Finite Group Databasebeta

← #16857613

Subgroups — #16857613

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#14521745C211yesmaximal, characteristic, complemented
2#14521403C211yesmaximal, characteristic, complemented
3#14521387C211yesmaximal, characteristic, complemented
4#14521365C211yesmaximal, characteristic, complemented
5#14521356C211yesmaximal, characteristic, complemented
6#14521283C211yesmaximal, characteristic, complemented
7#14521280C211yesmaximal, characteristic, complemented
8#14521261C211yesmaximal, characteristic, complemented
9#14521194C211yesmaximal, characteristic, complemented
10#14521188C211yesmaximal, characteristic, complemented
11C4×#92481C211yesmaximal, characteristic, complemented
12D4×C31⋊C8C211yesmaximal, characteristic, complemented
13#14521045C211yesmaximal, characteristic, complemented
14C2×#11758423C211yesmaximal, characteristic, complemented
15C31×#548C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C22×Q8×C31C2211yescharacteristic
18C31×#124—21no—
19C31×#124C2211yescharacteristic
20C31×C22⋊Q8—21no—
21C31×C22⋊Q8C2211yescharacteristic
22C31×#121—21no—
23C31×#121C2211yescharacteristic
24C4×Q8×C31C2211yescharacteristic
25C4×D4×C31—21no—
26C4×D4×C31C2211yescharacteristic
27C2×#92481C2211yescharacteristic
28C2×#92481C2211yescharacteristic
29#11758516—21no—
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758507C2211yescharacteristic
33#11758503C2211yescharacteristic
34C2×C4⋊Dic31C2211yescharacteristic
35C22×C31⋊C8C2211yescharacteristic
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#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758420C2211yescharacteristic
51C22⋊(C31⋊C8)C2211yescharacteristic
52C22⋊(C31⋊C8)C2211yescharacteristic
53#11758397C2211yescharacteristic
54#11758396C2211yescharacteristic
55#11758396C2211yescharacteristic
56#11758395C2211yescharacteristic
57C4⋊(C31⋊C8)C2211yescharacteristic
58C4×C31⋊C8C2211yescharacteristic
59#41×C31—22no—
60#41×C31—41no—
61C2×Q8×C31—21no—
62C2×Q8×C31—22no—
63C2×Q8×C31—41no—
64C2×Q8×C31C2311yescharacteristic
65C2×Q8×C31C2311yescharacteristic
66C2×D4×C31—21no—
67C2×D4×C31—21no—
68C2×D4×C31D411yescharacteristic
69C2×D4×C31C2311yescharacteristic
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31C2311yescharacteristic
73C22×C4×C31C2311yescharacteristic
74C2×C22⋊D31—21no—
75C2×C22⋊D31—21no—
76C22×Dic31—21no—
77C2×D124C2311yescharacteristic
78C2×C4×D31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31D411yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
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#92481—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—
105C2×C31⋊C8—41no—
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31—21no—
112C23×C31C2×D411yescharacteristic
113C23×C31C2×D411yescharacteristic
114C22×D31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118Q8×C31—42no—
119Q8×C31#4112yes—
120D4×C31—22no—
121D4×C31—21no—
122D4×C31—21no—
123D4×C31—42no—
124D4×C31—42no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—42no—
133C2×C4×C31—42no—
134C2×C4×C31C2×D411yescharacteristic
135C2×C4×C31C2×D411yescharacteristic
136C2×C4×C31C2×D411yescharacteristic
137C2×C4×C31C2×D411yescharacteristic
138C2×C4×C31C2411yescharacteristic
139C22⋊D31—42no—
140C22⋊D31—81no—
141C2×Dic31—21no—
142C2×Dic31—21no—
143C2×Dic31—21no—
144C2×Dic31—81no—
145D124—21no—
146D124—21no—
147C4×D31—81no—
148C31⋊C8—21no—
149C31⋊C8—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3301—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31#13512yes—
162C22×C31C22×D411yescharacteristic
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—22no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31C2×#4111yescharacteristic
174C4×C31H(5,𝔽2)11yescharacteristic
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178#553—311no—
179#548D3111yescharacteristic, complemented
180#488—311no—
181#485—311no—
182#481—311no—
183#479—311no—
184#466—311no—
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—41no—
195C2×C31—81no—
196C2×C31#54611yescharacteristic
197C2×C31C2×#13511yescharacteristic
198C2×C31#57711yescharacteristic
199D31—81no—
200C2×#41C2×D3111yescharacteristic
201C22×Q8C2×D3111yescharacteristic
202C2×SD16—311no—
203C2×SD16—311no—
204C2×D8—311no—
205C22×C8—311no—
206C22×C8—311no—
207#126—621no—
208#125—311no—
209#124—21no—
210#124C2×D3111yescharacteristic
211#123—621no—
212C22⋊Q8—21no—
213C22⋊Q8C2×D3111yescharacteristic
214#121—21no—
215#121—311no—
216#121—311no—
217#121—621no—
218#121C2×D3111yescharacteristic
219C4×Q8C2×D3111yescharacteristic
220C4×D4—21no—
221C4×D4—311no—
222C4×D4—621no—
223C4×D4C2×D3111yescharacteristic
224#117—311no—
225C2×C4⋊C4—311no—
226#107—311no—
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#102—311no—
239#102—311no—
240C22⋊C8—311no—
241C22⋊C8—311no—
242C4×C8—311no—
243C31#330111yescharacteristic, complemented, Sylow
244#41—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D3111yescharacteristic
250C2×Q8C22×D3111yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—311no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4C22⋊D3111yescharacteristic
257C2×D4C22×D3111yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4C22×D3111yescharacteristic
263C22×C4C22×D3111yescharacteristic
264SD16—622no—
265SD16—1241no—
266D8—1241no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8—311no—
270C2×C8—311no—
271C2×C8—1241no—
272C2×C8—1241no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—311no—
276C4⋊C4—311no—
277C4⋊C4—311no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4C22⋊D3111yescharacteristic
282C4⋊C4C22×D3111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4C22⋊D3111yescharacteristic
292C22⋊C4C22⋊D3111yescharacteristic
293C42—21no—
294C42—621no—
295C42C22×D3111yescharacteristic
296C23—21no—
297C23—621no—
298C23C2×C22⋊D3111yescharacteristic
299C23C2×C22⋊D3111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#9249712yes—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—42no—
310D4—621no—
311D4—621no—
312D4—1242no—
313D4—2481no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—2481no—
327C2×C4—2481no—
328C2×C4C2×C22⋊D3111yescharacteristic
329C2×C4C2×C22⋊D3111yescharacteristic
330C2×C4C2×C22⋊D3111yescharacteristic
331C2×C4C2×C22⋊D3111yescharacteristic
332C2×C4C23×D3111yescharacteristic
333C8—621no—
334C8—621no—
335C8—621no—
336C8—621no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22#1175852712yes—
349C22C22×C22⋊D3111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—22no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—1241no—
358C4—1241no—
359C4—1241no—
360C4C2×#9249711yescharacteristic
361C4#1175856111yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—2481no—
366C2#1452169311yescharacteristic
367C2C2×#1175852711yescharacteristic
368C2#1452185711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#548C2
socleC22×C31C22×D4
hypercenter#548D31
hypocenterC31#3301
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14521745C2semidirect
2. #14521403C2semidirect
3. #14521387C2semidirect
4. #14521365C2semidirect
5. #14521356C2semidirect
6. #14521283C2semidirect
7. #14521280C2semidirect
8. #14521261C2semidirect
9. #14521194C2semidirect
10. #14521188C2semidirect
11. C4×#92481C2semidirect
12. D4×C31⋊C8C2semidirect
13. #14521045C2semidirect
14. C2×#11758423C2semidirect
15. C31×#548C2semidirect
179. #548D31semidirect
243. C31#3301semidirect

Maximal subgroups

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

subgroupindex
#145217452
#145214032
#145213872
#145213652
#145213562
#145212832
#145212802
#145212612
#145211942
#145211882
C4×#924812
D4×C31⋊C82
#145210452
C2×#117584232
C31×#5482
#330131