Finite Group Databasebeta

← #30595571

Subgroups — #30595571

Order 15616.

510 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461604C211yesmaximal, characteristic, complemented
2#21461536C211yesmaximal, characteristic, complemented
3#21460637C212yesmaximal, complemented
4#21460635C212yesmaximal
5#21448284C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519832—21no—
8C2×#14519832—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519736—21no—
13#16839665C411yescharacteristic
14#16839665C2211yescharacteristic
15#16839661C411yescharacteristic
16#16839661C2211yescharacteristic
17#16839655—21no—
18#16839655—21no—
19C4×C4⋊Dic61C411yescharacteristic
20C4×C22⋊Dic61—21no—
21C42×Dic61C2211yescharacteristic
22C2×C4×D4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—24no—
26#14519832—24no—
27#14519832—42no—
28#14519736—44no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C22×D4×C61C2×C411yescharacteristic
48C23×C4×C61—21no—
49C4×D4×C61—22no—
50C4×D4×C61—22no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54C24×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D4×C61M1612yes—
59C22×C4×C61—24no—
60C22×C4×C61—21no—
61C22×C4×C61—42no—
62C22×C4×C61—42no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C2×#92420—24no—
73C2×#92420—24no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61M1612yes—
80C22⋊C4×C61—24no—
81C42×C61—21no—
82C42×C61—21no—
83C22⋊Dic61—42no—
84C22⋊Dic61—42no—
85C22⋊Dic61—41no—
86C22⋊Dic61—42no—
87C22⋊Dic61—41no—
88C4⋊Dic61—42no—
89C4⋊Dic61—42no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4×Dic61—22no—
93C4×Dic61—22no—
94C4×Dic61—21no—
95C4×Dic61—22no—
96C4×Dic61—21no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C4×Dic61—42no—
100C23×C61—22no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61C2×C22⋊C411yescharacteristic
108D4×C61—42no—
109D4×C61—42no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—48no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61#10412yes—
122C2×C4×C61C2×M1611yescharacteristic
123C2×C4×C61C2×M1611yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61#10412yes—
140C2×Dic61AGL(1,ℤ/8)11yescharacteristic
141C2×Dic61AGL(1,ℤ/8)12yes—
142C2×Dic61#13711yescharacteristic
143#92420—44no—
144#92420—44no—
145#7628—611nomaximal, Sylow
146C22×C61—42no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61—81no—
150C22×C61—81no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61#40711yescharacteristic
154C22×C61#41011yescharacteristic
155C22×C61#41311yescharacteristic
156C22×C61#41711yescharacteristic
157C22×C61#41811yescharacteristic
158C22×C61C2×#10411yescharacteristic
159C22×C61C2×#10411yescharacteristic
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—22no—
163C4×C61—41no—
164C4×C61—42no—
165Dic61—22no—
166Dic61—21no—
167Dic61—21no—
168Dic61—22no—
169Dic61—41no—
170Dic61—81no—
171Dic61—81no—
172#2293—611no—
173#1767—611no—
174#1745—611no—
175#1271—612no—
176#1270—612no—
177C2×C61—82no—
178C2×C61#146411yescharacteristic
179C2×C61#148911yescharacteristic
180C2×C61#149011yescharacteristic
181C2×C61#150511yescharacteristic
182C2×C61#150911yescharacteristic
183C2×C61#152411yescharacteristic
184C2×C61#155711yescharacteristic
185C2×C4×D4#692311yescharacteristic
186C2×#117—1221no—
187C2×C4⋊C8—1221no—
188C2×#97—1221no—
189C2×#97—1221no—
190#390—611no—
191#390—611no—
192#389—611no—
193#389—611no—
194#388—1221no—
195#388—1221no—
196C4×C4⋊C4—611no—
197C4×C22⋊C4—1221no—
198C43—611no—
199#336—612no—
200#336—612no—
201#336—1221no—
202C61#762811yescharacteristic, complemented, Sylow
203C22×D4C2×#692311yescharacteristic
204C23×C4—21no—
205C22×C8—1222no—
206C22×C8—1222no—
207C4×D4—22no—
208C4×D4—22no—
209#117—2444no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4C2×#692311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—1221no—
227C2×C42C2×#692311yescharacteristic
228C4⋊C8—1224no—
229#97—1224no—
230#97—2442no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234C24—21no—
235C2×D4—21no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4#1175821712yes—
239C22×C4—24no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4C22⋊#692311yescharacteristic
250C22×C4C22⋊#692311yescharacteristic
251C22×C4C22×#692311yescharacteristic
252C2×C8—1224no—
253C2×C8—1224no—
254C2×C8—2442no—
255C2×C8—2442no—
256C2×C8—2442no—
257C2×C8—2442no—
258C4⋊C4—21no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C4⋊C4—2442no—
262C4⋊C4—2442no—
263C4⋊C4#1175821712yes—
264C22⋊C4—24no—
265C22⋊C4—2442no—
266C22⋊C4—2441no—
267C22⋊C4—2441no—
268C22⋊C4—2442no—
269C22⋊C4—2442no—
270C42—21no—
271C42—21no—
272C42—1222no—
273C42—1221no—
274C42—1221no—
275C42—1222no—
276C42—1222no—
277C42—2441no—
278C42—2441no—
279C42—2442no—
280C23—22no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23C2×C22⋊#692311yescharacteristic
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—48no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—612no—
304C2×C4—612no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451984112yes—
321C2×C4C2×#1175821711yescharacteristic
322C2×C4C2×#1175821711yescharacteristic
323C8—2444no—
324C8—2444no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22#1684073211yescharacteristic
333C22#1684074111yescharacteristic
334C22#1684074811yescharacteristic
335C22#1684075311yescharacteristic
336C22#1684075411yescharacteristic
337C22C2×#1451984111yescharacteristic
338C22D61⋊#10411yescharacteristic
339C4—21no—
340C4—21no—
341C4—22no—
342C4—41no—
343C4—42no—
344C4—1222no—
345C4—1222no—
346C4—1221no—
347C4—1221no—
348C4—4881no—
349C4—4881no—
350C4—2441no—
351C2—82no—
352C2#2146107011yescharacteristic
353C2#2146115411yescharacteristic
354C2#2146115811yescharacteristic
355C2#2146120911yescharacteristic
356C2#2146122111yescharacteristic
357C2#2146126911yescharacteristic
358C2#2146135011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7628
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461604C2semidirect
2. #21461536C2semidirect
3. #21460637C2semidirect
202. C61#7628semidirect

Maximal subgroups

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

subgroupindex
#214616042
#214615362
#214606372
#214606352
#214482842
#762861