Finite Group Databasebeta

← #29581543

Subgroups — #29581543

Order 15616.

466 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 87 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#21457210C211yesmaximal, characteristic
2#21456769C211yesmaximal, characteristic
3#21456201C211yesmaximal, characteristic
4#21446808C211yesmaximal, characteristic
5#21444413C211yesmaximal, characteristic
6#21443710C211yesmaximal, characteristic
7C61×#1485C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840142—21no—
11#16840132—22no—
12#16840114—21no—
13#16840114—21no—
14#16840113—21no—
15#16840047—21no—
16#16840044—21no—
17#16840018—22no—
18#16839973—22no—
19#16839972—21no—
20#16839969—21no—
21#16839920—22no—
22#16839786C2211yescharacteristic
23#16839770—22no—
24C4×#11758194C2211yescharacteristic
25#16839530—22no—
26#16839503—22no—
27C61×#533C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×Q8⋊C8—22no—
31C22×Dic122D412yes—
32C2×Dic244—24no—
33C2×#11758202—22no—
34C2×#11758194—21no—
35C2×#11758194D412yes—
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777—21no—
40#14519777D411yescharacteristic
41#14519777D411yescharacteristic
42#14519769—21no—
43#14519756—21no—
44#14519756—21no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47#14519736—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50#14519708—22no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519702—24no—
54#14519701—22no—
55#14519700—22no—
56#14519700—24no—
57#14519700—24no—
58#14519688D412yes—
59C4×#92418—21no—
60C2×M16×C61—21no—
61C4⋊Q8×C61D411yescharacteristic
62C4⋊Q8×C61D411yescharacteristic
63#125×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68#117×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61D412yes—
71C22⋊C8×C61—21no—
72#97×C61—21no—
73C4×C8×C61—21no—
74C4×C8×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×Dic61—22no—
81C2×Dic122—22no—
82C2×Dic122—22no—
83C2×Dic122—21no—
84C2×Dic122—21no—
85C2×Dic122—44no—
86M16×C61—22no—
87M16×C61—41no—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C42×C61—41no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C22⋊Dic61—41no—
103#11758202—82no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112#11758196—41no—
113#11758196—41no—
114C4×Dic61—41no—
115#11758194—42no—
116#11758194—42no—
117C2×#92418—22no—
118C2×#92418—22no—
119Dic244—84no—
120C23×C61#12111yescharacteristic
121Q8×C61—41no—
122Q8×C61—41no—
123Q8×C61—42no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12711yescharacteristic
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—42no—
139C2×Dic61—82no—
140Dic122—44no—
141Dic122—42no—
142Dic122—44no—
143Dic122—41no—
144Dic122—41no—
145C8×C61—42no—
146C8×C61—42no—
147#92418—42no—
148#92418—42no—
149#10115—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61#39211yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—81no—
158C4×C61—81no—
159C4×C61#45512yes—
160C4×C61#45511yescharacteristic
161C4×C61#45611yescharacteristic
162C4×C61#47312yes—
163Dic61—82no—
164Dic61—81no—
165Dic61—81no—
166#3255—611no—
167#3209—611no—
168#3139—611no—
169#1997—611no—
170#1526—611no—
171#1485D6111yescharacteristic
172#1299—611no—
173C2×C61—41no—
174C2×C61#200411yescharacteristic
175C2×C61#200711yescharacteristic
176C2×C61#202011yescharacteristic
177#533—611no—
178#533C2×D6111yescharacteristic
179C2×C4⋊Q8—611no—
180#494—1221no—
181#491—1222no—
182#487—1221no—
183#487—1221no—
184#487—1221no—
185#475—1221no—
186#475—1221no—
187#470—1222no—
188#462—1221no—
189#462—1221no—
190#462—1222no—
191#451—1222no—
192#431C2×D6111yescharacteristic
193#423—611no—
194#419—1222no—
195C4×M16—611no—
196C4×M16C2×D6111yescharacteristic
197#343—1222no—
198#330—1222no—
199Q8⋊C8—22no—
200C61#1011511yescharacteristic, complemented, Sylow
201C22×Q8—612no—
202C2×Q16—1224no—
203C2×Q16—1222no—
204C2×M16—21no—
205C2×M16—612no—
206C2×M16—1221no—
207C4⋊Q8—611no—
208C4⋊Q8—611no—
209C4⋊Q8—1221no—
210C4⋊Q8—1221no—
211C4⋊Q8—1221no—
212C4⋊Q8—1221no—
213C4⋊Q8D24411yescharacteristic
214C4⋊Q8D24411yescharacteristic
215#125—21no—
216#125—1221no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C22⋊Q8—1221no—
220C22⋊Q8—1221no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—1221no—
224C4×Q8—1221no—
225#117—21no—
226#117—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C42C22×D6111yescharacteristic
230#106—1222no—
231C4⋊C8—1221no—
232C4⋊C8—1221no—
233C4⋊C8C22⋊D6112yes—
234#103—1224no—
235#103—1224no—
236#103—1222no—
237#103—1224no—
238#103—1222no—
239C22⋊C8—21no—
240#97—21no—
241#97—612no—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8—1221no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—1222no—
248C2×Q8—1221no—
249C2×Q8—1222no—
250C2×Q8—1221no—
251C2×Q8—2444no—
252C22×C4—1222no—
253C22×C4#1175822211yescharacteristic
254C22×C4D4×D6111yescharacteristic
255C22×C4D4×D6111yescharacteristic
256Q16—4884no—
257Q16—4882no—
258M16—22no—
259M16—41no—
260M16—2442no—
261M16—2442no—
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—1222no—
265C2×C8—1222no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C22⋊C4—41no—
283C22⋊C4—2441no—
284C42—41no—
285C42—2441no—
286C42C2×D24411yescharacteristic
287C42D4×D6111yescharacteristic
288C42D4×D6111yescharacteristic
289C42C2×C22⋊D6111yescharacteristic
290C23#1451975011yescharacteristic
291Q8—41no—
292Q8—41no—
293Q8—42no—
294Q8—2444no—
295Q8—2442no—
296Q8—2444no—
297Q8—2441no—
298Q8—2441no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—4882no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2442no—
309C2×C4#1451974511yescharacteristic
310C2×C4#1451974711yescharacteristic
311C2×C4#1451974711yescharacteristic
312C2×C4#1451975011yescharacteristic
313C2×C4#1451975111yescharacteristic
314C2×C4#1451977311yescharacteristic
315C8—42no—
316C8—42no—
317C8—2442no—
318C8—2442no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22#1683967111yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—4882no—
329C4—4881no—
330C4—4881no—
331C4#1683993812yes—
332C4#1683994111yescharacteristic
333C4#1683994611yescharacteristic
334C4#1684003712yes—
335C2—41no—
336C2#2144684911yescharacteristic
337C2#2144686711yescharacteristic
338C2#2144694011yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1485C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#1485D61
hypocenterC61#10115
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
200. C61#10115semidirect

Maximal subgroups

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

subgroupindex
#214572102
#214567692
#214562012
#214468082
#214444132
#214437102
C61×#14852
#1011561