Finite Group Databasebeta

← #11791418

Subgroups — #11791418

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic
5C2×#63641C211yesmaximal, characteristic
6C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
7C2×#63637C211yesmaximal, characteristic
8#70229—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13#64153—22no—
14#64153C414yescomplemented
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×#3750—21no—
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#103—22no—
22#63662—22no—
23#63658—21no—
24#63643—22no—
25#63641—22no—
26#63637—22no—
27C2×#944—34no—
28C2×C3×#103D314yes—
29C2×#835—34no—
30C2×#816—34no—
31C2×Dic3⋊C8—34no—
32Dic3×C4⋊C4—34no—
33C2×#810—34no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8C2×C412yes—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634C2×C412yes—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D412yes—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)D412yes—
60#3750—24no—
61#3750—24no—
62C4×C3⋊Dic3—42no—
63C4×C3⋊Dic3C2×C412yes—
64C4×C3⋊Dic3D412yes—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68#1981—91noSylow
69C22×C3×Q8C2×D314yes—
70C22×Dic6—34no—
71C22×C3×C8C2×D314yes—
72C2×C3×C4⋊C4C2×D314yes—
73#944—316no—
74#944—68no—
75C2×C4⋊Dic3—34no—
76C2×Dic3⋊C4—64no—
77C2×Dic3⋊C4—64no—
78C2×C4×Dic3—34no—
79C2×C4×Dic3—64no—
80C22×C3⋊C8—34no—
81C3×#103—28no—
82#835—68no—
83C3⋊#95—64no—
84#816—68no—
85Dic3⋊C8—68no—
86#810—68no—
87C23×C32C2×D411yescharacteristic
88C32×Q8—22no—
89C32×Q8—22no—
90C32×Q8—41no—
91C32×Q8—41no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3C22⋊C412yes—
113C2×C3⋊Dic3C22⋊C412yes—
114C2×C3⋊Dic3SD1612yes—
115C2×C3⋊Dic3Q1612yes—
116#634—22no—
117#634—22no—
118#634—41no—
119#634—41no—
120C32×C8—41no—
121C3⋊(C3⋊C8)—41no—
122C2×C4⋊Q8—91no—
123C2×C4⋊C8—91no—
124C2×#103—91no—
125C2×#103—91no—
126C2×#103—91no—
127C2×#103C3⋊D311yescharacteristic
128C4×C4⋊C4—91no—
129C2×C3×Q8—24no—
130C2×C3×Q8—24no—
131C2×C3×Q8—24no—
132C2×C3×Q8—24no—
133C2×C3×Q8—24no—
134C2×C3×Q8C4×D318yes—
135C22×C3×C4—24no—
136C22×C3×C4—24no—
137C22×C3×C4C22×D314yes—
138C22×Dic3—34no—
139C22×Dic3—34no—
140C22×Dic3—64no—
141C22×Dic3—64no—
142C2×Dic6—38no—
143C2×Dic6—64no—
144C2×Dic6—64no—
145C2×Dic6—64no—
146C2×Dic6—64no—
147C2×Dic6—64no—
148C2×C3×C8—24no—
149C2×C3×C8—24no—
150C2×C3×C8—24no—
151C3×C4⋊C4—24no—
152C3×C4⋊C4#6718yes—
153C4⋊Dic3—38no—
154C4⋊Dic3—64no—
155Dic3⋊C4—616no—
156Dic3⋊C4—616no—
157C4×Dic3—38no—
158C4×Dic3—38no—
159C4×Dic3—128no—
160C2×C3⋊C8—64no—
161C2×C3⋊C8—64no—
162C2×C3⋊C8—64no—
163C22×C32C2×C22⋊C411yescharacteristic
164C22×C32#12111yescharacteristic
165C22×C32#12111yescharacteristic
166C22×C32C2×SD1611yescharacteristic
167C22×C32C2×Q1611yescharacteristic
168C22×C32#13711yescharacteristic
169C22×C32#13711yescharacteristic
170C32×C4—42no—
171C32×C4—42no—
172C32×C4C4×D411yescharacteristic
173C32×C4C4×D411yescharacteristic
174C32×C4#12411yescharacteristic
175C32×C4#12711yescharacteristic
176C3⋊Dic3—22no—
177C3⋊Dic3—42no—
178C3⋊Dic3—42no—
179C3⋊Dic3#10314yescomplemented
180C22×Q8—91no—
181C22×Q8C2×C3⋊D311yescharacteristic
182C22×C8—91no—
183C22×C8C2×C3⋊D311yescharacteristic
184C4⋊Q8—94no—
185C4⋊Q8—182no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—181no—
188C2×C4⋊C4—181no—
189C2×C4⋊C4C2×C3⋊D311yescharacteristic
190C2×C42—91no—
191C2×C42—181no—
192C4⋊C8—182no—
193#103—22no—
194#103—182no—
195#103—182no—
196#103—182no—
197#95—181no—
198C23×C3D3×D414yes—
199C3×Q8—28no—
200C3×Q8—28no—
201C3×Q8—44no—
202C3×Q8—44no—
203C2×C3×C4—28no—
204C2×C3×C4—28no—
205C2×C3×C4—44no—
206C2×C3×C4—44no—
207C2×C3×C4—44no—
208C2×C3×C4—44no—
209C2×C3×C4C2×C4×D314yes—
210C2×C3×C4#23514yes—
211C2×C3×C4D3×D414yes—
212C2×C3×C4D3×D414yes—
213C2×C3×C4#23714yes—
214C2×C3×C4C2×#6714yes—
215C2×Dic3—38no—
216C2×Dic3—38no—
217C2×Dic3—38no—
218C2×Dic3—38no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—68no—
222C2×Dic3—68no—
223C2×Dic3—124no—
224C2×Dic3—124no—
225C2×Dic3—124no—
226C2×Dic3—124no—
227Dic6—68no—
228Dic6—68no—
229Dic6—124no—
230Dic6—124no—
231C3×C8—44no—
232C3⋊C8—124no—
233C2×C32#39011yescharacteristic
234C2×C32C2×#10311yescharacteristic
235C2×C32#41911yescharacteristic
236C2×C32#46111yescharacteristic
237C2×C32#46111yescharacteristic
238C2×C32#46211yescharacteristic
239C2×C32#46211yescharacteristic
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—92no—
246C2×Q8—181no—
247C2×Q8—181no—
248C2×Q8—181no—
249C2×Q8—181no—
250C2×Q8—181no—
251C2×Q8C4×C3⋊D312yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—181no—
257C22×C4—181no—
258C22×C4C22×C3⋊D311yescharacteristic
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—181no—
263C2×C8—181no—
264C2×C8—181no—
265C4⋊C4—21no—
266C4⋊C4—92no—
267C4⋊C4—184no—
268C4⋊C4—184no—
269C4⋊C4—181no—
270C4⋊C4#63812yes—
271C42—92no—
272C42—92no—
273C42—362no—
274C22×C3D3×C22⋊C414yes—
275C22×C3#88414yes—
276C22×C3D3×SD1614yes—
277C22×C3#91514yes—
278C22×C3D3×Q1614yes—
279C22×C3#91814yes—
280C22×C3#93914yes—
281C3×C4—48no—
282C3×C4—48no—
283C3×C4#67⋊C414yes—
284C3×C4#88514yes—
285C3×C4C4×#6714yes—
286C3×C4#94014yes—
287Dic3—316no—
288Dic3—68no—
289Dic3—128no—
290Dic3—128no—
291C32#198111yescharacteristic, complemented, Sylow
292C23D4×C3⋊D311yescharacteristic
293Q8—22no—
294Q8—22no—
295Q8—41no—
296Q8—41no—
297Q8—182no—
298Q8—182no—
299Q8—361no—
300Q8—361no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—92no—
308C2×C4—92no—
309C2×C4—92no—
310C2×C4—92no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—182no—
314C2×C4—182no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4C2×C4×C3⋊D311yescharacteristic
320C2×C4#382811yescharacteristic
321C2×C4D4×C3⋊D311yescharacteristic
322C2×C4D4×C3⋊D311yescharacteristic
323C2×C4#383011yescharacteristic
324C2×C4C2×#63811yescharacteristic
325C8—41no—
326C8—361no—
327C2×C3#479514yes—
328C2×C3D3×#10314yes—
329C2×C3#480214yes—
330C2×C3#481814yes—
331C2×C3#495714yes—
332C2×C3#516214yes—
333C2×C3#518214yes—
334C22C22⋊C4×C3⋊D311yescharacteristic
335C22#6409311yescharacteristic
336C22SD16×C3⋊D311yescharacteristic
337C22#6412411yescharacteristic
338C22Q16×C3⋊D311yescharacteristic
339C22#6412711yescharacteristic
340C22#6414811yescharacteristic
341C4—42no—
342C4—42no—
343C4—94no—
344C4—182no—
345C4—362no—
346C4—362no—
347C4#6409011yescharacteristic
348C4#6409411yescharacteristic
349C4C4×#63811yescharacteristic
350C4#6414911yescharacteristic
351C3#7022914yescomplemented
352C2#1059249411yescharacteristic
353C2C3⋊D3×#10311yescharacteristic
354C2#1059250111yescharacteristic
355C2#1059251711yescharacteristic
356C2#1059265611yescharacteristic
357C2#1059286111yescharacteristic
358C2#1059288111yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×#103C3⋊D3
hypocenterC32#1981
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
14. #64153C4semidirect
179. C3⋊Dic3#103semidirect
291. C32#1981semidirect
351. C3#70229semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C32×#1032
C2×#636622
C2×#636432
C2×#636412
C4⋊C4×C3⋊Dic32
C2×#636372
#702293