Finite Group Databasebeta

← #29576566

Subgroups — #29576566

Order 15616.

492 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456762C211yesmaximal, characteristic
2#21454762C211yesmaximal, characteristic, complemented
3#21446658C211yesmaximal, characteristic
4#21444510C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443668C211yesmaximal, characteristic, complemented
7C61×#1301C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9C2×#14519774C2211yescharacteristic
10#16840135—21no—
11#16840109—21no—
12#16839963—22no—
13#16839915C414yes—
14#16839891—22no—
15#16839889—21no—
16#16839886—21no—
17#16839788—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519693—21no—
20C2×#14519693—21no—
21#16839717—21no—
22C4×#11758194C2211yescharacteristic
23#16839510—21no—
24#16839507—21no—
25#16839505—21no—
26#16839505—21no—
27C61×#431C2211yescharacteristic
28C61×#423C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C22×D244—21no—
31C22×D244—21no—
32C22×D244C2×C412yes—
33C2×#11758190—24no—
34C2×#11758194D411yescharacteristic
35C2×#11758194D411yescharacteristic
36C22×#92418—21no—
37#14519777D411yescharacteristic
38#14519777D411yescharacteristic
39#14519774—21no—
40#14519774—21no—
41#14519774—21no—
42#14519774—21no—
43#14519769—21no—
44#14519756—21no—
45#14519756C2×C412yes—
46C4×Dic122—21no—
47C4×Dic122D412yes—
48#14519736—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51#14519706—22no—
52#14519706—22no—
53#14519699—24no—
54#14519693—42no—
55#14519693—42no—
56#14519688—21no—
57#14519687—22no—
58C4×#92418—21no—
59C8×Dic61—22no—
60C2×M16×C61—21no—
61C22×C8×C61—21no—
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61D411yescharacteristic
68C4⋊C8×C61D411yescharacteristic
69C22⋊C8×C61C2×C412yes—
70C4×C8×C61—21no—
71C23×D61—22no—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61#4111yescharacteristic
75C2×D244—22no—
76C2×D244—22no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—82no—
86C2×D244—81no—
87C2×D244—81no—
88C2×Dic122—21no—
89C2×Dic122C22⋊C412yes—
90M16×C61—41no—
91M16×C61—41no—
92C2×C8×C61—22no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102C22⋊Dic61—22no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61C22⋊C412yes—
107#11758196—22no—
108#11758196—22no—
109C4×Dic61—22no—
110#11758194—21no—
111#11758194—21no—
112#11758194—21no—
113#11758194SD1612yescomplemented
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—41no—
117C2×#92418—81no—
118#11758190—84no—
119C23×C61C4×D411yescharacteristic
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—82no—
124C22×D61—82no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12311yescharacteristic
134C2×C4×C61C2×SD1611yescharacteristic
135C2×C4×C61#13511yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61#13711yescharacteristic
138C2×Dic61—22no—
139C2×Dic61—22no—
140D244—44no—
141D244—82no—
142D244—82no—
143D244—81no—
144D244—81no—
145D244—81no—
146D244—81no—
147D244—81no—
148D244—81no—
149Dic122—41no—
150Dic122—41no—
151Dic122—42no—
152C8×C61—42no—
153C8×C61—41no—
154C8×C61—41no—
155C8×C61—81no—
156#92418—22no—
157#92418—41no—
158#92418—81no—
159#9274—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#38611yescharacteristic
163C22×C61C4×SD1611yescharacteristic
164C22×C61#44011yescharacteristic
165C2×D61—82no—
166C2×D61—82no—
167C2×D61—82no—
168C2×D61—162no—
169C2×D61—162no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61#44811yescharacteristic
174C4×C61#44911yescharacteristic
175C4×C61#46011yescharacteristic
176C4×C61#46411yescharacteristic
177C4×C61#47111yescharacteristic
178C4×C61#47211yescharacteristic
179Dic61—42no—
180Dic61—42no—
181#3208—611no—
182#2962—611no—
183#1965—611no—
184#1550—611no—
185C2×#331—611no—
186#1301D6111yescharacteristic, complemented
187#1283—611no—
188C2×C61—21no—
189C2×C61—21no—
190C2×C61#188011yescharacteristic
191C2×C61#190711yescharacteristic
192C2×C61#191411yescharacteristic
193D61—162no—
194#533—611no—
195C2×#127—611no—
196#492—1221no—
197#486—1221no—
198#460—1222no—
199#450—614no—
200#446—1222no—
201#446—1221no—
202C8×Q8—1221no—
203#431C2×D6111yescharacteristic
204#424—1221no—
205#423C2×D6111yescharacteristic
206C2×C4⋊C8—611no—
207C2×C4⋊C8C2×D6111yescharacteristic
208C2×#100—1221no—
209C2×#100—1221no—
210#405—1221no—
211C4×M16—611no—
212#333—1221no—
213#332—1221no—
214#331—1221no—
215#331—1221no—
216C61#927411yescharacteristic, complemented, Sylow
217C22×D4—612no—
218C22×D4—1221no—
219C22×D4—1221no—
220C2×SD16—1224no—
221C2×M16—21no—
222C2×M16—611no—
223C2×M16—611no—
224C22×C8—21no—
225C22×C8—1221no—
226C4⋊Q8—611no—
227C4⋊Q8—611no—
228#127—1221no—
229#127—1221no—
230#127—1221no—
231#127—1221no—
232#125—1221no—
233C22⋊Q8—612no—
234C22⋊Q8—1221no—
235C4×Q8—612no—
236C4×Q8—1221no—
237#117—1221no—
238C2×C42C22×D6111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—1222no—
244C4⋊C8—1222no—
245C4⋊C8—1221no—
246C4⋊C8—1221no—
247C4⋊C8D24411yescharacteristic
248C4⋊C8D24411yescharacteristic
249#102—1224no—
250#100—2442no—
251#100—2442no—
252C22⋊C8C4×D6112yes—
253#97—1222no—
254#97—1221no—
255C4×C8—21no—
256C4×C8—1222no—
257C4×C8—1221no—
258C24—1222no—
259C2×Q8—612no—
260C2×Q8—1221no—
261C2×D4—1222no—
262C2×D4—1222no—
263C2×D4—4881no—
264C2×D4—4881no—
265C2×D4—4882no—
266C2×D4—2441no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2441no—
273C2×D4—2441no—
274C22×C4C2×C4×D6111yescharacteristic
275C22×C4D4×D6111yescharacteristic
276C22×C4#1175822611yescharacteristic
277SD16—4884no—
278M16—41no—
279M16—41no—
280M16—612no—
281M16—1221no—
282M16—1221no—
283M16—1221no—
284C2×C8—22no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—4881no—
293C2×C8—2441no—
294C4⋊C4—612no—
295C4⋊C4—1222no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1222no—
300C22⋊C4—1222no—
301C42—1222no—
302C42C2×D24411yescharacteristic
303C42#1175822211yescharacteristic
304C42D4×D6111yescharacteristic
305C42D4×D6111yescharacteristic
306C23—4882no—
307C23—4882no—
308C23—2442no—
309C23—2442no—
310C23—2442no—
311C23#1451973911yescharacteristic
312Q8—2442no—
313Q8—2441no—
314Q8—2441no—
315D4—4882no—
316D4—4882no—
317D4—4881no—
318D4—4881no—
319D4—4881no—
320D4—4881no—
321D4—4881no—
322D4—4881no—
323D4—2444no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4C22⋊C4×D6111yescharacteristic
330C2×C4C4×D24411yescharacteristic
331C2×C4#1451974711yescharacteristic
332C2×C4#1451975011yescharacteristic
333C2×C4#1451975211yescharacteristic
334C2×C4#1451976211yescharacteristic
335C2×C4SD16×D6111yescharacteristic
336C2×C4#1451979811yescharacteristic
337C2×C4#1451980111yescharacteristic
338C2×C4#1451980911yescharacteristic
339C8—42no—
340C8—41no—
341C8—41no—
342C8—81no—
343C8—1222no—
344C8—4881no—
345C8—2441no—
346C22—21no—
347C22—21no—
348C22—9762no—
349C22—9762no—
350C22—4882no—
351C22—4882no—
352C22—4882no—
353C22#1683964011yescharacteristic
354C22#1683984911yescharacteristic
355C22#1683986111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—2442no—
360C4—2442no—
361C4#1683990211yescharacteristic
362C4#1683990811yescharacteristic
363C4#1683996111yescharacteristic
364C4#1683998711yescharacteristic
365C4#1684002611yescharacteristic
366C4#1684003311yescharacteristic
367C2—21no—
368C2—21no—
369C2—9762no—
370C2#2144617511yescharacteristic
371C2#2144632611yescharacteristic
372C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#386
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1301D61
hypocenterC61#9274
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
2. #21454762C2semidirect
4. #21444510C2semidirect
6. #21443668C2semidirect
7. C61×#1301C2semidirect
113. #11758194SD16semidirect
186. #1301D61semidirect
216. C61#9274semidirect

Maximal subgroups

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

subgroupindex
#214567622
#214547622
#214466582
#214445102
C2×#168395052
#214436682
C61×#13012
#927461