Finite Group Databasebeta

← #29576515

Subgroups — #29576515

Order 15616.

492 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
1#21456746C211yesmaximal, characteristic
2#21454565C211yesmaximal, characteristic
3#21446808C211yesmaximal, characteristic, complemented
4#21444494C211yesmaximal, characteristic
5C2×#16839510C211yesmaximal, characteristic, complemented
6#21443715C211yesmaximal, characteristic, complemented
7C61×#1283C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9#16840312C2211yescharacteristic
10C2×#14519777C2211yescharacteristic
11#16840135—21no—
12#16840113—21no—
13#16839968—22no—
14#16839903C414yes—
15#16839841—21no—
16#16839835—22no—
17C8×D244—21no—
18#16839786C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20#16839730—21no—
21#16839530—21no—
22#16839530—21no—
23#16839510—21no—
24#16839510—21no—
25#16839507—21no—
26#16839505—21no—
27C61×#431C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C2×#11758222—21no—
31C22×Dic122C2×C412yes—
32C2×#11758190—24no—
33#14519785—42no—
34#14519785—42no—
35C2×#11758194—21no—
36C2×#11758189—22no—
37C22×#92418—21no—
38C2×C8×D61—22no—
39#14519777—21no—
40#14519777—21no—
41#14519777—21no—
42#14519777—21no—
43#14519777D411yescharacteristic
44#14519774D411yescharacteristic
45#14519765—21no—
46#14519751—21no—
47#14519751C2×C412yes—
48C4×D244—21no—
49C4×D244D412yes—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C4⋊#92418D411yescharacteristic
56C4⋊#92418D411yescharacteristic
57#14519702—24no—
58#14519689—22no—
59#14519689—22no—
60C2×M16×C61D411yescharacteristic
61C2×M16×C61D411yescharacteristic
62C22×C8×C61—21no—
63C2×C42×C61C2311yescharacteristic
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C22⋊C8×C61C2×C412yes—
68#97×C61—21no—
69C4×C8×C61—21no—
70C4×C8×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4111yescharacteristic
74C2×C22⋊D61—22no—
75C22×Dic61—22no—
76#11758222—41no—
77#11758222—41no—
78#11758222—41no—
79#11758222—41no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244C22⋊C412yes—
83C2×C4×D61—22no—
84C2×Dic122—21no—
85C2×Dic122—22no—
86C2×Dic122—22no—
87C2×Dic122—82no—
88M16×C61—21no—
89M16×C61—21no—
90M16×C61—21no—
91M16×C61SD1612yescomplemented
92C2×C8×C61—21no—
93C2×C8×C61—22no—
94C2×C8×C61—21no—
95C2×C8×C61—41no—
96C2×C8×C61—81no—
97C42×C61C2×D411yescharacteristic
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101#11758198—22no—
102#11758198—22no—
103C4⋊Dic61—21no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107C4⋊Dic61—41no—
108C4⋊Dic61C22⋊C412yes—
109#11758194—41no—
110#11758194—41no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—41no—
114C2×#92418—41no—
115C2×#92418—41no—
116#11758190—84no—
117#11758189—44no—
118C8×D61—44no—
119C23×C61C4×D411yescharacteristic
120C22×D61—22no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61C2×C22⋊C411yescharacteristic
125C2×C4×C61C4×D411yescharacteristic
126C2×C4×C61#12011yescharacteristic
127C2×C4×C61#12111yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12311yescharacteristic
130C2×C4×C61C2×SD1611yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C22⋊D61—42no—
135C22⋊D61—42no—
136C2×Dic61—22no—
137C2×Dic61—42no—
138C2×Dic61—82no—
139D244—42no—
140D244—41no—
141D244—41no—
142D244—41no—
143D244—41no—
144C4×D61—42no—
145C4×D61—42no—
146Dic122—41no—
147Dic122—41no—
148Dic122—44no—
149Dic122—82no—
150C8×C61—22no—
151C8×C61—42no—
152C8×C61—41no—
153C8×C61—81no—
154#92418—41no—
155#92418—41no—
156#92418—81no—
157#9267—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61#38611yescharacteristic
161C22×C61C4×SD1611yescharacteristic
162C22×C61#44011yescharacteristic
163C2×D61—42no—
164C2×D61—42no—
165C2×D61—42no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61#45011yescharacteristic
170C4×C61#45211yescharacteristic
171C4×C61#46111yescharacteristic
172C4×C61#46311yescharacteristic
173C4×C61#47111yescharacteristic
174C4×C61#47311yescharacteristic
175Dic61—42no—
176Dic61—82no—
177#3206—611no—
178#2935—611no—
179#1997—611no—
180#1547—611no—
181C2×#333—611no—
182#1301—611no—
183#1283D6111yescharacteristic, complemented
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#187711yescharacteristic
187C2×C61#190811yescharacteristic
188C2×C61#191411yescharacteristic
189D61—82no—
190C2×#131—1221no—
191#532—611no—
192C2×C4⋊Q8—611no—
193#492—1221no—
194#487—1221no—
195#461—1222no—
196#448—614no—
197#436—1221no—
198#435—1222no—
199C8×D4—1221no—
200#431C2×D6111yescharacteristic
201#423—611no—
202C2×C4⋊C8—611no—
203C2×C4⋊C8C2×D6111yescharacteristic
204#408—1221no—
205C4×M16C2×D6111yescharacteristic
206#343—1221no—
207#343—1221no—
208#333—1221no—
209#333—1221no—
210#332—1221no—
211#331—1221no—
212C61#926711yescharacteristic, complemented, Sylow
213C2×#41—1221no—
214C22×Q8—612no—
215C2×SD16—1224no—
216#131—2442no—
217#131—2442no—
218C2×M16—1222no—
219C2×M16—1221no—
220C2×M16D24411yescharacteristic
221C2×M16D24411yescharacteristic
222C22×C8—21no—
223C22×C8—1222no—
224C22×C8—1221no—
225C4⋊Q8—611no—
226C4⋊Q8—1221no—
227C4⋊Q8—1221no—
228C4⋊Q8—1221no—
229C4⋊Q8—1221no—
230#127—611no—
231#124—1221no—
232#121—612no—
233#121—1221no—
234C4×D4—612no—
235C4×D4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C42C22×D6111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—611no—
243C4⋊C8—611no—
244C4⋊C8—1221no—
245C4⋊C8—1221no—
246C4⋊C8—1221no—
247#103—1224no—
248C22⋊C8—1222no—
249C22⋊C8—1222no—
250C22⋊C8C4×D6112yes—
251#97—21no—
252C4×C8—21no—
253C4×C8—21no—
254#41—2441no—
255#41—2441no—
256#41—2441no—
257#41—2441no—
258C2×Q8—1221no—
259C2×Q8—1222no—
260C2×Q8—1222no—
261C2×Q8—4882no—
262C2×D4—612no—
263C2×D4—1222no—
264C2×D4—1221no—
265C2×D4—1221no—
266C22×C4—1222no—
267C22×C4—1222no—
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4C2×D24411yescharacteristic
270C22×C4#1175822211yescharacteristic
271SD16—4884no—
272M16—21no—
273M16—21no—
274M16—21no—
275M16—2444no—
276M16—2441no—
277M16—2441no—
278M16#1175819012yescomplemented
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—81no—
284C2×C8—1221no—
285C2×C8—1221no—
286C2×C8—2444no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2441no—
290C4⋊C4—612no—
291C4⋊C4—1221no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C22⋊C4—1222no—
297C22⋊C4—1222no—
298C42D4×D6111yescharacteristic
299C42D4×D6111yescharacteristic
300C42D4×D6111yescharacteristic
301C42#1175822611yescharacteristic
302C23—1222no—
303C23C4×D24411yescharacteristic
304Q8—4882no—
305Q8—2444no—
306Q8—2441no—
307Q8—2441no—
308D4—2442no—
309D4—2442no—
310D4—2442no—
311D4—2441no—
312D4—2441no—
313D4—2441no—
314D4—2441no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—1222no—
319C2×C4—4882no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4C22⋊C4×D6111yescharacteristic
324C2×C4#1451973911yescharacteristic
325C2×C4#1451974711yescharacteristic
326C2×C4#1451975011yescharacteristic
327C2×C4#1451975211yescharacteristic
328C2×C4#1451976211yescharacteristic
329C2×C4C2×#1175819011yescharacteristic
330C2×C4#1451979911yescharacteristic
331C2×C4#1451980511yescharacteristic
332C2×C4#1451981011yescharacteristic
333C8—22no—
334C8—42no—
335C8—41no—
336C8—81no—
337C8—4881no—
338C8—2441no—
339C8—2441no—
340C22—21no—
341C22—21no—
342C22—2442no—
343C22—2442no—
344C22—2442no—
345C22#1683964011yescharacteristic
346C22C4×#1175819011yescharacteristic
347C22#1683986411yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—4882no—
352C4—2442no—
353C4#1683991511yescharacteristic
354C4#1683992611yescharacteristic
355C4#1683996811yescharacteristic
356C4#1683997811yescharacteristic
357C4#1684002411yescharacteristic
358C4#1684003611yescharacteristic
359C2—21no—
360C2—21no—
361C2—4882no—
362C2#2144615211yescharacteristic
363C2#2144633511yescharacteristic
364C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1283C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1283D61
hypocenterC61#9267
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
3. #21446808C2semidirect
5. C2×#16839510C2semidirect
6. #21443715C2semidirect
7. C61×#1283C2semidirect
91. M16×C61SD16semidirect
183. #1283D61semidirect
212. C61#9267semidirect
278. M16#11758190semidirect

Maximal subgroups

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

subgroupindex
#214567462
#214545652
#214468082
#214444942
C2×#168395102
#214437152
C61×#12832
#926761