—
411C42—91no—
412C42—272no—
413C22×C3—22no—
414C22×C3—21no—
415C22×C3—41no—
416C22×C3C22×D3212yes—
417C22×C3C22×D3211yescharacteristic
418C3×C4—22no—
419C3×C4—22no—
420C3×C4—21no—
421C3×C4—22no—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—42no—
429C3×C4—82no—
430C3×C4—182no—
431C3×C4—182no—
432C3×C4—182no—
433C3×C4—181no—
434C3×C4—182no—
435C3×C4—182no—
436C3×C4—181no—
437Dic3—64no—
438Dic3—62no—
439Dic3—62no—
440Dic3—62no—
441Dic3—62no—
442Dic3—62no—
443Dic3—62no—
444Dic3—62no—
445Dic3—62no—
446Dic3—62no—
447Dic3—62no—
448Dic3—62no—
449Dic3—62no—
450Dic3—122no—
451Dic3—122no—
452Dic3—121no—
453Dic3—122no—
454Dic3—121no—
455Dic3—122no—
456C32—22no—
457C32—21no—
458C32—41no—
459C32C3⋊#56411yescharacteristic, complemented
460C32C3⋊#56412yescomplemented
461C2×C4—92no—
462C2×C4—91no—
463C2×C4—92no—
464C2×C4—91no—
465C2×C4—92no—
466C2×C4—92no—
467C2×C4—92no—
468C2×C4C2×#111311yescharacteristic
469C2×C4C2×#111312yes—
470C2×C3—22no—
471C2×C3—21no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—41no—
477C2×C3—41no—
478C2×C3—41no—
479C2×C3#6429712yes—
480C2×C3#6429811yescharacteristic
481C2×C3#6430912yes—
482C2×C3#6430911yescharacteristic
483C2×C3#6431512yes—
484C2×C3#6431611yescharacteristic
485C22C22×#111311yescharacteristic
486C4—21no—
487C4—22no—
488C4—182no—
489C4—182no—
490C4—181no—
491C4—182no—
492C4—182no—
493C4—181no—
494C4—182no—
495C3—22no—
496C3—21no—
497C3—41no—
498C3#1059432612yescomplemented
499C3#1059435411yescharacteristic, complemented
500C2#1172461411yescharacteristic
501C2#1172462011yescharacteristic
502C2#1172462411yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, prime radical, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4#1113
hypocenterC33#564
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
338. C33#564semidirect
459. C32C3⋊#564semidirect
460. C32C3⋊#564semidirect
498. C3#10594326semidirect
499. C3#10594354semidirect

Maximal subgroups

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

subgroupindex
C3×#640992
C3×#640982
#117236802
#117236792
#117236692
#105943543
#105943263