Finite Group Databasebeta

← #16857717

Subgroups — #16857717

Order 3968.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521745C211yesmaximal, characteristic, complemented
2#14521413C211yesmaximal, characteristic, complemented
3#14521370C211yesmaximal, characteristic, complemented
4#14521360C211yesmaximal, characteristic, complemented
5#14521356C211yesmaximal, characteristic, complemented
6#14521300C211yesmaximal, characteristic, complemented
7#14521283C211yesmaximal, characteristic, complemented
8#14521241C211yesmaximal, characteristic, complemented
9#14521194C211yesmaximal, characteristic, complemented
10#14521194C211yesmaximal, characteristic, complemented
11#14521147C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521050C211yesmaximal, characteristic, complemented
14#14521045C211yesmaximal, characteristic, complemented
15C31×#550C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×#41×C31C2211yescharacteristic
18C31×#127—21no—
19C31×#127C2211yescharacteristic
20C31×#121—21no—
21C31×#121—21no—
22C31×#121C2211yescharacteristic
23C31×#121C2211yescharacteristic
24C4×Q8×C31C2211yescharacteristic
25C4×D4×C31—21no—
26C4×D4×C31C2211yescharacteristic
27C2×#92481C2211yescharacteristic
28#11758516—21no—
29C2×#92479C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758507C2211yescharacteristic
33#11758503C2211yescharacteristic
34C2×C4⋊Dic31C2211yescharacteristic
35C2×#92474C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37#11758475—21no—
38#11758460—21no—
39(C22⋊D31)⋊C4—21no—
40C4×D124C2211yescharacteristic
41#11758447C2211yescharacteristic
42#11758423C2211yescharacteristic
43#11758423C2211yescharacteristic
44#11758423C2211yescharacteristic
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758420C2211yescharacteristic
51C22⋊(C31⋊C8)C2211yescharacteristic
52C22⋊(C31⋊C8)C2211yescharacteristic
53#11758397C2211yescharacteristic
54#11758396C2211yescharacteristic
55#11758395C2211yescharacteristic
56#11758395C2211yescharacteristic
57C4⋊(C31⋊C8)C2211yescharacteristic
58#11758391C2211yescharacteristic
59#41×C31—22no—
60#41×C31—22no—
61#41×C31—41no—
62#41×C31—41no—
63C2×Q8×C31C2311yescharacteristic
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31—21no—
67C2×D4×C31—21no—
68C2×D4×C31—21no—
69C2×D4×C31—21no—
70C2×D4×C31D411yescharacteristic
71C2×D4×C31C2311yescharacteristic
72C2×D4×C31C2311yescharacteristic
73C22×C4×C31—21no—
74C22×C4×C31—21no—
75C22×C4×C31C2311yescharacteristic
76C22×C4×C31C2311yescharacteristic
77C2×C22⋊D31—21no—
78C2×C22⋊D31—21no—
79C22×Dic31—21no—
80C2×D124C2311yescharacteristic
81C2×C4×D31—21no—
82C4⋊C4×C31—21no—
83C4⋊C4×C31D411yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C22⋊C4×C31D411yescharacteristic
88C22⋊C4×C31D411yescharacteristic
89C42×C31—21no—
90C42×C31C2311yescharacteristic
91C22⋊Dic31—21no—
92#92481—22no—
93#92479—41no—
94#92479—41no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105#92474—41no—
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31—21no—
112C23×C31—21no—
113C23×C31C2×D411yescharacteristic
114C23×C31C2×D411yescharacteristic
115C22×D31—21no—
116Q8×C31—21no—
117Q8×C31#4112yes—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—21no—
121D4×C31—21no—
122D4×C31—41no—
123D4×C31—42no—
124D4×C31—42no—
125D4×C31—42no—
126D4×C31—81no—
127D4×C31—81no—
128D4×C31—81no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—21no—
135C2×C4×C31—42no—
136C2×C4×C31—42no—
137C2×C4×C31C2×D411yescharacteristic
138C2×C4×C31C2×D411yescharacteristic
139C2×C4×C31C2×D411yescharacteristic
140C2×C4×C31C2×D411yescharacteristic
141C2×C4×C31C2411yescharacteristic
142C22⋊D31—42no—
143C22⋊D31—81no—
144C2×Dic31—21no—
145C2×Dic31—21no—
146C2×Dic31—21no—
147C2×Dic31—81no—
148D124—21no—
149D124—21no—
150C4×D31—81no—
151C31⋊C8—21no—
152C31⋊C8—21no—
153C31⋊C8—21no—
154C31⋊C8—21no—
155#3309—311nomaximal, Sylow
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31C22×D411yescharacteristic
169C2×D31—41no—
170C2×D31—41no—
171C2×D31—41no—
172C4×C31—21no—
173C4×C31—21no—
174C4×C31—22no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31—41no—
178C4×C31C2×#4111yescharacteristic
179C4×C31H(5,𝔽2)11yescharacteristic
180Dic31—41no—
181Dic31—41no—
182Dic31—41no—
183#553—311no—
184#550D3111yescharacteristic, complemented
185#490—311no—
186#482—311no—
187#480—311no—
188#479—311no—
189#469—311no—
190#466—311no—
191#459—311no—
192#449—311no—
193#449—311no—
194#440—311no—
195#435—311no—
196#417—311no—
197#416—311no—
198C2×C31—41no—
199C2×C31—41no—
200C2×C31—81no—
201C2×C31—81no—
202C2×C31#54611yescharacteristic
203C2×C31#57511yescharacteristic
204C2×C31#57611yescharacteristic
205D31—81no—
206C2×#41C2×D3111yescharacteristic
207C2×#41C2×D3111yescharacteristic
208C2×SD16—311no—
209C2×D8—311no—
210C2×D8—311no—
211C2×M16—311no—
212C22×C8—311no—
213#127—21no—
214#127C2×D3111yescharacteristic
215#126—621no—
216#125—311no—
217#123—621no—
218#121—21no—
219#121—21no—
220#121—311no—
221#121—311no—
222#121—621no—
223#121C2×D3111yescharacteristic
224#121C2×D3111yescharacteristic
225C4×Q8C2×D3111yescharacteristic
226C4×D4—21no—
227C4×D4—311no—
228C4×D4—621no—
229C4×D4C2×D3111yescharacteristic
230#117—311no—
231C2×C4⋊C4—311no—
232#107—311no—
233#107—311no—
234#106—311no—
235C4⋊C8—311no—
236#103—311no—
237#103—311no—
238#103—311no—
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246C22⋊C8—311no—
247C22⋊C8—311no—
248#97—311no—
249C31#330911yescharacteristic, complemented, Sylow
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C22×D3111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—311no—
262C2×D4—621no—
263C2×D4—621no—
264C2×D4C22⋊D3111yescharacteristic
265C2×D4C22×D3111yescharacteristic
266C2×D4C22×D3111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—621no—
270C22×C4—621no—
271C22×C4C22×D3111yescharacteristic
272C22×C4C22×D3111yescharacteristic
273SD16—622no—
274D8—1241no—
275D8—1241no—
276M16—1241no—
277C2×C8—311no—
278C2×C8—311no—
279C2×C8—311no—
280C2×C8—311no—
281C2×C8—1241no—
282C4⋊C4—21no—
283C4⋊C4—311no—
284C4⋊C4—311no—
285C4⋊C4—311no—
286C4⋊C4—621no—
287C4⋊C4—621no—
288C4⋊C4—621no—
289C4⋊C4C22⋊D3111yescharacteristic
290C4⋊C4C22×D3111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4C22⋊D3111yescharacteristic
298C22⋊C4C22⋊D3111yescharacteristic
299C42—21no—
300C42—621no—
301C42C22×D3111yescharacteristic
302C23—21no—
303C23—21no—
304C23—621no—
305C23C2×C22⋊D3111yescharacteristic
306C23C2×C22⋊D3111yescharacteristic
307Q8—21no—
308Q8#9249712yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4—81no—
319D4—81no—
320D4—621no—
321D4—621no—
322D4—1242no—
323D4—2481no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—621no—
333C2×C4—621no—
334C2×C4—621no—
335C2×C4—2481no—
336C2×C4—2481no—
337C2×C4C2×C22⋊D3111yescharacteristic
338C2×C4C2×C22⋊D3111yescharacteristic
339C2×C4C2×C22⋊D3111yescharacteristic
340C2×C4C2×C22⋊D3111yescharacteristic
341C2×C4C23×D3111yescharacteristic
342C8—621no—
343C8—621no—
344C8—621no—
345C8—621no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—1241no—
359C22—1241no—
360C22—1241no—
361C22C22×C22⋊D3111yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—1241no—
369C4—1241no—
370C4—1241no—
371C4C2×#9249711yescharacteristic
372C4#1175856111yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—2481no—
378C2#1452169311yescharacteristic
379C2#1452184711yescharacteristic
380C2#1452185211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#550C2
socleC22×C31C22×D4
hypercenter#550D31
hypocenterC31#3309
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #14521745C2semidirect
2. #14521413C2semidirect
3. #14521370C2semidirect
4. #14521360C2semidirect
5. #14521356C2semidirect
6. #14521300C2semidirect
7. #14521283C2semidirect
8. #14521241C2semidirect
9. #14521194C2semidirect
10. #14521194C2semidirect
11. #14521147C2semidirect
12. #14521121C2semidirect
13. #14521050C2semidirect
14. #14521045C2semidirect
15. C31×#550C2semidirect
184. #550D31semidirect
249. C31#3309semidirect

Maximal subgroups

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

subgroupindex
#145217452
#145214132
#145213702
#145213602
#145213562
#145213002
#145212832
#145212412
#145211942
#145211472
#145211212
#145210502
#145210452
C31×#5502
#330931