Finite Group Databasebeta

← #16855907

Subgroups — #16855907

Order 3968.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521653C211yesmaximal, characteristic, complemented
2#14521528C211yesmaximal, characteristic, complemented
3#14521366C211yesmaximal, characteristic, complemented
4#14521361C211yesmaximal, characteristic, complemented
5#14521357C211yesmaximal, characteristic, complemented
6#14521349C211yesmaximal, characteristic, complemented
7#14521246C211yesmaximal, characteristic, complemented
8#14521191C211yesmaximal, characteristic, complemented
9#14521191C211yesmaximal, characteristic, complemented
10#14521161C211yesmaximal, characteristic, complemented
11#14521146C211yesmaximal, characteristic, complemented
12#14521140C211yesmaximal, characteristic, complemented
13D8×Dic31C211yesmaximal, characteristic, complemented
14#14521109C211yesmaximal, characteristic, complemented
15C31×#459C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×D8×C31C2211yescharacteristic
18C2×D8×C31C2211yescharacteristic
19C31×#127C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21#11758516—21no—
22#11758516—21no—
23#11758515C2211yescharacteristic
24#11758515C2211yescharacteristic
25#11758512—21no—
26#11758512—21no—
27D4×Dic31C2211yescharacteristic
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic
30C2×#92480C2211yescharacteristic
31C2×#92480C2211yescharacteristic
32C4×C22⋊D31—21no—
33C2×Dic31⋊C4—21no—
34C4⋊C4×D31C2211yescharacteristic
35#11758464C2211yescharacteristic
36(C22⋊D31)⋊C4—21no—
37#11758454—21no—
38#11758449C2211yescharacteristic
39#11758447C2211yescharacteristic
40C4×Dic62C2211yescharacteristic
41C31×C4⋊C8C2211yescharacteristic
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic
44#11758420C2211yescharacteristic
45#11758420C2211yescharacteristic
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×D4×C31—21no—
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C2×D4×C31C2311yescharacteristic
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C22×Dic31—21no—
69C22×Dic31—21no—
70C22×Dic31—21no—
71C22×Dic31—21no—
72#92497—22no—
73#92497—22no—
74C2×C4×D31—21no—
75C2×C4×D31C2311yescharacteristic
76C2×Dic62C2311yescharacteristic
77D8×C31—22no—
78D8×C31—22no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C22⋊C4×C31—21no—
83C42×C31C2311yescharacteristic
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89#92480—22no—
90#92480—22no—
91(C2×D31)⋊C4D411yescharacteristic
92(C2×D31)⋊C4D411yescharacteristic
93C4⋊Dic31C2311yescharacteristic
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4D411yescharacteristic
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31—21no—
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31—21no—
110C23×C31—21no—
111C22×D31C2×D411yescharacteristic
112D4×C31—21no—
113D4×C31—21no—
114D4×C31—21no—
115D4×C31—21no—
116D4×C31—21no—
117D4×C31—81no—
118D4×C31—81no—
119D4×C31#4112yes—
120C2×C4×C31—21no—
121C2×C4×C31—81no—
122C2×C4×C31C2×D411yescharacteristic
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C22⋊D31—24no—
126C22⋊D31—81no—
127C22⋊D31—81no—
128C2×Dic31—24no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—81no—
134C2×Dic31—81no—
135C2×Dic31—81no—
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138C2×Dic31C2×D411yescharacteristic
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—81no—
142Dic62—21no—
143Dic62#4112yes—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3119—311nomaximal, Sylow
149C22×C31—22no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31C22×D411yescharacteristic
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—21no—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31C2×#4111yescharacteristic
166C4×C31C2×#4111yescharacteristic
167Dic31—22no—
168Dic31—21no—
169Dic31—21no—
170Dic31—21no—
171Dic31—41no—
172Dic31—41no—
173Dic31—41no—
174#540—311no—
175#520—311no—
176#481—311no—
177#480—311no—
178#479—311no—
179#478—311no—
180#460—311no—
181#459D3111yescharacteristic, complemented
182#449—311no—
183#449—311no—
184#442—311no—
185#440—311no—
186C4×SD16—311no—
187C4×D8—311no—
188#433—311no—
189C2×C31—42no—
190C2×C31—81no—
191C2×C31—81no—
192C2×C31#52511yescharacteristic
193C2×C31#57611yescharacteristic
194C2×C31#57711yescharacteristic
195D31—41no—
196C2×#41—311no—
197C2×SD16—311no—
198C2×SD16—311no—
199C2×D8C2×D3111yescharacteristic
200C2×D8C2×D3111yescharacteristic
201#127C2×D3111yescharacteristic
202#125—311no—
203#123—621no—
204#123—621no—
205#121—311no—
206#121—311no—
207#121—621no—
208#121—621no—
209C4×Q8—311no—
210C4×Q8—311no—
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—621no—
215C4×D4—621no—
216C4×D4C2×D3111yescharacteristic
217#117—311no—
218#117—621no—
219C2×C4⋊C4—311no—
220C2×C4⋊C4—621no—
221#107—311no—
222#107—311no—
223#106—311no—
224#106—311no—
225C4⋊C8—311no—
226C4⋊C8C2×D3111yescharacteristic
227#103—311no—
228#103—311no—
229#102—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102C2×D3111yescharacteristic
234#102C2×D3111yescharacteristic
235C22⋊C8—311no—
236C22⋊C8—311no—
237#97—311no—
238C4×C8—311no—
239C31#311911yescharacteristic, complemented, Sylow
240#41—622no—
241#41—622no—
242C2×Q8—311no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—621no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4C22×D3111yescharacteristic
249C2×D4C22×D3111yescharacteristic
250C2×D4C22×D3111yescharacteristic
251C22×C4—21no—
252C22×C4—311no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258SD16—622no—
259SD16—622no—
260D8—22no—
261D8—22no—
262C2×C8—311no—
263C2×C8—311no—
264C2×C8C22×D3111yescharacteristic
265C2×C8C22×D3111yescharacteristic
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—311no—
270C4⋊C4—311no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4—621no—
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—311no—
279C22⋊C4—311no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C42—311no—
286C42—621no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—311no—
293Q8—312no—
294Q8—621no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—624no—
303D4—2481no—
304D4—2481no—
305D4#9249712yes—
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—311no—
309C2×C4—311no—
310C2×C4—311no—
311C2×C4—624no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—2481no—
319C2×C4—2481no—
320C2×C4—2481no—
321C2×C4—2481no—
322C2×C4D4×D3111yescharacteristic
323C2×C4D4×D3111yescharacteristic
324C2×C4C23×D3111yescharacteristic
325C8—21no—
326C8—21no—
327C8—621no—
328C8—621no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—621no—
339C22—621no—
340C22—621no—
341C22C2×D4×D3111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—621no—
346C4—621no—
347C4—622no—
348C4—621no—
349C4—1241no—
350C4—1241no—
351C4—1241no—
352C4C2×#9249711yescharacteristic
353C4#41×D3111yescharacteristic
354C2—42no—
355C2—81no—
356C2—81no—
357C2—1241no—
358C2#1452155911yescharacteristic
359C2#1452185011yescharacteristic
360C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#459C2
socleC22×C31C22×D4
hypercenter#459D31
hypocenterC31#3119
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14521653C2semidirect
2. #14521528C2semidirect
3. #14521366C2semidirect
4. #14521361C2semidirect
5. #14521357C2semidirect
6. #14521349C2semidirect
7. #14521246C2semidirect
8. #14521191C2semidirect
9. #14521191C2semidirect
10. #14521161C2semidirect
11. #14521146C2semidirect
12. #14521140C2semidirect
13. D8×Dic31C2semidirect
14. #14521109C2semidirect
15. C31×#459C2semidirect
181. #459D31semidirect
239. C31#3119semidirect

Maximal subgroups

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

subgroupindex
#145216532
#145215282
#145213662
#145213612
#145213572
#145213492
#145212462
#145211912
#145211612
#145211462
#145211402
D8×Dic312
#145211092
C31×#4592
#311931