Finite Group Databasebeta

← #11791500

Subgroups — #11791500

Order 1152.

606 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 83 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×#63915C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic, complemented
3C2×#63740C212yesmaximal, complemented
4C2×#63739C212yesmaximal
5C4×#3724C211yesmaximal, characteristic, complemented
6C22×#627C2211yescharacteristic
7C22×#625C2211yescharacteristic
8C22×#622C2212yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×(C2×D3)⋊C4—21no—
11C2×C3×C4×Dic3—21no—
12C2×#3724C2212yes—
13C2×(C2×D3)⋊Dic3—21no—
14#63915—22no—
15#63915C414yescomplemented
16#63779—22no—
17#63740—24no—
18#63739—24no—
19#63579—21no—
20C2×#885—61no—
21C4×Dic3⋊C4—61no—
22C23×C3×D3—21no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C22×C3×Dic3—22no—
27C22×C3×Dic3—21no—
28C2×#627—22no—
29C2×#627—22no—
30C2×#627—21no—
31C2×#627C2×C412yes—
32C2×#625—22no—
33C2×#625—22no—
34C2×#625—21no—
35C2×#625C2×C412yes—
36C2×#622—22no—
37C2×#622—22no—
38C2×#622—22no—
39C4×C3⋊Dic3C2×C412yes—
40C4×C3⋊Dic3D412yes—
41C3×(C2×D3)⋊C4—24no—
42C3×C4×Dic3—42no—
43#3724—22no—
44#3724D414yes—
45(C2×D3)⋊Dic3—24no—
46#1983—91nomaximal, Sylow
47C22×#67—61no—
48C22×Dic6—61no—
49C2×C3×C22⋊C4—61no—
50C2×C3×C42—61no—
51C2×#217—61no—
52C2×(C2×D3)⋊C4—21no—
53C2×(C2×D3)⋊C4—61no—
54C2×Dic3⋊C4—62no—
55C2×C4×Dic3—21no—
56C2×C4×Dic3—61no—
57C2×C4×Dic3—61no—
58#885—64no—
59#885—64no—
60C3⋊#95—62no—
61C23×C32C2×D411yescharacteristic
62C22×C3×D3—22no—
63C22×C3×D3—42no—
64C22×C3×D3—42no—
65C22×C3×D3—41no—
66C22×C3×D3—41no—
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4C22⋊C412yes—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C22⋊C412yes—
72C2×C3⋊Dic3C22×C411yescharacteristic
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3#4112yes—
76C2×C3×Dic3—22no—
77C2×C3×Dic3—24no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81#627—24no—
82#627—41no—
83#627—41no—
84#625—24no—
85#625—41no—
86#625—41no—
87#622—42no—
88C2×#124—91no—
89C2×C4⋊C8—91no—
90C2×#103—92no—
91C2×#102—92no—
92C4×C4⋊C4—91no—
93C24×C3—61no—
94C23×D3—21no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—62no—
98C22×C3×C4—61no—
99C2×#67—62no—
100C2×#67—62no—
101C2×#67—122no—
102C2×#67—122no—
103C22×Dic3—22no—
104C22×Dic3—21no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C22×Dic3—61no—
109C2×Dic6—62no—
110C2×Dic6—62no—
111C2×Dic6—122no—
112C2×Dic6—122no—
113C3×C22⋊C4—64no—
114C3×C42—122no—
115#217—64no—
116(C2×D3)⋊C4—24no—
117(C2×D3)⋊C4—64no—
118Dic3⋊C4—64no—
119Dic3⋊C4—64no—
120C4×Dic3—42no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C22×C32C2×C22⋊C411yescharacteristic
126C22×C32#12112yes—
127C22×C32#13512yes—
128C22×C32AGL(1,ℤ/8)11yescharacteristic
129C22×C32#13711yescharacteristic
130C2×C3×D3—42no—
131C2×C3×D3—42no—
132C2×C3×D3—42no—
133C2×C3×D3—82no—
134C2×C3×D3—82no—
135C32×C4—22no—
136C3⋊Dic3—22no—
137C3⋊Dic3C4×D412yes—
138C3⋊Dic3#12411yescharacteristic
139C3⋊Dic3#12711yescharacteristic
140C3×Dic3—42no—
141C3×Dic3—44no—
142C22×Q8—91no—
143C22×D4—91no—
144C22×C8—92no—
145#124—94no—
146#124—182no—
147C2×C4⋊C4—92no—
148C2×C22⋊C4—61no—
149C2×C22⋊C4—181no—
150C2×C42—61no—
151C2×C42—91no—
152C4⋊C8—182no—
153#103—184no—
154#102—184no—
155#95—181no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—62no—
159C23×C3—122no—
160C23×C3—122no—
161C23×C3—121no—
162C23×C3—121no—
163C22×D3—22no—
164C22×D3—42no—
165C22×D3—42no—
166C22×D3—41no—
167C22×D3—41no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4—64no—
175C2×C3×C4—62no—
176C2×C3×C4—122no—
177C2×C3×C4—122no—
178C2×C3×C4—122no—
179#67—124no—
180#67—122no—
181#67—122no—
182C2×Dic3—24no—
183C2×Dic3—22no—
184C2×Dic3—42no—
185C2×Dic3—42no—
186C2×Dic3—42no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—62no—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—122no—
198C2×Dic3—122no—
199Dic6—124no—
200Dic6—122no—
201Dic6—122no—
202C2×C32#39011yescharacteristic
203C2×C32#41611yescharacteristic
204C2×C32#41711yescharacteristic
205C2×C32#46312yes—
206C2×C32#46412yes—
207C3×D3—82no—
208C24—61no—
209C2×Q8—92no—
210C2×Q8—181no—
211C2×Q8—182no—
212C2×Q8—182no—
213C2×D4—92no—
214C2×D4—182no—
215C2×D4—182no—
216C2×D4—181no—
217C22×C4—62no—
218C22×C4—61no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4GO+(4,𝔽2)11yescharacteristic
222C2×C8—182no—
223C2×C8—182no—
224C2×C8—182no—
225C4⋊C4—94no—
226C4⋊C4—182no—
227C22⋊C4—64no—
228C22⋊C4—184no—
229C42—92no—
230C42—92no—
231C42—122no—
232C22×C3—22no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—122no—
243C22×C3—122no—
244C22×C3—122no—
245C22×C3—242no—
246C22×C3—242no—
247C2×D3—42no—
248C2×D3—42no—
249C2×D3—42no—
250C2×D3—82no—
251C2×D3—82no—
252C3×C4—24no—
253C3×C4—42no—
254C3×C4—122no—
255C3×C4—124no—
256Dic3—42no—
257Dic3—44no—
258Dic3—62no—
259Dic3—61no—
260Dic3—61no—
261Dic3—62no—
262Dic3—61no—
263Dic3—61no—
264Dic3—122no—
265Dic3—122no—
266C32#198311yescharacteristic, complemented, Sylow
267C23—62no—
268C23—122no—
269C23—122no—
270C23—121no—
271C23—121no—
272C23C2×GO+(4,𝔽2)11yescharacteristic
273Q8—184no—
274Q8—361no—
275Q8—361no—
276D4—184no—
277D4—361no—
278D4—361no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—64no—
282C2×C4—62no—
283C2×C4—92no—
284C2×C4—92no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—92no—
288C2×C4—122no—
289C2×C4—122no—
290C2×C4—122no—
291C2×C4—182no—
292C2×C4D32⋊C412yes—
293C8—362no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—22no—
297C2×C3—22no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—22no—
301C2×C3—22no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—242no—
305D3—82no—
306C22—122no—
307C22—122no—
308C22—122no—
309C22—242no—
310C22—242no—
311C22#6422312yes—
312C22#6423012yes—
313C22C2×D32⋊C411yescharacteristic
314C22#6423611yescharacteristic
315C22#6423911yescharacteristic
316C4—22no—
317C4—91no—
318C4—92no—
319C4—91no—
320C4—122no—
321C4—124no—
322C4—182no—
323C3—21no—
324C3—21no—
325C2—242no—
326C2#1059334911yescharacteristic
327C2#1059335212yes—
328C2#1059340511yescharacteristic
329C2#1059342212yes—
330C2#1059349611yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1983
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
2. C2×#63779C2semidirect
3. C2×#63740C2semidirect
5. C4×#3724C2semidirect
15. #63915C4semidirect
266. C32#1983semidirect

Maximal subgroups

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

subgroupindex
C2×#639152
C2×#637792
C2×#637402
C2×#637392
C4×#37242
#19839