Finite Group Databasebeta

← #29580881

Subgroups — #29580881

Order 15616.

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

normal subgroups only

This group has 528 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#21455854C211yesmaximal, characteristic
2#21449110C211yesmaximal, characteristic
3#21446801C211yesmaximal, characteristic
4#21444249C211yesmaximal, characteristic
5#21444248C211yesmaximal, characteristic
6#21443647C211yesmaximal, characteristic
7C61×#3104C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16840095—21no—
10#16840054—21no—
11#16839969—21no—
12#16839917—21no—
13C4×#11758202—22no—
14#16839815C2211yescharacteristic
15#16839786C2211yescharacteristic
16#16839693—21no—
17#16839692—21no—
18#16839682—21no—
19#16839681—21no—
20C4×#11758196—22no—
21#16839608C2211yescharacteristic
22#16839521—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×#11758202—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#14519710—22no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519701—22no—
51#14519700—22no—
52C22⋊#92418—21no—
53C4×#92418D412yes—
54#14519684—22no—
55#14519684—22no—
56#14519684—21no—
57#14519684—21no—
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—42no—
98Q16×C61—44no—
99C2×C8×C61—22no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C42×C61—41no—
112C42×C61—41no—
113C42×C61—41no—
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118#11758202—44no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121#11758196—44no—
122#11758196—44no—
123#11758196—41no—
124#11758196—41no—
125C4×Dic61—22no—
126C4×Dic61—41no—
127C4×Dic61—41no—
128C4×Dic61Q1614yescomplemented
129#11758194—42no—
130C2×#92418—22no—
131C2×#92418—41no—
132C23×C61#12011yescharacteristic
133Q8×C61—22no—
134Q8×C61—22no—
135Q8×C61—41no—
136Q8×C61—41no—
137Q8×C61—42no—
138Q8×C61—42no—
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—41no—
147C2×C4×C61—41no—
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12711yescharacteristic
154C2×C4×C61C2×Q1612yes—
155C2×C4×C61#13712yes—
156C2×Dic61—22no—
157C2×Dic61—24no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—41no—
164Dic122—22no—
165Dic122—22no—
166Dic122—41no—
167Dic122—41no—
168C8×C61—42no—
169#92418—42no—
170#92418—81no—
171#10017—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#39211yescharacteristic
175C22×C61#45112yes—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61—81no—
182C4×C61—81no—
183C4×C61—81no—
184C4×C61#46212yes—
185C4×C61#49411yescharacteristic
186C4×C61#49711yescharacteristic
187Dic61—44no—
188Dic61—42no—
189Dic61—81no—
190#3104—611no—
191#3104D6111yescharacteristic
192#2399—611no—
193#1995—611no—
194#1487—611no—
195#1487—611no—
196#1274—611no—
197C2×C61—22no—
198C2×C61#201011yescharacteristic
199C2×C61#201011yescharacteristic
200C2×C61#201611yescharacteristic
201#533C2×D6111yescharacteristic
202C2×C4×Q8—611no—
203C2×C4×Q8C2×D6111yescharacteristic
204#484—21no—
205#484—1221no—
206#477—21no—
207#477—1221no—
208#462—21no—
209#462—1221no—
210#451—21no—
211#451—1221no—
212C4×Q16—22no—
213C4×Q16—1222no—
214#431—611no—
215#431C2×D6111yescharacteristic
216#423—611no—
217#398—1221no—
218#398—1221no—
219#395—1221no—
220#395—1221no—
221C4×C4⋊C4—1222no—
222#376—611no—
223#339—1222no—
224Q8⋊C8—1222no—
225Q8⋊C8—1222no—
226C61#1001711yescharacteristic, complemented, Sylow
227C22×Q8—611no—
228C22×Q8C22⋊D6111yescharacteristic
229C2×Q16—22no—
230C2×Q16—1222no—
231C2×M16—1221no—
232C4⋊Q8C22⋊D6111yescharacteristic
233C4⋊Q8C22⋊D6111yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—1221no—
244C4×Q8—1221no—
245C4×Q8—1221no—
246C4×Q8—1221no—
247#117—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1222no—
251C2×C4⋊C4—1222no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4C22⋊D6111yescharacteristic
254C2×C42—21no—
255C2×C42—612no—
256C2×C42—1221no—
257C2×C42C22×D6111yescharacteristic
258#107—22no—
259#107—1222no—
260C4⋊C8—21no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8—1221no—
264#103—22no—
265#103—22no—
266#103—1222no—
267#103—1222no—
268C22⋊C8—21no—
269C22⋊C8—1221no—
270C4×C8—612no—
271C4×C8C22⋊D6112yes—
272#95—1222no—
273#95—1222no—
274#95—1221no—
275#95—1221no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—42no—
281C2×Q8—1221no—
282C2×Q8—1221no—
283C2×Q8—2442no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—1222no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4D4×D6111yescharacteristic
290C22×C4D4×D6111yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292Q16—44no—
293Q16—2444no—
294M16—2442no—
295C2×C8—22no—
296C2×C8—1222no—
297C2×C8—2441no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—2444no—
311C4⋊C4—2444no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—41no—
315C42—41no—
316C42—41no—
317C42—41no—
318C42—614no—
319C42—1222no—
320C42—2441no—
321C42—2441no—
322C42D4×D6111yescharacteristic
323C42#1175822411yescharacteristic
324C42C2×C22⋊D6111yescharacteristic
325C42C2×C22⋊D6111yescharacteristic
326C23#1451974511yescharacteristic
327Q8—22no—
328Q8—22no—
329Q8—41no—
330Q8—41no—
331Q8—42no—
332Q8—42no—
333Q8—1222no—
334Q8—1222no—
335Q8—2441no—
336Q8—2441no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—1222no—
347C2×C4—1224no—
348C2×C4—2442no—
349C2×C4—2441no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4#1451974511yescharacteristic
355C2×C4#1451974611yescharacteristic
356C2×C4#1451974811yescharacteristic
357C2×C4#1451974911yescharacteristic
358C2×C4#1451974911yescharacteristic
359C2×C4#1451977311yescharacteristic
360C2×C4Q16×D6112yes—
361C2×C4#1451980912yes—
362C8—42no—
363C8—4881no—
364C8—2442no—
365C22—21no—
366C22—21no—
367C22#1683967011yescharacteristic
368C22#1683991612yes—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4—4881no—
378C4—2444no—
379C4—2442no—
380C4#1683997012yes—
381C4#1684014011yescharacteristic
382C4#1684015511yescharacteristic
383C2—22no—
384C2#2144688311yescharacteristic
385C2#2144688411yescharacteristic
386C2#2144691711yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3104C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#3104D61
hypocenterC61#10017
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
128. C4×Dic61Q16semidirect
226. C61#10017semidirect

Maximal subgroups

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

subgroupindex
#214558542
#214491102
#214468012
#214442492
#214442482
#214436472
C61×#31042
#1001761