Finite Group Databasebeta

← #11785770

Subgroups — #11785770

Order 1152.

789 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 789 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3#10591325C211yesmaximal, characteristic
4C3×#4551C212yesmaximal, complemented
5#10589163C212yesmaximal, complemented
6#68871—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624—21no—
9C22×C32×C8C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C2×#3724—21no—
14C2×#3722—21no—
15#63900—22no—
16#63900C414yescomplemented
17#63647—22no—
18#63579—21no—
19C2×D3×C4⋊C4—32no—
20C2×(C2×D3)⋊C8—32no—
21C2×(C2×D3)⋊C8—61no—
22#4987—32no—
23C3×#340—32no—
24#4551D312yescomplemented
25#4529—32no—
26#4529—32no—
27C23×C3⋊D3D411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3C2×C412yes—
33C2×C4×C3⋊D3D412yes—
34C22×C3×Dic3—22no—
35C22×C3×Dic3—22no—
36C2×#624—24no—
37C2×#624—42no—
38C2×#624—42no—
39C2×C32×C8—21no—
40C2×C32×C8—22no—
41C2×C3⋊(C3⋊C8)—21no—
42C2×C3⋊(C3⋊C8)—22no—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3C2×C414yes—
47#3724—24no—
48#3722—42no—
49#1823—91noSylow
50C22×C4×D3—32no—
51C22×C4×D3—61no—
52C22×C4×D3—62no—
53C22×C3×C8—21no—
54C22×C3×C8C2×D312yes—
55C2×C3×C4⋊C4—32no—
56C2×C3×C4⋊C4—32no—
57C2×(C2×D3)⋊C4—62no—
58C2×C4⋊Dic3C2×D312yes—
59C2×C4⋊Dic3C2×D312yes—
60C2×Dic3⋊C4—62no—
61C22×C3⋊C8—32no—
62C22×C3⋊C8—61no—
63D3×C4⋊C4—38no—
64D3×C4⋊C4—64no—
65C3⋊#95—62no—
66(C2×D3)⋊C8—64no—
67(C2×D3)⋊C8—64no—
68C23×C32C2×D411yescharacteristic
69C22×C3⋊D3—22no—
70C22×C3⋊D3—22no—
71C22×C3⋊D3C22⋊C412yes—
72C22×C3⋊D3D812yes—
73C22×C3⋊D3SD1612yes—
74C2×C32×C4C22×C411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C32×C4#4112yes—
77C2×C32×C4#4112yes—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3C22⋊C412yes—
80C4×C3⋊D3—24no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3—22no—
83C2×C3×Dic3—24no—
84C2×C3×Dic3—42no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—42no—
87C2×C3×Dic3—42no—
88C2×C3×Dic3—42no—
89#624—48no—
90C32×C8—41no—
91C3⋊(C3⋊C8)—41no—
92C22×C4⋊C4—91no—
93C2×C22⋊C8—91no—
94#380—91no—
95#340—32no—
96#340—92no—
97C23×D3—32no—
98C23×D3—61no—
99C22×C3×C4—21no—
100C22×C3×C4—62no—
101C22×C3×C4—62no—
102C22×C3×C4C22×D312yes—
103C22×Dic3—22no—
104C22×Dic3—22no—
105C22×Dic3—32no—
106C22×Dic3—61no—
107C2×C4×D3—34no—
108C2×C4×D3—34no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—68no—
116C2×C4×D3—122no—
117C2×C4×D3—122no—
118C2×C4×D3—124no—
119C2×C4×D3—124no—
120C2×C3×C8—22no—
121C2×C3×C8—22no—
122C2×C3×C8—22no—
123C2×C3×C8—22no—
124C2×C3×C8—42no—
125C3×C4⋊C4—34no—
126C3×C4⋊C4—62no—
127C3×C4⋊C4—62no—
128C3×C4⋊C4—62no—
129(C2×D3)⋊C4—124no—
130C4⋊Dic3—22no—
131C4⋊Dic3—22no—
132C4⋊Dic3—22no—
133C4⋊Dic3C4×D314yes—
134Dic3⋊C4—68no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—122no—
140C22×C32C2×C22⋊C411yescharacteristic
141C22×C32#12312yes—
142C22×C32C2×D811yescharacteristic
143C22×C32C2×SD1611yescharacteristic
144C22×C32#13712yes—
145C2×C3⋊D3—22no—
146C2×C3⋊D3—22no—
147C2×C3⋊D3—24no—
148C2×C3⋊D3—24no—
149C2×C3⋊D3#10214yes—
150C32×C4#11712yes—
151C32×C4#12311yescharacteristic
152C32×C4#12311yescharacteristic
153C3⋊Dic3—22no—
154C3×Dic3—44no—
155C3×Dic3—82no—
156C23×C4—91no—
157C23×C4—181no—
158C22×C8—91no—
159C22×C8D3211yescharacteristic
160C2×C4⋊C4—32no—
161C2×C4⋊C4—32no—
162C2×C4⋊C4—94no—
163C2×C4⋊C4—182no—
164C2×C4⋊C4—181no—
165C2×C22⋊C4—181no—
166C22⋊C8—182no—
167#95—181no—
168C23×C3—21no—
169C23×C3D3×D412yes—
170C22×D3—34no—
171C22×D3—34no—
172C22×D3—34no—
173C22×D3—62no—
174C22×D3—62no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—62no—
178C22×D3—62no—
179C22×D3—62no—
180C22×D3—122no—
181C22×D3—122no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—64no—
187C2×C3×C4—122no—
188C2×C3×C4—122no—
189C2×C3×C4—122no—
190C2×C3×C4—122no—
191C2×C3×C4—122no—
192C2×C3×C4C2×C4×D312yes—
193C2×C3×C4#23512yes—
194C2×C3×C4#23512yes—
195C2×C3×C4D3×D412yes—
196C2×C3×C4#23712yes—
197C2×C3×C4#23912yes—
198C2×Dic3—24no—
199C2×Dic3—34no—
200C2×Dic3—42no—
201C2×Dic3—42no—
202C2×Dic3—42no—
203C2×Dic3—42no—
204C2×Dic3—42no—
205C2×Dic3—62no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—122no—
209C4×D3—64no—
210C4×D3—64no—
211C4×D3—64no—
212C4×D3—64no—
213C4×D3—124no—
214C4×D3—122no—
215C4×D3—122no—
216C4×D3—1216no—
217C3×C8—42no—
218C3×C8—42no—
219C3⋊C8—122no—
220C3⋊C8—122no—
221C2×C32#38111yescharacteristic
222C2×C32C2×#10211yescharacteristic
223C2×C32#41911yescharacteristic
224C2×C32#48012yes—
225C2×C32#48312yes—
226C3⋊D3—24no—
227C24—91no—
228C22×C4—62no—
229C22×C4—62no—
230C22×C4—91no—
231C22×C4—92no—
232C22×C4—92no—
233C22×C4—184no—
234C22×C4—182no—
235C22×C4—182no—
236C22×C4—362no—
237C22×C4—362no—
238C22×C4C2×D3211yescharacteristic
239C2×C8—22no—
240C2×C8—21no—
241C2×C8—182no—
242C2×C8—181no—
243C4⋊C4—34no—
244C4⋊C4—62no—
245C4⋊C4—62no—
246C4⋊C4—62no—
247C4⋊C4—184no—
248C22⋊C4—362no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—22no—
252C22×C3—22no—
253C22×C3—21no—
254C22×C3D3×C22⋊C412yes—
255C22×C3#88312yes—
256C22×C3#89412yes—
257C22×C3D3×D812yes—
258C22×C3D3×SD1612yes—
259C22×C3#91512yes—
260C22×C3#91812yes—
261C2×D3—38no—
262C2×D3—64no—
263C2×D3—64no—
264C2×D3—64no—
265C2×D3—64no—
266C2×D3—64no—
267C2×D3—64no—
268C2×D3—64no—
269C2×D3—122no—
270C2×D3—124no—
271C2×D3—124no—
272C2×D3—122no—
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—124no—
277C3×C4—242no—
278C3×C4#87212yes—
279C3×C4#88312yes—
280C3×C4#89212yes—
281C3×C4#89412yes—
282Dic3—44no—
283Dic3—64no—
284Dic3—82no—
285Dic3—122no—
286C32#182311yescharacteristic, complemented, Sylow
287C23—92no—
288C23—92no—
289C23—92no—
290C23—182no—
291C23—182no—
292C23#380211yescharacteristic
293C2×C4—64no—
294C2×C4—92no—
295C2×C4—122no—
296C2×C4—122no—
297C2×C4—122no—
298C2×C4—122no—
299C2×C4—122no—
300C2×C4—182no—
301C2×C4—184no—
302C2×C4—182no—
303C2×C4—182no—
304C2×C4—368no—
305C2×C4#379912yes—
306C2×C4C4×D3211yescharacteristic
307C2×C4#380412yes—
308C2×C4#381111yescharacteristic
309C8—41no—
310C8—361no—
311C2×C3—21no—
312C2×C3—22no—
313C2×C3—21no—
314C2×C3—22no—
315C2×C3—21no—
316C2×C3#466412yes—
317C2×C3D3×#10212yes—
318C2×C3#477412yes—
319C2×C3#480212yes—
320C2×C3#480512yes—
321C2×C3#486212yes—
322C2×C3#488212yes—
323D3—68no—
324D3—124no—
325C22—94no—
326C22—182no—
327C22—184no—
328C22—184no—
329C22—182no—
330C22#6379611yescharacteristic
331C22#6379711yescharacteristic
332C22#6381112yes—
333C22#6385412yes—
334C22#6392111yescharacteristic
335C4—124no—
336C4—182no—
337C4—242no—
338C4#6383612yes—
339C4#6389711yescharacteristic
340C4#6397511yescharacteristic
341C3—21no—
342C3#6887112yescomplemented
343C2—184no—
344C2#1059065012yes—
345C2#1059068612yes—
346C2#1059069111yescharacteristic
347C2#1059094011yescharacteristic
348C2#1059137111yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1823
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C3×#4551C2semidirect
5. #10589163C2semidirect
16. #63900C4semidirect
24. #4551D3semidirect
286. C32#1823semidirect
342. C3#68871semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#636472
#105913252
C3×#45512
#105891632
#688713