Finite Group Databasebeta

← #29580864

Subgroups — #29580864

Order 15616.

566 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 101 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#21455846C211yesmaximal, characteristic
2#21449110C211yesmaximal, characteristic, complemented
3#21446652C211yesmaximal, characteristic
4#21444249C211yesmaximal, characteristic, complemented
5#21444248C211yesmaximal, characteristic, complemented
6#21443647C211yesmaximal, characteristic, complemented
7C61×#3103C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16840078—21no—
10#16840044—21no—
11#16839959—21no—
12#16839900—21no—
13C4×#11758200—22no—
14#16839815C2211yescharacteristic
15#16839786C2211yescharacteristic
16C2×#14519704—22no—
17#16839693—21no—
18#16839692—21no—
19#16839682—21no—
20#16839681—21no—
21C4×#11758196—22no—
22#16839608C2211yescharacteristic
23#16839494—22no—
24Q8⋊#92418—22no—
25C61×#532C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C61×#481—21no—
28C61×#475—21no—
29C61×#460—21no—
30C61×#448—21no—
31C4×SD16×C61—22no—
32C61×#431C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×#11758200—22no—
35C2×#11758194—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—22no—
42C2×#11758196—22no—
43C2×#11758196—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61D412yes—
46#14519708—22no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519704—44no—
51#14519700—22no—
52#14519698—22no—
53C22⋊#92418—21no—
54C4×#92418D412yes—
55#14519684—22no—
56#14519684—22no—
57#14519684—21no—
58#14519684—21no—
59C2×#41×C61—21no—
60C22×Q8×C61D411yescharacteristic
61C2×SD16×C61—22no—
62C4⋊Q8×C61D411yescharacteristic
63#127×C61D411yescharacteristic
64#124×C61—21no—
65#121×C61—21no—
66#121×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C42×C61—21no—
76C2×C42×C61C2311yescharacteristic
77#106×C61—22no—
78C4⋊C8×C61—21no—
79#103×C61—22no—
80#102×C61—22no—
81C22⋊C8×C61—21no—
82C4×C8×C61D412yes—
83#41×C61—42no—
84#41×C61—42no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61—42no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—41no—
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×Dic61—21no—
100C22×Dic61—22no—
101C22×Dic61—21no—
102C2×Dic122—21no—
103C2×Dic122—21no—
104C2×Dic122—42no—
105SD16×C61—44no—
106C2×C8×C61—22no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C42×C61—41no—
116C42×C61—41no—
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121#11758200—44no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124#11758196—44no—
125#11758196—44no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—22no—
129C4×Dic61—41no—
130C4×Dic61—41no—
131C4×Dic61SD1614yescomplemented
132#11758194—42no—
133C2×#92418—22no—
134C2×#92418—41no—
135C23×C61—41no—
136C23×C61#12011yescharacteristic
137Q8×C61—22no—
138Q8×C61—22no—
139Q8×C61—41no—
140Q8×C61—41no—
141Q8×C61—42no—
142D4×C61—42no—
143D4×C61—42no—
144D4×C61—42no—
145D4×C61—82no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—42no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—81no—
155C2×C4×C61—81no—
156C2×C4×C61#12011yescharacteristic
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12711yescharacteristic
162C2×C4×C61C2×SD1612yes—
163C2×C4×C61#13712yes—
164C2×Dic61—22no—
165C2×Dic61—24no—
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—42no—
171C2×Dic61—41no—
172Dic122—22no—
173Dic122—22no—
174Dic122—41no—
175Dic122—41no—
176C8×C61—42no—
177#92418—42no—
178#92418—81no—
179#10014—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61#39211yescharacteristic
186C22×C61#44812yes—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—42no—
192C4×C61—81no—
193C4×C61—81no—
194C4×C61#46112yes—
195C4×C61#49211yescharacteristic
196C4×C61#49711yescharacteristic
197Dic61—44no—
198Dic61—42no—
199Dic61—81no—
200#3103—611no—
201#3103D6111yescharacteristic
202#2399—611no—
203#1963—611no—
204#1487—611no—
205#1487—611no—
206#1274—611no—
207C2×C61—22no—
208C2×C61—161no—
209C2×C61#201011yescharacteristic
210C2×C61#201011yescharacteristic
211C2×C61#201311yescharacteristic
212#532C2×D6111yescharacteristic
213C2×C4×Q8—611no—
214C2×C4×Q8C2×D6111yescharacteristic
215#481—21no—
216#481—1221no—
217#475—21no—
218#475—1221no—
219#460—21no—
220#460—1221no—
221#448—21no—
222#448—1221no—
223C4×SD16—22no—
224C4×SD16—1222no—
225#431—611no—
226#431C2×D6111yescharacteristic
227#423—611no—
228C2×#104—1222no—
229#398—1221no—
230#398—1221no—
231#395—1221no—
232#395—1221no—
233C4×C4⋊C4—1222no—
234#376—611no—
235Q8⋊C8—1222no—
236Q8⋊C8—1222no—
237C61#1001411yescharacteristic, complemented, Sylow
238C2×#41—21no—
239C22×Q8—611no—
240C22×Q8C22⋊D6111yescharacteristic
241C2×SD16—22no—
242C2×SD16—1222no—
243C2×M16—1221no—
244C4⋊Q8C22⋊D6111yescharacteristic
245#127C22⋊D6111yescharacteristic
246#124—21no—
247#121—21no—
248#121—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—1221no—
254C4×Q8—1221no—
255C4×Q8—1221no—
256C4×Q8—1221no—
257C4×D4—21no—
258C4×D4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—1222no—
262C2×C4⋊C4—1222no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4C22⋊D6111yescharacteristic
265C2×C42—21no—
266C2×C42—612no—
267C2×C42—1221no—
268C2×C42C22×D6111yescharacteristic
269#106—22no—
270#106—1222no—
271C4⋊C8—21no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274C4⋊C8—1221no—
275#104—2444no—
276#103—22no—
277#103—1222no—
278#102—22no—
279#102—1222no—
280C22⋊C8—21no—
281C22⋊C8—1221no—
282C4×C8—612no—
283C4×C8C22⋊D6112yes—
284#95—1222no—
285#95—1222no—
286#95—1221no—
287#95—1221no—
288#41—42no—
289#41—42no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—42no—
294C2×Q8—1221no—
295C2×Q8—1221no—
296C2×Q8—2442no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—41no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—1222no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4D4×D6111yescharacteristic
308C22×C4D4×D6111yescharacteristic
309C22×C4C2×C22⋊D6111yescharacteristic
310SD16—44no—
311SD16—2444no—
312M16—2442no—
313C2×C8—22no—
314C2×C8—1222no—
315C2×C8—2441no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—2444no—
325C4⋊C4—2444no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C42—41no—
331C42—41no—
332C42—614no—
333C42—1222no—
334C42—2441no—
335C42—2441no—
336C42D4×D6111yescharacteristic
337C42#1175822411yescharacteristic
338C42C2×C22⋊D6111yescharacteristic
339C42C2×C22⋊D6111yescharacteristic
340C23—41no—
341C23#1451974511yescharacteristic
342Q8—22no—
343Q8—22no—
344Q8—41no—
345Q8—41no—
346Q8—42no—
347Q8—1222no—
348Q8—1222no—
349Q8—2441no—
350Q8—2441no—
351D4—42no—
352D4—42no—
353D4—42no—
354D4—82no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—1222no—
366C2×C4—1224no—
367C2×C4—2442no—
368C2×C4—2441no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4#1451974511yescharacteristic
374C2×C4#1451974611yescharacteristic
375C2×C4#1451974811yescharacteristic
376C2×C4#1451974911yescharacteristic
377C2×C4#1451974911yescharacteristic
378C2×C4#1451977311yescharacteristic
379C2×C4SD16×D6112yes—
380C2×C4#1451980612yes—
381C8—42no—
382C8—4881no—
383C8—2442no—
384C22—21no—
385C22—21no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22#1683967011yescharacteristic
390C22#1683989912yes—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—42no—
396C4—81no—
397C4—81no—
398C4—4881no—
399C4—2444no—
400C4—2442no—
401C4#1683996512yes—
402C4#1684013311yescharacteristic
403C4#1684015311yescharacteristic
404C2—22no—
405C2—161no—
406C2#2144688311yescharacteristic
407C2#2144688411yescharacteristic
408C2#2144690011yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3103C2
socleC22×C61#392
prime radicalC61×#532C22
hypercenter#3103D61
hypocenterC61#10014
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
2. #21449110C2semidirect
4. #21444249C2semidirect
5. #21444248C2semidirect
6. #21443647C2semidirect
131. C4×Dic61SD16semidirect
237. C61#10014semidirect

Maximal subgroups

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

subgroupindex
#214558462
#214491102
#214466522
#214442492
#214442482
#214436472
C61×#31032
#1001461