Finite Group Databasebeta

← #30600152

Subgroups — #30600152

Order 15616.

726 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
1C2×C4×D61⋊C8C211yesmaximal, characteristic
2#21461674C211yesmaximal, characteristic
3C2×#16840612C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448349C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×C4⋊#92420C2212yes—
8C2×#14519834—21no—
9C4×D61⋊C8—24no—
10C2×C4×#92420—21no—
11C2×C4×#92420C2212yes—
12#16840628—21no—
13#16840612—24no—
14C2×#14519757C411yescharacteristic
15C2×#14519742C2211yescharacteristic
16C2×C42×D61C2211yescharacteristic
17#16839668C411yescharacteristic
18#16839645—21no—
19#16839633—21no—
20#16839619C411yescharacteristic
21C4⋊C4×Dic61—21no—
22C4⋊C4×Dic61C2211yescharacteristic
23#16839609—21no—
24C61×#389C411yescharacteristic
25C2×D61⋊C8—24no—
26C2×D61⋊C8—24no—
27C2×D61⋊C8—24no—
28C22×#92420—22no—
29C22×#92420—22no—
30C4⋊#92420—22no—
31C4⋊#92420—22no—
32#14519834—42no—
33C4×#92420—24no—
34C4×#92420—22no—
35C4×#92420D414yes—
36C22×Dic122C2×C411yescharacteristic
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40#14519757—22no—
41#14519757C814yescomplemented
42#14519742—22no—
43#14519742—22no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54C42×D61—22no—
55C42×D61—22no—
56#14519684—21no—
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—22no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—22no—
82C2×C4×D61—21no—
83C2×C4×D61—22no—
84C2×C4×D61C2×C812yes—
85C2×C4×D61M1612yes—
86C2×C4×D61SD1612yes—
87C2×C4×D61Q1612yes—
88C2×Dic122—22no—
89C2×Dic122—22no—
90C2×Dic122—21no—
91C2×Dic122C2×C812yescomplemented
92C2×#92420—24no—
93C2×#92420—24no—
94C2×#92420—24no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98D61⋊C8—216no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—42no—
102C4⋊C4×C61C2×C812yescomplemented
103C42×C61—22no—
104#11758198—24no—
105#11758198—42no—
106C4⋊Dic61—24no—
107C4⋊Dic61—22no—
108#11758196—41no—
109#11758196—41no—
110C4×Dic61—21no—
111C4×Dic61—22no—
112C4×Dic61—21no—
113C4×Dic61—42no—
114C4×Dic61—42no—
115C4×Dic61C2×D412yes—
116C4×Dic61#4112yes—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61C22⋊C812yes—
123C22×D61#10312yes—
124C22×D61#10412yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#10312yes—
136C2×C4×C61#10412yes—
137C2×C4×C61C4×D412yes—
138C2×C4×C61C22×C811yescharacteristic
139C2×C4×C61C2×M1611yescharacteristic
140C2×C4×C61#13112yes—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61C22⋊C812yes—
152C2×Dic61#12011yescharacteristic
153C2×Dic61#12112yes—
154C2×Dic61#12311yescharacteristic
155C2×Dic61C2×SD1611yescharacteristic
156C2×Dic61C2×Q1611yescharacteristic
157C2×Dic61#13512yes—
158C4×D61—24no—
159C4×D61—24no—
160C4×D61—24no—
161C4×D61—24no—
162C4×D61—24no—
163C4×D61—24no—
164Dic122—24no—
165Dic122—42no—
166#92420—28no—
167#92420—82no—
168#9071—611nomaximal, Sylow
169C22×C61#38611yescharacteristic
170C22×C61C2×C22⋊C811yescharacteristic
171C22×C61#40811yescharacteristic
172C22×C61C2×#10311yescharacteristic
173C22×C61#41611yescharacteristic
174C22×C61C2×#10411yescharacteristic
175C22×C61C2×#10411yescharacteristic
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61Q8⋊C814yescomplemented
183C4×C61—22no—
184C4×C61—22no—
185C4×C61—42no—
186C4×C61—81no—
187C4×C61C8×D412yes—
188C4×C61#43512yes—
189Dic61—22no—
190Dic61—21no—
191Dic61—21no—
192Dic61—42no—
193Dic61—81no—
194Dic61#46512yes—
195Dic61#46712yes—
196C22×C4×C8—611no—
197C4×C22⋊Q8—611no—
198#1797—611no—
199C2×Q8⋊C8—612no—
200#1279—612no—
201C2×C61C2×Q8⋊C811yescharacteristic
202C2×C61#147611yescharacteristic
203C2×C61#149311yescharacteristic
204C2×C61#149411yescharacteristic
205C2×C61#186911yescharacteristic
206C2×C61#189211yescharacteristic
207C2×C61#189611yescharacteristic
208D61—24no—
209C23×C8—1221no—
210C2×C22⋊Q8—611no—
211C2×C4×Q8—611no—
212C22×C42—611no—
213C2×C4⋊C8—612no—
214C2×C22⋊C8—1221no—
215C2×C4×C8—612no—
216C2×C4×C8—1224no—
217C2×C4×C8—1221no—
218#391—611no—
219#389#692311yescharacteristic
220#387—1221no—
221#385—1221no—
222#380—611no—
223C4×C4⋊C4—611no—
224C4×C4⋊C4—1221no—
225C4×C22⋊C4—1221no—
226#336—1221no—
227Q8⋊C8—1224no—
228C61#907111yescharacteristic, complemented, Sylow
229C22×Q8—611no—
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—611no—
233C22×C8—1222no—
234C22×C8—1224no—
235C22×C8—1224no—
236C22×C8—1224no—
237C22×C8—1222no—
238C22⋊Q8—614no—
239C22⋊Q8—1222no—
240C4×Q8—1222no—
241C4×Q8—1222no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4C2×#692311yescharacteristic
247C2×C4⋊C4C2×#692311yescharacteristic
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—1222no—
254C2×C42—1222no—
255C2×C42—1221no—
256C2×C42—1221no—
257C2×C42C2×#692311yescharacteristic
258C4⋊C8—1222no—
259C4⋊C8—1222no—
260C22⋊C8—2442no—
261C4×C8—614no—
262C4×C8—1222no—
263C4×C8—1224no—
264#95—21no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268#95—1221no—
269C24—611no—
270C2×Q8—612no—
271C2×Q8—1221no—
272C2×Q8—1222no—
273C2×Q8—1222no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—612no—
280C22×C4—612no—
281C22×C4—612no—
282C22×C4—612no—
283C22×C4—1221no—
284C22×C4—1222no—
285C22×C4—1221no—
286C22×C4—1222no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—1222no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4C22⋊#692311yescharacteristic
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22×#692311yescharacteristic
296C2×C8—1224no—
297C2×C8—12216no—
298C2×C8—1224no—
299C2×C8—1224no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—42no—
306C4⋊C4—1224no—
307C4⋊C4—1222no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C4⋊C4D61⋊C812yescomplemented
311C22⋊C4—1224no—
312C22⋊C4—2442no—
313C42—22no—
314C42—612no—
315C42—612no—
316C42—1221no—
317C42—1222no—
318C42—1221no—
319C42—2442no—
320C42—2442no—
321C23—612no—
322C23—612no—
323C23—612no—
324C23—1221no—
325C23—1221no—
326C23—1221no—
327C23—1221no—
328C23C2×C22⋊#692311yescharacteristic
329Q8—1224no—
330Q8—2442no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—612no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—612no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—612no—
348C2×C4—1224no—
349C2×C4—1224no—
350C2×C4—1224no—
351C2×C4—1224no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1224no—
357C2×C4—1224no—
358C2×C4—1222no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4#1451984012yes—
365C2×C4#1451984112yes—
366C2×C4D4×#692312yes—
367C2×C4C2×D61⋊C811yescharacteristic
368C2×C4D61⋊M1611yescharacteristic
369C2×C4#1451986512yes—
370C8—1228no—
371C8—4882no—
372C22—614no—
373C22—1222no—
374C22—1222no—
375C22—1222no—
376C22—1222no—
377C22—1222no—
378C22—1222no—
379C22#1684071011yescharacteristic
380C22D61⋊(C22⋊C8)11yescharacteristic
381C22#1684073711yescharacteristic
382C22C2×#1451984011yescharacteristic
383C22#1684075211yescharacteristic
384C22C2×#1451984111yescharacteristic
385C22D61⋊#10411yescharacteristic
386C4—22no—
387C4—22no—
388C4—42no—
389C4—81no—
390C4—612no—
391C4—612no—
392C4—1222no—
393C4—1221no—
394C4—1221no—
395C4—4881no—
396C4—2442no—
397C4#1684079012yes—
398C4#1684079212yes—
399C2—1224no—
400C2D61⋊(Q8⋊C8)11yescharacteristic
401C2#2146111111yescharacteristic
402C2#2146116911yescharacteristic
403C2#2146117311yescharacteristic
404C2#2146179511yescharacteristic
405C2#2146183211yescharacteristic
406C2#2146183711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#9071
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C2×#16840612C2semidirect
4. #21460655C2semidirect
41. #14519757C8semidirect
91. C2×Dic122C2×C8semidirect
102. C4⋊C4×C61C2×C8semidirect
182. C2×D61Q8⋊C8semidirect
228. C61#9071semidirect
310. C4⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D61⋊C82
#214616742
C2×#168406122
#214606552
#214483492
#907161