Finite Group Databasebeta

← #16855966

Subgroups — #16855966

Order 3968.

384 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#14521666C211yesmaximal, characteristic, complemented
2#14521532C211yesmaximal, characteristic, complemented
3#14521385C211yesmaximal, characteristic, complemented
4#14521360C211yesmaximal, characteristic, complemented
5#14521342C211yesmaximal, characteristic, complemented
6#14521327C211yesmaximal, characteristic, complemented
7#14521269C211yesmaximal, characteristic, complemented
8#14521262C211yesmaximal, characteristic, complemented
9#14521211C211yesmaximal, characteristic, complemented
10#14521150C211yesmaximal, characteristic, complemented
11#14521146C211yesmaximal, characteristic, complemented
12#14521141C211yesmaximal, characteristic, complemented
13D8×Dic31C211yesmaximal, characteristic, complemented
14#14521107C211yesmaximal, characteristic, complemented
15C31×#449C211yesmaximal, characteristic
16C2×#41×C31C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C2×D8×C31C2211yescharacteristic
19C31×#121C2211yescharacteristic
20Q8×Dic31C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22C2×#92482C2211yescharacteristic
23#11758513—21no—
24#11758513C2211yescharacteristic
25#11758512—21no—
26D4×Dic31—21no—
27D4×Dic31—21no—
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic
30D4×Dic31C2211yescharacteristic
31C2×#92480C2211yescharacteristic
32#11758503—21no—
33#11758503C2211yescharacteristic
34C2×C4⋊Dic31—21no—
35C2×C4⋊Dic31C2211yescharacteristic
36#11758501C2211yescharacteristic
37#11758465C2211yescharacteristic
38#11758464C2211yescharacteristic
39#11758456—21no—
40#11758455—21no—
41C31×#103C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×C22⋊C8C2211yescharacteristic
44#11758423C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758406C2211yescharacteristic
50#11758406C2211yescharacteristic
51#11758404C2211yescharacteristic
52#11758404C2211yescharacteristic
53#11758403C2211yescharacteristic
54Dic31⋊C8C2211yescharacteristic
55Dic31⋊C8C2211yescharacteristic
56C8×Dic31C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758395C2211yescharacteristic
59#41×C31—22no—
60#41×C31—22no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31—21no—
64C2×D4×C31C2311yescharacteristic
65C2×D4×C31C2311yescharacteristic
66C22×C4×C31—21no—
67C22×C4×C31C2311yescharacteristic
68C22×Dic31—21no—
69C22×Dic31—21no—
70C22×Dic31—21no—
71C22×Dic31—21no—
72C2×Dic62—21no—
73C2×Dic62C2311yescharacteristic
74SD16×C31—22no—
75D8×C31—22no—
76C2×C8×C31C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C4⋊C4×C31C2311yescharacteristic
79C22⋊C4×C31—21no—
80C22⋊Dic31—21no—
81C22⋊Dic31—21no—
82C22⋊Dic31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31D411yescharacteristic
87C22⋊Dic31D411yescharacteristic
88#92482—22no—
89#92480—22no—
90C4⋊Dic31—21no—
91C4⋊Dic31—21no—
92C4⋊Dic31—21no—
93C4⋊Dic31D411yescharacteristic
94C4⋊Dic31D411yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31—21no—
110C23×C31C2×D411yescharacteristic
111Q8×C31—21no—
112Q8×C31#4112yes—
113D4×C31—24no—
114D4×C31—21no—
115D4×C31—21no—
116D4×C31—21no—
117D4×C31—81no—
118D4×C31#4112yes—
119C2×C4×C31—24no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—81no—
131C2×Dic31—81no—
132C2×Dic31—81no—
133C2×Dic31—81no—
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138Dic62—21no—
139Dic62—21no—
140Dic62—81no—
141C8×C31—21no—
142C8×C31—21no—
143C31⋊C8—21no—
144C31⋊C8—21no—
145#3124—311nomaximal, Sylow
146C22×C31—21no—
147C22×C31—22no—
148C22×C31—21no—
149C22×C31—21no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C4×C31—21no—
157C4×C31—22no—
158C4×C31—41no—
159C4×C31C2×#4111yescharacteristic
160C4×C31C2×#4111yescharacteristic
161Dic31—21no—
162Dic31—21no—
163Dic31—21no—
164Dic31—21no—
165Dic31—41no—
166Dic31—41no—
167Dic31—41no—
168Dic31—41no—
169#542—311no—
170#520—311no—
171#484—311no—
172#480—311no—
173#477—311no—
174#474—311no—
175#464—311no—
176#463—311no—
177#452—311no—
178#449D3111yescharacteristic
179#440—311no—
180#440—311no—
181C4×Q16—311no—
182C4×D8—311no—
183#433—311no—
184C2×C31—41no—
185C2×C31—42no—
186C2×C31—81no—
187C2×C31#52511yescharacteristic
188C2×C31#57611yescharacteristic
189C2×C31#57811yescharacteristic
190C2×#41C2×D3111yescharacteristic
191C2×Q16—311no—
192C2×SD16—311no—
193C2×SD16C2×D3111yescharacteristic
194C2×D8C2×D3111yescharacteristic
195C4⋊Q8—311no—
196#126—621no—
197#124—311no—
198#124—621no—
199#123—621no—
200C22⋊Q8—311no—
201C22⋊Q8—621no—
202#121C2×D3111yescharacteristic
203C4×Q8—311no—
204C4×Q8—311no—
205C4×Q8—311no—
206C4×D4—311no—
207C4×D4—311no—
208C4×D4—311no—
209C4×D4—621no—
210C4×D4—621no—
211#117—311no—
212#117—621no—
213C2×C4⋊C4—311no—
214C2×C4⋊C4—621no—
215#107—311no—
216#107—311no—
217#107—311no—
218#107—311no—
219C4⋊C8—311no—
220C4⋊C8—311no—
221#103—311no—
222#103—311no—
223#103—311no—
224#103C2×D3111yescharacteristic
225#102—311no—
226#102—311no—
227#102—311no—
228#102C2×D3111yescharacteristic
229C22⋊C8—311no—
230C22⋊C8C2×D3111yescharacteristic
231#97—311no—
232C4×C8—311no—
233C31#312411yescharacteristic, complemented, Sylow
234#41—22no—
235#41—22no—
236C2×Q8—311no—
237C2×Q8—621no—
238C2×Q8C22×D3111yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C22×D3111yescharacteristic
242C2×D4C22×D3111yescharacteristic
243C22×C4—21no—
244C22×C4—621no—
245C22×C4—621no—
246C22×C4—621no—
247C22×C4—621no—
248C22×C4C22×D3111yescharacteristic
249Q16—622no—
250SD16—22no—
251SD16—622no—
252D8—22no—
253C2×C8—311no—
254C2×C8—311no—
255C2×C8C22×D3111yescharacteristic
256C2×C8C22×D3111yescharacteristic
257C4⋊C4—311no—
258C4⋊C4—311no—
259C4⋊C4—311no—
260C4⋊C4—311no—
261C4⋊C4—311no—
262C4⋊C4—621no—
263C4⋊C4—621no—
264C4⋊C4—621no—
265C4⋊C4—621no—
266C4⋊C4—621no—
267C4⋊C4—621no—
268C4⋊C4C22×D3111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—311no—
271C22⋊C4—311no—
272C22⋊C4—621no—
273C22⋊C4—621no—
274C22⋊C4—621no—
275C22⋊C4—621no—
276C22⋊C4—621no—
277C22⋊C4—621no—
278C42—311no—
279C42—311no—
280C42—621no—
281C42—621no—
282C42—621no—
283C23—21no—
284C23—21no—
285C23D4×D3111yescharacteristic
286Q8—21no—
287Q8—621no—
288Q8—621no—
289Q8—2481no—
290Q8#9249712yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#9249712yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—311no—
303C2×C4—311no—
304C2×C4—311no—
305C2×C4—311no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—2481no—
311C2×C4—2481no—
312C2×C4—2481no—
313C2×C4—2481no—
314C2×C4D4×D3111yescharacteristic
315C2×C4C23×D3111yescharacteristic
316C8—21no—
317C8—21no—
318C8—621no—
319C8—621no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D3111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—621no—
334C4—621no—
335C4—621no—
336C4—621no—
337C4—1241no—
338C4—1241no—
339C4—1241no—
340C4—1241no—
341C4C2×#9249711yescharacteristic
342C4C2×#9249711yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#1452155511yescharacteristic
347C2#1452185311yescharacteristic
348C2#1452186311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#449C2
socleC22×C31C22×D4
hypercenter#449D31
hypocenterC31#3124
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14521666C2semidirect
2. #14521532C2semidirect
3. #14521385C2semidirect
4. #14521360C2semidirect
5. #14521342C2semidirect
6. #14521327C2semidirect
7. #14521269C2semidirect
8. #14521262C2semidirect
9. #14521211C2semidirect
10. #14521150C2semidirect
11. #14521146C2semidirect
12. #14521141C2semidirect
13. D8×Dic31C2semidirect
14. #14521107C2semidirect
233. C31#3124semidirect

Maximal subgroups

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

subgroupindex
#145216662
#145215322
#145213852
#145213602
#145213422
#145213272
#145212692
#145212622
#145212112
#145211502
#145211462
#145211412
D8×Dic312
#145211072
C31×#4492
#312431