Finite Group Databasebeta

← #29597133

Subgroups — #29597133

Order 15616.

462 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458953C211yesmaximal, characteristic
2C2×#16839568C211yesmaximal, characteristic, complemented
3#21447526C211yesmaximal, characteristic, complemented
4#21446717C211yesmaximal, characteristic, complemented
5#21443933C211yesmaximal, characteristic, complemented
6#21443908C211yesmaximal, characteristic, complemented
7C61×#2957C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9#16840203—21no—
10#16840202C412yescomplemented
11#16840198—21no—
12#16840197C412yescomplemented
13#16840192—22no—
14C2×#14519717C2211yescharacteristic
15C22×#11758185C2211yescharacteristic
16#16839800C2211yescharacteristic
17#16839778—21no—
18#16839735—21no—
19#16839568—22no—
20#16839566—21no—
21#16839563—21no—
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#14519717C2×C412yes—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185—21no—
48#14519711—21no—
49#14519709—21no—
50#14519703—42no—
51#14519691—42no—
52C2×#41×C61—21no—
53#135×C61—21no—
54#135×C61—21no—
55#135×C61C2×C412yes—
56#135×C61D412yes—
57C2×Q16×C61D411yescharacteristic
58C2×SD16×C61—21no—
59C2×D8×C61D411yescharacteristic
60#131×C61—24no—
61#131×C61—42no—
62C2×M16×C61—21no—
63C2×M16×C61—42no—
64C2×M16×C61D411yescharacteristic
65C22×C8×C61C2311yescharacteristic
66#117×C61D411yescharacteristic
67#108×C61—21no—
68#108×C61D412yes—
69#104×C61—24no—
70#97×C61—21no—
71C4×C8×C61—21no—
72#41×C61—22no—
73#41×C61—22no—
74#41×C61—41no—
75#41×C61—41no—
76C2×Q8×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61C2×D411yescharacteristic
81C2×C22⋊D61—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86C2×D244—21no—
87C2×C4×D61—41no—
88C2×Dic122—21no—
89Q16×C61—21no—
90Q16×C61C22⋊C412yes—
91SD16×C61—22no—
92SD16×C61—22no—
93D8×C61—21no—
94D8×C61C22⋊C412yes—
95M16×C61—21no—
96M16×C61—22no—
97M16×C61—44no—
98M16×C61—41no—
99M16×C61D812yes—
100C2×C8×C61—21no—
101C2×C8×C61—44no—
102C2×C8×C61—41no—
103C2×C8×C61C22×C411yescharacteristic
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61#4111yescharacteristic
108C2×C8×C61#4111yescharacteristic
109C4⋊C4×C61—21no—
110C22⋊C4×C61—21no—
111C42×C61—21no—
112C22⋊Dic61—41no—
113C4⋊Dic61—41no—
114C4×Dic61—41no—
115Dic244—21no—
116Dic244—21no—
117D488—21no—
118D488—21no—
119#11758190—41no—
120#11758190—41no—
121#11758185—22no—
122#11758185—41no—
123C23×C61—41no—
124C23×C61AGL(1,ℤ/8)11yescharacteristic
125C22×D61—41no—
126Q8×C61—22no—
127Q8×C61—41no—
128D4×C61—22no—
129D4×C61—42no—
130D4×C61—42no—
131D4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61C2×D811yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C22⋊D61—81no—
143C22⋊D61—81no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146D244—41no—
147D244—41no—
148C4×D61—81no—
149C4×D61—81no—
150Dic122—41no—
151Dic122—41no—
152C8×C61—22no—
153C8×C61—42no—
154C8×C61C2×C22⋊C411yescharacteristic
155C8×C61C4×D411yescharacteristic
156C8×C61#12111yescharacteristic
157C8×C61#12311yescharacteristic
158#13021—611nomaximal, Sylow
159C22×C61—41no—
160C22×C61—42no—
161C22×C61—161no—
162C22×C61#44211yescharacteristic
163C22×C61#44911yescharacteristic
164C22×C61#45911yescharacteristic
165C2×D61—81no—
166C2×D61—161no—
167C4×C61—42no—
168C4×C61—81no—
169C4×C61#38611yescharacteristic
170C4×C61C4×D811yescharacteristic
171C4×C61#44711yescharacteristic
172C4×C61#46311yescharacteristic
173Dic61—81no—
174Dic61—161no—
175#3414—611no—
176#2957D6111yescharacteristic, complemented
177C2×#359—611no—
178#2138—611no—
179#1976—611no—
180#1389—611no—
181#1379—611no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—82no—
186C2×C61#187911yescharacteristic
187D61—161no—
188C2×#135—611no—
189C2×#135C2×D6111yescharacteristic
190#568—21no—
191#510—612no—
192#510—1221no—
193#509—612no—
194#509—1221no—
195#508—1222no—
196C2×M32—611no—
197C22×C16—611no—
198#444—22no—
199#443—22no—
200C2×#108C2×D6111yescharacteristic
201#427—611no—
202#421—21no—
203#421—1221no—
204#410—1221no—
205#405C2×D6111yescharacteristic
206#359—1222no—
207#358—1221no—
208#357—1221no—
209C61#1302111yescharacteristic, complemented, Sylow
210C2×#41—21no—
211C2×#41—1221no—
212#135—21no—
213#135—21no—
214#135—1221no—
215#135—1221no—
216#135—1221no—
217#135—1221no—
218#135C4×D6112yes—
219#135C22⋊D6112yes—
220C2×Q16—611no—
221C2×Q16D24411yescharacteristic
222C2×SD16—21no—
223C2×SD16—1221no—
224C2×D8—611no—
225C2×D8D24411yescharacteristic
226#131—24no—
227#131—42no—
228C2×M16—21no—
229C2×M16—42no—
230C2×M16C22⋊D6111yescharacteristic
231C22×C8C22×D6111yescharacteristic
232#117—1221no—
233#117C22⋊D6111yescharacteristic
234Q32—1222no—
235SD32—1222no—
236SD32—1222no—
237D16—1222no—
238M32—612no—
239M32—1221no—
240C2×C16—1221no—
241C2×C16—1221no—
242C2×C16—1221no—
243C2×C16—1221no—
244#108—21no—
245#108C22⋊D6112yes—
246#107—1221no—
247#106—1221no—
248#104—24no—
249#104—2442no—
250#99—2442no—
251#97—21no—
252C4×C8—21no—
253#41—22no—
254#41—22no—
255#41—41no—
256#41—41no—
257#41—2441no—
258#41—2441no—
259#41—2441no—
260#41—2441no—
261C2×Q8—21no—
262C2×Q8—1221no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—1221no—
266C2×D4—2441no—
267C22×C4—41no—
268C22×C4—2441no—
269C22×C4C2×C22⋊D6111yescharacteristic
270Q16—21no—
271Q16—1221no—
272Q16—1221no—
273Q16#1175819812yes—
274SD16—22no—
275SD16—22no—
276SD16—2441no—
277SD16—2441no—
278D8—21no—
279D8—1221no—
280D8—1221no—
281D8#1175819812yes—
282M16—21no—
283M16—22no—
284M16—44no—
285M16—41no—
286M16#1175819912yes—
287C2×C8—21no—
288C2×C8—44no—
289C2×C8—41no—
290C2×C8C2×C4×D6111yescharacteristic
291C2×C8C2×D24411yescharacteristic
292C2×C8#1175822211yescharacteristic
293C2×C8#1175822211yescharacteristic
294C2×C8C2×C22⋊D6111yescharacteristic
295C2×C8C2×C22⋊D6111yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—2441no—
298C22⋊C4—21no—
299C22⋊C4—2441no—
300C42—21no—
301C42—2441no—
302C16—1222no—
303C16—2441no—
304C23—41no—
305C23—2441no—
306C23#1451980211yescharacteristic
307Q8—22no—
308Q8—41no—
309Q8—2441no—
310Q8—2441no—
311D4—22no—
312D4—42no—
313D4—42no—
314D4—41no—
315D4—4881no—
316D4—4881no—
317D4—2441no—
318D4—2441no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—2441no—
327C2×C4C4×C22⋊D6111yescharacteristic
328C2×C4#1451974611yescharacteristic
329C2×C4#1451975111yescharacteristic
330C2×C4C2×#1175819911yescharacteristic
331C2×C4#1451979711yescharacteristic
332C2×C4#1451980311yescharacteristic
333C8—22no—
334C8—42no—
335C8C2×#1175819811yescharacteristic
336C8C4×C22⋊D6111yescharacteristic
337C8#1451975111yescharacteristic
338C8#1451976011yescharacteristic
339C22—41no—
340C22—42no—
341C22—161no—
342C22—9761no—
343C22—4881no—
344C22#1683987211yescharacteristic
345C22#1683990711yescharacteristic
346C22#1683995711yescharacteristic
347C4—42no—
348C4—81no—
349C4—9761no—
350C4—4881no—
351C4#1683964111yescharacteristic
352C4C4×#1175819911yescharacteristic
353C4#1683989611yescharacteristic
354C4#1683997711yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—82no—
359C2—9761no—
360C2#2144616711yescharacteristic
subgroupG/H
centerC4#16839896
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#2957C2
socleC2×C61#1879
prime radical#21458953C2
cosocleC22×C8×C61C23
hypercenter#2957D61
hypocenterC61#13021
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. C2×#16839568C2semidirect
3. #21447526C2semidirect
4. #21446717C2semidirect
5. #21443933C2semidirect
6. #21443908C2semidirect
7. C61×#2957C2semidirect
10. #16840202C4semidirect
12. #16840197C4semidirect
176. #2957D61semidirect
209. C61#13021semidirect

Maximal subgroups

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

subgroupindex
#214589532
C2×#168395682
#214475262
#214467172
#214439332
#214439082
C61×#29572
#1302161