Finite Group Databasebeta

← #11791122

Subgroups — #11791122

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×C32×#107C211yesmaximal, characteristic, complemented
3C2×#63642C211yesmaximal, characteristic, complemented
4#10592687C211yesmaximal, characteristic
5#10592672C211yesmaximal, characteristic, complemented
6C2×#63637C211yesmaximal, characteristic, complemented
7C2×#63636C211yesmaximal, characteristic
8#70629—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—22no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×#3744—22no—
18C2×#3744—22no—
19C2×#3744C414yescomplemented
20C32×#107—22no—
21#63658—22no—
22#63642—22no—
23#63637—22no—
24#63636—22no—
25C22×#204—34no—
26C2×C3×#107D314yescomplemented
27C2×#815—34no—
28#4988—34no—
29#4973—34no—
30C2×#810—34no—
31C2×#809—34no—
32C23×C3⋊D3—21no—
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D412yes—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)C2×C412yes—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634C2×C412yes—
50C2×C32×C8C2×C412yes—
51C2×C32×C8D412yes—
52C2×C32×C8D412yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57#3752—44no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)D412yes—
63#3744—28no—
64#1973—91noSylow
65C22×D12—34no—
66C22×Dic6—34no—
67C22×C3×C8C2×D314yes—
68C2×C3×C4⋊C4C2×D314yes—
69C2×C3×C4⋊C4C2×D314yes—
70C2×(C2×D3)⋊C4—68no—
71C2×C4×Dic3—34no—
72C22×C3⋊C8—34no—
73C2×#204—316no—
74C2×#204—68no—
75C2×#204—68no—
76C3×#107—28no—
77C3⋊#95—68no—
78#815—68no—
79#810—68no—
80#809—68no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—22no—
83C22×C3⋊D3—41no—
84C22×C3⋊D3—41no—
85C22×C3⋊D3—42no—
86C22×C3⋊D3—42no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—42no—
90C2×C32×C4—42no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C4⋊(C3⋊D3)—22no—
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107#634—22no—
108#634—22no—
109#634—41no—
110#634—41no—
111C32×C8C22⋊C414yescomplemented
112C3⋊(C3⋊C8)—22no—
113C22×SD16—91no—
114C2×#107C3⋊D311yescharacteristic, complemented
115C2×#103—91no—
116C2×#102—91no—
117C2×#97—91no—
118#391—91no—
119#390—91no—
120C23×D3—64no—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4C22×D314yes—
124C22×Dic3—38no—
125C22×Dic3—64no—
126C2×D12—38no—
127C2×D12—64no—
128C2×D12—64no—
129C2×D12—64no—
130C2×D12—64no—
131C2×D12—64no—
132C2×Dic6—38no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×Dic6—64no—
136C2×Dic6—64no—
137C2×Dic6—64no—
138C2×C3×C8C4×D318yes—
139C2×C3×C8D1218yes—
140C2×C3×C8#6718yes—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—24no—
143C3×C4⋊C4—24no—
144C3×C4⋊C4—24no—
145(C2×D3)⋊C4—1216no—
146C4×Dic3—64no—
147C4×Dic3—64no—
148C2×C3⋊C8—38no—
149C2×C3⋊C8—64no—
150C2×C3⋊C8—64no—
151#204—632no—
152C22×C32C4×D411yescharacteristic
153C22×C32#12111yescharacteristic
154C22×C32#12711yescharacteristic
155C22×C32AGL(1,ℤ/8)12yes—
156C22×C32#13712yes—
157C2×C3⋊D3—42no—
158C2×C3⋊D3—44no—
159C2×C3⋊D3—82no—
160C2×C3⋊D3—81no—
161C2×C3⋊D3—81no—
162C32×C4—81no—
163C32×C4—81no—
164C32×C4C2×C22⋊C411yescharacteristic
165C32×C4C4×D411yescharacteristic
166C32×C4#12111yescharacteristic
167C32×C4#12411yescharacteristic
168C3⋊Dic3—42no—
169C3⋊Dic3—42no—
170C22×Q8—91no—
171C22×D4—91no—
172C2×SD16—94no—
173C2×SD16—182no—
174C2×SD16—182no—
175C22×C8—91no—
176C22×C8C2×C3⋊D311yescharacteristic
177C2×C4⋊C4C2×C3⋊D311yescharacteristic
178C2×C4⋊C4C2×C3⋊D311yescharacteristic
179C2×C22⋊C4—182no—
180C2×C42—91no—
181#107—22no—
182#103—182no—
183#102—182no—
184#97—182no—
185#95—182no—
186C23×C3D3×D414yes—
187C22×D3—68no—
188C22×D3—124no—
189C22×D3—128no—
190C22×D3—128no—
191C22×D3—124no—
192C2×C3×C4—48no—
193C2×C3×C4—48no—
194C2×C3×C4—44no—
195C2×C3×C4—44no—
196C2×C3×C4C2×C4×D314yes—
197C2×C3×C4C2×D1214yes—
198C2×C3×C4D3×D414yes—
199C2×C3×C4#23914yes—
200C2×C3×C4#23914yes—
201C2×C3×C4C2×#6714yes—
202C2×Dic3—68no—
203C2×Dic3—68no—
204C2×Dic3—68no—
205C2×Dic3—68no—
206C2×Dic3—124no—
207C2×Dic3—124no—
208D12—68no—
209D12—68no—
210D12—124no—
211D12—124no—
212Dic6—68no—
213Dic6—68no—
214Dic6—124no—
215Dic6—124no—
216C3×C8(C2×D3)⋊C4116yescomplemented
217C3⋊C8—68no—
218C2×C32#39011yescharacteristic
219C2×C32#44012yes—
220C2×C32#46812yes—
221C2×C32#49611yescharacteristic
222C2×C32#49711yescharacteristic
223C3⋊D3—82no—
224C24—181no—
225C2×Q8—92no—
226C2×Q8—181no—
227C2×Q8—181no—
228C2×Q8—181no—
229C2×Q8—181no—
230C2×Q8—181no—
231C2×D4—92no—
232C2×D4—181no—
233C2×D4—181no—
234C2×D4—181no—
235C2×D4—181no—
236C2×D4—181no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—92no—
240C22×C4—181no—
241C22×C4C22×C3⋊D311yescharacteristic
242SD16—188no—
243C2×C8—92no—
244C2×C8—181no—
245C2×C8—181no—
246C2×C8C4×C3⋊D312yes—
247C2×C8C4⋊(C3⋊D3)12yes—
248C2×C8#63812yes—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C22⋊C4—364no—
254C42—181no—
255C42—181no—
256C22×C3#89314yes—
257C22×C3#89514yes—
258C22×C3#91118yes—
259C22×C3#91818yes—
260C22×C3#94014yes—
261C2×D3—1216no—
262C2×D3—128no—
263C2×D3—248no—
264C2×D3—244no—
265C2×D3—244no—
266C3×C4—84no—
267C3×C4—84no—
268C3×C4#89314yes—
269C3×C4#89514yes—
270C3×C4C2×(C2×D3)⋊C414yes—
271C3×C4#94714yes—
272Dic3—128no—
273Dic3—128no—
274C32#197311yescharacteristic, complemented, Sylow
275C23—182no—
276C23—361no—
277C23—362no—
278C23—362no—
279C23—361no—
280C23D4×C3⋊D311yescharacteristic
281Q8—182no—
282Q8—182no—
283Q8—361no—
284Q8—361no—
285D4—182no—
286D4—182no—
287D4—361no—
288D4—361no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—361no—
298C2×C4—361no—
299C2×C4C2×C4×C3⋊D311yescharacteristic
300C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
301C2×C4D4×C3⋊D311yescharacteristic
302C2×C4#383211yescharacteristic
303C2×C4#383211yescharacteristic
304C2×C4C2×#63811yescharacteristic
305C8—182no—
306C8#375214yescomplemented
307C2×C3#488618yes—
308C2×C3#488918yes—
309C2×C3#498814yes—
310C2×C3#515414yes—
311C2×C3#519014yes—
312D3—248no—
313C22—364no—
314C22—362no—
315C22—722no—
316C22—721no—
317C22—721no—
318C22#6410211yescharacteristic
319C22#6410411yescharacteristic
320C22#6412012yes—
321C22#6412712yes—
322C22#6414911yescharacteristic
323C4—81no—
324C4—81no—
325C4—362no—
326C4—362no—
327C4#6410211yescharacteristic
328C4#6410411yescharacteristic
329C4C2×#375211yescharacteristic
330C4#6415611yescharacteristic
331C3#7062914yescomplemented
332C2—722no—
333C2#1059258512yes—
334C2#1059258812yes—
335C2#1059268711yescharacteristic
336C2#1059285311yescharacteristic
337C2#1059288911yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#107C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×#107C3⋊D3
hypocenterC32#1973
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C32×#107C2semidirect
3. C2×#63642C2semidirect
5. #10592672C2semidirect
6. C2×#63637C2semidirect
19. C2×#3744C4semidirect
26. C2×C3×#107D3semidirect
111. C32×C8C22⋊C4semidirect
114. C2×#107C3⋊D3semidirect
216. C3×C8(C2×D3)⋊C4semidirect
274. C32#1973semidirect
306. C8#3752semidirect
331. C3#70629semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×C32×#1072
C2×#636422
#105926872
#105926722
C2×#636372
C2×#636362
#706293