Finite Group Databasebeta

← #11782030

Subgroups — #11782030

Order 1152.

328 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592790C211yesmaximal, characteristic
2C3×#5078C211yesmaximal, characteristic
3#10590296C211yesmaximal, characteristic
4#10590284C211yesmaximal, characteristic
5C3×#4546C211yesmaximal, characteristic
6#10589097C211yesmaximal, characteristic
7#10589095C211yesmaximal, characteristic
8#71380—31nomaximal
9#68513—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13#63637—21no—
14#63634—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×#807—21no—
17C3×#807—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63575—21no—
22#63572—21no—
23#63567—21no—
24#63555—21no—
25C3×#500—31no—
26#5091—31no—
27#5091—31no—
28#5091—31no—
29#5091—61no—
30#5078D311yescharacteristic
31#4850—31no—
32#4831—31no—
33#4679—31no—
34C3×#333—31no—
35#4546—31no—
36#4546D311yescharacteristic
37#4481—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8—21no—
41C2×#634D411yescharacteristic
42C2×C3×Dic6—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)D411yescharacteristic
47#3750—21no—
48C4×C3⋊Dic3—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#1696—91noSylow
57C3×C4⋊Q8—21no—
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4⋊Q8C2×D311yescharacteristic
61#869C2×D311yescharacteristic
62C4×Dic6—31no—
63C4×Dic6—31no—
64C4×Dic6—61no—
65C3×#107—61no—
66C3×#107—61no—
67C3×C4⋊C8—31no—
68C3×C4⋊C8—31no—
69C3×C4×C8—31no—
70#818—61no—
71#816—61no—
72#815—61no—
73#815—61no—
74Dic3⋊C8—61no—
75Dic3⋊C8—61no—
76#810—61no—
77#810—61no—
78#810—61no—
79#810—62no—
80#807—21no—
81#807—21no—
82#807—61no—
83#807—61no—
84#807—61no—
85#807—62no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C32×Q8—81no—
93C2×C32×C4—41no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99#634—21no—
100#634—21no—
101C2×C3×Dic3—41no—
102C3×Dic6—81no—
103C3⋊(C3⋊C8)—41no—
104C3×C3⋊C8—21no—
105C3×C3⋊C8—41no—
106C3×C3⋊C8—41no—
107C3×C3⋊C8Q1612yes—
108#500—31no—
109#477—91no—
110#477—91no—
111#446—91no—
112#334—91no—
113#333—31no—
114#333—91no—
115C2×C3×Q8—21no—
116C2×C3×Q8—21no—
117C2×C3×Q8—41no—
118C2×C3×Q8—61no—
119C2×Dic6—21no—
120C2×Dic6—31no—
121C2×Dic6—31no—
122C2×Dic6—61no—
123C2×C3×C8—31no—
124C2×C3×C8—31no—
125C2×C3×C8—61no—
126C2×C3×C8—61no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—41no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C42—21no—
136C3×C42C22×D311yescharacteristic
137C3×C42C22×D311yescharacteristic
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—31no—
141C4⋊Dic3—31no—
142C4⋊Dic3—61no—
143Dic3⋊C4—61no—
144Dic3⋊C4—61no—
145Dic3⋊C4—121no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—121no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—62no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8#6711yescharacteristic
155C2×C3⋊C8#6711yescharacteristic
156C22×C32#12111yescharacteristic
157C32×C4—21no—
158C32×C4—81no—
159C32×C4C2×Q1611yescharacteristic
160C32×C4#13711yescharacteristic
161C32×C4#13711yescharacteristic
162C32×C4#13711yescharacteristic
163C3⋊Dic3—41no—
164C3⋊Dic3—41no—
165C3×Dic3—81no—
166C4⋊Q8—31no—
167C4⋊Q8D3211yescharacteristic
168C4×Q8—91no—
169#107—61no—
170#107—61no—
171#107—181no—
172#107—181no—
173C4⋊C8—31no—
174C4⋊C8—31no—
175C4⋊C8—91no—
176C4⋊C8—181no—
177#103—181no—
178#103—181no—
179#97—181no—
180C4×C8—31no—
181C3×Q8—81no—
182C3×Q8—81no—
183C3×Q8—82no—
184C3×Q8—241no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—42no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—121no—
192C2×C3×C4#23511yescharacteristic
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4#23711yescharacteristic
197C2×C3×C4C2×#6711yescharacteristic
198C2×Dic3—41no—
199C2×Dic3—61no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—61no—
203C2×Dic3—121no—
204C2×Dic3—121no—
205Dic6—62no—
206Dic6—61no—
207Dic6—61no—
208Dic6—61no—
209Dic6—61no—
210Dic6—81no—
211Dic6—121no—
212C3×C8—32no—
213C3×C8—61no—
214C3×C8—121no—
215C3×C8—121no—
216C3⋊C8—21no—
217C3⋊C8—41no—
218C3⋊C8—41no—
219C3⋊C8—122no—
220C3⋊C8—121no—
221C3⋊C8—121no—
222C3⋊C8#21612yes—
223C2×C32#46211yescharacteristic
224C2×C32#47011yescharacteristic
225C2×C32#47211yescharacteristic
226C2×Q8—21no—
227C2×Q8—61no—
228C2×Q8—91no—
229C2×C8—31no—
230C2×C8—31no—
231C2×C8—61no—
232C2×C8—61no—
233C2×C8—181no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—91no—
239C4⋊C4—181no—
240C42—181no—
241C42C2×D3211yescharacteristic
242C22×C3—21no—
243C22×C3#88411yescharacteristic
244C22×C3#93811yescharacteristic
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—41no—
252C3×C4—82no—
253C3×C4—81no—
254C3×C4—81no—
255C3×C4—241no—
256C3×C4#91511yescharacteristic
257C3×C4#91511yescharacteristic
258C3×C4D3×Q1611yescharacteristic
259C3×C4#91811yescharacteristic
260C3×C4#91811yescharacteristic
261C3×C4#91811yescharacteristic
262C3×C4#94211yescharacteristic
263C3×C4C2×#21611yescharacteristic
264Dic3—81no—
265Dic3—122no—
266Dic3—121no—
267Dic3—121no—
268Dic3—121no—
269Dic3—121no—
270Dic3—241no—
271C32#169611yescharacteristic, complemented, Sylow
272Q8—81no—
273Q8—181no—
274Q8—181no—
275Q8—241no—
276C2×C4—41no—
277C2×C4—121no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4#380411yescharacteristic
281C2×C4D3×#6711yescharacteristic
282C2×C4#381111yescharacteristic
283C8—32no—
284C8—61no—
285C8—121no—
286C8—121no—
287C8—361no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3#474911yescharacteristic
292C2×C3#479511yescharacteristic
293C2×C3#481611yescharacteristic
294C2×C3#509011yescharacteristic
295C2×C3#516011yescharacteristic
296C2×C3#518911yescharacteristic
297C22#6395811yescharacteristic
298C4—21no—
299C4—81no—
300C4—241no—
301C4—361no—
302C4—361no—
303C4D3×#21611yescharacteristic
304C4#6394511yescharacteristic
305C4#6394611yescharacteristic
306C4#6395111yescharacteristic
307C3—21no—
308C3#6851311yescharacteristic, complemented
309C3#7138011yescharacteristic, complemented
310C2#1059140611yescharacteristic
311C2#1059157511yescharacteristic
312C2#1059160011yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊Q8D32
hypocenterC32#1696
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
271. C32#1696semidirect
308. C3#68513semidirect
309. C3#71380semidirect

Maximal subgroups

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

subgroupindex
#105927902
C3×#50782
#105902962
#105902842
C3×#45462
#105890972
#105890952
#713803
#685133