Finite Group Databasebeta

← #29596904

Subgroups — #29596904

Order 15616.

508 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C16×D61C211yesmaximal, characteristic, complemented
2#21454511C211yesmaximal, characteristic
3C2×#16839546C211yesmaximal, characteristic, complemented
4#21447429C211yesmaximal, characteristic, complemented
5#21443909C211yesmaximal, characteristic, complemented
6#21443907C211yesmaximal, characteristic, complemented
7C2×C61×#350C211yesmaximal, characteristic, complemented
8C22×C8×D61C2211yescharacteristic
9#16840269C411yescharacteristic
10C2×#14519717C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12C2×C16×D61—22no—
13C2×C16×D61—22no—
14C2×C16×D61—22no—
15#16839831—22no—
16C8×C22⋊D61—22no—
17#16839790C411yescharacteristic
18#16839729C411yescharacteristic
19#16839725C411yescharacteristic
20#16839717C2211yescharacteristic
21#16839546—22no—
22#16839541—22no—
23C2×#131×C61C2211yescharacteristic
24C2×M32×C61C2211yescharacteristic
25C22×C16×C61C2211yescharacteristic
26C61×#350—22no—
27C22×C4×D61C2×C411yescharacteristic
28C2×#11758194C2×C411yescharacteristic
29C22×#92418C2×C411yescharacteristic
30C2×C8×D61—21no—
31C2×C8×D61—21no—
32C2×C8×D61—21no—
33C2×C8×D61—21no—
34C2×C8×D61D412yes—
35C2×C8×D61D412yes—
36#14519758—21no—
37#14519753C812yes—
38#14519748C812yes—
39#14519745—21no—
40C4×C22⋊D61—22no—
41#14519736C2×C411yescharacteristic
42#14519717—21no—
43#14519717—21no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185D412yescomplemented
48C16×D61—28no—
49#14519706—22no—
50C22⋊#92418—22no—
51#14519689—22no—
52#14519687—21no—
53C8×Dic61—21no—
54C2×#41×C61C2×C411yescharacteristic
55#131×C61—21no—
56#131×C61—21no—
57#131×C61—21no—
58#131×C61—21no—
59C2×M16×C61—21no—
60C2×M16×C61C2×C411yescharacteristic
61C22×C8×C61—21no—
62C22×C8×C61C2311yescharacteristic
63M32×C61—21no—
64M32×C61—21no—
65C2×C16×C61—21no—
66C2×C16×C61—21no—
67C2×C16×C61—21no—
68C2×C16×C61D412yescomplemented
69C23×D61M1611yescharacteristic
70#41×C61—21no—
71#41×C61—21no—
72#41×C61—21no—
73#41×C61—21no—
74C2×Q8×C61C2×C811yescharacteristic
75C2×D4×C61—21no—
76C2×D4×C61C2×C811yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61C22×C411yescharacteristic
79C2×C22⋊D61—22no—
80C22×Dic61M1611yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61C22⋊C412yes—
86C2×C4×D61C2×C812yes—
87M16×C61—21no—
88M16×C61—21no—
89M16×C61—41no—
90M16×C61—41no—
91C2×C8×C61—21no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61#4111yescharacteristic
99C2×C8×C61#4111yescharacteristic
100C22⋊Dic61—21no—
101C22⋊Dic61—22no—
102#11758198—22no—
103C4⋊Dic61C2×C812yes—
104#11758196—22no—
105C4×Dic61—21no—
106#11758194—21no—
107#11758194—21no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418C22⋊C412yes—
112C8×D61—22no—
113C8×D61—22no—
114C8×D61—22no—
115C8×D61—22no—
116C16×C61—22no—
117C16×C61—41no—
118#11758185—22no—
119#11758185—41no—
120C23×C61—21no—
121C23×C61C2×M1611yescharacteristic
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—24no—
125C22×D61C22⋊C812yes—
126Q8×C61—21no—
127Q8×C61—21no—
128D4×C61—21no—
129D4×C61—21no—
130D4×C61—41no—
131D4×C61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C22×C811yescharacteristic
139C2×C4×C61#13111yescharacteristic
140C2×C4×C61#13111yescharacteristic
141C22⋊D61—44no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—22no—
145C2×Dic61C22⋊C812yes—
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—22no—
149C4×D61—22no—
150C8×C61—41no—
151C8×C61#12011yescharacteristic
152C8×C61#12111yescharacteristic
153C8×C61#12111yescharacteristic
154C8×C61#12311yescharacteristic
155#92418—22no—
156#92418—41no—
157#12983—611nomaximal, Sylow
158C22×C61—22no—
159C22×C61—42no—
160C22×C61—41no—
161C22×C61C2×C22⋊C811yescharacteristic
162C22×C61#43511yescharacteristic
163C22×C61#43511yescharacteristic
164C2×D61—24no—
165C2×D61—24no—
166C2×D61—22no—
167C2×D61—22no—
168C2×D61#35014yescomplemented
169C4×C61—41no—
170C4×C61#38611yescharacteristic
171C4×C61#40811yescharacteristic
172C4×C61C8×D411yescharacteristic
173C4×C61C8×D411yescharacteristic
174Dic61—22no—
175Dic61—42no—
176C23×C16—611no—
177#2929—611no—
178C2×#350—611no—
179C2×#350D6111yescharacteristic, complemented
180#2112—611no—
181#1379—611no—
182#1379—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—81no—
186C2×C61#186911yescharacteristic
187C2×C61C2×#35012yes—
188D61—24no—
189C2×#131C2×D6111yescharacteristic
190C23×C8—611no—
191#525—611no—
192C2×M32—611no—
193C2×M32C2×D6111yescharacteristic
194C22×C16—611no—
195C22×C16—1222no—
196C22×C16—1222no—
197C22×C16—1222no—
198C22×C16C2×D6111yescharacteristic
199#435—1222no—
200C8×D4—1222no—
201#424—611no—
202#408—611no—
203#407—611no—
204#405—611no—
205#350—22no—
206#350—1222no—
207C22⋊C16—1222no—
208C61#1298311yescharacteristic, complemented, Sylow
209C2×#41C4×D6111yescharacteristic
210C23×C4—611no—
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215C2×M16—21no—
216C2×M16—611no—
217C2×M16C4×D6111yescharacteristic
218C22×C8—21no—
219C22×C8—611no—
220C22×C8—612no—
221C22×C8—612no—
222C22×C8—1221no—
223C22×C8—1221no—
224C22×C8—1221no—
225C22×C8—1221no—
226C22×C8C22×D6111yescharacteristic
227#123—1221no—
228C22⋊Q8—612no—
229#121—612no—
230#120—1221no—
231C4×D4—1222no—
232#117—611no—
233M32—21no—
234M32—21no—
235M32—1221no—
236M32—1221no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—612no—
241C2×C16—1228no—
242C2×C16—1221no—
243C2×C16—1221no—
244C2×C16—1221no—
245C2×C16C22⋊D6112yescomplemented
246C4⋊C8—1222no—
247C22⋊C8—1222no—
248C22⋊C8—1222no—
249#97—1221no—
250C4×C8—1221no—
251C24—611no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256C2×Q8C8×D6111yescharacteristic
257C2×D4—21no—
258C2×D4—1222no—
259C2×D4C8×D6111yescharacteristic
260C22×C4—21no—
261C22×C4—611no—
262C22×C4—612no—
263C22×C4—612no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4C2×C4×D6111yescharacteristic
269M16—21no—
270M16—21no—
271M16—41no—
272M16—41no—
273M16—1221no—
274M16—1221no—
275C2×C8—21no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—612no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—1222no—
282C2×C8—1222no—
283C2×C8—1222no—
284C2×C8—1222no—
285C2×C8—1221no—
286C2×C8#1175822211yescharacteristic
287C2×C8D4×D6111yescharacteristic
288C2×C8D4×D6111yescharacteristic
289C2×C8D4×D6111yescharacteristic
290C2×C8#1175822411yescharacteristic
291C2×C8C2×C22⋊D6111yescharacteristic
292C4⋊C4—612no—
293C4⋊C4—1222no—
294C22⋊C4—1222no—
295C22⋊C4—1222no—
296C22⋊C4—1221no—
297C42—1221no—
298C16—22no—
299C16—41no—
300C16—1222no—
301C16—2441no—
302C23—21no—
303C23—612no—
304C23—1224no—
305C23—1221no—
306C23—1221no—
307C23M16×D6111yescharacteristic
308Q8—21no—
309Q8—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—2444no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—612no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4C22⋊C4×D6111yescharacteristic
327C2×C4#1451973711yescharacteristic
328C2×C4C4×C22⋊D6111yescharacteristic
329C2×C4C2×C8×D6111yescharacteristic
330C2×C4#1451978311yescharacteristic
331C2×C4#1451978511yescharacteristic
332C8—41no—
333C8—1222no—
334C8—2441no—
335C8#1451974511yescharacteristic
336C8#1451974811yescharacteristic
337C8#1451975011yescharacteristic
338C8#1451975911yescharacteristic
339C22—22no—
340C22—42no—
341C22—41no—
342C22—614no—
343C22—1224no—
344C22—1224no—
345C22—1222no—
346C22—1222no—
347C22C22⋊C8×D6111yescharacteristic
348C22#1683983111yescharacteristic
349C22#1683983611yescharacteristic
350C4—41no—
351C4—1222no—
352C4—2442no—
353C4#1683963811yescharacteristic
354C4#1683972711yescharacteristic
355C4#1683982511yescharacteristic
356C4C8×C22⋊D6111yescharacteristic
357C2—21no—
358C2—21no—
359C2—81no—
360C2—1224no—
361C2#2144610811yescharacteristic
362C2#350×D6112yes—
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#350C2
socleC22×C61C2×C22⋊C8
prime radical#16840269C4
cosocleC22×C8×C61C23
hypercenterC2×#350D61
hypocenterC61#12983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. C22×C16×D61C2semidirect
3. C2×#16839546C2semidirect
4. #21447429C2semidirect
5. #21443909C2semidirect
6. #21443907C2semidirect
7. C2×C61×#350C2semidirect
47. C2×#11758185D4semidirect
68. C2×C16×C61D4semidirect
168. C2×D61#350semidirect
179. C2×#350D61semidirect
208. C61#12983semidirect
245. C2×C16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C22×C16×D612
#214545112
C2×#168395462
#214474292
#214439092
#214439072
C2×C61×#3502
#1298361