Finite Group Databasebeta

← #30596484

Subgroups — #30596484

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic
2#21462498C211yesmaximal, characteristic
3#21460670C214yesmaximal, complemented
4#21448223C211yesmaximal, characteristic
5#16840785—21no—
6#16840785C412yescomplemented
7#16840782C2212yes—
8#16840782C2212yes—
9#16840780—21no—
10#16840780C412yescomplemented
11#16840779—21no—
12#16840779—21no—
13#16840767—21no—
14#16840767C412yescomplemented
15#16840733—21no—
16#16840733—21no—
17C4×#11758213—21no—
18C4×#11758213C412yescomplemented
19C2×#14519734C412yes—
20C2×C42×D61C2211yescharacteristic
21#16839631—21no—
22#16839626—21no—
23#16839621—21no—
24#16839619—21no—
25C4×#11758196C2212yes—
26C4×C4⋊Dic61C411yescharacteristic
27C4×C4⋊C4×C61C411yescharacteristic
28C2×#11758213—22no—
29C2×#11758213—22no—
30#14519844—22no—
31#14519844—22no—
32#14519844—22no—
33#14519844C2×C414yes—
34#14519834—22no—
35#14519834—22no—
36C22⋊#92420—22no—
37C22⋊#92420—22no—
38#14519832—22no—
39#14519832C2×C414yes—
40C4×#92420—22no—
41C4×#92420—22no—
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45#14519734—44no—
46C2×C4⋊Dic61—21no—
47C2×#11758196—22no—
48C2×#11758196—22no—
49C2×#11758198—22no—
50C2×C4×Dic61C2×C412yes—
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54C42×D61C2×C411yescharacteristic
55C42×D61C2×C411yescharacteristic
56C42×D61C2×C411yescharacteristic
57C42×D61C2×C411yescharacteristic
58C42×D61D411yescharacteristic
59C42×D61D411yescharacteristic
60C42×D61Q811yescharacteristic
61C42×D61Q811yescharacteristic
62#14519684—21no—
63#14519684—22no—
64C2×C4⋊C4×C61—21no—
65C2×C42×C61C2×C412yes—
66C2×C42×C61C2×C411yescharacteristic
67#95×C61—21no—
68C23×D61C22⋊C411yescharacteristic
69C22×C4×C61—22no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61—22no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61C4211yescharacteristic
82C2×C4×D61C4211yescharacteristic
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61C22⋊C411yescharacteristic
86C2×C4×D61C22⋊C411yescharacteristic
87C2×C4×D61C4⋊C411yescharacteristic
88C2×C4×D61C4⋊C411yescharacteristic
89C2×C4×D61C4⋊C411yescharacteristic
90C2×C4×D61C4⋊C411yescharacteristic
91C2×C4×D61C4⋊C411yescharacteristic
92C2×C4×D61C4⋊C411yescharacteristic
93C2×#92420—24no—
94C2×#92420—24no—
95#11758213—44no—
96#11758213—44no—
97C4⋊C4×C61—42no—
98C42×C61—42no—
99C42×C61C4211yescharacteristic
100C42×C61C4211yescharacteristic
101C42×C61C4⋊C411yescharacteristic
102C42×C61C4⋊C411yescharacteristic
103#11758198—44no—
104C4⋊Dic61—42no—
105#11758196—44no—
106#11758196—44no—
107C4×Dic61—42no—
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C4⋊C411yescharacteristic
113C4×Dic61C4⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C22×C411yescharacteristic
117C4×Dic61C22×C411yescharacteristic
118C4×Dic61C2×D411yescharacteristic
119C4×Dic61C2×Q811yescharacteristic
120C23×C61C2×C22⋊C411yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61#9511yescharacteristic
126C22×D61#9511yescharacteristic
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61#9511yescharacteristic
135C2×C4×C61#9511yescharacteristic
136C2×C4×C61#9511yescharacteristic
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61C2×C4211yescharacteristic
139C2×C4×C61C2×C4⋊C411yescharacteristic
140C2×Dic61—22no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61#9511yescharacteristic
146C2×Dic61#9511yescharacteristic
147C2×Dic61#10012yes—
148C2×Dic61#10112yes—
149C2×Dic61C2×C22⋊C411yescharacteristic
150C2×Dic61C2×C22⋊C411yescharacteristic
151C2×Dic61C2×C4⋊C411yescharacteristic
152C2×Dic61C2×C4⋊C411yescharacteristic
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165#92420—44no—
166#92420—44no—
167#7953—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61C2×#9511yescharacteristic
171C22×C61C2×#10011yescharacteristic
172C22×C61C2×#10111yescharacteristic
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—42no—
180C2×D61—42no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—82no—
187C4×C61H(3,ℤ/4)12yes—
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—82no—
192Dic61#34312yes—
193Dic61#34312yes—
194Dic61#42112yes—
195#2920—611no—
196#2920—611no—
197#2285—611no—
198#1285—614no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61C2×H(3,ℤ/4)11yescharacteristic
202C2×C61#173311yescharacteristic
203C2×C61C2×#34311yescharacteristic
204D61—41no—
205D61—41no—
206C2×#117—612no—
207C22×C42—611no—
208#432—612no—
209#432—612no—
210#432—612no—
211#432—1221no—
212#431—612no—
213#431—1221no—
214#431—1221no—
215#431—1221no—
216#423—612no—
217#423—1221no—
218#407—1221no—
219#407—1221no—
220C4×M16—612no—
221C4×M16—1221no—
222#384—1221no—
223#382—1221no—
224#380—1221no—
225#380—1221no—
226C4×C4⋊C4—612no—
227C4×C4⋊C4—611no—
228C4×C4⋊C4#692311yescharacteristic
229C61#795311yescharacteristic, complemented, Sylow
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—611no—
233C2×M16—1222no—
234C2×M16—1222no—
235#117—2444no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1222no—
239C2×C4⋊C4—1221no—
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—612no—
253C2×C42C2×#692312yes—
254C2×C42C2×#692311yescharacteristic
255C4⋊C8—614no—
256C4⋊C8—1222no—
257C4⋊C8—1222no—
258C4⋊C8—1222no—
259C22⋊C8—1222no—
260C22⋊C8—1222no—
261C22⋊C8—1222no—
262C22⋊C8—1222no—
263#97—614no—
264#97—1222no—
265C4×C8—1222no—
266C4×C8—1222no—
267#95—21no—
268#95—1222no—
269#95—1221no—
270C24—611no—
271C22×C4—22no—
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—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4C22⋊#692311yescharacteristic
293C22×C4C22⋊#692311yescharacteristic
294C22×C4C22×#692311yescharacteristic
295M16—2444no—
296M16—2444no—
297C2×C8—1224no—
298C2×C8—1224no—
299C4⋊C4—42no—
300C4⋊C4—2442no—
301C4⋊C4—2444no—
302C4⋊C4—2444no—
303C22⋊C4—2444no—
304C42—42no—
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—2442no—
318C42C4×#692311yescharacteristic
319C42C4×#692311yescharacteristic
320C42C4⋊#692311yescharacteristic
321C42C4⋊#692311yescharacteristic
322C23—611no—
323C23—611no—
324C23—1221no—
325C23—1221no—
326C23—2441no—
327C23—2441no—
328C23C2×C22⋊#692311yescharacteristic
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—612no—
337C2×C4—612no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4(C2×#6923)⋊C411yescharacteristic
362C2×C4(C2×#6923)⋊C411yescharacteristic
363C2×C4(C2×#6923)⋊C411yescharacteristic
364C2×C4(C2×#6923)⋊C411yescharacteristic
365C2×C4C2×C4×#692311yescharacteristic
366C2×C4C2×C4⋊#692311yescharacteristic
367C8—2444no—
368C8—2444no—
369C22—21no—
370C22—21no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—2442no—
378C22—2442no—
379C22C2×(C2×#6923)⋊C411yescharacteristic
380C22D61⋊#10011yescharacteristic
381C22D61⋊#10111yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—82no—
388C4—612no—
389C4—612no—
390C4—612no—
391C4—1221no—
392C4—1221no—
393C4—1221no—
394C4—4882no—
395C4#1684062912yes—
396C2—21no—
397C2—21no—
398C2—2441no—
399C2—2441no—
400C2C2×#1684062911yescharacteristic
401C2#2146150011yescharacteristic
402C2#2146152211yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7953
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460670C2semidirect
6. #16840785C4semidirect
10. #16840780C4semidirect
14. #16840767C4semidirect
18. C4×#11758213C4semidirect
229. C61#7953semidirect

Maximal subgroups

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

subgroupindex
#214624982
#214606702
#214482232
#795361