Finite Group Databasebeta

← #16857445

Subgroups — #16857445

Order 3968.

482 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758493C211yesmaximal, characteristic, complemented
2C22×#92482C211yesmaximal, characteristic, complemented
3#14521710C211yesmaximal, characteristic, complemented
4#14521705C211yesmaximal, characteristic, complemented
5#14521430C211yesmaximal, characteristic, complemented
6#14521289C211yesmaximal, characteristic, complemented
7#14521283C211yesmaximal, characteristic, complemented
8#14521274C211yesmaximal, characteristic, complemented
9#14521269C211yesmaximal, characteristic, complemented
10#14521214C211yesmaximal, characteristic, complemented
11#14521208C211yesmaximal, characteristic, complemented
12#14521190C211yesmaximal, characteristic, complemented
13#14521141C211yesmaximal, characteristic, complemented
14(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
15C31×#448C211yesmaximal, characteristic, complemented
16C22×Q8×C31C2211yescharacteristic
17C2×#92499C2211yescharacteristic
18C2×#92497C2211yescharacteristic
19C22×Dic62C2211yescharacteristic
20C2×SD16×C31C2211yescharacteristic
21C2×SD16×C31C2211yescharacteristic
22C31×#121C2211yescharacteristic
23#11758524—21no—
24#11758524C2211yescharacteristic
25#11758523—21no—
26#11758523C2211yescharacteristic
27Q8×Dic31C2211yescharacteristic
28C2×#92482—24no—
29C2×#92482C2211yescharacteristic
30C2×#92482C2211yescharacteristic
31C2×#92482C2211yescharacteristic
32C2×#92482C2211yescharacteristic
33#11758516—21no—
34#11758513C2211yescharacteristic
35D4×Dic31—21no—
36C2×#92479C2211yescharacteristic
37#11758507—21no—
38#11758507C2211yescharacteristic
39C4×C22⋊D31—21no—
40C4×C22⋊D31C2211yescharacteristic
41C22×C31⋊C8C2211yescharacteristic
42#11758493—24no—
43C2×#92470C2211yescharacteristic
44C2×#92470C2211yescharacteristic
45C2×C8×D31C2211yescharacteristic
46#11758474C2211yescharacteristic
47#11758464C2211yescharacteristic
48#11758462—21no—
49#11758455—21no—
50C31×#103C2211yescharacteristic
51C31×#103C2211yescharacteristic
52C31×C22⋊C8C2211yescharacteristic
53#11758420C2211yescharacteristic
54(C2×D31)⋊C8C2211yescharacteristic
55#11758404C2211yescharacteristic
56#11758404C2211yescharacteristic
57Dic31⋊C8C2211yescharacteristic
58C8×Dic31C2211yescharacteristic
59#11758397C2211yescharacteristic
60#11758395C2211yescharacteristic
61C2×Q8×C31—21no—
62C2×Q8×C31—22no—
63C2×Q8×C31—41no—
64C2×Q8×C31C2311yescharacteristic
65C2×Q8×C31C2311yescharacteristic
66C2×D4×C31—21no—
67C2×D4×C31C2311yescharacteristic
68C22×C4×C31—21no—
69C22×C4×C31C2311yescharacteristic
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31D411yescharacteristic
73C22×Dic31—21no—
74C22×Dic31—21no—
75#92499—22no—
76#92499—41no—
77#92497—22no—
78#92497—41no—
79C2×D124—21no—
80C2×D124C2311yescharacteristic
81C2×C4×D31—21no—
82C2×C4×D31C2311yescharacteristic
83C2×Dic62—22no—
84C2×Dic62—21no—
85C2×Dic62—41no—
86C2×Dic62C2311yescharacteristic
87C2×Dic62C2311yescharacteristic
88SD16×C31—22no—
89SD16×C31—41no—
90C2×C8×C31C2311yescharacteristic
91C2×C8×C31C2311yescharacteristic
92C4⋊C4×C31C2311yescharacteristic
93C22⋊C4×C31—21no—
94C22⋊Dic31—21no—
95C22⋊Dic31—21no—
96C22⋊Dic31D411yescharacteristic
97#92482—22no—
98#92482—22no—
99#92482—22no—
100#92482D414yescomplemented
101#92479—22no—
102(C2×D31)⋊C4—21no—
103(C2×D31)⋊C4—21no—
104(C2×D31)⋊C4—21no—
105(C2×D31)⋊C4—21no—
106(C2×D31)⋊C4—21no—
107(C2×D31)⋊C4D411yescharacteristic
108C4⋊Dic31—21no—
109C4⋊Dic31—21no—
110C4⋊Dic31C2311yescharacteristic
111Dic31⋊C4—21no—
112Dic31⋊C4—21no—
113Dic31⋊C4D411yescharacteristic
114C4×Dic31—21no—
115C4×Dic31—21no—
116C4×Dic31C2311yescharacteristic
117C2×C31⋊C8—22no—
118C2×C31⋊C8C2311yescharacteristic
119C2×C31⋊C8C2311yescharacteristic
120#92470—22no—
121#92470—41no—
122C8×D31—22no—
123C23×C31—21no—
124C23×C31C2×D411yescharacteristic
125C22×D31—21no—
126C22×D31C2×D411yescharacteristic
127Q8×C31—21no—
128Q8×C31—21no—
129Q8×C31—21no—
130Q8×C31—42no—
131Q8×C31C2×D412yes—
132D4×C31—21no—
133D4×C31—21no—
134D4×C31—42no—
135C2×C4×C31—21no—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—42no—
141C2×C4×C31C2×D411yescharacteristic
142C2×C4×C31C2411yescharacteristic
143C22⋊D31—22no—
144C22⋊D31—42no—
145C22⋊D31—42no—
146C2×Dic31—21no—
147C2×Dic31—21no—
148C2×Dic31—21no—
149C2×Dic31—42no—
150C2×Dic31—42no—
151C2×Dic31C2×D411yescharacteristic
152C2×Dic31C2×D411yescharacteristic
153C2×Dic31C2×D411yescharacteristic
154D124—21no—
155D124—21no—
156D124—42no—
157C4×D31—21no—
158C4×D31—21no—
159C4×D31—42no—
160Dic62—21no—
161Dic62—21no—
162Dic62—21no—
163Dic62—42no—
164Dic62C2×D412yes—
165C8×C31—21no—
166C8×C31—21no—
167C31⋊C8—21no—
168C31⋊C8C2×D412yes—
169#3285—311nomaximal, Sylow
170C22×C31—21no—
171C22×C31—21no—
172C22×C31—41no—
173C22×C31—41no—
174C22×C31—41no—
175C22×C31#13512yescomplemented
176C22×C31C22×D411yescharacteristic
177C2×D31—21no—
178C2×D31—21no—
179C2×D31—21no—
180C2×D31—41no—
181C2×D31—41no—
182C2×D31—41no—
183C4×C31—21no—
184C4×C31—22no—
185C4×C31—41no—
186C4×C31—41no—
187C4×C31C22×D411yescharacteristic
188C4×C31H(5,𝔽2)11yescharacteristic
189Dic31—22no—
190Dic31—21no—
191Dic31—21no—
192Dic31—21no—
193Dic31—41no—
194Dic31—41no—
195C2×#135—311no—
196C22×Q16—311no—
197#548—311no—
198#548—311no—
199#495—311no—
200#467—311no—
201#466—311no—
202#464—311no—
203#464—311no—
204#452—311no—
205#452—311no—
206#448—311no—
207#448D3111yescharacteristic, complemented
208C4×Q16—311no—
209C8×D4—311no—
210C2×C31—22no—
211C2×C31—81no—
212C2×C31D4211yescharacteristic
213C2×C31C2×#13511yescharacteristic
214C2×C31#57811yescharacteristic
215D31—41no—
216D31—81no—
217C2×#41—311no—
218C2×#41—311no—
219C22×Q8—311no—
220C22×Q8C2×D3111yescharacteristic
221#135—624no—
222C2×Q16—311no—
223C2×Q16—311no—
224C2×Q16—311no—
225C2×Q16—311no—
226C2×Q16—624no—
227C2×SD16—311no—
228C2×SD16—311no—
229C2×SD16C2×D3111yescharacteristic
230C2×SD16C2×D3111yescharacteristic
231C2×D8—311no—
232C22×C8—311no—
233C22×C8—311no—
234#124—311no—
235#124—311no—
236#124—621no—
237#124—621no—
238C22⋊Q8—311no—
239C22⋊Q8—311no—
240C22⋊Q8—621no—
241C22⋊Q8—621no—
242#121—311no—
243#121—621no—
244#121—621no—
245#121C2×D3111yescharacteristic
246C4×Q8—311no—
247C4×Q8—311no—
248C4×D4—311no—
249C4×D4—621no—
250C4×D4—621no—
251#107—311no—
252C4⋊C8—311no—
253#103—311no—
254#103—311no—
255#103C2×D3111yescharacteristic
256#103C2×D3111yescharacteristic
257#102—311no—
258#102—311no—
259C22⋊C8—311no—
260C22⋊C8C2×D3111yescharacteristic
261C4×C8—311no—
262C31#328511yescharacteristic, complemented, Sylow
263#41—622no—
264#41—622no—
265#41—1241no—
266#41—1241no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—311no—
271C2×Q8—311no—
272C2×Q8—622no—
273C2×Q8—621no—
274C2×Q8—1241no—
275C2×Q8C22×D3111yescharacteristic
276C2×Q8C22×D3111yescharacteristic
277C2×D4—21no—
278C2×D4—311no—
279C2×D4—311no—
280C2×D4—621no—
281C2×D4—621no—
282C2×D4—621no—
283C2×D4C22×D3111yescharacteristic
284C22×C4—21no—
285C22×C4—311no—
286C22×C4—621no—
287C22×C4—621no—
288C22×C4—621no—
289C22×C4C22×D3111yescharacteristic
290Q16—314no—
291Q16—622no—
292Q16—622no—
293Q16—622no—
294SD16—22no—
295SD16—41no—
296SD16—622no—
297SD16—1241no—
298D8—622no—
299C2×C8—311no—
300C2×C8—311no—
301C2×C8—622no—
302C2×C8—622no—
303C2×C8C22×D3111yescharacteristic
304C2×C8C22×D3111yescharacteristic
305C4⋊C4—311no—
306C4⋊C4—311no—
307C4⋊C4—621no—
308C4⋊C4—621no—
309C4⋊C4—621no—
310C4⋊C4—621no—
311C4⋊C4C22×D3111yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—311no—
314C22⋊C4—311no—
315C22⋊C4—621no—
316C22⋊C4—621no—
317C22⋊C4—621no—
318C22⋊C4—621no—
319C22⋊C4—621no—
320C22⋊C4—621no—
321C22⋊C4—621no—
322C42—311no—
323C42—621no—
324C42—621no—
325C23—21no—
326C23—311no—
327C23—621no—
328C23D4×D3111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—312no—
334Q8—621no—
335Q8—621no—
336Q8—621no—
337Q8—1242no—
338Q8D4×D3112yes—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—622no—
343D4—621no—
344D4—621no—
345D4—1242no—
346D4—1242no—
347D4—1242no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—311no—
355C2×C4—311no—
356C2×C4—311no—
357C2×C4—621no—
358C2×C4—621no—
359C2×C4—621no—
360C2×C4—621no—
361C2×C4—621no—
362C2×C4—1242no—
363C2×C4—1242no—
364C2×C4—1242no—
365C2×C4D4×D3111yescharacteristic
366C2×C4C23×D3111yescharacteristic
367C8—21no—
368C8—21no—
369C8—312no—
370C8—621no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—621no—
377C22—621no—
378C22—621no—
379C22—1241no—
380C22—1241no—
381C22—1241no—
382C22#1175849312yescomplemented
383C22C2×D4×D3111yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—621no—
389C4—621no—
390C4—622no—
391C4—621no—
392C4—1241no—
393C4—1241no—
394C4C2×D4×D3111yescharacteristic
395C4#1175856111yescharacteristic
396C2—22no—
397C2—81no—
398C2—1241no—
399C2—2481no—
400C2#1452168111yescharacteristic
401C2C2×#1175849311yescharacteristic
402C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#448C2
socleC22×C31C22×D4
hypercenter#448D31
hypocenterC31#3285
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#11758493C2semidirect
2. C22×#92482C2semidirect
3. #14521710C2semidirect
4. #14521705C2semidirect
5. #14521430C2semidirect
6. #14521289C2semidirect
7. #14521283C2semidirect
8. #14521274C2semidirect
9. #14521269C2semidirect
10. #14521214C2semidirect
11. #14521208C2semidirect
12. #14521190C2semidirect
13. #14521141C2semidirect
14. (C22⋊D31)⋊C8C2semidirect
15. C31×#448C2semidirect
100. #92482D4semidirect
175. C22×C31#135semidirect
207. #448D31semidirect
262. C31#3285semidirect
382. C22#11758493semidirect

Maximal subgroups

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

subgroupindex
C2×#117584932
C22×#924822
#145217102
#145217052
#145214302
#145212892
#145212832
#145212742
#145212692
#145212142
#145212082
#145211902
#145211412
(C22⋊D31)⋊C82
C31×#4482
#328531