Finite Group Databasebeta

← #30597053

Subgroups — #30597053

Order 15616.

564 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462497C211yesmaximal, characteristic
2D61⋊#432C211yesmaximal, characteristic
3#21460707C214yesmaximal, complemented
4#21448212C211yesmaximal, characteristic
5#16840785—21no—
6#16840785C412yescomplemented
7#16840784C412yescomplemented
8#16840784C412yescomplemented
9#16840783C2212yes—
10#16840782—21no—
11#16840781—21no—
12#16840780—21no—
13#16840765—21no—
14D61⋊(C4⋊C8)C412yescomplemented
15#16840734—21no—
16D61⋊(C22⋊C8)—21no—
17C4×#11758217C2212yes—
18#16840721—21no—
19C2×C42×D61C2211yescharacteristic
20#16839629—21no—
21#16839628C411yescharacteristic
22#16839624C412yes—
23#16839619—21no—
24C4⋊C4×Dic61—21no—
25#16839609—21no—
26#16839607C2212yes—
27C61×#382C411yescharacteristic
28C2×#11758217—22no—
29C2×D61⋊C8—22no—
30#14519844—22no—
31#14519844—22no—
32C4⋊#92420—22no—
33C4⋊#92420C2×C414yes—
34#14519834—22no—
35#14519834—22no—
36#14519834—22no—
37C22⋊#92420—22no—
38#14519832—22no—
39#14519832—22no—
40#14519832C2×C414yes—
41C4×#92420—22no—
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C2×C4⋊Dic61—21no—
46C2×#11758198—22no—
47C2×C4×Dic61—22no—
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
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×D61C22⋊C411yescharacteristic
68C22×C4×C61—22no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—22no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×C4×D61—42no—
77C2×C4×D61—42no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61C4211yescharacteristic
81C2×C4×D61C4211yescharacteristic
82C2×C4×D61C22⋊C411yescharacteristic
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61C22⋊C411yescharacteristic
86C2×C4×D61C4⋊C411yescharacteristic
87C2×C4×D61C4⋊C411yescharacteristic
88C2×C4×D61C4⋊C411yescharacteristic
89C2×C4×D61C4⋊C411yescharacteristic
90C2×C4×D61C4⋊C411yescharacteristic
91C2×C4×D61C4⋊C411yescharacteristic
92#11758217—42no—
93#11758217—42no—
94C2×#92420—24no—
95C2×#92420—24no—
96D61⋊C8—44no—
97C4⋊C4×C61—42no—
98C42×C61C4211yescharacteristic
99C42×C61C4211yescharacteristic
100C42×C61C4⋊C411yescharacteristic
101C42×C61C4⋊C411yescharacteristic
102#11758198—44no—
103C4⋊Dic61—42no—
104C4×Dic61—44no—
105C4×Dic61C22⋊C411yescharacteristic
106C4×Dic61C22⋊C411yescharacteristic
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C4⋊C411yescharacteristic
110C4×Dic61C4⋊C411yescharacteristic
111C4×Dic61C4⋊C411yescharacteristic
112C4×Dic61C4⋊C411yescharacteristic
113C4×Dic61C22×C411yescharacteristic
114C4×Dic61C22×C411yescharacteristic
115C4×Dic61C2×D411yescharacteristic
116C4×Dic61C2×Q811yescharacteristic
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—22no—
121C22×D61—41no—
122C22×D61#9511yescharacteristic
123C22×D61#9511yescharacteristic
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61#9511yescharacteristic
132C2×C4×C61#9511yescharacteristic
133C2×C4×C61#9511yescharacteristic
134C2×C4×C61#9511yescharacteristic
135C2×C4×C61C2×C4211yescharacteristic
136C2×C4×C61C2×C4⋊C411yescharacteristic
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—22no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61#9511yescharacteristic
145C2×Dic61#9511yescharacteristic
146C2×Dic61C2×C22⋊C411yescharacteristic
147C2×Dic61C2×C22⋊C411yescharacteristic
148C2×Dic61C2×C4⋊C411yescharacteristic
149C2×Dic61C2×C4⋊C411yescharacteristic
150C4×D61—22no—
151C4×D61—22no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—41no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—41no—
162#92420—44no—
163#92420—44no—
164#8069—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61C2×#9511yescharacteristic
168C22×C61#42111yescharacteristic
169C22×C61#42111yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61#34412yes—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—82no—
185Dic61—21no—
186Dic61—21no—
187Dic61—21no—
188Dic61—21no—
189Dic61—21no—
190Dic61—82no—
191Dic61#42112yes—
192#2920—611no—
193C2×#432—611no—
194#2283—611no—
195#1300—614no—
196C2×C61—21no—
197C2×C61—21no—
198C2×C61#173311yescharacteristic
199C2×C61#173311yescharacteristic
200C2×C61C2×#34411yescharacteristic
201D61—22no—
202D61—41no—
203C22×C42—611no—
204#432—612no—
205#432—612no—
206#432—612no—
207#432—612no—
208#432—1221no—
209#432—1221no—
210#431—1221no—
211#431—1221no—
212#423—1221no—
213C2×C4⋊C8—612no—
214#407—1221no—
215C2×C22⋊C8—1221no—
216C4×M16—612no—
217C2×#97—1221no—
218#383—1221no—
219#382—611no—
220#382#692311yescharacteristic
221#381—612no—
222#380—1221no—
223C4×C4⋊C4—1221no—
224C4×C22⋊C4—1221no—
225#376—612no—
226C61#806911yescharacteristic, complemented, Sylow
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C2×M16—1222no—
231C22×C8—1222no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—1221no—
234C2×C22⋊C4—1222no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—1222no—
247C2×C42C2×#692311yescharacteristic
248C4⋊C8—614no—
249C4⋊C8—1222no—
250C4⋊C8—1222no—
251C4⋊C8—1222no—
252C22⋊C8—1222no—
253C22⋊C8—1222no—
254C22⋊C8—1222no—
255C22⋊C8—1222no—
256#97—614no—
257#97—1222no—
258#97—1222no—
259C4×C8—1222no—
260#95—21no—
261#95—612no—
262#95—1222no—
263#95—1222no—
264#95—1221no—
265#95C2×#692312yes—
266C24—611no—
267C22×C4—22no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
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—1222no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4—2442no—
287C22×C4—2442no—
288C22×C4C22⋊#692311yescharacteristic
289C22×C4C22⋊#692311yescharacteristic
290C22×C4C22×#692311yescharacteristic
291M16—2442no—
292M16—2442no—
293C2×C8—1224no—
294C2×C8—1224no—
295C2×C8—2444no—
296C4⋊C4—42no—
297C4⋊C4—2442no—
298C22⋊C4—2444no—
299C42—611no—
300C42—611no—
301C42—611no—
302C42—611no—
303C42—611no—
304C42—611no—
305C42—611no—
306C42—611no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—611no—
311C42—2444no—
312C42C4×#692311yescharacteristic
313C42C4×#692311yescharacteristic
314C42C4⋊#692311yescharacteristic
315C42C4⋊#692311yescharacteristic
316C23—611no—
317C23—611no—
318C23—1222no—
319C23—1221no—
320C23—1221no—
321C23—2441no—
322C23C2×C22⋊#692311yescharacteristic
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—1222no—
340C2×C4—1222no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4(C2×#6923)⋊C411yescharacteristic
356C2×C4(C2×#6923)⋊C411yescharacteristic
357C2×C4(C2×#6923)⋊C411yescharacteristic
358C2×C4(C2×#6923)⋊C411yescharacteristic
359C2×C4C2×C4×#692311yescharacteristic
360C2×C4C2×C4⋊#692311yescharacteristic
361C8—2444no—
362C8—2444no—
363C22—21no—
364C22—21no—
365C22—612no—
366C22—1221no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—2442no—
372C22—2442no—
373C22C2×(C2×#6923)⋊C411yescharacteristic
374C22#1684076011yescharacteristic
375C22#1684076111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—612no—
384C4—1221no—
385C4—1221no—
386C4—1221no—
387C4—1221no—
388C4—1221no—
389C4—4882no—
390C2—21no—
391C2—21no—
392C2—1222no—
393C2—2441no—
394C2#2146149811yescharacteristic
395C2#2146150011yescharacteristic
396C2#2146152711yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#95
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#8069
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
3. #21460707C2semidirect
6. #16840785C4semidirect
7. #16840784C4semidirect
8. #16840784C4semidirect
14. D61⋊(C4⋊C8)C4semidirect
226. C61#8069semidirect

Maximal subgroups

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

subgroupindex
#214624972
D61⋊#4322
#214607072
#214482122
#806961