Finite Group Databasebeta

← #29596563

Subgroups — #29596563

Order 15616.

420 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D61C211yesmaximal, characteristic
2C2×#16839584C211yesmaximal, characteristic, complemented
3#21447429C211yesmaximal, characteristic
4#21445841C211yesmaximal, characteristic
5#21443919C211yesmaximal, characteristic, complemented
6#21443918C211yesmaximal, characteristic, complemented
7C2×C61×#365C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C22×C8×D61C2211yescharacteristic
10C2×#14519717C2211yescharacteristic
11C2×#14519713C2211yescharacteristic
12C2×#14519712—21no—
13#108×D61—22no—
14#108×D61—22no—
15C2×#14519709C2211yescharacteristic
16#16839619—21no—
17#16839584—22no—
18#16839541C412yescomplemented
19#16839541C412yescomplemented
20#16839524—21no—
21C2×M32×C61C2211yescharacteristic
22C2×#108×C61C2211yescharacteristic
23C2×#106×C61C2211yescharacteristic
24C61×#365—22no—
25C22×C4×D61D411yescharacteristic
26C2×#11758194—21no—
27C2×#11758189—41no—
28M16×D61—24no—
29M16×D61—42no—
30C22×#92418D411yescharacteristic
31C2×C8×D61—21no—
32C2×C8×D61—21no—
33C2×C8×D61—21no—
34C2×C8×D61—21no—
35C2×C8×D61—41no—
36C2×C8×D61C2×C411yescharacteristic
37C2×C8×D61C2×C411yescharacteristic
38C2×C8×D61Q811yescharacteristic
39C2×C8×D61Q811yescharacteristic
40C2×C4⋊Dic61—21no—
41C2×#11758198—41no—
42#14519717—21no—
43#14519717—21no—
44C2×#11758185C2×C412yes—
45#14519713—21no—
46#14519713D412yes—
47#14519712—24no—
48#14519709—21no—
49#14519709—21no—
50#14519684—41no—
51C2×M16×C61—21no—
52C22×C8×C61C2311yescharacteristic
53C2×C4⋊C4×C61—21no—
54M32×C61—21no—
55M32×C61—21no—
56C2×C16×C61C2×C412yes—
57#108×C61—21no—
58#108×C61D412yes—
59#106×C61—21no—
60#106×C61—21no—
61C23×D61SD1611yescharacteristic
62C22×C4×C61—41no—
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—41no—
65C22×Dic61SD1611yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61C4⋊C411yescharacteristic
71C2×C4×D61C4⋊C411yescharacteristic
72C2×C4×D61SD1611yescharacteristic
73C2×C4×D61SD1611yescharacteristic
74M16×C61—22no—
75M16×C61—41no—
76C2×C8×C61—41no—
77C2×C8×C61C22×C411yescharacteristic
78C2×C8×C61C2×D411yescharacteristic
79C2×C8×C61C2×D411yescharacteristic
80C2×C8×C61C2×Q811yescharacteristic
81C2×C8×C61#4111yescharacteristic
82C2×C8×C61#4111yescharacteristic
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85#11758198—82no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88#11758194—22no—
89#11758194—41no—
90C2×#92418—21no—
91C2×#92418—21no—
92C2×#92418—41no—
93C2×#92418C4⋊C411yescharacteristic
94C2×#92418C4⋊C411yescharacteristic
95#11758189—44no—
96C8×D61—21no—
97C8×D61—21no—
98C8×D61—21no—
99C8×D61—21no—
100C8×D61—21no—
101C8×D61—21no—
102C8×D61—21no—
103C8×D61—21no—
104C8×D61—44no—
105C16×C61—22no—
106#11758185—22no—
107C23×C61C2×SD1611yescharacteristic
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—22no—
111C22×D61—41no—
112C22×D61#10611yescharacteristic
113C22×D61#10611yescharacteristic
114C2×C4×C61—81no—
115C2×C4×C61—81no—
116C2×C4×C61—81no—
117C2×C4×C61C2×C4⋊C411yescharacteristic
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61#12311yescharacteristic
120C2×C4×C61C2×SD1611yescharacteristic
121C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C61#13711yescharacteristic
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—81no—
126C2×Dic61—81no—
127C2×Dic61—81no—
128C2×Dic61#10611yescharacteristic
129C2×Dic61#10611yescharacteristic
130C4×D61—21no—
131C4×D61—21no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—21no—
138C8×C61—42no—
139C8×C61C4×D411yescharacteristic
140C8×C61C4×D411yescharacteristic
141C8×C61C22⋊Q811yescharacteristic
142C8×C61C22⋊Q811yescharacteristic
143#92418—21no—
144#92418—21no—
145#92418—42no—
146#12928—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—21no—
149C22×C61C2×#10611yescharacteristic
150C22×C61#44811yescharacteristic
151C22×C61#48111yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—42no—
158C2×D61—42no—
159C2×D61#36512yescomplemented
160C4×C61—161no—
161C4×C61#38511yescharacteristic
162C4×C61#42811yescharacteristic
163C4×C61#45011yescharacteristic
164C4×C61#48311yescharacteristic
165Dic61—21no—
166Dic61—21no—
167Dic61—161no—
168C22×#108—611no—
169C2×#365—611no—
170C2×#365D6111yescharacteristic, complemented
171#2112—611no—
172#1807—611no—
173#1383—611no—
174#1383—611no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61#185311yescharacteristic
178C2×C61C2×#36511yescharacteristic
179C2×C61#215511yescharacteristic
180D61—22no—
181D61—41no—
182C22×M16—1221no—
183C23×C8—611no—
184C2×M32—611no—
185C2×M32C2×D6111yescharacteristic
186C2×#108—611no—
187C2×#108—1222no—
188C2×#108—1221no—
189C2×#108—1222no—
190C2×#108C2×D6111yescharacteristic
191C2×#106—611no—
192C2×#106C2×D6111yescharacteristic
193#380—1221no—
194#365—22no—
195#365—1222no—
196C22⋊C16—612no—
197C22⋊C16—612no—
198#340—1221no—
199C61#1292811yescharacteristic, complemented, Sylow
200C23×C4—611no—
201C2×M16—21no—
202C2×M16—1224no—
203C2×M16—1221no—
204C2×M16—2441no—
205C2×M16—2442no—
206C22×C8—611no—
207C22×C8—611no—
208C22×C8—611no—
209C22×C8—611no—
210C22×C8—611no—
211C22×C8—1221no—
212C22×C8—1221no—
213C22×C8—1221no—
214C22×C8—1221no—
215C22×C8—2441no—
216C22×C8C22×D6111yescharacteristic
217C2×C4⋊C4—21no—
218C2×C4⋊C4—1221no—
219C2×C22⋊C4—2441no—
220M32—21no—
221M32—21no—
222M32—1221no—
223M32—1221no—
224C2×C16—612no—
225C2×C16C4×D6112yes—
226#108—21no—
227#108—612no—
228#108—1224no—
229#108—1221no—
230#108C22⋊D6112yes—
231#106—21no—
232#106—21no—
233#106—1221no—
234#106—1221no—
235#95—2441no—
236C24—611no—
237C22×C4—41no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—2441no—
248C22×C4D4×D6111yescharacteristic
249M16—22no—
250M16—41no—
251M16—1222no—
252M16—2444no—
253M16—2441no—
254C2×C8—41no—
255C2×C8—611no—
256C2×C8—611no—
257C2×C8—1221no—
258C2×C8—1221no—
259C2×C8—1221no—
260C2×C8—1221no—
261C2×C8—1221no—
262C2×C8—1221no—
263C2×C8—1221no—
264C2×C8—1221no—
265C2×C8—1221no—
266C2×C8—1221no—
267C2×C8—2444no—
268C2×C8—2441no—
269C2×C8C2×C4×D6111yescharacteristic
270C2×C8#1175822211yescharacteristic
271C2×C8D4×D6111yescharacteristic
272C2×C8Q8×D6111yescharacteristic
273C2×C8#1175822611yescharacteristic
274C2×C8C2×C22⋊D6111yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C22⋊C4—4882no—
280C16—22no—
281C16—1222no—
282C23—611no—
283C23—611no—
284C23—1222no—
285C23—1221no—
286C23—1221no—
287C23—2441no—
288C23SD16×D6111yescharacteristic
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—4881no—
305C2×C4—4881no—
306C2×C4—4881no—
307C2×C4C4⋊C4×D6111yescharacteristic
308C2×C4#1451974511yescharacteristic
309C2×C4#1451976211yescharacteristic
310C2×C4SD16×D6111yescharacteristic
311C2×C4#1451980411yescharacteristic
312C2×C4#1451980611yescharacteristic
313C8—42no—
314C8—1221no—
315C8—1221no—
316C8—2442no—
317C8C4×C22⋊D6111yescharacteristic
318C8#1451973911yescharacteristic
319C8#1451975311yescharacteristic
320C8#1451975511yescharacteristic
321C22—21no—
322C22—21no—
323C22—612no—
324C22—1221no—
325C22—1221no—
326C22—1221no—
327C22—1221no—
328C22—1221no—
329C22—2442no—
330C22—2442no—
331C22#106×D6111yescharacteristic
332C22#1683989911yescharacteristic
333C22#1684008211yescharacteristic
334C4—161no—
335C4—1221no—
336C4—1221no—
337C4—9761no—
338C4#1683963311yescharacteristic
339C4#1683980111yescharacteristic
340C4#1683991111yescharacteristic
341C4#1684009411yescharacteristic
342C2—21no—
343C2—21no—
344C2—1222no—
345C2—2441no—
346C2#2144601011yescharacteristic
347C2#365×D6111yescharacteristic
348C2#2144759011yescharacteristic
subgroupG/H
centerC22#106×D61
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#365C2
socleC22×C61C2×#106
prime radicalC23×D61SD16
cosocleC22×C8×C61C23
hypercenterC2×#365D61
hypocenterC61#12928
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
2. C2×#16839584C2semidirect
5. #21443919C2semidirect
6. #21443918C2semidirect
7. C2×C61×#365C2semidirect
18. #16839541C4semidirect
19. #16839541C4semidirect
159. C2×D61#365semidirect
170. C2×#365D61semidirect
199. C61#12928semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D612
C2×#168395842
#214474292
#214458412
#214439192
#214439182
C2×C61×#3652
#1292861