Finite Group Databasebeta

← #11808189

Subgroups — #11808189

Order 1152.

1981 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×#63900C212yesmaximal
3C2×#63883C211yesmaximal, characteristic
4C3⋊D3×#95C211yesmaximal, characteristic
5C3×#4656C212yesmaximal, complemented
6#10591370C212yesmaximal
7#10591344C212yesmaximal, complemented
8#10591338C214yesmaximal, complemented
9D3×#395—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C4×C3⋊D3C2212yes—
12C22×C3×Dic6C2212yes—
13C22×#627C2212yes—
14C22×#624C2211yescharacteristic
15C22×#624C2212yes—
16C22×#624C2211yescharacteristic
17C2×#3797—24no—
18C2×#3797—28no—
19C2×C3×C4⋊Dic3C2214yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×#3724C2214yes—
22C2×Dic3⋊Dic3C2212yes—
23#63900—28no—
24#63883—24no—
25C32×#95C2211yescharacteristic
26#63658C2212yes—
27#63658C2211yescharacteristic
28C3×C3⋊#95C2214yes—
29#63579C2214yes—
30C22×D3×Q8—32no—
31C2×D3×C4⋊C4—34no—
32C2×D3×C4⋊C4—32no—
33C3×#395—32no—
34#5230—32no—
35#4979—32no—
36#4979—34no—
37D3×#95—32no—
38D3×#95—34no—
39D3×#95—61no—
40#4656—34no—
41#4656D312yescomplemented
42C23×C3⋊D3C2311yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C32×C4C2312yes—
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3⋊Dic3C2312yes—
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3—24no—
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3D414yes—
51C2×C4×C3⋊D3Q818yescomplemented
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2314yes—
54C22×C3×Dic3C2312yes—
55C2×C3×Dic6—24no—
56C2×C3×Dic6—28no—
57C2×#627—24no—
58C2×#627—28no—
59C2×#624—24no—
60C2×#624—24no—
61C2×#624—22no—
62C2×#624—22no—
63C2×#624—22no—
64C2×#624—24no—
65C2×#624D418yes—
66C2×#624Q814yescomplemented
67#3797—232no—
68C3×C4⋊Dic3—28no—
69C3×Dic3⋊C4—24no—
70#3724—28no—
71Dic3⋊Dic3—24no—
72C2×#395—91noSylow
73C22×C3×Q8—32no—
74C2×D3×Q8—68no—
75C2×D3×Q8—616no—
76C22×C4×D3—34no—
77C22×C4×D3—32no—
78C22×C4×D3—32no—
79C22×C4×D3—34no—
80C22×C4×D3—32no—
81C22×C4×D3—61no—
82C22×C4×D3—62no—
83C22×Dic6—34no—
84C22×Dic6C2×D312yes—
85C2×C3×C4⋊C4—32no—
86C2×C3×C4⋊C4—34no—
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3C2×D314yes—
89C2×Dic3⋊C4—34no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—34no—
92C2×Dic3⋊C4C2×D312yes—
93D3×C4⋊C4—68no—
94D3×C4⋊C4—616no—
95C3×#95—21no—
96C3×#95—34no—
97C3×#95C2×D312yes—
98C3⋊#95—34no—
99C3⋊#95—32no—
100C3⋊#95—34no—
101C3⋊#95—34no—
102C3⋊#95—62no—
103C3⋊#95—61no—
104C3⋊#95C2×D314yes—
105C23×C32C2411yescharacteristic
106C22×C3⋊D3C2×D412yes—
107C22×C3⋊D3C2×D414yes—
108C22×C3⋊D3C2×Q812yes—
109C22×C3⋊D3C2×Q814yes—
110C22×C3⋊D3#4112yes—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4C2×D412yes—
115C2×C32×C4C2×Q814yescomplemented
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3C2×D412yes—
120C2×C3⋊Dic3C2×Q814yescomplemented
121C4×C3⋊D3—28no—
122C4×C3⋊D3—216no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3C2×D418yes—
130C2×C3×Dic3C2×Q814yescomplemented
131C3×Dic6—216no—
132#627—216no—
133#624—216no—
134#624—28no—
135#624—44no—
136C23×Q8—91no—
137C22×C4⋊C4—91no—
138C22×C4⋊C4—92no—
139#395—32no—
140#395—94no—
141#395—92no—
142C2×#95—92no—
143C2×#95—91no—
144C23×D3—32no—
145C23×D3—61no—
146C2×C3×Q8—68no—
147C2×C3×Q8—64no—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4—32no—
151C22×C3×C4—34no—
152C22×C3×C4—32no—
153C22×C3×C4C22×D312yes—
154C22×C3×C4C22×D314yes—
155C22×Dic3—34no—
156C22×Dic3—32no—
157C22×Dic3—62no—
158C22×Dic3—61no—
159C22×Dic3C22×D312yes—
160C22×Dic3C22×D314yes—
161C22×Dic3C22×D312yes—
162D3×Q8—664no—
163C2×C4×D3—38no—
164C2×C4×D3—316no—
165C2×C4×D3—316no—
166C2×C4×D3—38no—
167C2×C4×D3—64no—
168C2×C4×D3—68no—
169C2×C4×D3—64no—
170C2×C4×D3—64no—
171C2×C4×D3—68no—
172C2×C4×D3—68no—
173C2×C4×D3—68no—
174C2×C4×D3—68no—
175C2×C4×D3—68no—
176C2×C4×D3—64no—
177C2×C4×D3—68no—
178C2×C4×D3—124no—
179C2×C4×D3—124no—
180C2×C4×D3—124no—
181C2×Dic6—24no—
182C2×Dic6—28no—
183C2×Dic6—68no—
184C2×Dic6—68no—
185C2×Dic6—68no—
186C3×C4⋊C4—68no—
187C3×C4⋊C4—64no—
188C4⋊Dic3—28no—
189C4⋊Dic3—64no—
190Dic3⋊C4—24no—
191Dic3⋊C4—64no—
192Dic3⋊C4—68no—
193Dic3⋊C4—68no—
194C22×C32C22×D411yescharacteristic
195C22×C32C22×D412yes—
196C22×C32C22×Q811yescharacteristic
197C22×C32C22×Q812yes—
198C22×C32C2×#4111yescharacteristic
199C2×C3⋊D3#12014yes—
200C2×C3⋊D3C22⋊Q814yes—
201C2×C3⋊D3C22⋊Q818yes—
202C2×C3⋊D3C4⋊Q814yes—
203C2×C3⋊D3C4⋊Q818yes—
204C32×C4—22no—
205C32×C4—24no—
206C3⋊Dic3—22no—
207C3⋊Dic3—24no—
208C3×Dic3—28no—
209C3×Dic3—24no—
210C3×Dic3—42no—
211C22×Q8—32no—
212C22×Q8—92no—
213C22×Q8—188no—
214C22×Q8—184no—
215C23×C4—92no—
216C23×C4—91no—
217C23×C4—91no—
218C23×C4—91no—
219C23×C4—92no—
220C2×C4⋊C4—32no—
221C2×C4⋊C4—34no—
222C2×C4⋊C4—94no—
223C2×C4⋊C4—92no—
224C2×C4⋊C4—188no—
225C2×C4⋊C4—184no—
226#95—34no—
227#95—94no—
228#95—91no—
229#95—92no—
230#95D3211yescharacteristic
231C23×C3—21no—
232C23×C3C23×D312yes—
233C22×D3—34no—
234C22×D3—38no—
235C22×D3—38no—
236C22×D3—34no—
237C22×D3—34no—
238C22×D3—62no—
239C22×D3—64no—
240C22×D3—64no—
241C22×D3—62no—
242C22×D3—62no—
243C3×Q8—616no—
244C2×C3×C4—24no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—22no—
249C2×C3×C4—38no—
250C2×C3×C4—34no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
253C2×C3×C4—42no—
254C2×C3×C4—62no—
255C2×C3×C4—64no—
256C2×C3×C4—64no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—64no—
260C2×C3×C4D3×D414yes—
261C2×C3×C4D3×Q818yescomplemented
262C2×Dic3—22no—
263C2×Dic3—24no—
264C2×Dic3—24no—
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—24no—
268C2×Dic3—34no—
269C2×Dic3—38no—
270C2×Dic3—62no—
271C2×Dic3—64no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C2×Dic3—64no—
275C2×Dic3—122no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278C2×Dic3D3×D418yes—
279C2×Dic3D3×Q814yescomplemented
280C4×D3—616no—
281C4×D3—632no—
282C4×D3—632no—
283C4×D3—616no—
284C4×D3—128no—
285C4×D3—1216no—
286C4×D3—128no—
287Dic6—216no—
288Dic6—632no—
289C2×C32C2×#12011yescharacteristic
290C2×C32C2×C22⋊Q811yescharacteristic
291C2×C32C2×C22⋊Q812yes—
292C2×C32C2×C4⋊Q812yes—
293C2×C32C2×C4⋊Q811yescharacteristic
294C3⋊D3#39518yescomplemented
295C24—91no—
296C2×Q8—68no—
297C2×Q8—64no—
298C2×Q8—188no—
299C2×Q8—184no—
300C2×Q8—1832no—
301C22×C4—32no—
302C22×C4—34no—
303C22×C4—32no—
304C22×C4—98no—
305C22×C4—94no—
306C22×C4—92no—
307C22×C4—91no—
308C22×C4—98no—
309C22×C4—94no—
310C22×C4—184no—
311C22×C4—184no—
312C22×C4—184no—
313C22×C4—182no—
314C22×C4—184no—
315C22×C4—184no—
316C22×C4—182no—
317C22×C4—182no—
318C22×C4—184no—
319C22×C4C2×D3212yes—
320C22×C4C2×D3211yescharacteristic
321C4⋊C4—68no—
322C4⋊C4—64no—
323C4⋊C4—188no—
324C4⋊C4—184no—
325C22×C3—22no—
326C22×C3—21no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3C2×D3×D412yes—
331C22×C3C2×D3×D414yes—
332C22×C3C2×D3×Q814yes—
333C22×C3C2×D3×Q812yes—
334C22×C3D3×#4112yes—
335C2×D3—316no—
336C2×D3—38no—
337C2×D3—38no—
338C2×D3—316no—
339C2×D3—38no—
340C2×D3—64no—
341C2×D3—68no—
342C2×D3—64no—
343C2×D3—68no—
344C2×D3—64no—
345C3×C4—24no—
346C3×C4—28no—
347C3×C4—44no—
348C3×C4—42no—
349C3×C4—68no—
350C3×C4—64no—
351C3×C4—122no—
352Dic3—28no—
353Dic3—24no—
354Dic3—42no—
355Dic3—64no—
356Dic3—68no—
357Dic3—124no—
358Dic3—122no—
359C32C2×#39511yescharacteristic, complemented, Sylow
360C23—94no—
361C23—92no—
362C23—94no—
363C23—92no—
364C23—92no—
365C23C22×D3211yescharacteristic
366Q8—616no—
367Q8—1816no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—38no—
372C2×C4—34no—
373C2×C4—62no—
374C2×C4—64no—
375C2×C4—64no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—64no—
379C2×C4—94no—
380C2×C4—92no—
381C2×C4—188no—
382C2×C4—1816no—
383C2×C4—1816no—
384C2×C4—188no—
385C2×C4—182no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—364no—
389C2×C4#379714yescomplemented
390C2×C4#380212yes—
391C2×C3—22no—
392C2×C3—22no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3D3×#12012yes—
397C2×C3D3×C22⋊Q814yes—
398C2×C3D3×C22⋊Q812yes—
399C2×C3D3×C4⋊Q814yes—
400C2×C3D3×C4⋊Q812yes—
401D3—316no—
402D3—68no—
403C22—98no—
404C22—98no—
405C22—94no—
406C22—94no—
407C22—94no—
408C22C2×#379712yes—
409C22C2×#380211yescharacteristic
410C22D32×D412yes—
411C22#6431211yescharacteristic
412C22D32×Q811yescharacteristic
413C4—24no—
414C4—22no—
415C4—64no—
416C4—68no—
417C4—122no—
418C4—184no—
419C4—182no—
420C3—21no—
421C3D3×#39512yescomplemented
422C2—98no—
423C2#1059390911yescharacteristic
424C2#1059406712yes—
425C2#1059425811yescharacteristic
426C2#1059437412yes—
427C2#1059463111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32C2×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C3×#4656C2semidirect
7. #10591344C2semidirect
8. #10591338C2semidirect
41. #4656D3semidirect
51. C2×C4×C3⋊D3Q8semidirect
66. C2×#624Q8semidirect
115. C2×C32×C4C2×Q8semidirect
120. C2×C3⋊Dic3C2×Q8semidirect
130. C2×C3×Dic3C2×Q8semidirect
261. C2×C3×C4D3×Q8semidirect
279. C2×Dic3D3×Q8semidirect
294. C3⋊D3#395semidirect
359. C32C2×#395semidirect
389. C2×C4#3797semidirect
421. C3D3×#395semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×#639002
C2×#638832
C3⋊D3×#952
C3×#46562
#105913702
#105913442
#105913382
D3×#3953