Finite Group Databasebeta

← #29576549

Subgroups — #29576549

Order 15616.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456960C211yesmaximal, characteristic
2#21454768C211yesmaximal, characteristic
3#21446662C211yesmaximal, characteristic
4C2×#16839507C211yesmaximal, characteristic
5#21443714C211yesmaximal, characteristic
6#21443669C211yesmaximal, characteristic
7C61×#1550C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9#16840158—21no—
10#16840112—21no—
11#16840090C414yes—
12#16840047—22no—
13#16839893—21no—
14#16839893—22no—
15Q8×#92418—21no—
16#16839815C2211yescharacteristic
17#16839789—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519695—21no—
20C2×#14519695—21no—
21#16839718—21no—
22C4×#11758194C2211yescharacteristic
23#16839507—21no—
24#16839507—21no—
25C61×#533C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C2×C4⋊C8×C61C2211yescharacteristic
28C61×#333—21no—
29C61×#332—21no—
30C22×Dic122—21no—
31C2×#11758194D411yescharacteristic
32C2×#11758194D411yescharacteristic
33C22×#92418—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C412yes—
40#14519708—24no—
41C4⋊#92418—22no—
42C4⋊#92418—22no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46C4⋊#92418D411yescharacteristic
47#14519701—24no—
48#14519695—42no—
49#14519695—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—
71C2×Q8×C61—21no—
72C2×Q8×C61C22⋊C412yes—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×Dic61—22no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83M16×C61—41no—
84M16×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—81no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61C22⋊C412yes—
94C22⋊C4×C61—22no—
95C42×C61—22no—
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61C2×D411yescharacteristic
99C42×C61#4111yescharacteristic
100C4⋊Dic61—22no—
101C4⋊Dic61—22no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758194—21no—
105#11758194—21no—
106#11758194—21no—
107#11758194SD1612yes—
108C2×#92418—21no—
109C2×#92418—22no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—41no—
114C2×#92418—41no—
115C23×C61C4×D411yescharacteristic
116Q8×C61—42no—
117Q8×C61—41no—
118Q8×C61—41no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
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
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137Dic122—81no—
138Dic122—81no—
139Dic122—81no—
140Dic122—81no—
141C8×C61—81no—
142C8×C61—81no—
143#92418—22no—
144#92418—42no—
145#92418—41no—
146#92418—41no—
147#92418—41no—
148#9272—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61#38611yescharacteristic
152C22×C61C4×SD1611yescharacteristic
153C22×C61#44011yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—42no—
158C4×C61—42no—
159C4×C61#44811yescharacteristic
160C4×C61#44911yescharacteristic
161C4×C61#46011yescharacteristic
162C4×C61#46411yescharacteristic
163C4×C61#47111yescharacteristic
164C4×C61#47311yescharacteristic
165Dic61—82no—
166#3229—611no—
167#2962—611no—
168#1966—611no—
169#1550D6111yescharacteristic
170C2×#332—611no—
171#1301—611no—
172#1283—611no—
173C2×C61—21no—
174C2×C61—21no—
175C2×C61#188011yescharacteristic
176C2×C61#190811yescharacteristic
177C2×C61#191511yescharacteristic
178#533C2×D6111yescharacteristic
179C2×C4⋊Q8—611no—
180#498—1221no—
181#487—1221no—
182#483—614no—
183#475—1222no—
184#446—1221no—
185#446—1222no—
186C8×Q8—1221no—
187#431—611no—
188#424—1221no—
189#423C2×D6111yescharacteristic
190C2×C4⋊C8—611no—
191C2×C4⋊C8C2×D6111yescharacteristic
192C2×#101—1221no—
193C2×#101—1221no—
194#405—1221no—
195C4×M16—611no—
196#333—21no—
197#332—21no—
198#332—1221no—
199#332—1221no—
200C61#927211yescharacteristic, complemented, Sylow
201C22×Q8—1221no—
202C2×M16—21no—
203C2×M16—611no—
204C2×M16—611no—
205C22×C8—21no—
206C22×C8—1221no—
207C4⋊Q8—1221no—
208C4⋊Q8—1221no—
209C4⋊Q8—1221no—
210C4⋊Q8—1221no—
211C4⋊Q8C22⋊D6111yescharacteristic
212C4⋊Q8C22⋊D6111yescharacteristic
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8C4×D6112yes—
216C4×Q8—21no—
217C4×Q8D24412yes—
218#117—21no—
219C2×C4⋊C4—612no—
220C2×C4⋊C4—1221no—
221C2×C42C22×D6111yescharacteristic
222#106—1224no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—611no—
228C4⋊C8—611no—
229C4⋊C8—1222no—
230C4⋊C8—1222no—
231C4⋊C8—1221no—
232C4⋊C8—1221no—
233#103—1224no—
234#101—2442no—
235#101—2442no—
236C22⋊C8—612no—
237#97—1222no—
238#97—1221no—
239C4×C8—1222no—
240C4×C8—1221no—
241C4×C8—1221no—
242C2×Q8—21no—
243C2×Q8—2441no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×Q8#1175819812yes—
250C22×C4—1222no—
251C22×C4C2×C4×D6111yescharacteristic
252C22×C4D4×D6111yescharacteristic
253C22×C4#1175822411yescharacteristic
254M16—41no—
255M16—41no—
256M16—612no—
257M16—1221no—
258M16—1221no—
259M16—1221no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—81no—
263C2×C8—1221no—
264C2×C8—1222no—
265C2×C8—1221no—
266C2×C8—1221no—
267C2×C8—1221no—
268C2×C8—2441no—
269C2×C8—2441no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—1222no—
276C4⋊C4—1222no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4#1175819812yes—
280C22⋊C4—22no—
281C42—22no—
282C42C2×D24411yescharacteristic
283C42D4×D6111yescharacteristic
284C42#1175822411yescharacteristic
285C42C2×C22⋊D6111yescharacteristic
286C23#1451973711yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—4881no—
291Q8—4881no—
292Q8—4881no—
293Q8—4881no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4C2×#1175819811yescharacteristic
303C2×C4#1451973711yescharacteristic
304C2×C4#1451974711yescharacteristic
305C2×C4#1451974911yescharacteristic
306C2×C4#1451974911yescharacteristic
307C2×C4#1451976111yescharacteristic
308C2×C4SD16×D6111yescharacteristic
309C2×C4#1451980011yescharacteristic
310C2×C4#1451980411yescharacteristic
311C2×C4#1451980911yescharacteristic
312C8—81no—
313C8—81no—
314C8—1222no—
315C8—2442no—
316C8—2441no—
317C8—2441no—
318C8—2441no—
319C22—21no—
320C22—21no—
321C22#1683963911yescharacteristic
322C22#1683984711yescharacteristic
323C22#1683986511yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—4882no—
330C4#1683990211yescharacteristic
331C4#1683991011yescharacteristic
332C4#1683996011yescharacteristic
333C4#1683998611yescharacteristic
334C4#1684002311yescharacteristic
335C4#1684003511yescharacteristic
336C2—21no—
337C2—21no—
338C2#2144617211yescharacteristic
339C2#2144633211yescharacteristic
340C2#2144636911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1550C2
socleC22×C61#386
prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#1550D61
hypocenterC61#9272
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
200. C61#9272semidirect

Maximal subgroups

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

subgroupindex
#214569602
#214547682
#214466622
C2×#168395072
#214437142
#214436692
C61×#15502
#927261