Finite Group Databasebeta

← #29665299

Subgroups — #29665299

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456746C211yesmaximal, characteristic
2C2×#16840048C211yesmaximal, characteristic, complemented
3#21455293C211yesmaximal, characteristic
4#21454899C211yesmaximal, characteristic, complemented
5#21445250C214yesmaximal, complemented
6#21445168C214yesmaximal, complemented
7#21444505C211yesmaximal, characteristic, complemented
8#21444469C211yesmaximal, characteristic
9C61×#1570C211yesmaximal, characteristic, complemented
10C2×#14519810—21no—
11#16840312C2211yescharacteristic
12C2×#14519777C2211yescharacteristic
13C2×C4×Dic122C2211yescharacteristic
14#16840135C2212yes—
15#16840113C2212yes—
16#16840048—22no—
17#16840048C2214yes—
18#16839985—22no—
19#16839973C2212yes—
20#16839968—22no—
21#16839963C2212yes—
22#16839903—22no—
23C8×Dic122C2214yes—
24#16839886—22no—
25#16839815C2211yescharacteristic
26#16839812—22no—
27C2×#14519709—21no—
28#16839764—21no—
29C2×#14519702—21no—
30#16839509C2212yes—
31#16839507C2214yes—
32#16839505C2212yes—
33C61×#431C2211yescharacteristic
34C61×#423C2211yescharacteristic
35C2×C4⋊C8×C61C2211yescharacteristic
36C61×#334C2214yes—
37C2×#11758222—21no—
38C22×Dic122—21no—
39C22×Dic122D411yescharacteristic
40#14519810—44no—
41C2×Dic244—22no—
42C2×#11758190—22no—
43C2×#11758190—24no—
44#14519777—21no—
45#14519777—21no—
46#14519777—21no—
47#14519777C2311yescharacteristic
48#14519777C2312yes—
49#14519774C2311yescharacteristic
50#14519765—21no—
51#14519751—21no—
52#14519751—21no—
53C4×Dic122—21no—
54C4×Dic122—21no—
55C4×Dic122D412yes—
56C4×Dic122C2312yes—
57C4×D244—21no—
58C4×D244—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61D411yescharacteristic
62C2×#11758196—21no—
63C2×C4×Dic61—21no—
64#14519709—24no—
65C4⋊#92418C2312yes—
66#14519706—24no—
67#14519702—24no—
68#14519702—24no—
69#14519702—22no—
70#14519699—22no—
71C22⋊#92418—21no—
72C4×#92418—21no—
73C8×Dic61—24no—
74C2×M16×C61—21no—
75C22×C8×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61D412yes—
80C4⋊C8×C61C2312yes—
81C4⋊C8×C61C2312yes—
82C22⋊C8×C61D412yes—
83C4×C8×C61C2312yes—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—41no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—41no—
91#11758222—42no—
92#11758222—42no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×C4×D61—41no—
97C2×Dic122—21no—
98C2×Dic122—22no—
99C2×Dic122—22no—
100C2×Dic122—21no—
101C2×Dic122—41no—
102C2×Dic122—82no—
103C2×Dic122SD1614yescomplemented
104C2×Dic122C2×D412yes—
105M16×C61—42no—
106C2×C8×C61—22no—
107C2×C8×C61—22no—
108C2×C8×C61—42no—
109C2×C8×C61C2×D414yes—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C42×C61C2411yescharacteristic
114#11758198—41no—
115#11758198—41no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120C4⋊Dic61—21no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61C2×D412yes—
124#11758196—22no—
125#11758196—22no—
126C4×Dic61—22no—
127C4×Dic61—22no—
128C2×#92418—22no—
129Dic244—44no—
130#11758190—44no—
131#11758190—84no—
132C23×C61#12111yescharacteristic
133C22×D61—41no—
134C2×C4×C61—22no—
135C2×C4×C61—41no—
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61C2×SD1612yes—
140C2×C4×C61#13512yes—
141C2×C4×C61C22×D411yescharacteristic
142C2×C4×C61C22×D411yescharacteristic
143C2×C4×C61C2×#4111yescharacteristic
144C22⋊D61—82no—
145C2×Dic61—22no—
146C2×Dic61—24no—
147C2×Dic61—22no—
148C2×Dic61—42no—
149C2×Dic61—41no—
150C2×Dic61—81no—
151C2×Dic61—82no—
152D244—41no—
153D244—41no—
154D244—42no—
155D244—81no—
156C4×D61—82no—
157Dic122—22no—
158Dic122—24no—
159Dic122—41no—
160Dic122—41no—
161Dic122—44no—
162Dic122—82no—
163Dic122C2×SD1614yes—
164C8×C61—24no—
165C8×C61—42no—
166C8×C61—42no—
167#92418—42no—
168#19397—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61#46512yes—
172C22×C61C2×#12111yescharacteristic
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61#46512yes—
180C4×C61C22×SD1611yescharacteristic
181C4×C61C2×#13511yescharacteristic
182C4×C61#57712yes—
183Dic61—24no—
184Dic61—42no—
185Dic61—82no—
186Dic61—81no—
187#3206—611no—
188C2×#475—611no—
189#3037—611no—
190#2982—611no—
191#1680—614no—
192#1666—614no—
193#1570D6111yescharacteristic, complemented
194#1549—611no—
195#1540—611no—
196C2×C61—22no—
197C2×C61#304311yescharacteristic
198C2×C61C2×#46511yescharacteristic
199C2×C61#306911yescharacteristic
200D61—161no—
201C2×#137—1221no—
202#532—611no—
203C2×C4⋊Q8—611no—
204C2×C4×Q8—611no—
205#492—612no—
206#487—612no—
207#475—614no—
208#475—1222no—
209#464—1222no—
210#462—612no—
211#461—1222no—
212#460—612no—
213#448—1222no—
214C8×Q8—614no—
215C8×Q8—1222no—
216#431—611no—
217#431—1222no—
218#431C2×D6111yescharacteristic
219C2×#106—1221no—
220#423C2×D6111yescharacteristic
221C2×C4⋊C8C2×D6111yescharacteristic
222#417—1221no—
223C2×#103—1221no—
224#334C2×D6114yes—
225#332—612no—
226#332—614no—
227#331—612no—
228C61#1939711yescharacteristic, complemented, Sylow
229C2×#41—1221no—
230C22×Q8—611no—
231C22×Q8—1221no—
232#137—2444no—
233C2×Q16—1222no—
234C2×SD16—1222no—
235C2×SD16—1224no—
236C2×M16—21no—
237C22×C8—21no—
238C4⋊Q8—612no—
239C4⋊Q8—611no—
240C4⋊Q8—1221no—
241C4⋊Q8—1221no—
242C4⋊Q8—1221no—
243#127—611no—
244#124—1221no—
245#121—1221no—
246#121—1221no—
247C4×Q8—612no—
248C4×Q8—612no—
249C4×Q8—1221no—
250C4×Q8—1221no—
251C4×D4—1221no—
252C4×D4—1221no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C42—1221no—
258C2×C42C22×D6111yescharacteristic
259#106—1224no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—612no—
263C4⋊C8—1224no—
264C4⋊C8D24412yes—
265C4⋊C8C22×D6112yes—
266C4⋊C8C22×D6112yes—
267#103—1222no—
268#103—1224no—
269#103—1224no—
270#102—1222no—
271C22⋊C8—1221no—
272C22⋊C8D24412yes—
273C4×C8—1224no—
274C4×C8—1221no—
275C4×C8C22×D6112yes—
276#41—2442no—
277#41—2442no—
278C2×Q8—612no—
279C2×Q8—614no—
280C2×Q8—1221no—
281C2×Q8—1222no—
282C2×Q8—1221no—
283C2×Q8—1222no—
284C2×Q8—4882no—
285C2×Q8—2441no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—2441no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4C2×D24411yescharacteristic
295C22×C4D4×D6111yescharacteristic
296C22×C4#1175822611yescharacteristic
297Q16—2444no—
298SD16—4884no—
299SD16—2444no—
300M16—42no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—42no—
304C2×C8—1222no—
305C2×C8C2×D24414yes—
306C4⋊C4—612no—
307C4⋊C4—1222no—
308C4⋊C4—1221no—
309C4⋊C4—1222no—
310C4⋊C4—1222no—
311C4⋊C4—1221no—
312C4⋊C4—1222no—
313C4⋊C4—1221no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C42—1222no—
319C42—1222no—
320C42C2×D24411yescharacteristic
321C42D4×D6111yescharacteristic
322C42#1175822611yescharacteristic
323C42C23×D6111yescharacteristic
324C23—2441no—
325C23#1451975211yescharacteristic
326Q8—614no—
327Q8—1224no—
328Q8—1222no—
329Q8—4882no—
330Q8—2441no—
331Q8—2441no—
332Q8—2444no—
333D4—4881no—
334D4—4882no—
335D4—2441no—
336D4—2441no—
337D4—2442no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—1224no—
341C2×C4—1222no—
342C2×C4—1222no—
343C2×C4—4882no—
344C2×C4—4882no—
345C2×C4—4881no—
346C2×C4—2441no—
347C2×C4—2442no—
348C2×C4#1451975211yescharacteristic
349C2×C4#1451975211yescharacteristic
350C2×C4#1451975211yescharacteristic
351C2×C4SD16×D6112yes—
352C2×C4#1451979812yes—
353C2×C4C2×D4×D6111yescharacteristic
354C2×C4C22×D24411yescharacteristic
355C2×C4C2×#1175822611yescharacteristic
356C8—24no—
357C8—42no—
358C8—42no—
359C8—2442no—
360C22—21no—
361C22—21no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22#1683999212yes—
366C22C2×#1451975211yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—1224no—
371C4—4881no—
372C4—4882no—
373C4—2442no—
374C4#1683999212yes—
375C4C2×SD16×D6111yescharacteristic
376C4C2×#1451979811yescharacteristic
377C4#1684057412yes—
378C2—22no—
379C2—9761no—
380C2#2145534111yescharacteristic
381C2C2×#1683999211yescharacteristic
382C2#2145555711yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1570C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1570D61
hypocenterC61#19397
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
2. C2×#16840048C2semidirect
4. #21454899C2semidirect
5. #21445250C2semidirect
6. #21445168C2semidirect
7. #21444505C2semidirect
9. C61×#1570C2semidirect
103. C2×Dic122SD16semidirect
193. #1570D61semidirect
228. C61#19397semidirect

Maximal subgroups

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

subgroupindex
#214567462
C2×#168400482
#214552932
#214548992
#214452502
#214451682
#214445052
#214444692
C61×#15702
#1939761