Finite Group Databasebeta

← #29581545

Subgroups — #29581545

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#21457213C211yesmaximal, characteristic
2#21456767C211yesmaximal, characteristic
3#21456199C211yesmaximal, characteristic
4#21444413C211yesmaximal, characteristic
5#21444241C211yesmaximal, characteristic
6#21443708C211yesmaximal, characteristic
7C61×#1997C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840319C2211yescharacteristic
10#16840141—21no—
11#16840130—22no—
12#16840112—21no—
13#16840112—21no—
14#16840112—21no—
15#16840048—21no—
16#16840048—21no—
17#16840020—22no—
18#16839973—21no—
19#16839973—21no—
20#16839969—22no—
21#16839918—22no—
22#16839815C2211yescharacteristic
23#16839771—22no—
24C4×#11758194C2211yescharacteristic
25#16839503—22no—
26#16839494—22no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C61×#423C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#343—22no—
31C2×Dic244—22no—
32C2×#11758202—24no—
33C2×#11758194—21no—
34#14519777D411yescharacteristic
35#14519777D411yescharacteristic
36#14519777D411yescharacteristic
37#14519777D411yescharacteristic
38#14519769—21no—
39#14519769—21no—
40#14519756—21no—
41#14519756—21no—
42#14519756—21no—
43#14519756—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47C4×Dic122—21no—
48#14519736—21no—
49#14519736—21no—
50#14519709—22no—
51C4⋊#92418D412yes—
52#14519702—22no—
53#14519702—22no—
54#14519701—24no—
55#14519701—24no—
56#14519701—24no—
57C22⋊#92418—21no—
58#14519688D412yes—
59C4×#92418—21no—
60C4×#92418—21no—
61C22×Q8×C61D412yes—
62C2×M16×C61—21no—
63C2×M16×C61D412yes—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73#97×C61—21no—
74C4×C8×C61—21no—
75C2×Q8×C61—22no—
76C2×Q8×C61—22no—
77C2×Q8×C61—44no—
78C22×C4×C61—22no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C2×Dic122—21no—
83C2×Dic122—21no—
84C2×Dic122—21no—
85C2×Dic122—21no—
86M16×C61—22no—
87M16×C61—41no—
88M16×C61—42no—
89C2×C8×C61—22no—
90C2×C8×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C42×C61C2×D411yescharacteristic
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61C2×D411yescharacteristic
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101#11758202—84no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110#11758196—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—41no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116#11758194—42no—
117C2×#92418—22no—
118C2×#92418—22no—
119Dic244—82no—
120C23×C61#12111yescharacteristic
121Q8×C61—44no—
122Q8×C61—44no—
123C2×C4×C61—22no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—42no—
128C2×C4×C61—82no—
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12011yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12711yescharacteristic
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139Dic122—41no—
140Dic122—41no—
141Dic122—42no—
142Dic122—41no—
143Dic122—41no—
144Dic122—42no—
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—82no—
158C4×C61#45511yescharacteristic
159C4×C61#45512yes—
160C4×C61#45611yescharacteristic
161C4×C61#47312yes—
162Dic61—81no—
163Dic61—81no—
164Dic61—81no—
165Dic61—81no—
166#3255—611no—
167#3209—611no—
168#3139—611no—
169#1997D6111yescharacteristic
170#1526—611no—
171#1485—611no—
172#1299—611no—
173C2×C61—41no—
174C2×C61#200411yescharacteristic
175C2×C61#200711yescharacteristic
176C2×C61#202011yescharacteristic
177#533—611no—
178#533—611no—
179C2×C4⋊Q8C2×D6111yescharacteristic
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#431—611no—
193#423C2×D6111yescharacteristic
194#419—1222no—
195C4×M16—611no—
196C4×M16C2×D6111yescharacteristic
197#343—22no—
198#330—1222no—
199Q8⋊C8—1222no—
200C61#1011511yescharacteristic, complemented, Sylow
201C22×Q8D24412yes—
202C2×Q16—1222no—
203C2×Q16—1224no—
204C2×M16—21no—
205C2×M16—1221no—
206C2×M16C22⋊D6112yes—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—611no—
212C4⋊Q8—611no—
213C4⋊Q8—611no—
214C4⋊Q8—611no—
215#125—1221no—
216#125—1221no—
217C22⋊Q8—1221no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220C22⋊Q8—1221no—
221C4×Q8—1221no—
222C4×Q8—1221no—
223C4×Q8—1221no—
224C4×Q8—1221no—
225#117—1221no—
226#117—1221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C42C22×D6111yescharacteristic
230#106—1222no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—612no—
234#103—1222no—
235#103—1222no—
236#103—1224no—
237#103—1224no—
238#103—1224no—
239C22⋊C8—1221no—
240#97—21no—
241#97—612no—
242C4×C8—21no—
243C4×C8—1221no—
244C4×C8—1221no—
245C2×Q8—22no—
246C2×Q8—22no—
247C2×Q8—44no—
248C2×Q8—1221no—
249C2×Q8—1221no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C22×C4—22no—
253C22×C4C2×D24411yescharacteristic
254C22×C4#1175822211yescharacteristic
255C22×C4C2×C22⋊D6111yescharacteristic
256Q16—4882no—
257Q16—4884no—
258M16—22no—
259M16—41no—
260M16—42no—
261M16—2442no—
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—1222no—
265C2×C8—1222no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C42—2441no—
285C42—2441no—
286C42D4×D6111yescharacteristic
287C42D4×D6111yescharacteristic
288C42D4×D6111yescharacteristic
289C42D4×D6111yescharacteristic
290C23#1451975111yescharacteristic
291Q8—44no—
292Q8—44no—
293Q8—2441no—
294Q8—2441no—
295Q8—2442no—
296Q8—2441no—
297Q8—2441no—
298Q8—2442no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4#1451974511yescharacteristic
310C2×C4#1451974711yescharacteristic
311C2×C4#1451974711yescharacteristic
312C2×C4#1451975011yescharacteristic
313C2×C4#1451975011yescharacteristic
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—82no—
327C4—4881no—
328C4—4881no—
329C4—4881no—
330C4—4881no—
331C4#1683993911yescharacteristic
332C4#1683994212yes—
333C4#1683994411yescharacteristic
334C4#1684003612yes—
335C2—41no—
336C2#2144685011yescharacteristic
337C2#2144686511yescharacteristic
338C2#2144693911yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1997C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#1997D61
hypocenterC61#10115
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

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
#214572132
#214567672
#214561992
#214444132
#214442412
#214437082
C61×#19972
#1011561