Finite Group Databasebeta

← #30595521

Subgroups — #30595521

Order 15616.

504 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461735C211yesmaximal, characteristic, complemented
2#21461604C211yesmaximal, characteristic, complemented
3#21460637C212yesmaximal, complemented
4#21460635C212yesmaximal
5#21448284C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519844—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#14519844—42no—
27#14519832—42no—
28#14519736—42no—
29#14519736—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×D4×C61C2×C411yescharacteristic
49C23×C4×C61—21no—
50C4×D4×C61—22no—
51C4×D4×C61—22no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C42×C61C2×C411yescharacteristic
55C24×C61—21no—
56C2×D4×C61—21no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61M1612yes—
60C22×C4×C61—24no—
61C22×C4×C61—21no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×#92420—24no—
74C2×#92420—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61M1612yes—
81C22⋊C4×C61—24no—
82C42×C61—21no—
83C42×C61—21no—
84C22⋊Dic61—42no—
85C22⋊Dic61—42no—
86C22⋊Dic61—41no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C22⋊Dic61—41no—
90C4⋊Dic61—42no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4×Dic61—22no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C4×Dic61—42no—
102C4×Dic61D812yes—
103C4×Dic61SD1612yes—
104C23×C61—22no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112D4×C61—42no—
113D4×C61—42no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—48no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#10212yes—
126C2×C4×C61C2×M1611yescharacteristic
127C2×C4×C61C2×M1611yescharacteristic
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#10212yes—
143C2×Dic61#10412yes—
144C2×Dic61C2×D811yescharacteristic
145C2×Dic61C2×SD1611yescharacteristic
146C2×Dic61AGL(1,ℤ/8)11yescharacteristic
147C2×Dic61#13711yescharacteristic
148#92420—44no—
149#92420—82no—
150#7614—611nomaximal, Sylow
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61#40711yescharacteristic
159C22×C61#41011yescharacteristic
160C22×C61#41311yescharacteristic
161C22×C61C2×#10211yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C22×C61#42111yescharacteristic
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—22no—
168C4×C61—42no—
169C4×C61—41no—
170Dic61—22no—
171Dic61—21no—
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—22no—
176Dic61—81no—
177Dic61—81no—
178#2293—611no—
179#1831—611no—
180#1767—611no—
181#1271—612no—
182#1270—612no—
183C2×C61—82no—
184C2×C61#146411yescharacteristic
185C2×C61#148611yescharacteristic
186C2×C61#148911yescharacteristic
187C2×C61#150211yescharacteristic
188C2×C61#151211yescharacteristic
189C2×C61#153211yescharacteristic
190C2×C61#154711yescharacteristic
191C2×C4×D4#692311yescharacteristic
192C2×#117—1221no—
193C2×C4⋊C8—1221no—
194C2×C4⋊C8—1221no—
195C2×#97—1221no—
196#390—611no—
197#390—611no—
198#389—611no—
199#389—611no—
200#388—1221no—
201#388—1221no—
202C4×C4⋊C4—611no—
203C4×C22⋊C4—1221no—
204C43—611no—
205#336—612no—
206#336—612no—
207#336—1221no—
208C61#761411yescharacteristic, complemented, Sylow
209C22×D4C2×#692311yescharacteristic
210C23×C4—21no—
211C22×C8—1222no—
212C22×C8—1222no—
213C4×D4—22no—
214C4×D4—22no—
215#117—2442no—
216#117—2442no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C42—611no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—1221no—
234C2×C42C2×#692311yescharacteristic
235C4⋊C8—1224no—
236C4⋊C8—2442no—
237#97—2442no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24—21no—
242C2×D4—21no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4#1175821712yes—
246C22×C4—24no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4C22⋊#692311yescharacteristic
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22×#692311yescharacteristic
259C2×C8—1224no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C4⋊C4—21no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2442no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4#1175821712yes—
272C22⋊C4—24no—
273C22⋊C4—2442no—
274C22⋊C4—2441no—
275C22⋊C4—2441no—
276C22⋊C4—2441no—
277C22⋊C4—2441no—
278C22⋊C4—2442no—
279C42—21no—
280C42—21no—
281C42—612no—
282C42—612no—
283C42—1222no—
284C42—1221no—
285C42—1221no—
286C42—2441no—
287C42—2441no—
288C42—2441no—
289C42—2442no—
290C23—22no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊#692311yescharacteristic
298D4—42no—
299D4—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—48no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—612no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—612no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451983912yes—
332C2×C4C2×#1175821711yescharacteristic
333C2×C4C2×#1175821711yescharacteristic
334C8—4882no—
335C8—2444no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22#1684073211yescharacteristic
344C22#1684074111yescharacteristic
345C22#1684074811yescharacteristic
346C22C2×#1451983911yescharacteristic
347C22#1684075311yescharacteristic
348C22D61⋊#10411yescharacteristic
349C22#1684076011yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—42no—
354C4—41no—
355C4—1222no—
356C4—1222no—
357C4—1221no—
358C4—1221no—
359C4—1221no—
360C4—1221no—
361C4—4881no—
362C4—4881no—
363C2—82no—
364C2#2146107011yescharacteristic
365C2#2146114411yescharacteristic
366C2#2146115411yescharacteristic
367C2#2146119811yescharacteristic
368C2#2146123011yescharacteristic
369C2#2146129411yescharacteristic
370C2#2146133011yescharacteristic
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#7614
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. #21461735C2semidirect
2. #21461604C2semidirect
3. #21460637C2semidirect
208. C61#7614semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214616042
#214606372
#214606352
#214482842
#761461