Finite Group Databasebeta

← #29597268

Subgroups — #29597268

Order 15616.

508 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839884C211yesmaximal, characteristic, complemented
2C2×#16839575C211yesmaximal, characteristic, complemented
3C2×#16839572C211yesmaximal, characteristic, complemented
4#21446696C211yesmaximal, characteristic, complemented
5#21443918C211yesmaximal, characteristic, complemented
6#21443898C211yesmaximal, characteristic, complemented
7C2×C61×#509C211yesmaximal, characteristic
8C2×#14519784—21no—
9C2×#14519717C2211yescharacteristic
10#16839884—22no—
11#16839884—22no—
12C2×#14519713C2211yescharacteristic
13C2×#14519709C2211yescharacteristic
14C2×#14519704—21no—
15C2×#14519698—21no—
16C2×#14519687C2211yescharacteristic
17#16839665—21no—
18#16839575—22no—
19#16839572—22no—
20C2×#135×C61C2211yescharacteristic
21C22×D8×C61C2211yescharacteristic
22C61×#509—22no—
23C61×#509—22no—
24C2×SD32×C61C412yescomplemented
25C2×D16×C61C412yescomplemented
26C2×M32×C61C2211yescharacteristic
27#14519784—24no—
28#14519784—42no—
29C2×#11758194—21no—
30C2×#11758194—41no—
31C22×#92418—41no—
32C22×#92418D411yescharacteristic
33C2×C4⋊Dic61—21no—
34C2×C22⋊Dic61—42no—
35C2×C4×Dic61D411yescharacteristic
36#14519717—21no—
37#14519717—21no—
38C2×#11758185—21no—
39#14519713—21no—
40#14519713D412yes—
41#14519709—21no—
42#14519709—21no—
43#14519704—24no—
44#14519698—42no—
45#14519687—21no—
46#14519687—21no—
47C2×#41×C61—21no—
48C22×D4×C61—21no—
49#135×C61—21no—
50#135×C61—21no—
51#135×C61D412yes—
52#135×C61D412yes—
53C2×Q16×C61C2×C411yescharacteristic
54C2×SD16×C61—21no—
55C2×D8×C61—21no—
56C2×D8×C61—21no—
57C2×D8×C61—21no—
58C2×D8×C61—21no—
59C2×D8×C61—21no—
60C2×D8×C61C2×C412yes—
61C2×D8×C61C2×C411yescharacteristic
62C22×C8×C61C2311yescharacteristic
63SD32×C61—24no—
64D16×C61—24no—
65M32×C61—21no—
66M32×C61—21no—
67C2×C16×C61C2×C412yes—
68C24×C61—41no—
69#41×C61—22no—
70#41×C61—22no—
71#41×C61—41no—
72#41×C61—41no—
73C2×Q8×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61—22no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—41no—
86Q16×C61—21no—
87Q16×C61C22⋊C412yescomplemented
88SD16×C61—22no—
89SD16×C61—22no—
90D8×C61—22no—
91D8×C61—21no—
92D8×C61—22no—
93D8×C61—41no—
94D8×C61—41no—
95D8×C61C22⋊C412yescomplemented
96C2×C8×C61C22×C411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C2×C8×C61#4111yescharacteristic
102C22⋊Dic61—84no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107#11758194—22no—
108#11758194—44no—
109#11758194—41no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—44no—
113C2×#92418—41no—
114C2×#92418D812yes—
115C16×C61—22no—
116#11758185—41no—
117C23×C61—41no—
118C23×C61—42no—
119C23×C61—82no—
120C23×C61—82no—
121C23×C61—81no—
122C23×C61—81no—
123C23×C61AGL(1,ℤ/8)11yescharacteristic
124Q8×C61—22no—
125Q8×C61—41no—
126D4×C61—22no—
127D4×C61—42no—
128D4×C61—42no—
129D4×C61—42no—
130D4×C61—41no—
131D4×C61—42no—
132D4×C61—81no—
133D4×C61—81no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61#12011yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61C2×D811yescharacteristic
141C2×C4×C61#13511yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—82no—
146C2×Dic61—81no—
147C8×C61C2×C22⋊C411yescharacteristic
148C8×C61C4×D411yescharacteristic
149C8×C61#12111yescharacteristic
150C8×C61#12311yescharacteristic
151#92418—22no—
152#92418—42no—
153#13040—611nomaximal, Sylow
154C22×C61—22no—
155C22×C61—42no—
156C22×C61—82no—
157C22×C61—82no—
158C22×C61—84no—
159C22×C61—162no—
160C22×C61—161no—
161C22×C61—161no—
162C22×C61#44211yescharacteristic
163C22×C61#44911yescharacteristic
164C22×C61#45911yescharacteristic
165C4×C61—42no—
166C4×C61#38611yescharacteristic
167C4×C61C4×D811yescharacteristic
168C4×C61#44711yescharacteristic
169C4×C61#46311yescharacteristic
170Dic61—81no—
171Dic61—161no—
172C2×#509D6111yescharacteristic
173C2×#444—611no—
174C2×#361—611no—
175C2×#360—611no—
176#1972—611no—
177#1383—611no—
178#1375—611no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—82no—
182C2×C61—162no—
183C2×C61#187911yescharacteristic
184C2×C61AGL(1,ℤ/16)12yes—
185C2×#135C2×D6111yescharacteristic
186C22×D8C2×D6111yescharacteristic
187C2×#131—1221no—
188#509—22no—
189#509—22no—
190C2×SD32Dic6112yescomplemented
191C2×D16Dic6112yescomplemented
192C2×M32—611no—
193C2×M32C2×D6111yescharacteristic
194#444—1222no—
195#444—1222no—
196C2×#108—611no—
197C2×#106—611no—
198C2×#104—1221no—
199C2×#102—1221no—
200C2×#97—611no—
201#390—1221no—
202#361—1222no—
203#360—1222no—
204C61#1304011yescharacteristic, complemented, Sylow
205C2×#41—21no—
206C22×D4—21no—
207#135—21no—
208#135—21no—
209#135C22⋊D6112yes—
210#135C22⋊D6112yes—
211C2×Q16C2×Dic6111yescharacteristic
212C2×SD16—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8C2×Dic6112yes—
219C2×D8C2×Dic6111yescharacteristic
220#131—1224no—
221#131—2442no—
222C2×M16—1221no—
223C2×M16—2441no—
224C22×C8—611no—
225C22×C8—2441no—
226C22×C8C22×D6111yescharacteristic
227C2×C4⋊C4—1221no—
228C2×C22⋊C4—2442no—
229C2×C42—611no—
230SD32—24no—
231D16—24no—
232M32—21no—
233M32—21no—
234M32—1221no—
235M32—1221no—
236C2×C16—1221no—
237C2×C16C2×Dic6112yes—
238#108—612no—
239#108—1221no—
240#106—1221no—
241#106—1221no—
242#104—1224no—
243#102—2442no—
244#97—1221no—
245#97—1221no—
246C24—41no—
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4—1221no—
262C22×C4—2441no—
263C22×C4D4×D6111yescharacteristic
264Q16—21no—
265Q16C22⋊Dic6112yescomplemented
266SD16—22no—
267SD16—22no—
268D8—22no—
269D8—21no—
270D8—22no—
271D8—41no—
272D8—41no—
273D8C22⋊Dic6112yescomplemented
274M16—1222no—
275M16—2444no—
276M16—2441no—
277C2×C8—612no—
278C2×C8—1221no—
279C2×C8—1221no—
280C2×C8—2444no—
281C2×C8—2441no—
282C2×C8D4×D6111yescharacteristic
283C2×C8#1175822411yescharacteristic
284C2×C8#1175822411yescharacteristic
285C2×C8C22×Dic6111yescharacteristic
286C2×C8C2×C22⋊D6111yescharacteristic
287C2×C8C2×C22⋊D6111yescharacteristic
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C22⋊C4—4884no—
291C42—1221no—
292C42—1221no—
293C16—22no—
294C16—2441no—
295C23—41no—
296C23—42no—
297C23—82no—
298C23—82no—
299C23—81no—
300C23—81no—
301C23#1451980111yescharacteristic
302Q8—22no—
303Q8—41no—
304D4—22no—
305D4—42no—
306D4—42no—
307D4—41no—
308D4—42no—
309D4—42no—
310D4—81no—
311D4—81no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—4882no—
316C2×C4—4881no—
317C2×C4—2442no—
318C2×C4—2441no—
319C2×C4D4×Dic6111yescharacteristic
320C2×C4#1451974511yescharacteristic
321C2×C4#1451974911yescharacteristic
322C2×C4D8×D6111yescharacteristic
323C2×C4#1451979611yescharacteristic
324C2×C4#1451980111yescharacteristic
325C8—1222no—
326C8—2442no—
327C8C2×C22⋊Dic6111yescharacteristic
328C8D4×Dic6111yescharacteristic
329C8#1451974911yescharacteristic
330C8#1451975811yescharacteristic
331C22—22no—
332C22—42no—
333C22—82no—
334C22—82no—
335C22—84no—
336C22—161no—
337C22—161no—
338C22—162no—
339C22#1683987411yescharacteristic
340C22#1683990411yescharacteristic
341C22#1683995511yescharacteristic
342C4—42no—
343C4—9761no—
344C4—4881no—
345C4#1683964211yescharacteristic
346C4D8×Dic6111yescharacteristic
347C4#1683989411yescharacteristic
348C4#1683997511yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2—162no—
353C2#2144616911yescharacteristic
354C2#2144771812yes—
subgroupG/H
centerC22#16839874
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
Fitting, prime radicalC2×C61×#509C2
socleC22×C61#442
cosocleC22×C8×C61C23
hypercenterC2×#509D61
hypocenterC61#13040
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#16839884C2semidirect
2. C2×#16839575C2semidirect
3. C2×#16839572C2semidirect
4. #21446696C2semidirect
5. #21443918C2semidirect
6. #21443898C2semidirect
24. C2×SD32×C61C4semidirect
25. C2×D16×C61C4semidirect
87. Q16×C61C22⋊C4semidirect
95. D8×C61C22⋊C4semidirect
190. C2×SD32Dic61semidirect
191. C2×D16Dic61semidirect
204. C61#13040semidirect
265. Q16C22⋊Dic61semidirect
273. D8C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398842
C2×#168395752
C2×#168395722
#214466962
#214439182
#214438982
C2×C61×#5092
#1304061