Finite Group Databasebeta

← #29569253

Subgroups — #29569253

Order 15616.

434 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 81 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#21452748C211yesmaximal, characteristic
2#21447348C211yesmaximal, characteristic
3#21447296C211yesmaximal, characteristic, complemented
4#21443642C211yesmaximal, characteristic, complemented
5#21443641C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2084C211yesmaximal, characteristic, complemented
8C2×#14519762—21no—
9C2×#14519710—21no—
10C2×#14519708—21no—
11C2×#14519697—21no—
12#16839695—21no—
13#16839689—21no—
14#16839688—21no—
15#16839664C2211yescharacteristic
16#16839660C2211yescharacteristic
17#16839636—21no—
18#16839633—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×#106×C61—21no—
23C61×#389C2211yescharacteristic
24C61×#384C2211yescharacteristic
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×D244D411yescharacteristic
28C22×C4×D61—21no—
29C22×#92418—21no—
30C22×#92418—21no—
31#14519762—42no—
32#14519762—42no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43#14519710—42no—
44#14519708—42no—
45#14519697—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C22×C8×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58#106×C61—42no—
59#95×C61—21no—
60C23×D61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—41no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244—41no—
73C2×D244SD1612yes—
74C2×C4×D61—42no—
75C2×C4×D61—81no—
76C2×C4×D61—81no—
77C2×C8×C61—22no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C42×C61—41no—
92#11758198—42no—
93#11758198—42no—
94#11758198—42no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758198—41no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103#11758196—41no—
104#11758196—41no—
105#11758196—81no—
106C2×#92418—22no—
107C2×#92418—22no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C23×C61#12011yescharacteristic
113C22×D61—22no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150D244—42no—
151D244—81no—
152C4×D61—84no—
153C8×C61—42no—
154#92418—42no—
155#92418—42no—
156#7819—611nomaximal, Sylow
157C22×C61#44911yescharacteristic
158C22×C61#44911yescharacteristic
159C22×C61#45011yescharacteristic
160C22×C61#45311yescharacteristic
161C22×C61#45611yescharacteristic
162C22×C61#45611yescharacteristic
163C22×C61#45811yescharacteristic
164C2×D61—42no—
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—81no—
178C4×C61—81no—
179C4×C61—161no—
180Dic61—81no—
181Dic61—81no—
182Dic61—81no—
183#2724—611no—
184#2093—611no—
185#2084—611no—
186#2084D6111yescharacteristic, complemented
187#1271—611no—
188#1271—611no—
189#1270—611no—
190C2×C61#160911yescharacteristic
191C2×C61#160911yescharacteristic
192C2×C61#161311yescharacteristic
193C2×C61#162011yescharacteristic
194C2×C61#165411yescharacteristic
195C2×C61#165411yescharacteristic
196C2×C61#166011yescharacteristic
197D61—82no—
198C2×#123—1221no—
199C2×#107—1221no—
200C2×#106—21no—
201C2×#106—1221no—
202C2×#102—1221no—
203#398—1221no—
204#397—1221no—
205#397—1221no—
206#390—611no—
207#389—611no—
208#389C2×D6111yescharacteristic
209#385—1221no—
210#385—1221no—
211#384C2×D6111yescharacteristic
212#340—21no—
213#340—1221no—
214#336—611no—
215#336—611no—
216#336C2×D6111yescharacteristic
217C61#781911yescharacteristic, complemented, Sylow
218C22×D4—611no—
219C23×C4—1221no—
220C22×C8—21no—
221C22×C8—1221no—
222C22×C8—1221no—
223#123—2442no—
224#123—2442no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4C22⋊D6111yescharacteristic
235C2×C4⋊C4C22⋊D6111yescharacteristic
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C42C22×D6111yescharacteristic
242#107—2442no—
243#106—42no—
244#106—2442no—
245#102—2442no—
246#95—21no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251C24—1221no—
252C2×D4—612no—
253C2×D4—1221no—
254C2×D4—2441no—
255C2×D4—2441no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—4881no—
263C22×C4—4881no—
264C22×C4—2442no—
265C22×C4D4×D6111yescharacteristic
266C22×C4D4×D6111yescharacteristic
267C22×C4C2×C22⋊D6111yescharacteristic
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—1222no—
272C2×C8—1222no—
273C2×C8—2441no—
274C2×C8—2441no—
275C2×C8—2441no—
276C2×C8—2441no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—4881no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C22⋊C4—2442no—
296C22⋊C4—2442no—
297C22⋊C4—2442no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C42—41no—
303C23—1222no—
304C23—2441no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23—2441no—
310C23#1451974511yescharacteristic
311D4—4881no—
312D4—2442no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—4884no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4SD16×D6111yescharacteristic
339C2×C4#1451979711yescharacteristic
340C2×C4#1451979811yescharacteristic
341C2×C4#1451980311yescharacteristic
342C2×C4#1451980411yescharacteristic
343C2×C4#1451980411yescharacteristic
344C8—42no—
345C8—2442no—
346C8—2442no—
347C22—4881no—
348C22—4881no—
349C22—4881no—
350C22—4881no—
351C22—2442no—
352C22—2442no—
353C22—2442no—
354C22#1683990511yescharacteristic
355C22#1683990611yescharacteristic
356C22#1683991111yescharacteristic
357C22#1683992811yescharacteristic
358C22#1683994311yescharacteristic
359C22#1683994411yescharacteristic
360C22#1683995111yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—81no—
368C4—81no—
369C4—161no—
370C4—4881no—
371C4—4881no—
372C4—4881no—
373C2—4882no—
374C2#2144481411yescharacteristic
375C2#2144481511yescharacteristic
376C2#2144483711yescharacteristic
377C2#2144487711yescharacteristic
378C2#2144510011yescharacteristic
379C2#2144510111yescharacteristic
380C2#2144512911yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2084C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2084D61
hypocenterC61#7819
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
3. #21447296C2semidirect
4. #21443642C2semidirect
5. #21443641C2semidirect
7. C61×#2084C2semidirect
186. #2084D61semidirect
217. C61#7819semidirect

Maximal subgroups

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

subgroupindex
#214527482
#214473482
#214472962
#214436422
#214436412
#214436392
C61×#20842
#781961