Finite Group Databasebeta

← #29597140

Subgroups — #29597140

Order 15616.

494 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840197C211yesmaximal, characteristic
2C2×#16839569C211yesmaximal, characteristic, complemented
3C2×#16839562C211yesmaximal, characteristic, complemented
4#21446729C211yesmaximal, characteristic, complemented
5#21443927C211yesmaximal, characteristic, complemented
6#21443908C211yesmaximal, characteristic, complemented
7C61×#2951C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9#16840197—22no—
10#16840197C414yescomplemented
11C2×#14519720—21no—
12C2×#14519718—21no—
13C2×#14519717C2211yescharacteristic
14C22×#11758185C2211yescharacteristic
15C2×#14519713C2211yescharacteristic
16#16839766—21no—
17C2×#14519693—21no—
18#16839569—22no—
19#16839562—22no—
20C2×#135×C61C2211yescharacteristic
21C61×#520—21no—
22C61×#440—22no—
23C4×Q16×C61—21no—
24C4×D8×C61—21no—
25C2×#107×C61C2211yescharacteristic
26C61×#417—21no—
27C61×#405C2211yescharacteristic
28C22×D244—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488C2×C412yescomplemented
35C2×#11758194—21no—
36#14519720—24no—
37#14519718—24no—
38#14519717—21no—
39#14519717C2×C412yescomplemented
40C2×#11758185—21no—
41C2×#11758185—21no—
42C2×#11758185—21no—
43C2×#11758185—21no—
44#14519713—21no—
45#14519713—21no—
46#14519697—41no—
47#14519697—41no—
48#14519693—42no—
49C2×#41×C61—21no—
50#135×C61—21no—
51#135×C61—21no—
52#135×C61C2×C412yes—
53#135×C61D412yes—
54C2×Q16×C61D411yescharacteristic
55C2×SD16×C61—21no—
56C2×D8×C61D411yescharacteristic
57C2×M16×C61D411yescharacteristic
58C22×C8×C61C2311yescharacteristic
59C4×Q8×C61—22no—
60C4×D4×C61—22no—
61C4×D4×C61—42no—
62#117×C61—41no—
63#117×C61D411yescharacteristic
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—41no—
66#107×C61—21no—
67#107×C61D412yes—
68#103×C61—22no—
69#102×C61—22no—
70#97×C61—21no—
71C4×C8×C61—21no—
72C23×D61—41no—
73#41×C61—22no—
74#41×C61—22no—
75#41×C61—41no—
76#41×C61—41no—
77C2×Q8×C61—21no—
78C2×D4×C61—21no—
79C2×D4×C61—41no—
80C22×C4×C61—42no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C2×D244—22no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90Q16×C61—21no—
91Q16×C61C22⋊C412yes—
92SD16×C61—22no—
93SD16×C61—22no—
94D8×C61—21no—
95D8×C61C22⋊C412yes—
96M16×C61—21no—
97M16×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61C22×C411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61#4111yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C4⋊C4×C61—22no—
106C4⋊C4×C61—42no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61D811yescharacteristic
109C4⋊C4×C61D811yescharacteristic
110C22⋊C4×C61—21no—
111C22⋊C4×C61—42no—
112C42×C61—21no—
113C42×C61—42no—
114#11758194—41no—
115#11758194—41no—
116C2×#92418—41no—
117D488—22no—
118D488—22no—
119D488—41no—
120D488—41no—
121#11758185—22no—
122#11758185—41no—
123C23×C61—41no—
124C23×C61AGL(1,ℤ/8)11yescharacteristic
125C22×D61—42no—
126C22×D61—81no—
127C22×D61—81no—
128C22×D61—161no—
129C22×D61—161no—
130Q8×C61—22no—
131Q8×C61—41no—
132D4×C61—22no—
133D4×C61—42no—
134D4×C61—42no—
135D4×C61—41no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61—162no—
143C2×C4×C61—161no—
144C2×C4×C61C4×D411yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150D244—42no—
151D244—42no—
152D244—81no—
153D244—81no—
154C8×C61—41no—
155C8×C61C2×C22⋊C411yescharacteristic
156C8×C61C4×D411yescharacteristic
157C8×C61#12111yescharacteristic
158C8×C61#12311yescharacteristic
159#92418—81no—
160#13022—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—42no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61#44211yescharacteristic
167C22×C61#44711yescharacteristic
168C22×C61#46311yescharacteristic
169C2×D61—82no—
170C2×D61—162no—
171C2×D61—161no—
172C2×D61—161no—
173C2×D61—162no—
174C4×C61—42no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—82no—
178C4×C61#38611yescharacteristic
179C4×C61C4×D811yescharacteristic
180C4×C61#44911yescharacteristic
181C4×C61#45911yescharacteristic
182C2×#509—611no—
183#2951D6111yescharacteristic, complemented
184C2×#359—611no—
185C2×#357—611no—
186#1978—611no—
187#1387—611no—
188#1379—611no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—82no—
192C2×C61#187911yescharacteristic
193C2×C61#219211yescharacteristic
194C2×C61#219311yescharacteristic
195D61—162no—
196C2×#135C2×D6111yescharacteristic
197C22×D8—611no—
198#520—21no—
199#509—614no—
200#509—1222no—
201C2×SD32—1221no—
202C2×D16—1221no—
203C2×M32—611no—
204C22×C16—611no—
205#440—22no—
206C4×Q16—21no—
207C4×D8—21no—
208C2×#108—611no—
209C2×#107C2×D6111yescharacteristic
210#418—1221no—
211#417—21no—
212C2×#100—1221no—
213#405C2×D6111yescharacteristic
214#359—1222no—
215#357—1222no—
216C61#1302211yescharacteristic, complemented, Sylow
217C2×#41—21no—
218C22×D4—1221no—
219#135—21no—
220#135—21no—
221#135C4×D6112yes—
222#135D24412yes—
223C2×Q16C22⋊D6111yescharacteristic
224C2×SD16—21no—
225C2×D8—612no—
226C2×D8—1221no—
227C2×D8—1221no—
228C2×D8—1221no—
229C2×D8—1221no—
230C2×D8—1221no—
231C2×D8C22⋊D6111yescharacteristic
232C2×M16—1221no—
233C2×M16C22⋊D6111yescharacteristic
234C22×C8C22×D6111yescharacteristic
235C4×Q8—22no—
236C4×D4—22no—
237C4×D4—42no—
238#117—41no—
239#117C22⋊D6111yescharacteristic
240C2×C4⋊C4—21no—
241C2×C4⋊C4—41no—
242SD32—1224no—
243D16—1224no—
244M32—612no—
245M32—1221no—
246C2×C16—1221no—
247C2×C16—1221no—
248C2×C16—1221no—
249C2×C16—1221no—
250#108—1221no—
251#108—1221no—
252#107—21no—
253#107C22⋊D6112yes—
254#103—22no—
255#102—22no—
256#102—2441no—
257#102—2441no—
258#100—2442no—
259#97—21no—
260C4×C8—21no—
261C24—2441no—
262#41—22no—
263#41—22no—
264#41—41no—
265#41—41no—
266C2×Q8—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—1222no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2441no—
273C2×D4—2441no—
274C2×D4—2441no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×C22⋊D6111yescharacteristic
279Q16—21no—
280Q16#1175819812yes—
281SD16—22no—
282SD16—22no—
283D8—21no—
284D8—1222no—
285D8—1222no—
286D8—2441no—
287D8—2441no—
288D8#1175819812yes—
289M16—21no—
290M16—21no—
291M16—2441no—
292M16—2441no—
293C2×C8—21no—
294C2×C8—2441no—
295C2×C8C2×C4×D6111yescharacteristic
296C2×C8C2×D24411yescharacteristic
297C2×C8#1175822211yescharacteristic
298C2×C8#1175822211yescharacteristic
299C2×C8C2×C22⋊D6111yescharacteristic
300C2×C8C2×C22⋊D6111yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—41no—
304C4⋊C4#1175819911yescharacteristic
305C4⋊C4#1175819911yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—42no—
308C42—21no—
309C42—42no—
310C16—1222no—
311C16—2441no—
312C23—41no—
313C23—9761no—
314C23—9761no—
315C23—4881no—
316C23—4881no—
317C23—2442no—
318C23#1451980311yescharacteristic
319Q8—22no—
320Q8—41no—
321D4—22no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—4881no—
326D4—4881no—
327D4—2442no—
328D4—2442no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—162no—
336C2×C4—161no—
337C2×C4C4×C22⋊D6111yescharacteristic
338C2×C4#1451974611yescharacteristic
339C2×C4#1451975111yescharacteristic
340C2×C4C2×#1175819911yescharacteristic
341C2×C4#1451979711yescharacteristic
342C2×C4#1451980211yescharacteristic
343C8—41no—
344C8—4881no—
345C8C2×#1175819811yescharacteristic
346C8C4×C22⋊D6111yescharacteristic
347C8#1451975111yescharacteristic
348C8#1451976011yescharacteristic
349C22—21no—
350C22—21no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—9762no—
355C22—9762no—
356C22—9761no—
357C22—9761no—
358C22—4882no—
359C22#1683987211yescharacteristic
360C22#1683989611yescharacteristic
361C22#1683997711yescharacteristic
362C4—42no—
363C4—41no—
364C4—41no—
365C4—82no—
366C4#1683964111yescharacteristic
367C4C4×#1175819911yescharacteristic
368C4#1683990711yescharacteristic
369C4#1683995711yescharacteristic
370C2—21no—
371C2—21no—
372C2—82no—
373C2—9762no—
374C2#2144616711yescharacteristic
375C2#2144777611yescharacteristic
376C2#2144778311yescharacteristic
subgroupG/H
centerC22#16839896
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#2951C2
socleC22×C61#447
prime radicalC2×#16840197C2
cosocleC22×C8×C61C23
hypercenter#2951D61
hypocenterC61#13022
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
2. C2×#16839569C2semidirect
3. C2×#16839562C2semidirect
4. #21446729C2semidirect
5. #21443927C2semidirect
6. #21443908C2semidirect
7. C61×#2951C2semidirect
10. #16840197C4semidirect
34. C2×D488C2×C4semidirect
39. #14519717C2×C4semidirect
183. #2951D61semidirect
216. C61#13022semidirect

Maximal subgroups

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

subgroupindex
C2×#168401972
C2×#168395692
C2×#168395622
#214467292
#214439272
#214439082
C61×#29512
#1302261