Finite Group Databasebeta

← #29575961

Subgroups — #29575961

Order 15616.

548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455285C211yesmaximal, characteristic
2#21448790C211yesmaximal, characteristic, complemented
3#21444380C211yesmaximal, characteristic, complemented
4#21444313C211yesmaximal, characteristic, complemented
5#21444211C211yesmaximal, characteristic, complemented
6#21443679C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8C2×#14519805—21no—
9#16840312C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839978—22no—
12#16839968C412yescomplemented
13#16839958C412yescomplemented
14#16839815C2211yescharacteristic
15#16839764—21no—
16#16839664—21no—
17#16839652—22no—
18#16839628C2211yescharacteristic
19#16839624—21no—
20C4×C4⋊Dic61—21no—
21#16839609—21no—
22#16839497—22no—
23#16839495—21no—
24#16839495—21no—
25#16839491—22no—
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C4×C4⋊C4×C61C2211yescharacteristic
29C2×#11758222—21no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32#14519805—42no—
33#14519805—42no—
34C2×#11758190—22no—
35C2×D488—22no—
36#14519777C2×C411yescharacteristic
37#14519774C2×C411yescharacteristic
38#14519765—21no—
39#14519751—21no—
40#14519751—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244C2×C412yes—
46C4×D244D412yes—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61D411yescharacteristic
49C2×#11758198—21no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52C2×C4×Dic61—22no—
53C4⋊#92418—21no—
54#14519702—22no—
55#14519699—22no—
56C22⋊#92418—21no—
57C4×#92418—21no—
58#14519684—22no—
59#14519684—21no—
60#14519684D412yes—
61C2×M16×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C42×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C4⋊C8×C61C2×C412yes—
68C22⋊C8×C61—21no—
69C4×C8×C61—21no—
70#95×C61D411yescharacteristic
71#95×C61D411yescharacteristic
72C23×D61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—41no—
79C22×Dic61—21no—
80C22×Dic61—22no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—21no—
93C2×D244C22⋊C412yes—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C2×C4×D61—82no—
98C2×Dic122—21no—
99M16×C61—41no—
100M16×C61—41no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C4⋊C4×C61—42no—
104C42×C61—41no—
105C42×C61—41no—
106C42×C61C22×C411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—22no—
111#11758198—22no—
112#11758198—44no—
113#11758198—41no—
114#11758198—41no—
115#11758198—82no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61C22⋊C412yes—
122C4×Dic61—82no—
123C2×#92418—41no—
124D488—44no—
125#11758190—44no—
126C23×C61#12011yescharacteristic
127C22×D61—22no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12311yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C22⋊D61—81no—
152C22⋊D61—81no—
153C2×Dic61—22no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159D244—22no—
160D244—22no—
161D244—41no—
162D244—41no—
163D244—41no—
164D244—41no—
165D244—81no—
166D244—81no—
167C4×D61—82no—
168C4×D61—82no—
169C4×D61—81no—
170C4×D61—81no—
171Dic122—41no—
172Dic122—41no—
173C8×C61—42no—
174C8×C61—81no—
175#92418—81no—
176#9181—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61#38611yescharacteristic
180C22×C61#44911yescharacteristic
181C22×C61#44911yescharacteristic
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—82no—
186C2×D61—82no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—42no—
195C4×C61—81no—
196C4×C61#41611yescharacteristic
197C4×C61#41811yescharacteristic
198C4×C61#48211yescharacteristic
199C4×C61#48211yescharacteristic
200Dic61—42no—
201Dic61—82no—
202Dic61—81no—
203#3036—611no—
204#2357—611no—
205#1517—611no—
206#1502—611no—
207#1478—611no—
208#1303D6111yescharacteristic, complemented
209#1286—611no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61#187511yescharacteristic
213C2×C61#190411yescharacteristic
214C2×C61#190611yescharacteristic
215D61—82no—
216D61—161no—
217C2×AGL(1,ℤ/8)—1221no—
218#532—611no—
219C2×C4×D4—611no—
220#463—1222no—
221#461—612no—
222#459—612no—
223#431—611no—
224#431C2×D6111yescharacteristic
225#423C2×D6111yescharacteristic
226#417—1221no—
227#390—1221no—
228#388—1222no—
229#382—611no—
230#381—1221no—
231C4×C4⋊C4—1221no—
232C4×C4⋊C4C2×D6111yescharacteristic
233C4×C22⋊C4—1221no—
234#327—1222no—
235#327—1221no—
236#327—1221no—
237D4⋊C8—1222no—
238C61#918111yescharacteristic, complemented, Sylow
239C2×#41—1221no—
240C22×D4—611no—
241C23×C4—1221no—
242AGL(1,ℤ/8)—2442no—
243AGL(1,ℤ/8)—2442no—
244C2×SD16—1222no—
245C2×D8—1222no—
246C2×M16—21no—
247C4⋊Q8—611no—
248#127—611no—
249#124—1221no—
250#121—1221no—
251#121—1221no—
252C4×D4—612no—
253C4×D4—612no—
254C4×D4—1221no—
255C4×D4—1221no—
256C4×D4—1221no—
257C4×D4—1221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1222no—
263C2×C22⋊C4—1222no—
264C2×C42—21no—
265C2×C42—1222no—
266C2×C42C22×D6111yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—1221no—
270C4⋊C8C4×D6112yes—
271#103—1222no—
272#102—1222no—
273C22⋊C8—21no—
274C22⋊C8—1221no—
275C4×C8—21no—
276C4×C8—1221no—
277#95—612no—
278#95—1222no—
279#95—1221no—
280#95D24411yescharacteristic
281#95D24411yescharacteristic
282C24—1221no—
283#41—2441no—
284#41—2441no—
285#41—2441no—
286#41—2441no—
287C2×Q8—1221no—
288C2×D4—612no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—2441no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—1221no—
301C22×C4—1222no—
302C22×C4—1222no—
303C22×C4—1222no—
304C22×C4—4882no—
305C22×C4—2441no—
306C22×C4C2×D24411yescharacteristic
307C22×C4D4×D6111yescharacteristic
308C22×C4D4×D6111yescharacteristic
309SD16—2444no—
310D8—2444no—
311M16—41no—
312M16—41no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—2441no—
316C4⋊C4—42no—
317C4⋊C4—612no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C22⋊C4—1222no—
324C22⋊C4—1222no—
325C22⋊C4—4882no—
326C22⋊C4—2444no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C42—41no—
330C42—41no—
331C42—4882no—
332C42C2×C4×D6111yescharacteristic
333C42#1175822211yescharacteristic
334C42D4×D6111yescharacteristic
335C42#1175822611yescharacteristic
336C23—1222no—
337C23—2442no—
338C23—2442no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23#1451974711yescharacteristic
343Q8—2441no—
344Q8—2441no—
345D4—1222no—
346D4—1222no—
347D4—4881no—
348D4—4881no—
349D4—4881no—
350D4—4881no—
351D4—2441no—
352D4—2441no—
353D4—2441no—
354D4—2441no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—1222no—
364C2×C4—4882no—
365C2×C4—4882no—
366C2×C4—4881no—
367C2×C4—4881no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2441no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4C22⋊C4×D6111yescharacteristic
374C2×C4#1451973911yescharacteristic
375C2×C4C4×D24411yescharacteristic
376C2×C4#1451975011yescharacteristic
377C2×C4#1451975211yescharacteristic
378C2×C4#1451976211yescharacteristic
379C2×C4#1451979811yescharacteristic
380C2×C4#1451980011yescharacteristic
381C2×C4#1451980111yescharacteristic
382C2×C4#1451980411yescharacteristic
383C8—42no—
384C8—81no—
385C8—4881no—
386C22—21no—
387C22—21no—
388C22—4882no—
389C22—4882no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—2442no—
394C22—2442no—
395C22—2442no—
396C22#1683964011yescharacteristic
397C22#1683990811yescharacteristic
398C22#1683991011yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—81no—
405C4—4882no—
406C4—4881no—
407C4—2442no—
408C4#1683975711yescharacteristic
409C4#1683976511yescharacteristic
410C4#1684008811yescharacteristic
411C4#1684008911yescharacteristic
412C2—21no—
413C2—21no—
414C2—9761no—
415C2—4882no—
416C2#2144614011yescharacteristic
417C2#2144630511yescharacteristic
418C2#2144631911yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radical#21455285C2
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9181
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
2. #21448790C2semidirect
3. #21444380C2semidirect
4. #21444313C2semidirect
5. #21444211C2semidirect
6. #21443679C2semidirect
7. C61×#1303C2semidirect
12. #16839968C4semidirect
13. #16839958C4semidirect
208. #1303D61semidirect
238. C61#9181semidirect

Maximal subgroups

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

subgroupindex
#214552852
#214487902
#214443802
#214443132
#214442112
#214436792
C61×#13032
#918161