Finite Group Databasebeta

← #29835019

Subgroups — #29835019

Order 15616.

552 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456389C211yesmaximal, characteristic
2C2×C4×Dic244C211yesmaximal, characteristic, complemented
3#21448017C211yesmaximal, characteristic, complemented
4#21448000C211yesmaximal, characteristic
5#21447984C212yesmaximal, complemented
6#21447882C212yesmaximal, complemented
7#21447755C211yesmaximal, characteristic, complemented
8#21447738C211yesmaximal, characteristic
9C4×Dic488C212yesmaximal, complemented
10C4×#14519722C212yesmaximal, complemented
11C61×#2162C211yesmaximal, characteristic, complemented
12C22×Dic244C2211yescharacteristic
13#16840296—21no—
14C2×C4×Dic122—21no—
15C2×Dic488C2212yes—
16C2×#14519722C2212yes—
17#16840164C2211yescharacteristic
18#16840146C2211yescharacteristic
19#16840117—21no—
20#16840003C2211yescharacteristic
21#16839998C2211yescharacteristic
22#16839991—21no—
23C4×Dic244—21no—
24C4×Dic244—21no—
25C4×Dic244C2211yescharacteristic
26C4×Dic244C2212yes—
27C4×Dic244C2212yes—
28C4×#11758190—21no—
29C4×D488C2211yescharacteristic
30C2×#14519711C2211yescharacteristic
31C2×#14519702—21no—
32#16839590C2212yes—
33#16839588C2212yes—
34#16839567C2212yes—
35#16839567C2212yes—
36#16839567C2212yes—
37#16839564C2212yes—
38C2×C4×C8×C61C2211yescharacteristic
39C61×C4⋊C16C2212yes—
40C61×C22⋊C16C2211yescharacteristic
41C61×C22⋊C16C2211yescharacteristic
42C4×C16×C61C2212yes—
43C22×Dic122—21no—
44C2×Dic244—21no—
45C2×Dic244—24no—
46C2×Dic244C2311yescharacteristic
47C2×Dic244C2312yes—
48C2×#11758190—21no—
49C2×D488C2311yescharacteristic
50#14519771—41no—
51#14519769—21no—
52#14519765—21no—
53#14519760—41no—
54#14519756—21no—
55#14519751—21no—
56C4×Dic122—22no—
57C4×Dic122—22no—
58C4×Dic122—21no—
59C4×Dic122—41no—
60C4×Dic122—41no—
61C4×D244—21no—
62C4×C22⋊D61—41no—
63#14519734—41no—
64C2×C4⋊Dic61—21no—
65C2×#11758196—41no—
66C2×C4×Dic61—41no—
67Dic488—24no—
68#14519722—24no—
69#14519711—21no—
70#14519711C2311yescharacteristic
71#14519711C2311yescharacteristic
72#14519711C2312yes—
73#14519709—21no—
74#14519702—21no—
75#14519702—21no—
76#14519702—22no—
77#14519702—22no—
78#14519699—21no—
79#14519699—21no—
80C22×C8×C61D411yescharacteristic
81C22×C8×C61C2311yescharacteristic
82C2×C42×C61D411yescharacteristic
83C2×C16×C61C2312yes—
84C2×C16×C61C2312yes—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89C22×C4×C61D811yescharacteristic
90C22×C4×C61D811yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C2×D244—21no—
96C2×C4×D61—41no—
97C2×Dic122—24no—
98C2×Dic122—22no—
99C2×Dic122—21no—
100C2×Dic122—42no—
101C2×Dic122—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2×D411yescharacteristic
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2411yescharacteristic
108C42×C61D811yescharacteristic
109C42×C61D811yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C22⋊Dic61—41no—
113#11758198—41no—
114#11758198—41no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—22no—
120C4⋊Dic61—41no—
121#11758196—42no—
122#11758196—42no—
123#11758196—41no—
124#11758196—41no—
125#11758196—41no—
126#11758196—41no—
127C4×Dic61—42no—
128C4×Dic61—42no—
129C4×Dic61—41no—
130Dic244—24no—
131Dic244—22no—
132Dic244—22no—
133Dic244#4114yes—
134D488—22no—
135#11758190—42no—
136C16×C61—22no—
137C16×C61—22no—
138C23×C61C2×D811yescharacteristic
139C22×D61—41no—
140C2×C4×C61—22no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—22no—
144C2×C4×C61C2×D811yescharacteristic
145C2×C4×C61C2×D811yescharacteristic
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C2×D811yescharacteristic
149C2×C4×C61C22×D411yescharacteristic
150C22⋊D61—82no—
151C2×Dic61—44no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—82no—
158D244—41no—
159D244—41no—
160C4×D61—82no—
161Dic122—24no—
162Dic122—44no—
163Dic122—42no—
164Dic122—41no—
165Dic122—41no—
166C8×C61—21no—
167C8×C61—21no—
168C8×C61—21no—
169C8×C61C2×#4112yes—
170#33668—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61#50812yes—
174C22×C61C22×D811yescharacteristic
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61#51012yes—
183C4×C61#52511yescharacteristic
184C4×C61#57511yescharacteristic
185Dic61—44no—
186Dic61—81no—
187Dic61—82no—
188Dic61—81no—
189Dic61—81no—
190#3168—611no—
191C2×C4×Q16—611no—
192#2235—611no—
193#2232—611no—
194#2229—612no—
195#2211—612no—
196#2188—611no—
197#2185—611no—
198C4×Q32—612no—
199C4×SD32—612no—
200#2162D6111yescharacteristic, complemented
201C2×C61—22no—
202C2×C61#310011yescharacteristic
203C2×C61C2×#50811yescharacteristic
204C2×C61C2×#51011yescharacteristic
205D61—161no—
206C22×Q16—611no—
207#529—1221no—
208C2×C4×Q8—1221no—
209C2×Q32—612no—
210C2×SD32—612no—
211#499—611no—
212#495—611no—
213#488—1221no—
214#467—611no—
215#466—611no—
216#465—1221no—
217C4×Q16—611no—
218C4×Q16—612no—
219C4×Q16—612no—
220C4×Q16—1221no—
221C4×Q16—1221no—
222C4×SD16—1221no—
223C4×D8—611no—
224C2×#107—611no—
225C2×#103—1221no—
226C2×C4×C8C2×D6111yescharacteristic
227#367—612no—
228#366—612no—
229C4⋊C16C2×D6112yes—
230#358—612no—
231#358—612no—
232#358—612no—
233#357—612no—
234C22⋊C16C2×D6111yescharacteristic
235C22⋊C16C2×D6111yescharacteristic
236C4×C16C2×D6112yes—
237C61#3366811yescharacteristic, complemented, Sylow
238C22×Q8—1221no—
239C2×Q16—612no—
240C2×Q16—611no—
241C2×Q16—1224no—
242C2×Q16—1221no—
243C2×SD16—1221no—
244C2×D8—611no—
245C22×C8D24411yescharacteristic
246C22×C8C22×D6111yescharacteristic
247#126—2441no—
248#125—1221no—
249#124—1221no—
250#123—2441no—
251C22⋊Q8—1221no—
252#121—1221no—
253C4×Q8—1222no—
254C4×Q8—1222no—
255C4×Q8—1221no—
256C4×Q8—2441no—
257C4×Q8—2441no—
258C4×D4—1221no—
259C4×D4—2441no—
260#117—2441no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—2441no—
263C2×C42—2441no—
264C2×C42D24411yescharacteristic
265Q32—1224no—
266SD32—1224no—
267C2×C16C22×D6112yes—
268C2×C16C22×D6112yes—
269#107—612no—
270#107—611no—
271#107—611no—
272#107—1221no—
273#106—1221no—
274#103—1222no—
275#103—1222no—
276#103—1221no—
277#103—1221no—
278#102—1221no—
279#102—1221no—
280C4×C8D24411yescharacteristic
281C4×C8D24411yescharacteristic
282C4×C8C22×D6111yescharacteristic
283C4×C8C22×D6111yescharacteristic
284C2×Q8—1224no—
285C2×Q8—1222no—
286C2×Q8—1221no—
287C2×Q8—2442no—
288C2×Q8—2441no—
289C2×D4—1221no—
290C2×D4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4D48811yescharacteristic
295C22×C4D48811yescharacteristic
296C22×C4C2×D24411yescharacteristic
297Q16—614no—
298Q16—1224no—
299Q16—1222no—
300Q16—1222no—
301SD16—2442no—
302D8—1222no—
303C2×C8—22no—
304C2×C8—41no—
305C2×C8C2×D24411yescharacteristic
306C2×C8C2×D24411yescharacteristic
307C2×C8C2×D24411yescharacteristic
308C2×C8C23×D6111yescharacteristic
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1222no—
312C4⋊C4—2441no—
313C4⋊C4—2442no—
314C4⋊C4—2442no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C42—2442no—
325C42—2442no—
326C42—2441no—
327C42D48811yescharacteristic
328C42D48811yescharacteristic
329C42C2×D24411yescharacteristic
330C42C2×D24411yescharacteristic
331C16—22no—
332C16—22no—
333C23—2441no—
334C23C2×D48811yescharacteristic
335Q8—1224no—
336Q8—2444no—
337Q8—2441no—
338Q8—2441no—
339Q8—2442no—
340D4—4882no—
341D4—2441no—
342D4—2441no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—4882no—
348C2×C4—4882no—
349C2×C4—2442no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2444no—
354C2×C4—2442no—
355C2×C4C2×D48811yescharacteristic
356C2×C4C2×D48811yescharacteristic
357C2×C4C2×D48811yescharacteristic
358C2×C4C2×D48811yescharacteristic
359C2×C4C2×D48811yescharacteristic
360C2×C4C22×D24411yescharacteristic
361C8—21no—
362C8—21no—
363C8—21no—
364C8#41×D6112yes—
365C22—21no—
366C22—21no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22#1684019412yes—
371C22C22×D48811yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—4881no—
377C4—4881no—
378C4—4882no—
379C4—4881no—
380C4—2444no—
381C4#1684020512yes—
382C4#1684027411yescharacteristic
383C4#1684056211yescharacteristic
384C2—22no—
385C2—9761no—
386C2#2145582011yescharacteristic
387C2C2×#1684019411yescharacteristic
388C2C2×#1684020511yescharacteristic
subgroupG/H
centerC2×C4C2×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2162C2
socleC22×C61C22×D8
prime radical#16839998C22
hypercenter#2162D61
hypocenterC61#33668
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2162

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic244C2semidirect
3. #21448017C2semidirect
5. #21447984C2semidirect
6. #21447882C2semidirect
7. #21447755C2semidirect
9. C4×Dic488C2semidirect
10. C4×#14519722C2semidirect
11. C61×#2162C2semidirect
200. #2162D61semidirect
237. C61#33668semidirect

Maximal subgroups

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

subgroupindex
#214563892
C2×C4×Dic2442
#214480172
#214480002
#214479842
#214478822
#214477552
#214477382
C4×Dic4882
C4×#145197222
C61×#21622
#3366861