Finite Group Databasebeta

← #30596948

Subgroups — #30596948

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic
2#21462266C211yesmaximal, characteristic
3#21460700C214yesmaximal
4#21448212C211yesmaximal, characteristic
5#16840785—21no—
6#16840782—21no—
7#16840780—21no—
8#16840779—21no—
9#16840767C412yescomplemented
10#16840733C2212yes—
11C4×#11758213C412yescomplemented
12#16840707C412yescomplemented
13#16840706C412yescomplemented
14#16840705—21no—
15#16840704—21no—
16C4×C4⋊#6923—21no—
17C4×C22⋊#6923C2212yes—
18#16840698—21no—
19C2×C42×D61C2211yescharacteristic
20#16839629C412yescomplemented
21#16839628C411yescharacteristic, complemented
22#16839624—21no—
23#16839619—21no—
24C4⋊C4×Dic61—21no—
25#16839609C2212yes—
26#16839607—21no—
27C61×#382C411yescharacteristic, complemented
28C2×#11758213C2×C414yes—
29C2×C4⋊#6923—22no—
30C2×C22⋊#6923—22no—
31C2×C4×#6923—22no—
32#14519844—22no—
33#14519844—22no—
34#14519834—22no—
35C22⋊#92420—22no—
36#14519832—22no—
37C4×#92420—22no—
38(C2×#6923)⋊C4—22no—
39(C2×#6923)⋊C4—22no—
40(C2×#6923)⋊C4—22no—
41(C2×#6923)⋊C4C2×C414yes—
42C22×C4×D61D411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61C2311yescharacteristic
45C2×C4⋊Dic61—21no—
46C2×#11758198—22no—
47C2×C4×Dic61—22no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C42×D61C2×C411yescharacteristic
52C42×D61C2×C411yescharacteristic
53C42×D61C2×C411yescharacteristic
54C42×D61C2×C411yescharacteristic
55C42×D61D411yescharacteristic
56C42×D61D411yescharacteristic
57C42×D61Q811yescharacteristic
58C42×D61Q811yescharacteristic
59#14519684—21no—
60#14519684—22no—
61#14519684—22no—
62#14519684C2×C412yes—
63C2×C4⋊C4×C61—21no—
64C2×C42×C61C2×C411yescharacteristic
65#95×C61—21no—
66#95×C61C2×C412yes—
67C23×D61C2×D411yescharacteristic
68C22×#6923—24no—
69C22×C4×C61—22no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61—22no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61C22⋊C411yescharacteristic
82C2×C4×D61C22⋊C411yescharacteristic
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61C4⋊C411yescharacteristic
86C2×C4×D61C4⋊C411yescharacteristic
87C2×C4×D61C4⋊C411yescharacteristic
88C2×C4×D61C4⋊C411yescharacteristic
89C2×C4×D61C22×C411yescharacteristic
90C2×C4×D61C22×C411yescharacteristic
91C2×C4×D61C2×D411yescharacteristic
92C2×C4×D61C2×Q811yescharacteristic
93C22⋊#6923—42no—
94C22⋊#6923—42no—
95C2×#92420—24no—
96C4⋊#6923—44no—
97C4×#6923—44no—
98#11758213—44no—
99C4⋊C4×C61—42no—
100C42×C61C4211yescharacteristic
101C42×C61C4211yescharacteristic
102C42×C61C4⋊C411yescharacteristic
103C42×C61C4⋊C411yescharacteristic
104#11758198—44no—
105C4⋊Dic61—42no—
106C4×Dic61—44no—
107C4×Dic61C4211yescharacteristic
108C4×Dic61C4211yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C4⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—22no—
123C22×D61—41no—
124C22×D61C2×C22⋊C411yescharacteristic
125C22×D61C2×C4⋊C411yescharacteristic
126C2×#6923—44no—
127C2×#6923—44no—
128C2×#6923—44no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61#9511yescharacteristic
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61C2×C4211yescharacteristic
141C2×C4×C61C2×C4⋊C411yescharacteristic
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—22no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61#9511yescharacteristic
150C2×Dic61#9511yescharacteristic
151C2×Dic61#9511yescharacteristic
152C2×Dic61#9511yescharacteristic
153C2×Dic61C2×C22⋊C411yescharacteristic
154C2×Dic61C2×C4⋊C411yescharacteristic
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C4×D61—41no—
167#92420—44no—
168#8050—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61C2×#9511yescharacteristic
172C22×C61#42111yescharacteristic
173C22×C61#42111yescharacteristic
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—42no—
180C2×D61—42no—
181C2×D61#42112yes—
182#6923—84no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—82no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—82no—
196Dic61#41012yes—
197#2920—611no—
198#2283—611no—
199#2283—611no—
200#1297—614no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61#173311yescharacteristic
204C2×C61#173311yescharacteristic
205C2×C61#174011yescharacteristic
206D61—22no—
207D61—41no—
208C22×C42—611no—
209#432—1221no—
210#432—1221no—
211#431—1221no—
212#431—1221no—
213#423—612no—
214#407—612no—
215C4×M16—612no—
216#383—612no—
217#383—612no—
218#382—612no—
219#382—611no—
220#382#692311yescharacteristic, complemented
221#381—1221no—
222#381—1221no—
223#380—1221no—
224#380—1221no—
225C4×C4⋊C4—1221no—
226C4×C4⋊C4—1221no—
227C4×C22⋊C4—612no—
228C4×C22⋊C4—612no—
229#376—1221no—
230#376—1221no—
231C61#805011yescharacteristic, complemented, Sylow
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—611no—
235C2×M16—614no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1221no—
239C2×C22⋊C4—1222no—
240C2×C22⋊C4—1222no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—1222no—
253C2×C42—1222no—
254C2×C42C2×#692311yescharacteristic
255C4⋊C8—1222no—
256C4⋊C8—1222no—
257C22⋊C8—1222no—
258C22⋊C8—1222no—
259#97—1222no—
260C4×C8—1222no—
261#95—21no—
262#95—614no—
263#95—612no—
264#95—1222no—
265#95—1222no—
266#95—1222no—
267#95—1222no—
268#95—1222no—
269#95—1221no—
270#95C2×#692312yes—
271C24—611no—
272C22×C4—22no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1224no—
289C22×C4—1222no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22×#692311yescharacteristic
297M16—2444no—
298C2×C8—1224no—
299C4⋊C4—42no—
300C4⋊C4—2442no—
301C4⋊C4—2444no—
302C22⋊C4—2444no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C42—611no—
306C42—611no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—2444no—
318C42—2444no—
319C42C4×#692311yescharacteristic
320C42C4×#692311yescharacteristic
321C42C4⋊#692311yescharacteristic
322C42C4⋊#692311yescharacteristic
323C23—611no—
324C23—611no—
325C23—1222no—
326C23—1221no—
327C23—1221no—
328C23—2441no—
329C23C2×C22⋊#692311yescharacteristic
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4—2444no—
362C2×C4—2444no—
363C2×C4—2444no—
364C2×C4—2442no—
365C2×C4(C2×#6923)⋊C411yescharacteristic
366C2×C4(C2×#6923)⋊C411yescharacteristic
367C2×C4(C2×#6923)⋊C411yescharacteristic
368C2×C4(C2×#6923)⋊C411yescharacteristic
369C2×C4C2×C4×#692311yescharacteristic
370C2×C4C2×C4⋊#692311yescharacteristic
371C8—2444no—
372C22—21no—
373C22—21no—
374C22—612no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—2442no—
381C22—2442no—
382C22C2×(C2×#6923)⋊C411yescharacteristic
383C22#1684076011yescharacteristic
384C22#1684076111yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—82no—
392C4—612no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—1221no—
397C4—1221no—
398C4—4882no—
399C4—4884no—
400C2—21no—
401C2—21no—
402C2—1222no—
403C2—2441no—
404C2#2146149811yescharacteristic
405C2#2146150011yescharacteristic
406C2#2146151711yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#95
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#382#6923
hypocenterC61#8050
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
9. #16840767C4semidirect
11. C4×#11758213C4semidirect
12. #16840707C4semidirect
13. #16840706C4semidirect
20. #16839629C4semidirect
21. #16839628C4semidirect
27. C61×#382C4semidirect
220. #382#6923semidirect
231. C61#8050semidirect

Maximal subgroups

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

subgroupindex
#214624982
#214622662
#214607002
#214482122
#805061