Finite Group Databasebeta

← #29599361

Subgroups — #29599361

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×#16840147C211yesmaximal, characteristic
2C2×#16839566C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic
4C2×#16839562C211yesmaximal, characteristic
5#21446553C211yesmaximal, characteristic, complemented
6#21443896C211yesmaximal, characteristic, complemented
7C2×C61×#358C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C22×D488C2211yescharacteristic
10C2×#14519766—21no—
11C22×#11758185C2211yescharacteristic
12#16840147—22no—
13#16840147—22no—
14C2×#14519711C2211yescharacteristic
15C2×C8×Dic61C2211yescharacteristic
16#16839661—21no—
17#16839566—22no—
18#16839564—22no—
19#16839562—22no—
20#16839524—21no—
21C22×Q16×C61C2211yescharacteristic
22C22×C16×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#358—22no—
25C22×D244—21no—
26C2×#11758201—24no—
27C2×#11758201—42no—
28C2×#11758201—42no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488D412yes—
35C22×#92418D411yescharacteristic
36#14519766—24no—
37#14519766—42no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—41no—
40C2×#11758198—41no—
41C2×#11758198—41no—
42C2×C4×Dic61D411yescharacteristic
43C2×#11758185—21no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46#14519711—21no—
47#14519711—21no—
48C8×Dic61—21no—
49C8×Dic61—21no—
50#14519684—41no—
51C22×Q8×C61—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C2×Q16×C61—21no—
55C2×Q16×C61—21no—
56C2×Q16×C61—21no—
57C2×Q16×C61D412yes—
58C22×C8×C61C2311yescharacteristic
59C2×C4⋊C4×C61—21no—
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C2×C16×C61—21no—
63#107×C61—21no—
64#107×C61D412yes—
65C23×D61—41no—
66C2×Q8×C61—22no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—41no—
76C22×Dic61D811yescharacteristic
77C22×Dic61D811yescharacteristic
78C2×D244—22no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84Q16×C61—22no—
85Q16×C61—22no—
86Q16×C61—41no—
87Q16×C61—41no—
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61C2×D411yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C2×C8×C61#4111yescharacteristic
93C2×C8×C61#4111yescharacteristic
94C4⋊C4×C61—22no—
95C4⋊C4×C61—41no—
96#11758201—48no—
97#11758198—44no—
98#11758198—44no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—82no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C2×#92418—21no—
105C2×#92418—21no—
106C2×#92418SD1612yes—
107D488—22no—
108D488—22no—
109D488—41no—
110D488—41no—
111C16×C61—41no—
112#11758185—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—
121Q8×C61—42no—
122Q8×C61—42no—
123Q8×C61—81no—
124Q8×C61—81no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12411yescharacteristic
134C2×C4×C61C2×SD1611yescharacteristic
135C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146D244—42no—
147D244—42no—
148D244—81no—
149D244—81no—
150C8×C61#12111yescharacteristic
151C8×C61#12111yescharacteristic
152C8×C61#12311yescharacteristic
153C8×C61#12311yescharacteristic
154#92418—22no—
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—82no—
171C4×C61—82no—
172C4×C61#39411yescharacteristic
173C4×C61#45011yescharacteristic
174C4×C61#46011yescharacteristic
175C4×C61#49011yescharacteristic
176Dic61—41no—
177Dic61—41no—
178Dic61—161no—
179C2×#495—611no—
180C2×#358—611no—
181C2×#358D6111yescharacteristic, complemented
182C2×#357—611no—
183C2×#357—611no—
184#1942—611no—
185#1374—611no—
186C2×C61#204111yescharacteristic
187C2×C61#218611yescharacteristic
188C2×C61#218911yescharacteristic
189C2×C61#221011yescharacteristic
190C2×C61#221111yescharacteristic
191C2×C61#224211yescharacteristic
192C2×C61#224311yescharacteristic
193D61—162no—
194C22×Q16C2×D6111yescharacteristic
195C22×SD16—1221no—
196C22×D8—611no—
197C2×#124—1221no—
198C22×C16—611no—
199C22×C16C2×D6111yescharacteristic
200#495—1222no—
201#495—1222no—
202C2×#107—611no—
203C2×#107C2×D6111yescharacteristic
204C2×C4×C8—611no—
205#389—1221no—
206#358—22no—
207#358—1222no—
208#357—1222no—
209#357—1222no—
210#340—1221no—
211C61#1340811yescharacteristic, complemented, Sylow
212C22×Q8—21no—
213C22×D4—1221no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16D24412yes—
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×C8—611no—
230C22×C8C22×D6111yescharacteristic
231#124—1224no—
232#124—2442no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—2441no—
236C2×C22⋊C4—2441no—
237C2×C22⋊C4—2441no—
238C2×C42—611no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—1221no—
243C2×C16—1221no—
244C2×C16—1221no—
245#107—21no—
246#107—1221no—
247#107—1221no—
248#107C22⋊D6112yes—
249C4×C8—1221no—
250C4×C8—1221no—
251#95—2441no—
252C24—2441no—
253C2×Q8—22no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—1222no—
260C2×D4—2441no—
261C2×D4—2441no—
262C2×D4—2441no—
263C2×D4—2441no—
264C2×D4—2441no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—2441no—
270C22×C4D4×D6111yescharacteristic
271Q16—22no—
272Q16—22no—
273Q16—41no—
274Q16—41no—
275SD16—2448no—
276D8—1222no—
277D8—1222no—
278D8—2441no—
279D8—2441no—
280C2×C8—612no—
281C2×C8—1221no—
282C2×C8—1221no—
283C2×C8C2×D24411yescharacteristic
284C2×C8#1175822211yescharacteristic
285C2×C8D4×D6111yescharacteristic
286C2×C8#1175822411yescharacteristic
287C2×C8#1175822411yescharacteristic
288C2×C8C2×C22⋊D6111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—4882no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C22⋊C4—2444no—
295C22⋊C4—2444no—
296C42—1221no—
297C42—1221no—
298C16—41no—
299C16—2441no—
300C23—4881no—
301C23—4881no—
302C23—4881no—
303C23—4881no—
304C23—4881no—
305C23—4881no—
306C23—2442no—
307C23D8×D6111yescharacteristic
308Q8—42no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312D4—4881no—
313D4—4881no—
314D4—2442no—
315D4—2442no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4#1451974711yescharacteristic
332C2×C4#1451974911yescharacteristic
333C2×C4#1451976311yescharacteristic
334C2×C4SD16×D6111yescharacteristic
335C2×C4#1451980111yescharacteristic
336C2×C4#1451980411yescharacteristic
337C8—1222no—
338C8#1451974811yescharacteristic
339C8#1451975111yescharacteristic
340C8#1451975911yescharacteristic
341C8#1451976111yescharacteristic
342C22—9761no—
343C22—9761no—
344C22—9761no—
345C22—9761no—
346C22—4882no—
347C22—4882no—
348C22—4882no—
349C22#1683989711yescharacteristic
350C22#1683995511yescharacteristic
351C22#1684010711yescharacteristic
352C22#1684019311yescharacteristic
353C22#1684019511yescharacteristic
354C22#1684019911yescharacteristic
355C22#1684020411yescharacteristic
356C4—82no—
357C4—82no—
358C4—9761no—
359C4—2441no—
360C4—2441no—
361C4#1683967811yescharacteristic
362C4#1683991411yescharacteristic
363C4#1683996011yescharacteristic
364C4#1684012511yescharacteristic
365C2—9762no—
366C2#2144705211yescharacteristic
367C2#2144774511yescharacteristic
368C2#2144776211yescharacteristic
369C2#2144787611yescharacteristic
370C2#2144788311yescharacteristic
371C2#2144805211yescharacteristic
372C2#2144805711yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×#358C2
socleC23×C61C2×D8
prime radicalC22×D488C22
hypercenterC2×#358D61
hypocenterC61#13408
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#16839566C2semidirect
5. #21446553C2semidirect
6. #21443896C2semidirect
7. C2×C61×#358C2semidirect
181. C2×#358D61semidirect
211. C61#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#168401472
C2×#168395662
C2×#168395642
C2×#168395622
#214465532
#214438962
C2×C61×#3582
#1340861