Finite Group Databasebeta

← #16857770

Subgroups — #16857770

Order 3968.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521770C211yesmaximal, characteristic, complemented
2#14521710C211yesmaximal, characteristic
3#14521410C211yesmaximal, characteristic, complemented
4#14521388C211yesmaximal, characteristic, complemented
5#14521374C211yesmaximal, characteristic, complemented
6#14521342C211yesmaximal, characteristic, complemented
7#14521297C211yesmaximal, characteristic, complemented
8#14521287C211yesmaximal, characteristic, complemented
9#14521273C211yesmaximal, characteristic, complemented
10#14521210C211yesmaximal, characteristic, complemented
11#14521156C211yesmaximal, characteristic, complemented
12#14521123C211yesmaximal, characteristic, complemented
13#14521058C211yesmaximal, characteristic, complemented
14#14521044C211yesmaximal, characteristic, complemented
15C31×#451C211yesmaximal, characteristic, complemented
16C22×Q8×C31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C2×Q16×C31C2211yescharacteristic
19C2×Q16×C31C2211yescharacteristic
20C31×C22⋊Q8C2211yescharacteristic
21#11758524—21no—
22#11758524C2211yescharacteristic
23#11758523—21no—
24#11758523C2211yescharacteristic
25#11758523C2211yescharacteristic
26Q8×Dic31C2211yescharacteristic
27Q8×Dic31C2211yescharacteristic
28C2×#92481C2211yescharacteristic
29#11758507—21no—
30#11758507C2211yescharacteristic
31C4×C22⋊D31—21no—
32C4×C22⋊D31C2211yescharacteristic
33#11758503C2211yescharacteristic
34C2×#92474C2211yescharacteristic
35C2×C8×D31C2211yescharacteristic
36#11758475—21no—
37#11758469C2211yescharacteristic
38#11758465C2211yescharacteristic
39#11758464—21no—
40#11758462—21no—
41#11758456—21no—
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758423C2211yescharacteristic
49#11758423C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52(C2×D31)⋊C8C2211yescharacteristic
53#11758406C2211yescharacteristic
54#11758405C2211yescharacteristic
55#11758403C2211yescharacteristic
56Dic31⋊C8C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758395C2211yescharacteristic
59C2×Q8×C31—21no—
60C2×Q8×C31—22no—
61C2×Q8×C31—41no—
62C2×Q8×C31C2311yescharacteristic
63C2×Q8×C31C2311yescharacteristic
64C2×Q8×C31C2311yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31D411yescharacteristic
69#92499—22no—
70#92499—41no—
71C2×D124—21no—
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31C2311yescharacteristic
75C2×Dic62—21no—
76Q16×C31—22no—
77Q16×C31—41no—
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31—21no—
81C4⋊C4×C31C2311yescharacteristic
82C22⋊C4×C31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31D411yescharacteristic
85#92481—41no—
86(C2×D31)⋊C4—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4D411yescharacteristic
93C4⋊Dic31—21no—
94C4⋊Dic31—21no—
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4D411yescharacteristic
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107#92474—41no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C8×D31—41no—
111C23×C31C2×D411yescharacteristic
112C22×D31—21no—
113C22×D31C2×D411yescharacteristic
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118Q8×C31—21no—
119Q8×C31—42no—
120Q8×C31#4112yes—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—42no—
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2411yescharacteristic
130C22⋊D31—41no—
131C22⋊D31—42no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138D124—21no—
139D124—21no—
140D124—42no—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—42no—
144Dic62—42no—
145C8×C31—21no—
146C8×C31—21no—
147C31⋊C8—21no—
148C31⋊C8—21no—
149#3313—311nomaximal, Sylow
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31C22×D411yescharacteristic
154C2×D31—21no—
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C4×C31—22no—
161C4×C31—21no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31—41no—
165C4×C31C2×#4111yescharacteristic
166C4×C31H(5,𝔽2)11yescharacteristic
167Dic31—21no—
168Dic31—21no—
169Dic31—21no—
170Dic31—41no—
171Dic31—41no—
172Dic31—41no—
173#556—311no—
174#548—311no—
175#489—311no—
176#485—311no—
177#482—311no—
178#477—311no—
179#468—311no—
180#467—311no—
181#464—311no—
182#452—311no—
183#451D3111yescharacteristic, complemented
184#441—311no—
185#435—311no—
186#419—311no—
187#416—311no—
188C2×C31—41no—
189C2×C31#54611yescharacteristic
190C2×C31#57511yescharacteristic
191C2×C31#57811yescharacteristic
192D31—41no—
193D31—81no—
194C2×#41—311no—
195C22×Q8C2×D3111yescharacteristic
196C2×Q16C2×D3111yescharacteristic
197C2×Q16C2×D3111yescharacteristic
198C2×SD16—311no—
199C2×M16—311no—
200C22×C8—311no—
201C4⋊Q8—311no—
202#126—621no—
203#126—621no—
204#124—311no—
205#124—621no—
206#124—621no—
207C22⋊Q8—311no—
208C22⋊Q8—311no—
209C22⋊Q8—621no—
210C22⋊Q8C2×D3111yescharacteristic
211#121—311no—
212#121—621no—
213C4×Q8—311no—
214C4×Q8—311no—
215C4×Q8—621no—
216C4×D4—311no—
217C4×D4—621no—
218#117—311no—
219#117—311no—
220#107—311no—
221#107—311no—
222#106—311no—
223C4⋊C8—311no—
224#103—311no—
225#103—311no—
226#103—311no—
227#103—311no—
228#103—311no—
229#103C2×D3111yescharacteristic
230#103C2×D3111yescharacteristic
231#102—311no—
232#102—311no—
233#102—311no—
234C22⋊C8—311no—
235C22⋊C8C2×D3111yescharacteristic
236#97—311no—
237C31#331311yescharacteristic, complemented, Sylow
238#41—622no—
239#41—1241no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—621no—
244C2×Q8C22×D3111yescharacteristic
245C2×Q8C22×D3111yescharacteristic
246C2×Q8C22×D3111yescharacteristic
247C2×D4—311no—
248C2×D4—311no—
249C2×D4—621no—
250C2×D4—621no—
251C22×C4—21no—
252C22×C4—311no—
253C22×C4—621no—
254C22×C4C22×D3111yescharacteristic
255Q16—22no—
256Q16—41no—
257SD16—1241no—
258M16—1241no—
259C2×C8—311no—
260C2×C8—311no—
261C2×C8—1241no—
262C2×C8C22×D3111yescharacteristic
263C2×C8C22×D3111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4C22×D3111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—311no—
277C22⋊C4—311no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C42—311no—
286C42—621no—
287C42—621no—
288C42—621no—
289C42—621no—
290C23—311no—
291C23—621no—
292C23D4×D3111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—1242no—
300Q8#9249712yes—
301D4—621no—
302D4—621no—
303D4—1242no—
304D4—1241no—
305D4—1242no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—311no—
314C2×C4—311no—
315C2×C4—311no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—1242no—
322C2×C4D4×D3111yescharacteristic
323C2×C4C23×D3111yescharacteristic
324C8—21no—
325C8—21no—
326C8—621no—
327C8—621no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—621no—
332C22—621no—
333C22—621no—
334C22—1241no—
335C22—1241no—
336C22—1241no—
337C22C2×D4×D3111yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—621no—
344C4—621no—
345C4—621no—
346C4—1241no—
347C4—1241no—
348C4—1241no—
349C4C2×#9249711yescharacteristic
350C4#1175856111yescharacteristic
351C2—41no—
352C2—1241no—
353C2—2481no—
354C2#1452168611yescharacteristic
355C2#1452184811yescharacteristic
356C2#1452186211yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#451C2
socleC22×C31C22×D4
prime radical#14521710C2
hypercenter#451D31
hypocenterC31#3313
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. #14521770C2semidirect
3. #14521410C2semidirect
4. #14521388C2semidirect
5. #14521374C2semidirect
6. #14521342C2semidirect
7. #14521297C2semidirect
8. #14521287C2semidirect
9. #14521273C2semidirect
10. #14521210C2semidirect
11. #14521156C2semidirect
12. #14521123C2semidirect
13. #14521058C2semidirect
14. #14521044C2semidirect
15. C31×#451C2semidirect
183. #451D31semidirect
237. C31#3313semidirect

Maximal subgroups

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

subgroupindex
#145217702
#145217102
#145214102
#145213882
#145213742
#145213422
#145212972
#145212872
#145212732
#145212102
#145211562
#145211232
#145210582
#145210442
C31×#4512
#331331