Finite Group Databasebeta

← #30595809

Subgroups — #30595809

Order 15616.

494 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461709C211yesmaximal, characteristic
2#21461482C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#21454159C211yesmaximal, characteristic
6C22×#11758217—21no—
7C2×C22⋊#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519756C411yescharacteristic
13C22×C4×Dic61C2211yescharacteristic
14#16839667C411yescharacteristic
15#16839667C2211yescharacteristic
16#16839661C411yescharacteristic
17#16839661C2211yescharacteristic
18#16839647—21no—
19#16839647—21no—
20#16839637—21no—
21#16839623—21no—
22C61×#380C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—42no—
25C2×#11758217—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28C22⋊#92420—42no—
29C22×Dic122C2×C411yescharacteristic
30C23×Dic61D411yescharacteristic
31C23×Dic61D411yescharacteristic
32#14519756—42no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—42no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C23×C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—21no—
53#95×C61—21no—
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—41no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78#11758217—48no—
79C2×#92420—24no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊Dic61—42no—
89C4⋊Dic61—42no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93#11758196—42no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61#9912yes—
105C23×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—44no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61#13112yes—
119C2×Dic61—24no—
120C2×Dic61—24no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—44no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61#10412yes—
138C2×Dic61AGL(1,ℤ/8)11yescharacteristic
139C2×Dic61#13711yescharacteristic
140C2×Dic61#13712yes—
141Dic122—82no—
142#92420—44no—
143#92420—82no—
144#7695—611nomaximal, Sylow
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61#40811yescharacteristic
153C22×C61C2×#9911yescharacteristic
154C22×C61#41311yescharacteristic
155C22×C61#41711yescharacteristic
156C22×C61#41911yescharacteristic
157C22×C61C2×#10411yescharacteristic
158C22×C61#42111yescharacteristic
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—81no—
162C4×C61—81no—
163Dic61—21no—
164Dic61—22no—
165Dic61—21no—
166Dic61—22no—
167Dic61—41no—
168Dic61—81no—
169Dic61—81no—
170#2855—611no—
171#1817—611no—
172#1728—611no—
173#1272—612no—
174#1271—612no—
175C2×C61—42no—
176C2×C61#146811yescharacteristic
177C2×C61#148511yescharacteristic
178C2×C61#149511yescharacteristic
179C2×C61#150411yescharacteristic
180C2×C61#151111yescharacteristic
181C2×C61#152911yescharacteristic
182C2×C61#155911yescharacteristic
183C22×M16—1221no—
184C2×C22⋊Q8—611no—
185C22×C42—611no—
186C2×C22⋊C8—1221no—
187#391—611no—
188#391—611no—
189#389—611no—
190#389—611no—
191#387—1221no—
192#387—1221no—
193#385—1221no—
194#381—1221no—
195#380#692311yescharacteristic
196#336—612no—
197#336—612no—
198#336—1221no—
199#336—1221no—
200C61#769511yescharacteristic, complemented, Sylow
201C22×Q8—611no—
202C23×C4—611no—
203C23×C4—611no—
204C23×C4C2×#692311yescharacteristic
205C2×M16—1224no—
206C2×M16—2442no—
207C2×M16—2442no—
208C22×C8—1222no—
209C22×C8—1222no—
210C22⋊Q8—2442no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4C2×#692311yescharacteristic
216C2×C4⋊C4C2×#692311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—1221no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223C2×C42—2442no—
224C22⋊C8—2442no—
225#95—21no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232C24C22⋊#692311yescharacteristic
233C2×Q8—1222no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—1222no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—2441no—
254C22×C4C22⋊#692311yescharacteristic
255C22×C4C22×#692311yescharacteristic
256M16—2448no—
257C2×C8—1224no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C2×C8—2442no—
262C2×C8—2442no—
263C4⋊C4—22no—
264C4⋊C4—41no—
265C4⋊C4—2441no—
266C4⋊C4—2442no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2442no—
270C22⋊C4—42no—
271C22⋊C4—2442no—
272C42—2441no—
273C42—2441no—
274C42—2441no—
275C42—2441no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23#1451983612yes—
283C23C2×C22⋊#692311yescharacteristic
284Q8—4882no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—612no—
300C2×C4—612no—
301C2×C4—1224no—
302C2×C4—1224no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—2444no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451986412yes—
320C8—4882no—
321C8—2444no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22#1684073511yescharacteristic
330C22C2×#1451983611yescharacteristic
331C22#1684074911yescharacteristic
332C22#1684075311yescharacteristic
333C22#1684075511yescharacteristic
334C22D61⋊#10411yescharacteristic
335C22#1684076011yescharacteristic
336C4—22no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—1221no—
341C4—1222no—
342C4—1221no—
343C4—1222no—
344C4—4881no—
345C4—4881no—
346C4—2441no—
347C2—42no—
348C2#2146108611yescharacteristic
349C2#2146114111yescharacteristic
350C2#2146117411yescharacteristic
351C2#2146120711yescharacteristic
352C2#2146122711yescharacteristic
353C2#2146128511yescharacteristic
354C2#2146135511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7695
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460637C2semidirect
200. C61#7695semidirect

Maximal subgroups

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

subgroupindex
#214617092
#214614822
#214606402
#214606372
#214541592
#769561