Finite Group Databasebeta

← #29577412

Subgroups — #29577412

Order 15616.

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

normal subgroups only

This group has 466 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#21451027C211yesmaximal, characteristic
3#21445812C211yesmaximal, characteristic
4#21444501C211yesmaximal, characteristic
5#21444499C211yesmaximal, characteristic
6#21443722C211yesmaximal, characteristic
7C61×#1303C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16839892—22no—
11#16839889—22no—
12#16839816—22no—
13#16839815C2211yescharacteristic
14#16839786C2211yescharacteristic
15C2×#14519695—21no—
16#16839683C414yes—
17#16839668—21no—
18#16839661—22no—
19#16839632—21no—
20#16839530—21no—
21#16839510—22no—
22#16839510—22no—
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C22×Dic122C2×C412yes—
27C22×Dic122D411yescharacteristic
28C2×#11758194—21no—
29#14519777—21no—
30#14519777—21no—
31#14519777—21no—
32#14519777—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—24no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196C2×C412yes—
42C2×C4×Dic61D412yes—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418D412yes—
46#14519706—24no—
47#14519695—42no—
48C22⋊#92418—21no—
49#14519687—24no—
50C4×#92418—21no—
51#14519684—24no—
52C2×M16×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C42×C61—21no—
55C2×C42×C61C2311yescharacteristic
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61D412yes—
59C22⋊C8×C61—21no—
60C4×C8×C61—21no—
61#95×C61C2×C412yes—
62C22×C4×C61—22no—
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—22no—
67C22×Dic61C22⋊C412yes—
68C22×Dic61C22⋊C412yes—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—22no—
76C2×Dic122—22no—
77C2×Dic122—82no—
78M16×C61—41no—
79M16×C61—41no—
80C2×C8×C61—22no—
81C2×C8×C61—41no—
82C4⋊C4×C61—24no—
83C42×C61—41no—
84C42×C61—41no—
85C42×C61C2×D411yescharacteristic
86C42×C61C2×D411yescharacteristic
87C42×C61#4111yescharacteristic
88C42×C61#4111yescharacteristic
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—84no—
96#11758196—22no—
97#11758196—22no—
98C4×Dic61—22no—
99C4×Dic61—22no—
100#11758194—41no—
101#11758194—41no—
102C2×#92418—22no—
103C2×#92418—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61—22no—
106C2×C4×C61—24no—
107C2×C4×C61—41no—
108C2×C4×C61—42no—
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—44no—
126C2×Dic61—42no—
127Dic122—41no—
128Dic122—41no—
129Dic122—41no—
130Dic122—41no—
131Dic122—82no—
132Dic122—82no—
133C8×C61—42no—
134C8×C61—81no—
135#92418—42no—
136#92418—81no—
137#9400—611nomaximal, Sylow
138C22×C61—21no—
139C22×C61—21no—
140C22×C61#38611yescharacteristic
141C22×C61#41711yescharacteristic
142C22×C61#41911yescharacteristic
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—44no—
147C4×C61#45612yes—
148C4×C61#46811yescharacteristic
149C4×C61#46811yescharacteristic
150C4×C61#47011yescharacteristic
151C4×C61#47011yescharacteristic
152Dic61—42no—
153Dic61—42no—
154Dic61—82no—
155#2983—611no—
156#2567—611no—
157#1801—611no—
158#1548—611no—
159#1548—611no—
160#1303—611no—
161#1303D6111yescharacteristic
162C2×C61—21no—
163C2×C61—21no—
164C2×C61#188611yescharacteristic
165C2×C61#189411yescharacteristic
166C2×C61#191411yescharacteristic
167C2×C4⋊Q8—611no—
168C2×C4×Q8—611no—
169#446—1222no—
170#446—1222no—
171#432—1222no—
172#431—611no—
173#431C2×D6111yescharacteristic
174#423—611no—
175#423C2×D6111yescharacteristic
176C2×#101—1221no—
177#395—614no—
178#391—1221no—
179#389—1222no—
180#384—1221no—
181C4×C4⋊C4C2×D6111yescharacteristic
182#343—1221no—
183#333—1222no—
184#333—1222no—
185C61#940011yescharacteristic, complemented, Sylow
186C22×Q8—611no—
187C22×Q8—612no—
188C2×M16—21no—
189C2×M16—1221no—
190C4⋊Q8—1221no—
191C4⋊Q8—1221no—
192C4⋊Q8—1221no—
193C4⋊Q8—1221no—
194C4×Q8—1221no—
195C4×Q8—1221no—
196C4×Q8—1221no—
197C4×Q8—1221no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—612no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—1224no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C42—21no—
205C2×C42—612no—
206C2×C42C22×D6111yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—612no—
210C4⋊C8—1224no—
211C4⋊C8—1221no—
212C4⋊C8—1221no—
213C4⋊C8D24412yes—
214#101—2442no—
215C22⋊C8—21no—
216C22⋊C8—1221no—
217#97—1224no—
218C4×C8—21no—
219C4×C8—1221no—
220#95—1224no—
221#95C4×D6112yes—
222C2×Q8—1221no—
223C2×Q8—1221no—
224C2×Q8—1221no—
225C2×Q8—1221no—
226C2×Q8—1221no—
227C2×Q8—1221no—
228C2×Q8—1222no—
229C2×Q8—1222no—
230C2×Q8—4882no—
231C22×C4—22no—
232C22×C4—612no—
233C22×C4—612no—
234C22×C4—1222no—
235C22×C4C2×C4×D6111yescharacteristic
236C22×C4D4×D6111yescharacteristic
237C22×C4D4×D6111yescharacteristic
238M16—41no—
239M16—41no—
240M16—2441no—
241M16—2441no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—1222no—
245C2×C8—2441no—
246C4⋊C4—24no—
247C4⋊C4—1222no—
248C4⋊C4—1222no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—4884no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C42—41no—
257C42—41no—
258C42—1222no—
259C42—1222no—
260C42C2×D24411yescharacteristic
261C42#1175822211yescharacteristic
262C42D4×D6111yescharacteristic
263C42#1175822611yescharacteristic
264C23C22⋊C4×D6111yescharacteristic
265Q8—4882no—
266Q8—4882no—
267Q8—2441no—
268Q8—2441no—
269Q8—2441no—
270Q8—2441no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—1222no—
277C2×C4—1222no—
278C2×C4—1222no—
279C2×C4—1222no—
280C2×C4—2444no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4#1451973911yescharacteristic
284C2×C4C4×D24411yescharacteristic
285C2×C4#1451974711yescharacteristic
286C2×C4#1451975011yescharacteristic
287C2×C4#1451975211yescharacteristic
288C2×C4#1451976211yescharacteristic
289C2×C4#1451980111yescharacteristic
290C2×C4#1451980611yescharacteristic
291C2×C4#1451980611yescharacteristic
292C2×C4#1451980911yescharacteristic
293C8—42no—
294C8—81no—
295C8—4881no—
296C8—2442no—
297C22—21no—
298C22—21no—
299C22#1683964011yescharacteristic
300C22#1683976011yescharacteristic
301C22#1683976911yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—44no—
306C4—4882no—
307C4—2442no—
308C4—2442no—
309C4#1683994612yes—
310C4#1684000711yescharacteristic
311C4#1684000911yescharacteristic
312C4#1684001911yescharacteristic
313C4#1684002111yescharacteristic
314C2—21no—
315C2—21no—
316C2#2144621111yescharacteristic
317C2#2144625111yescharacteristic
318C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9400
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
185. C61#9400semidirect

Maximal subgroups

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

subgroupindex
#214549022
#214510272
#214458122
#214445012
#214444992
#214437222
C61×#13032
#940061