Finite Group Databasebeta

← #11808017

Subgroups — #11808017

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2#10592635C211yesmaximal, characteristic
3C3×#4936C211yesmaximal, characteristic
4#10591272C212yesmaximal
5#10591270C212yesmaximal
6#10591269C212yesmaximal
7#10591268C212yesmaximal
8#10591265C212yesmaximal
9#10591262C212yesmaximal
10#83027—31nomaximal
11#74161—31nomaximal
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C3×#870C418yescomplemented
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic32C2212yes—
25C2×Dic32C2212yes—
26#63658C2212yes—
27#63658C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34C2×C3×#125—31no—
35C2×#870D311yescharacteristic
36C3×#382—31no—
37#4984—32no—
38#4984—32no—
39#4980—32no—
40#4980—32no—
41#4980—32no—
42#4980—32no—
43#4978—32no—
44#4976—32no—
45#4936—31no—
46#4936—31no—
47#4936—61no—
48#4936D311yescharacteristic
49#4655—32no—
50#4654—32no—
51#4653—32no—
52#4647—32no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C32×C42C2×C414yes—
63C4⋊(C3⋊Dic3)—41no—
64C4⋊(C3⋊Dic3)—41no—
65C3×C4⋊Dic3—41no—
66C3×C4⋊Dic3—41no—
67C3×C4⋊Dic3C2×C414yes—
68C3×C4⋊Dic3C2×C414yes—
69C3×Dic3⋊C4C2×C418yes—
70C3×Dic3⋊C4C2×C418yes—
71Dic3⋊Dic3—42no—
72Dic3⋊Dic3—42no—
73Dic32—42no—
74Dic32—42no—
75#2382—91noSylow
76C3×#125—38no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C42—21no—
84C2×C3×C42C2×D311yescharacteristic
85C2×C3×C42C2×D311yescharacteristic
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—32no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4C2×D312yes—
101C2×Dic3⋊C4C2×D312yes—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—32no—
106#870Dic318yescomplemented
107C3×#95—32no—
108C3×#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—32no—
114C3⋊#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—62no—
122C3⋊#95—62no—
123C3⋊#95C2×D312yes—
124C3⋊#95C2×D312yes—
125C23×C32C2411yescharacteristic
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C22×C412yes—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3C22×C414yes—
152C2×C3×Dic3C22×C414yes—
153C2×#125—31no—
154#389—92no—
155#389—92no—
156#387—92no—
157#387—92no—
158#387—92no—
159#387—92no—
160#382—31no—
161#382—91no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—32no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—32no—
176C22×Dic3—32no—
177C22×Dic3—32no—
178C22×Dic3—32no—
179C22×Dic3—62no—
180C22×Dic3—62no—
181C22×Dic3C22×D312yes—
182C22×Dic3C22×D312yes—
183C22×Dic3C22×D312yes—
184C22×Dic3C22×D312yes—
185C3×C4⋊C4—38no—
186C3×C4⋊C4—38no—
187C3×C4⋊C4—34no—
188C3×C4⋊C4—34no—
189C3×C4⋊C4—121no—
190C3×C4⋊C4—121no—
191C3×C42—24no—
192C3×C42C4×D314yes—
193C3×C42C2×Dic314yes—
194C4⋊Dic3—41no—
195C4⋊Dic3—41no—
196C4⋊Dic3—122no—
197C4⋊Dic3—122no—
198C4⋊Dic3—121no—
199C4⋊Dic3—121no—
200C4⋊Dic3—121no—
201C4⋊Dic3—121no—
202C4⋊Dic3—122no—
203C4⋊Dic3—122no—
204C4⋊Dic3C2×Dic314yes—
205C4⋊Dic3C2×Dic314yes—
206Dic3⋊C4—122no—
207Dic3⋊C4—122no—
208Dic3⋊C4C2×Dic318yes—
209Dic3⋊C4C2×Dic318yes—
210C4×Dic3—122no—
211C4×Dic3—122no—
212C4×Dic3—122no—
213C4×Dic3—122no—
214C22×C32C23×C411yescharacteristic
215C22×C32H(5,𝔽2)11yescharacteristic
216C22×C32H(5,𝔽2)11yescharacteristic
217C22×C322−1+411yescharacteristic
218C22×C322−1+411yescharacteristic
219C22×C322−1+411yescharacteristic
220C22×C322−1+411yescharacteristic
221C32×C4—22no—
222C32×C4—22no—
223C32×C4—22no—
224C3⋊Dic3—42no—
225C3⋊Dic3—42no—
226C3×Dic3—24no—
227C3×Dic3—24no—
228C3×Dic3—42no—
229C3×Dic3—42no—
230#125—38no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—32no—
234C2×C4⋊C4—32no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—92no—
238C2×C4⋊C4—92no—
239C2×C4⋊C4—91no—
240C2×C4⋊C4—91no—
241C2×C42—92no—
242C2×C42—92no—
243C2×C42D3211yescharacteristic
244#95—32no—
245#95—32no—
246#95—92no—
247#95—92no—
248#95—92no—
249#95—92no—
250#95—92no—
251#95—92no—
252C23×C3—21no—
253C23×C3C23×D311yescharacteristic
254C23×C3C23×D311yescharacteristic
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—34no—
273C2×C3×C4—34no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4C2×C4×D312yes—
289C2×C3×C4C2×C4×D312yes—
290C2×C3×C4C2×C4×D312yes—
291C2×C3×C4C22×Dic312yes—
292C2×C3×C4C22×Dic312yes—
293C2×C3×C4C22×Dic312yes—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3C22×Dic314yes—
323C2×Dic3C22×Dic314yes—
324C2×C32#51911yescharacteristic
325C2×C32#52011yescharacteristic
326C2×C32#52011yescharacteristic
327C2×C32#56211yescharacteristic
328C2×C32#56311yescharacteristic
329C2×C32#56311yescharacteristic
330C2×C32#56411yescharacteristic
331C22×C4—32no—
332C22×C4—32no—
333C22×C4—32no—
334C22×C4—32no—
335C22×C4—92no—
336C22×C4—92no—
337C22×C4C2×D3211yescharacteristic
338C22×C4C2×D3211yescharacteristic
339C22×C4C2×D3211yescharacteristic
340C4⋊C4—38no—
341C4⋊C4—38no—
342C4⋊C4—34no—
343C4⋊C4—34no—
344C4⋊C4—121no—
345C4⋊C4—121no—
346C4⋊C4—361no—
347C4⋊C4—361no—
348C4⋊C4—362no—
349C4⋊C4—362no—
350C42—362no—
351C42—362no—
352C42D3×Dic314yes—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3C22×C4×D311yescharacteristic
361C22×C3#100411yescharacteristic
362C22×C3#100711yescharacteristic
363C22×C3#100711yescharacteristic
364C22×C3#100711yescharacteristic
365C22×C3#100911yescharacteristic
366C22×C3#100911yescharacteristic
367C22×C3#100911yescharacteristic
368C22×C3#101011yescharacteristic
369C22×C3#101011yescharacteristic
370C22×C3#101011yescharacteristic
371C22×C3#101011yescharacteristic
372C22×C3#101011yescharacteristic
373C22×C3C23×Dic311yescharacteristic
374C3×C4—24no—
375C3×C4—22no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4—22no—
380C3×C4—22no—
381C3×C4—42no—
382C3×C4—42no—
383C3×C4—64no—
384C3×C4—64no—
385C3×C4—122no—
386C3×C4—122no—
387Dic3—24no—
388Dic3—24no—
389Dic3—42no—
390Dic3—42no—
391Dic3—122no—
392Dic3—122no—
393Dic3—122no—
394Dic3—122no—
395Dic3—242no—
396Dic3—242no—
397C32#238211yescharacteristic, complemented, Sylow
398C23C22×D3211yescharacteristic
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—34no—
406C2×C4—34no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—182no—
418C2×C4—182no—
419C2×C4—182no—
420C2×C4—182no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4C2×D3×Dic312yes—
424C2×C4C2×D3×Dic312yes—
425C2×C4C2×D3×Dic312yes—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3#550411yescharacteristic
434C2×C3#551611yescharacteristic
435C2×C3#552311yescharacteristic
436C2×C3#567211yescharacteristic
437C2×C3#568411yescharacteristic
438C2×C3C3⋊#56411yescharacteristic
439C2×C3C3⋊#56411yescharacteristic
440C2×C3#569911yescharacteristic
441C2×C3#569911yescharacteristic
442C2×C3#569911yescharacteristic
443C2×C3#570011yescharacteristic
444C2×C3#581211yescharacteristic
445C2×C3#582711yescharacteristic
446C2×C3#582711yescharacteristic
447C22#6429711yescharacteristic
448C22#6429711yescharacteristic
449C22#6429711yescharacteristic
450C22#6429811yescharacteristic
451C22#6430711yescharacteristic
452C22#6430811yescharacteristic
453C22C22×D3×Dic311yescharacteristic
454C4—22no—
455C4—22no—
456C4—22no—
457C4—64no—
458C4—64no—
459C4—122no—
460C4—122no—
461C4—362no—
462C4—362no—
463C3—21no—
464C3#7416111yescharacteristic, complemented
465C3#8302711yescharacteristic, complemented
466C2#1059385711yescharacteristic
467C2#1059386811yescharacteristic
468C2#1059395211yescharacteristic
469C2#1059395311yescharacteristic
470C2#1059481811yescharacteristic
471C2#1059498611yescharacteristic
472C2#1059499211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2382
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
21. C3×#870C4semidirect
106. #870Dic3semidirect
397. C32#2382semidirect
464. C3#74161semidirect
465. C3#83027semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8702
#105926352
C3×#49362
#105912722
#105912702
#105912692
#105912682
#105912652
#105912622
#830273
#741613