Finite Group Databasebeta

← #11878929

Subgroups — #11878929

Order 1152.

640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#10593909C211yesmaximal, characteristic
2#10593882C211yesmaximal, characteristic
3#10593727C211yesmaximal, characteristic
4#10593450C212yesmaximal, complemented
5#10593447C214yesmaximal, complemented
6#10593377C212yesmaximal, complemented
7#10593371C214yesmaximal
8C2×#3797C2212yes—
9C2×#3776C2218yes—
10C42×C3⋊D3C2211yescharacteristic
11C3×#869—21no—
12C3×C4×Dic6—21no—
13#63919C2211yescharacteristic
14#63919C2212yes—
15#63919C2212yes—
16C4×#627C2212yes—
17#63900—21no—
18#63900—21no—
19#63874—21no—
20#63873—21no—
21#63873C2211yescharacteristic
22#63871—21no—
23#63870—21no—
24#63865C2212yes—
25#63778C2212yes—
26C4⋊#622C2212yes—
27C4×#622C2212yes—
28#63740C2218yes—
29D3×C4⋊Q8—61no—
30#5578—61no—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3C2311yescharacteristic
34C2×C3×Dic6—22no—
35C2×C3×Dic6—21no—
36C2×#627C2314yes—
37C2×#627C2312yes—
38C2×#624—22no—
39#3797—44no—
40C2×#622C2314yes—
41#3776—48no—
42C32×C42D411yescharacteristic
43C4×C3⋊Dic3D411yescharacteristic
44C4×C3⋊Dic3C2311yescharacteristic
45C4×C3⋊Dic3C2311yescharacteristic
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3—22no—
49C3×Dic3⋊C4—22no—
50C3×C4×Dic3—22no—
51#3724—21no—
52#3724—21no—
53#3724—22no—
54#3724—22no—
55#3724C2312yes—
56Dic3⋊Dic3—22no—
57#3722—22no—
58#3209—91nomaximal, Sylow
59C2×D3×Q8—62no—
60C3×C4⋊Q8—61no—
61C3×C4×Q8—61no—
62#946—61no—
63#944—61no—
64#944—62no—
65#897—61no—
66#896—62no—
67D3×C4⋊C4—62no—
68D3×C4⋊C4—62no—
69#889—62no—
70#888—62no—
71#888—62no—
72#888—61no—
73#872—62no—
74C42×D3—61no—
75C42×D3—61no—
76#869—21no—
77C4×Dic6—21no—
78C4×Dic6—62no—
79C22×C3⋊D3C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3C2×D411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C2×C3⋊Dic3C2411yescharacteristic
86C4×C3⋊D3—22no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3Q1614yescomplemented
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—24no—
92C3×Dic6—44no—
93C3×Dic6—42no—
94#627—24no—
95#627—28no—
96#624—44no—
97#622—24no—
98#533—91no—
99C2×C4⋊Q8—91no—
100#494—92no—
101#487—92no—
102#462—94no—
103#451—94no—
104#431—91no—
105C2×C3×Q8—61no—
106C2×C3×Q8—62no—
107D3×Q8—128no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—61no—
113C2×C4×D3—61no—
114C2×C4×D3—64no—
115C2×Dic6—21no—
116C2×Dic6—22no—
117C2×Dic6—62no—
118C2×Dic6—64no—
119C3×C4⋊C4—62no—
120C3×C4⋊C4—62no—
121C3×C4⋊C4—61no—
122C3×C4⋊C4—62no—
123C3×C42—21no—
124C3×C42—21no—
125C3×C42—62no—
126(C2×D3)⋊C4—62no—
127(C2×D3)⋊C4—62no—
128C4⋊Dic3—21no—
129C4⋊Dic3—22no—
130C4⋊Dic3—22no—
131C4⋊Dic3—62no—
132Dic3⋊C4—22no—
133Dic3⋊C4—62no—
134Dic3⋊C4—62no—
135Dic3⋊C4—62no—
136Dic3⋊C4—62no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139C4×Dic3—22no—
140C4×Dic3—61no—
141C4×Dic3—61no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C22×C32C22×D411yescharacteristic
147C2×C3⋊D3—21no—
148C2×C3⋊D3—21no—
149C2×C3⋊D3C2×Q1612yes—
150C32×C4—21no—
151C32×C4C2×Q1612yes—
152C32×C4#13712yes—
153C3⋊Dic3—21no—
154C3⋊Dic3C2×Q1612yes—
155C3⋊Dic3H(5,𝔽2)12yes—
156C3×Dic3—44no—
157C3×Dic3—42no—
158C3×Dic3—42no—
159C22×Q8—92no—
160C2×Q16—98no—
161C4⋊Q8—61no—
162C4⋊Q8—92no—
163C4⋊Q8—92no—
164C4⋊Q8—91no—
165C4⋊Q8—91no—
166C4⋊Q8—181no—
167#125—181no—
168C22⋊Q8—92no—
169C22⋊Q8—181no—
170C4×Q8—61no—
171C4×Q8—92no—
172#117—181no—
173C2×C4⋊C4—181no—
174C2×C4⋊C4—181no—
175C2×C42—91no—
176C4⋊C8—92no—
177#103—98no—
178C22⋊C8—92no—
179C4×C8—92no—
180C22×D3—61no—
181C22×D3—61no—
182C3×Q8—124no—
183C3×Q8—122no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—62no—
191C2×C3×C4—64no—
192C2×C3×C4—62no—
193C2×Dic3—22no—
194C2×Dic3—22no—
195C2×Dic3—24no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—64no—
205C4×D3—64no—
206C4×D3—122no—
207C4×D3—122no—
208C4×D3—128no—
209Dic6—42no—
210Dic6—44no—
211Dic6—124no—
212Dic6—128no—
213C2×C32#53511yescharacteristic
214C2×C32C22×Q1611yescharacteristic
215C2×C32C2×#13711yescharacteristic
216C3⋊D3—22no—
217C2×Q8—61no—
218C2×Q8—62no—
219C2×Q8—94no—
220C2×Q8—92no—
221C2×Q8—364no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—91no—
225C22×C4—182no—
226Q16—368no—
227C2×C8—94no—
228C4⋊C4—62no—
229C4⋊C4—62no—
230C4⋊C4—62no—
231C4⋊C4—61no—
232C4⋊C4—92no—
233C4⋊C4—182no—
234C4⋊C4—182no—
235C4⋊C4—181no—
236C4⋊C4—181no—
237C4⋊C4—182no—
238C22⋊C4—182no—
239C42—62no—
240C42—91no—
241C42—91no—
242C42—91no—
243C42GO+(4,𝔽2)11yescharacteristic
244C22×C3—21no—
245C22×C3—21no—
246C2×D3—62no—
247C2×D3—62no—
248C2×D3—62no—
249C2×D3—62no—
250C2×D3—121no—
251C2×D3—121no—
252C3×C4—22no—
253C3×C4—22no—
254C3×C4—22no—
255C3×C4—22no—
256C3×C4—22no—
257C3×C4—41no—
258C3×C4—124no—
259C3×C4—122no—
260C3×C4—122no—
261Dic3—44no—
262Dic3—42no—
263Dic3—42no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—62no—
268Dic3—62no—
269Dic3—121no—
270C32#320911yescharacteristic, complemented, Sylow
271C23—91no—
272Q8—124no—
273Q8—122no—
274Q8—184no—
275Q8—188no—
276C2×C4—62no—
277C2×C4—62no—
278C2×C4—64no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—94no—
282C2×C4—91no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—364no—
286C2×C4C2×GO+(4,𝔽2)11yescharacteristic
287C2×C4C2×GO+(4,𝔽2)11yescharacteristic
288C2×C4C2×GO+(4,𝔽2)11yescharacteristic
289C8—184no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296D3—64no—
297D3—122no—
298C22—92no—
299C22—181no—
300C22—181no—
301C22C22×GO+(4,𝔽2)11yescharacteristic
302C4—21no—
303C4—92no—
304C4—92no—
305C4—122no—
306C4—124no—
307C4—122no—
308C4—181no—
309C4#6422612yes—
310C4#6422812yes—
311C3—21no—
312C3—21no—
313C2—182no—
314C2C2×#6422611yescharacteristic
315C2C2×#6422811yescharacteristic
316C2#1059651211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32#3209
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10593450C2semidirect
5. #10593447C2semidirect
6. #10593377C2semidirect
88. C4×C3⋊D3Q16semidirect
270. C32#3209semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105938822
#105937272
#105934502
#105934472
#105933772
#105933712
#32099