Finite Group Databasebeta

← #29577430

Subgroups — #29577430

Order 15616.

450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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#21454902C211yesmaximal, characteristic
2#21451035C211yesmaximal, characteristic
3#21445812C211yesmaximal, characteristic
4#21444504C211yesmaximal, characteristic
5#21443721C211yesmaximal, characteristic
6#21443720C211yesmaximal, characteristic
7C61×#1549C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16839892—22no—
10#16839889—22no—
11#16839816—22no—
12#16839815C2211yescharacteristic
13#16839786C2211yescharacteristic
14C2×#14519695—21no—
15#16839700C414yes—
16#16839669—22no—
17#16839667—21no—
18#16839627—21no—
19C4×C4⋊Dic61C2211yescharacteristic
20#16839530—21no—
21#16839508—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C61×#332—22no—
26C22×Dic122D411yescharacteristic
27C2×#11758194—21no—
28C4×Dic122—21no—
29C4×Dic122—21no—
30C4×Dic122—21no—
31C4×Dic122—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196C2×C412yes—
35C2×C4×Dic61—21no—
36C2×C4×Dic61D412yes—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418D412yes—
40#14519706—24no—
41#14519695—42no—
42C22⋊#92418—21no—
43#14519687—24no—
44C4×#92418—21no—
45#14519684—24no—
46#14519684—24no—
47#14519684C2×C412yes—
48C22×Q8×C61—21no—
49C2×M16×C61—21no—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61C2×C412yes—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61D412yes—
60C22⋊C8×C61—21no—
61C4×C8×C61—21no—
62C2×Q8×C61—44no—
63C2×Q8×C61—41no—
64C2×Q8×C61—41no—
65C22×C4×C61—22no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×Dic61—22no—
70C22×Dic61C22⋊C412yes—
71C22×Dic61C22⋊C412yes—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122—21no—
78M16×C61—41no—
79M16×C61—41no—
80C2×C8×C61—22no—
81C2×C8×C61—41no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—22no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C42×C61C2×D411yescharacteristic
87C42×C61C2×D411yescharacteristic
88C42×C61#4111yescharacteristic
89C42×C61#4111yescharacteristic
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—42no—
93#11758196—22no—
94#11758196—22no—
95C4×Dic61—22no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99#11758194—41no—
100#11758194—41no—
101C2×#92418—22no—
102C2×#92418—41no—
103C23×C61C2×C22⋊C411yescharacteristic
104Q8×C61—82no—
105Q8×C61—82no—
106C2×C4×C61—22no—
107C2×C4×C61—41no—
108C2×C4×C61—44no—
109C2×C4×C61—42no—
110C2×C4×C61C4×D411yescharacteristic
111C2×C4×C61C4×D411yescharacteristic
112C2×C4×C61#12011yescharacteristic
113C2×C4×C61#12111yescharacteristic
114C2×C4×C61#12111yescharacteristic
115C2×C4×C61#12311yescharacteristic
116C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C61#13711yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—42no—
125C2×Dic61—42no—
126C2×Dic61—42no—
127C2×Dic61—42no—
128Dic122—41no—
129Dic122—41no—
130Dic122—41no—
131Dic122—41no—
132C8×C61—42no—
133C8×C61—81no—
134#92418—42no—
135#92418—81no—
136#9404—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61#38611yescharacteristic
140C22×C61#41711yescharacteristic
141C22×C61#41911yescharacteristic
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—82no—
146C4×C61#45412yes—
147C4×C61#46811yescharacteristic
148C4×C61#46811yescharacteristic
149C4×C61#47011yescharacteristic
150C4×C61#47011yescharacteristic
151Dic61—42no—
152Dic61—42no—
153Dic61—82no—
154#2983—611no—
155#2568—611no—
156#1801—611no—
157#1549—611no—
158#1549D6111yescharacteristic
159#1303—611no—
160#1303—611no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61#188811yescharacteristic
164C2×C61#189411yescharacteristic
165C2×C61#191511yescharacteristic
166C2×C4⋊Q8C2×D6111yescharacteristic
167C2×C4×Q8—611no—
168#446—1222no—
169#446—1222no—
170#432—1222no—
171#431—611no—
172#431C2×D6111yescharacteristic
173#423—611no—
174#423C2×D6111yescharacteristic
175C2×#101—1221no—
176#400—614no—
177#391—1222no—
178#391—1221no—
179#382—1221no—
180C4×C4⋊C4—611no—
181#343—1221no—
182#332—22no—
183#332—1222no—
184C61#940411yescharacteristic, complemented, Sylow
185C22×Q8—21no—
186C22×Q8—611no—
187C2×M16—21no—
188C2×M16—1221no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4×Q8—1221no—
194C4×Q8—1221no—
195C4×Q8—1221no—
196C4×Q8—1221no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—612no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4C4×D6112yes—
202C2×C42—612no—
203C2×C42—1221no—
204C2×C42C22×D6111yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—612no—
208C4⋊C8—1224no—
209C4⋊C8—1221no—
210C4⋊C8—1221no—
211C4⋊C8C22⋊D6112yes—
212#101—2442no—
213C22⋊C8—21no—
214C22⋊C8—1221no—
215#97—1224no—
216C4×C8—21no—
217C4×C8—1221no—
218#95—612no—
219#95—1224no—
220#95—1224no—
221C2×Q8—44no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—1221no—
225C2×Q8—1221no—
226C2×Q8—1221no—
227C2×Q8—1221no—
228C2×Q8—1221no—
229C2×Q8—1221no—
230C22×C4—22no—
231C22×C4—612no—
232C22×C4—612no—
233C22×C4—1222no—
234C22×C4C2×C4×D6111yescharacteristic
235C22×C4D4×D6111yescharacteristic
236C22×C4D4×D6111yescharacteristic
237M16—41no—
238M16—41no—
239M16—2441no—
240M16—2441no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—1222no—
244C2×C8—2441no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—1222no—
250C4⋊C4—1222no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—2442no—
254C42—1222no—
255C42—1222no—
256C42—2441no—
257C42—2441no—
258C42#1175822211yescharacteristic
259C42D4×D6111yescharacteristic
260C42#1175822411yescharacteristic
261C42C2×C22⋊D6111yescharacteristic
262C23C22⋊C4×D6111yescharacteristic
263Q8—82no—
264Q8—82no—
265Q8—2441no—
266Q8—2441no—
267Q8—2441no—
268Q8—2441no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—42no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1222no—
276C2×C4—1222no—
277C2×C4—2442no—
278C2×C4—2442no—
279C2×C4—2442no—
280C2×C4—2442no—
281C2×C4#1451973711yescharacteristic
282C2×C4C4×C22⋊D6111yescharacteristic
283C2×C4#1451974511yescharacteristic
284C2×C4#1451974811yescharacteristic
285C2×C4#1451975011yescharacteristic
286C2×C4#1451975911yescharacteristic
287C2×C4#1451980411yescharacteristic
288C2×C4#1451980611yescharacteristic
289C2×C4#1451980911yescharacteristic
290C2×C4#1451980911yescharacteristic
291C8—42no—
292C8—81no—
293C8—4881no—
294C8—2442no—
295C22—21no—
296C22—21no—
297C22#1683963811yescharacteristic
298C22#1683976211yescharacteristic
299C22#1683976911yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—4882no—
305C4—2442no—
306C4—2442no—
307C4#1683993312yes—
308C4#1684000511yescharacteristic
309C4#1684001111yescharacteristic
310C4#1684001711yescharacteristic
311C4#1684001911yescharacteristic
312C2—21no—
313C2—21no—
314C2#2144621911yescharacteristic
315C2#2144624911yescharacteristic
316C2#2144636811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1549C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1549D61
hypocenterC61#9404
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
184. C61#9404semidirect

Maximal subgroups

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

subgroupindex
#214549022
#214510352
#214458122
#214445042
#214437212
#214437202
C61×#15492
#940461