Finite Group Databasebeta

← #29574324

Subgroups — #29574324

Order 15616.

438 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#21454388C211yesmaximal, characteristic
2#21445836C211yesmaximal, characteristic
3#21444591C211yesmaximal, characteristic, complemented
4#21444202C211yesmaximal, characteristic
5#21443720C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C61×#1566C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9C4×#11758222C2211yescharacteristic
10#16839815C2211yescharacteristic
11#16839790—21no—
12#16839787—22no—
13#16839784—21no—
14C2×C4⋊#92418C2211yescharacteristic
15C4⋊C8×D61—21no—
16C2×#14519703—21no—
17C4×C4⋊Dic61C2211yescharacteristic
18#16839523—21no—
19#16839512—21no—
20#16839512—21no—
21#16839494C411yescharacteristic, complemented
22#16839494C411yescharacteristic, complemented
23#16839491C411yescharacteristic, complemented
24#16839491C411yescharacteristic, complemented
25C61×#423C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C61×#334—22no—
29C2×#11758222D411yescharacteristic
30#14519785—42no—
31#14519785—42no—
32C2×#11758189—22no—
33C22×#92418—21no—
34C2×C8×D61—22no—
35C4×Dic122C2×C411yescharacteristic
36C4×Dic122Q811yescharacteristic
37C4×D244C2×C411yescharacteristic
38C4×D244Q811yescharacteristic
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41#14519736D411yescharacteristic
42#14519734—21no—
43C2×C4⋊Dic61—21no—
44C2×C4×Dic61—21no—
45C42×D61—21no—
46C4⋊#92418—21no—
47C4⋊#92418C2×C411yescharacteristic
48C4⋊#92418C2×C411yescharacteristic
49C4⋊#92418D411yescharacteristic
50C4⋊#92418D411yescharacteristic
51#14519706—22no—
52#14519706—22no—
53#14519703—42no—
54C22⋊#92418—21no—
55C4×#92418—21no—
56#14519684—21no—
57C2×M16×C61—21no—
58C2×M16×C61—21no—
59C22×C8×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61D412yes—
65C4×C8×C61—21no—
66C4×C8×C61C2×C411yescharacteristic
67C4×C8×C61C2×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C2×C22⋊D61—21no—
72C22×Dic61—41no—
73#11758222—21no—
74#11758222—21no—
75#11758222SD1612yes—
76#11758222SD1612yes—
77C2×D244C4⋊C411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×Dic122C4⋊C411yescharacteristic
82M16×C61—41no—
83M16×C61—41no—
84M16×C61—41no—
85M16×C61—41no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61—22no—
89C2×C8×C61—42no—
90C2×C8×C61—41no—
91C42×C61C22×C411yescharacteristic
92C42×C61C2×D411yescharacteristic
93C42×C61C2×D411yescharacteristic
94C42×C61C2×Q811yescharacteristic
95C22⋊Dic61—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61—22no—
99C4⋊Dic61—41no—
100C4⋊Dic61C4⋊C411yescharacteristic
101C4⋊Dic61C4⋊C411yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—41no—
114C2×#92418—41no—
115#11758189—44no—
116C8×D61—44no—
117C23×C61#12311yescharacteristic
118C22×D61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61C2×C4⋊C411yescharacteristic
123C2×C4×C61C4×D411yescharacteristic
124C2×C4×C61C4×D411yescharacteristic
125C2×C4×C61#12011yescharacteristic
126C2×C4×C61C22⋊Q811yescharacteristic
127C2×C4×C61C22⋊Q811yescharacteristic
128C2×C4×C61C2×SD1611yescharacteristic
129C2×C4×C61C2×SD1611yescharacteristic
130C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C22⋊D61—22no—
133C22⋊D61—22no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140D244—21no—
141D244#10612yes—
142C4×D61—22no—
143C4×D61—22no—
144C4×D61—41no—
145C4×D61—41no—
146C4×D61—81no—
147Dic122—21no—
148Dic122#10612yes—
149C8×C61—22no—
150C8×C61—41no—
151C8×C61—42no—
152C8×C61—81no—
153#92418—41no—
154#92418—41no—
155#92418—41no—
156#92418—41no—
157#8904—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61#38511yescharacteristic
161C22×C61#48111yescharacteristic
162C22×C61#48311yescharacteristic
163C2×D61—22no—
164C2×D61—41no—
165C2×D61—41no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61C2×#10611yescharacteristic
170C4×C61#42811yescharacteristic
171C4×C61#44311yescharacteristic
172C4×C61#44411yescharacteristic
173C4×C61#44811yescharacteristic
174C4×C61#45011yescharacteristic
175Dic61—22no—
176Dic61—41no—
177Dic61—41no—
178Dic61—82no—
179#2906—611no—
180#1806—611no—
181#1570—611no—
182#1566D6111yescharacteristic, complemented
183#1476—611no—
184#1303—611no—
185#1279—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61#185311yescharacteristic
189C2×C61#186111yescharacteristic
190C2×C61#186611yescharacteristic
191D61—42no—
192C2×#131—1221no—
193C4×#41—611no—
194#431—611no—
195#424—1221no—
196#424—1222no—
197#423—1221no—
198#423C2×D6111yescharacteristic
199#423C2×D6111yescharacteristic
200C2×C4⋊C8—611no—
201C2×C4⋊C8—1221no—
202C2×#104—1221no—
203C2×C4×C8C2×D6111yescharacteristic
204C4×C4⋊C4—611no—
205#339—1221no—
206#334—22no—
207#334—1221no—
208#334—1221no—
209Q8⋊C8—611no—
210Q8⋊C8—611no—
211D4⋊C8—611no—
212D4⋊C8—611no—
213C61#890411yescharacteristic, complemented, Sylow
214C2×#41—611no—
215#131—2442no—
216#131—2442no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—1222no—
220C22×C8—21no—
221C22×C8—1222no—
222C22×C8—1221no—
223C4×Q8—611no—
224C4×Q8—611no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C4×D4—1221no—
229#117—611no—
230#117—1221no—
231C2×C4⋊C4—1221no—
232C2×C42—1221no—
233C2×C42—1221no—
234C2×C42C22×D6111yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—611no—
239C4⋊C8—611no—
240C4⋊C8—611no—
241C4⋊C8—611no—
242C4⋊C8—1222no—
243C4⋊C8—1222no—
244C4⋊C8—1221no—
245C4⋊C8C22⋊D6112yes—
246#104—2442no—
247C22⋊C8—1221no—
248C4×C8—21no—
249C4×C8—1221no—
250C4×C8C4×D6111yescharacteristic
251C4×C8C4×D6111yescharacteristic
252#95—1221no—
253#41—612no—
254#41—612no—
255#41—1221no—
256#41—1221no—
257C2×Q8—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—2441no—
264C22×C4#1175822211yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C22×C4#1175822611yescharacteristic
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—2444no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—22no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—2444no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—1222no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—2441no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—1221no—
294C42—1221no—
295C42—1221no—
296C42—2441no—
297C42—2441no—
298C42C2×C4×D6111yescharacteristic
299C42D4×D6111yescharacteristic
300C42Q8×D6111yescharacteristic
301C42C2×C22⋊D6111yescharacteristic
302C23—1221no—
303C23#1451976211yescharacteristic
304Q8—612no—
305Q8—1221no—
306D4—612no—
307D4—1222no—
308D4—1222no—
309D4—1221no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—1221no—
314C2×C4—1222no—
315C2×C4—1222no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—2442no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4C4⋊C4×D6111yescharacteristic
325C2×C4C4×C22⋊D6111yescharacteristic
326C2×C4#1451973911yescharacteristic
327C2×C4#1451974511yescharacteristic
328C2×C4#1451975311yescharacteristic
329C2×C4#1451975511yescharacteristic
330C2×C4SD16×D6111yescharacteristic
331C2×C4SD16×D6111yescharacteristic
332C2×C4#1451980411yescharacteristic
333C2×C4#1451980611yescharacteristic
334C8—22no—
335C8—41no—
336C8—42no—
337C8—81no—
338C8—2441no—
339C8—2441no—
340C8—2441no—
341C8—2441no—
342C22—21no—
343C22—21no—
344C22—1222no—
345C22—2441no—
346C22—2441no—
347C22#1683963311yescharacteristic
348C22#1684008211yescharacteristic
349C22#1684009411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—1222no—
354C4—4882no—
355C4—2441no—
356C4—2441no—
357C4#106×D6111yescharacteristic
358C4#1683980111yescharacteristic
359C4#1683987811yescharacteristic
360C4#1683988311yescharacteristic
361C4#1683989911yescharacteristic
362C4#1683991111yescharacteristic
363C2—21no—
364C2—21no—
365C2—2442no—
366C2#2144601011yescharacteristic
367C2#2144605811yescharacteristic
368C2#2144609111yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1566C2
socleC22×C61#385
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1566D61
hypocenterC61#8904
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
3. #21444591C2semidirect
5. #21443720C2semidirect
6. #21443659C2semidirect
7. C61×#1566C2semidirect
21. #16839494C4semidirect
22. #16839494C4semidirect
23. #16839491C4semidirect
24. #16839491C4semidirect
182. #1566D61semidirect
213. C61#8904semidirect

Maximal subgroups

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

subgroupindex
#214543882
#214458362
#214445912
#214442022
#214437202
#214436592
C61×#15662
#890461