Finite Group Databasebeta

← #29599365

Subgroups — #29599365

Order 15616.

482 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
1C2×#16840146C211yesmaximal, characteristic
2C2×#16839567C211yesmaximal, characteristic, complemented
3C2×#16839567C211yesmaximal, characteristic, complemented
4C2×#16839564C211yesmaximal, characteristic
5C2×#16839564C211yesmaximal, characteristic
6#21446552C211yesmaximal, characteristic, complemented
7C61×#1374C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×#11758190—21no—
10C22×D488C2211yescharacteristic
11C2×#14519765—21no—
12#16840146—22no—
13#16840146—22no—
14C2×#14519711C2211yescharacteristic
15C2×#14519711C2211yescharacteristic
16#16839660—21no—
17#16839567—22no—
18#16839567—22no—
19#16839564—22no—
20#16839564—22no—
21#16839525—21no—
22C22×C16×C61C2211yescharacteristic
23C22×C16×C61C2211yescharacteristic
24C2×C4×C8×C61C2211yescharacteristic
25C22×Dic122—21no—
26C22×D244—21no—
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×Dic244—21no—
30C2×Dic244—21no—
31C2×Dic244—21no—
32C2×Dic244D412yes—
33C2×#11758190—24no—
34C2×#11758190—42no—
35C2×#11758190—42no—
36C2×D488—21no—
37C2×D488—21no—
38C2×D488—21no—
39C2×D488—21no—
40C2×D488—21no—
41C2×D488D412yes—
42#14519765—24no—
43#14519765—42no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×#11758196—41no—
47C2×#11758198—41no—
48C2×#11758198—41no—
49#14519711—21no—
50#14519711—21no—
51#14519711—21no—
52#14519711D412yes—
53#14519684—41no—
54C22×C8×C61D411yescharacteristic
55C22×C8×C61C2311yescharacteristic
56C2×C42×C61D411yescharacteristic
57C2×C16×C61—21no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63C4×C8×C61—21no—
64C4×C8×C61—21no—
65C23×D61—41no—
66C22×C4×C61D811yescharacteristic
67C22×C4×C61D811yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—41no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C2×D244—22no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×Dic122—22no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×Dic122—41no—
84C2×C8×C61—21no—
85C2×C8×C61—21no—
86C2×C8×C61SD1612yes—
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C42×C61—21no—
94C42×C61—21no—
95#11758198—44no—
96#11758198—44no—
97C4⋊Dic61—22no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101#11758196—82no—
102Dic244—22no—
103Dic244—22no—
104Dic244—41no—
105Dic244—41no—
106D488—22no—
107D488—22no—
108D488—41no—
109D488—41no—
110#11758190—48no—
111C16×C61—41no—
112C16×C61—41no—
113C23×C61C2×D811yescharacteristic
114C22×D61—42no—
115C22×D61—81no—
116C22×D61—81no—
117C22×D61—81no—
118C22×D61—81no—
119C22×D61—81no—
120C22×D61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61#12011yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12411yescharacteristic
130C2×C4×C61C2×SD1611yescharacteristic
131C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61—81no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142D244—42no—
143D244—42no—
144D244—81no—
145D244—81no—
146Dic122—42no—
147Dic122—42no—
148Dic122—81no—
149Dic122—81no—
150C8×C61—22no—
151C8×C61#12111yescharacteristic
152C8×C61#12111yescharacteristic
153C8×C61#12311yescharacteristic
154C8×C61#12311yescharacteristic
155#13408—611nomaximal, Sylow
156C22×C61#44711yescharacteristic
157C22×C61#45911yescharacteristic
158C22×C61#48611yescharacteristic
159C22×C61#50811yescharacteristic
160C22×C61#50811yescharacteristic
161C22×C61#50911yescharacteristic
162C22×C61#51011yescharacteristic
163C2×D61—82no—
164C2×D61—82no—
165C2×D61—82no—
166C2×D61—161no—
167C2×D61—161no—
168C2×D61—161no—
169C2×D61—161no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61#39411yescharacteristic
173C4×C61#45011yescharacteristic
174C4×C61#46011yescharacteristic
175C4×C61#49011yescharacteristic
176Dic61—82no—
177Dic61—82no—
178Dic61—161no—
179C2×#495—611no—
180C2×#358—611no—
181C2×#358—611no—
182C2×#357—611no—
183C2×#357—611no—
184#1942—611no—
185#1374D6111yescharacteristic, complemented
186C2×C61#204111yescharacteristic
187C2×C61#218611yescharacteristic
188C2×C61#218911yescharacteristic
189C2×C61#221011yescharacteristic
190C2×C61#221111yescharacteristic
191C2×C61#224211yescharacteristic
192C2×C61#224311yescharacteristic
193D61—162no—
194C22×Q16—611no—
195C22×SD16—1221no—
196C22×D8—611no—
197C2×#124—1221no—
198C22×C16C2×D6111yescharacteristic
199C22×C16C2×D6111yescharacteristic
200#495—1222no—
201#495—1222no—
202C2×#107—611no—
203C2×#107—611no—
204C2×C4×C8C2×D6111yescharacteristic
205#389—1221no—
206#358—1222no—
207#358—1222no—
208#357—1222no—
209#357—1222no—
210#340—1221no—
211C61#1340811yescharacteristic, complemented, Sylow
212C22×Q8—1221no—
213C22×D4—1221no—
214C2×Q16—612no—
215C2×Q16—1221no—
216C2×Q16—1221no—
217C2×Q16—1221no—
218C2×Q16—1221no—
219C2×Q16—1221no—
220C2×SD16—1224no—
221C2×SD16—2442no—
222C2×SD16—2442no—
223C2×D8—612no—
224C2×D8—1221no—
225C2×D8—1221no—
226C2×D8—1221no—
227C2×D8—1221no—
228C2×D8—1221no—
229C22×C8D24411yescharacteristic
230C22×C8C22×D6111yescharacteristic
231#124—1224no—
232#124—2442no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—2441no—
236C2×C22⋊C4—2441no—
237C2×C22⋊C4—2441no—
238C2×C42D24411yescharacteristic
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243C2×C16—21no—
244C2×C16—21no—
245#107—612no—
246#107—1221no—
247#107—1221no—
248#107—1221no—
249C4×C8—21no—
250C4×C8—21no—
251#95—2441no—
252C24—2441no—
253C2×Q8—1222no—
254C2×Q8—2441no—
255C2×Q8—2441no—
256C2×Q8—2441no—
257C2×Q8—2441no—
258C2×Q8—2441no—
259C2×D4—1222no—
260C2×D4—2441no—
261C2×D4—2441no—
262C2×D4—2441no—
263C2×D4—2441no—
264C2×D4—2441no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4D48811yescharacteristic
269C22×C4D48811yescharacteristic
270C22×C4C2×D24411yescharacteristic
271Q16—1222no—
272Q16—1222no—
273Q16—2441no—
274Q16—2441no—
275SD16—2448no—
276D8—1222no—
277D8—1222no—
278D8—2441no—
279D8—2441no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8#1175819012yes—
283C2×C8#1175822211yescharacteristic
284C2×C8#1175822211yescharacteristic
285C2×C8D4×D6111yescharacteristic
286C2×C8D4×D6111yescharacteristic
287C2×C8D4×D6111yescharacteristic
288C2×C8#1175822611yescharacteristic
289C4⋊C4—1222no—
290C4⋊C4—4882no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C22⋊C4—2444no—
295C22⋊C4—2444no—
296C42—21no—
297C42—21no—
298C16—41no—
299C16—41no—
300C23—4881no—
301C23—4881no—
302C23—4881no—
303C23—4881no—
304C23—4881no—
305C23—4881no—
306C23—2442no—
307C23C2×D48811yescharacteristic
308Q8—4881no—
309Q8—4881no—
310Q8—2442no—
311Q8—2442no—
312D4—4881no—
313D4—4881no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4#1451974711yescharacteristic
332C2×C4#1451975211yescharacteristic
333C2×C4#1451976511yescharacteristic
334C2×C4C2×#1175819011yescharacteristic
335C2×C4#1451980511yescharacteristic
336C2×C4#1451980511yescharacteristic
337C8—22no—
338C8#1451975011yescharacteristic
339C8#1451975011yescharacteristic
340C8#1451976211yescharacteristic
341C8#1451976211yescharacteristic
342C22—9761no—
343C22—9761no—
344C22—9761no—
345C22—9761no—
346C22—4882no—
347C22—4882no—
348C22—4882no—
349C22#1683989811yescharacteristic
350C22#1683995811yescharacteristic
351C22#1684010911yescharacteristic
352C22#1684019411yescharacteristic
353C22#1684019411yescharacteristic
354C22#1684020011yescharacteristic
355C22#1684020511yescharacteristic
356C4—41no—
357C4—41no—
358C4—9761no—
359C4—4882no—
360C4—4882no—
361C4#1683968011yescharacteristic
362C4#1683991511yescharacteristic
363C4#1683996311yescharacteristic
364C4#1684012711yescharacteristic
365C2—9762no—
366C2#2144705411yescharacteristic
367C2#2144774411yescharacteristic
368C2#2144776111yescharacteristic
369C2#2144787511yescharacteristic
370C2#2144788211yescharacteristic
371C2#2144805111yescharacteristic
372C2#2144805611yescharacteristic
subgroupG/H
centerC23C2×D488
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1374C2
socleC23×C61C2×D8
prime radicalC22×D488C22
hypercenter#1374D61
hypocenterC61#13408
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×#16839567C2semidirect
3. C2×#16839567C2semidirect
6. #21446552C2semidirect
7. C61×#1374C2semidirect
185. #1374D61semidirect
211. C61#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#168401462
C2×#168395672
C2×#168395642
#214465522
C61×#13742
#1340861