Finite Group Databasebeta

← #11785789

Subgroups — #11785789

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2#10592686C211yesmaximal, characteristic
3C2×#63557C211yesmaximal, characteristic
4C3×#4529C212yesmaximal, complemented
5#10589164C212yesmaximal, complemented
6#68872—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624—21no—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3752—21no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C22×C3×C3⋊C8C2212yes—
14C2×#3724—21no—
15#63900—22no—
16#63900C414yescomplemented
17#63658—21no—
18#63557—22no—
19C2×D3×C4⋊C4—32no—
20C2×(C2×D3)⋊C8—32no—
21#4987—32no—
22#4987—61no—
23C3×#340—32no—
24#4551—32no—
25#4529—32no—
26#4529D312yescomplemented
27C23×C3⋊D3D411yescharacteristic
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3C2×C412yes—
35C2×C4×C3⋊D3D412yes—
36C22×C3×Dic3—22no—
37C2×#624—24no—
38C2×#624—42no—
39C2×#624—42no—
40C32×C4⋊C4—22no—
41#3752—42no—
42C4⋊(C3⋊Dic3)—22no—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3C2×C414yes—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—22no—
48#3724—24no—
49#1824—91noSylow
50C22×C4×D3—32no—
51C22×C4×D3—61no—
52C22×C4×D3—62no—
53C22×C3×C8—32no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4—32no—
56C2×C3×C4⋊C4C2×D312yes—
57C2×(C2×D3)⋊C4—62no—
58C2×(C2×D3)⋊C4—62no—
59C2×C4⋊Dic3—32no—
60C2×C4⋊Dic3—61no—
61C2×C4⋊Dic3C2×D312yes—
62C2×Dic3⋊C4—62no—
63C22×C3⋊C8C2×D312yes—
64D3×C4⋊C4—38no—
65D3×C4⋊C4—64no—
66C3⋊#95—62no—
67C3⋊#95—62no—
68(C2×D3)⋊C8—64no—
69C23×C32C2×D411yescharacteristic
70C22×C3⋊D3—21no—
71C22×C3⋊D3—21no—
72C22×C3⋊D3—21no—
73C22×C3⋊D3—21no—
74C22×C3⋊D3C22⋊C412yes—
75C22×C3⋊D3SD1612yes—
76C22×C3⋊D3Q1612yes—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4#4112yes—
83C2×C32×C4#4112yes—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3C22⋊C412yes—
90C4×C3⋊D3—24no—
91C4×C3⋊D3—24no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—42no—
94C2×C3×Dic3—42no—
95#624—48no—
96C3×C3⋊C8—42no—
97C22×C4⋊C4—91no—
98C2×C22⋊C8—91no—
99#380—91no—
100#340—32no—
101#340—92no—
102C23×D3—32no—
103C23×D3—61no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—21no—
107C22×C3×C4—62no—
108C22×C3×C4C22×D312yes—
109C22×Dic3—22no—
110C22×Dic3—32no—
111C22×Dic3—61no—
112C22×Dic3—62no—
113C22×Dic3—62no—
114C2×C4×D3—34no—
115C2×C4×D3—34no—
116C2×C4×D3—62no—
117C2×C4×D3—62no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—68no—
123C2×C4×D3—122no—
124C2×C4×D3—122no—
125C2×C4×D3—124no—
126C2×C4×D3—124no—
127C2×C3×C8—62no—
128C2×C3×C8—62no—
129C2×C3×C8—62no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—34no—
133C3×C4⋊C4—42no—
134C3×C4⋊C4—62no—
135(C2×D3)⋊C4—124no—
136(C2×D3)⋊C4—124no—
137C4⋊Dic3—22no—
138C4⋊Dic3—62no—
139C4⋊Dic3—62no—
140C4⋊Dic3—122no—
141C4⋊Dic3C4×D314yes—
142Dic3⋊C4—68no—
143C2×C3⋊C8—22no—
144C2×C3⋊C8—22no—
145C2×C3⋊C8—22no—
146C22×C32C2×C22⋊C411yescharacteristic
147C22×C32#12311yescharacteristic
148C22×C32#12311yescharacteristic
149C22×C32C2×SD1611yescharacteristic
150C22×C32C2×Q1611yescharacteristic
151C22×C32AGL(1,ℤ/8)11yescharacteristic
152C22×C32AGL(1,ℤ/8)11yescharacteristic
153C2×C3⋊D3—22no—
154C2×C3⋊D3—22no—
155C2×C3⋊D3—22no—
156C2×C3⋊D3—22no—
157C2×C3⋊D3—22no—
158C2×C3⋊D3—22no—
159C2×C3⋊D3#10314yes—
160C32×C4—81no—
161C32×C4#11712yes—
162C32×C4#12312yes—
163C3⋊Dic3—22no—
164C3⋊Dic3—81no—
165C3×Dic3—44no—
166C23×C4—91no—
167C23×C4—181no—
168C22×C8—32no—
169C2×C4⋊C4—32no—
170C2×C4⋊C4—94no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—182no—
173C2×C4⋊C4—181no—
174C2×C4⋊C4D3211yescharacteristic
175C2×C22⋊C4—181no—
176C22⋊C8—182no—
177#95—181no—
178C23×C3—21no—
179C23×C3D3×D412yes—
180C22×D3—34no—
181C22×D3—34no—
182C22×D3—34no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—62no—
189C22×D3—62no—
190C22×D3—121no—
191C22×D3—121no—
192C22×D3—121no—
193C22×D3—121no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—22no—
198C2×C3×C4—42no—
199C2×C3×C4—42no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—64no—
205C2×C3×C4—122no—
206C2×C3×C4—122no—
207C2×C3×C4C2×C4×D312yes—
208C2×C3×C4#23512yes—
209C2×C3×C4#23512yes—
210C2×C3×C4D3×D412yes—
211C2×C3×C4#23712yes—
212C2×C3×C4#23912yes—
213C2×Dic3—24no—
214C2×Dic3—34no—
215C2×Dic3—42no—
216C2×Dic3—42no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—121no—
221C2×Dic3—121no—
222C2×Dic3—122no—
223C2×Dic3—122no—
224C2×Dic3—122no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227C2×Dic3—122no—
228C4×D3—64no—
229C4×D3—64no—
230C4×D3—64no—
231C4×D3—64no—
232C4×D3—124no—
233C4×D3—124no—
234C4×D3—1216no—
235C3×C8—122no—
236C3⋊C8—42no—
237C2×C32#38111yescharacteristic
238C2×C32C2×#10311yescharacteristic
239C2×C32#41811yescharacteristic
240C2×C32#48111yescharacteristic
241C2×C32#48111yescharacteristic
242C2×C32#48411yescharacteristic
243C2×C32#48411yescharacteristic
244C3⋊D3—24no—
245C24—91no—
246C22×C4—21no—
247C22×C4—62no—
248C22×C4—91no—
249C22×C4—92no—
250C22×C4—92no—
251C22×C4—184no—
252C22×C4—182no—
253C22×C4—182no—
254C22×C4—181no—
255C22×C4—362no—
256C22×C4—362no—
257C22×C4C2×D3211yescharacteristic
258C2×C8—62no—
259C2×C8—62no—
260C2×C8—62no—
261C4⋊C4—22no—
262C4⋊C4—34no—
263C4⋊C4—62no—
264C4⋊C4—184no—
265C4⋊C4—182no—
266C22⋊C4—362no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3D3×C22⋊C412yes—
275C22×C3#88312yes—
276C22×C3#89412yes—
277C22×C3#91112yes—
278C22×C3D3×SD1612yes—
279C22×C3#91412yes—
280C22×C3D3×Q1612yes—
281C2×D3—38no—
282C2×D3—64no—
283C2×D3—64no—
284C2×D3—64no—
285C2×D3—64no—
286C2×D3—64no—
287C2×D3—64no—
288C2×D3—64no—
289C2×D3—122no—
290C2×D3—122no—
291C2×D3—122no—
292C2×D3—122no—
293C2×D3—122no—
294C2×D3—122no—
295C3×C4—22no—
296C3×C4—22no—
297C3×C4—82no—
298C3×C4—82no—
299C3×C4—124no—
300C3×C4#87212yes—
301C3×C4#88312yes—
302C3×C4#89212yes—
303C3×C4#89412yes—
304Dic3—44no—
305Dic3—64no—
306Dic3—122no—
307Dic3—242no—
308Dic3—242no—
309C32#182411yescharacteristic, complemented, Sylow
310C23—92no—
311C23—92no—
312C23—92no—
313C23—181no—
314C23—181no—
315C23—181no—
316C23—181no—
317C23#381111yescharacteristic
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—64no—
322C2×C4—92no—
323C2×C4—122no—
324C2×C4—122no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4—184no—
328C2×C4—184no—
329C2×C4—368no—
330C2×C4—361no—
331C2×C4—361no—
332C2×C4—361no—
333C2×C4#379912yes—
334C2×C4C4×D3211yescharacteristic
335C2×C4#380211yescharacteristic
336C2×C4#380412yes—
337C8—122no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3#466412yes—
346C2×C3#477012yes—
347C2×C3#477712yes—
348C2×C3D3×#10312yes—
349C2×C3#481112yes—
350C2×C3#486312yes—
351C2×C3#488412yes—
352D3—68no—
353D3—124no—
354C22—94no—
355C22—182no—
356C22—182no—
357C22—182no—
358C22—182no—
359C22—182no—
360C22—182no—
361C22#6389711yescharacteristic
362C22#6392111yescharacteristic
363C22#6392711yescharacteristic
364C22#6393011yescharacteristic
365C22#6394111yescharacteristic
366C22#6394411yescharacteristic
367C22#6397511yescharacteristic
368C4—81no—
369C4—124no—
370C4—182no—
371C4—721no—
372C4#6383612yes—
373C4#6385412yes—
374C3—21no—
375C3#6887212yescomplemented
376C2—184no—
377C2#1059044411yescharacteristic
378C2#1059044511yescharacteristic
379C2#1059059411yescharacteristic
380C2#1059060111yescharacteristic
381C2#1059137111yescharacteristic
382C2#1059141911yescharacteristic
383C2#1059155511yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1824
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4529C2semidirect
5. #10589164C2semidirect
16. #63900C4semidirect
26. #4529D3semidirect
309. C32#1824semidirect
375. C3#68872semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
#105926862
C2×#635572
C3×#45292
#105891642
#688723