Finite Group Databasebeta

← #16856001

Subgroups — #16856001

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#14521650C211yesmaximal, characteristic
2#14521525C211yesmaximal, characteristic, complemented
3#14521376C211yesmaximal, characteristic, complemented
4#14521371C211yesmaximal, characteristic, complemented
5#14521358C211yesmaximal, characteristic, complemented
6#14521355C211yesmaximal, characteristic, complemented
7#14521248C211yesmaximal, characteristic, complemented
8#14521247C211yesmaximal, characteristic, complemented
9#14521189C211yesmaximal, characteristic, complemented
10#14521186C211yesmaximal, characteristic, complemented
11#14521151C211yesmaximal, characteristic, complemented
12C4×#92481C211yesmaximal, characteristic, complemented
13C4×#92480C211yesmaximal, characteristic, complemented
14#14521111C211yesmaximal, characteristic, complemented
15C31×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D31C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C4×Q8×C31C2211yescharacteristic
19C4×D4×C31C2211yescharacteristic
20Q8×Dic31C2211yescharacteristic
21C2×#92481C2211yescharacteristic
22#11758517C2211yescharacteristic
23#11758515C2211yescharacteristic
24C2×#92480C2211yescharacteristic
25#11758507—21no—
26#11758506—21no—
27C2×#92470C2211yescharacteristic
28#11758472C2211yescharacteristic
29#11758469—21no—
30#11758469C2211yescharacteristic
31#11758467C2211yescharacteristic
32#11758464—21no—
33#11758464C2211yescharacteristic
34#11758461—21no—
35#11758460—21no—
36C4×D124C2211yescharacteristic
37#11758449—21no—
38#11758449C2211yescharacteristic
39C4×Dic62—21no—
40C4×Dic62C2211yescharacteristic
41C31×#107C2211yescharacteristic
42C31×#103C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×#97C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758409C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758406C2211yescharacteristic
51#11758404C2211yescharacteristic
52Dic31⋊C8C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic
57#11758396C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65Q8×D31—22no—
66Q8×D31—22no—
67C2×D124—21no—
68C2×D124C2311yescharacteristic
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31C2311yescharacteristic
72C2×Dic62—21no—
73C2×Dic62C2311yescharacteristic
74SD16×C31—22no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C4⋊C4×C31—21no—
78C4⋊C4×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C42×C31—21no—
82C42×C31C2311yescharacteristic
83C22⋊Dic31—21no—
84#92481—22no—
85#92480—22no—
86(C2×D31)⋊C4—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4D411yescharacteristic
90(C2×D31)⋊C4D411yescharacteristic
91C4⋊Dic31—21no—
92C4⋊Dic31—21no—
93C4⋊Dic31C2311yescharacteristic
94C4⋊Dic31C2311yescharacteristic
95Dic31⋊C4—21no—
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4D411yescharacteristic
99Dic31⋊C4D411yescharacteristic
100C4×Dic31—21no—
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107#92470—22no—
108C23×C31—21no—
109C22×D31—21no—
110C22×D31C2×D411yescharacteristic
111Q8×C31—21no—
112Q8×C31#4112yes—
113D4×C31—21no—
114D4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—81no—
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2411yescharacteristic
122C22⋊D31—81no—
123C22⋊D31—81no—
124C22⋊D31—81no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131D124—21no—
132D124—21no—
133D124—81no—
134C4×D31—24no—
135C4×D31—21no—
136C4×D31—21no—
137C4×D31—81no—
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×C31C22×D411yescharacteristic
150C2×D31—21no—
151C2×D31—21no—
152C2×D31—21no—
153C2×D31—41no—
154C2×D31—41no—
155C2×D31—41no—
156C4×C31—22no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31C2×#4111yescharacteristic
162C4×C31C2×#4111yescharacteristic
163Dic31—21no—
164Dic31—22no—
165Dic31—21no—
166Dic31—21no—
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#460—311no—
177#448—311no—
178#448—311no—
179#440—311no—
180#440D3111yescharacteristic, complemented
181C4×SD16—311no—
182C4×SD16—311no—
183#433—311no—
184C2×C31—81no—
185C2×C31#52511yescharacteristic
186C2×C31#57711yescharacteristic
187C2×C31#57711yescharacteristic
188D31—41no—
189D31—81no—
190C22×Q8—311no—
191C2×SD16—311no—
192C2×SD16—311no—
193C2×SD16—311no—
194C2×SD16C2×D3111yescharacteristic
195#127—311no—
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×D4C2×D3111yescharacteristic
211#117—311no—
212#117—311no—
213#117—621no—
214#117—621no—
215#107—311no—
216#107C2×D3111yescharacteristic
217#106—311no—
218#106—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⋊C8—311no—
231#97C2×D3111yescharacteristic
232C4×C8—311no—
233C31#312611yescharacteristic, complemented, Sylow
234C2×Q8—311no—
235C2×Q8—621no—
236C2×Q8—622no—
237C2×Q8—622no—
238C2×Q8C22×D3111yescharacteristic
239C2×D4—311no—
240C2×D4—621no—
241C2×D4—621no—
242C2×D4—621no—
243C2×D4—621no—
244C2×D4C22×D3111yescharacteristic
245C22×C4—21no—
246C22×C4—311no—
247C22×C4—621no—
248C22×C4—621no—
249SD16—22no—
250SD16—622no—
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—621no—
263C4⋊C4—621no—
264C4⋊C4—621no—
265C4⋊C4—621no—
266C4⋊C4—621no—
267C4⋊C4C22×D3111yescharacteristic
268C4⋊C4C22×D3111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—311no—
271C22⋊C4—311no—
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—311no—
285C23—621no—
286Q8—21no—
287Q8—312no—
288Q8—624no—
289Q8—621no—
290Q8#9249512yes—
291D4—21no—
292D4—21no—
293D4—621no—
294D4—621no—
295D4—2481no—
296D4—2481no—
297D4—2481no—
298D4—2481no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—311no—
304C2×C4—311no—
305C2×C4—311no—
306C2×C4—624no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—621no—
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—621no—
324C22—621no—
325C22—621no—
326C22—1241no—
327C22—1241no—
328C22—1241no—
329C22C2×D4×D3111yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—621no—
336C4—621no—
337C4—621no—
338C4—622no—
339C4—1241no—
340C4—1241no—
341C4C2×#9249511yescharacteristic
342C4#41×D3111yescharacteristic
343C2—81no—
344C2—1241no—
345C2—2481no—
346C2#1452155811yescharacteristic
347C2#1452185811yescharacteristic
348C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#440C2
socleC22×C31C22×D4
prime radical#14521650C2
hypercenter#440D31
hypocenterC31#3126
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #14521525C2semidirect
3. #14521376C2semidirect
4. #14521371C2semidirect
5. #14521358C2semidirect
6. #14521355C2semidirect
7. #14521248C2semidirect
8. #14521247C2semidirect
9. #14521189C2semidirect
10. #14521186C2semidirect
11. #14521151C2semidirect
12. C4×#92481C2semidirect
13. C4×#92480C2semidirect
14. #14521111C2semidirect
15. C31×#440C2semidirect
180. #440D31semidirect
233. C31#3126semidirect

Maximal subgroups

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

subgroupindex
#145216502
#145215252
#145213762
#145213712
#145213582
#145213552
#145212482
#145212472
#145211892
#145211862
#145211512
C4×#924812
C4×#924802
#145211112
C31×#4402
#312631