Finite Group Databasebeta

← #16857619

Subgroups — #16857619

Order 3968.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521751C211yesmaximal, characteristic, complemented
2#14521705C211yesmaximal, characteristic, complemented
3#14521402C211yesmaximal, characteristic, complemented
4#14521392C211yesmaximal, characteristic, complemented
5#14521365C211yesmaximal, characteristic, complemented
6#14521355C211yesmaximal, characteristic, complemented
7#14521277C211yesmaximal, characteristic, complemented
8#14521262C211yesmaximal, characteristic, complemented
9#14521191C211yesmaximal, characteristic, complemented
10#14521187C211yesmaximal, characteristic, complemented
11#14521140C211yesmaximal, characteristic, complemented
12C8×C22⋊D31C211yesmaximal, characteristic, complemented
13#14521042C211yesmaximal, characteristic, complemented
14C2×#11758404C211yesmaximal, characteristic, complemented
15C31×#466C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C22×Dic62C2211yescharacteristic
18C2×D8×C31C2211yescharacteristic
19C22×C8×C31C2211yescharacteristic
20C31×#121C2211yescharacteristic
21C31×#121C2211yescharacteristic
22#11758516—21no—
23#11758516—21no—
24#11758515C2211yescharacteristic
25#11758513C2211yescharacteristic
26D4×Dic31—21no—
27D4×Dic31—21no—
28D4×Dic31C2211yescharacteristic
29C2×#92480C2211yescharacteristic
30C2×#92480C2211yescharacteristic
31C4×C22⋊D31C2211yescharacteristic
32C2×C4⋊Dic31C2211yescharacteristic
33C2×C8×D31C2211yescharacteristic
34#11758474C2211yescharacteristic
35#11758469C2211yescharacteristic
36#11758467C2211yescharacteristic
37#11758464C2211yescharacteristic
38#11758463—21no—
39#11758462—21no—
40#11758456—21no—
41#11758455—21no—
42C31×#107C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×#102C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47C22⋊(C31⋊C8)C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49#11758404C2211yescharacteristic
50#11758404C2211yescharacteristic
51#11758404C2211yescharacteristic
52#11758404C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54C8×Dic31C2211yescharacteristic
55#11758398C2211yescharacteristic
56#11758398C2211yescharacteristic
57#11758396C2211yescharacteristic
58#11758396C2211yescharacteristic
59C2×D4×C31—21no—
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C2×D4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31D411yescharacteristic
67C22×Dic31—21no—
68C22×Dic31—21no—
69C22×Dic31—21no—
70C22×Dic31—21no—
71#92497—22no—
72#92497—41no—
73C2×C4×D31C2311yescharacteristic
74C2×Dic62—22no—
75C2×Dic62—21no—
76C2×Dic62—41no—
77C2×Dic62C2311yescharacteristic
78C2×Dic62C2311yescharacteristic
79D8×C31—41no—
80C2×C8×C31—41no—
81C2×C8×C31C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31D411yescharacteristic
92#92480—22no—
93#92480—41no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4D411yescharacteristic
97C4⋊Dic31—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31—21no—
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4D411yescharacteristic
105C4×Dic31—21no—
106C4×Dic31—21no—
107C4×Dic31C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C8×D31—41no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31C2×D411yescharacteristic
114C22×D31C2×D411yescharacteristic
115D4×C31—21no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—42no—
120D4×C31—42no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—22no—
128C22⋊D31—42no—
129C22⋊D31—81no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—42no—
135C2×Dic31—42no—
136C2×Dic31—81no—
137C2×Dic31—81no—
138C2×Dic31C2×D411yescharacteristic
139C2×Dic31C2×D411yescharacteristic
140C2×Dic31C2×D411yescharacteristic
141C4×D31—21no—
142C4×D31—21no—
143Dic62—21no—
144Dic62—21no—
145Dic62—21no—
146Dic62—42no—
147Dic62#4112yes—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3301—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31#13512yes—
162C22×C31C22×D411yescharacteristic
163C2×D31—21no—
164C2×D31—21no—
165C2×D31—21no—
166C4×C31—21no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31C2×#4111yescharacteristic
170C4×C31H(5,𝔽2)11yescharacteristic
171Dic31—22no—
172Dic31—21no—
173Dic31—21no—
174Dic31—21no—
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178#553—311no—
179#548—311no—
180#488—311no—
181#485—311no—
182#481—311no—
183#479—311no—
184#466D3111yescharacteristic, complemented
185#465—311no—
186#463—311no—
187#449—311no—
188#448—311no—
189C4×SD16—311no—
190C8×D4—311no—
191#416—311no—
192C2×#103—311no—
193C2×C31—22no—
194C2×C31—81no—
195C2×C31—81no—
196C2×C31#54611yescharacteristic
197C2×C31C2×#13511yescharacteristic
198C2×C31#57711yescharacteristic
199D31—41no—
200C2×#41—311no—
201C22×Q8—311no—
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8C2×D3111yescharacteristic
205C22×C8—311no—
206C22×C8C2×D3111yescharacteristic
207#126—621no—
208#125—311no—
209#124—311no—
210#124—621no—
211#123—621no—
212C22⋊Q8—311no—
213C22⋊Q8—621no—
214#121—311no—
215#121—621no—
216#121—621no—
217#121C2×D3111yescharacteristic
218#121C2×D3111yescharacteristic
219C4×Q8—311no—
220C4×D4—311no—
221C4×D4—311no—
222C4×D4—621no—
223C4×D4—621no—
224#117—311no—
225C2×C4⋊C4—311no—
226#107C2×D3111yescharacteristic
227#106—311no—
228#106—311no—
229C4⋊C8—311no—
230#103—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#102—311no—
237#102—311no—
238#102C2×D3111yescharacteristic
239#102C2×D3111yescharacteristic
240C22⋊C8—311no—
241C22⋊C8—311no—
242C4×C8—311no—
243C31#330111yescharacteristic, complemented, Sylow
244#41—622no—
245#41—1241no—
246C2×Q8—311no—
247C2×Q8—311no—
248C2×Q8—622no—
249C2×Q8—621no—
250C2×Q8—1241no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—311no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4C22×D3111yescharacteristic
257C2×D4C22×D3111yescharacteristic
258C22×C4—311no—
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4—621no—
263C22×C4C22×D3111yescharacteristic
264SD16—622no—
265SD16—1241no—
266D8—41no—
267C2×C8—41no—
268C2×C8—311no—
269C2×C8—311no—
270C2×C8—1241no—
271C2×C8C22×D3111yescharacteristic
272C2×C8C22×D3111yescharacteristic
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—621no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4C22×D3111yescharacteristic
282C4⋊C4C22×D3111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—311no—
286C22⋊C4—311no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C42—311no—
294C42—621no—
295C42—621no—
296C23—21no—
297C23—21no—
298C23—311no—
299C23D4×D3111yescharacteristic
300Q8—312no—
301Q8—621no—
302Q8—621no—
303Q8—621no—
304Q8—1242no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—42no—
311D4—622no—
312D4—1242no—
313D4—2481no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—311no—
319C2×C4—311no—
320C2×C4—311no—
321C2×C4—621no—
322C2×C4—621no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—1242no—
328C2×C4—1242no—
329C2×C4—2481no—
330C2×C4—2481no—
331C2×C4D4×D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—21no—
334C8—21no—
335C8—621no—
336C8—621no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—621no—
346C22—621no—
347C22—621no—
348C22#1175848912yes—
349C22C2×D4×D3111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—621no—
354C4—621no—
355C4—622no—
356C4—621no—
357C4—1241no—
358C4—1241no—
359C4—1241no—
360C4#1175856111yescharacteristic
361C4#41×D3111yescharacteristic
362C2—22no—
363C2—81no—
364C2—81no—
365C2—1241no—
366C2#1452168811yescharacteristic
367C2C2×#1175848911yescharacteristic
368C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#466C2
socleC22×C31C22×D4
hypercenter#466D31
hypocenterC31#3301
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14521751C2semidirect
2. #14521705C2semidirect
3. #14521402C2semidirect
4. #14521392C2semidirect
5. #14521365C2semidirect
6. #14521355C2semidirect
7. #14521277C2semidirect
8. #14521262C2semidirect
9. #14521191C2semidirect
10. #14521187C2semidirect
11. #14521140C2semidirect
12. C8×C22⋊D31C2semidirect
13. #14521042C2semidirect
14. C2×#11758404C2semidirect
15. C31×#466C2semidirect
184. #466D31semidirect
243. C31#3301semidirect

Maximal subgroups

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

subgroupindex
#145217512
#145217052
#145214022
#145213922
#145213652
#145213552
#145212772
#145212622
#145211912
#145211872
#145211402
C8×C22⋊D312
#145210422
C2×#117584042
C31×#4662
#330131