Finite Group Databasebeta

← #11790771

Subgroups — #11790771

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596303C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic, complemented
3C2×#63664C211yesmaximal, characteristic, complemented
4C2×#63652C211yesmaximal, characteristic, complemented
5#10592817C211yesmaximal, characteristic, complemented
6C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63632C211yesmaximal, characteristic, complemented
8#70356—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64156C411yescharacteristic, complemented
14#64153C411yescharacteristic, complemented
15#64149C411yescharacteristic, complemented
16#64148—22no—
17#64145C411yescharacteristic, complemented
18C4×#638—22no—
19C2×C4×C3⋊Dic3—22no—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×#3748C2211yescharacteristic
23C32×#104—22no—
24#63664—22no—
25#63652—22no—
26#63641—22no—
27#63632—22no—
28#5832—34no—
29C2×C3×#104D314yescomplemented
30C2×#837—34no—
31C2×#825—34no—
32#5118—34no—
33C42×Dic3—34no—
34C2×#805—34no—
35C32×#41—21no—
36C32×#41—21no—
37C32×#41—21no—
38C32×#41—21no—
39C2×C32×Q8C2×C411yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4C2×C411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C2×#638—22no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D412yes—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52#3828—21no—
53C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634C2×C411yescharacteristic
56C32×M16—21no—
57C32×M16—21no—
58C2×C32×C8—21no—
59C32×C42—21no—
60C32×C42D412yescomplemented
61#3757—22no—
62#3752—22no—
63#3750—22no—
64C4×C3⋊Dic3—28no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3C2×C411yescharacteristic
67C4×C3⋊Dic3C2×C411yescharacteristic
68C4×C3⋊Dic3D412yes—
69C4×C3⋊Dic3D412yescomplemented
70#3748—21no—
71#3748—21no—
72C2×C3⋊(C3⋊C8)—21no—
73#1962—91noSylow
74C2×C3×#41C2×D314yes—
75C2×#235—34no—
76C2×C3×M16C2×D314yes—
77C2×C3×C42C2×D314yes—
78#947—34no—
79#944—34no—
80#940—34no—
81#939—68no—
82#936—34no—
83C4×#67—68no—
84C2×C4×Dic3—34no—
85C2×C4×Dic3—34no—
86C2×C4×Dic3—68no—
87C2×#208—34no—
88C3×#104—28no—
89#837—68no—
90#825—68no—
91Dic3⋊C8—68no—
92#805—68no—
93C23×C32—21no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—21no—
96C32×Q8—21no—
97C32×Q8—21no—
98C32×D4—21no—
99C32×D4—21no—
100C32×D4—41no—
101C32×D4—41no—
102C2×C32×C4—24no—
103C2×C32×C4—22no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113#638—41no—
114#638—41no—
115#638—44no—
116C2×C3⋊Dic3—24no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—24no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3C22⋊C412yes—
121C2×C3⋊Dic3C22⋊C412yes—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)—21no—
124C4×C3⋊D3—41no—
125C4×C3⋊D3—41no—
126#634—21no—
127#634—21no—
128C32×C8—41no—
129C3⋊(C3⋊C8)—41no—
130#532—91no—
131#423—91no—
132C2×#104—91no—
133C2×#104—91no—
134C2×#104—91no—
135C2×#104C3⋊D311yescharacteristic, complemented
136C43—91no—
137C3×#41—24no—
138C3×#41—24no—
139C3×#41—24no—
140C3×#41—24no—
141C2×C3×Q8C4×D314yes—
142C2×C3×D4—24no—
143C2×C3×D4C4×D314yes—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4C22×D314yes—
147C2×#67—68no—
148C2×#67—64no—
149C22×Dic3—38no—
150C22×Dic3—64no—
151#235—64no—
152#235—64no—
153#235—64no—
154#235—64no—
155C2×D12—34no—
156C2×C4×D3—64no—
157C2×Dic6—34no—
158C3×M16—24no—
159C3×M16—24no—
160C2×C3×C8—24no—
161C3×C42—24no—
162C3×C42#6718yescomplemented
163#217—68no—
164(C2×D3)⋊C4—68no—
165Dic3⋊C4—68no—
166C4×Dic3—34no—
167C4×Dic3—34no—
168C4×Dic3—38no—
169C4×Dic3—38no—
170C4×Dic3—632no—
171C4×Dic3—64no—
172#208—64no—
173#208—64no—
174C2×C3⋊C8—64no—
175C22×C32—22no—
176C22×C32—41no—
177C22×C32—42no—
178C22×C32C2×C22⋊C411yescharacteristic
179C22×C32#12111yescharacteristic
180C22×C32#12111yescharacteristic
181C2×C3⋊D3—41no—
182C2×C3⋊D3—42no—
183C32×C4—24no—
184C32×C4—41no—
185C32×C4C4×D411yescharacteristic
186C32×C4C4×D411yescharacteristic
187C32×C4#12411yescharacteristic
188C32×C4#12711yescharacteristic
189C3⋊Dic3—24no—
190C3⋊Dic3—22no—
191C3⋊Dic3—41no—
192C3⋊Dic3#10414yescomplemented
193C2×#41—91no—
194C2×#41C2×C3⋊D311yescharacteristic
195C2×M16—91no—
196C2×M16C2×C3⋊D311yescharacteristic
197C4⋊Q8—91no—
198#127—91no—
199#124—91no—
200#124—91no—
201#121—182no—
202C4×D4—182no—
203C2×C42—91no—
204C2×C42—91no—
205C2×C42—182no—
206C2×C42C2×C3⋊D311yescharacteristic
207C4⋊C8—182no—
208#104—22no—
209#104—182no—
210#104—182no—
211#104—182no—
212C23×C3—24no—
213C23×C3D3×D414yes—
214C22×D3—64no—
215C3×Q8—24no—
216C3×Q8—24no—
217C3×D4—24no—
218C3×D4—24no—
219C3×D4—44no—
220C3×D4—44no—
221C2×C3×C4—216no—
222C2×C3×C4—28no—
223C2×C3×C4—24no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4C2×C4×D314yes—
227C2×C3×C4#23514yes—
228C2×C3×C4D3×D414yes—
229C2×C3×C4D3×D414yes—
230C2×C3×C4#23714yes—
231C2×C3×C4C2×#6714yes—
232#67—1216no—
233#67—124no—
234#67—124no—
235C2×Dic3—38no—
236C2×Dic3—38no—
237C2×Dic3—616no—
238C2×Dic3—616no—
239C2×Dic3—68no—
240C2×Dic3—64no—
241D12—64no—
242D12—64no—
243C4×D3—124no—
244C4×D3—124no—
245Dic6—64no—
246Dic6—64no—
247C3×C8—44no—
248C3⋊C8—124no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—81no—
252C2×C32#39011yescharacteristic
253C2×C32C2×#10412yes—
254C3⋊D3—81no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41—181no—
260#41—181no—
261#41—181no—
262#41—181no—
263C2×Q8—91no—
264C2×Q8C4×C3⋊D311yescharacteristic
265C2×D4—21no—
266C2×D4—91no—
267C2×D4—182no—
268C2×D4—181no—
269C2×D4C4×C3⋊D311yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—92no—
273C22×C4—181no—
274C22×C4—181no—
275C22×C4C22×C3⋊D311yescharacteristic
276M16—21no—
277M16—21no—
278M16—181no—
279M16—181no—
280C2×C8—21no—
281C2×C8—181no—
282C4⋊C4—182no—
283C22⋊C4—182no—
284C22⋊C4—182no—
285C42—21no—
286C42—91no—
287C42—91no—
288C42—92no—
289C42—92no—
290C42—188no—
291C42—181no—
292C42#63812yescomplemented
293C22×C3—28no—
294C22×C3—44no—
295C22×C3—48no—
296C22×C3D3×C22⋊C414yes—
297C22×C3#88414yes—
298C22×C3#93914yes—
299C2×D3—124no—
300C2×D3—128no—
301C3×C4—216no—
302C3×C4—44no—
303C3×C4#67⋊C414yes—
304C3×C4#88514yes—
305C3×C4C4×#6714yes—
306C3×C4#94014yes—
307Dic3—316no—
308Dic3—616no—
309Dic3—68no—
310Dic3—124no—
311C32#196211yescharacteristic, complemented, Sylow
312C23—21no—
313C23—181no—
314C23D4×C3⋊D311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—181no—
318Q8—181no—
319D4—21no—
320D4—21no—
321D4—41no—
322D4—41no—
323D4—181no—
324D4—181no—
325D4—364no—
326D4—361no—
327D4—361no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—92no—
334C2×C4—92no—
335C2×C4—184no—
336C2×C4—184no—
337C2×C4—182no—
338C2×C4—181no—
339C2×C4—361no—
340C2×C4—361no—
341C2×C4C2×C4×C3⋊D311yescharacteristic
342C2×C4#382811yescharacteristic
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4#383011yescharacteristic
346C2×C4C2×#63811yescharacteristic
347C8—41no—
348C8—361no—
349C2×C3—24no—
350C2×C3—24no—
351C2×C3—84no—
352C2×C3D3×#10418yes—
353C2×C3#495714yes—
354D3—244no—
355C22—22no—
356C22—42no—
357C22—41no—
358C22—362no—
359C22—361no—
360C22C22⋊C4×C3⋊D311yescharacteristic
361C22#6409311yescharacteristic
362C22#6414811yescharacteristic
363C4—24no—
364C4—41no—
365C4—94no—
366C4—184no—
367C4—182no—
368C4—361no—
369C4#6409011yescharacteristic
370C4#6409411yescharacteristic
371C4C4×#63811yescharacteristic
372C4#6414911yescharacteristic
373C3#7035614yescomplemented
374C2—21no—
375C2—21no—
376C2—81no—
377C2—721no—
378C2C3⋊D3×#10412yes—
379C2#1059265611yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenterC2×#104C3⋊D3
hypocenterC32#1962
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C32×#104C2semidirect
3. C2×#63664C2semidirect
4. C2×#63652C2semidirect
5. #10592817C2semidirect
6. C42×C3⋊Dic3C2semidirect
7. C2×#63632C2semidirect
13. #64156C4semidirect
14. #64153C4semidirect
15. #64149C4semidirect
17. #64145C4semidirect
29. C2×C3×#104D3semidirect
60. C32×C42D4semidirect
69. C4×C3⋊Dic3D4semidirect
135. C2×#104C3⋊D3semidirect
162. C3×C42#67semidirect
192. C3⋊Dic3#104semidirect
292. C42#638semidirect
311. C32#1962semidirect
373. C3#70356semidirect

Maximal subgroups

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

subgroupindex
#105963032
C2×C32×#1042
C2×#636642
C2×#636522
#105928172
C42×C3⋊Dic32
C2×#636322
#703563