Finite Group Databasebeta

← #29597455

Subgroups — #29597455

Order 15616.

478 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×#16840032C211yesmaximal, characteristic
2C2×#16839576C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic, complemented
4#21445883C211yesmaximal, characteristic, complemented
5#21443928C211yesmaximal, characteristic, complemented
6#21443913C211yesmaximal, characteristic, complemented
7C2×C61×#504C211yesmaximal, characteristic, complemented
8C2×#14519802—21no—
9C22×D488C2211yescharacteristic
10#16840032—22no—
11#16840032C414yescomplemented
12C2×#14519713C2211yescharacteristic
13C2×#14519713C2211yescharacteristic
14C2×#14519711C2211yescharacteristic
15#16839763—21no—
16C2×#14519693—21no—
17#16839576—22no—
18#16839564—21no—
19#16839564—21no—
20#16839530—21no—
21C2×#131×C61C2211yescharacteristic
22C61×#504—22no—
23C61×#504—22no—
24C2×M32×C61—21no—
25C2×M32×C61C2211yescharacteristic
26C22×C16×C61—21no—
27C22×C16×C61C2211yescharacteristic
28C22×D244—21no—
29#14519802—24no—
30#14519802—42no—
31C2×#11758201—41no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488—21no—
37C2×D488C2×C412yes—
38C2×#11758199—41no—
39C2×#11758194—21no—
40C2×#11758194—21no—
41C2×C4⋊Dic61—21no—
42#14519713—21no—
43#14519713—21no—
44#14519713—21no—
45#14519713C2×C412yes—
46#14519711—21no—
47#14519711—21no—
48#14519701—41no—
49#14519698—41no—
50#14519693—24no—
51C2×#41×C61D411yescharacteristic
52#131×C61—21no—
53#131×C61—21no—
54#131×C61C2×C412yes—
55#131×C61D412yes—
56C2×M16×C61—21no—
57C2×M16×C61D411yescharacteristic
58C22×C8×C61—21no—
59C22×C8×C61C2311yescharacteristic
60M32×C61—24no—
61M32×C61—21no—
62M32×C61D412yes—
63C2×C16×C61—24no—
64C2×C16×C61—21no—
65C2×C16×C61—21no—
66C2×C16×C61—21no—
67C2×C16×C61D411yescharacteristic
68C2×C16×C61D411yescharacteristic
69C23×D61—41no—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61C22⋊C412yes—
73#41×C61SD1612yes—
74C2×Q8×C61D811yescharacteristic
75C2×D4×C61—21no—
76C2×D4×C61D811yescharacteristic
77C22×C4×C61—21no—
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—
86M16×C61—21no—
87M16×C61—22no—
88M16×C61—22no—
89M16×C61C22⋊C412yes—
90C2×C8×C61—21no—
91C2×C8×C61—22no—
92C2×C8×C61—22no—
93C2×C8×C61C22×C411yescharacteristic
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C2×C8×C61#4111yescharacteristic
99#11758201—44no—
100#11758199—44no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103#11758194—22no—
104#11758194—41no—
105#11758194—41no—
106#11758194—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109D488—22no—
110D488—22no—
111D488—41no—
112D488—41no—
113C16×C61—21no—
114C16×C61—22no—
115C16×C61—21no—
116C23×C61—21no—
117C23×C61#13511yescharacteristic
118C22×D61—42no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61—161no—
122C22×D61—161no—
123Q8×C61—21no—
124Q8×C61#10212yes—
125D4×C61—22no—
126D4×C61—22no—
127D4×C61—21no—
128D4×C61#10212yes—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61C2×D811yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×Dic61—81no—
139C2×Dic61—161no—
140D244—42no—
141D244—42no—
142D244—81no—
143D244—81no—
144C8×C61—22no—
145C8×C61C4×D411yescharacteristic
146C8×C61C4×D411yescharacteristic
147C8×C61#12011yescharacteristic
148C8×C61#12311yescharacteristic
149#92418—42no—
150#92418—81no—
151#13073—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—22no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61#41611yescharacteristic
158C22×C61#46511yescharacteristic
159C22×C61#46611yescharacteristic
160C2×D61—82no—
161C2×D61—162no—
162C2×D61—161no—
163C2×D61—161no—
164C2×D61—162no—
165C4×C61—22no—
166C4×C61#38611yescharacteristic
167C4×C61C2×#10211yescharacteristic
168C4×C61#46511yescharacteristic
169C4×C61#46611yescharacteristic
170Dic61—161no—
171C2×#504D6111yescharacteristic, complemented
172C2×#472—611no—
173C2×#361—611no—
174C2×#357—611no—
175#1816—611no—
176#1387—611no—
177#1381—611no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—42no—
181C2×C61#189311yescharacteristic
182C2×C61#222111yescharacteristic
183C2×C61#222311yescharacteristic
184D61—162no—
185C2×AGL(1,ℤ/8)—1221no—
186C22×D8—611no—
187C2×#131C2×D6111yescharacteristic
188#504—22no—
189#504—22no—
190C2×M32—21no—
191C2×M32C2×D6111yescharacteristic
192C22×C16—21no—
193C22×C16C2×D6111yescharacteristic
194#472—614no—
195#472—1222no—
196C2×#108—611no—
197C2×#108—611no—
198C2×#107—611no—
199#417—1221no—
200C2×#100—1221no—
201#361—1222no—
202#357—1221no—
203#357—1221no—
204#343—1221no—
205C61#1307311yescharacteristic, complemented, Sylow
206C2×#41D24411yescharacteristic
207C22×D4—1221no—
208AGL(1,ℤ/8)—1224no—
209AGL(1,ℤ/8)—2442no—
210C2×SD16—2441no—
211C2×D8—612no—
212C2×D8—1221no—
213C2×D8—1221no—
214C2×D8—1221no—
215C2×D8—1221no—
216C2×D8—1221no—
217C2×D8—2441no—
218#131—21no—
219#131—21no—
220#131C4×D6112yes—
221#131C22⋊D6112yes—
222C2×M16—21no—
223C2×M16—1221no—
224C2×M16—1221no—
225C2×M16D24411yescharacteristic
226C22×C8—21no—
227C22×C8C22×D6111yescharacteristic
228C2×C4⋊C4—1221no—
229M32—24no—
230M32—21no—
231M32C22⋊D6112yes—
232C2×C16—24no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16C22⋊D6111yescharacteristic
237C2×C16C22⋊D6111yescharacteristic
238#108—612no—
239#108—1221no—
240#108—1221no—
241#108—1221no—
242#107—1221no—
243#107—1221no—
244#103—2441no—
245#102—2441no—
246#100—1224no—
247C24—2441no—
248#41—21no—
249#41—21no—
250#41#1175819012yes—
251#41#1175819812yes—
252C2×Q8D48811yescharacteristic
253C2×D4—21no—
254C2×D4—1222no—
255C2×D4—2441no—
256C2×D4—2441no—
257C2×D4—2441no—
258C2×D4—2441no—
259C2×D4—2441no—
260C2×D4D48811yescharacteristic
261C22×C4—21no—
262C22×C4—2441no—
263C22×C4C2×D24411yescharacteristic
264SD16—2444no—
265D8—1222no—
266D8—1222no—
267D8—2444no—
268D8—2441no—
269D8—2441no—
270M16—21no—
271M16—22no—
272M16—22no—
273M16—1222no—
274M16—2441no—
275M16—2441no—
276M16—2441no—
277M16#1175819812yes—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—2441no—
282C2×C8—2441no—
283C2×C8C2×C4×D6111yescharacteristic
284C2×C8#1175822211yescharacteristic
285C2×C8#1175822211yescharacteristic
286C2×C8C2×C22⋊D6111yescharacteristic
287C2×C8C2×C22⋊D6111yescharacteristic
288C2×C8C2×C22⋊D6111yescharacteristic
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C16—21no—
292C16—22no—
293C16—21no—
294C23—21no—
295C23—9761no—
296C23—9761no—
297C23—4881no—
298C23—4881no—
299C23—2442no—
300C23#1451979911yescharacteristic
301Q8—21no—
302Q8#1451969912yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—4881no—
307D4—4881no—
308D4—2442no—
309D4—2442no—
310D4#1451969912yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—9761no—
315C2×C4—4881no—
316C2×C4C2×#1175819811yescharacteristic
317C2×C4#1451975111yescharacteristic
318C2×C4#1451975111yescharacteristic
319C2×C4C2×D48811yescharacteristic
320C2×C4C2×#1175819011yescharacteristic
321C2×C4#1451979911yescharacteristic
322C8—22no—
323C8—4881no—
324C8—2442no—
325C8C4×C22⋊D6111yescharacteristic
326C8C4×C22⋊D6111yescharacteristic
327C8#1451974611yescharacteristic
328C8#1451976011yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—9762no—
335C22—9762no—
336C22—9761no—
337C22—9761no—
338C22—4882no—
339C22#1683975911yescharacteristic
340C22#1683999111yescharacteristic
341C22#1683999811yescharacteristic
342C4—22no—
343C4—9761no—
344C4#1683964111yescharacteristic
345C4C2×#1451969911yescharacteristic
346C4#1683999111yescharacteristic
347C4#1683999811yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—9762no—
352C2#2144624711yescharacteristic
353C2#2144793911yescharacteristic
354C2#2144794911yescharacteristic
subgroupG/H
centerC22#16839998
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#504C2
socleC22×C61#466
prime radicalC2×#16840032C2
cosocleC22×C8×C61C23
hypercenterC2×#504D61
hypocenterC61#13073
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
2. C2×#16839576C2semidirect
3. C2×#16839564C2semidirect
4. #21445883C2semidirect
5. #21443928C2semidirect
6. #21443913C2semidirect
7. C2×C61×#504C2semidirect
11. #16840032C4semidirect
171. C2×#504D61semidirect
205. C61#13073semidirect

Maximal subgroups

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

subgroupindex
C2×#168400322
C2×#168395762
C2×#168395642
#214458832
#214439282
#214439132
C2×C61×#5042
#1307361