Finite Group Databasebeta

← #11781966

Subgroups — #11781966

Order 1152.

336 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×#5090C211yesmaximal, characteristic
2C3×#5078C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic
4#10590258C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic
6#10589097C211yesmaximal, characteristic
7#10589093C211yesmaximal, characteristic
8#71379—31nomaximal
9#71057—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×C3×#216—21no—
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C2×#3718—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#835—21no—
18C3×#807—21no—
19C3×#807—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22Dic3⋊(C3⋊C8)—21no—
23#63565—21no—
24#63554—21no—
25C3×#500—31no—
26C3×#462—31no—
27#5090—31no—
28#5090D311yescharacteristic
29#5078D311yescharacteristic
30#5031—31no—
31#5024—31no—
32#4679—31no—
33#4547—31no—
34#4547—31no—
35#4547—31no—
36#4547—61no—
37#4482—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8—21no—
41C2×C3×Dic6—21no—
42C2×C3×Dic6D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×#216—42no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3D411yescharacteristic
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3718—42no—
58#1694—91noSylow
59C2×C3×Q16—61no—
60C3×C4⋊Q8—21no—
61C3×C4⋊Q8—31no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×C4×Q8—31no—
65C2×#216—21no—
66C2×#216—61no—
67C2×#216—61no—
68#869C2×D311yescharacteristic
69C4×Dic6C2×D311yescharacteristic
70C3×#107—61no—
71C3×#107—61no—
72C3×C4⋊C8—31no—
73C3×#103—61no—
74C3×C4×C8—31no—
75#835—21no—
76#835—61no—
77#815—61no—
78Dic3⋊C8—61no—
79#810—61no—
80#807—21no—
81#807—21no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90#803—61no—
91C4×C3⋊C8C2×D311yescharacteristic
92C32×Q8—41no—
93C32×Q8—41no—
94C2×C32×C4—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3×Dic3—21no—
99C2×C3×Dic3—21no—
100C2×C3×Dic3—41no—
101C3×Dic6—21no—
102C3×Dic6—21no—
103C3×Dic6—41no—
104C3×Dic6—41no—
105C3⋊(C3⋊C8)—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8Q1612yescomplemented
110#500—31no—
111#462—31no—
112#462—91no—
113#446—91no—
114#334—91no—
115#332—91no—
116#332—91no—
117C2×C3×Q8—21no—
118C2×C3×Q8—21no—
119C2×C3×Q8—31no—
120C2×C3×Q8—41no—
121C2×C3×Q8—61no—
122C2×Dic6—21no—
123C2×Dic6#6711yescharacteristic
124C3×Q16—122no—
125C2×C3×C8—31no—
126C2×C3×C8—31no—
127C2×C3×C8—61no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—31no—
134C3×C4⋊C4—41no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C42—21no—
139C3×C42—61no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142#216—42no—
143#216—122no—
144#216—122no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3#6711yescharacteristic
148Dic3⋊C4—21no—
149C4×Dic3—21no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—121no—
156C2×C3⋊C8—121no—
157C2×C3⋊C8#6711yescharacteristic
158C2×C3⋊C8#6711yescharacteristic
159C22×C32#12111yescharacteristic
160C32×C4—21no—
161C32×C4—81no—
162C32×C4C2×Q1611yescharacteristic
163C32×C4AGL(1,ℤ/8)11yescharacteristic
164C32×C4AGL(1,ℤ/8)11yescharacteristic
165C32×C4#13711yescharacteristic
166C3×Dic3—41no—
167C3×Dic3—41no—
168C3×Dic3—81no—
169C2×Q16—61no—
170C2×Q16—181no—
171C4⋊Q8—31no—
172C4⋊Q8D3211yescharacteristic
173C4×Q8—31no—
174#107—61no—
175#107—61no—
176C4⋊C8—31no—
177C4⋊C8—91no—
178C4⋊C8—91no—
179C4⋊C8—181no—
180#103—61no—
181#103—181no—
182#97—181no—
183C4×C8—31no—
184C3×Q8—41no—
185C3×Q8—41no—
186C3×Q8—41no—
187C3×Q8—41no—
188C3×Q8—61no—
189C3×Q8—61no—
190C3×Q8—81no—
191C3×Q8—81no—
192C3×Q8—121no—
193C3×Q8—121no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—42no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4—61no—
201C2×C3×C4—61no—
202C2×C3×C4—121no—
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×D411yescharacteristic
205C2×C3×C4#23711yescharacteristic
206C2×C3×C4#23711yescharacteristic
207C2×C3×C4C2×#6711yescharacteristic
208C2×C3×C4C2×#6711yescharacteristic
209C2×Dic3—21no—
210C2×Dic3—21no—
211C2×Dic3—41no—
212Dic6—21no—
213Dic6—21no—
214Dic6—41no—
215Dic6—41no—
216C3×C8—32no—
217C3×C8—61no—
218C3×C8—121no—
219C3⋊C8—21no—
220C3⋊C8—41no—
221C3⋊C8—121no—
222C3⋊C8—121no—
223C3⋊C8—121no—
224C3⋊C8—121no—
225C3⋊C8—241no—
226C3⋊C8—241no—
227C3⋊C8#21612yescomplemented
228C2×C32#46211yescharacteristic
229C2×C32#46911yescharacteristic
230C2×C32#47311yescharacteristic
231C2×Q8—21no—
232C2×Q8—31no—
233C2×Q8—61no—
234Q16—122no—
235Q16—362no—
236C2×C8—31no—
237C2×C8—31no—
238C2×C8—61no—
239C2×C8—181no—
240C2×C8—181no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—31no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C42—61no—
248C42C2×D3211yescharacteristic
249C22×C3—21no—
250C22×C3#93811yescharacteristic
251C22×C3#93911yescharacteristic
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—41no—
259C3×C4—82no—
260C3×C4—81no—
261C3×C4—81no—
262C3×C4—121no—
263C3×C4—121no—
264C3×C4—241no—
265C3×C4#91111yescharacteristic
266C3×C4#91111yescharacteristic
267C3×C4D3×Q1611yescharacteristic
268C3×C4#91811yescharacteristic
269C3×C4#93211yescharacteristic
270C3×C4#94211yescharacteristic
271C3×C4C2×#21611yescharacteristic
272C3×C4#94911yescharacteristic
273Dic3—41no—
274Dic3—41no—
275Dic3—81no—
276C32#169411yescharacteristic, complemented, Sylow
277Q8—41no—
278Q8—41no—
279Q8—61no—
280Q8—61no—
281Q8—121no—
282Q8—121no—
283C2×C4—41no—
284C2×C4—61no—
285C2×C4—61no—
286C2×C4—121no—
287C2×C4#380511yescharacteristic
288C2×C4D3×#6711yescharacteristic
289C2×C4D3×#6711yescharacteristic
290C8—32no—
291C8—61no—
292C8—121no—
293C8—361no—
294C8—361no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3#503911yescharacteristic
299C2×C3#509011yescharacteristic
300C2×C3#515911yescharacteristic
301C2×C3#518211yescharacteristic
302C2×C3#519211yescharacteristic
303C2×C3#520411yescharacteristic
304C22#6397011yescharacteristic
305C4—21no—
306C4—81no—
307C4—121no—
308C4—121no—
309C4—241no—
310C4#6392511yescharacteristic
311C4#6393211yescharacteristic
312C4D3×#21611yescharacteristic
313C4#6394811yescharacteristic
314C3—21no—
315C3#7105711yescharacteristic, complemented
316C3#7137911yescharacteristic, complemented
317C2#1059145111yescharacteristic
318C2#1059157411yescharacteristic
319C2#1059164111yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1694
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
109. C3×C3⋊C8Q16semidirect
227. C3⋊C8#216semidirect
276. C32#1694semidirect
315. C3#71057semidirect
316. C3#71379semidirect

Maximal subgroups

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

subgroupindex
C3×#50902
C3×#50782
#105903842
#105902582
#105894132
#105890972
#105890932
#713793
#710573