Finite Group Databasebeta

← #16857759

Subgroups — #16857759

Order 3968.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521737C211yesmaximal, characteristic
2Q8×D124C211yesmaximal, characteristic
3#14521419C211yesmaximal, characteristic, complemented
4#14521392C211yesmaximal, characteristic, complemented
5#14521381C211yesmaximal, characteristic, complemented
6#14521308C211yesmaximal, characteristic, complemented
7#14521291C211yesmaximal, characteristic, complemented
8#14521260C211yesmaximal, characteristic, complemented
9#14521206C211yesmaximal, characteristic, complemented
10#14521206C211yesmaximal, characteristic, complemented
11#14521154C211yesmaximal, characteristic, complemented
12#14521119C211yesmaximal, characteristic
13#14521056C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#479C211yesmaximal, characteristic, complemented
16C2×Q8×D31C2211yescharacteristic
17C2×Q8×D31C2211yescharacteristic
18C31×#125C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic
20C2×#92482C2211yescharacteristic
21C2×Dic124C2211yescharacteristic
22C2×Dic124C2211yescharacteristic
23C2×#92469C2211yescharacteristic
24C2×C8×D31C2211yescharacteristic
25#11758475—21no—
26#11758474—21no—
27#11758474—21no—
28#11758474C2211yescharacteristic
29#11758474C2211yescharacteristic
30#11758474C2211yescharacteristic
31#11758474C2211yescharacteristic
32#11758471—21no—
33#11758469—21no—
34#11758469C2211yescharacteristic
35C4⋊C4×D31C2211yescharacteristic
36#11758467—21no—
37C4×D124—21no—
38C4×D124C2211yescharacteristic
39#11758446—21no—
40#11758446C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42C31×#107C2211yescharacteristic
43C31×#106C2211yescharacteristic
44C31×C4⋊C8C2211yescharacteristic
45C31×#103C2211yescharacteristic
46C31×#103C2211yescharacteristic
47#11758423C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758404C2211yescharacteristic
51#11758404C2211yescharacteristic
52#11758398C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758398C2211yescharacteristic
56#11758398C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60Q8×D31—22no—
61Q8×D31—22no—
62Q8×D31—41no—
63Q8×D31—41no—
64C2×D124D411yescharacteristic
65C2×C4×D31—21no—
66C2×C4×D31—21no—
67C2×C4×D31—21no—
68C2×C4×D31C2311yescharacteristic
69C2×C4×D31C2311yescharacteristic
70C2×Dic62—21no—
71C2×Dic62—21no—
72C2×Dic62C2311yescharacteristic
73C2×Dic62C2311yescharacteristic
74C2×Dic62C2311yescharacteristic
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C42×C31—21no—
84C42×C31C2311yescharacteristic
85#92482—22no—
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)⋊C4D411yescharacteristic
92(C2×D31)⋊C4D411yescharacteristic
93C4⋊Dic31—21no—
94C4⋊Dic31—21no—
95C4⋊Dic31—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31D411yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103C4×Dic31—21no—
104C4×Dic31—21no—
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107Dic124—41no—
108Dic124—41no—
109#92469—41no—
110C8×D31—41no—
111C22×D31C2×D411yescharacteristic
112C22×D31C2×D411yescharacteristic
113Q8×C31—21no—
114Q8×C31#4112yes—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2411yescharacteristic
122C2×Dic31—21no—
123C2×Dic31—21no—
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31C2×D411yescharacteristic
127C2×Dic31C2×D411yescharacteristic
128D124—22no—
129C4×D31—21no—
130C4×D31—21no—
131C4×D31—21no—
132C4×D31—21no—
133C4×D31—42no—
134C4×D31—42no—
135C4×D31—42no—
136Dic62—21no—
137Dic62—21no—
138Dic62—21no—
139Dic62—21no—
140Dic62—21no—
141Dic62—21no—
142Dic62—42no—
143Dic62—42no—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3312—311nomaximal, Sylow
149C22×C31C22×D411yescharacteristic
150C2×D31—21no—
151C2×D31—21no—
152C2×D31—21no—
153C2×D31—21no—
154C2×D31—21no—
155C2×D31#13712yes—
156C4×C31—22no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31C2×#4111yescharacteristic
163C4×C31H(5,𝔽2)11yescharacteristic
164Dic31—21no—
165Dic31—21no—
166Dic31—41no—
167Dic31—41no—
168Dic31—41no—
169Dic31—41no—
170#552—311no—
171D4×Q8—311no—
172#491—311no—
173#485—311no—
174#483—311no—
175#479D3111yescharacteristic, complemented
176#470—311no—
177#467—311no—
178#462—311no—
179#451—311no—
180#451—311no—
181#441—311no—
182#435—311no—
183#419—311no—
184C2×#103—311no—
185C2×C31#54611yescharacteristic
186C2×C31C2×#13711yescharacteristic
187C2×C31#57811yescharacteristic
188D31—22no—
189D31—41no—
190C22×Q8—311no—
191C22×Q8—311no—
192C2×Q16—311no—
193C2×Q16—311no—
194C2×Q16—311no—
195C2×M16—311no—
196C22×C8—311no—
197C4⋊Q8—311no—
198C4⋊Q8—621no—
199#126—621no—
200#125—621no—
201#125C2×D3111yescharacteristic
202#123—621no—
203C22⋊Q8—311no—
204C22⋊Q8—311no—
205C22⋊Q8—311no—
206C22⋊Q8—311no—
207C22⋊Q8—621no—
208C22⋊Q8—621no—
209C4×Q8—311no—
210C4×Q8C2×D3111yescharacteristic
211C4×D4—311no—
212C4×D4—621no—
213#117—311no—
214#117—621no—
215C2×C4⋊C4—311no—
216#107C2×D3111yescharacteristic
217#106—311no—
218#106C2×D3111yescharacteristic
219C4⋊C8C2×D3111yescharacteristic
220#103—311no—
221#103—311no—
222#103—311no—
223#103—311no—
224#103—311no—
225#103—311no—
226#103—311no—
227#103—311no—
228#103C2×D3111yescharacteristic
229#103C2×D3111yescharacteristic
230C22⋊C8—311no—
231C22⋊C8—311no—
232#97—311no—
233C31#331211yescharacteristic, complemented, Sylow
234C2×Q8—311no—
235C2×Q8—311no—
236C2×Q8—311no—
237C2×Q8—621no—
238C2×Q8—621no—
239C2×Q8—622no—
240C2×Q8—622no—
241C2×Q8—1241no—
242C2×Q8—1241no—
243C2×Q8C22×D3111yescharacteristic
244C2×D4—311no—
245C22×C4—311no—
246C22×C4—311no—
247C22×C4—621no—
248C22×C4—621no—
249C22×C4—621no—
250Q16—622no—
251Q16—1241no—
252Q16—1241no—
253M16—1241no—
254C2×C8—311no—
255C2×C8—311no—
256C2×C8—1241no—
257C2×C8C22×D3111yescharacteristic
258C2×C8C22×D3111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—311no—
263C4⋊C4—311no—
264C4⋊C4—621no—
265C4⋊C4—621no—
266C4⋊C4—621no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4C22×D3111yescharacteristic
273C4⋊C4C22×D3111yescharacteristic
274C4⋊C4C22×D3111yescharacteristic
275C22⋊C4—311no—
276C22⋊C4—311no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C42—21no—
283C42—621no—
284C42—621no—
285C42C22×D3111yescharacteristic
286C23—311no—
287C23—311no—
288Q8—21no—
289Q8—621no—
290Q8—621no—
291Q8—621no—
292Q8—621no—
293Q8—621no—
294Q8—621no—
295Q8—1242no—
296Q8—1242no—
297Q8#9249912yes—
298D4—622no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—311no—
304C2×C4—311no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—621no—
313C2×C4—1242no—
314C2×C4—1242no—
315C2×C4—1242no—
316C2×C4D4×D3111yescharacteristic
317C2×C4D4×D3111yescharacteristic
318C2×C4C23×D3111yescharacteristic
319C8—21no—
320C8—21no—
321C8—621no—
322C8—621no—
323C22—312no—
324C22—621no—
325C22—621no—
326C22—621no—
327C22—621no—
328C22—621no—
329C22C2×D4×D3111yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—621no—
337C4—621no—
338C4—1241no—
339C4—1241no—
340C4—1241no—
341C4—1241no—
342C4C2×#9249911yescharacteristic
343C4#1175856611yescharacteristic
344C2—622no—
345C2—1241no—
346C2#1452169011yescharacteristic
347C2#137×D3111yescharacteristic
348C2#1452186311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#479C2
socleC22×C31C22×D4
prime radicalC2×D124D4
hypercenter#479D31
hypocenterC31#3312
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
3. #14521419C2semidirect
4. #14521392C2semidirect
5. #14521381C2semidirect
6. #14521308C2semidirect
7. #14521291C2semidirect
8. #14521260C2semidirect
9. #14521206C2semidirect
10. #14521206C2semidirect
11. #14521154C2semidirect
13. #14521056C2semidirect
14. #103×D31C2semidirect
15. C31×#479C2semidirect
175. #479D31semidirect
233. C31#3312semidirect

Maximal subgroups

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

subgroupindex
#145217372
Q8×D1242
#145214192
#145213922
#145213812
#145213082
#145212912
#145212602
#145212062
#145211542
#145211192
#145210562
#103×D312
C31×#4792
#331231