Finite Group Databasebeta

← #16856000

Subgroups — #16856000

Order 3968.

382 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#14521653C211yesmaximal, characteristic
2#14521525C211yesmaximal, characteristic, complemented
3#14521372C211yesmaximal, characteristic, complemented
4#14521371C211yesmaximal, characteristic, complemented
5#14521357C211yesmaximal, characteristic, complemented
6#14521356C211yesmaximal, characteristic, complemented
7#14521246C211yesmaximal, characteristic, complemented
8#14521186C211yesmaximal, characteristic, complemented
9#14521186C211yesmaximal, characteristic, complemented
10#14521150C211yesmaximal, characteristic, complemented
11#14521146C211yesmaximal, characteristic, complemented
12#14521140C211yesmaximal, characteristic, complemented
13SD16×Dic31C211yesmaximal, characteristic, complemented
14#14521109C211yesmaximal, characteristic, complemented
15C31×#460C211yesmaximal, characteristic, complemented
16C2×Q8×D31C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C31×#127C2211yescharacteristic
20C4×Q8×C31C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22#11758516—21no—
23#11758516—21no—
24#11758515C2211yescharacteristic
25#11758515C2211yescharacteristic
26#11758512—21no—
27#11758512—21no—
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic
30C2×#92480C2211yescharacteristic
31C2×#92480C2211yescharacteristic
32#11758469—21no—
33#11758469C2211yescharacteristic
34#11758464—21no—
35#11758464C2211yescharacteristic
36#11758449—21no—
37#11758449C2211yescharacteristic
38#11758447C2211yescharacteristic
39C4×Dic62—21no—
40C4×Dic62C2211yescharacteristic
41C31×C4⋊C8C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic
44#11758423C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758406C2211yescharacteristic
51#11758405C2211yescharacteristic
52#11758404C2211yescharacteristic
53#11758404C2211yescharacteristic
54#11758403C2211yescharacteristic
55C8×Dic31C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31—21no—
61C2×D4×C31—21no—
62C2×D4×C31C2311yescharacteristic
63C2×D4×C31C2311yescharacteristic
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C22×Dic31—21no—
67C22×Dic31—21no—
68Q8×D31—22no—
69Q8×D31—22no—
70C2×C4×D31—21no—
71C2×C4×D31C2311yescharacteristic
72C2×Dic62—21no—
73C2×Dic62C2311yescharacteristic
74SD16×C31—22no—
75SD16×C31—22no—
76C2×C8×C31C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C4⋊C4×C31—21no—
79C4⋊C4×C31C2311yescharacteristic
80C42×C31—21no—
81C42×C31C2311yescharacteristic
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86#92480—22no—
87#92480—22no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4D411yescharacteristic
90(C2×D31)⋊C4D411yescharacteristic
91C4⋊Dic31—21no—
92C4⋊Dic31C2311yescharacteristic
93C4⋊Dic31C2311yescharacteristic
94C4⋊Dic31C2311yescharacteristic
95Dic31⋊C4—21no—
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4D411yescharacteristic
100Dic31⋊C4D411yescharacteristic
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31—21no—
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31—21no—
110C22×D31C2×D411yescharacteristic
111Q8×C31—21no—
112Q8×C31#4112yes—
113D4×C31—21no—
114D4×C31—21no—
115D4×C31—21no—
116D4×C31—21no—
117D4×C31—81no—
118D4×C31—81no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2411yescharacteristic
124C22⋊D31—81no—
125C22⋊D31—81no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—81no—
131C2×Dic31—81no—
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135C4×D31—24no—
136C4×D31—21no—
137C4×D31—21no—
138Dic62—24no—
139Dic62—21no—
140Dic62#4112yes—
141C8×C31—21no—
142C8×C31—21no—
143C31⋊C8—21no—
144C31⋊C8—21no—
145#3126—311nomaximal, Sylow
146C22×C31—41no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31C22×D411yescharacteristic
153C2×D31—21no—
154C2×D31—21no—
155C2×D31—21no—
156C4×C31—22no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—41no—
160C4×C31C2×#4111yescharacteristic
161C4×C31C2×#4111yescharacteristic
162Dic31—21no—
163Dic31—22no—
164Dic31—21no—
165Dic31—21no—
166Dic31—41no—
167Dic31—41no—
168Dic31—41no—
169#540—311no—
170#519—311no—
171#482—311no—
172#482—311no—
173#479—311no—
174#479—311no—
175#460—311no—
176#460D3111yescharacteristic, complemented
177#448—311no—
178#448—311no—
179#440—311no—
180#440—311no—
181C4×SD16—311no—
182C4×SD16—311no—
183#433—311no—
184C2×C31—81no—
185C2×C31—81no—
186C2×C31#52511yescharacteristic
187C2×C31#57711yescharacteristic
188C2×C31#57711yescharacteristic
189D31—41no—
190C22×Q8—311no—
191C2×SD16—311no—
192C2×SD16—311no—
193C2×SD16C2×D3111yescharacteristic
194C2×SD16C2×D3111yescharacteristic
195#127C2×D3111yescharacteristic
196#125—311no—
197#123—621no—
198#123—621no—
199#121—311no—
200#121—311no—
201#121—621no—
202#121—621no—
203C4×Q8—311no—
204C4×Q8—311no—
205C4×Q8—311no—
206C4×Q8—621no—
207C4×Q8—621no—
208C4×Q8C2×D3111yescharacteristic
209C4×D4—311no—
210C4×D4—311no—
211#117—311no—
212#117—311no—
213#117—621no—
214#117—621no—
215#107—311no—
216#107—311no—
217#106—311no—
218#106—311no—
219C4⋊C8—311no—
220C4⋊C8C2×D3111yescharacteristic
221#103—311no—
222#103—311no—
223#103—311no—
224#103—311no—
225#102—311no—
226#102—311no—
227#102C2×D3111yescharacteristic
228#102C2×D3111yescharacteristic
229C22⋊C8—311no—
230C22⋊C8—311no—
231#97—311no—
232C4×C8—311no—
233C31#312611yescharacteristic, complemented, Sylow
234C2×Q8—311no—
235C2×Q8—621no—
236C2×Q8—622no—
237C2×Q8—622no—
238C2×Q8C22×D3111yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—621no—
242C2×D4—621no—
243C2×D4C22×D3111yescharacteristic
244C2×D4C22×D3111yescharacteristic
245C22×C4—311no—
246C22×C4—621no—
247C22×C4—621no—
248C22×C4—621no—
249SD16—22no—
250SD16—22no—
251SD16—622no—
252SD16—622no—
253C2×C8—311no—
254C2×C8—311no—
255C2×C8C22×D3111yescharacteristic
256C2×C8C22×D3111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—311no—
259C4⋊C4—311no—
260C4⋊C4—311no—
261C4⋊C4—311no—
262C4⋊C4—311no—
263C4⋊C4—621no—
264C4⋊C4—621no—
265C4⋊C4—621no—
266C4⋊C4—621no—
267C4⋊C4—621no—
268C4⋊C4C22×D3111yescharacteristic
269C22⋊C4—311no—
270C22⋊C4—311no—
271C22⋊C4—621no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C42—21no—
277C42—311no—
278C42—621no—
279C42—621no—
280C42—621no—
281C42—621no—
282C42C22×D3111yescharacteristic
283C23—21no—
284C23—21no—
285C23—311no—
286Q8—21no—
287Q8—312no—
288Q8—624no—
289Q8—621no—
290Q8#9249712yes—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4—81no—
297D4—2481no—
298D4—2481no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—311no—
302C2×C4—311no—
303C2×C4—311no—
304C2×C4—624no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—2481no—
312C2×C4—2481no—
313C2×C4D4×D3111yescharacteristic
314C2×C4D4×D3111yescharacteristic
315C2×C4C23×D3111yescharacteristic
316C8—21no—
317C8—21no—
318C8—621no—
319C8—621no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—621no—
327C22—621no—
328C22—621no—
329C22C2×D4×D3111yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—41no—
334C4—621no—
335C4—621no—
336C4—622no—
337C4—621no—
338C4—1241no—
339C4—1241no—
340C4—1241no—
341C4C2×#9249711yescharacteristic
342C4#41×D3111yescharacteristic
343C2—81no—
344C2—81no—
345C2—1241no—
346C2#1452155911yescharacteristic
347C2#1452185511yescharacteristic
348C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#460C2
socleC22×C31C22×D4
prime radical#14521653C2
hypercenter#460D31
hypocenterC31#3126
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #14521525C2semidirect
3. #14521372C2semidirect
4. #14521371C2semidirect
5. #14521357C2semidirect
6. #14521356C2semidirect
7. #14521246C2semidirect
8. #14521186C2semidirect
9. #14521186C2semidirect
10. #14521150C2semidirect
11. #14521146C2semidirect
12. #14521140C2semidirect
13. SD16×Dic31C2semidirect
14. #14521109C2semidirect
15. C31×#460C2semidirect
176. #460D31semidirect
233. C31#3126semidirect

Maximal subgroups

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

subgroupindex
#145216532
#145215252
#145213722
#145213712
#145213572
#145213562
#145212462
#145211862
#145211502
#145211462
#145211402
SD16×Dic312
#145211092
C31×#4602
#312631