Finite Group Databasebeta

← #11807970

Subgroups — #11807970

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic
2#10592928C211yesmaximal, characteristic
3C3×#5229C211yesmaximal, characteristic
4#10591272C212yesmaximal
5#10591262C212yesmaximal
6#10591261C212yesmaximal
7#10591223C212yesmaximal
8#10591201C212yesmaximal
9#10591192C212yesmaximal
10#83231—31nomaximal
11#76497—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C3×#944C418yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic32C2212yes—
24#63658C2212yes—
25#63658C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28#63579C2212yes—
29#63579C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34C2×C3×C4⋊Q8—31no—
35C2×#944D311yescharacteristic
36C3×#391—31no—
37#5229—31no—
38#5229—31no—
39#5229—32no—
40#5229—61no—
41#5229D311yescharacteristic
42#4980—32no—
43#4980—32no—
44#4980—32no—
45#4980—32no—
46#4978—32no—
47#4937—32no—
48#4933—32no—
49#4655—32no—
50#4652—32no—
51#4651—32no—
52#4646—32no—
53C2×C32×Q8—41no—
54C2×C32×Q8—41no—
55C2×C32×Q8C2×C414yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×C3×Dic6—41no—
66C2×C3×Dic6—41no—
67C2×C3×Dic6C2×C414yes—
68C4⋊(C3⋊Dic3)—41no—
69C4×C3⋊Dic3—41no—
70C3×C4⋊Dic3—41no—
71C3×Dic3⋊C4C2×C418yes—
72C3×Dic3⋊C4C2×C418yes—
73C3×C4×Dic3—41no—
74C3×C4×Dic3C2×C414yes—
75Dic3⋊Dic3—42no—
76Dic32—42no—
77#2381—91noSylow
78C22×C3×Q8—21no—
79C22×C3×Q8—31no—
80C22×C3×Q8C2×D311yescharacteristic
81C22×C3×Q8C2×D311yescharacteristic
82C22×Dic6C2×D311yescharacteristic
83C3×C4⋊Q8—38no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C4⋊C4—32no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C42—31no—
88C2×C3×C42—31no—
89#944Dic318yescomplemented
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—32no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4C2×D312yes—
97C2×Dic3⋊C4C2×D312yes—
98C2×C4×Dic3—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—61no—
103C2×C4×Dic3C2×D311yescharacteristic
104C2×C4×Dic3C2×D311yescharacteristic
105C3×#95—32no—
106C3×#95—32no—
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—32no—
122C3⋊#95—32no—
123C3⋊#95—62no—
124C3⋊#95—62no—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C23×C32C2411yescharacteristic
128C32×Q8—44no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4C22×C412yes—
136C2×C32×C4C22×C412yes—
137C2×C32×C4C22×C412yes—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—24no—
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×Dic3—24no—
152C2×C3×Dic3C22×C414yes—
153C2×C3×Dic3C22×C414yes—
154C3×Dic6—44no—
155C2×C4⋊Q8—31no—
156#391—31no—
157#391—92no—
158#391—91no—
159#387—92no—
160#387—92no—
161#387—92no—
162#387—92no—
163#383—92no—
164C2×C3×Q8—24no—
165C2×C3×Q8—34no—
166C2×C3×Q8—41no—
167C2×C3×Q8—41no—
168C2×C3×Q8—41no—
169C2×C3×Q8—41no—
170C2×C3×Q8—42no—
171C2×C3×Q8—42no—
172C2×C3×Q8—121no—
173C2×C3×Q8—121no—
174C2×C3×Q8C4×D314yes—
175C2×C3×Q8C2×Dic314yes—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—32no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—32no—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—32no—
193C22×Dic3—62no—
194C22×Dic3—62no—
195C22×Dic3C22×D312yes—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C2×Dic6—41no—
200C2×Dic6—41no—
201C2×Dic6C2×Dic314yes—
202C3×C4⋊C4—38no—
203C3×C4⋊C4—38no—
204C3×C4⋊C4—121no—
205C3×C42—34no—
206C3×C42—121no—
207C4⋊Dic3—41no—
208C4⋊Dic3—122no—
209C4⋊Dic3—121no—
210C4⋊Dic3—121no—
211C4⋊Dic3—122no—
212Dic3⋊C4—122no—
213Dic3⋊C4C2×Dic318yes—
214Dic3⋊C4C2×Dic318yes—
215C4×Dic3—41no—
216C4×Dic3—122no—
217C4×Dic3—122no—
218C4×Dic3—121no—
219C4×Dic3—121no—
220C4×Dic3—122no—
221C4×Dic3C2×Dic314yes—
222C22×C32C23×C411yescharacteristic
223C22×C32H(5,𝔽2)11yescharacteristic
224C22×C32H(5,𝔽2)11yescharacteristic
225C22×C322−1+412yes—
226C22×C322−1+412yes—
227C32×C4—22no—
228C32×C4—22no—
229C32×C4—22no—
230C3⋊Dic3—42no—
231C3⋊Dic3—42no—
232C3×Dic3—24no—
233C3×Dic3—24no—
234C3×Dic3—42no—
235C3×Dic3—42no—
236C22×Q8—31no—
237C22×Q8D3211yescharacteristic
238C4⋊Q8—38no—
239C2×C4⋊C4—32no—
240C2×C4⋊C4—32no—
241C2×C4⋊C4—31no—
242C2×C4⋊C4—92no—
243C2×C4⋊C4—91no—
244C2×C42—31no—
245C2×C42—31no—
246C2×C42—92no—
247C2×C42—91no—
248#95—32no—
249#95—32no—
250#95—92no—
251#95—92no—
252#95—92no—
253#95—92no—
254#95—92no—
255#95—92no—
256#95—92no—
257#95—92no—
258C23×C3—21no—
259C23×C3C23×D311yescharacteristic
260C23×C3C23×D311yescharacteristic
261C3×Q8—44no—
262C3×Q8—44no—
263C3×Q8—48no—
264C3×Q8—124no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—34no—
283C2×C3×C4—34no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—64no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4C2×C4×D312yes—
298C2×C3×C4C2×C4×D312yes—
299C2×C3×C4C2×C4×D312yes—
300C2×C3×C4C22×Dic312yes—
301C2×C3×C4C22×Dic312yes—
302C2×C3×C4C22×Dic312yes—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—24no—
312C2×Dic3—64no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—64no—
320C2×Dic3—62no—
321C2×Dic3—64no—
322C2×Dic3—62no—
323C2×Dic3—122no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3—124no—
327C2×Dic3C22×Dic314yes—
328C2×Dic3C22×Dic314yes—
329Dic6—44no—
330C2×C32#51811yescharacteristic
331C2×C32#51912yes—
332C2×C32#56312yes—
333C2×C32#56311yescharacteristic
334C2×C32#56311yescharacteristic
335C2×Q8—34no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×Q8—121no—
339C2×Q8—121no—
340C2×Q8D3×Dic314yes—
341C22×C4—32no—
342C22×C4—32no—
343C22×C4—32no—
344C22×C4—32no—
345C22×C4—92no—
346C22×C4—92no—
347C22×C4C2×D3211yescharacteristic
348C22×C4C2×D3211yescharacteristic
349C22×C4C2×D3211yescharacteristic
350C4⋊C4—38no—
351C4⋊C4—38no—
352C4⋊C4—121no—
353C4⋊C4—361no—
354C4⋊C4—362no—
355C42—34no—
356C42—121no—
357C42—361no—
358C42—362no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3C22×C4×D311yescharacteristic
365C22×C3#100411yescharacteristic
366C22×C3#100411yescharacteristic
367C22×C3#100411yescharacteristic
368C22×C3#100411yescharacteristic
369C22×C3#100712yes—
370C22×C3#100712yes—
371C22×C3#100712yes—
372C22×C3#101012yes—
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—124no—
392Dic3—122no—
393Dic3—122no—
394Dic3—122no—
395Dic3—122no—
396Dic3—242no—
397C32#238111yescharacteristic, complemented, Sylow
398C23C22×D3211yescharacteristic
399Q8—44no—
400Q8—124no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—34no—
408C2×C4—34no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—64no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—182no—
419C2×C4—182no—
420C2×C4—184no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4C2×D3×Dic312yes—
424C2×C4C2×D3×Dic312yes—
425C2×C4C2×D3×Dic312yes—
426C2×C3—22no—
427C2×C3—22no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3#548611yescharacteristic
432C2×C3#557212yes—
433C2×C3#564612yes—
434C2×C3#567211yescharacteristic
435C2×C3#573512yes—
436C2×C3#573511yescharacteristic
437C2×C3#573511yescharacteristic
438C2×C3#573511yescharacteristic
439C2×C3#579811yescharacteristic
440C2×C3#581212yes—
441C22#6431512yes—
442C22#6431612yes—
443C22C22×D3×Dic311yescharacteristic
444C22#6433011yescharacteristic
445C22#6433011yescharacteristic
446C4—22no—
447C4—22no—
448C4—22no—
449C4—64no—
450C4—64no—
451C4—122no—
452C4—122no—
453C4—362no—
454C4—362no—
455C3—21no—
456C3#7649711yescharacteristic, complemented
457C3#8323111yescharacteristic, complemented
458C2#1059534512yes—
459C2#1059534712yes—
460C2#1059535211yescharacteristic
461C2#1059539311yescharacteristic
462C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, prime radical, cosocleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
16. C3×#944C4semidirect
89. #944Dic3semidirect
397. C32#2381semidirect
456. C3#76497semidirect
457. C3#83231semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9442
#105929282
C3×#52292
#105912722
#105912622
#105912612
#105912232
#105912012
#105911922
#832313
#764973