Finite Group Databasebeta

← #30597768

Subgroups — #30597768

Order 15616.

640 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C4×#14519834C211yesmaximal, characteristic
2C2×#16840615C212yesmaximal
3#21460995C211yesmaximal, characteristic
4#21460692C212yesmaximal
5C4×#14519757C211yesmaximal, characteristic
6C2×#14519834C2212yes—
7C2×C4×#92420—21no—
8C2×(C2×#6923)⋊C4—21no—
9C2×(C2×#6923)⋊C4—21no—
10C2×(C2×#6923)⋊C4C2212yes—
11#16840628—21no—
12#16840615C418yescomplemented
13C2×#14519757C2211yescharacteristic
14C2×C4×Dic122C411yescharacteristic, complemented
15C2×C42×D61C2211yescharacteristic
16#16839667C411yescharacteristic, complemented
17#16839661C411yescharacteristic, complemented
18#16839647—21no—
19#16839636—21no—
20#16839619C2211yescharacteristic
21C4×C4⋊Dic61—21no—
22C4×#11758198—21no—
23C4×C4⋊C4×C61C411yescharacteristic, complemented
24C23×#6923—22no—
25C22×#92420—22no—
26#14519834—22no—
27#14519834C2×C414yes—
28C4×#92420—42no—
29(C2×#6923)⋊C4—22no—
30(C2×#6923)⋊C4—42no—
31(C2×#6923)⋊C4—42no—
32(C2×#6923)⋊C4C2×C414yes—
33C22×Dic122C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61C2311yescharacteristic
37#14519757—22no—
38#14519757C2×C414yes—
39C4×Dic122—42no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C42×D61—42no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C42×C61—21no—
58C2×C42×C61C2×C411yescharacteristic
59#95×C61—21no—
60C23×D61C2×D411yescharacteristic
61C22×#6923—24no—
62C22×#6923—42no—
63C22×#6923—42no—
64C22×#6923—42no—
65C22×#6923—42no—
66C22×#6923—42no—
67C22×#6923—42no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61SD1612yes—
86C2×C4×D61Q1612yes—
87C2×C4×D61C22×C412yes—
88C2×C4×D61#4112yes—
89C2×Dic122—21no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122C4212yes—
93C2×#92420—24no—
94C2×#92420—42no—
95C2×#92420—42no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61C4212yes—
99C42×C61—22no—
100C42×C61—42no—
101#11758198—24no—
102#11758198—42no—
103C4⋊Dic61—24no—
104C4⋊Dic61—42no—
105C4⋊Dic61—41no—
106#11758196—42no—
107C4×Dic61—22no—
108C4×Dic61—41no—
109C4×Dic61—41no—
110C4×Dic61—42no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61C4×D412yes—
117C22×D61C2×SD1611yescharacteristic
118C22×D61C2×Q1611yescharacteristic
119C22×D61#13512yes—
120C2×#6923—44no—
121C2×#6923—44no—
122C2×#6923—44no—
123C2×#6923—82no—
124C2×#6923—82no—
125C2×#6923—82no—
126C2×#6923—82no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61#9912yes—
140C2×C4×C61#10312yes—
141C2×C4×C61C2×C4211yescharacteristic
142C2×C4×C61#11711yescharacteristic
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—22no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61#10312yes—
157C2×Dic61C4×D412yes—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—44no—
163Dic122—42no—
164Dic122—42no—
165#92420—44no—
166#8221—611nomaximal, Sylow
167C22×C61C4×C22⋊C411yescharacteristic
168C22×C61C2×#9911yescharacteristic
169C22×C61#41011yescharacteristic
170C22×C61C2×#10311yescharacteristic
171C22×C61#41611yescharacteristic
172C22×C61#42111yescharacteristic
173C22×C61#42111yescharacteristic
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—22no—
182C2×D61C4×SD1612yes—
183C2×D61C4×Q1612yes—
184#6923—84no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—22no—
188C4×C61—22no—
189C4×C61—42no—
190C4×C61—81no—
191Dic61—22no—
192Dic61—22no—
193Dic61—42no—
194Dic61—41no—
195Dic61—81no—
196C4×C22⋊Q8—611no—
197C4×C22⋊C8—611no—
198C2×#328—612no—
199#1434—611no—
200#1294—612no—
201C2×C61#151611yescharacteristic
202C2×C61#151811yescharacteristic
203C2×C61#152011yescharacteristic
204C2×C61#152111yescharacteristic
205C2×C61C4×#9911yescharacteristic
206C2×C61#175911yescharacteristic
207C2×C61C4×#10311yescharacteristic
208D61—22no—
209D61—22no—
210C2×C22⋊Q8—611no—
211C2×C4×Q8—611no—
212C22×C42—611no—
213C2×C22⋊C8—612no—
214C2×C4×C8—1221no—
215#391—611no—
216#389—611no—
217#387—1221no—
218#385—1221no—
219#380—611no—
220C4×C4⋊C4—1221no—
221C4×C4⋊C4#692311yescharacteristic, complemented
222C4×C22⋊C4—1221no—
223C2×#95—612no—
224C2×#95—1221no—
225C2×#95—1221no—
226#336—1221no—
227#328—618no—
228C61#822111yescharacteristic, complemented, Sylow
229C22×Q8—611no—
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—1222no—
234C22×C8—1222no—
235C22⋊Q8—614no—
236C22⋊Q8—1222no—
237C4×Q8—2442no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4C2×#692311yescharacteristic
243C2×C4⋊C4C2×#692311yescharacteristic
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C42—21no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—1221no—
251C2×C42—2442no—
252C2×C42C2×#692311yescharacteristic
253C22⋊C8—614no—
254C22⋊C8—1222no—
255C4×C8—2442no—
256#95—21no—
257#95—614no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—1222no—
263#95—2442no—
264#95—2442no—
265C24—611no—
266C2×Q8—612no—
267C2×Q8—1221no—
268C2×Q8—2441no—
269C2×Q8—2441no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—611no—
279C22×C4—1222no—
280C22×C4—1221no—
281C22×C4—1222no—
282C22×C4—1224no—
283C22×C4—1221no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2442no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4—2442no—
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298C2×C8—1224no—
299C2×C8—2442no—
300C2×C8—2442no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—1224no—
304C4⋊C4—2441no—
305C4⋊C4—2442no—
306C4⋊C4—2442no—
307C4⋊C4C4×#692312yes—
308C22⋊C4—1224no—
309C22⋊C4—2442no—
310C42—22no—
311C42—42no—
312C42—1222no—
313C42—2441no—
314C42—2441no—
315C42—2442no—
316C23—611no—
317C23—611no—
318C23—612no—
319C23—612no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23C2×C22⋊#692311yescharacteristic
325Q8—2442no—
326Q8—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1222no—
349C2×C4—4882no—
350C2×C4—4882no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2444no—
358C2×C4—2444no—
359C2×C4—2444no—
360C2×C4—2444no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4#1451983612yes—
367C2×C4#1451984012yes—
368C2×C4C2×C4×#692311yescharacteristic
369C2×C4#1451985611yescharacteristic
370C8—2444no—
371C22—612no—
372C22—612no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1222no—
378C22—1222no—
379C22—1222no—
380C22—1222no—
381C22C4×C22⋊#692311yescharacteristic
382C22C2×#1451983611yescharacteristic
383C22#1684074111yescharacteristic
384C22C2×#1451984011yescharacteristic
385C22#1684075211yescharacteristic
386C22#1684075911yescharacteristic
387C22#1684076011yescharacteristic
388C4—22no—
389C4—21no—
390C4—21no—
391C4—22no—
392C4—42no—
393C4—81no—
394C4—1222no—
395C4—1222no—
396C4—4884no—
397C4—4881no—
398C4—2442no—
399C4—2441no—
400C2—1222no—
401C2—1222no—
402C2#2146124711yescharacteristic
403C2#2146125211yescharacteristic
404C2#2146125811yescharacteristic
405C2#2146126111yescharacteristic
406C2C4×#1451983611yescharacteristic
407C2#2146158211yescharacteristic
408C2C4×#1451984011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8221
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. #16840615C4semidirect
14. C2×C4×Dic122C4semidirect
16. #16839667C4semidirect
17. #16839661C4semidirect
23. C4×C4⋊C4×C61C4semidirect
221. C4×C4⋊C4#6923semidirect
228. C61#8221semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
C2×#168406152
#214609952
#214606922
C4×#145197572
#822161