Finite Group Databasebeta

← #11805932

Subgroups — #11805932

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C3×#4935C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4#10591274C212yesmaximal
5Dic3×C4⋊Dic3C212yesmaximal
6#10591263C214yesmaximal
7#10591230C212yesmaximal
8#10591213C212yesmaximal
9#74325—31nomaximal
10#73640—31nomaximal
11C22×#634C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C4×#634C418yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2212yes—
23C2×Dic32C2214yes—
24C3×C3⋊#95C2212yes—
25#63579C2214yes—
26#63579C2214yes—
27#63579C2214yes—
28C2×C4×Dic6—31no—
29C2×C4×Dic6—31no—
30C2×C4×Dic6—61no—
31C3×#384—31no—
32C3×C4×C4⋊C4—31no—
33#4978—34no—
34#4977—32no—
35#4977—32no—
36Dic3×C4⋊C4—32no—
37Dic3×C4⋊C4—32no—
38Dic3×C4⋊C4—32no—
39#4973—32no—
40#4935D311yescharacteristic
41C4×C4⋊Dic3—32no—
42C4×C4⋊Dic3D311yescharacteristic
43#4929—32no—
44#4655—34no—
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2312yes—
50C2×#634—22no—
51C2×#634—22no—
52C2×#634C2×C414yes—
53C22×C3×Dic3C2312yes—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2312yes—
56C32×C42C2×C414yes—
57C4⋊(C3⋊Dic3)C2×C414yes—
58#3750C2×C418yes—
59C4×C3⋊Dic3C2×C418yes—
60C3×C4⋊Dic3—22no—
61C3×C4⋊Dic3—24no—
62C3×C4⋊Dic3—24no—
63C3×C4⋊Dic3—42no—
64C3×C4⋊Dic3Q814yescomplemented
65C3×C4×Dic3—24no—
66Dic32—44no—
67#2355—91noSylow
68C22×Dic6—31no—
69C22×Dic6—31no—
70C22×Dic6—61no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4—32no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C42—21no—
77C2×C3×C42—32no—
78C2×C3×C42C2×D311yescharacteristic
79C2×C3×C42C2×D311yescharacteristic
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—61no—
83C2×C4⋊Dic3C2×D312yes—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D312yes—
86C2×C4⋊Dic3C2×D312yes—
87C2×C4⋊Dic3C2×D311yescharacteristic
88C2×Dic3⋊C4—32no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—62no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—62no—
96C2×C4×Dic3C2×D312yes—
97C4×Dic6—38no—
98C4×Dic6—38no—
99C4×Dic6—68no—
100C3×#95—32no—
101C3⋊#95—34no—
102C3⋊#95—34no—
103C3⋊#95—34no—
104C3⋊#95—34no—
105C3⋊#95—34no—
106C3⋊#95—34no—
107C3⋊#95C2×D312yes—
108C23×C32C2411yescharacteristic
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C22×C412yes—
112C2×C32×C4C22×C412yes—
113C2×C32×C4C22×C412yes—
114C2×C32×C4C2×Q812yes—
115C2×C32×C4#4112yes—
116C2×C32×C4#4112yes—
117C2×C32×C4#4112yes—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3C22×C414yes—
123C2×C3⋊Dic3C22×C414yes—
124#634—28no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3C2×Q814yes—
134C2×C4×Q8—91no—
135#391—92no—
136#387—94no—
137#384—31no—
138#382—92no—
139C4×C4⋊C4—31no—
140C4×C4⋊C4—92no—
141C4×C4⋊C4—92no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—32no—
146C22×C3×C4—32no—
147C22×C3×C4—34no—
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—62no—
159C22×Dic3—62no—
160C22×Dic3C22×D312yes—
161C22×Dic3C22×D314yes—
162C22×Dic3C22×D312yes—
163C2×Dic6—34no—
164C2×Dic6—34no—
165C2×Dic6—64no—
166C2×Dic6—64no—
167C2×Dic6—64no—
168C2×Dic6—62no—
169C2×Dic6—62no—
170C2×Dic6—62no—
171C2×Dic6—62no—
172C3×C4⋊C4—34no—
173C3×C4⋊C4—64no—
174C3×C4⋊C4—62no—
175C3×C4⋊C4—64no—
176C3×C4⋊C4—122no—
177C3×C42—24no—
178C3×C42—64no—
179C3×C42C4×D314yes—
180C3×C42C4×D314yes—
181C4⋊Dic3—22no—
182C4⋊Dic3—24no—
183C4⋊Dic3—24no—
184C4⋊Dic3—34no—
185C4⋊Dic3—34no—
186C4⋊Dic3—42no—
187C4⋊Dic3—64no—
188C4⋊Dic3Dic614yescomplemented
189Dic3⋊C4—38no—
190Dic3⋊C4—38no—
191Dic3⋊C4—68no—
192C4×Dic3—24no—
193C4×Dic3—38no—
194C4×Dic3—38no—
195C4×Dic3—68no—
196C4×Dic3—124no—
197C4×Dic3—124no—
198C22×C32C23×C411yescharacteristic
199C22×C32C22×Q811yescharacteristic
200C22×C32C2×#4111yescharacteristic
201C22×C32C2×#4111yescharacteristic
202C22×C32C2×#4111yescharacteristic
203C22×C32H(5,𝔽2)11yescharacteristic
204C22×C322−1+411yescharacteristic
205C32×C4—22no—
206C32×C4#11714yes—
207C32×C4C4×Q814yes—
208C3⋊Dic3—24no—
209C3⋊Dic3—24no—
210C3×Dic3—24no—
211C3×Dic3—42no—
212C3×Dic3—44no—
213C22×Q8—91no—
214C4×Q8—98no—
215C2×C4⋊C4—31no—
216C2×C4⋊C4—31no—
217C2×C4⋊C4—32no—
218C2×C4⋊C4—32no—
219C2×C4⋊C4—32no—
220C2×C4⋊C4—91no—
221C2×C4⋊C4—92no—
222C2×C42—32no—
223C2×C42—92no—
224C2×C42—94no—
225C2×C42D3211yescharacteristic
226#95—32no—
227#95—94no—
228#95—94no—
229#95—94no—
230C23×C3—21no—
231C23×C3C23×D311yescharacteristic
232C23×C3C23×D311yescharacteristic
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—34no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—62no—
248C2×C3×C4—62no—
249C2×C3×C4—64no—
250C2×C3×C4—62no—
251C2×C3×C4—62no—
252C2×C3×C4—64no—
253C2×C3×C4—62no—
254C2×C3×C4—64no—
255C2×C3×C4C2×Dic612yes—
256C2×C3×C4C2×C4×D312yes—
257C2×C3×C4C2×C4×D312yes—
258C2×C3×C4C2×C4×D312yes—
259C2×C3×C4C2×C4×D312yes—
260C2×C3×C4C2×C4×D312yes—
261C2×C3×C4C2×C4×D312yes—
262C2×C3×C4#23512yes—
263C2×C3×C4#23712yes—
264C2×C3×C4#23712yes—
265C2×C3×C4#23712yes—
266C2×C3×C4D3×Q812yes—
267C2×C3×C4#23912yes—
268C2×C3×C4#23912yes—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—22no—
273C2×Dic3—24no—
274C2×Dic3—24no—
275C2×Dic3—24no—
276C2×Dic3—22no—
277C2×Dic3—34no—
278C2×Dic3—34no—
279C2×Dic3—34no—
280C2×Dic3—34no—
281C2×Dic3—64no—
282C2×Dic3—64no—
283C2×Dic3—64no—
284C2×Dic3—64no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—122no—
294C2×Dic3—122no—
295C2×Dic3C2×Dic614yes—
296Dic6—616no—
297Dic6—68no—
298Dic6—68no—
299C2×C32C2×#11711yescharacteristic
300C2×C32C2×C4×Q811yescharacteristic
301C2×C32#52011yescharacteristic
302C2×C32#55411yescharacteristic
303C2×C32#55611yescharacteristic
304C2×C32#55711yescharacteristic
305C2×C32#55911yescharacteristic
306C2×Q8—94no—
307C2×Q8—182no—
308C2×Q8—182no—
309C22×C4—32no—
310C22×C4—32no—
311C22×C4—34no—
312C22×C4—92no—
313C22×C4—92no—
314C22×C4C2×D3211yescharacteristic
315C22×C4C2×D3211yescharacteristic
316C22×C4C2×D3211yescharacteristic
317C4⋊C4—34no—
318C4⋊C4—62no—
319C4⋊C4—64no—
320C4⋊C4—64no—
321C4⋊C4—98no—
322C4⋊C4—94no—
323C4⋊C4—122no—
324C42—64no—
325C42—98no—
326C42—364no—
327C42#62414yes—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3C22×Dic611yescharacteristic
336C22×C3C22×C4×D311yescharacteristic
337C22×C3C22×C4×D311yescharacteristic
338C22×C3C2×#23511yescharacteristic
339C22×C3C2×#23711yescharacteristic
340C22×C3C2×#23711yescharacteristic
341C22×C3C2×#23711yescharacteristic
342C22×C3#100411yescharacteristic
343C22×C3C2×D3×Q811yescharacteristic
344C22×C3C2×#23911yescharacteristic
345C22×C3C2×#23911yescharacteristic
346C22×C3#100711yescharacteristic
347C22×C3#100911yescharacteristic
348C22×C3#101011yescharacteristic
349C3×C4—22no—
350C3×C4—22no—
351C3×C4—24no—
352C3×C4—24no—
353C3×C4—42no—
354C3×C4—64no—
355C3×C4—122no—
356C3×C4—124no—
357C3×C4C4×Dic614yes—
358C3×C4#88714yes—
359C3×C4#89214yes—
360C3×C4#89214yes—
361Dic3—24no—
362Dic3—44no—
363Dic3—42no—
364Dic3—68no—
365Dic3—64no—
366Dic3—64no—
367Dic3—64no—
368Dic3—64no—
369Dic3—124no—
370C32#235511yescharacteristic, complemented, Sylow
371C23C22×D3211yescharacteristic
372Q8—188no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—34no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—64no—
380C2×C4—62no—
381C2×C4—64no—
382C2×C4—62no—
383C2×C4—64no—
384C2×C4—94no—
385C2×C4—94no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4D3×Dic612yes—
391C2×C4#379512yes—
392C2×C4#379612yes—
393C2×C4#379612yes—
394C2×C4C2×#62412yes—
395C2×C4C2×#62412yes—
396C2×C4C2×#62412yes—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3C2×C4×Dic611yescharacteristic
405C2×C3C2×#88711yescharacteristic
406C2×C3C2×#89211yescharacteristic
407C2×C3C2×#89211yescharacteristic
408C2×C3#550411yescharacteristic
409C2×C3#552311yescharacteristic
410C2×C3#554211yescharacteristic
411C2×C3#554311yescharacteristic
412C2×C3#557011yescharacteristic
413C2×C3#558511yescharacteristic
414C2×C3#571311yescharacteristic
415C2×C3#572111yescharacteristic
416C2×C3#573011yescharacteristic
417C2×C3#573211yescharacteristic
418C22C2×D3×Dic611yescharacteristic
419C22C2×#379511yescharacteristic
420C22C2×#379611yescharacteristic
421C22C2×#379611yescharacteristic
422C22#6429711yescharacteristic
423C22#6430711yescharacteristic
424C22C22×#62411yescharacteristic
425C4—22no—
426C4—64no—
427C4—122no—
428C4—124no—
429C4—184no—
430C4—184no—
431C4#6384414yes—
432C4#6384914yes—
433C3—21no—
434C3#7364011yescharacteristic, complemented
435C3#7432511yescharacteristic, complemented
436C2#1059386111yescharacteristic
437C2#1059386311yescharacteristic
438C2#1059395111yescharacteristic
439C2#1059395611yescharacteristic
440C2C2×#6384411yescharacteristic
441C2C2×#6384911yescharacteristic
442C2#1059499011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
16. C4×#634C4semidirect
64. C3×C4⋊Dic3Q8semidirect
188. C4⋊Dic3Dic6semidirect
370. C32#2355semidirect
434. C3#73640semidirect
435. C3#74325semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C3×#49352
C3×C4×C4⋊Dic32
#105912742
Dic3×C4⋊Dic32
#105912632
#105912302
#105912132
#743253
#736403