Finite Group Databasebeta

← #30607435

Subgroups — #30607435

Order 15616.

384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462598C211yesmaximal, characteristic
2C2×#16840686C211yesmaximal, characteristic, complemented
3D61⋊#360C211yesmaximal, characteristic
4#21461936C211yesmaximal, characteristic, complemented
5#21460888C211yesmaximal, characteristic, complemented
6#21460868C211yesmaximal, characteristic, complemented
7#21447545C211yesmaximal, characteristic
8#16840841—21no—
9D61⋊M32C2211yescharacteristic
10#16840809—21no—
11#16840808—21no—
12#16840805—22no—
13C2×#14519847C2211yescharacteristic
14#16840773—21no—
15C2×#14519845C2211yescharacteristic
16#16840759—21no—
17#16840725C2211yescharacteristic
18#16840686—22no—
19#16840679—21no—
20#16840678—21no—
21#16840641—21no—
22#135×D61C2211yescharacteristic
23C2×#14519716C2211yescharacteristic
24#108×D61C2211yescharacteristic
25#16839570C411yescharacteristic, complemented
26#16839569C411yescharacteristic, complemented
27#16839568C411yescharacteristic, complemented
28C61×#359C411yescharacteristic, complemented
29#14519865—22no—
30#14519864—22no—
31#14519864—42no—
32C2×#11758213—21no—
33C2×#11758213—41no—
34D61⋊M16—41no—
35D61⋊M16D411yescharacteristic
36#14519856D411yescharacteristic
37C2×C4⋊#6923—21no—
38#14519852—21no—
39#14519851—21no—
40D61⋊C16—21no—
41#14519847—21no—
42#14519847D412yes—
43#14519846—41no—
44#14519845—21no—
45#14519845—21no—
46#14519845—41no—
47#14519842—22no—
48#14519841—22no—
49#14519831—21no—
50C8×#6923—21no—
51#41×D61—21no—
52#14519800D411yescharacteristic
53#14519799C2×C411yescharacteristic
54#14519798—21no—
55#14519797—21no—
56#14519796D411yescharacteristic
57Q16×D61Q811yescharacteristic
58SD16×D61—21no—
59D8×D61Q811yescharacteristic
60M16×D61—21no—
61C2×C8×D61C2311yescharacteristic
62#14519716—21no—
63#14519716—21no—
64C2×#11758185C2×C411yescharacteristic
65#14519713C2×C411yescharacteristic
66#14519712—21no—
67#135×C61C2×C411yescharacteristic
68C2×C16×C61C2×C411yescharacteristic
69#108×C61C2×C411yescharacteristic
70C22×#6923—41no—
71#41×C61—21no—
72#11758226—21no—
73Q8×D61—21no—
74#11758224—21no—
75#11758224—41no—
76D4×D61—21no—
77D4×D61—41no—
78#11758222—21no—
79#11758222—41no—
80C2×C4×D61—41no—
81C2×C4×D61C2×D411yescharacteristic
82C22⋊#6923—21no—
83#11758217—42no—
84#11758217SD1612yes—
85C2×#92420—42no—
86C2×#92420—41no—
87C4⋊#6923—21no—
88C4⋊#6923—41no—
89C4⋊#6923—41no—
90C4×#6923—21no—
91#11758213—21no—
92#11758213—22no—
93#11758213—42no—
94#11758213—41no—
95D61⋊C8—21no—
96D61⋊C8—42no—
97Q16×C61C4⋊C411yescharacteristic
98SD16×C61—21no—
99D8×C61C4⋊C411yescharacteristic
100M16×C61—21no—
101C2×C8×C61C22×C411yescharacteristic
102#11758202—21no—
103#11758201—21no—
104#11758200—21no—
105#11758199—21no—
106#11758194—21no—
107C2×#92418#4111yescharacteristic
108Dic244C4⋊C411yescharacteristic
109D488C4⋊C411yescharacteristic
110#11758190—21no—
111#11758189—41no—
112C8×D61—41no—
113C8×D61C2×D411yescharacteristic
114C8×D61C2×D411yescharacteristic
115C8×D61C2×Q811yescharacteristic
116C8×D61#4111yescharacteristic
117#11758187—41no—
118C16×C61—21no—
119#11758185—21no—
120C22×D61—41no—
121C22×D61#13511yescharacteristic
122C2×#6923—41no—
123C2×#6923—81no—
124C2×#6923—161no—
125Q8×C61—21no—
126D4×C61—21no—
127D4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61C4×D411yescharacteristic
130C22⋊D61—41no—
131C22⋊D61—41no—
132C22⋊D61—41no—
133C2×Dic61—41no—
134C2×Dic61C2×SD1611yescharacteristic
135D244—21no—
136D244—41no—
137C4×D61—41no—
138C4×D61—41no—
139C4×D61—41no—
140C4×D61#12011yescharacteristic
141C4×D61C22⋊Q811yescharacteristic
142C4×D61AGL(1,ℤ/8)11yescharacteristic
143C4×D61AGL(1,ℤ/8)11yescharacteristic
144Dic122—21no—
145Dic122—41no—
146#92420—22no—
147#92420—42no—
148C8×C61—41no—
149C8×C61C2×C4⋊C411yescharacteristic
150C8×C61C4×D411yescharacteristic
151#92418—41no—
152#92418C22⋊Q811yescharacteristic
153#92418#12311yescharacteristic
154#12948—611nomaximal, Sylow
155C22×C61—41no—
156C22×C61C4×SD1611yescharacteristic
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—161no—
160C2×D61#44911yescharacteristic
161C2×D61#47811yescharacteristic
162#6923—81no—
163#6923—161no—
164C4×C61—41no—
165C4×C61#38511yescharacteristic
166C4×C61#44211yescharacteristic
167Dic61—41no—
168Dic61#45011yescharacteristic
169Dic61#47611yescharacteristic
170#2957—611no—
171C2×#365—611no—
172C2×#360—611no—
173#2143—611no—
174#1951—611no—
175#1385—611no—
176#1378—611no—
177C2×C61—21no—
178C2×C61—81no—
179C2×C61#186411yescharacteristic
180D61—21no—
181D61—21no—
182D61—81no—
183C2×#135—611no—
184#568—1221no—
185C2×M32—611no—
186C2×M32—611no—
187#444—1221no—
188#444—1221no—
189#443—1222no—
190C2×#108—611no—
191C2×#108—611no—
192#428—1221no—
193C2×#106—611no—
194#421—1221no—
195#405—611no—
196#365—1222no—
197#360—1221no—
198#360—1221no—
199#359—611no—
200#359—611no—
201#359—611no—
202#359#692311yescharacteristic, complemented
203#343—1221no—
204C61#1294811yescharacteristic, complemented, Sylow
205C2×#41—1221no—
206#135—611no—
207#135—611no—
208#135—611no—
209#135—1221no—
210#135—1221no—
211#135C2×#692311yescharacteristic
212C2×Q16—611no—
213C2×SD16—1221no—
214C2×D8—611no—
215#131—1222no—
216#131—1222no—
217#131—2442no—
218C2×M16—611no—
219C2×M16—1221no—
220C2×M16—1221no—
221C2×M16—2441no—
222C2×M16—2441no—
223C22×C8—611no—
224#117—611no—
225C2×C4⋊C4—1221no—
226M32—1221no—
227M32—1221no—
228M32—1221no—
229M32—1221no—
230C2×C16—611no—
231C2×C16—1221no—
232C2×C16C2×#692311yescharacteristic
233#108—612no—
234#108—611no—
235#108—1221no—
236#108—1221no—
237#108C2×#692311yescharacteristic
238#107—2441no—
239#106—1221no—
240#106—1221no—
241#106—2441no—
242#104—1222no—
243#104—1222no—
244#97—1221no—
245C4×C8—1221no—
246#41—21no—
247#41—1221no—
248#41—1221no—
249#41—1221no—
250#41—2441no—
251#41—2441no—
252C2×Q8—1221no—
253C2×D4—1221no—
254C2×D4—2441no—
255C22×C4—611no—
256C22×C4—2441no—
257C22×C4—2441no—
258Q16—611no—
259Q16—1221no—
260Q16C4⋊#692311yescharacteristic
261SD16—21no—
262SD16—1221no—
263SD16—1221no—
264SD16—1221no—
265D8—611no—
266D8—1221no—
267D8C4⋊#692311yescharacteristic
268M16—21no—
269M16—612no—
270M16—1221no—
271M16—1222no—
272M16—1221no—
273M16—2441no—
274M16—2442no—
275M16—2442no—
276M16—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8—611no—
281C2×C8—611no—
282C2×C8—1221no—
283C2×C8—2441no—
284C2×C8—2442no—
285C2×C8—2442no—
286C2×C8—2441no—
287C2×C8C22×#692311yescharacteristic
288C4⋊C4—1221no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C22⋊C4—1221no—
292C42—1221no—
293C16—21no—
294C16—1221no—
295C16—2441no—
296C23—611no—
297C23—2441no—
298Q8—21no—
299Q8—1221no—
300Q8—2441no—
301D4—21no—
302D4—41no—
303D4—1221no—
304D4—2441no—
305D4—2441no—
306D4—2441no—
307D4—2441no—
308C2×C4—41no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—9761no—
315C2×C4—4881no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4D4×#692311yescharacteristic
322C8—41no—
323C8—611no—
324C8—611no—
325C8—1222no—
326C8—2442no—
327C8—2441no—
328C8C2×C4⋊#692311yescharacteristic
329C8D4×#692311yescharacteristic
330C22—41no—
331C22—611no—
332C22—611no—
333C22—9761no—
334C22—2441no—
335C22—2441no—
336C22SD16×#692311yescharacteristic
337C4—41no—
338C4—611no—
339C4—611no—
340C4—9761no—
341C4—4881no—
342C4—2441no—
343C4#1684070911yescharacteristic
344C4#1684080311yescharacteristic
345C2—21no—
346C2—81no—
347C2—1221no—
348C2—1221no—
349C2—4881no—
350C2#2146178411yescharacteristic
subgroupG/H
centerC2#21461784
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#359C4
socleC2×C61#1864
prime radical#135×D61C22
cosocleC2×C8×D61C23
hypercenter#359#6923
hypocenterC61#12948
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
2. C2×#16840686C2semidirect
4. #21461936C2semidirect
5. #21460888C2semidirect
6. #21460868C2semidirect
25. #16839570C4semidirect
26. #16839569C4semidirect
27. #16839568C4semidirect
28. C61×#359C4semidirect
202. #359#6923semidirect
204. C61#12948semidirect

Maximal subgroups

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

subgroupindex
#214625982
C2×#168406862
D61⋊#3602
#214619362
#214608882
#214608682
#214475452
#1294861