Finite Group Databasebeta

← #30595507

Subgroups — #30595507

Order 15616.

612 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 110 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#21461711C211yesmaximal, characteristic
2#21461483C211yesmaximal, characteristic
3#21460638C212yesmaximal, complemented
4#21460637C212yesmaximal, complemented
5#389×D61C211yesmaximal, characteristic
6C22×#11758213—21no—
7C2×#14519834—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×C4⋊C4×D61—21no—
13C2×C4⋊C4×D61C411yescharacteristic
14C2×C4⋊C4×D61C411yescharacteristic
15C2×C42×D61C2211yescharacteristic
16#16839661C2211yescharacteristic
17#16839660C411yescharacteristic
18#16839659—21no—
19#16839658C2211yescharacteristic
20#16839657—21no—
21#95×D61—21no—
22C61×#389C411yescharacteristic
23C2×#11758213—24no—
24C2×#11758213—42no—
25C2×#11758213—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519834—42no—
29C22×C4×D61—21no—
30C22×C4×D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C4⋊C4×D61—22no—
42C4⋊C4×D61—22no—
43C4⋊C4×D61—42no—
44C4⋊C4×D61—42no—
45C4⋊C4×D61—42no—
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49C42×D61—42no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57#95×C61—21no—
58C23×D61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—22no—
75C2×C4×D61—24no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×C4×D61D812yes—
85C2×C4×D61SD1612yes—
86C2×#92420—24no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92#11758213—48no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—42no—
96C4⋊C4×C61M1612yescomplemented
97C42×C61—41no—
98C4⋊Dic61—21no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61M1612yescomplemented
103#11758196—24no—
104#11758196—42no—
105#11758196—42no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—41no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61#9912yes—
117C22×D61#10212yes—
118C22×D61#10412yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—22no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61#10212yes—
133C2×C4×C61C2×M1611yescharacteristic
134C2×C4×C61C2×M1611yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—22no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#10112yes—
148C2×Dic61C2×D811yescharacteristic
149C2×Dic61C2×SD1611yescharacteristic
150C2×Dic61#13712yes—
151C4×D61—24no—
152C4×D61—24no—
153C4×D61—24no—
154C4×D61—24no—
155C4×D61—44no—
156C4×D61—48no—
157C4×D61—84no—
158#92420—44no—
159#92420—82no—
160#7610—611nomaximal, Sylow
161C22×C61#40711yescharacteristic
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#10111yescharacteristic
164C22×C61C2×#10211yescharacteristic
165C22×C61#41911yescharacteristic
166C22×C61C2×#10411yescharacteristic
167C22×C61#42111yescharacteristic
168C2×D61—22no—
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—22no—
174C2×D61#32714yes—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—22no—
178C4×C61—42no—
179C4×C61—41no—
180C4×C61—81no—
181Dic61—22no—
182Dic61—21no—
183Dic61—21no—
184Dic61—22no—
185Dic61—42no—
186Dic61—81no—
187C2×#389—611no—
188#1817—611no—
189#1728—611no—
190#1271—612no—
191#1271—612no—
192C2×C61#146311yescharacteristic
193C2×C61#148611yescharacteristic
194C2×C61#149111yescharacteristic
195C2×C61C2×#32711yescharacteristic
196C2×C61#151111yescharacteristic
197C2×C61#152811yescharacteristic
198C2×C61#154611yescharacteristic
199D61—24no—
200C22×M16—1221no—
201C22×C4⋊C4—611no—
202C22×C4⋊C4—611no—
203C22×C4⋊C4—1221no—
204C22×C42—611no—
205C2×C22⋊C8—1221no—
206#389—611no—
207#389—611no—
208#389—611no—
209#389—1221no—
210#389—1221no—
211#389#692311yescharacteristic
212C2×#95—1221no—
213#336—612no—
214#336—612no—
215#336—1221no—
216#336—1221no—
217C61#761011yescharacteristic, complemented, Sylow
218C23×C4—611no—
219C23×C4—611no—
220C23×C4—611no—
221C23×C4—1221no—
222C23×C4—1221no—
223C2×M16—1224no—
224C2×M16—2442no—
225C2×M16—2442no—
226C22×C8—1222no—
227C22×C8—1222no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—1222no—
232C2×C4⋊C4—1221no—
233C2×C4⋊C4—1222no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—2442no—
239C2×C4⋊C4—2442no—
240C2×C4⋊C4—2442no—
241C2×C4⋊C4C2×#692311yescharacteristic
242C2×C4⋊C4C2×#692311yescharacteristic
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—2442no—
247C2×C42C2×#692311yescharacteristic
248C22⋊C8—2442no—
249#95—21no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253C24—611no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—612no—
260C22×C4—612no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4—1222no—
266C22×C4—1222no—
267C22×C4—1224no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—2441no—
273C22×C4—2442no—
274C22×C4—2442no—
275C22×C4—2442no—
276C22×C4—2442no—
277C22×C4—2442no—
278C22×C4C22⋊#692311yescharacteristic
279C22×C4C22⋊#692311yescharacteristic
280C22×C4C22×#692311yescharacteristic
281M16—2448no—
282C2×C8—1224no—
283C2×C8—2442no—
284C2×C8—2442no—
285C2×C8—2442no—
286C2×C8—2442no—
287C2×C8—2442no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C4⋊C4—612no—
292C4⋊C4—1224no—
293C4⋊C4—1221no—
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2442no—
300C4⋊C4—2442no—
301C4⋊C4#1175821312yescomplemented
302C42—41no—
303C42—2441no—
304C42—2441no—
305C42—2441no—
306C23—612no—
307C23—612no—
308C23—612no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23—1221no—
313C23C2×C22⋊#692311yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—612no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—612no—
331C2×C4—1224no—
332C2×C4—1224no—
333C2×C4—1224no—
334C2×C4—1224no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1222no—
342C2×C4—4884no—
343C2×C4—2444no—
344C2×C4—2448no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4#1451983912yes—
351C2×C4D61⋊M1611yescharacteristic
352C2×C4C2×#1175821311yescharacteristic
353C8—4882no—
354C8—2444no—
355C22—614no—
356C22—1222no—
357C22—1222no—
358C22—1222no—
359C22—1222no—
360C22—1222no—
361C22—1222no—
362C22#1684073311yescharacteristic
363C22D61⋊#9911yescharacteristic
364C22D61⋊#10111yescharacteristic
365C22C2×#1451983911yescharacteristic
366C22#1684075511yescharacteristic
367C22D61⋊#10411yescharacteristic
368C22#1684075911yescharacteristic
369C4—21no—
370C4—21no—
371C4—22no—
372C4—42no—
373C4—41no—
374C4—81no—
375C4—1222no—
376C4—1221no—
377C4—1221no—
378C4—1222no—
379C4—4881no—
380C4—2442no—
381C2—1224no—
382C2#2146106811yescharacteristic
383C2#2146114511yescharacteristic
384C2#2146116211yescharacteristic
385C2D61⋊#32711yescharacteristic
386C2#2146122811yescharacteristic
387C2#2146128211yescharacteristic
388C2#2146132911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7610
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #21460638C2semidirect
4. #21460637C2semidirect
96. C4⋊C4×C61M16semidirect
102. C4⋊Dic61M16semidirect
217. C61#7610semidirect
301. C4⋊C4#11758213semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214614832
#214606382
#214606372
#389×D612
#761061