Finite Group Databasebeta

← #29580794

Subgroups — #29580794

Order 15616.

500 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 99 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#21455859C211yesmaximal, characteristic
2#21455624C211yesmaximal, characteristic
3#21451181C211yesmaximal, characteristic
4#21444384C211yesmaximal, characteristic
5#21444249C211yesmaximal, characteristic
6#21443678C211yesmaximal, characteristic
7C61×#1479C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16840098—21no—
11#16840069—22no—
12#16840058—21no—
13#16840057—21no—
14#16840047—21no—
15#16839973—21no—
16#16839920—21no—
17C4×Dic244—22no—
18#16839802—21no—
19#16839786C2211yescharacteristic
20#16839771—21no—
21#16839701—21no—
22#16839682—21no—
23#16839669—21no—
24#16839658—21no—
25#16839646—22no—
26#16839628C2211yescharacteristic
27#16839500—22no—
28#16839494—22no—
29C2×C4×Q8×C61C2211yescharacteristic
30C61×#431C2211yescharacteristic
31C61×#431C2211yescharacteristic
32C61×Q8⋊C8—22no—
33C22×Dic122D411yescharacteristic
34C2×Dic244—22no—
35C2×#11758194—21no—
36#14519777D411yescharacteristic
37#14519777D411yescharacteristic
38#14519769—21no—
39#14519756—21no—
40#14519756—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47#14519736—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61D411yescharacteristic
50C2×#11758196—22no—
51C2×#11758196—21no—
52C2×C4×Dic61—21no—
53#14519711—22no—
54#14519710—22no—
55#14519708—22no—
56C4⋊#92418—21no—
57C4⋊#92418D412yes—
58#14519702—22no—
59#14519702—22no—
60#14519701—22no—
61#14519701—22no—
62#14519684—22no—
63#14519684—22no—
64#14519684—22no—
65#14519684—21no—
66#14519684D412yes—
67C22×Q8×C61D411yescharacteristic
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C42×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C4×C8×C61—21no—
81C4×C8×C61D412yes—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61Q1612yescomplemented
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×Dic61—21no—
94C22×Dic61—22no—
95C22×Dic61—21no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—21no—
100C2×Dic122—42no—
101C2×C8×C61—22no—
102C2×C8×C61—41no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113C22⋊Dic61—41no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—41no—
121C4⋊Dic61—41no—
122#11758196—44no—
123#11758196—41no—
124#11758196—41no—
125#11758196—41no—
126#11758196—41no—
127C4×Dic61—41no—
128C4×Dic61—41no—
129C4×Dic61—41no—
130#11758194—41no—
131#11758194—41no—
132C2×#92418—22no—
133Dic244—44no—
134C23×C61#12011yescharacteristic
135Q8×C61—22no—
136Q8×C61—22no—
137Q8×C61—41no—
138Q8×C61—41no—
139C2×C4×C61—22no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61#12011yescharacteristic
147C2×C4×C61#12011yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12711yescharacteristic
152C2×C4×C61C2×Q1611yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61#13711yescharacteristic
155C2×C4×C61#13711yescharacteristic
156C2×Dic61—22no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—42no—
160C2×Dic61—42no—
161C2×Dic61—42no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—42no—
166Dic122—22no—
167Dic122—22no—
168Dic122—41no—
169Dic122—41no—
170Dic122—42no—
171Dic122—81no—
172C8×C61—42no—
173C8×C61—81no—
174#92418—42no—
175#10003—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61#39211yescharacteristic
179C22×C61#45111yescharacteristic
180C22×C61#45211yescharacteristic
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—42no—
186C4×C61—81no—
187C4×C61#45111yescharacteristic
188C4×C61#45211yescharacteristic
189C4×C61#46711yescharacteristic
190C4×C61#47011yescharacteristic
191Dic61—42no—
192Dic61—82no—
193Dic61—81no—
194Dic61—81no—
195Dic61—81no—
196#3104—611no—
197#3078—611no—
198#2581—611no—
199#1518—611no—
200#1487—611no—
201#1479D6111yescharacteristic
202#1286—611no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61#200111yescharacteristic
206C2×C61#200911yescharacteristic
207C2×C61#201011yescharacteristic
208#533—611no—
209C2×C4×Q8—611no—
210C2×C4×Q8C2×D6111yescharacteristic
211#484—1221no—
212#479—1222no—
213#477—1221no—
214#477—1221no—
215#475—1221no—
216#462—1221no—
217#451—1221no—
218C4×Q16—1222no—
219#431C2×D6111yescharacteristic
220#431C2×D6111yescharacteristic
221#428—1221no—
222#423—611no—
223#419—1221no—
224#400—1221no—
225#395—1221no—
226#391—1221no—
227#389—1221no—
228#387—1222no—
229#382—611no—
230#328—1222no—
231Q8⋊C8—22no—
232Q8⋊C8—1222no—
233C61#1000311yescharacteristic, complemented, Sylow
234C22×Q8—611no—
235C22×Q8D24411yescharacteristic
236C2×Q16—1222no—
237C2×M16—1221no—
238C4⋊Q8—611no—
239C4⋊Q8—611no—
240#125—1221no—
241C22⋊Q8—1221no—
242C22⋊Q8—1221no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—1221no—
248C4×Q8—1221no—
249C4×Q8—1221no—
250C4×Q8—1221no—
251C4×Q8—1221no—
252C4×Q8—1221no—
253#117—1221no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—1222no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4D24411yescharacteristic
260C2×C42—21no—
261C2×C42—1221no—
262C2×C42C22×D6111yescharacteristic
263#107—1222no—
264#107—1222no—
265#106—1222no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—612no—
269C4⋊C8—1221no—
270#103—1222no—
271#103—1222no—
272#103—1222no—
273#103—1222no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C4×C8—21no—
277C4×C8C22⋊D6112yes—
278#95—612no—
279#95—1222no—
280#95—1222no—
281#95—1222no—
282#95—1221no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—1221no—
289C2×Q8—1221no—
290C2×Q8—1221no—
291C2×Q8—1221no—
292C2×Q8—2442no—
293C2×Q8Dic24412yescomplemented
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—1221no—
297C22×C4—1222no—
298C22×C4—1221no—
299C22×C4C2×D24411yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4D4×D6111yescharacteristic
302Q16—2444no—
303M16—2441no—
304M16—2441no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—1222no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—2444no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C22⋊C4—2441no—
326C42—41no—
327C42—41no—
328C42—2441no—
329C42—2441no—
330C42—2441no—
331C42#1175822211yescharacteristic
332C42D4×D6111yescharacteristic
333C42D4×D6111yescharacteristic
334C42C2×C22⋊D6111yescharacteristic
335C23#1451974711yescharacteristic
336Q8—22no—
337Q8—22no—
338Q8—41no—
339Q8—41no—
340Q8—1222no—
341Q8—1222no—
342Q8—4881no—
343Q8—2442no—
344Q8—2441no—
345Q8—2441no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—1222no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4#1451974511yescharacteristic
364C2×C4#1451974711yescharacteristic
365C2×C4#1451975011yescharacteristic
366C2×C4#1451975011yescharacteristic
367C2×C4#1451975111yescharacteristic
368C2×C4#1451977311yescharacteristic
369C2×C4C2×Dic24411yescharacteristic
370C2×C4#1451979911yescharacteristic
371C2×C4#1451981011yescharacteristic
372C2×C4#1451981011yescharacteristic
373C8—42no—
374C8—81no—
375C8—2442no—
376C22—21no—
377C22—21no—
378C22#1683967111yescharacteristic
379C22#1683992011yescharacteristic
380C22#1683992611yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—81no—
387C4—4882no—
388C4—4881no—
389C4—4881no—
390C4—4881no—
391C4—2442no—
392C4#1683992011yescharacteristic
393C4#1683992611yescharacteristic
394C4#1684000311yescharacteristic
395C4#1684002011yescharacteristic
396C2—21no—
397C2—21no—
398C2#2144682911yescharacteristic
399C2#2144688111yescharacteristic
400C2#2144688511yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1479C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#1479D61
hypocenterC61#10003
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
87. C2×Q8×C61Q16semidirect
233. C61#10003semidirect
293. C2×Q8Dic244semidirect

Maximal subgroups

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

subgroupindex
#214558592
#214556242
#214511812
#214443842
#214442492
#214436782
C61×#14792
#1000361