Finite Group Databasebeta

← #11788757

Subgroups — #11788757

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596290C211yesmaximal, characteristic, complemented
2C3×#5830C211yesmaximal, characteristic
3C3×#5240C211yesmaximal, characteristic, complemented
4#10591085C212yesmaximal, complemented
5#10589157C212yesmaximal, complemented
6#71854—31nomaximal
7#70047—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C22×C3×D12C2211yescharacteristic
10#64157—24no—
11C2×#3748—22no—
12C2×#3748C2212yes—
13C3×#947C412yescomplemented
14C3×#940C412yescomplemented
15C3×#937—22no—
16C3×#930—22no—
17C3×#926C2212yes—
18C3×#926C2211yescharacteristic
19C3×#834—22no—
20#63562—24no—
21C3×#535—31no—
22#5830D311yescharacteristic
23#5819—31no—
24#5819—31no—
25#5819—61no—
26C3×#410—31no—
27#5240D311yescharacteristic, complemented
28#5215—32no—
29#5001—32no—
30#4531—32no—
31#4531—32no—
32C23×C3×D3—21no—
33C32×#41—22no—
34C32×#41—22no—
35C2×C32×Q8C2×C411yescharacteristic
36C2×C32×D4C2×C411yescharacteristic
37C2×C32×D4D412yes—
38C22×C32×C4D412yes—
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—24no—
41C2×C3×D12—22no—
42C2×C3×D12—22no—
43C2×C3×D12—21no—
44C2×C3×D12C2×C412yes—
45#3748—24no—
46#3748—22no—
47#3748—22no—
48C2×C3⋊(C3⋊C8)—24no—
49C2×C3⋊(C3⋊C8)D414yescomplemented
50C3×#217—21no—
51C3×#217—22no—
52C3×(C2×D3)⋊C4—24no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—22no—
55C3×C4×Dic3—22no—
56C3×C4×Dic3C2×C412yes—
57#1910—91noSylow
58C2×C3×#41—21no—
59C2×C3×#41C2×D311yescharacteristic
60C2×C3×#41C2×D311yescharacteristic
61C22×C3×D4—31no—
62C22×D12C2×D311yescharacteristic
63C3×#127—32no—
64C3×#124—32no—
65C3×#121—62no—
66C3×#120—62no—
67C3×#117—31no—
68C3×#117—32no—
69#948—64no—
70#948—64no—
71#948—68no—
72#947Dic312yescomplemented
73#940Dic312yescomplemented
74#937—22no—
75#930—22no—
76#926C2×D312yes—
77#926C2×D311yescharacteristic
78C2×#208—32no—
79C2×#208—32no—
80C2×#208—62no—
81C2×#208—64no—
82C2×#208—62no—
83C2×#208—62no—
84C3×#99—62no—
85#834—22no—
86#832—64no—
87#809—64no—
88C23×C32C22⋊C412yes—
89C23×C32C2×D411yescharacteristic
90C22×C3×D3—22no—
91C22×C3×D3—42no—
92C22×C3×D3—82no—
93C32×Q8—22no—
94C32×D4—24no—
95C32×D4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4C22⋊C412yes—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D412yes—
102C2×C32×C4#4112yes—
103C3×#67—84no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—42no—
106C3×D12—24no—
107C3×D12—41no—
108C3×D12—41no—
109C3⋊(C3⋊C8)—24no—
110#568—91no—
111#535—31no—
112#418—92no—
113#410—31no—
114H(3,ℤ/4)—92no—
115C24×C3—61no—
116C23×D3—21no—
117C3×#41—24no—
118C3×#41—24no—
119C3×#41—22no—
120C3×#41—22no—
121C3×#41—22no—
122C3×#41—22no—
123C2×C3×Q8—21no—
124C2×C3×Q8C4×D311yescharacteristic
125C2×C3×Q8C2×Dic311yescharacteristic
126C2×C3×D4—21no—
127C2×C3×D4—22no—
128C2×C3×D4—32no—
129C2×C3×D4—64no—
130C2×C3×D4—61no—
131C2×C3×D4—62no—
132C2×C3×D4—62no—
133C2×C3×D4C4×D311yescharacteristic
134C2×C3×D4C2×Dic311yescharacteristic
135C2×C3×D4#6712yes—
136C2×C3×D4#6712yes—
137C22×C3×C4—22no—
138C22×C3×C4—21no—
139C22×C3×C4D1212yes—
140C22×C3×C4#6712yes—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C2×#67—24no—
144C2×D12—22no—
145C2×D12—22no—
146C2×D12—21no—
147C2×D12C2×Dic312yes—
148C3×C4⋊C4—61no—
149C3×C4⋊C4—62no—
150C3×C22⋊C4—61no—
151C3×C22⋊C4—64no—
152C3×C22⋊C4—62no—
153C3×C42—32no—
154C3×C42—62no—
155#217—21no—
156#217—22no—
157(C2×D3)⋊C4—24no—
158C4⋊Dic3—21no—
159C4⋊Dic3—22no—
160C4×Dic3—22no—
161C4×Dic3C2×Dic312yes—
162#208—64no—
163#208—68no—
164#208—64no—
165#208—64no—
166#208—64no—
167#208—62no—
168#208—62no—
169#208—62no—
170#208—62no—
171C2×C3⋊C8—34no—
172C2×C3⋊C8—34no—
173C2×C3⋊C8—64no—
174C2×C3⋊C8—68no—
175C2×C3⋊C8—64no—
176C2×C3⋊C8—64no—
177C22×C32—22no—
178C22×C32—41no—
179C22×C32—42no—
180C22×C32C2×C22⋊C411yescharacteristic
181C22×C32#12112yes—
182C2×C3×D3—44no—
183C2×C3×D3—42no—
184C2×C3×D3—84no—
185C32×C4—22no—
186C32×C4C4×D412yes—
187C32×C4#12011yescharacteristic
188C32×C4#12311yescharacteristic
189C3×Dic3—42no—
190C3×Dic3—82no—
191C2×#41D3211yescharacteristic
192C22×D4—31no—
193#131—184no—
194C2×M16—92no—
195C2×M16—182no—
196#127—32no—
197#124—32no—
198#121—62no—
199#120—62no—
200#117—31no—
201#117—32no—
202#102—184no—
203#99—62no—
204C23×C3—22no—
205C23×C3—21no—
206C23×C3—62no—
207C23×C3—122no—
208C23×C3—242no—
209C23×C3(C2×D3)⋊C412yes—
210C23×C3#21712yes—
211C23×C3C2×#6711yescharacteristic
212C23×C3C2×#6711yescharacteristic
213C22×D3—22no—
214C22×D3—42no—
215C22×D3—82no—
216C3×Q8—24no—
217C3×Q8—22no—
218C3×Q8—22no—
219C3×D4—28no—
220C3×D4—24no—
221C3×D4—24no—
222C3×D4—24no—
223C3×D4—22no—
224C3×D4—22no—
225C3×D4—64no—
226C3×D4—121no—
227C3×D4—121no—
228C3×D4—244no—
229C2×C3×C4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—22no—
238C2×C3×C4—21no—
239C2×C3×C4—22no—
240C2×C3×C4—62no—
241C2×C3×C4—122no—
242C2×C3×C4(C2×D3)⋊C412yes—
243C2×C3×C4#21712yes—
244C2×C3×C4C2×C4×D311yescharacteristic
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4D3×D412yes—
247C2×C3×C4D3×D412yes—
248C2×C3×C4#23712yes—
249C2×C3×C4#23712yes—
250C2×C3×C4C22×Dic311yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252#67—84no—
253C2×Dic3—22no—
254C2×Dic3—42no—
255D12—24no—
256D12—41no—
257D12—41no—
258C3⋊C8—68no—
259C3⋊C8—64no—
260C3⋊C8—64no—
261C2×C32—21no—
262C2×C32—22no—
263C2×C32—42no—
264C2×C32#38611yescharacteristic
265C3×D3—82no—
266C24—61no—
267#41—22no—
268#41—22no—
269C2×Q8D3×Dic311yescharacteristic
270C2×D4—32no—
271C2×D4—64no—
272C2×D4—62no—
273C2×D4—61no—
274C2×D4—62no—
275C2×D4D3×Dic311yescharacteristic
276C2×D4#62512yes—
277C22×C4#62612yes—
278C22×C4C2×D3211yescharacteristic
279M16—184no—
280M16—182no—
281M16—182no—
282C2×C8—94no—
283C2×C8—184no—
284C4⋊C4—61no—
285C4⋊C4—62no—
286C22⋊C4—61no—
287C22⋊C4—64no—
288C22⋊C4—62no—
289C42—32no—
290C42—62no—
291C22×C3—24no—
292C22×C3—22no—
293C22×C3—22no—
294C22×C3—21no—
295C22×C3—22no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3—81no—
301C22×C3—82no—
302C22×C3—124no—
303C22×C3—122no—
304C22×C3—244no—
305C22×C3C2×(C2×D3)⋊C411yescharacteristic
306C22×C3#93912yes—
307C22×C3#93912yes—
308C22×C3C2×#21711yescharacteristic
309C2×D3—44no—
310C2×D3—42no—
311C2×D3—84no—
312C3×C4—24no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—21no—
316C3×C4—22no—
317C3×C4—21no—
318C3×C4—122no—
319C3×C4—242no—
320C3×C4#67⋊C412yes—
321C3×C4#88211yescharacteristic
322C3×C4#88611yescharacteristic
323C3×C4D4×Dic312yes—
324C3×C4#93511yescharacteristic
325C3×C4#93711yescharacteristic
326Dic3—42no—
327Dic3—82no—
328C32#191011yescharacteristic, complemented, Sylow
329C23—62no—
330C23—122no—
331C23—242no—
332C23(C2×D3)⋊Dic312yes—
333C23C2×#62511yescharacteristic
334Q8—22no—
335D4—24no—
336D4—22no—
337D4—64no—
338D4—121no—
339D4—121no—
340D4—244no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—62no—
344C2×C4—122no—
345C2×C4(C2×D3)⋊Dic312yes—
346C2×C4C2×D3×Dic311yescharacteristic
347C2×C4#380512yes—
348C2×C4C2×#62611yescharacteristic
349C2×C4#381112yes—
350C8—184no—
351C2×C3—22no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—22no—
355C2×C3—21no—
356C2×C3—41no—
357C2×C3—42no—
358C2×C3—44no—
359C2×C3—42no—
360C2×C3—42no—
361C2×C3—242no—
362C2×C3#495811yescharacteristic
363C2×C3#522011yescharacteristic
364D3—82no—
365C22—22no—
366C22—41no—
367C22—42no—
368C22—124no—
369C22—122no—
370C22—244no—
371C22C2×(C2×D3)⋊Dic311yescharacteristic
372C22#6398012yes—
373C4—22no—
374C4—122no—
375C4—242no—
376C4#6396211yescharacteristic
377C4#67⋊Dic312yes—
378C4#6398111yescharacteristic
379C3—21no—
380C3#7004711yescharacteristic, complemented
381C3#7185411yescharacteristic, complemented
382C2—21no—
383C2—22no—
384C2—42no—
385C2—242no—
386C2#1059171311yescharacteristic
subgroupG/H
centerC2#10591713
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radicalC3×#5830C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1910
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596290C2semidirect
3. C3×#5240C2semidirect
4. #10591085C2semidirect
5. #10589157C2semidirect
13. C3×#947C4semidirect
14. C3×#940C4semidirect
27. #5240D3semidirect
49. C2×C3⋊(C3⋊C8)D4semidirect
72. #947Dic3semidirect
73. #940Dic3semidirect
328. C32#1910semidirect
380. C3#70047semidirect
381. C3#71854semidirect

Maximal subgroups

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

subgroupindex
#105962902
C3×#58302
C3×#52402
#105910852
#105891572
#718543
#700473