Finite Group Databasebeta

← #16855814

Subgroups — #16855814

Order 3968.

392 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
1C4×#92495C211yesmaximal, characteristic, complemented
2#14521387C211yesmaximal, characteristic, complemented
3#14521370C211yesmaximal, characteristic, complemented
4#14521353C211yesmaximal, characteristic, complemented
5#14521346C211yesmaximal, characteristic, complemented
6#14521268C211yesmaximal, characteristic, complemented
7#14521261C211yesmaximal, characteristic, complemented
8#14521209C211yesmaximal, characteristic, complemented
9#14521192C211yesmaximal, characteristic
10#14521159C211yesmaximal, characteristic, complemented
11#14521154C211yesmaximal, characteristic, complemented
12#14521149C211yesmaximal, characteristic, complemented
13#14521147C211yesmaximal, characteristic, complemented
14#14521106C211yesmaximal, characteristic, complemented
15C31×#529C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C31×#126—21no—
18C31×#125C2211yescharacteristic
19C31×#124C2211yescharacteristic
20C31×#123—21no—
21C31×C22⋊Q8C2211yescharacteristic
22C31×#121C2211yescharacteristic
23C4×Q8×C31C2211yescharacteristic
24C4×D4×C31—21no—
25C4×D4×C31C2211yescharacteristic
26C31×#117—21no—
27C2×C42×C31C2211yescharacteristic
28C2×#92482C2211yescharacteristic
29C2×#92481C2211yescharacteristic
30C2×#92480C2211yescharacteristic
31C2×#92479C2211yescharacteristic
32C4×C22⋊D31—21no—
33C4×C22⋊D31—21no—
34#11758503C2211yescharacteristic
35C4×D124C2211yescharacteristic
36C4×D124C2211yescharacteristic
37#11758449—21no—
38C42×D31—21no—
39C4×Dic62C2211yescharacteristic
40C4×Dic62C2211yescharacteristic
41#11758423C2211yescharacteristic
42#11758423C2211yescharacteristic
43#11758420C2211yescharacteristic
44#11758420C2211yescharacteristic
45C22⋊(C31⋊C8)C2211yescharacteristic
46C22⋊(C31⋊C8)C2211yescharacteristic
47#11758398C2211yescharacteristic
48#11758398C2211yescharacteristic
49#11758397C2211yescharacteristic
50#11758397C2211yescharacteristic
51#11758396C2211yescharacteristic
52#11758396C2211yescharacteristic
53#11758395C2211yescharacteristic
54#11758395C2211yescharacteristic
55C4⋊(C31⋊C8)C2211yescharacteristic
56C4⋊(C31⋊C8)C2211yescharacteristic
57#11758391C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31—21no—
63C22×C4×C31D411yescharacteristic
64C22×C4×C31D411yescharacteristic
65C22×C4×C31C2311yescharacteristic
66C2×C22⋊D31—21no—
67#92495—22no—
68#92495—22no—
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×Dic62C2311yescharacteristic
74C4⋊C4×C31—21no—
75C4⋊C4×C31—21no—
76C4⋊C4×C31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C22⋊C4×C31—21no—
82C22⋊C4×C31—21no—
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
85C42×C31—21no—
86C42×C31D411yescharacteristic
87C42×C31D411yescharacteristic
88C42×C31C2311yescharacteristic
89C42×C31C2311yescharacteristic
90C22⋊Dic31—21no—
91#92482—22no—
92#92481—22no—
93#92480—22no—
94#92479—22no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31C2×D411yescharacteristic
110C22×D31—21no—
111Q8×C31—21no—
112Q8×C31—21no—
113D4×C31—21no—
114D4×C31—21no—
115D4×C31—42no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—41no—
122C2×C4×C31—41no—
123C2×C4×C31—42no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2411yescharacteristic
130C22⋊D31—24no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134D124—21no—
135D124#4112yes—
136C4×D31—24no—
137C4×D31—42no—
138C4×D31—42no—
139Dic62—21no—
140Dic62#4112yes—
141C31⋊C8—21no—
142C31⋊C8—21no—
143C31⋊C8—21no—
144C31⋊C8—21no—
145#3111—311nomaximal, Sylow
146C22×C31—21no—
147C22×C31—21no—
148C22×C31—21no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31C22×D411yescharacteristic
153C2×D31—22no—
154C2×D31—41no—
155C2×D31—41no—
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31C2×#4111yescharacteristic
165C4×C31C2×#4111yescharacteristic
166Dic31—22no—
167Dic31—41no—
168Dic31—41no—
169#529D3111yescharacteristic, complemented
170C4×#41—311no—
171#485—311no—
172#482—311no—
173#479—311no—
174#478—311no—
175#464—311no—
176#463—311no—
177#452—311no—
178#449—311no—
179#442—311no—
180#441—311no—
181#440—311no—
182#440—311no—
183#432—311no—
184C2×C31—41no—
185C2×C31—81no—
186C2×C31#52511yescharacteristic
187C2×C31#57511yescharacteristic
188C2×C31#57511yescharacteristic
189D31—42no—
190C2×#41—311no—
191C2×Q16—311no—
192C2×SD16—311no—
193C2×SD16—311no—
194C2×D8—311no—
195#126—21no—
196#125C2×D3111yescharacteristic
197#124C2×D3111yescharacteristic
198#123—21no—
199C22⋊Q8C2×D3111yescharacteristic
200#121C2×D3111yescharacteristic
201C4×Q8—311no—
202C4×Q8—311no—
203C4×Q8C2×D3111yescharacteristic
204C4×D4—21no—
205C4×D4—311no—
206C4×D4—311no—
207C4×D4—621no—
208C4×D4—621no—
209C4×D4C2×D3111yescharacteristic
210#117—21no—
211#117—311no—
212#117—621no—
213C2×C42—621no—
214C2×C42C2×D3111yescharacteristic
215#107—311no—
216#107—311no—
217#106—311no—
218#106—311no—
219C4⋊C8—311no—
220C4⋊C8—311no—
221#103—311no—
222#103—311no—
223#103—311no—
224#103—311no—
225#102—311no—
226#102—311no—
227#102—311no—
228#102—311no—
229C22⋊C8—311no—
230C22⋊C8—311no—
231#97—311no—
232#97—311no—
233C31#311111yescharacteristic, complemented, Sylow
234#41—622no—
235#41—622no—
236C2×Q8—311no—
237C2×Q8C22×D3111yescharacteristic
238C2×D4—21no—
239C2×D4—311no—
240C2×D4—621no—
241C2×D4C22×D3111yescharacteristic
242C22×C4—21no—
243C22×C4—621no—
244C22×C4—621no—
245C22×C4—621no—
246C22×C4C22⋊D3111yescharacteristic
247C22×C4C22⋊D3111yescharacteristic
248C22×C4C22×D3111yescharacteristic
249Q16—622no—
250SD16—622no—
251SD16—622no—
252D8—622no—
253C2×C8—311no—
254C2×C8—311no—
255C2×C8—311no—
256C2×C8—311no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—311no—
262C4⋊C4—311no—
263C4⋊C4—621no—
264C4⋊C4—621no—
265C4⋊C4C22×D3111yescharacteristic
266C4⋊C4C22×D3111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C42—21no—
276C42—621no—
277C42—621no—
278C42—621no—
279C42C22⋊D3111yescharacteristic
280C42C22⋊D3111yescharacteristic
281C42C22×D3111yescharacteristic
282C42C22×D3111yescharacteristic
283C23—21no—
284C23—621no—
285C23C2×C22⋊D3111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—312no—
289Q8—621no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—312no—
294D4—624no—
295D4—621no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—624no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—1242no—
309C2×C4—1242no—
310C2×C4C2×C22⋊D3111yescharacteristic
311C2×C4C2×C22⋊D3111yescharacteristic
312C2×C4C2×C22⋊D3111yescharacteristic
313C2×C4C2×C22⋊D3111yescharacteristic
314C2×C4C2×C22⋊D3111yescharacteristic
315C2×C4C23×D3111yescharacteristic
316C8—621no—
317C8—621no—
318C8—621no—
319C8—621no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—622no—
327C22—1241no—
328C22—1241no—
329C22C22×C22⋊D3111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—622no—
339C4—1241no—
340C4—1241no—
341C4#41×D3111yescharacteristic
342C4#41×D3111yescharacteristic
343C2—41no—
344C2—81no—
345C2—1242no—
346C2#1452155611yescharacteristic
347C2#1452184711yescharacteristic
348C2#1452184711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#529C2
socleC22×C31C22×D4
prime radical#14521192C2
hypercenter#529D31
hypocenterC31#3111
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#92495C2semidirect
2. #14521387C2semidirect
3. #14521370C2semidirect
4. #14521353C2semidirect
5. #14521346C2semidirect
6. #14521268C2semidirect
7. #14521261C2semidirect
8. #14521209C2semidirect
10. #14521159C2semidirect
11. #14521154C2semidirect
12. #14521149C2semidirect
13. #14521147C2semidirect
14. #14521106C2semidirect
15. C31×#529C2semidirect
169. #529D31semidirect
233. C31#3111semidirect

Maximal subgroups

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

subgroupindex
C4×#924952
#145213872
#145213702
#145213532
#145213462
#145212682
#145212612
#145212092
#145211922
#145211592
#145211542
#145211492
#145211472
#145211062
C31×#5292
#311131