Finite Group Databasebeta

← #29597266

Subgroups — #29597266

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×#16840197C211yesmaximal, characteristic
2C2×#16839574C211yesmaximal, characteristic, complemented
3C2×#16839572C211yesmaximal, characteristic, complemented
4#21446695C211yesmaximal, characteristic, complemented
5#21443919C211yesmaximal, characteristic, complemented
6#21443899C211yesmaximal, characteristic, complemented
7C2×C61×#444C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9#16840197—22no—
10#16840197—22no—
11C2×#14519720C412yescomplemented
12C2×#14519718C412yescomplemented
13C2×#14519717C2211yescharacteristic
14C2×#14519717C2211yescharacteristic
15C2×#14519709C2211yescharacteristic
16C2×#14519699—21no—
17#16839664—21no—
18#16839574—22no—
19#16839572—22no—
20C2×#135×C61C2211yescharacteristic
21C2×#131×C61—21no—
22C61×#444—22no—
23C61×#444—22no—
24C2×#108×C61C2211yescharacteristic
25C2×#104×C61—21no—
26C2×#97×C61C2211yescharacteristic
27C22×D244—21no—
28C2×D488—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488C2×C412yes—
34C2×C4⋊Dic61—21no—
35C2×#11758198—42no—
36#14519720—24no—
37#14519718—24no—
38#14519717—21no—
39#14519717—21no—
40#14519717—21no—
41#14519717—21no—
42C2×#11758185—21no—
43C2×#11758185C2×C412yes—
44#14519709—21no—
45#14519709—21no—
46#14519699—42no—
47C2×#41×C61—21no—
48#135×C61—21no—
49#135×C61—21no—
50#135×C61D412yes—
51#135×C61D412yes—
52C2×Q16×C61C2×C411yescharacteristic
53C2×SD16×C61—21no—
54C2×D8×C61C2×C411yescharacteristic
55#131×C61—24no—
56#131×C61—42no—
57C2×M16×C61—21no—
58C2×M16×C61—41no—
59C22×C8×C61—41no—
60C22×C8×C61D411yescharacteristic
61C22×C8×C61C2311yescharacteristic
62C2×C42×C61D411yescharacteristic
63#108×C61—21no—
64#108×C61D412yes—
65#104×C61—24no—
66#97×C61—21no—
67#97×C61—21no—
68C23×D61—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—41no—
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—41no—
80C2×D244—22no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86Q16×C61—21no—
87Q16×C61C22⋊C412yescomplemented
88SD16×C61—22no—
89SD16×C61—22no—
90D8×C61—21no—
91D8×C61C22⋊C412yescomplemented
92M16×C61—22no—
93M16×C61—44no—
94M16×C61—41no—
95C2×C8×C61—21no—
96C2×C8×C61—21no—
97C2×C8×C61—44no—
98C2×C8×C61—41no—
99C2×C8×C61D812yes—
100C2×C8×C61C22×C411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61C2×D411yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C2×C8×C61#4111yescharacteristic
106C42×C61—21no—
107C42×C61—21no—
108#11758198—84no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111D488—22no—
112D488—22no—
113D488—41no—
114D488—41no—
115#11758185—22no—
116#11758185—41no—
117C23×C61—41no—
118C23×C61AGL(1,ℤ/8)11yescharacteristic
119C22×D61—42no—
120C22×D61—82no—
121C22×D61—82no—
122C22×D61—81no—
123C22×D61—81no—
124Q8×C61—22no—
125Q8×C61—41no—
126D4×C61—22no—
127D4×C61—42no—
128D4×C61—42no—
129D4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61#12011yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61C2×D811yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×Dic61—82no—
142C2×Dic61—81no—
143D244—42no—
144D244—42no—
145D244—81no—
146D244—81no—
147C8×C61—22no—
148C8×C61—42no—
149C8×C61C2×C22⋊C411yescharacteristic
150C8×C61C4×D411yescharacteristic
151C8×C61#12111yescharacteristic
152C8×C61#12311yescharacteristic
153#13040—611nomaximal, Sylow
154C22×C61—22no—
155C22×C61—42no—
156C22×C61—82no—
157C22×C61#44211yescharacteristic
158C22×C61#44911yescharacteristic
159C22×C61#45911yescharacteristic
160C2×D61—82no—
161C2×D61—84no—
162C2×D61—161no—
163C2×D61—161no—
164C2×D61—162no—
165C4×C61—42no—
166C4×C61—81no—
167C4×C61#38611yescharacteristic
168C4×C61C4×D811yescharacteristic
169C4×C61#44711yescharacteristic
170C4×C61#46311yescharacteristic
171Dic61—161no—
172C2×#509—611no—
173C2×#444D6111yescharacteristic, complemented
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#187911yescharacteristic
183C2×C61AGL(1,ℤ/16)12yes—
184D61—162no—
185C2×#135C2×D6111yescharacteristic
186C22×D8—611no—
187C2×#131—21no—
188#509—1222no—
189#509—1222no—
190C2×SD32—612no—
191C2×D16—612no—
192C2×M32—611no—
193C2×M32—611no—
194#444—22no—
195#444—22no—
196C2×#108C2×D6111yescharacteristic
197C2×#106—611no—
198C2×#104—21no—
199C2×#102—1221no—
200C2×#97C2×D6111yescharacteristic
201#390—1221no—
202#361—1222no—
203#360—1222no—
204C61#1304011yescharacteristic, complemented, Sylow
205C2×#41—21no—
206C22×D4—1221no—
207#135—21no—
208#135—21no—
209#135D24412yes—
210#135C22⋊D6112yes—
211C2×Q16C4×D6111yescharacteristic
212C2×SD16—21no—
213C2×D8—612no—
214C2×D8—1221no—
215C2×D8—1221no—
216C2×D8—1221no—
217C2×D8—1221no—
218C2×D8—1221no—
219C2×D8C4×D6111yescharacteristic
220#131—24no—
221#131—42no—
222C2×M16—21no—
223C2×M16—41no—
224C22×C8—41no—
225C22×C8C22⋊D6111yescharacteristic
226C22×C8C22×D6111yescharacteristic
227C2×C4⋊C4—1221no—
228C2×C22⋊C4—2442no—
229C2×C42C22⋊D6111yescharacteristic
230SD32—1224no—
231D16—1224no—
232M32—1221no—
233M32—1221no—
234M32—1221no—
235M32—1221no—
236C2×C16—612no—
237C2×C16—1221no—
238#108—21no—
239#108C22⋊D6112yes—
240#106—1221no—
241#106—1221no—
242#104—24no—
243#102—2442no—
244#97—21no—
245#97—21no—
246C24—2441no—
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—41no—
254C2×D4—1222no—
255C2×D4—2441no—
256C2×D4—2441no—
257C2×D4—2441no—
258C2×D4—2441no—
259C2×D4—2441no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—2441no—
263C22×C4C2×C22⋊D6111yescharacteristic
264Q16—21no—
265Q16#1175819812yescomplemented
266SD16—22no—
267SD16—22no—
268D8—21no—
269D8—1222no—
270D8—1222no—
271D8—2441no—
272D8—2441no—
273D8#1175819812yescomplemented
274M16—22no—
275M16—44no—
276M16—41no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—44no—
280C2×C8—41no—
281C2×C8#1175819912yes—
282C2×C8C2×C4×D6111yescharacteristic
283C2×C8C2×D24411yescharacteristic
284C2×C8#1175822211yescharacteristic
285C2×C8#1175822211yescharacteristic
286C2×C8C2×C22⋊D6111yescharacteristic
287C2×C8C2×C22⋊D6111yescharacteristic
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C22⋊C4—4884no—
291C42—21no—
292C42—21no—
293C16—1222no—
294C16—2441no—
295C23—41no—
296C23—4882no—
297C23—4882no—
298C23—4881no—
299C23—4881no—
300C23—2442no—
301C23#1451980211yescharacteristic
302Q8—22no—
303Q8—41no—
304D4—22no—
305D4—42no—
306D4—42no—
307D4—41no—
308D4—4881no—
309D4—4881no—
310D4—2442no—
311D4—2442no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—4882no—
318C2×C4—4881no—
319C2×C4C4×C22⋊D6111yescharacteristic
320C2×C4#1451974611yescharacteristic
321C2×C4#1451975111yescharacteristic
322C2×C4C2×#1175819911yescharacteristic
323C2×C4#1451979711yescharacteristic
324C2×C4#1451980311yescharacteristic
325C8—22no—
326C8—42no—
327C8C2×#1175819811yescharacteristic
328C8C4×C22⋊D6111yescharacteristic
329C8#1451975111yescharacteristic
330C8#1451976011yescharacteristic
331C22—22no—
332C22—42no—
333C22—82no—
334C22—9762no—
335C22—9761no—
336C22—9761no—
337C22—4882no—
338C22—4884no—
339C22#1683987211yescharacteristic
340C22#1683990711yescharacteristic
341C22#1683995711yescharacteristic
342C4—42no—
343C4—81no—
344C4—9761no—
345C4#1683964111yescharacteristic
346C4C4×#1175819911yescharacteristic
347C4#1683989611yescharacteristic
348C4#1683997711yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2—9762no—
353C2#2144616711yescharacteristic
354C2#2144771712yes—
subgroupG/H
centerC22#16839872
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#444C2
socleC22×C61#442
prime radicalC2×#16840197C2
cosocleC22×C8×C61C23
hypercenterC2×#444D61
hypocenterC61#13040
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. C2×#16839574C2semidirect
3. C2×#16839572C2semidirect
4. #21446695C2semidirect
5. #21443919C2semidirect
6. #21443899C2semidirect
7. C2×C61×#444C2semidirect
11. C2×#14519720C4semidirect
12. C2×#14519718C4semidirect
87. Q16×C61C22⋊C4semidirect
91. D8×C61C22⋊C4semidirect
173. C2×#444D61semidirect
204. C61#13040semidirect
265. Q16#11758198semidirect
273. D8#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#168401972
C2×#168395742
C2×#168395722
#214466952
#214439192
#214438992
C2×C61×#4442
#1304061