Finite Group Databasebeta

← #29581005

Subgroups — #29581005

Order 15616.

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

normal subgroups only

This group has 476 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#21456341C211yesmaximal, characteristic
2#21455858C211yesmaximal, characteristic
3#21446760C211yesmaximal, characteristic
4#21444223C211yesmaximal, characteristic
5#21444222C211yesmaximal, characteristic
6#21443649C211yesmaximal, characteristic
7C61×#3104C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840172—21no—
10#16840172—21no—
11#16840168—21no—
12#16840168—21no—
13#16840097—21no—
14#16840057—21no—
15#16839972—21no—
16#16839918—21no—
17C4×#11758202—22no—
18#16839815C2211yescharacteristic
19#16839798—22no—
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519688C2211yescharacteristic
22#16839517—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
33C2×#11758202—22no—
34C22×#92418—21no—
35C22×#92418D412yes—
36#14519777D411yescharacteristic
37#14519777D411yescharacteristic
38#14519769—21no—
39#14519756—21no—
40#14519756—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43#14519736—21no—
44#14519710—22no—
45#14519710—22no—
46#14519710—22no—
47#14519708—22no—
48#14519708—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52#14519701—22no—
53#14519700—22no—
54C22⋊#92418—21no—
55#14519688—21no—
56#14519688—21no—
57C4×#92418D412yes—
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×C61#4111yescharacteristic
92C2×Dic122—21no—
93C2×Dic122—21no—
94Q16×C61—44no—
95C2×C8×C61—22no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61—41no—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C22⋊Dic61—41no—
115#11758202—44no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120#11758196—41no—
121#11758196—41no—
122C4×Dic61—41no—
123C2×#92418—22no—
124C2×#92418—22no—
125C2×#92418—22no—
126C2×#92418—41no—
127C2×#92418—42no—
128C2×#92418Q1614yescomplemented
129C23×C61#12111yescharacteristic
130Q8×C61—22no—
131Q8×C61—22no—
132Q8×C61—41no—
133Q8×C61—41no—
134Q8×C61—42no—
135Q8×C61—42no—
136C2×C4×C61—22no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12011yescharacteristic
147C2×C4×C61#12011yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12711yescharacteristic
151C2×C4×C61C2×Q1612yes—
152C2×C4×C61#13712yes—
153C2×Dic61—41no—
154C2×Dic61—41no—
155Dic122—42no—
156Dic122—42no—
157C8×C61—42no—
158#92418—24no—
159#92418—42no—
160#92418—81no—
161#10037—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61#39211yescharacteristic
165C22×C61#46212yes—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—42no—
171C4×C61—81no—
172C4×C61—81no—
173C4×C61—81no—
174C4×C61#45112yes—
175C4×C61#49411yescharacteristic
176C4×C61#49711yescharacteristic
177Dic61—81no—
178Dic61—81no—
179#3162—611no—
180#3104—611no—
181#3104D6111yescharacteristic
182#1985—611no—
183#1481—611no—
184#1481—611no—
185#1275—611no—
186C2×C61—22no—
187C2×C61#201011yescharacteristic
188C2×C61#201611yescharacteristic
189C2×C61#201711yescharacteristic
190#533—611no—
191#533C2×D6111yescharacteristic
192C2×C4×Q8C2×D6111yescharacteristic
193#501—1221no—
194#501—1221no—
195#501—1221no—
196#501—1221no—
197#484—21no—
198#484—1221no—
199#477—21no—
200#477—1221no—
201#462—21no—
202#462—1221no—
203#451—21no—
204#451—1221no—
205C4×Q16—22no—
206C4×Q16—1222no—
207#431—611no—
208#431C2×D6111yescharacteristic
209#427—1222no—
210C2×C4⋊C8—611no—
211C2×#97—611no—
212#336—1222no—
213Q8⋊C8—1222no—
214Q8⋊C8—1222no—
215C61#1003711yescharacteristic, complemented, Sylow
216C22×Q8C22⋊D6111yescharacteristic
217C2×Q16—22no—
218C2×Q16—1222no—
219C22×C8—612no—
220C22×C8—1221no—
221C4⋊Q8—611no—
222C4⋊Q8—611no—
223C4⋊Q8C22⋊D6111yescharacteristic
224C4⋊Q8C22⋊D6111yescharacteristic
225#125—21no—
226#125—1221no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—1221no—
230C22⋊Q8—1221no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—1221no—
238C4×Q8—1221no—
239#117—21no—
240#117—1221no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C22⋊D6111yescharacteristic
243C2×C42—21no—
244C2×C42C22×D6111yescharacteristic
245#107—22no—
246#107—1222no—
247#107—1222no—
248#107—1222no—
249#106—1222no—
250#106—1222no—
251C4⋊C8—21no—
252C4⋊C8—1221no—
253C4⋊C8—1221no—
254C4⋊C8—1221no—
255#103—22no—
256#103—22no—
257#103—1222no—
258#103—1222no—
259C22⋊C8—21no—
260C22⋊C8—1221no—
261#97—1221no—
262#97—1221no—
263C4×C8—612no—
264C4×C8C22⋊D6112yes—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—42no—
270C2×Q8—1221no—
271C2×Q8—1221no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4D4×D6111yescharacteristic
275C22×C4#1175822411yescharacteristic
276C22×C4C2×C22⋊D6111yescharacteristic
277Q16—44no—
278Q16—2444no—
279C2×C8—22no—
280C2×C8—614no—
281C2×C8—1222no—
282C2×C8—1222no—
283C2×C8—1222no—
284C2×C8—2442no—
285C2×C8—2441no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C22⋊C4—41no—
303C22⋊C4—2441no—
304C42—41no—
305C42—41no—
306C42—41no—
307C42—2441no—
308C42D4×D6111yescharacteristic
309C42D4×D6111yescharacteristic
310C42C2×C22⋊D6111yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23#1451974911yescharacteristic
313Q8—22no—
314Q8—22no—
315Q8—41no—
316Q8—41no—
317Q8—42no—
318Q8—42no—
319Q8—2442no—
320Q8—2442no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451974511yescharacteristic
333C2×C4#1451974511yescharacteristic
334C2×C4#1451974611yescharacteristic
335C2×C4#1451974811yescharacteristic
336C2×C4#1451974911yescharacteristic
337C2×C4#1451977311yescharacteristic
338C2×C4Q16×D6112yes—
339C2×C4#1451980912yes—
340C8—42no—
341C8—1224no—
342C8—4881no—
343C8—2442no—
344C22—21no—
345C22—21no—
346C22#1683967011yescharacteristic
347C22#1683997012yes—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4—4881no—
357C4—4881no—
358C4#1683991612yes—
359C4#1684014011yescharacteristic
360C4#1684015511yescharacteristic
361C2—22no—
362C2#2144688411yescharacteristic
363C2#2144691711yescharacteristic
364C2#2144692211yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3104C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#3104D61
hypocenterC61#10037
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. C2×#92418Q16semidirect
215. C61#10037semidirect

Maximal subgroups

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

subgroupindex
#214563412
#214558582
#214467602
#214442232
#214442222
#214436492
C61×#31042
#1003761