Finite Group Databasebeta

← #29665366

Subgroups — #29665366

Order 15616.

676 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#21456942C211yesmaximal, characteristic
2#21455293C211yesmaximal, characteristic
3C2×#16839973C211yesmaximal, characteristic, complemented
4#21454899C211yesmaximal, characteristic, complemented
5#21445264C214yesmaximal, complemented
6#21445214C214yesmaximal, complemented
7#21444492C211yesmaximal, characteristic, complemented
8#21444469C211yesmaximal, characteristic
9C61×#1571C211yesmaximal, characteristic, complemented
10C2×#14519810—21no—
11C22×Dic244—21no—
12#16840312C2211yescharacteristic
13C2×#14519777C2211yescharacteristic
14C2×C4×Dic122C2211yescharacteristic
15#16840167C2212yes—
16#16840109C2212yes—
17#16840076—22no—
18#16840043—22no—
19#16839985—22no—
20#16839973—22no—
21#16839973C2212yes—
22#16839973C2214yes—
23#16839963C2212yes—
24C8×Dic122C2214yes—
25#16839886—22no—
26#16839815C2211yescharacteristic
27#16839812—22no—
28#16839764—21no—
29C2×#14519702—21no—
30#16839509C2212yes—
31#16839509C2214yes—
32#16839505C2212yes—
33C61×#431C2211yescharacteristic
34C61×#423C2211yescharacteristic
35C2×C4⋊C8×C61C2211yescharacteristic
36C61×#335C2214yes—
37C2×#11758222—21no—
38C22×Dic122—21no—
39C22×Dic122D411yescharacteristic
40#14519810—44no—
41C2×Dic244—24no—
42C2×Dic244—22no—
43C2×Dic244—44no—
44C2×#11758190—22no—
45#14519777—21no—
46#14519777—21no—
47#14519777—21no—
48#14519777C2312yes—
49#14519777C2311yescharacteristic
50#14519774C2311yescharacteristic
51#14519765—21no—
52#14519751—21no—
53#14519751—21no—
54C4×Dic122—21no—
55C4×Dic122—21no—
56C4×Dic122D412yes—
57C4×Dic122C2312yes—
58C4×D244—21no—
59C4×D244—21no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61D411yescharacteristic
63C2×#11758196—21no—
64C2×C4×Dic61—21no—
65#14519711—24no—
66C4⋊#92418C2312yes—
67#14519706—24no—
68#14519702—24no—
69#14519702—22no—
70#14519699—24no—
71#14519699—22no—
72C22⋊#92418—21no—
73C4×#92418—21no—
74C8×Dic61—24no—
75C2×M16×C61—21no—
76C22×C8×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61—21no—
80C4⋊C8×C61D412yes—
81C4⋊C8×C61C2312yes—
82C4⋊C8×C61C2312yes—
83C22⋊C8×C61D412yes—
84C4×C8×C61C2312yes—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C2×C22⋊D61—41no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—41no—
92#11758222—42no—
93#11758222—42no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—21no—
97C2×C4×D61—41no—
98C2×Dic122—21no—
99C2×Dic122—22no—
100C2×Dic122—22no—
101C2×Dic122—21no—
102C2×Dic122—42no—
103C2×Dic122—42no—
104C2×Dic122—41no—
105C2×Dic122D814yes—
106C2×Dic122C2×D412yes—
107M16×C61—42no—
108C2×C8×C61—22no—
109C2×C8×C61—22no—
110C2×C8×C61—42no—
111C2×C8×C61C2×D414yes—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C42×C61C2411yescharacteristic
116#11758198—41no—
117#11758198—41no—
118C4⋊Dic61—21no—
119C4⋊Dic61—22no—
120C4⋊Dic61—21no—
121C4⋊Dic61—22no—
122C4⋊Dic61—21no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125C4⋊Dic61C2×D412yes—
126#11758196—22no—
127#11758196—22no—
128C4×Dic61—22no—
129C4×Dic61—22no—
130C2×#92418—22no—
131Dic244—44no—
132Dic244—48no—
133#11758190—44no—
134C23×C61#12111yescharacteristic
135C22×D61—41no—
136C2×C4×C61—22no—
137C2×C4×C61—41no—
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61C2×D812yes—
142C2×C4×C61#13512yes—
143C2×C4×C61C22×D411yescharacteristic
144C2×C4×C61C22×D411yescharacteristic
145C2×C4×C61C2×#4111yescharacteristic
146C22⋊D61—82no—
147C2×Dic61—22no—
148C2×Dic61—24no—
149C2×Dic61—22no—
150C2×Dic61—42no—
151C2×Dic61—41no—
152C2×Dic61—81no—
153C2×Dic61—82no—
154D244—41no—
155D244—41no—
156D244—42no—
157D244—81no—
158C4×D61—82no—
159Dic122—22no—
160Dic122—24no—
161Dic122—42no—
162Dic122—41no—
163Dic122—42no—
164Dic122—41no—
165Dic122—82no—
166Dic122C2×D814yes—
167C8×C61—24no—
168C8×C61—42no—
169C8×C61—42no—
170#92418—42no—
171#19404—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#46612yes—
175C22×C61C2×#12111yescharacteristic
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61#46612yes—
183C4×C61C22×D811yescharacteristic
184C4×C61C2×#13511yescharacteristic
185C4×C61#57812yes—
186Dic61—24no—
187Dic61—42no—
188Dic61—82no—
189Dic61—81no—
190#3226—611no—
191#3037—611no—
192C2×#462—611no—
193#2982—611no—
194#1682—614no—
195#1674—614no—
196#1571D6111yescharacteristic, complemented
197#1546—611no—
198#1540—611no—
199C2×C61—22no—
200C2×C61#304411yescharacteristic
201C2×C61C2×#46611yescharacteristic
202C2×C61#306911yescharacteristic
203D61—161no—
204C2×#137—1221no—
205C22×Q16—1221no—
206#532—611no—
207C2×C4⋊Q8—611no—
208C2×C4×Q8—611no—
209#500—612no—
210#486—612no—
211#480—1222no—
212#474—1222no—
213#464—1222no—
214#462—612no—
215#462—614no—
216#462—1222no—
217#460—612no—
218C8×Q8—614no—
219C8×Q8—1222no—
220#431—611no—
221#431—1222no—
222#431C2×D6111yescharacteristic
223#423C2×D6111yescharacteristic
224C2×C4⋊C8C2×D6111yescharacteristic
225#417—1221no—
226C2×#103—1221no—
227#335C2×D6114yes—
228#332—612no—
229#332—614no—
230#331—612no—
231C61#1940411yescharacteristic, complemented, Sylow
232C2×#41—1221no—
233C22×Q8—611no—
234C22×Q8—1221no—
235#137—2444no—
236C2×Q16—1224no—
237C2×Q16—1222no—
238C2×Q16—2444no—
239C2×SD16—1222no—
240C2×M16—21no—
241C22×C8—21no—
242C4⋊Q8—612no—
243C4⋊Q8—611no—
244C4⋊Q8—1221no—
245C4⋊Q8—1221no—
246C4⋊Q8—1221no—
247#127—611no—
248#124—1221no—
249#121—1221no—
250#121—1221no—
251C4×Q8—612no—
252C4×Q8—612no—
253C4×Q8—1221no—
254C4×Q8—1221no—
255C4×D4—1221no—
256C4×D4—1221no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C42—1221no—
262C2×C42C22×D6111yescharacteristic
263#107—1224no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—612no—
267C4⋊C8—1224no—
268C4⋊C8D24412yes—
269C4⋊C8C22×D6112yes—
270C4⋊C8C22×D6112yes—
271#103—1224no—
272#103—1222no—
273#102—1222no—
274#102—1224no—
275C22⋊C8—1221no—
276C22⋊C8D24412yes—
277C4×C8—1224no—
278C4×C8—1221no—
279C4×C8C22×D6112yes—
280#41—2442no—
281#41—2442no—
282C2×Q8—612no—
283C2×Q8—614no—
284C2×Q8—1221no—
285C2×Q8—1222no—
286C2×Q8—1221no—
287C2×Q8—1222no—
288C2×Q8—2442no—
289C2×Q8—2442no—
290C2×Q8—2441no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—2441no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—2441no—
298C22×C4—2441no—
299C22×C4C2×D24411yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4#1175822611yescharacteristic
302Q16—2448no—
303Q16—2444no—
304SD16—2444no—
305M16—42no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—42no—
309C2×C8—1222no—
310C2×C8C2×D24414yes—
311C4⋊C4—612no—
312C4⋊C4—1222no—
313C4⋊C4—1221no—
314C4⋊C4—1222no—
315C4⋊C4—1222no—
316C4⋊C4—1221no—
317C4⋊C4—1222no—
318C4⋊C4—1221no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C22⋊C4—2441no—
322C22⋊C4—2441no—
323C42—1222no—
324C42—1222no—
325C42C2×D24411yescharacteristic
326C42D4×D6111yescharacteristic
327C42#1175822611yescharacteristic
328C42C23×D6111yescharacteristic
329C23—2441no—
330C23#1451975211yescharacteristic
331Q8—614no—
332Q8—1224no—
333Q8—1222no—
334Q8—4882no—
335Q8—2442no—
336Q8—2441no—
337Q8—2442no—
338Q8—2441no—
339D4—4881no—
340D4—4882no—
341D4—2441no—
342D4—2441no—
343D4—2442no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—1224no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—4882no—
350C2×C4—4882no—
351C2×C4—4881no—
352C2×C4—2441no—
353C2×C4—2442no—
354C2×C4#1451975211yescharacteristic
355C2×C4#1451975211yescharacteristic
356C2×C4#1451975211yescharacteristic
357C2×C4D8×D6112yes—
358C2×C4#1451980012yes—
359C2×C4C2×D4×D6111yescharacteristic
360C2×C4C22×D24411yescharacteristic
361C2×C4C2×#1175822611yescharacteristic
362C8—24no—
363C8—42no—
364C8—42no—
365C8—2442no—
366C22—21no—
367C22—21no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22#1683999912yes—
372C22C2×#1451975211yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—1224no—
377C4—4881no—
378C4—4882no—
379C4—2442no—
380C4#1683999912yes—
381C4C2×D8×D6111yescharacteristic
382C4C2×#1451980011yescharacteristic
383C4#1684057912yes—
384C2—22no—
385C2—9761no—
386C2#2145535011yescharacteristic
387C2C2×#1683999911yescharacteristic
388C2#2145555711yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1571C2
socleC22×C61C2×#121
prime radical#16840312C22
hypercenter#1571D61
hypocenterC61#19404
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
3. C2×#16839973C2semidirect
4. #21454899C2semidirect
5. #21445264C2semidirect
6. #21445214C2semidirect
7. #21444492C2semidirect
9. C61×#1571C2semidirect
196. #1571D61semidirect
231. C61#19404semidirect

Maximal subgroups

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

subgroupindex
#214569422
#214552932
C2×#168399732
#214548992
#214452642
#214452142
#214444922
#214444692
C61×#15712
#1940461