Finite Group Databasebeta

← #16857771

Subgroups — #16857771

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#14521708C211yesmaximal, characteristic
2#14521411C211yesmaximal, characteristic, complemented
3#14521390C211yesmaximal, characteristic, complemented
4#14521373C211yesmaximal, characteristic, complemented
5#14521341C211yesmaximal, characteristic, complemented
6#14521297C211yesmaximal, characteristic, complemented
7#14521288C211yesmaximal, characteristic, complemented
8#14521271C211yesmaximal, characteristic, complemented
9#14521209C211yesmaximal, characteristic, complemented
10#14521204C211yesmaximal, characteristic, complemented
11#14521154C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521057C211yesmaximal, characteristic, complemented
14#14521043C211yesmaximal, characteristic, complemented
15C31×#556C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C22×Dic62C2211yescharacteristic
18C31×C4⋊Q8C2211yescharacteristic
19C31×#126—21no—
20C31×#126—21no—
21C31×#124—21no—
22C31×C22⋊Q8C2211yescharacteristic
23C31×C22⋊Q8C2211yescharacteristic
24C4×Q8×C31—21no—
25C4×Q8×C31C2211yescharacteristic
26C4×D4×C31C2211yescharacteristic
27C31×#117C2211yescharacteristic
28C31×#117C2211yescharacteristic
29C2×#92482C2211yescharacteristic
30C2×#92482C2211yescharacteristic
31C2×#92481C2211yescharacteristic
32#11758516—21no—
33#11758507C2211yescharacteristic
34#11758501C2211yescharacteristic
35C2×#92474C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37#11758473—21no—
38#11758462—21no—
39(C22⋊D31)⋊C4—21no—
40#11758452C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42#11758423C2211yescharacteristic
43C22⋊(C31⋊C8)C2211yescharacteristic
44C22⋊(C31⋊C8)C2211yescharacteristic
45#11758398C2211yescharacteristic
46#11758398C2211yescharacteristic
47#11758398C2211yescharacteristic
48#11758398C2211yescharacteristic
49#11758398C2211yescharacteristic
50#11758398C2211yescharacteristic
51#11758397C2211yescharacteristic
52#11758397C2211yescharacteristic
53#11758397C2211yescharacteristic
54#11758396C2211yescharacteristic
55#11758395C2211yescharacteristic
56#11758395C2211yescharacteristic
57C4⋊(C31⋊C8)C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31—21no—
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31D411yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C22×Dic31—21no—
67#92495—22no—
68#92495—41no—
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×Dic62—22no—
72C2×Dic62—21no—
73C2×Dic62—41no—
74C2×Dic62C2311yescharacteristic
75C2×Dic62C2311yescharacteristic
76C4⋊C4×C31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31D411yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C22⋊C4×C31—21no—
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C22⋊C4×C31—21no—
88C22⋊C4×C31D411yescharacteristic
89C22⋊C4×C31D411yescharacteristic
90C42×C31—21no—
91C42×C31—21no—
92C42×C31—21no—
93C42×C31C2311yescharacteristic
94C22⋊Dic31—21no—
95#92482—22no—
96#92482—41no—
97#92481—41no—
98(C2×D31)⋊C4—21no—
99(C2×D31)⋊C4—21no—
100(C2×D31)⋊C4—21no—
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105#92474—41no—
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31C2×D411yescharacteristic
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—42no—
117D4×C31—41no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2411yescharacteristic
131C22⋊D31—42no—
132C22⋊D31—42no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—42no—
137D124—21no—
138D124—21no—
139C4×D31—42no—
140Dic62—21no—
141Dic62—21no—
142Dic62—21no—
143Dic62—42no—
144Dic62#4112yes—
145C31⋊C8—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148C31⋊C8—21no—
149#3313—311nomaximal, Sylow
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31C22×D411yescharacteristic
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C4×C31—21no—
161C4×C31—21no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31C2×#4111yescharacteristic
169C4×C31H(5,𝔽2)11yescharacteristic
170Dic31—22no—
171Dic31—41no—
172Dic31—41no—
173#556D3111yescharacteristic, complemented
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#451—311no—
184#441—311no—
185#435—311no—
186#419—311no—
187#416—311no—
188C2×C31—41no—
189C2×C31—41no—
190C2×C31#54611yescharacteristic
191C2×C31#57511yescharacteristic
192C2×C31#57811yescharacteristic
193D31—81no—
194C2×#41—311no—
195C22×Q8—311no—
196C2×Q16—311no—
197C2×Q16—311no—
198C2×SD16—311no—
199C2×M16—311no—
200C22×C8—311no—
201C4⋊Q8C2×D3111yescharacteristic
202#126—21no—
203#126—21no—
204#124—21no—
205#124—311no—
206#124—621no—
207C22⋊Q8—311no—
208C22⋊Q8—621no—
209C22⋊Q8C2×D3111yescharacteristic
210C22⋊Q8C2×D3111yescharacteristic
211#121—311no—
212#121—621no—
213C4×Q8—21no—
214C4×Q8—311no—
215C4×Q8C2×D3111yescharacteristic
216C4×D4—621no—
217C4×D4C2×D3111yescharacteristic
218#117C2×D3111yescharacteristic
219#117C2×D3111yescharacteristic
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#103—311no—
230#103—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234C22⋊C8—311no—
235C22⋊C8—311no—
236#97—311no—
237C31#331311yescharacteristic, complemented, Sylow
238#41—622no—
239#41—1241no—
240C2×Q8—21no—
241C2×Q8—311no—
242C2×Q8—311no—
243C2×Q8—622no—
244C2×Q8—621no—
245C2×Q8—1241no—
246C2×Q8C22×D3111yescharacteristic
247C2×D4—311no—
248C2×D4—621no—
249C2×D4—621no—
250C2×D4C22⋊D3111yescharacteristic
251C22×C4—621no—
252C22×C4—621no—
253C22×C4C22×D3111yescharacteristic
254C22×C4C22×D3111yescharacteristic
255Q16—622no—
256Q16—1241no—
257SD16—1241no—
258M16—1241no—
259C2×C8—311no—
260C2×C8—311no—
261C2×C8—311no—
262C2×C8—311no—
263C2×C8—1241no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4C22⋊D3111yescharacteristic
272C4⋊C4C22×D3111yescharacteristic
273C4⋊C4C22×D3111yescharacteristic
274C4⋊C4C22×D3111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4C22⋊D3111yescharacteristic
284C22⋊C4C22⋊D3111yescharacteristic
285C42—21no—
286C42—21no—
287C42—21no—
288C42—621no—
289C42C22×D3111yescharacteristic
290C23—621no—
291C23C2×C22⋊D3111yescharacteristic
292C23C2×C22⋊D3111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—312no—
297Q8—621no—
298Q8—621no—
299Q8—621no—
300Q8—1242no—
301D4—41no—
302D4—621no—
303D4—621no—
304D4—1242no—
305D4—1242no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—1242no—
318C2×C4—1242no—
319C2×C4C2×C22⋊D3111yescharacteristic
320C2×C4C2×C22⋊D3111yescharacteristic
321C2×C4C2×C22⋊D3111yescharacteristic
322C2×C4C2×C22⋊D3111yescharacteristic
323C2×C4C23×D3111yescharacteristic
324C8—621no—
325C8—621no—
326C8—621no—
327C8—621no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—1241no—
335C22—1241no—
336C22—1241no—
337C22C22×C22⋊D3111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—622no—
347C4—1241no—
348C4—1241no—
349C4#41×D3111yescharacteristic
350C4#1175856611yescharacteristic
351C2—41no—
352C2—41no—
353C2—2481no—
354C2#1452168711yescharacteristic
355C2#1452184711yescharacteristic
356C2#1452186411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#556C2
socleC22×C31C22×D4
prime radical#14521708C2
hypercenter#556D31
hypocenterC31#3313
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #14521411C2semidirect
3. #14521390C2semidirect
4. #14521373C2semidirect
5. #14521341C2semidirect
6. #14521297C2semidirect
7. #14521288C2semidirect
8. #14521271C2semidirect
9. #14521209C2semidirect
10. #14521204C2semidirect
11. #14521154C2semidirect
12. #14521121C2semidirect
13. #14521057C2semidirect
14. #14521043C2semidirect
15. C31×#556C2semidirect
173. #556D31semidirect
237. C31#3313semidirect

Maximal subgroups

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

subgroupindex
#145217082
#145214112
#145213902
#145213732
#145213412
#145212972
#145212882
#145212712
#145212092
#145212042
#145211542
#145211212
#145210572
#145210432
C31×#5562
#331331