Finite Group Databasebeta

← #29597098

Subgroups — #29597098

Order 15616.

462 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840192C211yesmaximal, characteristic
2#21447555C211yesmaximal, characteristic, complemented
3#21447546C211yesmaximal, characteristic, complemented
4#21446717C211yesmaximal, characteristic, complemented
5#21443916C211yesmaximal, characteristic, complemented
6#21443908C211yesmaximal, characteristic, complemented
7C61×#2957C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9#16840192—22no—
10#16840192—22no—
11C2×#14519723C411yescharacteristic, complemented
12C2×#14519721C411yescharacteristic, complemented
13C2×#14519720C411yescharacteristic, complemented
14C2×#14519718C411yescharacteristic, complemented
15C2×#14519717C2211yescharacteristic
16C22×#11758185C2211yescharacteristic
17#16839800C2211yescharacteristic
18#16839778—21no—
19#16839735—21no—
20#16839572—22no—
21#16839568—22no—
22C2×#135×C61C2211yescharacteristic
23C61×#568—21no—
24C61×#444—22no—
25C61×#443—22no—
26C2×#108×C61C2211yescharacteristic
27C61×#421—21no—
28C61×#405C2211yescharacteristic
29C2×#11758222—21no—
30#14519799—21no—
31#14519799—21no—
32#14519799—21no—
33#14519799—21no—
34C2×Dic244C2×C411yescharacteristic
35C2×#11758190—21no—
36C2×D488C2×C411yescharacteristic
37#14519736—21no—
38#14519723—22no—
39#14519721—22no—
40#14519720—22no—
41#14519718—22no—
42#14519717—21no—
43#14519717—21no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185C2×C411yescharacteristic
48C2×#11758185C2×C411yescharacteristic
49#14519711—21no—
50#14519709—21no—
51#14519703—42no—
52#14519691—42no—
53C2×#41×C61—21no—
54#135×C61—21no—
55#135×C61—21no—
56#135×C61D412yes—
57#135×C61D412yes—
58C2×Q16×C61C2×C411yescharacteristic
59C2×SD16×C61—21no—
60C2×D8×C61C2×C411yescharacteristic
61#131×C61—24no—
62#131×C61—42no—
63C2×M16×C61—21no—
64C2×M16×C61—42no—
65C2×M16×C61D411yescharacteristic
66C22×C8×C61C2311yescharacteristic
67#117×C61D411yescharacteristic
68#108×C61—21no—
69#108×C61D412yes—
70#104×C61—24no—
71#97×C61—21no—
72C4×C8×C61—21no—
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—41no—
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—21no—
88C2×C4×D61—41no—
89C2×Dic122—21no—
90Q16×C61—21no—
91Q16×C61C22⋊C412yes—
92SD16×C61—22no—
93SD16×C61—22no—
94D8×C61—21no—
95D8×C61C22⋊C412yes—
96M16×C61—21no—
97M16×C61—22no—
98M16×C61—44no—
99M16×C61—41no—
100M16×C61D812yes—
101C2×C8×C61—21no—
102C2×C8×C61—44no—
103C2×C8×C61—41no—
104C2×C8×C61C22×C411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61#4111yescharacteristic
109C2×C8×C61#4111yescharacteristic
110C4⋊C4×C61—21no—
111C22⋊C4×C61—21no—
112C42×C61—21no—
113C22⋊Dic61—41no—
114C4⋊Dic61—41no—
115C4×Dic61—41no—
116Dic244—21no—
117Dic244—21no—
118D488—21no—
119D488—21no—
120#11758190—41no—
121#11758190—41no—
122#11758185—21no—
123#11758185—21no—
124#11758185—41no—
125C23×C61—41no—
126C23×C61AGL(1,ℤ/8)11yescharacteristic
127C22×D61—41no—
128Q8×C61—22no—
129Q8×C61—41no—
130D4×C61—22no—
131D4×C61—42no—
132D4×C61—42no—
133D4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—41no—
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61C2×D811yescharacteristic
142C2×C4×C61#13511yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C22⋊D61—81no—
145C22⋊D61—81no—
146C2×Dic61—41no—
147C2×Dic61—81no—
148D244—41no—
149D244—41no—
150C4×D61—81no—
151C4×D61—81no—
152Dic122—41no—
153Dic122—41no—
154C8×C61—22no—
155C8×C61—42no—
156C8×C61C2×C22⋊C411yescharacteristic
157C8×C61C4×D411yescharacteristic
158C8×C61#12111yescharacteristic
159C8×C61#12311yescharacteristic
160#13016—611nomaximal, Sylow
161C22×C61—41no—
162C22×C61—42no—
163C22×C61—161no—
164C22×C61#44211yescharacteristic
165C22×C61#44911yescharacteristic
166C22×C61#45911yescharacteristic
167C2×D61—81no—
168C2×D61—161no—
169C4×C61—42no—
170C4×C61—81no—
171C4×C61#38611yescharacteristic
172C4×C61C4×D811yescharacteristic
173C4×C61#44711yescharacteristic
174C4×C61#46311yescharacteristic
175Dic61—81no—
176Dic61—161no—
177C2×#508—611no—
178#2957D6111yescharacteristic, complemented
179#2145—611no—
180#2143—611no—
181#1976—611no—
182#1382—611no—
183#1379—611no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—82no—
188C2×C61#187911yescharacteristic
189D61—161no—
190C2×#135—611no—
191C2×#135C2×D6111yescharacteristic
192#568—21no—
193#508—1222no—
194#508—1222no—
195C2×Q32—611no—
196C2×SD32—611no—
197C2×SD32—611no—
198C2×D16—611no—
199C2×M32—611no—
200C22×C16—611no—
201#444—22no—
202#443—22no—
203C2×#108C2×D6111yescharacteristic
204#427—611no—
205#421—21no—
206#421—1221no—
207#410—1221no—
208#405C2×D6111yescharacteristic
209#360—1222no—
210#359—1222no—
211C61#1301611yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C2×#41—1221no—
214#135—21no—
215#135—21no—
216#135—1221no—
217#135—1221no—
218#135—1221no—
219#135—1221no—
220#135D24412yes—
221#135C22⋊D6112yes—
222C2×Q16—611no—
223C2×Q16C4×D6111yescharacteristic
224C2×SD16—21no—
225C2×SD16—1221no—
226C2×D8—611no—
227C2×D8C4×D6111yescharacteristic
228#131—24no—
229#131—42no—
230C2×M16—21no—
231C2×M16—42no—
232C2×M16C22⋊D6111yescharacteristic
233C22×C8C22×D6111yescharacteristic
234#117—1221no—
235#117C22⋊D6111yescharacteristic
236Q32—1222no—
237SD32—1222no—
238SD32—1222no—
239D16—1222no—
240M32—1221no—
241M32—1221no—
242C2×C16—611no—
243C2×C16—611no—
244C2×C16—1221no—
245C2×C16—1221no—
246C2×C16—1221no—
247#108—21no—
248#108C22⋊D6112yes—
249#107—1221no—
250#106—1221no—
251#104—24no—
252#104—2442no—
253#99—2442no—
254#97—21no—
255C4×C8—21no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260#41—2441no—
261#41—2441no—
262#41—2441no—
263#41—2441no—
264C2×Q8—21no—
265C2×Q8—1221no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—1221no—
269C2×D4—2441no—
270C22×C4—41no—
271C22×C4—2441no—
272C22×C4C2×C22⋊D6111yescharacteristic
273Q16—21no—
274Q16—1221no—
275Q16—1221no—
276Q16#1175819812yes—
277SD16—22no—
278SD16—22no—
279SD16—2441no—
280SD16—2441no—
281D8—21no—
282D8—1221no—
283D8—1221no—
284D8#1175819812yes—
285M16—21no—
286M16—22no—
287M16—44no—
288M16—41no—
289M16#1175819912yes—
290C2×C8—21no—
291C2×C8—44no—
292C2×C8—41no—
293C2×C8C2×C4×D6111yescharacteristic
294C2×C8C2×D24411yescharacteristic
295C2×C8#1175822211yescharacteristic
296C2×C8#1175822211yescharacteristic
297C2×C8C2×C22⋊D6111yescharacteristic
298C2×C8C2×C22⋊D6111yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—2441no—
301C22⋊C4—21no—
302C22⋊C4—2441no—
303C42—21no—
304C42—2441no—
305C16—1221no—
306C16—1221no—
307C16—2441no—
308C23—41no—
309C23—2441no—
310C23#1451980211yescharacteristic
311Q8—22no—
312Q8—41no—
313Q8—2441no—
314Q8—2441no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—4881no—
320D4—4881no—
321D4—2441no—
322D4—2441no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—2441no—
331C2×C4C4×C22⋊D6111yescharacteristic
332C2×C4#1451974611yescharacteristic
333C2×C4#1451975111yescharacteristic
334C2×C4C2×#1175819911yescharacteristic
335C2×C4#1451979711yescharacteristic
336C2×C4#1451980311yescharacteristic
337C8—22no—
338C8—42no—
339C8C2×#1175819811yescharacteristic
340C8C4×C22⋊D6111yescharacteristic
341C8#1451975111yescharacteristic
342C8#1451976011yescharacteristic
343C22—41no—
344C22—42no—
345C22—161no—
346C22—9761no—
347C22—4881no—
348C22#1683987211yescharacteristic
349C22#1683990711yescharacteristic
350C22#1683995711yescharacteristic
351C4—42no—
352C4—81no—
353C4—9761no—
354C4—4881no—
355C4#1683964111yescharacteristic
356C4C4×#1175819911yescharacteristic
357C4#1683989611yescharacteristic
358C4#1683997711yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—9761no—
364C2#2144616711yescharacteristic
subgroupG/H
centerC4#16839896
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#2957C2
socleC2×C61#1879
prime radicalC2×#16840192C2
cosocleC22×C8×C61C23
hypercenter#2957D61
hypocenterC61#13016
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #21447555C2semidirect
3. #21447546C2semidirect
4. #21446717C2semidirect
5. #21443916C2semidirect
6. #21443908C2semidirect
7. C61×#2957C2semidirect
11. C2×#14519723C4semidirect
12. C2×#14519721C4semidirect
13. C2×#14519720C4semidirect
14. C2×#14519718C4semidirect
178. #2957D61semidirect
211. C61#13016semidirect

Maximal subgroups

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

subgroupindex
C2×#168401922
#214475552
#214475462
#214467172
#214439162
#214439082
C61×#29572
#1301661