Finite Group Databasebeta

← #29576563

Subgroups — #29576563

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#21456757C211yesmaximal, characteristic
2#21454768C211yesmaximal, characteristic, complemented
3#21446658C211yesmaximal, characteristic
4C2×#16839505C211yesmaximal, characteristic
5#21443714C211yesmaximal, characteristic, complemented
6#21443669C211yesmaximal, characteristic, complemented
7C61×#1550C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9#16840136—21no—
10#16840110—21no—
11#16839962—22no—
12#16839912C414yes—
13#16839893—21no—
14#16839893—22no—
15Q8×#92418—21no—
16#16839815C2211yescharacteristic
17#16839789—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519693—21no—
20C2×#14519693—21no—
21#16839718—21no—
22C4×#11758194C2211yescharacteristic
23#16839505—21no—
24#16839505—21no—
25C61×#533C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#333—21no—
29C61×#332—21no—
30C22×D244—21no—
31C22×D244—21no—
32C22×D244C2×C412yes—
33C2×#11758201—24no—
34C2×#11758194D411yescharacteristic
35C2×#11758194D411yescharacteristic
36C22×#92418—21no—
37#14519774—21no—
38#14519774—21no—
39#14519774—21no—
40#14519774—21no—
41C4⋊#92418—22no—
42C4⋊#92418—22no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46C4⋊#92418D411yescharacteristic
47#14519697—24no—
48#14519693—42no—
49#14519693—42no—
50C22⋊#92418C2×C412yes—
51#14519688—22no—
52#14519688—21no—
53C4×#92418—22no—
54C4×#92418—21no—
55C4×#92418—21no—
56C2×M16×C61—21no—
57C22×C8×C61—21no—
58C4⋊Q8×C61D411yescharacteristic
59C4⋊Q8×C61D411yescharacteristic
60#125×C61—21no—
61C22⋊Q8×C61—21no—
62C22⋊Q8×C61C2×C412yes—
63C4×Q8×C61—21no—
64C4×Q8×C61D412yes—
65#117×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C23×D61—22no—
72C2×Q8×C61—21no—
73C2×Q8×C61C22⋊C412yes—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C2×D244—22no—
78C2×D244—22no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—82no—
88C2×D244—81no—
89C2×D244—81no—
90M16×C61—41no—
91M16×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—81no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61C22⋊C412yes—
101C22⋊C4×C61—22no—
102C42×C61—22no—
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107#11758201—84no—
108#11758194—21no—
109#11758194—21no—
110#11758194—21no—
111#11758194SD1612yescomplemented
112C2×#92418—21no—
113C2×#92418—22no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—41no—
118C2×#92418—41no—
119C23×C61C4×D411yescharacteristic
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—82no—
124C22×D61—82no—
125Q8×C61—42no—
126Q8×C61—41no—
127Q8×C61—41no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12311yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×C4×C61#13511yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61#13711yescharacteristic
143D244—44no—
144D244—82no—
145D244—82no—
146D244—81no—
147D244—81no—
148D244—81no—
149D244—81no—
150D244—81no—
151D244—81no—
152C8×C61—81no—
153C8×C61—81no—
154#92418—22no—
155#92418—42no—
156#92418—41no—
157#92418—41no—
158#92418—41no—
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—42no—
174C4×C61—42no—
175C4×C61#44811yescharacteristic
176C4×C61#44911yescharacteristic
177C4×C61#46011yescharacteristic
178C4×C61#46411yescharacteristic
179C4×C61#47111yescharacteristic
180C4×C61#47211yescharacteristic
181#3208—611no—
182#2962—611no—
183#1965—611no—
184#1550D6111yescharacteristic, complemented
185C2×#331—611no—
186#1301—611no—
187#1283—611no—
188C2×C61—21no—
189C2×C61—21no—
190C2×C61#188011yescharacteristic
191C2×C61#190711yescharacteristic
192C2×C61#191411yescharacteristic
193D61—162no—
194#533C2×D6111yescharacteristic
195C2×#127—611no—
196#492—1221no—
197#486—1221no—
198#460—1222no—
199#450—614no—
200#446—1221no—
201#446—1222no—
202C8×Q8—1221no—
203#431—611no—
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—21no—
213#332—21no—
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⋊Q8C22⋊D6111yescharacteristic
227C4⋊Q8C22⋊D6111yescharacteristic
228#127—1221no—
229#127—1221no—
230#127—1221no—
231#127—1221no—
232#125—21no—
233C22⋊Q8—21no—
234C22⋊Q8C4×D6112yes—
235C4×Q8—21no—
236C4×Q8D24412yes—
237#117—21no—
238C2×C42C22×D6111yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—611no—
244C4⋊C8—611no—
245C4⋊C8—1222no—
246C4⋊C8—1222no—
247C4⋊C8—1221no—
248C4⋊C8—1221no—
249#102—1224no—
250#100—2442no—
251#100—2442no—
252C22⋊C8—612no—
253#97—1222no—
254#97—1221no—
255C4×C8—1222no—
256C4×C8—1221no—
257C4×C8—1221no—
258C24—1222no—
259C2×Q8—21no—
260C2×Q8#1175819812yes—
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#1175822411yescharacteristic
277SD16—4884no—
278M16—41no—
279M16—41no—
280M16—612no—
281M16—1221no—
282M16—1221no—
283M16—1221no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—81no—
287C2×C8—1221no—
288C2×C8—1222no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—2441no—
293C2×C8—2441no—
294C4⋊C4—22no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4#1175819812yes—
300C22⋊C4—22no—
301C42—22no—
302C42C2×D24411yescharacteristic
303C42D4×D6111yescharacteristic
304C42#1175822411yescharacteristic
305C42C2×C22⋊D6111yescharacteristic
306C23—4882no—
307C23—4882no—
308C23—2442no—
309C23—2442no—
310C23—2442no—
311C23#1451973711yescharacteristic
312Q8—42no—
313Q8—41no—
314Q8—41no—
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—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4C2×#1175819811yescharacteristic
330C2×C4#1451973711yescharacteristic
331C2×C4#1451974711yescharacteristic
332C2×C4#1451974911yescharacteristic
333C2×C4#1451974911yescharacteristic
334C2×C4#1451976111yescharacteristic
335C2×C4SD16×D6111yescharacteristic
336C2×C4#1451980011yescharacteristic
337C2×C4#1451980411yescharacteristic
338C2×C4#1451980911yescharacteristic
339C8—81no—
340C8—81no—
341C8—1222no—
342C8—2442no—
343C8—2441no—
344C8—2441no—
345C8—2441no—
346C22—21no—
347C22—21no—
348C22—9762no—
349C22—9762no—
350C22—4882no—
351C22—4882no—
352C22—4882no—
353C22#1683963911yescharacteristic
354C22#1683984711yescharacteristic
355C22#1683986511yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4#1683990211yescharacteristic
362C4#1683991011yescharacteristic
363C4#1683996011yescharacteristic
364C4#1683998611yescharacteristic
365C4#1684002711yescharacteristic
366C4#1684003011yescharacteristic
367C2—21no—
368C2—21no—
369C2—9762no—
370C2#2144617211yescharacteristic
371C2#2144632511yescharacteristic
372C2#2144636411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1550C2
socleC22×C61#386
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1550D61
hypocenterC61#9274
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
2. #21454768C2semidirect
5. #21443714C2semidirect
6. #21443669C2semidirect
7. C61×#1550C2semidirect
111. #11758194SD16semidirect
184. #1550D61semidirect
216. C61#9274semidirect

Maximal subgroups

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

subgroupindex
#214567572
#214547682
#214466582
C2×#168395052
#214437142
#214436692
C61×#15502
#927461