Finite Group Databasebeta

← #29835009

Subgroups — #29835009

Order 15616.

552 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456405C211yesmaximal, characteristic, complemented
2C4×#14519799C211yesmaximal, characteristic
3#21448028C212yesmaximal, complemented
4#21447962C211yesmaximal, characteristic, complemented
5#21447957C211yesmaximal, characteristic, complemented
6#21447870C211yesmaximal, characteristic, complemented
7#21447865C211yesmaximal, characteristic, complemented
8#21447761C212yesmaximal
9C4×Dic488C212yesmaximal, complemented
10C4×#14519722C212yesmaximal, complemented
11C61×#2162C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13#16840319—21no—
14C4×#11758222—21no—
15C2×Dic488C2212yes—
16C2×#14519722C2212yes—
17#16840167C2211yescharacteristic
18#16840142C2211yescharacteristic
19#16840113—21no—
20#16840003—21no—
21#16840003C2212yes—
22C4×Dic244—21no—
23C4×Dic244C2211yescharacteristic
24C4×Dic244C2211yescharacteristic
25C4×Dic244C2212yes—
26C4×#11758190—21no—
27C4×#11758190—21no—
28C4×D488C2211yescharacteristic
29C4×D488C2211yescharacteristic
30#16839800C2211yescharacteristic
31#16839759—21no—
32#16839590C2212yes—
33#16839588C2212yes—
34#16839567C2212yes—
35#16839567C2212yes—
36#16839567C2212yes—
37#16839564C2212yes—
38C2×C4×C8×C61C2211yescharacteristic
39C61×C4⋊C16C2211yescharacteristic
40C61×C4⋊C16C2211yescharacteristic
41C61×C22⋊C16C2212yes—
42C4×C16×C61C2212yes—
43C2×#11758222—21no—
44#14519799—22no—
45#14519799—22no—
46C2×Dic244—21no—
47C2×Dic244C2312yes—
48C2×Dic244C2311yescharacteristic
49C2×#11758190—21no—
50C2×D488C2311yescharacteristic
51#14519777—21no—
52#14519777—21no—
53#14519769—41no—
54#14519756—22no—
55#14519756—41no—
56C4×Dic122—21no—
57C4×Dic122—21no—
58C4×Dic122—22no—
59C4×Dic122—41no—
60C4×D244—21no—
61C4×D244—21no—
62C4×C22⋊D61—41no—
63C4×C22⋊D61—41no—
64#14519736—21no—
65#14519736—41no—
66#14519734—41no—
67C42×D61—41no—
68Dic488—24no—
69#14519722—24no—
70#14519711—21no—
71#14519711C2312yes—
72#14519711C2311yescharacteristic
73#14519711C2311yescharacteristic
74#14519709—21no—
75#14519702—22no—
76#14519702—22no—
77#14519702—21no—
78#14519702—21no—
79#14519699—21no—
80#14519699—21no—
81C22×C8×C61D411yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C2×C42×C61D411yescharacteristic
84C2×C16×C61C2312yes—
85C2×C16×C61C2312yes—
86C4×C8×C61D411yescharacteristic
87C4×C8×C61D411yescharacteristic
88C4×C8×C61C2311yescharacteristic
89C4×C8×C61C2311yescharacteristic
90C22×C4×C61D811yescharacteristic
91C22×C4×C61D811yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C2×C22⋊D61—41no—
94#11758222—24no—
95#11758222—42no—
96C2×D244—21no—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×Dic122—21no—
101C2×Dic122—22no—
102C2×Dic122—41no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—41no—
106C2×C8×C61C2×D411yescharacteristic
107C2×C8×C61C2×D411yescharacteristic
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2411yescharacteristic
110C42×C61D811yescharacteristic
111C42×C61D811yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C22⋊Dic61—41no—
115C22⋊Dic61—42no—
116#11758198—41no—
117#11758198—41no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—22no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124#11758196—41no—
125#11758196—41no—
126#11758196—42no—
127#11758196—42no—
128C4×Dic61—41no—
129C4×Dic61—41no—
130C4×Dic61—41no—
131C4×Dic61—42no—
132Dic244—21no—
133Dic244—22no—
134Dic244—22no—
135Dic244—42no—
136Dic244#4112yes—
137D488—21no—
138D488#4112yes—
139#11758190—24no—
140C16×C61—22no—
141C16×C61—22no—
142C23×C61C2×D811yescharacteristic
143C22×D61—41no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—22no—
147C2×C4×C61—22no—
148C2×C4×C61C2×D811yescharacteristic
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61C2×D811yescharacteristic
151C2×C4×C61C2×D811yescharacteristic
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61C22×D411yescharacteristic
154C22⋊D61—44no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160D244—22no—
161D244—41no—
162C4×D61—44no—
163C4×D61—82no—
164C4×D61—82no—
165Dic122—22no—
166Dic122—41no—
167Dic122—42no—
168Dic122—42no—
169Dic122—82no—
170C8×C61—21no—
171C8×C61—21no—
172C8×C61—21no—
173C8×C61C2×#4111yescharacteristic
174C8×C61C2×#4111yescharacteristic
175#33667—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61C22×D811yescharacteristic
180C2×D61—42no—
181C2×D61—81no—
182C2×D61—81no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61#50812yes—
187C4×C61#51012yes—
188C4×C61#52511yescharacteristic
189C4×C61#57511yescharacteristic
190Dic61—42no—
191Dic61—82no—
192Dic61—82no—
193Dic61—81no—
194Dic61—81no—
195#3170—611no—
196C4×#135—611no—
197#2237—612no—
198#2225—611no—
199#2224—611no—
200#2209—611no—
201#2208—611no—
202#2189—612no—
203C4×Q32—612no—
204C4×SD32—612no—
205#2162D6111yescharacteristic, complemented
206C2×C61—41no—
207C2×C61#310011yescharacteristic
208C2×C61C2×#50811yescharacteristic
209C2×C61C2×#51011yescharacteristic
210D61—82no—
211C2×#135—611no—
212#533—1221no—
213C4×#41—1221no—
214C2×Q32—612no—
215C2×SD32—612no—
216#500—611no—
217#494—611no—
218#487—1221no—
219#467—612no—
220#467—1221no—
221C4×Q16—612no—
222C4×Q16—611no—
223C4×Q16—611no—
224C4×Q16—1221no—
225C4×SD16—1221no—
226C4×SD16—1221no—
227C4×D8—611no—
228C4×D8—611no—
229#427—611no—
230#416—1221no—
231C2×C4×C8C2×D6111yescharacteristic
232#367—612no—
233#366—612no—
234C4⋊C16C2×D6111yescharacteristic
235C4⋊C16C2×D6111yescharacteristic
236#358—612no—
237#358—612no—
238#358—612no—
239#357—612no—
240C22⋊C16C2×D6112yes—
241C4×C16C2×D6112yes—
242C61#3366711yescharacteristic, complemented, Sylow
243C2×#41—1221no—
244#135—1222no—
245#135—1222no—
246C2×Q16—611no—
247C2×Q16—612no—
248C2×Q16—1221no—
249C2×SD16—1221no—
250C2×D8—611no—
251C22×C8D24411yescharacteristic
252C22×C8C22×D6111yescharacteristic
253C4⋊Q8—1221no—
254C4⋊Q8—1221no—
255#125—2441no—
256C22⋊Q8—1222no—
257C22⋊Q8—2441no—
258C4×Q8—1221no—
259C4×Q8—1221no—
260C4×Q8—1222no—
261C4×Q8—2441no—
262C4×D4—1221no—
263C4×D4—1221no—
264C4×D4—2441no—
265C4×D4—2441no—
266#117—1221no—
267#117—2441no—
268#117—2441no—
269C2×C42—2441no—
270C2×C42D24411yescharacteristic
271Q32—1224no—
272SD32—1224no—
273C2×C16C22×D6112yes—
274C2×C16C22×D6112yes—
275#107—612no—
276#107—611no—
277#107—611no—
278#107—1221no—
279#106—1221no—
280#103—1221no—
281#103—1221no—
282#103—1222no—
283#103—1222no—
284#102—1221no—
285#102—1221no—
286C4×C8D24411yescharacteristic
287C4×C8D24411yescharacteristic
288C4×C8C22×D6111yescharacteristic
289C4×C8C22×D6111yescharacteristic
290#41—1224no—
291#41—2442no—
292C2×Q8—1221no—
293C2×Q8—1222no—
294C2×Q8—2441no—
295C2×D4—1221no—
296C2×D4—2441no—
297C22×C4—2441no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4D48811yescharacteristic
301C22×C4D48811yescharacteristic
302C22×C4C2×D24411yescharacteristic
303Q16—612no—
304Q16—1221no—
305Q16—1222no—
306Q16—1222no—
307Q16—2442no—
308SD16—1224no—
309D8—612no—
310D8—1221no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8C2×D24411yescharacteristic
315C2×C8C2×D24411yescharacteristic
316C2×C8C2×D24411yescharacteristic
317C2×C8C23×D6111yescharacteristic
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—1222no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C4⋊C4—2442no—
324C4⋊C4—2442no—
325C4⋊C4—2441no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C22⋊C4—2441no—
329C22⋊C4—2442no—
330C22⋊C4—2441no—
331C22⋊C4—2441no—
332C42—2441no—
333C42—2441no—
334C42—2441no—
335C42—2442no—
336C42D48811yescharacteristic
337C42D48811yescharacteristic
338C42C2×D24411yescharacteristic
339C42C2×D24411yescharacteristic
340C16—22no—
341C16—22no—
342C23—2441no—
343C23C2×D48811yescharacteristic
344Q8—1222no—
345Q8—4882no—
346Q8—2442no—
347Q8—2442no—
348Q8—2441no—
349D4—1222no—
350D4—2444no—
351D4—2441no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—4882no—
357C2×C4—4882no—
358C2×C4—2444no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4C2×D48811yescharacteristic
365C2×C4C2×D48811yescharacteristic
366C2×C4C2×D48811yescharacteristic
367C2×C4C2×D48811yescharacteristic
368C2×C4C2×D48811yescharacteristic
369C2×C4C22×D24411yescharacteristic
370C8—21no—
371C8—21no—
372C8—21no—
373C8#41×D6111yescharacteristic
374C8#41×D6111yescharacteristic
375C22—21no—
376C22—21no—
377C22—21no—
378C22—4881no—
379C22—4881no—
380C22—2442no—
381C22C22×D48811yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—4881no—
386C4—4882no—
387C4—4881no—
388C4—4882no—
389C4—2442no—
390C4#1684019412yes—
391C4#1684020512yes—
392C4#1684027411yescharacteristic
393C4#1684056211yescharacteristic
394C2—41no—
395C2—4882no—
396C2#2145582011yescharacteristic
397C2C2×#1684019411yescharacteristic
398C2C2×#1684020511yescharacteristic
subgroupG/H
centerC2×C4C2×D488
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2162C2
socleC22×C61C22×D8
prime radicalC2×#14519799C22
hypercenter#2162D61
hypocenterC61#33667
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
1. #21456405C2semidirect
3. #21448028C2semidirect
4. #21447962C2semidirect
5. #21447957C2semidirect
6. #21447870C2semidirect
7. #21447865C2semidirect
9. C4×Dic488C2semidirect
10. C4×#14519722C2semidirect
11. C61×#2162C2semidirect
205. #2162D61semidirect
242. C61#33667semidirect

Maximal subgroups

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

subgroupindex
#214564052
C4×#145197992
#214480282
#214479622
#214479572
#214478702
#214478652
#214477612
C4×Dic4882
C4×#145197222
C61×#21622
#3366761