Finite Group Databasebeta

← #11805320

Subgroups — #11805320

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4#10591703C214yesmaximal
5#10591360C212yesmaximal, complemented
6Dic3×C4⋊Dic3C212yesmaximal, complemented
7#10591252C212yesmaximal, complemented
8#10591212C212yesmaximal, complemented
9#73881—31nomaximal
10#73459—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C2×#3757C2212yes—
13#64135C418yescomplemented
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3C2212yes—
17C2×C3×#217C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×#3724C2214yes—
22C2×Dic32C2214yes—
23C3×C3⋊#95C2211yescharacteristic
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2211yescharacteristic
26#63579C2214yes—
27#63579C2214yes—
28C2×#926—31no—
29C2×#926—31no—
30C2×#926—61no—
31C3×#380—31no—
32C3×C4×C22⋊C4—31no—
33#5212D311yescharacteristic
34C4×#217D311yescharacteristic
35Dic3×C4⋊C4—32no—
36#4972—32no—
37#4945—34no—
38#4944—34no—
39C4×C4⋊Dic3—32no—
40#4928—32no—
41#4650—32no—
42#4650—32no—
43#4648—32no—
44#4648—32no—
45C24×C32C2311yescharacteristic
46C22×C32×C4—24no—
47C22×C32×C4C2×C414yes—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2314yes—
54C22×C3×Dic3C2312yes—
55#3757C2×C418yes—
56C4⋊(C3⋊Dic3)C2×C414yes—
57C4⋊(C3⋊Dic3)C2×C414yes—
58C4×C3⋊Dic3C2×C418yes—
59C3×#217—24no—
60C3×#217—42no—
61C3×C4⋊Dic3—24no—
62C3×C4×Dic3—24no—
63#3724—44no—
64Dic32—28no—
65#2346—91noSylow
66C23×C3×C4—21no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C2×D311yescharacteristic
69C2×C3×C4⋊C4—32no—
70C2×C3×C22⋊C4—32no—
71C2×C3×C22⋊C4—32no—
72C2×C3×C42—32no—
73C2×#217—32no—
74C2×#217—32no—
75C2×#217—62no—
76C2×#217C2×D312yes—
77C2×#217C2×D312yes—
78#926—38no—
79#926—38no—
80#926—68no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—61no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3C2×D312yes—
88C2×Dic3⋊C4—34no—
89C2×Dic3⋊C4—34no—
90C2×C4×Dic3—32no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—34no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—62no—
95C2×C4×Dic3C2×D312yes—
96C3×#95—31no—
97C3×#95—32no—
98C3×#95—31no—
99C3⋊#95—34no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C3⋊#95C2×D311yescharacteristic
104C3⋊#95C2×D312yes—
105C3⋊#95C2×D311yescharacteristic
106C23×C32—22no—
107C23×C32—22no—
108C23×C32—21no—
109C23×C32—21no—
110C23×C32C22×C412yes—
111C23×C32C2411yescharacteristic
112C2×C32×C4—22no—
113C2×C32×C4—28no—
114C2×C32×C4C22×C412yes—
115C2×C32×C4C22×C412yes—
116C2×C32×C4#4114yes—
117C2×C3⋊Dic3—24no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3C22×C414yes—
121C2×C3⋊Dic3C22×C414yes—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3#4114yes—
131C2×#117—91no—
132#389—92no—
133#388—94no—
134#382—92no—
135#380—31no—
136C4×C4⋊C4—92no—
137C4×C22⋊C4—31no—
138#376—92no—
139C24×C3—21no—
140C24×C3C22×D311yescharacteristic
141C24×C3C22×D311yescharacteristic
142C22×C3×C4—28no—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—32no—
149C22×C3×C4—34no—
150C22×C3×C4—32no—
151C22×C3×C4C4×D314yes—
152C22×C3×C4C4×D314yes—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—32no—
158C22×Dic3—32no—
159C22×Dic3—32no—
160C22×Dic3—32no—
161C22×Dic3—62no—
162C22×Dic3—62no—
163C22×Dic3C22×D314yes—
164C22×Dic3C22×D312yes—
165C22×Dic3C22×D312yes—
166C3×C4⋊C4—64no—
167C3×C22⋊C4—64no—
168C3×C22⋊C4—122no—
169C3×C42—64no—
170#217—24no—
171#217—38no—
172#217—38no—
173#217—42no—
174#217—68no—
175C4⋊Dic3—24no—
176C4⋊Dic3—34no—
177C4⋊Dic3—34no—
178C4⋊Dic3—34no—
179C4⋊Dic3—34no—
180C4⋊Dic3—64no—
181C4⋊Dic3—64no—
182Dic3⋊C4—124no—
183Dic3⋊C4—124no—
184C4×Dic3—24no—
185C4×Dic3—38no—
186C4×Dic3—38no—
187C4×Dic3—68no—
188C4×Dic3—68no—
189C4×Dic3—68no—
190C22×C32—22no—
191C22×C32—22no—
192C22×C32—22no—
193C22×C32—42no—
194C22×C32—42no—
195C22×C32C23×C411yescharacteristic
196C22×C32C2×#4112yes—
197C22×C32C2×#4112yes—
198C22×C32H(5,𝔽2)11yescharacteristic
199C22×C322−1+411yescharacteristic
200C32×C4—22no—
201C32×C4#11714yes—
202C3⋊Dic3—24no—
203C3⋊Dic3—24no—
204C3×Dic3—24no—
205C3×Dic3—42no—
206C3×Dic3—44no—
207C23×C4D3211yescharacteristic
208#117—98no—
209C2×C4⋊C4—32no—
210C2×C4⋊C4—91no—
211C2×C4⋊C4—91no—
212C2×C4⋊C4—94no—
213C2×C22⋊C4—32no—
214C2×C22⋊C4—32no—
215C2×C22⋊C4—92no—
216C2×C42—32no—
217C2×C42—92no—
218C2×C42—94no—
219#95—31no—
220#95—32no—
221#95—31no—
222#95—94no—
223#95—94no—
224C23×C3—24no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—22no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—22no—
235C23×C3—41no—
236C23×C3—42no—
237C23×C3—41no—
238C23×C3C2×C4×D312yes—
239C23×C3C2×C4×D312yes—
240C23×C3C23×D311yescharacteristic
241C23×C3C23×D311yescharacteristic
242C2×C3×C4—24no—
243C2×C3×C4—216no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—28no—
247C2×C3×C4—28no—
248C2×C3×C4—24no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—34no—
252C2×C3×C4—62no—
253C2×C3×C4—62no—
254C2×C3×C4—64no—
255C2×C3×C4—62no—
256C2×C3×C4—64no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—64no—
260C2×C3×C4C2×C4×D312yes—
261C2×C3×C4C2×C4×D312yes—
262C2×C3×C4C2×C4×D312yes—
263C2×C3×C4C2×C4×D312yes—
264C2×C3×C4#23714yes—
265C2×C3×C4#23714yes—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—22no—
270C2×Dic3—24no—
271C2×Dic3—24no—
272C2×Dic3—24no—
273C2×Dic3—22no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—64no—
279C2×Dic3—64no—
280C2×Dic3—64no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—64no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—122no—
287C2×Dic3—124no—
288C2×Dic3—122no—
289C2×Dic3#23514yes—
290C2×C32—42no—
291C2×C32C2×#11711yescharacteristic
292C2×C32C4×#4111yescharacteristic
293C2×C32#52011yescharacteristic
294C2×C32#55212yes—
295C2×C32#55512yes—
296C24C2×D3211yescharacteristic
297C22×C4—24no—
298C22×C4—32no—
299C22×C4—32no—
300C22×C4—34no—
301C22×C4—92no—
302C22×C4—92no—
303C22×C4#62414yes—
304C22×C4C2×D3211yescharacteristic
305C22×C4C2×D3211yescharacteristic
306C4⋊C4—64no—
307C4⋊C4—94no—
308C4⋊C4—94no—
309C4⋊C4—364no—
310C22⋊C4—64no—
311C22⋊C4—98no—
312C22⋊C4—122no—
313C42—64no—
314C42—98no—
315C42—188no—
316C22×C3—24no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—22no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—44no—
331C22×C3—44no—
332C22×C3—42no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—42no—
336C22×C3C22×C4×D311yescharacteristic
337C22×C3C22×C4×D311yescharacteristic
338C22×C3C2×#23512yes—
339C22×C3C2×#23712yes—
340C22×C3C2×#23712yes—
341C22×C3#100411yescharacteristic
342C22×C3#100711yescharacteristic
343C22×C3D3×#4112yes—
344C22×C3#100911yescharacteristic
345C22×C3#101011yescharacteristic
346C3×C4—24no—
347C3×C4—22no—
348C3×C4—22no—
349C3×C4—24no—
350C3×C4—64no—
351C3×C4—124no—
352C3×C4—122no—
353C3×C4#87714yes—
354C3×C4#87714yes—
355Dic3—24no—
356Dic3—42no—
357Dic3—44no—
358Dic3—64no—
359Dic3—64no—
360Dic3—64no—
361Dic3—64no—
362Dic3—124no—
363Dic3—124no—
364C32#234611yescharacteristic, complemented, Sylow
365C23—21no—
366C23—22no—
367C23—21no—
368C23—22no—
369C23C2×#62412yes—
370C23C22×D3211yescharacteristic
371C2×C4—22no—
372C2×C4—28no—
373C2×C4—34no—
374C2×C4—62no—
375C2×C4—62no—
376C2×C4—64no—
377C2×C4—62no—
378C2×C4—64no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—64no—
382C2×C4—94no—
383C2×C4—94no—
384C2×C4—182no—
385C2×C4—184no—
386C2×C4—182no—
387C2×C4#380514yes—
388C2×C4C2×#62412yes—
389C2×C4C2×#62412yes—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—22no—
395C2×C3—44no—
396C2×C3—42no—
397C2×C3—42no—
398C2×C3C4×#23511yescharacteristic
399C2×C3C2×#87711yescharacteristic
400C2×C3C2×#87711yescharacteristic
401C2×C3#550411yescharacteristic
402C2×C3#552211yescharacteristic
403C2×C3#552311yescharacteristic
404C2×C3#554112yes—
405C2×C3#556312yes—
406C2×C3#561612yes—
407C2×C3#563912yes—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—42no—
412C22—42no—
413C22#6429711yescharacteristic
414C22D3×#23512yes—
415C22#6430711yescharacteristic
416C22C2×#380512yes—
417C22C22×#62411yescharacteristic
418C4—22no—
419C4—64no—
420C4—124no—
421C4—122no—
422C4—184no—
423C4—184no—
424C4#6395714yes—
425C3—21no—
426C3#7345911yescharacteristic, complemented
427C3#7388111yescharacteristic, complemented
428C2—42no—
429C2#1059494212yes—
430C2#1059495411yescharacteristic
431C2#1059499011yescharacteristic
432C2#1059502612yes—
433C2C2×#6395711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2346
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
5. #10591360C2semidirect
6. Dic3×C4⋊Dic3C2semidirect
7. #10591252C2semidirect
8. #10591212C2semidirect
13. #64135C4semidirect
364. C32#2346semidirect
426. C3#73459semidirect
427. C3#73881semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C3×#52122
C3×C4×#2172
#105917032
#105913602
Dic3×C4⋊Dic32
#105912522
#105912122
#738813
#734593