Finite Group Databasebeta

← #16858772

Subgroups — #16858772

Order 3968.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521785C211yesmaximal, characteristic, complemented
2#14521768C211yesmaximal, characteristic, complemented
3#14521440C211yesmaximal, characteristic, complemented
4#14521432C211yesmaximal, characteristic, complemented
5#14521269C211yesmaximal, characteristic, complemented
6#14521268C211yesmaximal, characteristic, complemented
7#14521262C211yesmaximal, characteristic, complemented
8#14521262C211yesmaximal, characteristic, complemented
9#14521252C211yesmaximal, characteristic, complemented
10#14521246C211yesmaximal, characteristic, complemented
11#14521177C211yesmaximal, characteristic, complemented
12#14521161C211yesmaximal, characteristic, complemented
13#14521157C211yesmaximal, characteristic, complemented
14SD16×Dic31C211yesmaximal, characteristic, complemented
15C31×#496C211yesmaximal, characteristic
16C2×SD16×C31C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C2×D8×C31C2211yescharacteristic
19C2×D8×C31C2211yescharacteristic
20C31×#127C2211yescharacteristic
21C31×#124C2211yescharacteristic
22Q8×Dic31C2211yescharacteristic
23#11758521C2211yescharacteristic
24C2×#92482C2211yescharacteristic
25#11758513—21no—
26#11758513C2211yescharacteristic
27#11758513C2211yescharacteristic
28#11758513C2211yescharacteristic
29#11758512—21no—
30#11758512—21no—
31D4×Dic31—21no—
32D4×Dic31C2211yescharacteristic
33D4×Dic31C2211yescharacteristic
34D4×Dic31C2211yescharacteristic
35C2×#92480C2211yescharacteristic
36C2×#92480C2211yescharacteristic
37C2×#92480C2211yescharacteristic
38C2×Dic124C2211yescharacteristic
39#11758456—21no—
40#11758456—21no—
41#11758455—21no—
42#11758454—21no—
43C4×Dic62C2211yescharacteristic
44C4×Dic62C2211yescharacteristic
45C4×Dic62C2211yescharacteristic
46C31×#97C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758420C2211yescharacteristic
51#11758405C2211yescharacteristic
52#11758404C2211yescharacteristic
53#11758404C2211yescharacteristic
54#11758403C2211yescharacteristic
55Dic31⋊C8C2211yescharacteristic
56Dic31⋊C8C2211yescharacteristic
57C8×Dic31C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31—21no—
61C2×D4×C31—21no—
62C2×D4×C31C2311yescharacteristic
63C2×D4×C31C2311yescharacteristic
64C2×D4×C31C2311yescharacteristic
65C22×Dic31—21no—
66C22×Dic31—21no—
67C22×Dic31—21no—
68C2×Dic62D411yescharacteristic
69C2×Dic62C2311yescharacteristic
70C2×Dic62C2311yescharacteristic
71SD16×C31—22no—
72SD16×C31—41no—
73D8×C31—22no—
74D8×C31—41no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C22⋊C4×C31—21no—
78C22⋊C4×C31—21no—
79C42×C31C2311yescharacteristic
80C22⋊Dic31—21no—
81C22⋊Dic31—21no—
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89#92482—41no—
90#92480—41no—
91#92480—41no—
92#92480—41no—
93C4⋊Dic31—21no—
94C4⋊Dic31D411yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4D411yescharacteristic
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C4×Dic31C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110Dic124—22no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—21no—
114Q8×C31—21no—
115Q8×C31—21no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—21no—
121D4×C31—21no—
122D4×C31—42no—
123D4×C31—81no—
124C2×C4×C31—21no—
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—42no—
133C2×Dic31—81no—
134C2×Dic31—81no—
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138C2×Dic31C2×D411yescharacteristic
139Dic62—21no—
140Dic62—21no—
141Dic62—21no—
142Dic62—21no—
143Dic62—41no—
144C8×C31—21no—
145C8×C31#4112yes—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3401—311nomaximal, Sylow
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31C22×D411yescharacteristic
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—41no—
162C4×C31C2×#4111yescharacteristic
163C4×C31H(5,𝔽2)11yescharacteristic
164Dic31—21no—
165Dic31—21no—
166Dic31—21no—
167Dic31—21no—
168Dic31—41no—
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172#559—311no—
173#556—311no—
174#497—311no—
175#496D3111yescharacteristic
176#495—311no—
177#464—311no—
178#464—311no—
179#463—311no—
180#463—311no—
181#461—311no—
182#460—311no—
183#446—311no—
184#442—311no—
185#441—311no—
186C4×SD16—311no—
187C2×C31—81no—
188C2×C31—81no—
189C2×C31—81no—
190C2×C31#55011yescharacteristic
191C2×C31#57511yescharacteristic
192C2×C31#57711yescharacteristic
193C2×Q16—311no—
194C2×Q16—311no—
195C2×SD16—311no—
196C2×SD16—311no—
197C2×SD16—311no—
198C2×SD16C2×D3111yescharacteristic
199C2×SD16C2×D3111yescharacteristic
200C2×D8C2×D3111yescharacteristic
201C2×D8C2×D3111yescharacteristic
202C4⋊Q8—311no—
203#127C2×D3111yescharacteristic
204#126—621no—
205#126—621no—
206#124—311no—
207#124—311no—
208#124—311no—
209#124—621no—
210#124C2×D3111yescharacteristic
211#123—621no—
212#123—621no—
213C22⋊Q8—621no—
214C4×Q8—311no—
215C4×Q8—311no—
216C4×Q8—311no—
217C4×Q8—311no—
218C4×D4—311no—
219C4×D4—311no—
220C4×D4—311no—
221C4×D4—621no—
222#117—621no—
223#106—311no—
224C4⋊C8—311no—
225C4⋊C8—311no—
226C4⋊C8—311no—
227#103—311no—
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#97—311no—
234#97C2×D3111yescharacteristic
235C4×C8—311no—
236C31#340111yescharacteristic, complemented, Sylow
237C2×Q8—311no—
238C2×Q8—311no—
239C2×Q8—311no—
240C2×Q8C22×D3111yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4C22×D3111yescharacteristic
244C2×D4C22×D3111yescharacteristic
245C2×D4C22×D3111yescharacteristic
246C22×C4—621no—
247C22×C4—621no—
248C22×C4—621no—
249Q16—622no—
250Q16—1241no—
251SD16—22no—
252SD16—41no—
253SD16—1241no—
254SD16—1241no—
255SD16—1241no—
256D8—22no—
257D8—41no—
258C2×C8—311no—
259C2×C8—311no—
260C2×C8C22×D3111yescharacteristic
261C2×C8C22×D3111yescharacteristic
262C4⋊C4—311no—
263C4⋊C4—311no—
264C4⋊C4—311no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C22⋊C4—621no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C42—311no—
284C42—311no—
285C42—621no—
286C42—621no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292Q8—21no—
293Q8—21no—
294Q8—621no—
295Q8—621no—
296Q8—621no—
297Q8—621no—
298Q8—1241no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—311no—
309C2×C4—311no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—1242no—
317C2×C4—2481no—
318C2×C4—2481no—
319C2×C4D4×D3111yescharacteristic
320C2×C4D4×D3111yescharacteristic
321C2×C4C23×D3111yescharacteristic
322C8—21no—
323C8—621no—
324C8—621no—
325C8#9249712yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D3111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—621no—
340C4—621no—
341C4—621no—
342C4—621no—
343C4—1241no—
344C4—1241no—
345C4—1241no—
346C4—1241no—
347C4C2×#9249711yescharacteristic
348C4#1175856111yescharacteristic
349C2—81no—
350C2—81no—
351C2—81no—
352C2#1452171911yescharacteristic
353C2#1452184511yescharacteristic
354C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#496C2
socleC22×C31C22×D4
hypercenter#496D31
hypocenterC31#3401
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14521785C2semidirect
2. #14521768C2semidirect
3. #14521440C2semidirect
4. #14521432C2semidirect
5. #14521269C2semidirect
6. #14521268C2semidirect
7. #14521262C2semidirect
8. #14521262C2semidirect
9. #14521252C2semidirect
10. #14521246C2semidirect
11. #14521177C2semidirect
12. #14521161C2semidirect
13. #14521157C2semidirect
14. SD16×Dic31C2semidirect
236. C31#3401semidirect

Maximal subgroups

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

subgroupindex
#145217852
#145217682
#145214402
#145214322
#145212692
#145212682
#145212622
#145212522
#145212462
#145211772
#145211612
#145211572
SD16×Dic312
C31×#4962
#340131