Finite Group Databasebeta

← #16855910

Subgroups — #16855910

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#14521654C211yesmaximal, characteristic, complemented
2#14521367C211yesmaximal, characteristic, complemented
3#14521362C211yesmaximal, characteristic, complemented
4#14521356C211yesmaximal, characteristic, complemented
5#14521349C211yesmaximal, characteristic, complemented
6#14521249C211yesmaximal, characteristic, complemented
7#14521244C211yesmaximal, characteristic, complemented
8#14521194C211yesmaximal, characteristic, complemented
9#14521194C211yesmaximal, characteristic, complemented
10#14521159C211yesmaximal, characteristic, complemented
11#14521147C211yesmaximal, characteristic, complemented
12C4×#92481C211yesmaximal, characteristic, complemented
13C4×#92479C211yesmaximal, characteristic, complemented
14#14521110C211yesmaximal, characteristic, complemented
15C31×#520C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C4×Q8×C31C2211yescharacteristic
18C4×Q8×C31C2211yescharacteristic
19C4×D4×C31—21no—
20C4×D4×C31—21no—
21C4×D4×C31C2211yescharacteristic
22C4×D4×C31C2211yescharacteristic
23C31×#117—21no—
24C31×#117C2211yescharacteristic
25C2×C4⋊C4×C31—21no—
26C2×C4⋊C4×C31C2211yescharacteristic
27C2×#92481C2211yescharacteristic
28C2×#92481C2211yescharacteristic
29C2×#92479C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758507C2211yescharacteristic
33#11758471—21no—
34#11758471—21no—
35#11758461—21no—
36#11758461—21no—
37#11758451C2211yescharacteristic
38C4×D124C2211yescharacteristic
39C4×D124C2211yescharacteristic
40#11758447C2211yescharacteristic
41#11758423C2211yescharacteristic
42#11758423C2211yescharacteristic
43#11758420C2211yescharacteristic
44#11758420C2211yescharacteristic
45C22⋊(C31⋊C8)C2211yescharacteristic
46C22⋊(C31⋊C8)C2211yescharacteristic
47#11758397C2211yescharacteristic
48#11758397C2211yescharacteristic
49#11758397C2211yescharacteristic
50#11758397C2211yescharacteristic
51#11758396C2211yescharacteristic
52#11758396C2211yescharacteristic
53#11758395C2211yescharacteristic
54#11758395C2211yescharacteristic
55C4⋊(C31⋊C8)C2211yescharacteristic
56C4⋊(C31⋊C8)C2211yescharacteristic
57#11758391C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59#41×C31—22no—
60#41×C31—22no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31C2311yescharacteristic
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71C2×D124—21no—
72C2×D124—21no—
73C2×D124C2311yescharacteristic
74C2×D124C2311yescharacteristic
75C2×C4×D31—21no—
76C2×C4×D31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31D411yescharacteristic
81C4⋊C4×C31D411yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C22⋊C4×C31—21no—
85C22⋊C4×C31—21no—
86C22⋊C4×C31D411yescharacteristic
87C22⋊C4×C31D411yescharacteristic
88C42×C31—21no—
89C42×C31—21no—
90C42×C31C2311yescharacteristic
91C42×C31C2311yescharacteristic
92#92481—22no—
93#92481—22no—
94#92479—22no—
95#92479—22no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4—21no—
99(C2×D31)⋊C4—21no—
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31C2×D411yescharacteristic
110C22×D31—21no—
111C22×D31—21no—
112Q8×C31—21no—
113Q8×C31#4112yes—
114D4×C31—24no—
115D4×C31—21no—
116D4×C31#4112yes—
117C2×C4×C31—24no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—81no—
124C2×C4×C31—81no—
125C2×C4×C31—81no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2×D411yescharacteristic
131C2×C4×C31C2411yescharacteristic
132C22⋊D31—81no—
133C22⋊D31—81no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136D124—21no—
137D124—21no—
138D124—21no—
139D124—21no—
140D124—81no—
141D124—81no—
142C4×D31—81no—
143C4×D31—81no—
144C31⋊C8—21no—
145C31⋊C8—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3119—311nomaximal, Sylow
149C22×C31—21no—
150C22×C31—22no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C4×C31—21no—
163C4×C31—22no—
164C4×C31—21no—
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31C2×#4111yescharacteristic
172Dic31—41no—
173Dic31—41no—
174#540—311no—
175#520D3111yescharacteristic, complemented
176#481—311no—
177#480—311no—
178#479—311no—
179#478—311no—
180#460—311no—
181#459—311no—
182#449—311no—
183#449—311no—
184#442—311no—
185#440—311no—
186C4×SD16—311no—
187C4×D8—311no—
188#433—311no—
189C2×C31—41no—
190C2×C31—42no—
191C2×C31#52511yescharacteristic
192C2×C31#57611yescharacteristic
193C2×C31#57711yescharacteristic
194D31—81no—
195D31—81no—
196C2×#41C2×D3111yescharacteristic
197C2×SD16—311no—
198C2×SD16—311no—
199C2×D8—311no—
200C2×D8—311no—
201#127—311no—
202#125—311no—
203#123—621no—
204#123—621no—
205#121—311no—
206#121—311no—
207#121—621no—
208#121—621no—
209C4×Q8C2×D3111yescharacteristic
210C4×Q8C2×D3111yescharacteristic
211C4×D4—21no—
212C4×D4—21no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4C2×D3111yescharacteristic
216C4×D4C2×D3111yescharacteristic
217#117—21no—
218#117C2×D3111yescharacteristic
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×D3111yescharacteristic
221#107—311no—
222#107—311no—
223#106—311no—
224#106—311no—
225C4⋊C8—311no—
226C4⋊C8—311no—
227#103—311no—
228#103—311no—
229#102—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102—311no—
235C22⋊C8—311no—
236C22⋊C8—311no—
237#97—311no—
238C4×C8—311no—
239C31#311911yescharacteristic, complemented, Sylow
240#41—22no—
241#41—22no—
242C2×Q8C22×D3111yescharacteristic
243C2×D4—21no—
244C2×D4—311no—
245C2×D4—311no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4—621no—
250C2×D4C22×D3111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4C22×D3111yescharacteristic
258SD16—622no—
259SD16—622no—
260D8—622no—
261D8—622no—
262C2×C8—311no—
263C2×C8—311no—
264C2×C8—311no—
265C2×C8—311no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—311no—
270C4⋊C4—311no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4C22⋊D3111yescharacteristic
274C4⋊C4C22⋊D3111yescharacteristic
275C4⋊C4C22×D3111yescharacteristic
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4C22⋊D3111yescharacteristic
284C22⋊C4C22⋊D3111yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D3111yescharacteristic
288C42C22×D3111yescharacteristic
289C23—21no—
290C23—621no—
291C23—621no—
292C23C2×C22⋊D3111yescharacteristic
293Q8—21no—
294Q8#9249512yes—
295D4—24no—
296D4—21no—
297D4—621no—
298D4—621no—
299D4—621no—
300D4—621no—
301D4—2481no—
302D4—2481no—
303D4—2481no—
304D4—2481no—
305D4#9249512yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—2481no—
318C2×C4—2481no—
319C2×C4C2×C22⋊D3111yescharacteristic
320C2×C4C2×C22⋊D3111yescharacteristic
321C2×C4C2×C22⋊D3111yescharacteristic
322C2×C4C2×C22⋊D3111yescharacteristic
323C2×C4C2×C22⋊D3111yescharacteristic
324C2×C4C23×D3111yescharacteristic
325C8—621no—
326C8—621no—
327C8—621no—
328C8—621no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—1241no—
336C22—1241no—
337C22—1241no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22C22×C22⋊D3111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—1241no—
351C4—1241no—
352C4C2×#9249511yescharacteristic
353C4C2×#9249511yescharacteristic
354C2—41no—
355C2—42no—
356C2—2481no—
357C2—2481no—
358C2#1452156011yescharacteristic
359C2#1452185211yescharacteristic
360C2#1452185711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#520C2
socleC22×C31C22×D4
hypercenter#520D31
hypocenterC31#3119
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #14521654C2semidirect
2. #14521367C2semidirect
3. #14521362C2semidirect
4. #14521356C2semidirect
5. #14521349C2semidirect
6. #14521249C2semidirect
7. #14521244C2semidirect
8. #14521194C2semidirect
9. #14521194C2semidirect
10. #14521159C2semidirect
11. #14521147C2semidirect
12. C4×#92481C2semidirect
13. C4×#92479C2semidirect
14. #14521110C2semidirect
15. C31×#520C2semidirect
175. #520D31semidirect
239. C31#3119semidirect

Maximal subgroups

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

subgroupindex
#145216542
#145213672
#145213622
#145213562
#145213492
#145212492
#145212442
#145211942
#145211592
#145211472
C4×#924812
C4×#924792
#145211102
C31×#5202
#311931