Finite Group Databasebeta

← #30600378

Subgroups — #30600378

Order 15616.

644 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C4⋊C8)C211yesmaximal, characteristic
2#21461676C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21454170C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519844C2212yes—
8C2×#14519844C2212yes—
9D61⋊(C4⋊C8)—24no—
10C2×C4⋊#92420—21no—
11C2×#14519834—21no—
12#16840628—21no—
13#16840621—24no—
14C2×#14519776C2211yescharacteristic
15C2×#14519755—21no—
16C2×C42×D61C2211yescharacteristic
17#16839666—21no—
18#16839660C411yescharacteristic
19#16839657—21no—
20#16839631C2211yescharacteristic
21#16839621—21no—
22#16839619C411yescharacteristic
23#16839619C411yescharacteristic
24C61×#389C411yescharacteristic
25C2×D61⋊C8—24no—
26C2×D61⋊C8—42no—
27C2×D61⋊C8—42no—
28C22×#92420—22no—
29C22×#92420—22no—
30#14519844—22no—
31#14519844—22no—
32#14519844—22no—
33#14519844D414yes—
34C4⋊#92420—24no—
35#14519834—42no—
36C22×Dic122—21no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40#14519776—22no—
41#14519776—22no—
42#14519755—42no—
43#14519755—42no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61C2311yescharacteristic
55C42×D61—22no—
56C42×D61—22no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C42×C61C2×C411yescharacteristic
64#95×C61—21no—
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22×C411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—22no—
78C2×C4×D61—21no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—22no—
83C2×C4×D61—22no—
84C2×C4×D61—41no—
85C2×C4×D61D812yes—
86C2×C4×D61SD1612yes—
87C2×C4×D61SD1612yes—
88C2×C4×D61Q1612yes—
89C2×Dic122—42no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—42no—
93C2×#92420—24no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99D61⋊C8—48no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—42no—
103C42×C61—22no—
104#11758198—42no—
105#11758198—42no—
106C4⋊Dic61—22no—
107C4⋊Dic61—41no—
108#11758196—42no—
109#11758196—41no—
110#11758196—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—41no—
114#11758196—41no—
115C4×Dic61—21no—
116C4×Dic61—22no—
117C4×Dic61—21no—
118C4×Dic61C2×D412yes—
119C4×Dic61#4112yes—
120C23×C61C2×C22⋊C411yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61#10112yes—
126C22×D61#10212yes—
127C22×D61#10312yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61#10212yes—
141C2×C4×C61#10312yes—
142C2×C4×C61C4×D412yes—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61#12011yescharacteristic
153C2×Dic61#12112yes—
154C2×Dic61#12311yescharacteristic
155C2×Dic61C2×D811yescharacteristic
156C2×Dic61C2×SD1611yescharacteristic
157C2×Dic61C2×SD1611yescharacteristic
158C2×Dic61C2×Q1611yescharacteristic
159C2×Dic61#13512yes—
160C2×Dic61AGL(1,ℤ/8)11yescharacteristic
161C2×Dic61#13711yescharacteristic
162C4×D61—22no—
163C4×D61—22no—
164C4×D61—24no—
165C4×D61—24no—
166C4×D61—22no—
167C4×D61—22no—
168C4×D61—44no—
169Dic122—82no—
170Dic122—82no—
171#92420—44no—
172#92420—82no—
173#9129—611nomaximal, Sylow
174C22×C61#38611yescharacteristic
175C22×C61C2×#10111yescharacteristic
176C22×C61#41311yescharacteristic
177C22×C61C2×#10211yescharacteristic
178C22×C61C2×#10311yescharacteristic
179C22×C61#41611yescharacteristic
180C22×C61#41711yescharacteristic
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—22no—
186C2×D61—22no—
187C2×D61#33214yescomplemented
188C4×C61—22no—
189C4×C61—22no—
190C4×C61—22no—
191C4×C61—81no—
192C4×C61—81no—
193Dic61—41no—
194Dic61—81no—
195Dic61—81no—
196Dic61#45011yescharacteristic
197Dic61#45111yescharacteristic
198Dic61#46512yes—
199Dic61#46612yes—
200Dic61#48311yescharacteristic
201Dic61#48411yescharacteristic
202C22×C4⋊C8—611no—
203#2857—611no—
204#1797—611no—
205C2×#332—612no—
206#1296—612no—
207C2×C61C2×#33211yescharacteristic
208C2×C61#154211yescharacteristic
209C2×C61#154711yescharacteristic
210C2×C61#155211yescharacteristic
211C2×C61#187211yescharacteristic
212C2×C61#189311yescharacteristic
213C2×C61#190111yescharacteristic
214D61—24no—
215C23×C8—1221no—
216C2×C4⋊Q8—611no—
217C2×C22⋊Q8—1221no—
218C22×C42—611no—
219C2×C4⋊C8—612no—
220C2×C4⋊C8—612no—
221C2×C4⋊C8—1224no—
222C2×C4⋊C8—1221no—
223C2×C22⋊C8—1221no—
224#391—1221no—
225#389—611no—
226#389—1221no—
227#389#692311yescharacteristic
228#384—611no—
229#380—611no—
230#380—611no—
231#380—1221no—
232#336—1221no—
233#332—1224no—
234C61#912911yescharacteristic, complemented, Sylow
235C22×Q8—1221no—
236C23×C4—611no—
237C23×C4—611no—
238C23×C4—611no—
239C22×C8—1222no—
240C22×C8—1224no—
241C22×C8—1222no—
242C22×C8—2442no—
243C22×C8—2442no—
244C4⋊Q8—1222no—
245C4⋊Q8—1222no—
246C22⋊Q8—2442no—
247C22⋊Q8—2442no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4C2×#692311yescharacteristic
256C2×C4⋊C4C2×#692311yescharacteristic
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C42—611no—
260C2×C42—611no—
261C2×C42—611no—
262C2×C42—1222no—
263C2×C42—1222no—
264C2×C42C2×#692311yescharacteristic
265C4⋊C8—614no—
266C4⋊C8—1222no—
267C4⋊C8—1222no—
268C4⋊C8—1222no—
269C4⋊C8—1224no—
270C22⋊C8—2442no—
271#95—21no—
272#95—1221no—
273#95—1221no—
274#95—1221no—
275C24—611no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×Q8—2442no—
279C2×Q8—2442no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—612no—
285C22×C4—612no—
286C22×C4—612no—
287C22×C4—612no—
288C22×C4—611no—
289C22×C4—1221no—
290C22×C4—1222no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1222no—
294C22×C4—1221no—
295C22×C4—1222no—
296C22×C4—1222no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—2441no—
300C22×C4C22⋊#692311yescharacteristic
301C22×C4C22⋊#692311yescharacteristic
302C22×C4C22×#692311yescharacteristic
303C2×C8—1224no—
304C2×C8—2442no—
305C2×C8—2442no—
306C2×C8—2442no—
307C2×C8—2442no—
308C2×C8—2442no—
309C2×C8—2448no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—1222no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2441no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2442no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C42—22no—
325C42—612no—
326C42—612no—
327C42—1221no—
328C42—1222no—
329C42—1221no—
330C23—612no—
331C23—612no—
332C23—612no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23—1221no—
337C23C2×C22⋊#692311yescharacteristic
338Q8—4882no—
339Q8—4882no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—611no—
353C2×C4—612no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—612no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—1224no—
367C2×C4—1224no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—2444no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4#1451983912yes—
379C2×C4#1451984012yes—
380C2×C4D4×#692312yes—
381C8—4882no—
382C8—2444no—
383C22—614no—
384C22—1222no—
385C22—1222no—
386C22—1222no—
387C22—1222no—
388C22—1222no—
389C22—1222no—
390C22#1684071011yescharacteristic
391C22D61⋊#10111yescharacteristic
392C22#1684074811yescharacteristic
393C22C2×#1451983911yescharacteristic
394C22C2×#1451984011yescharacteristic
395C22#1684075211yescharacteristic
396C22#1684075311yescharacteristic
397C4—22no—
398C4—22no—
399C4—22no—
400C4—81no—
401C4—81no—
402C4—611no—
403C4—611no—
404C4—611no—
405C4—611no—
406C4—612no—
407C4—612no—
408C4—4881no—
409C4—4881no—
410C4—2441no—
411C2—1224no—
412C2D61⋊#33211yescharacteristic
413C2#2146132011yescharacteristic
414C2#2146133011yescharacteristic
415C2#2146134111yescharacteristic
416C2#2146180411yescharacteristic
417C2#2146183311yescharacteristic
418C2#2146184711yescharacteristic
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#9129
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. C2×#16840621C2semidirect
4. #21460697C2semidirect
187. C2×D61#332semidirect
234. C61#9129semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C4⋊C8)2
#214616762
C2×#168406212
#214606972
#214541702
#912961