Finite Group Databasebeta

← #11785253

Subgroups — #11785253

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#832C212yesmaximal
3#10591230C211yesmaximal, characteristic, complemented
4C2×#63572C211yesmaximal, characteristic, complemented
5#10589164C212yesmaximal, complemented
6#70154—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C23×C3⋊Dic3—21no—
9C2×#3757—21no—
10D4×C3⋊Dic3—22no—
11D4×C3⋊Dic3C414yescomplemented
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C3×#832—24no—
17#63579—21no—
18#63579—21no—
19#63572—22no—
20C2×D4×Dic3—32no—
21C2×D4×Dic3—61no—
22C2×C3×#102—32no—
23C2×#832D312yes—
24C2×Dic3⋊C8—32no—
25#4977—32no—
26#4551—32no—
27#4529—32no—
28C24×C32—21no—
29C2×C32×D4—21no—
30C2×C32×D4—21no—
31C2×C32×D4—21no—
32C2×C32×D4C2×C412yes—
33C2×C32×D4D412yes—
34C2×C32×D4Q812yes—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—24no—
38C22×C3⋊Dic3—44no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3×Dic3—22no—
42#3757—24no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C412yes—
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3D412yes—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52#1804—91noSylow
53C22×C3×D4—21no—
54C22×C3×D4C2×D312yes—
55C23×Dic3—62no—
56C23×Dic3—62no—
57C22×C3×C8—32no—
58C2×C3×C4⋊C4—32no—
59C2×#217—62no—
60C2×#217—62no—
61D4×Dic3—38no—
62D4×Dic3—64no—
63D4×Dic3—64no—
64D4×Dic3—64no—
65C2×C4⋊Dic3—32no—
66C2×C4⋊Dic3—61no—
67C2×C4⋊Dic3C2×D312yes—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C22×C3⋊C8C2×D312yes—
71C3×#102—64no—
72#832—24no—
73C3⋊#95—62no—
74C3⋊#95—62no—
75Dic3⋊C8—64no—
76C23×C32—22no—
77C23×C32—22no—
78C23×C32—22no—
79C23×C32—42no—
80C23×C32—42no—
81C23×C32C2×D411yescharacteristic
82C32×D4—22no—
83C32×D4—22no—
84C32×D4—22no—
85C32×D4C4⋊C414yes—
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×Q811yescharacteristic
90C2×C32×C4#4111yescharacteristic
91C2×C32×C4#4111yescharacteristic
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—48no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3C22⋊C412yes—
98C2×C3⋊Dic3C22⋊C412yes—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102C3×C3⋊C8—42no—
103C2×C4×D4—91no—
104C2×C4⋊C8—91no—
105C2×#102—32no—
106#382—91no—
107#340—92no—
108C24×C3—22no—
109C24×C3—22no—
110C2×C3×D4—22no—
111C2×C3×D4—22no—
112C2×C3×D4—22no—
113C2×C3×D4—22no—
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—22no—
118C2×C3×D4—22no—
119C2×C3×D4Dic614yes—
120C2×C3×D4C4×D314yes—
121C2×C3×D4#6714yes—
122C22×C3×C4—21no—
123C22×C3×C4—62no—
124C22×C3×C4C22×D312yes—
125C22×Dic3—22no—
126C22×Dic3—32no—
127C22×Dic3—32no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—68no—
131C22×Dic3—62no—
132C22×Dic3—68no—
133C22×Dic3—62no—
134C22×Dic3—128no—
135C22×Dic3—124no—
136C22×Dic3—124no—
137C2×C3×C8—62no—
138C2×C3×C8—62no—
139C2×C3×C8—62no—
140C3×C4⋊C4—62no—
141C3×C4⋊C4—62no—
142#217—68no—
143#217—68no—
144C4⋊Dic3—22no—
145C4⋊Dic3—22no—
146C4⋊Dic3—34no—
147C4⋊Dic3—62no—
148C4⋊Dic3—62no—
149C4⋊Dic3—62no—
150C4×Dic3—34no—
151C4×Dic3—34no—
152C4×Dic3—62no—
153C4×Dic3—62no—
154C2×C3⋊C8—22no—
155C2×C3⋊C8—22no—
156C2×C3⋊C8—22no—
157C22×C32—24no—
158C22×C32—42no—
159C22×C32—42no—
160C22×C32—44no—
161C22×C32—44no—
162C22×C32C2×C22⋊C411yescharacteristic
163C22×C32#12111yescharacteristic
164C22×C32C22⋊Q811yescharacteristic
165C22×C32#13512yes—
166C22×C32AGL(1,ℤ/8)12yes—
167C32×C4C2×C4⋊C411yescharacteristic
168C32×C4#11711yescharacteristic
169C32×C4#12111yescharacteristic
170C32×C4C22⋊Q811yescharacteristic
171C3⋊Dic3—22no—
172C3⋊Dic3—22no—
173C3⋊Dic3—42no—
174C3×Dic3—82no—
175C22×D4D3211yescharacteristic
176C23×C4—181no—
177C22×C8—32no—
178C4×D4—94no—
179C4×D4—182no—
180C2×C4⋊C4—32no—
181C2×C4⋊C4—91no—
182C2×C22⋊C4—181no—
183C2×C42—91no—
184C4⋊C8—182no—
185#102—64no—
186#95—181no—
187#95—181no—
188C23×C3—24no—
189C23×C3—24no—
190C23×C3—24no—
191C23×C3—24no—
192C23×C3—24no—
193C23×C3—24no—
194C23×C3—21no—
195C23×C3—44no—
196C23×C3—44no—
197C23×C3—42no—
198C23×C3—42no—
199C23×C3—42no—
200C23×C3—42no—
201C23×C3D3×D412yes—
202C3×D4—24no—
203C3×D4—24no—
204C3×D4—24no—
205C3×D4—24no—
206C3×D4—24no—
207C3×D4—24no—
208C3×D4—24no—
209C3×D4Dic3⋊C418yes—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—122no—
217C2×C3×C4—122no—
218C2×C3×C4—122no—
219C2×C3×C4C2×Dic612yes—
220C2×C3×C4C2×C4×D312yes—
221C2×C3×C4D3×D412yes—
222C2×C3×C4#23712yes—
223C2×C3×C4#23712yes—
224C2×C3×C4C2×#6712yes—
225C2×Dic3—34no—
226C2×Dic3—34no—
227C2×Dic3—42no—
228C2×Dic3—42no—
229C2×Dic3—42no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—64no—
233C2×Dic3—62no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—122no—
240C2×Dic3—1216no—
241C2×Dic3—1216no—
242C2×Dic3—124no—
243C2×Dic3—122no—
244C2×Dic3—122no—
245C3×C8—122no—
246C3⋊C8—42no—
247C2×C32—44no—
248C2×C32#38011yescharacteristic
249C2×C32#41611yescharacteristic
250C2×C32#41811yescharacteristic
251C2×C32#46312yes—
252C2×C32#47812yes—
253C24—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4#62412yes—
258C2×D4#62512yes—
259C2×D4#62712yes—
260C22×C4—62no—
261C22×C4—91no—
262C22×C4—91no—
263C22×C4—184no—
264C22×C4—181no—
265C22×C4—364no—
266C22×C4C2×D3211yescharacteristic
267C2×C8—62no—
268C2×C8—62no—
269C2×C8—62no—
270C4⋊C4—62no—
271C4⋊C4—62no—
272C4⋊C4—92no—
273C4⋊C4—181no—
274C22⋊C4—184no—
275C42—92no—
276C42—92no—
277C22×C3—28no—
278C22×C3—28no—
279C22×C3—22no—
280C22×C3—22no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—44no—
285C22×C3—44no—
286C22×C3—48no—
287C22×C3—48no—
288C22×C3—44no—
289C22×C3—44no—
290C22×C3—44no—
291C22×C3—44no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3#87812yes—
295C22×C3D3×C22⋊C412yes—
296C22×C3#91112yes—
297C22×C3#91212yes—
298C22×C3#91412yes—
299C22×C3#91612yes—
300C22×C3#93912yes—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—242no—
306C3×C4#87712yes—
307C3×C4#87812yes—
308C3×C4C2×Dic3⋊C412yes—
309C3×C4#93912yes—
310Dic3—64no—
311Dic3—64no—
312Dic3—64no—
313Dic3—82no—
314Dic3—122no—
315Dic3—124no—
316Dic3—124no—
317C32#180411yescharacteristic, complemented, Sylow
318C23—22no—
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23#381111yescharacteristic
324D4—22no—
325D4—22no—
326D4—22no—
327D4#372414yes—
328C2×C4—92no—
329C2×C4—92no—
330C2×C4—122no—
331C2×C4—122no—
332C2×C4—122no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—368no—
337C2×C4—362no—
338C2×C4#380511yescharacteristic
339C2×C4#380511yescharacteristic
340C2×C4C2×#62411yescharacteristic
341C2×C4C2×#62511yescharacteristic
342C2×C4C2×#62711yescharacteristic
343C2×C4#381111yescharacteristic
344C8—122no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—48no—
351C2×C3—48no—
352C2×C3#476312yes—
353C2×C3#476612yes—
354C2×C3#477012yes—
355C2×C3#477212yes—
356C2×C3#494212yes—
357C2×C3#515312yes—
358C2×C3#516512yes—
359C22—24no—
360C22—42no—
361C22—42no—
362C22—44no—
363C22—44no—
364C22#6393612yes—
365C22#6393712yes—
366C22#6397411yescharacteristic
367C22#6398011yescharacteristic
368C22#6398211yescharacteristic
369C4—182no—
370C4—182no—
371C4—242no—
372C4—362no—
373C4#6395711yescharacteristic
374C4C2×#372411yescharacteristic
375C4#6398011yescharacteristic
376C4#6398211yescharacteristic
377C3—21no—
378C3#7015412yescomplemented
379C2—44no—
380C2#1059142411yescharacteristic
381C2#1059142611yescharacteristic
382C2#1059147612yes—
383C2#1059147912yes—
384C2#1059172011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1804
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591230C2semidirect
4. C2×#63572C2semidirect
5. #10589164C2semidirect
11. D4×C3⋊Dic3C4semidirect
317. C32#1804semidirect
378. C3#70154semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#8322
#105912302
C2×#635722
#105891642
#701543