Finite Group Databasebeta

← #30596347

Subgroups — #30596347

Order 15616.

666 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
1D61⋊#432C211yesmaximal, characteristic
2C4×#14519856C211yesmaximal, characteristic
3#21460661C214yesmaximal
4C2×#16839818C211yesmaximal, characteristic
5C2×#14519856C412yes—
6#16840785—21no—
7#16840784—21no—
8#16840783C412yescomplemented
9#16840782C412yescomplemented
10D61⋊(C4⋊C8)—21no—
11D61⋊(C22⋊C8)C2212yes—
12#16840721—21no—
13C4×C4⋊#6923—21no—
14C4×C4⋊#6923—21no—
15C4×C22⋊#6923C412yes—
16C4×C22⋊#6923C2212yes—
17#16840698—21no—
18C42×#6923—21no—
19C2×C42×D61C2211yescharacteristic
20#16839818—21no—
21#16839818—21no—
22#16839818—21no—
23#16839818—21no—
24C2×C4⋊#92418C411yescharacteristic, complemented
25C2×#14519689C2212yes—
26C2×#14519687C412yescomplemented
27C2×C4⋊C8×C61C411yescharacteristic, complemented
28C2×D61⋊C8—22no—
29#14519856—28no—
30C2×C4⋊#6923—22no—
31C2×C22⋊#6923C2×C414yes—
32C2×C4×#6923—22no—
33C2×C4×#6923—22no—
34C2×C4×#6923—22no—
35#14519844—22no—
36C4⋊#92420—22no—
37#14519834—22no—
38C22⋊#92420C2×C414yes—
39#14519832—22no—
40#14519832—22no—
41(C2×#6923)⋊C4—22no—
42(C2×#6923)⋊C4—22no—
43C22×C4×D61C2×C411yescharacteristic
44C22×C4×D61C2×C411yescharacteristic
45C22×C4×D61C2311yescharacteristic
46C22×#92418C2×C412yes—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C42×D61D411yescharacteristic
51C42×D61D411yescharacteristic
52C42×D61D411yescharacteristic
53C42×D61D411yescharacteristic
54C42×D61D411yescharacteristic
55C42×D61D411yescharacteristic
56C42×D61Q811yescharacteristic
57C42×D61Q811yescharacteristic
58C4⋊#92418—21no—
59C4⋊#92418—21no—
60#14519689—22no—
61#14519689—22no—
62#14519687—22no—
63#14519687—22no—
64C22×C8×C61C2×C412yes—
65C2×C42×C61C2×C411yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C23×D61C22×C411yescharacteristic
69C22×#6923—24no—
70C22×C4×C61C4211yescharacteristic
71C22×C4×C61C4211yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61C4211yescharacteristic
74C22×Dic61C4211yescharacteristic
75C22×Dic61C22×C411yescharacteristic
76C2×C4×D61—24no—
77C2×C4×D61—42no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61C22⋊C411yescharacteristic
81C2×C4×D61C22⋊C411yescharacteristic
82C2×C4×D61C22⋊C411yescharacteristic
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C4⋊C411yescharacteristic
85C2×C4×D61C4⋊C411yescharacteristic
86C2×C4×D61C4⋊C411yescharacteristic
87C2×C4×D61C4⋊C411yescharacteristic
88C2×C4×D61C2×D411yescharacteristic
89C2×C4×D61C2×D411yescharacteristic
90C2×C4×D61C2×D411yescharacteristic
91C2×C4×D61C2×Q811yescharacteristic
92C22⋊#6923—24no—
93C22⋊#6923M1618yes—
94C2×#92420—24no—
95C4⋊#6923—28no—
96C4×#6923—28no—
97C4×#6923—44no—
98C4×#6923—42no—
99C4×#6923—42no—
100D61⋊C8—42no—
101D61⋊C8—42no—
102C2×C8×C61—22no—
103C2×C8×C61—42no—
104C42×C61C22⋊C411yescharacteristic
105C42×C61C22⋊C411yescharacteristic
106C42×C61C4⋊C411yescharacteristic
107C42×C61C4⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C2×#92418—22no—
121C2×#92418—42no—
122C23×C61C2×C4211yescharacteristic
123C22×D61—41no—
124C22×D61—41no—
125C22×D61C2×C22⋊C411yescharacteristic
126C22×D61C2×C4⋊C411yescharacteristic
127C22×D61C2×M1614yes—
128C2×#6923—28no—
129C2×#6923—44no—
130C2×#6923—44no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61#9511yescharacteristic
136C2×C4×C61#9511yescharacteristic
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×C4⋊C411yescharacteristic
141C2×Dic61—22no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#9511yescharacteristic
145C2×Dic61#9511yescharacteristic
146C2×Dic61#9511yescharacteristic
147C2×Dic61#9511yescharacteristic
148C2×Dic61C2×C22⋊C411yescharacteristic
149C2×Dic61C2×C4⋊C411yescharacteristic
150C4×D61—22no—
151C4×D61—22no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164#92420—44no—
165C8×C61—42no—
166#92418—42no—
167#7930—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61C2×#9511yescharacteristic
171C22×C61C4×M1612yes—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—44no—
177C2×D61#40712yes—
178C2×D61#42312yes—
179#6923—48no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61#34412yes—
185C4×C61#41011yescharacteristic
186C4×C61#41011yescharacteristic
187Dic61—21no—
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193C2×#432—611no—
194C2×#432—611no—
195C4×#117—611no—
196#1282—614no—
197C2×C61—22no—
198C2×C61#172811yescharacteristic
199C2×C61#174011yescharacteristic
200C2×C61C2×#34411yescharacteristic
201D61—22no—
202D61—22no—
203C2×#117—612no—
204C22×C42—611no—
205#432—612no—
206#432—612no—
207#432—1221no—
208#432—1221no—
209#432—1221no—
210#432—1221no—
211#432—1221no—
212#432—1221no—
213C2×C4⋊C8—611no—
214C2×C4⋊C8—1221no—
215C2×C4⋊C8#692311yescharacteristic, complemented
216C2×C22⋊C8—612no—
217C2×C22⋊C8—612no—
218C2×#97—612no—
219C2×#97—1221no—
220C4×C4⋊C4—1221no—
221C4×C4⋊C4—1221no—
222C4×C22⋊C4—612no—
223C4×C22⋊C4—612no—
224#376—1221no—
225C43—1221no—
226C61#793011yescharacteristic, complemented, Sylow
227C23×C4—611no—
228C23×C4—611no—
229C23×C4—611no—
230C22×C8—612no—
231C22×C8—1222no—
232C22×C8C2×#692312yes—
233#117—1228no—
234C2×C4⋊C4—1222no—
235C2×C22⋊C4—614no—
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—611no—
247C2×C42—1222no—
248C2×C42—1222no—
249C2×C42—1222no—
250C2×C42C2×#692311yescharacteristic
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—1222no—
254C4⋊C8—1222no—
255C4⋊C8—1221no—
256C4⋊C8—1221no—
257C22⋊C8—614no—
258C22⋊C8—1222no—
259C22⋊C8—1222no—
260C22⋊C8—1222no—
261#97—1222no—
262#97—1222no—
263#97—1222no—
264#97—1222no—
265#95—1222no—
266#95—1222no—
267C24—611no—
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—1224no—
284C22×C4—1224no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2442no—
288C22×C4C4×#692311yescharacteristic
289C22×C4C4×#692311yescharacteristic
290C22×C4C22×#692311yescharacteristic
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—1224no—
294C2×C8—1222no—
295C2×C8—2442no—
296C2×C8—2442no—
297C2×C8—2442no—
298C4⋊C4—1228no—
299C22⋊C4—618no—
300C22⋊C4—1224no—
301C42—611no—
302C42—611no—
303C42—611no—
304C42—611no—
305C42—611no—
306C42—611no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—1228no—
314C42—2442no—
315C42—2442no—
316C42—2444no—
317C42C4⋊#692311yescharacteristic
318C42C4⋊#692311yescharacteristic
319C42C22⋊#692311yescharacteristic
320C42C22⋊#692311yescharacteristic
321C23—611no—
322C23—611no—
323C23—614no—
324C23—2441no—
325C23—2441no—
326C23C2×C4×#692311yescharacteristic
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—1222no—
340C2×C4—1222no—
341C2×C4—1222no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1228no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2444no—
356C2×C4—2444no—
357C2×C4(C2×#6923)⋊C411yescharacteristic
358C2×C4(C2×#6923)⋊C411yescharacteristic
359C2×C4(C2×#6923)⋊C411yescharacteristic
360C2×C4(C2×#6923)⋊C411yescharacteristic
361C2×C4C2×C22⋊#692311yescharacteristic
362C2×C4C2×C4⋊#692311yescharacteristic
363C8—42no—
364C8—2444no—
365C8—2442no—
366C22—21no—
367C22—21no—
368C22—612no—
369C22—612no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—2444no—
375C22C2×(C2×#6923)⋊C411yescharacteristic
376C22M16×#692312yes—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—1221no—
382C4—1221no—
383C4—1221no—
384C4—1221no—
385C4—1221no—
386C4—1221no—
387C4—2448no—
388C4#1684064412yes—
389C4#1684074211yescharacteristic
390C4#1684074311yescharacteristic
391C2—22no—
392C2—1222no—
393C2—1222no—
394C2#2146148111yescharacteristic
395C2#2146151911yescharacteristic
396C2C2×#1684064411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61C2×#95
prime radicalC23×D61C22×C4
cosocleC22×C4×D61C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#7930
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
8. #16840783C4semidirect
9. #16840782C4semidirect
24. C2×C4⋊#92418C4semidirect
26. C2×#14519687C4semidirect
27. C2×C4⋊C8×C61C4semidirect
215. C2×C4⋊C8#6923semidirect
226. C61#7930semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4322
C4×#145198562
#214606612
C2×#168398182
#793061