Finite Group Databasebeta

← #11788052

Subgroups — #11788052

Order 1152.

658 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×#3787C211yesmaximal, characteristic
2C2×#63865C211yesmaximal, characteristic
3C2×#63740C212yesmaximal, complemented
4#10591355C211yesmaximal, characteristic
5#10590075C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#627C2211yescharacteristic
8C22×#622C2212yes—
9C2×#3787—22no—
10C2×#3787—24no—
11C2×C3×Dic3⋊C4—21no—
12C2×#3724C2212yes—
13C2×#3724C2211yescharacteristic
14C2×#3722—21no—
15C2×#3722—21no—
16#63865—22no—
17#63865C414yescomplemented
18#63740—24no—
19C3×C3⋊#95—21no—
20C2×#896—61no—
21#4667—61no—
22C23×C3⋊D3D411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3C2×C412yes—
28C2×C4×C3⋊D3D412yes—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C22×C3×Dic3—22no—
32C2×#627—22no—
33C2×#627—22no—
34C2×#627—21no—
35C2×#627C2×C412yes—
36C2×#622—22no—
37C2×#622—22no—
38C2×#622D414yes—
39#3787—28no—
40C3×Dic3⋊C4—24no—
41#3724—21no—
42#3724—22no—
43#3724—22no—
44#3724C2×C412yes—
45#3722—24no—
46#3722—42no—
47#1892—91nomaximal, Sylow
48C22×C4×D3—61no—
49C22×C4×D3—61no—
50C22×Dic6—61no—
51C2×C3×C4⋊C4—61no—
52C2×(C2×D3)⋊C4—61no—
53C2×(C2×D3)⋊C4—61no—
54C2×(C2×D3)⋊C4—62no—
55C2×Dic3⋊C4—21no—
56C2×Dic3⋊C4—61no—
57C2×Dic3⋊C4—62no—
58#896—64no—
59#896—64no—
60C3×#95—61no—
61C3⋊#95—21no—
62C23×C32C2×D411yescharacteristic
63C22×C3⋊D3—22no—
64C22×C3⋊D3—22no—
65C22×C3⋊D3C22⋊C412yes—
66C22×C3⋊D3SD1612yes—
67C22×C3⋊D3Q1612yes—
68C2×C32×C4—22no—
69C2×C32×C4C22⋊C412yes—
70C2×C3⋊Dic3C22×C411yescharacteristic
71C2×C3⋊Dic3C2×D412yes—
72C2×C3⋊Dic3C2×D411yescharacteristic
73C2×C3⋊Dic3#4112yes—
74C4×C3⋊D3—24no—
75C4×C3⋊D3—22no—
76C4×C3⋊D3—22no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C2×C3×Dic3—42no—
84#627—24no—
85#627—41no—
86#627—41no—
87#622—24no—
88C23×C8—91no—
89C2×C22⋊Q8—91no—
90C2×#103—92no—
91#380—91no—
92#340—92no—
93C23×D3—61no—
94C23×D3—61no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—61no—
98C22×C3×C4—61no—
99C22×C3×C4—62no—
100C22×Dic3—21no—
101C22×Dic3—21no—
102C22×Dic3—22no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—122no—
110C2×C4×D3—122no—
111C2×C4×D3—122no—
112C2×C4×D3—122no—
113C2×Dic6—62no—
114C2×Dic6—62no—
115C2×Dic6—122no—
116C2×Dic6—122no—
117C3×C4⋊C4—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120(C2×D3)⋊C4—124no—
121Dic3⋊C4—24no—
122Dic3⋊C4—62no—
123Dic3⋊C4—62no—
124Dic3⋊C4—122no—
125Dic3⋊C4—122no—
126C22×C32C2×C22⋊C411yescharacteristic
127C22×C32#12112yes—
128C22×C32C2×SD1611yescharacteristic
129C22×C32C2×Q1611yescharacteristic
130C22×C32#13512yes—
131C2×C3⋊D3—22no—
132C2×C3⋊D3—22no—
133C2×C3⋊D3—24no—
134C2×C3⋊D3—24no—
135C2×C3⋊D3#10314yescomplemented
136C32×C4—22no—
137C3⋊Dic3C4×D412yes—
138C3⋊Dic3#12011yescharacteristic
139C3⋊Dic3#12311yescharacteristic
140C3×Dic3—42no—
141C3×Dic3—42no—
142C3×Dic3—82no—
143C22×Q8—91no—
144C23×C4—91no—
145C22×C8—92no—
146C22×C8—184no—
147C22×C8—182no—
148C22⋊Q8—94no—
149C22⋊Q8—182no—
150C2×C4⋊C4—61no—
151C2×C4⋊C4—91no—
152C2×C4⋊C4—92no—
153C2×C22⋊C4—181no—
154C2×C22⋊C4—181no—
155#103—184no—
156#95—61no—
157C23×C3—21no—
158C23×C3—21no—
159C22×D3—62no—
160C22×D3—62no—
161C22×D3—62no—
162C22×D3—62no—
163C22×D3—62no—
164C22×D3—62no—
165C22×D3—122no—
166C22×D3—122no—
167C22×D3—122no—
168C22×D3—122no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—42no—
172C2×C3×C4—42no—
173C2×C3×C4—62no—
174C2×C3×C4—62no—
175C2×C3×C4—122no—
176C2×C3×C4—122no—
177C2×C3×C4—122no—
178C2×C3×C4—122no—
179C2×C3×C4—122no—
180C2×Dic3—22no—
181C2×Dic3—22no—
182C2×Dic3—42no—
183C2×Dic3—42no—
184C2×Dic3—42no—
185C2×Dic3—42no—
186C2×Dic3—42no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—61no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C4×D3—122no—
196C4×D3—122no—
197C4×D3—124no—
198C4×D3—122no—
199C4×D3—124no—
200C4×D3—122no—
201Dic6—124no—
202Dic6—122no—
203Dic6—122no—
204C2×C32#38611yescharacteristic
205C2×C32C2×#10311yescharacteristic
206C2×C32#41611yescharacteristic
207C2×C32#46512yes—
208C2×C32#46712yes—
209C3⋊D3—24no—
210C24—91no—
211C2×Q8—92no—
212C2×Q8—181no—
213C2×Q8—182no—
214C2×Q8—182no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4—62no—
218C22×C4—91no—
219C22×C4—92no—
220C22×C4—92no—
221C22×C4—182no—
222C22×C4—182no—
223C22×C4GO+(4,𝔽2)11yescharacteristic
224C2×C8—94no—
225C2×C8—182no—
226C2×C8—182no—
227C2×C8—188no—
228C4⋊C4—64no—
229C4⋊C4—92no—
230C4⋊C4—181no—
231C4⋊C4—182no—
232C4⋊C4—182no—
233C22⋊C4—184no—
234C22⋊C4—362no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—22no—
244C22×C3—22no—
245C2×D3—64no—
246C2×D3—64no—
247C2×D3—122no—
248C2×D3—122no—
249C2×D3—122no—
250C2×D3—122no—
251C2×D3—124no—
252C2×D3—124no—
253C2×D3—124no—
254C2×D3—124no—
255C3×C4—42no—
256C3×C4—42no—
257C3×C4—122no—
258C3×C4—122no—
259C3×C4—242no—
260Dic3—42no—
261Dic3—42no—
262Dic3—62no—
263Dic3—61no—
264Dic3—61no—
265Dic3—62no—
266Dic3—61no—
267Dic3—61no—
268Dic3—82no—
269C32#189211yescharacteristic, complemented, Sylow
270C23—92no—
271C23—92no—
272C23—92no—
273C23—182no—
274C23—182no—
275C23C2×GO+(4,𝔽2)11yescharacteristic
276Q8—184no—
277Q8—361no—
278Q8—361no—
279C2×C4—22no—
280C2×C4—62no—
281C2×C4—62no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—92no—
285C2×C4—92no—
286C2×C4—122no—
287C2×C4—122no—
288C2×C4—122no—
289C2×C4—122no—
290C2×C4—122no—
291C2×C4—182no—
292C2×C4—184no—
293C2×C4—182no—
294C2×C4D32⋊C412yes—
295C8—184no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—22no—
301C2×C3—22no—
302C2×C3—22no—
303C2×C3—22no—
304C2×C3—21no—
305C2×C3—21no—
306D3—124no—
307D3—124no—
308C22—94no—
309C22—182no—
310C22—184no—
311C22—184no—
312C22—182no—
313C22#6422312yes—
314C22#6422711yescharacteristic
315C22#6422811yescharacteristic
316C22C2×D32⋊C411yescharacteristic
317C22#6424212yes—
318C4—22no—
319C4—91no—
320C4—92no—
321C4—91no—
322C4—122no—
323C4—122no—
324C4—242no—
325C3—21no—
326C3—21no—
327C2—184no—
328C2#1059334911yescharacteristic
329C2#1059337511yescharacteristic
330C2#1059343512yes—
331C2#1059344612yes—
332C2#1059351511yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1892
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63740C2semidirect
5. #10590075C2semidirect
17. #63865C4semidirect
135. C2×C3⋊D3#103semidirect
269. C32#1892semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#638652
C2×#637402
#105913552
#105900752
#18929