Finite Group Databasebeta

← #11801849

Subgroups — #11801849

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic
3C2×#63849C211yesmaximal, characteristic
4C3×#4972C212yesmaximal, complemented
5#10591375C212yesmaximal
6#10591374C212yesmaximal
7#10591352C212yesmaximal, complemented
8#10591241C214yesmaximal, complemented
9#75963—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×#624C2211yescharacteristic
12C22×#624C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752C2212yes—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3C2212yes—
17#64101—24no—
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×Dic3⋊C4C2214yes—
20C2×C3×C4×Dic3C2212yes—
21C2×Dic3⋊Dic3C2214yes—
22C2×#3722C2212yes—
23C2×Dic32C2212yes—
24C2×Dic32C2212yes—
25C4×#624—24no—
26#63849C418yescomplemented
27C3×C3⋊#95C2214yes—
28#63579C2214yes—
29C2×#892—32no—
30C2×#892—32no—
31C2×#892—61no—
32C2×C42×D3—32no—
33C3×#389—32no—
34#4989—34no—
35#4984—32no—
36Dic3×C4⋊C4—34no—
37#4972D312yescomplemented
38#4928—32no—
39#4668—34no—
40#4649—34no—
41C23×C3⋊D3C2311yescharacteristic
42C22×C32×C4C2312yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2312yes—
45C22×C3⋊Dic3C2311yescharacteristic
46C2×C4×C3⋊D3C2×C414yes—
47C2×C4×C3⋊D3D414yes—
48C2×C4×C3⋊D3Q814yes—
49C22×C3×Dic3C2314yes—
50C22×C3×Dic3C2312yes—
51C22×C3×Dic3C2312yes—
52C2×#624—22no—
53C2×#624—22no—
54C2×#624—24no—
55C2×#624—24no—
56C32×C4⋊C4—22no—
57#3752—24no—
58C4⋊(C3⋊Dic3)—22no—
59C4×C3⋊Dic3—24no—
60C3×C4⋊Dic3C2×C418yescomplemented
61C3×Dic3⋊C4—28no—
62C3×C4×Dic3—24no—
63Dic3⋊Dic3—28no—
64#3722C2×C418yes—
65Dic32—24no—
66Dic32C2×C418yescomplemented
67#2296—91noSylow
68C22×C4×D3—32no—
69C22×C4×D3—32no—
70C22×C4×D3—32no—
71C22×C4×D3—61no—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4—32no—
74C2×C3×C4⋊C4—34no—
75C2×C3×C4⋊C4C2×D312yes—
76C2×C3×C42—32no—
77C2×(C2×D3)⋊C4—34no—
78C2×(C2×D3)⋊C4—34no—
79C2×(C2×D3)⋊C4—62no—
80C2×C4⋊Dic3—32no—
81C2×C4⋊Dic3—34no—
82C2×C4⋊Dic3—61no—
83C2×C4⋊Dic3C2×D312yes—
84C2×Dic3⋊C4—34no—
85C2×Dic3⋊C4C2×D314yes—
86C2×C4×Dic3—34no—
87C2×C4×Dic3—34no—
88C2×C4×Dic3—32no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—62no—
91C2×C4×Dic3C2×D312yes—
92#892—316no—
93#892—68no—
94#892—68no—
95C42×D3—68no—
96C3×#95—34no—
97C3⋊#95—34no—
98C3⋊#95—34no—
99C3⋊#95C2×D314yes—
100C23×C32C2411yescharacteristic
101C22×C3⋊D3—22no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3C22×C412yes—
104C22×C3⋊D3C2×D412yes—
105C22×C3⋊D3C2×Q812yes—
106C2×C32×C4—22no—
107C2×C32×C4—24no—
108C2×C32×C4C22×C412yes—
109C2×C32×C4C2×D412yes—
110C2×C32×C4C2×Q812yes—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3C22×C412yes—
114C2×C3⋊Dic3C2×D412yes—
115C2×C3⋊Dic3C2×Q812yes—
116C4×C3⋊D3C4⋊C4116yescomplemented
117C2×C3×Dic3—22no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3C22×C418yes—
124C2×C3×Dic3#4114yes—
125C2×C3×Dic3#4114yes—
126#624—28no—
127#624—28no—
128C2×#117—91no—
129C2×#117—91no—
130C22×C42—91no—
131#389—32no—
132#389—92no—
133#385—92no—
134#385—92no—
135C4×C4⋊C4—94no—
136C23×D3—32no—
137C23×D3—61no—
138C22×C3×C4—21no—
139C22×C3×C4—22no—
140C22×C3×C4—32no—
141C22×C3×C4—34no—
142C22×C3×C4—32no—
143C22×C3×C4C22×D314yes—
144C22×C3×C4C22×D312yes—
145C22×Dic3—32no—
146C22×Dic3—34no—
147C22×Dic3—61no—
148C22×Dic3—62no—
149C22×Dic3C22×D314yes—
150C22×Dic3C22×D312yes—
151C22×Dic3C22×D312yes—
152C2×C4×D3—38no—
153C2×C4×D3—38no—
154C2×C4×D3—38no—
155C2×C4×D3—64no—
156C2×C4×D3—64no—
157C2×C4×D3—64no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C4×D3—64no—
161C2×C4×D3—64no—
162C2×C4×D3—64no—
163C2×C4×D3—64no—
164C3×C4⋊C4—24no—
165C3×C4⋊C4—24no—
166C3×C4⋊C4—38no—
167C3×C4⋊C4—68no—
168C3×C42—64no—
169(C2×D3)⋊C4—316no—
170(C2×D3)⋊C4—68no—
171(C2×D3)⋊C4—68no—
172C4⋊Dic3—64no—
173C4⋊Dic3—64no—
174C4⋊Dic3—68no—
175C4⋊Dic3C4×D318yescomplemented
176Dic3⋊C4—28no—
177Dic3⋊C4—68no—
178C4×Dic3—24no—
179C4×Dic3—316no—
180C4×Dic3—64no—
181C4×Dic3—64no—
182C4×Dic3—68no—
183C4×Dic3—68no—
184C22×C32C23×C411yescharacteristic
185C22×C32C22×D411yescharacteristic
186C22×C32C22×Q811yescharacteristic
187C22×C32C2×#4112yes—
188C22×C32C2×#4112yes—
189C2×C3⋊D3—24no—
190C2×C3⋊D3—22no—
191C2×C3⋊D3—22no—
192C2×C3⋊D3—24no—
193C2×C3⋊D3C2×C4⋊C414yes—
194C32×C4—42no—
195C32×C4C2×C4⋊C414yes—
196C3⋊Dic3—42no—
197C3⋊Dic3C2×C4⋊C414yes—
198C3×Dic3—28no—
199C3×Dic3—24no—
200C3×Dic3—24no—
201C23×C4—91no—
202C23×C4—91no—
203C23×C4—91no—
204#117—98no—
205#117—184no—
206C2×C4⋊C4—32no—
207C2×C4⋊C4—34no—
208C2×C4⋊C4—94no—
209C2×C4⋊C4—91no—
210C2×C4⋊C4D3211yescharacteristic
211C2×C22⋊C4—92no—
212C2×C22⋊C4—92no—
213C2×C42—32no—
214C2×C42—92no—
215C2×C42—92no—
216C2×C42—92no—
217C2×C42—184no—
218#95—34no—
219#95—94no—
220C23×C3—21no—
221C23×C3C23×D312yes—
222C22×D3—34no—
223C22×D3—34no—
224C22×D3—34no—
225C22×D3—62no—
226C22×D3—62no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—62no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—122no—
233C22×D3—122no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—22no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—38no—
242C2×C3×C4—34no—
243C2×C3×C4—34no—
244C2×C3×C4—44no—
245C2×C3×C4—62no—
246C2×C3×C4—62no—
247C2×C3×C4—62no—
248C2×C3×C4—64no—
249C2×C3×C4—62no—
250C2×C3×C4—64no—
251C2×C3×C4C2×C4×D314yes—
252C2×C3×C4D3×D414yes—
253C2×C3×C4D3×Q814yes—
254C2×Dic3—22no—
255C2×Dic3—22no—
256C2×Dic3—24no—
257C2×Dic3—24no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—34no—
261C2×Dic3—34no—
262C2×Dic3—34no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—64no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—124no—
271C2×Dic3C2×C4×D318yes—
272C2×Dic3#23714yes—
273C2×Dic3#23914yes—
274C4×D3—332no—
275C4×D3—616no—
276C4×D3—616no—
277C4×D3—616no—
278C2×C32C22×C4⋊C411yescharacteristic
279C2×C32C4×#4112yes—
280C2×C32#52511yescharacteristic
281C2×C32#52511yescharacteristic
282C2×C32#53312yes—
283C3⋊D3—24no—
284C24—91no—
285C22×C4—32no—
286C22×C4—34no—
287C22×C4—32no—
288C22×C4—91no—
289C22×C4—94no—
290C22×C4—94no—
291C22×C4—94no—
292C22×C4—92no—
293C22×C4—184no—
294C22×C4—184no—
295C22×C4—182no—
296C22×C4—182no—
297C22×C4C2×D3212yes—
298C22×C4C2×D3211yescharacteristic
299C4⋊C4—22no—
300C4⋊C4—38no—
301C4⋊C4—68no—
302C4⋊C4—188no—
303C4⋊C4—182no—
304C22⋊C4—98no—
305C22⋊C4—184no—
306C42—64no—
307C42—98no—
308C42—184no—
309C42—184no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3C22×C4×D312yes—
316C22×C3C2×D3×D412yes—
317C22×C3C2×#23712yes—
318C22×C3C2×D3×Q812yes—
319C22×C3C2×#23912yes—
320C22×C3D3×#4112yes—
321C22×C3D3×#4112yes—
322C2×D3—38no—
323C2×D3—64no—
324C2×D3—64no—
325C2×D3—64no—
326C2×D3—64no—
327C2×D3—64no—
328C2×D3—64no—
329C2×D3—64no—
330C2×D3—124no—
331C2×D3—122no—
332C2×D3—124no—
333C2×D3—122no—
334C3×C4—24no—
335C3×C4—44no—
336C3×C4—44no—
337C3×C4—68no—
338C3×C4—64no—
339C3×C4—64no—
340C3×C4D3×C4⋊C418yes—
341Dic3—28no—
342Dic3—24no—
343Dic3—24no—
344Dic3—38no—
345Dic3—64no—
346Dic3—124no—
347Dic3—124no—
348C32#229611yescharacteristic, complemented, Sylow
349C23—92no—
350C23—92no—
351C23—92no—
352C23—182no—
353C23—182no—
354C23C22×D3211yescharacteristic
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—38no—
358C2×C4—34no—
359C2×C4—34no—
360C2×C4—64no—
361C2×C4—62no—
362C2×C4—64no—
363C2×C4—62no—
364C2×C4—62no—
365C2×C4—62no—
366C2×C4—92no—
367C2×C4—92no—
368C2×C4—92no—
369C2×C4—916no—
370C2×C4—188no—
371C2×C4—188no—
372C2×C4—184no—
373C2×C4—182no—
374C2×C4#379712yes—
375C2×C4C4×D3212yes—
376C2×C4#381112yes—
377C2×C3—22no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—22no—
381C2×C3—21no—
382C2×C3C2×D3×C4⋊C412yes—
383C2×C3C4×#23712yes—
384C2×C3C4×#23912yes—
385C2×C3#560612yes—
386C2×C3#562712yes—
387C2×C3#568812yes—
388C2×C3#572812yes—
389D3—68no—
390D3—124no—
391C22—94no—
392C22—184no—
393C22—182no—
394C22—184no—
395C22—182no—
396C22C2×#379711yescharacteristic
397C22C2×C4×D3211yescharacteristic
398C22D3×#23712yes—
399C22D3×#23912yes—
400C22C2×#381111yescharacteristic
401C4—42no—
402C4—68no—
403C4—64no—
404C4—64no—
405C4—94no—
406C4—362no—
407C4#6388314yes—
408C3—21no—
409C3#7596312yescomplemented
410C2—184no—
411C2#1059436012yes—
412C2#1059444812yes—
413C2C2×#6388311yescharacteristic
414C2#1059530611yescharacteristic
415C2#1059543011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4972C2semidirect
7. #10591352C2semidirect
8. #10591241C2semidirect
26. #63849C4semidirect
37. #4972D3semidirect
60. C3×C4⋊Dic3C2×C4semidirect
66. Dic32C2×C4semidirect
116. C4×C3⋊D3C4⋊C4semidirect
175. C4⋊Dic3C4×D3semidirect
348. C32#2296semidirect
409. C3#75963semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×C4×#6242
C2×#638492
C3×#49722
#105913752
#105913742
#105913522
#105912412
#759633