Finite Group Databasebeta

← #11785825

Subgroups — #11785825

Order 1152.

765 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 765 conjugacy classes of subgroups — too many to draw. Only its 156 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×#64101C211yesmaximal, characteristic
2#10591325C211yesmaximal, characteristic
3C2×#63557C211yesmaximal, characteristic
4C3×#4529C212yesmaximal, complemented
5#10589164C212yesmaximal, complemented
6#68873—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3752—21no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×C4×C3⋊Dic3—21no—
12#64101—22no—
13#64101C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×#3722—21no—
17#63579—21no—
18#63557—22no—
19C2×#892—32no—
20C2×#892—61no—
21C2×(C2×D3)⋊C8—32no—
22#4987—32no—
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—
37C32×C4⋊C4—21no—
38C32×C4⋊C4C2×C412yes—
39#3752—24no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)C2×C412yes—
42C4×C3⋊Dic3—24no—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3—22no—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—22no—
48#3722—42no—
49#1825—91noSylow
50C22×C4×D3—32no—
51C22×C4×D3—61no—
52C22×C3×C8—32no—
53C2×C3×C4⋊C4—21no—
54C2×C3×C4⋊C4—32no—
55C2×C3×C4⋊C4C2×D312yes—
56C2×(C2×D3)⋊C4—62no—
57C2×(C2×D3)⋊C4—62no—
58C2×(C2×D3)⋊C4—62no—
59C2×C4⋊Dic3—32no—
60C2×C4⋊Dic3—61no—
61C2×C4⋊Dic3C2×D312yes—
62C2×C4×Dic3—62no—
63C2×C4×Dic3—62no—
64C22×C3⋊C8C2×D312yes—
65#892—38no—
66#892—64no—
67#892—64no—
68#892—64no—
69C3⋊#95—62no—
70(C2×D3)⋊C8—64no—
71C23×C32C2×D411yescharacteristic
72C22×C3⋊D3—22no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3—21no—
75C22×C3⋊D3—21no—
76C22×C3⋊D3C22⋊C412yes—
77C2×C32×C4—22no—
78C2×C32×C4—42no—
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4#4112yes—
82C2×C32×C4#4112yes—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3C22⋊C412yes—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3—24no—
91C2×C3×Dic3—42no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94C3×C3⋊C8—42no—
95C2×#117—91no—
96C2×C22⋊C8—91no—
97#380—91no—
98#340—32no—
99#340—92no—
100C23×D3—32no—
101C23×D3—61no—
102C22×C3×C4—22no—
103C22×C3×C4—22no—
104C22×C3×C4—21no—
105C22×C3×C4—62no—
106C22×C3×C4C22×D312yes—
107C22×Dic3—22no—
108C22×Dic3—32no—
109C22×Dic3—61no—
110C22×Dic3—62no—
111C22×Dic3—62no—
112C2×C4×D3—34no—
113C2×C4×D3—34no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C3×C8—62no—
123C2×C3×C8—62no—
124C2×C3×C8—62no—
125C3×C4⋊C4—22no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—62no—
129C3×C4⋊C4—62no—
130C3×C4⋊C4C4×D314yes—
131(C2×D3)⋊C4—68no—
132(C2×D3)⋊C4—68no—
133(C2×D3)⋊C4—124no—
134C4⋊Dic3—22no—
135C4⋊Dic3—22no—
136C4⋊Dic3—34no—
137C4⋊Dic3—62no—
138C4⋊Dic3—62no—
139C4⋊Dic3—62no—
140C4×Dic3—68no—
141C4×Dic3—68no—
142C2×C3⋊C8—22no—
143C2×C3⋊C8—22no—
144C2×C3⋊C8—22no—
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32#12312yes—
147C22×C32#13512yes—
148C22×C32AGL(1,ℤ/8)11yescharacteristic
149C22×C32#13711yescharacteristic
150C2×C3⋊D3—22no—
151C2×C3⋊D3—22no—
152C2×C3⋊D3—22no—
153C2×C3⋊D3—42no—
154C2×C3⋊D3—42no—
155C32×C4—42no—
156C32×C4#11711yescharacteristic
157C32×C4#11711yescharacteristic
158C32×C4#12312yes—
159C3⋊Dic3—22no—
160C3⋊Dic3—42no—
161C3×Dic3—82no—
162C23×C4—91no—
163C22×C8—32no—
164#117—94no—
165#117—182no—
166C2×C4⋊C4—32no—
167C2×C4⋊C4—91no—
168C2×C4⋊C4D3211yescharacteristic
169C2×C22⋊C4—181no—
170C2×C22⋊C4—181no—
171C2×C42—181no—
172C22⋊C8—182no—
173#95—181no—
174C23×C3—21no—
175C23×C3D3×D412yes—
176C22×D3—34no—
177C22×D3—62no—
178C22×D3—64no—
179C22×D3—62no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—62no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—122no—
186C22×D3—121no—
187C22×D3—121no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—44no—
195C2×C3×C4—42no—
196C2×C3×C4—42no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×C3×C4—122no—
200C2×C3×C4C2×C4×D312yes—
201C2×C3×C4#23512yes—
202C2×C3×C4#23512yes—
203C2×C3×C4D3×D412yes—
204C2×C3×C4#23712yes—
205C2×C3×C4#23912yes—
206C2×Dic3—34no—
207C2×Dic3—42no—
208C2×Dic3—42no—
209C2×Dic3—42no—
210C2×Dic3—62no—
211C2×Dic3—64no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—64no—
215C2×Dic3—64no—
216C2×Dic3—122no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C4×D3—64no—
221C4×D3—68no—
222C4×D3—64no—
223C4×D3—64no—
224C4×D3—64no—
225C4×D3—64no—
226C4×D3—64no—
227C3×C8—122no—
228C3⋊C8—42no—
229C2×C32#38111yescharacteristic
230C2×C32#41611yescharacteristic
231C2×C32#41711yescharacteristic
232C2×C32#48212yes—
233C2×C32#48512yes—
234C3⋊D3—42no—
235C24—91no—
236C22×C4—21no—
237C22×C4—62no—
238C22×C4—91no—
239C22×C4—92no—
240C22×C4—92no—
241C22×C4—182no—
242C22×C4—182no—
243C22×C4—181no—
244C22×C4C2×D3211yescharacteristic
245C2×C8—62no—
246C2×C8—62no—
247C2×C8—62no—
248C4⋊C4—21no—
249C4⋊C4—62no—
250C4⋊C4—62no—
251C4⋊C4—92no—
252C4⋊C4—181no—
253C4⋊C4#62412yes—
254C22⋊C4—184no—
255C22⋊C4—362no—
256C42—184no—
257C22×C3—22no—
258C22×C3—22no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3D3×C22⋊C412yes—
263C22×C3#88312yes—
264C22×C3#89412yes—
265C22×C3#91212yes—
266C22×C3#91412yes—
267C22×C3#91612yes—
268C22×C3#91812yes—
269C2×D3—64no—
270C2×D3—64no—
271C2×D3—64no—
272C2×D3—64no—
273C2×D3—122no—
274C2×D3—122no—
275C2×D3—124no—
276C2×D3—124no—
277C2×D3—122no—
278C2×D3—122no—
279C2×D3—122no—
280C2×D3—122no—
281C3×C4—21no—
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—44no—
285C3×C4—44no—
286C3×C4—242no—
287C3×C4#87212yes—
288C3×C4#88312yes—
289C3×C4#89212yes—
290C3×C4#89412yes—
291Dic3—64no—
292Dic3—64no—
293Dic3—82no—
294Dic3—124no—
295Dic3—124no—
296C32#182511yescharacteristic, complemented, Sylow
297C23—92no—
298C23—182no—
299C23—182no—
300C23—181no—
301C23—181no—
302C23#381111yescharacteristic
303C2×C4—22no—
304C2×C4—42no—
305C2×C4—92no—
306C2×C4—122no—
307C2×C4—122no—
308C2×C4—122no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4—184no—
312C2×C4—182no—
313C2×C4—182no—
314C2×C4—361no—
315C2×C4—361no—
316C2×C4#379612yes—
317C2×C4#379812yes—
318C2×C4C2×#62411yescharacteristic
319C2×C4#381111yescharacteristic
320C8—122no—
321C2×C3—22no—
322C2×C3—22no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3#466412yes—
327C2×C3#477212yes—
328C2×C3#478412yes—
329C2×C3#480312yes—
330C2×C3#481512yes—
331C2×C3#486612yes—
332C2×C3#488812yes—
333D3—124no—
334D3—124no—
335C22—182no—
336C22—182no—
337C22—182no—
338C22—362no—
339C22—362no—
340C22#6385312yes—
341C22#6393612yes—
342C22#6394111yescharacteristic
343C22#6394511yescharacteristic
344C22#6397411yescharacteristic
345C4—42no—
346C4—182no—
347C4—242no—
348C4—362no—
349C4#6384911yescharacteristic
350C4#6385312yes—
351C4#6387411yescharacteristic
352C3—21no—
353C3#6887312yescomplemented
354C2—362no—
355C2#1059051312yes—
356C2#1059052612yes—
357C2#1059121911yescharacteristic
358C2#1059142411yescharacteristic
359C2#1059155411yescharacteristic
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#1825
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
13. #64101C4semidirect
26. #4529D3semidirect
296. C32#1825semidirect
353. C3#68873semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
#105913252
C2×#635572
C3×#45292
#105891642
#688733