Finite Group Databasebeta

← #30600160

Subgroups — #30600160

Order 15616.

610 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
1C2×#16840780C211yesmaximal, characteristic
2#21461674C211yesmaximal, characteristic
3C2×#16840612C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#21448349C211yesmaximal, characteristic
6#16840780—24no—
7C2×#14519844—21no—
8C2×C4⋊#92420C2212yes—
9C2×#14519834—21no—
10C2×#14519834—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
25C22×#92420—22no—
26C22×#92420—22no—
27#14519844—24no—
28C4⋊#92420—22no—
29C4⋊#92420—22no—
30#14519834—24no—
31#14519834—42no—
32C4×#92420—22no—
33C4×#92420D414yes—
34C22×Dic122C2×C411yescharacteristic
35C22×C4×D61C2×C411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61D411yescharacteristic
38#14519757—22no—
39#14519757C814yescomplemented
40#14519742—22no—
41#14519742—22no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52C42×D61—22no—
53C42×D61—22no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C42×C61C2×C411yescharacteristic
62#95×C61—21no—
63C23×D61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—21no—
77C2×C4×D61—22no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—22no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61C2×C812yes—
85C2×C4×D61M1612yes—
86C2×Dic122—22no—
87C2×Dic122—22no—
88C2×Dic122—21no—
89C2×Dic122C2×C812yes—
90C2×#92420—24no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—42no—
99C4⋊C4×C61C2×C812yes—
100C42×C61—22no—
101#11758198—24no—
102#11758198—42no—
103C4⋊Dic61—24no—
104C4⋊Dic61—22no—
105#11758196—41no—
106#11758196—41no—
107C4×Dic61—21no—
108C4×Dic61—22no—
109C4×Dic61—21no—
110C4×Dic61—42no—
111C4×Dic61—41no—
112C4×Dic61—41no—
113C4×Dic61C2×D412yes—
114C4×Dic61#4112yes—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61C22⋊C812yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61C4×D412yes—
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61#13112yes—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—22no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61C22⋊C812yes—
150C2×Dic61#12011yescharacteristic
151C2×Dic61#12112yes—
152C2×Dic61#12311yescharacteristic
153C2×Dic61AGL(1,ℤ/8)11yescharacteristic
154C2×Dic61#13712yes—
155C2×Dic61#13711yescharacteristic
156C4×D61—24no—
157C4×D61—24no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162Dic122—24no—
163Dic122—42no—
164#92420—44no—
165#92420—82no—
166#9073—611nomaximal, Sylow
167C22×C61#38611yescharacteristic
168C22×C61C2×C22⋊C811yescharacteristic
169C22×C61#40811yescharacteristic
170C22×C61#41711yescharacteristic
171C22×C61#41911yescharacteristic
172C22×C61#42111yescharacteristic
173C22×C61#42111yescharacteristic
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—42no—
184C4×C61—81no—
185C4×C61C8×D412yes—
186C4×C61#43512yes—
187Dic61—22no—
188Dic61—21no—
189Dic61—21no—
190Dic61—42no—
191Dic61—81no—
192Dic61#46812yes—
193Dic61#47012yes—
194C2×#431—611no—
195C4×C22⋊Q8—611no—
196#1797—611no—
197C2×Q8⋊C8—612no—
198#1279—612no—
199C2×C61#147711yescharacteristic
200C2×C61#147911yescharacteristic
201C2×C61#149511yescharacteristic
202C2×C61#149711yescharacteristic
203C2×C61#186911yescharacteristic
204C2×C61#189411yescharacteristic
205C2×C61#189711yescharacteristic
206D61—42no—
207C2×C22⋊Q8—611no—
208C2×C4×Q8—611no—
209C22×C42—611no—
210#431—1224no—
211C2×C4⋊C8—612no—
212C2×C4⋊C8—1221no—
213C2×C22⋊C8—1221no—
214C2×C22⋊C8—1221no—
215C2×C4×C8—612no—
216#391—611no—
217#389#692311yescharacteristic
218#387—1221no—
219#385—1221no—
220#380—611no—
221C4×C4⋊C4—611no—
222C4×C4⋊C4—1221no—
223C4×C22⋊C4—1221no—
224#336—1221no—
225Q8⋊C8—1224no—
226C61#907311yescharacteristic, complemented, Sylow
227C22×Q8—611no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—611no—
231C22×C8—1222no—
232C22×C8—1222no—
233C22⋊Q8—614no—
234C22⋊Q8—1222no—
235C4×Q8—1222no—
236C4×Q8—1222no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4C2×#692311yescharacteristic
242C2×C4⋊C4C2×#692311yescharacteristic
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—1222no—
249C2×C42—1222no—
250C2×C42—1221no—
251C2×C42—1221no—
252C2×C42C2×#692311yescharacteristic
253C4⋊C8—1222no—
254C4⋊C8—1222no—
255C4⋊C8—1224no—
256C22⋊C8—1224no—
257C22⋊C8—2442no—
258C4×C8—614no—
259C4×C8—1222no—
260#95—21no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265C24—611no—
266C2×Q8—612no—
267C2×Q8—1221no—
268C2×Q8—1222no—
269C2×Q8—1222no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1222no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4C22⋊#692311yescharacteristic
290C22×C4C22⋊#692311yescharacteristic
291C22×C4C22×#692311yescharacteristic
292C2×C8—1224no—
293C2×C8—2442no—
294C2×C8—2442no—
295C2×C8—2442no—
296C2×C8—2442no—
297C2×C8—2442no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—42no—
301C4⋊C4—1224no—
302C4⋊C4—1222no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4D61⋊C812yes—
306C22⋊C4—1224no—
307C22⋊C4—2442no—
308C42—22no—
309C42—612no—
310C42—612no—
311C42—1221no—
312C42—1222no—
313C42—1221no—
314C42—2441no—
315C42—2441no—
316C42—2442no—
317C23—612no—
318C23—1221no—
319C23—1221no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—1221no—
324C23C2×C22⋊#692311yescharacteristic
325Q8—1224no—
326Q8—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—612no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—612no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—612no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1224no—
351C2×C4—1224no—
352C2×C4—1222no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4D4×#692312yes—
363C2×C4C2×D61⋊C811yescharacteristic
364C2×C4D61⋊M1611yescharacteristic
365C2×C4#1451986512yes—
366C8—4882no—
367C8—2444no—
368C22—1222no—
369C22—1222no—
370C22—1222no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22#1684071011yescharacteristic
376C22D61⋊(C22⋊C8)11yescharacteristic
377C22#1684073711yescharacteristic
378C22#1684075311yescharacteristic
379C22#1684075511yescharacteristic
380C22#1684075911yescharacteristic
381C22#1684076011yescharacteristic
382C4—41no—
383C4—41no—
384C4—42no—
385C4—81no—
386C4—612no—
387C4—612no—
388C4—1222no—
389C4—1221no—
390C4—1221no—
391C4—4881no—
392C4—2442no—
393C4#1684079012yes—
394C4#1684079212yes—
395C2—2442no—
396C2#2146111511yescharacteristic
397C2#2146112211yescharacteristic
398C2#2146117711yescharacteristic
399C2#2146118311yescharacteristic
400C2#2146179511yescharacteristic
401C2#2146183411yescharacteristic
402C2#2146183911yescharacteristic
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#9073
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
39. #14519757C8semidirect
226. C61#9073semidirect

Maximal subgroups

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

subgroupindex
C2×#168407802
#214616742
C2×#168406122
#214606552
#214483492
#907361