Finite Group Databasebeta

← #11808346

Subgroups — #11808346

Order 1152.

1593 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63883C212yesmaximal
3C2×#63883C211yesmaximal, characteristic
4C3×#4983C212yesmaximal, complemented
5#10591370C212yesmaximal
6#10591370C211yesmaximal, characteristic
7#10591353C212yesmaximal, complemented
8#10591340C214yesmaximal, complemented
9D3×#398—32nomaximal
10C22×C4×C3⋊D3C2212yes—
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#624C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C22×#624C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2212yes—
18C4⋊C4×C3⋊D3—24no—
19C2×C3×Dic3⋊C4C2214yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×Dic3⋊Dic3C2212yes—
22C2×Dic3⋊Dic3C2214yes—
23#63883—24no—
24#63883—28no—
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2212yes—
27#63579C2212yes—
28#63579C2214yes—
29C2×D3×C4⋊C4—32no—
30C2×D3×C4⋊C4—32no—
31C2×D3×C4⋊C4—34no—
32C2×D3×C4⋊C4—61no—
33C3×#398—32no—
34#4983D312yescomplemented
35#4982—34no—
36#4981—32no—
37D3×#95—34no—
38D3×#95—32no—
39#4661—32no—
40#4657—34no—
41C23×C3⋊D3C2311yescharacteristic
42C22×C32×C4C2312yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2312yes—
45C22×C3⋊Dic3C2311yescharacteristic
46C2×C4×C3⋊D3—24no—
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3—24no—
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3D414yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C22×C3×Dic3C2314yes—
54C2×#624—22no—
55C2×#624—24no—
56C2×#624—22no—
57C2×#624—24no—
58C2×#624—22no—
59C2×#624—24no—
60C2×#624D414yes—
61C2×#624Q818yes—
62C32×C4⋊C4—22no—
63C4⋊(C3⋊Dic3)—22no—
64#3750—24no—
65C3×Dic3⋊C4—24no—
66C3×Dic3⋊C4—28no—
67Dic3⋊Dic3—24no—
68Dic3⋊Dic3—28no—
69C2×#398—91noSylow
70C22×C4×D3—32no—
71C22×C4×D3—34no—
72C22×C4×D3—32no—
73C22×C4×D3—34no—
74C22×C4×D3—32no—
75C22×C4×D3—61no—
76C22×C4×D3—62no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4C2×D312yes—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—34no—
83C2×C4⋊Dic3—32no—
84C2×C4⋊Dic3—61no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—34no—
88C2×Dic3⋊C4—62no—
89C2×Dic3⋊C4C2×D314yes—
90C2×Dic3⋊C4C2×D312yes—
91D3×C4⋊C4—68no—
92D3×C4⋊C4—616no—
93D3×C4⋊C4—68no—
94D3×C4⋊C4—68no—
95C3×#95—34no—
96C3×#95—32no—
97C3⋊#95—34no—
98C3⋊#95—34no—
99C3⋊#95—34no—
100C3⋊#95C2×D312yes—
101C3⋊#95C2×D314yes—
102C23×C32C2411yescharacteristic
103C22×C3⋊D3C2×D412yes—
104C22×C3⋊D3C2×D412yes—
105C22×C3⋊D3C2×Q814yes—
106C22×C3⋊D3#4112yes—
107C22×C3⋊D3#4114yes—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4C2×D412yes—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3C2×D412yes—
118C4×C3⋊D3—28no—
119C4×C3⋊D3—48no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3C2×D414yes—
127C2×C3×Dic3C2×Q818yes—
128#624—28no—
129#624—216no—
130#624—44no—
131C22×C4⋊C4—92no—
132C22×C4⋊C4—91no—
133C22×C4⋊C4—91no—
134#398—32no—
135#398—94no—
136#398—92no—
137C2×#95—91no—
138C2×#95—92no—
139C23×D3—32no—
140C23×D3—61no—
141C22×C3×C4—21no—
142C22×C3×C4—22no—
143C22×C3×C4—34no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4C22×D314yes—
147C22×C3×C4C22×D312yes—
148C22×Dic3—32no—
149C22×Dic3—34no—
150C22×Dic3—61no—
151C22×Dic3—62no—
152C22×Dic3C22×D312yes—
153C22×Dic3C22×D312yes—
154C22×Dic3C22×D314yes—
155C2×C4×D3—38no—
156C2×C4×D3—38no—
157C2×C4×D3—316no—
158C2×C4×D3—64no—
159C2×C4×D3—68no—
160C2×C4×D3—64no—
161C2×C4×D3—68no—
162C2×C4×D3—64no—
163C2×C4×D3—68no—
164C2×C4×D3—68no—
165C2×C4×D3—64no—
166C2×C4×D3—68no—
167C2×C4×D3—68no—
168C2×C4×D3—68no—
169C2×C4×D3—68no—
170C2×C4×D3—68no—
171C2×C4×D3—124no—
172C2×C4×D3—124no—
173C3×C4⋊C4—24no—
174C3×C4⋊C4—24no—
175C3×C4⋊C4—68no—
176C3×C4⋊C4—64no—
177C4⋊Dic3—64no—
178C4⋊Dic3—64no—
179C4⋊Dic3—64no—
180C4⋊Dic3—68no—
181Dic3⋊C4—24no—
182Dic3⋊C4—28no—
183Dic3⋊C4—64no—
184Dic3⋊C4—68no—
185Dic3⋊C4—68no—
186Dic3⋊C4—68no—
187C22×C32C22×D411yescharacteristic
188C22×C32C22×D411yescharacteristic
189C22×C32C22×Q812yes—
190C22×C32C2×#4111yescharacteristic
191C22×C32C2×#4112yes—
192C2×C3⋊D3#12114yes—
193C2×C3⋊D3C22⋊Q818yes—
194C2×C3⋊D3#12314yes—
195C2×C3⋊D3#12518yes—
196C2×C3⋊D3C4⋊Q814yes—
197C32×C4—22no—
198C32×C4—42no—
199C3⋊Dic3—22no—
200C3⋊Dic3—42no—
201C3×Dic3—24no—
202C3×Dic3—28no—
203C3×Dic3—42no—
204C23×C4—91no—
205C23×C4—92no—
206C23×C4—91no—
207C23×C4—91no—
208C23×C4—92no—
209C2×C4⋊C4—34no—
210C2×C4⋊C4—32no—
211C2×C4⋊C4—94no—
212C2×C4⋊C4—92no—
213C2×C4⋊C4—92no—
214C2×C4⋊C4—91no—
215C2×C4⋊C4—184no—
216C2×C4⋊C4—188no—
217C2×C4⋊C4—184no—
218C2×C4⋊C4D3211yescharacteristic
219#95—32no—
220#95—34no—
221#95—92no—
222#95—94no—
223C23×C3—21no—
224C23×C3C23×D312yes—
225C22×D3—34no—
226C22×D3—34no—
227C22×D3—38no—
228C22×D3—38no—
229C22×D3—34no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—64no—
233C22×D3—64no—
234C22×D3—62no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—22no—
242C2×C3×C4—34no—
243C2×C3×C4—38no—
244C2×C3×C4—42no—
245C2×C3×C4—42no—
246C2×C3×C4—64no—
247C2×C3×C4—62no—
248C2×C3×C4—64no—
249C2×C3×C4—62no—
250C2×C3×C4—62no—
251C2×C3×C4—64no—
252C2×C3×C4D3×D414yes—
253C2×Dic3—24no—
254C2×Dic3—22no—
255C2×Dic3—24no—
256C2×Dic3—22no—
257C2×Dic3—22no—
258C2×Dic3—24no—
259C2×Dic3—34no—
260C2×Dic3—62no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—64no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269C2×Dic3D3×D414yes—
270C2×Dic3D3×Q818yes—
271C4×D3—616no—
272C4×D3—632no—
273C4×D3—616no—
274C4×D3—616no—
275C4×D3—128no—
276C4×D3—1216no—
277C4×D3—1216no—
278C2×C32C2×#12111yescharacteristic
279C2×C32C2×C22⋊Q812yes—
280C2×C32C2×#12311yescharacteristic
281C2×C32C2×#12512yes—
282C2×C32C2×C4⋊Q811yescharacteristic
283C3⋊D3#39818yescomplemented
284C24—91no—
285C22×C4—34no—
286C22×C4—32no—
287C22×C4—32no—
288C22×C4—94no—
289C22×C4—98no—
290C22×C4—91no—
291C22×C4—94no—
292C22×C4—92no—
293C22×C4—184no—
294C22×C4—184no—
295C22×C4—184no—
296C22×C4—184no—
297C22×C4—184no—
298C22×C4—182no—
299C22×C4—184no—
300C22×C4—182no—
301C22×C4—182no—
302C22×C4—184no—
303C22×C4C2×D3212yes—
304C22×C4C2×D3211yescharacteristic
305C4⋊C4—22no—
306C4⋊C4—68no—
307C4⋊C4—64no—
308C4⋊C4—184no—
309C4⋊C4—188no—
310C4⋊C4—184no—
311C4⋊C4—182no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3C2×D3×D412yes—
318C22×C3C2×D3×D412yes—
319C22×C3C2×D3×Q814yes—
320C22×C3D3×#4114yes—
321C22×C3D3×#4112yes—
322C2×D3—38no—
323C2×D3—316no—
324C2×D3—38no—
325C2×D3—38no—
326C2×D3—316no—
327C2×D3—64no—
328C2×D3—64no—
329C2×D3—68no—
330C2×D3—68no—
331C2×D3—64no—
332C3×C4—24no—
333C3×C4—24no—
334C3×C4—44no—
335C3×C4—44no—
336C3×C4—64no—
337C3×C4—68no—
338C3×C4—122no—
339Dic3—24no—
340Dic3—28no—
341Dic3—42no—
342Dic3—64no—
343Dic3—64no—
344Dic3—124no—
345Dic3—124no—
346C32C2×#39811yescharacteristic, complemented, Sylow
347C23—94no—
348C23—92no—
349C23—92no—
350C23—94no—
351C23—92no—
352C23C22×D3211yescharacteristic
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—34no—
358C2×C4—38no—
359C2×C4—64no—
360C2×C4—64no—
361C2×C4—62no—
362C2×C4—62no—
363C2×C4—64no—
364C2×C4—62no—
365C2×C4—92no—
366C2×C4—188no—
367C2×C4—1816no—
368C2×C4—188no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—368no—
374C2×C4—364no—
375C2×C4#381112yes—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—22no—
379C2×C3—22no—
380C2×C3—21no—
381C2×C3D3×#12112yes—
382C2×C3D3×C22⋊Q814yes—
383C2×C3D3×#12312yes—
384C2×C3D3×#12514yes—
385C2×C3D3×C4⋊Q812yes—
386D3—316no—
387D3—68no—
388C22—94no—
389C22—94no—
390C22—98no—
391C22—98no—
392C22—94no—
393C22#6430612yes—
394C22D32×D411yescharacteristic
395C22#6431211yescharacteristic
396C22D32×Q812yes—
397C22C2×#381111yescharacteristic
398C4—22no—
399C4—42no—
400C4—68no—
401C4—64no—
402C4—122no—
403C4—182no—
404C4—362no—
405C3—21no—
406C3D3×#39812yescomplemented
407C2—98no—
408C2#1059439912yes—
409C2#1059462412yes—
410C2#1059507911yescharacteristic
411C2#1059528211yescharacteristic
412C2#1059536511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4983C2semidirect
7. #10591353C2semidirect
8. #10591340C2semidirect
34. #4983D3semidirect
283. C3⋊D3#398semidirect
346. C32C2×#398semidirect
406. C3D3×#398semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#638832
C3×#49832
#105913702
#105913532
#105913402
D3×#3983