Finite Group Databasebeta

← #29580789

Subgroups — #29580789

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#21455620C211yesmaximal, characteristic
2#21451185C211yesmaximal, characteristic
3#21444383C211yesmaximal, characteristic
4#21444248C211yesmaximal, characteristic
5#21444215C211yesmaximal, characteristic
6#21443678C211yesmaximal, characteristic
7C61×#3104C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16840066—22no—
10#16840054—21no—
11#16840044—21no—
12#16839815C2211yescharacteristic
13#16839805—21no—
14#16839786C2211yescharacteristic
15#16839770—21no—
16#16839700—21no—
17#16839681—21no—
18#16839668—21no—
19#16839660—21no—
20#16839643—22no—
21#16839628C2211yescharacteristic
22#16839499—22no—
23#16839494—22no—
24Q8⋊#92418—22no—
25C61×#533C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C61×#484—21no—
28C61×#477—21no—
29C61×#462—21no—
30C61×#451—21no—
31C4×Q16×C61—22no—
32C61×#431C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×#11758194—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—22no—
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44#14519710—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418D412yes—
49#14519700—22no—
50#14519700—22no—
51C22⋊#92418—21no—
52C4×#92418—21no—
53#14519684—22no—
54#14519684—22no—
55#14519684—22no—
56#14519684—21no—
57#14519684D412yes—
58C22×Q8×C61D411yescharacteristic
59C2×Q16×C61—22no—
60C4⋊Q8×C61D411yescharacteristic
61C4⋊Q8×C61D411yescharacteristic
62#125×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71#117×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C42×C61—21no—
75C2×C42×C61C2311yescharacteristic
76#107×C61—22no—
77C4⋊C8×C61—21no—
78#103×C61—22no—
79#103×C61—22no—
80C22⋊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—42no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×Dic61—21no—
93C22×Dic61—22no—
94C22×Dic61—21no—
95C2×Dic122—21no—
96C2×Dic122—21no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—21no—
100C2×Dic122Q1612yescomplemented
101Q16×C61—44no—
102C2×C8×C61—22no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C42×C61—41no—
115C42×C61—41no—
116C42×C61—41no—
117C42×C61C2×D411yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—41no—
124C4⋊Dic61—41no—
125#11758196—44no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—41no—
129C4×Dic61—41no—
130#11758194—41no—
131#11758194—41no—
132C2×#92418—22no—
133C2×#92418—41no—
134C23×C61#12011yescharacteristic
135Q8×C61—22no—
136Q8×C61—22no—
137Q8×C61—41no—
138Q8×C61—41no—
139Q8×C61—42no—
140Q8×C61—81no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—42no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12011yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12711yescharacteristic
156C2×C4×C61C2×Q1611yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61#13711yescharacteristic
159C2×C4×C61#13711yescharacteristic
160C2×Dic61—22no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—42no—
164C2×Dic61—42no—
165C2×Dic61—42no—
166C2×Dic61—41no—
167C2×Dic61—42no—
168Dic122—22no—
169Dic122—22no—
170Dic122—41no—
171Dic122—41no—
172C8×C61—42no—
173#92418—42no—
174#92418—81no—
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—81no—
188C4×C61—81no—
189C4×C61#45111yescharacteristic
190C4×C61#45211yescharacteristic
191C4×C61#46711yescharacteristic
192C4×C61#47011yescharacteristic
193Dic61—42no—
194Dic61—82no—
195Dic61—81no—
196#3104D6111yescharacteristic
197#3078—611no—
198#2581—611no—
199#1518—611no—
200#1487—611no—
201#1479—611no—
202#1286—611no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61#200111yescharacteristic
206C2×C61#200911yescharacteristic
207C2×C61#201011yescharacteristic
208#533C2×D6111yescharacteristic
209C2×C4×Q8—611no—
210C2×C4×Q8C2×D6111yescharacteristic
211#484—21no—
212#479—1222no—
213#477—21no—
214#477—1221no—
215#475—1221no—
216#462—21no—
217#451—21no—
218C4×Q16—22no—
219#431—611no—
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—1222no—
232Q8⋊C8—1222no—
233C61#1000311yescharacteristic, complemented, Sylow
234C22×Q8—611no—
235C22×Q8C22⋊D6111yescharacteristic
236C2×Q16—22no—
237C2×M16—1221no—
238C4⋊Q8C22⋊D6111yescharacteristic
239C4⋊Q8C22⋊D6111yescharacteristic
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—1221no—
250C4×Q8—1221no—
251C4×Q8—1221no—
252C4×Q8—1221no—
253#117—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—1222no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4C22⋊D6111yescharacteristic
260C2×C42—21no—
261C2×C42—1221no—
262C2×C42C22×D6111yescharacteristic
263#107—22no—
264#107—1222no—
265#106—1222no—
266C4⋊C8—21no—
267C4⋊C8—612no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270#103—22no—
271#103—22no—
272#103—1222no—
273#103—1222no—
274C22⋊C8—21no—
275C22⋊C8—1221no—
276C4×C8—1221no—
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—42no—
288C2×Q8—612no—
289C2×Q8—1221no—
290C2×Q8—1221no—
291C2×Q8—1221no—
292C2×Q8—1221no—
293C2×Q8—1221no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—1221no—
297C22×C4—1222no—
298C22×C4—1221no—
299C22×C4D4×D6111yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4C2×C22⋊D6111yescharacteristic
302Q16—44no—
303M16—2441no—
304M16—2441no—
305C2×C8—22no—
306C2×C8—1222no—
307C2×C8—2441no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—2444no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C22⋊C4—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—2441no—
330C42—2441no—
331C42D4×D6111yescharacteristic
332C42#1175822411yescharacteristic
333C42C2×C22⋊D6111yescharacteristic
334C42C2×C22⋊D6111yescharacteristic
335C23#1451974511yescharacteristic
336Q8—22no—
337Q8—22no—
338Q8—41no—
339Q8—41no—
340Q8—42no—
341Q8—81no—
342Q8—1222no—
343Q8—1222no—
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—41no—
354C2×C4—41no—
355C2×C4—1222no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4#1451974511yescharacteristic
364C2×C4#1451974611yescharacteristic
365C2×C4#1451974811yescharacteristic
366C2×C4#1451974911yescharacteristic
367C2×C4#1451974911yescharacteristic
368C2×C4#1451977311yescharacteristic
369C2×C4Q16×D6111yescharacteristic
370C2×C4#1451980011yescharacteristic
371C2×C4#1451980911yescharacteristic
372C2×C4#1451980911yescharacteristic
373C8—42no—
374C8—4881no—
375C8—2442no—
376C22—21no—
377C22—21no—
378C22#1683967011yescharacteristic
379C22#1683991611yescharacteristic
380C22#1683992311yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—4882no—
390C4—4881no—
391C4—2442no—
392C4#1683991611yescharacteristic
393C4#1683992311yescharacteristic
394C4#1684000011yescharacteristic
395C4#1684001711yescharacteristic
396C2—21no—
397C2—21no—
398C2#2144682611yescharacteristic
399C2#2144687611yescharacteristic
400C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3104C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#3104D61
hypocenterC61#10003
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
100. C2×Dic122Q16semidirect
233. C61#10003semidirect

Maximal subgroups

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

subgroupindex
#214556202
#214511852
#214443832
#214442482
#214442152
#214436782
C61×#31042
#1000361