Finite Group Databasebeta

← #29575352

Subgroups — #29575352

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×#16839815C211yesmaximal, characteristic
2C4×#14519756C211yesmaximal, characteristic
3C2×#16839492C212yesmaximal, complemented
4#21443658C212yesmaximal, complemented
5C61×#1797C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7C2×C4×Dic122C2211yescharacteristic
8#16839815—24no—
9C2×C4⋊#92418—21no—
10C2×C22⋊#92418—21no—
11C2×C4×#92418C2212yes—
12#16839668C411yescharacteristic
13#16839660C411yescharacteristic
14#16839646—21no—
15#16839635—21no—
16#16839622C411yescharacteristic
17C4×#11758196—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19C4×C22⋊Dic61—21no—
20#16839492—24no—
21C22×C42×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2212yes—
23C2×C22⋊C8×C61—21no—
24C61×#336—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×#92418—22no—
27#14519756—22no—
28#14519756C814yescomplemented
29C4×Dic122—22no—
30C4×Dic122—22no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41C4⋊#92418—24no—
42C22⋊#92418—24no—
43C4×#92418—22no—
44C4×#92418D414yes—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C22×C8×C61—22no—
54C2×C42×C61—22no—
55C2×C42×C61—22no—
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—22no—
61C4⋊C8×C61—22no—
62C22⋊C8×C61—42no—
63C24×C61C22⋊C411yescharacteristic
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—22no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C2×C812yes—
78C22×C4×C61M1612yes—
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C2×Dic122—22no—
87C2×Dic122—22no—
88C2×Dic122—21no—
89C2×Dic122C2×C812yes—
90C2×C8×C61—42no—
91C2×C8×C61—42no—
92C2×C8×C61—42no—
93C42×C61—22no—
94C42×C61—21no—
95C42×C61—22no—
96C42×C61—21no—
97C42×C61C2×D412yes—
98C42×C61#4112yes—
99C22⋊Dic61—24no—
100C22⋊Dic61—42no—
101C4⋊Dic61—21no—
102C4⋊Dic61—22no—
103C4⋊Dic61—22no—
104C4⋊Dic61C2×C812yes—
105#11758196—24no—
106#11758196—42no—
107#11758196—41no—
108#11758196—41no—
109C4×Dic61—42no—
110C4×Dic61—41no—
111C4×Dic61—41no—
112C2×#92418—24no—
113C2×#92418—42no—
114C2×#92418—42no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61C22⋊C812yes—
122C23×C61C2×C22⋊C411yescharacteristic
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—24no—
128C2×C4×C61—24no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61C22⋊C812yes—
140C2×C4×C61C4×D412yes—
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12112yes—
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61C22×C811yescharacteristic
145C2×C4×C61C2×M1611yescharacteristic
146C2×C4×C61#13112yes—
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61#13712yes—
149C2×C4×C61#13711yescharacteristic
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162Dic122—24no—
163Dic122—42no—
164C8×C61—82no—
165#92418—44no—
166#9073—611nomaximal, Sylow
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—22no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61#38611yescharacteristic
175C22×C61C2×C22⋊C811yescharacteristic
176C22×C61#40811yescharacteristic
177C22×C61#41711yescharacteristic
178C22×C61#41911yescharacteristic
179C22×C61#42111yescharacteristic
180C22×C61#42111yescharacteristic
181C4×C61—22no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61C8×D412yes—
187C4×C61#43512yes—
188C4×C61#46812yes—
189C4×C61#47012yes—
190Dic61—42no—
191Dic61—42no—
192Dic61—81no—
193Dic61—81no—
194C2×#431—611no—
195C4×C22⋊Q8—611no—
196#1797D6111yescharacteristic
197C2×Q8⋊C8—612no—
198#1279—612no—
199C2×C61—42no—
200C2×C61#147711yescharacteristic
201C2×C61#147911yescharacteristic
202C2×C61#149511yescharacteristic
203C2×C61#149711yescharacteristic
204C2×C61#186911yescharacteristic
205C2×C61#189411yescharacteristic
206C2×C61#189711yescharacteristic
207C2×C22⋊Q8—611no—
208C2×C4×Q8—611no—
209C22×C42C2×D6111yescharacteristic
210#431—1224no—
211C2×C4⋊C8—1221no—
212C2×C4⋊C8C2×D6112yes—
213C2×C22⋊C8—21no—
214C2×C22⋊C8—1221no—
215C2×C4×C8—612no—
216#391—611no—
217#389—611no—
218#387—1221no—
219#385—1221no—
220#380—611no—
221C4×C4⋊C4—611no—
222C4×C4⋊C4—1221no—
223C4×C22⋊C4—1221no—
224#336—21no—
225Q8⋊C8—1224no—
226C61#907311yescharacteristic, complemented, Sylow
227C22×Q8—611no—
228C23×C4C4×D6111yescharacteristic
229C23×C4D24411yescharacteristic
230C23×C4C22⋊D6111yescharacteristic
231C22×C8—22no—
232C22×C8—1222no—
233C22⋊Q8—614no—
234C22⋊Q8—1222no—
235C4×Q8—1222no—
236C4×Q8—1222no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—1221no—
248C2×C42—1221no—
249C2×C42C4×D6111yescharacteristic
250C2×C42D24411yescharacteristic
251C2×C42C22⋊D6111yescharacteristic
252C2×C42C22×D6111yescharacteristic
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—1224no—
256C22⋊C8—42no—
257C22⋊C8—1224no—
258C4×C8—614no—
259C4×C8—1222no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265C24#1175819811yescharacteristic
266C2×Q8—612no—
267C2×Q8—1221no—
268C2×Q8—1222no—
269C2×Q8—1222no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C8×D6112yes—
285C22×C4#1175818912yes—
286C22×C4#1175819811yescharacteristic
287C22×C4#1175819811yescharacteristic
288C22×C4#1175819811yescharacteristic
289C22×C4C2×C4×D6111yescharacteristic
290C22×C4C2×D24411yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—1224no—
296C2×C8—2442no—
297C2×C8—2442no—
298C4⋊C4—612no—
299C4⋊C4—1224no—
300C4⋊C4—1221no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—2442no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—1224no—
307C22⋊C4—2442no—
308C42—22no—
309C42—21no—
310C42—22no—
311C42—21no—
312C42—2441no—
313C42—2442no—
314C42—2441no—
315C42D4×D6112yes—
316C42#1175822412yes—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23#1451968912yes—
324C23C2×#1175819811yescharacteristic
325Q8—1224no—
326Q8—2442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4#1451968912yes—
356C2×C4#1451973712yes—
357C2×C4#1451974711yescharacteristic
358C2×C4#1451974912yes—
359C2×C4#1451976111yescharacteristic
360C2×C4C2×C8×D6111yescharacteristic
361C2×C4C2×#1175818911yescharacteristic
362C2×C4#1451978512yes—
363C2×C4#1451980311yescharacteristic
364C2×C4#1451980712yes—
365C2×C4#1451980811yescharacteristic
366C8—82no—
367C8—2444no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22#1683963911yescharacteristic
376C22C2×#1451968911yescharacteristic
377C22#1683973011yescharacteristic
378C22#1683976111yescharacteristic
379C22#1683977011yescharacteristic
380C22#1683977811yescharacteristic
381C22#1683977811yescharacteristic
382C4—21no—
383C4—21no—
384C4—22no—
385C4—41no—
386C4—41no—
387C4—4881no—
388C4—4881no—
389C4—2442no—
390C4—2442no—
391C4#1683982512yes—
392C4#1683983012yes—
393C4#1684000612yes—
394C4#1684001812yes—
395C2—42no—
396C2#2144420411yescharacteristic
397C2#2144421311yescharacteristic
398C2#2144428211yescharacteristic
399C2#2144429111yescharacteristic
400C2#2144610911yescharacteristic
401C2#2144625011yescharacteristic
402C2#2144626511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1797D61
hypocenterC61#9073
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. C2×#16839492C2semidirect
4. #21443658C2semidirect
28. #14519756C8semidirect
226. C61#9073semidirect

Maximal subgroups

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

subgroupindex
C2×#168398152
C4×#145197562
C2×#168394922
#214436582
C61×#17972
#907361