Finite Group Databasebeta

← #29594981

Subgroups — #29594981

Order 15616.

854 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839734C212yesmaximal
2#21448306C211yesmaximal, characteristic
3#21443944C211yesmaximal, characteristic, complemented
4#21443943C212yesmaximal, complemented
5C61×#1393C211yesmaximal, characteristic, complemented
6C22×#11758224C2211yescharacteristic
7C2×#14519735C411yescharacteristic, complemented
8C2×#14519733—22no—
9C2×C42×D61C411yescharacteristic, complemented
10#16839734—24no—
11#16839734C418yescomplemented
12C2×#14519692C2212yes—
13C2×#14519691—22no—
14#16839668C411yescharacteristic, complemented
15#16839667C411yescharacteristic, complemented
16#16839665C2211yescharacteristic
17#16839638—22no—
18C22⋊C4×Dic61—22no—
19C2×#99×C61C2212yes—
20C61×#390C2211yescharacteristic
21C2×#11758224—42no—
22C2×#11758224—41no—
23C2×#11758224—41no—
24C2×#11758224C2×C414yes—
25C2×#11758224D412yes—
26C2×#11758224Q812yes—
27C22×Dic122C2×C411yescharacteristic
28C22×C22⋊D61D412yes—
29C23×Dic61D412yes—
30C22×C4×D61—21no—
31C22×C4×D61C2×C411yescharacteristic
32#14519735—41no—
33#14519735—41no—
34#14519733—28no—
35#14519733—44no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—42no—
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61—22no—
40C2×#11758198—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—42no—
44C2×C4×Dic61C2×C411yescharacteristic
45C42×D61—42no—
46#14519692—22no—
47#14519692C2×C414yescomplemented
48#14519691—28no—
49#14519684—22no—
50#14519684—22no—
51C22×D4×C61C2311yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—22no—
54C2×C22⋊C4×C61—22no—
55C2×C42×C61C2×C411yescharacteristic
56#99×C61—22no—
57#99×C61C2×C414yescomplemented
58C24×C61C2×D412yes—
59C23×D61C22⋊C411yescharacteristic
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61C22×C412yes—
63C2×D4×C61C2×D411yescharacteristic
64C2×D4×C61C2×Q811yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—42no—
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61C22⋊C414yes—
72C2×C22⋊D61C4⋊C414yes—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—24no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—42no—
79C22×Dic61C22⋊C412yes—
80C22×Dic61C22⋊C414yes—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C4⋊C414yes—
83#11758224—44no—
84#11758224—44no—
85#11758224—42no—
86#11758224—42no—
87#11758224—42no—
88#11758224—42no—
89C2×C4×D61—22no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C4×D61—42no—
95C2×C4×D61C4212yes—
96C2×C4×D61C4⋊C412yes—
97C2×Dic122—41no—
98C2×Dic122—41no—
99C2×Dic122C4212yes—
100C2×Dic122C4⋊C412yes—
101C4⋊C4×C61—41no—
102C22⋊C4×C61—24no—
103C22⋊C4×C61—44no—
104C22⋊C4×C61—42no—
105C42×C61—41no—
106C22⋊Dic61—24no—
107C22⋊Dic61—44no—
108C22⋊Dic61—42no—
109#11758198—42no—
110C4⋊Dic61—41no—
111#11758196—48no—
112C4×Dic61—48no—
113C4×Dic61—42no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C4×Dic61—41no—
117C23×C61—22no—
118C23×C61—22no—
119C23×C61—42no—
120C23×C61—42no—
121C23×C61C2×C22⋊C411yescharacteristic
122C23×C61C2×C22⋊C412yes—
123C23×C61C2×C4⋊C412yes—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61#9512yes—
129D4×C61—42no—
130D4×C61—41no—
131D4×C61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—22no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—44no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—82no—
141C2×C4×C61—82no—
142C2×C4×C61C2×C4211yescharacteristic
143C2×C4×C61C2×C4⋊C411yescharacteristic
144C22⋊D61—44no—
145C22⋊D61—44no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—24no—
149C2×Dic61—24no—
150C2×Dic61—24no—
151C2×Dic61—24no—
152C2×Dic61—22no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—44no—
156C2×Dic61—42no—
157C2×Dic61—41no—
158C2×Dic61—82no—
159C2×Dic61—82no—
160C2×Dic61#9514yes—
161C2×Dic61#9512yes—
162C2×Dic61#9912yes—
163C2×Dic61#9911yescharacteristic
164C2×Dic61#9911yescharacteristic
165C4×D61—22no—
166C4×D61—22no—
167C4×D61—22no—
168C4×D61—22no—
169C4×D61—48no—
170Dic122—42no—
171Dic122—42no—
172#12581—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—42no—
178C22×C61—42no—
179C22×C61—42no—
180C22×C61—42no—
181C22×C61—82no—
182C22×C61C2×#9511yescharacteristic
183C22×C61C2×#9911yescharacteristic
184C22×C61C2×#9911yescharacteristic
185C2×D61—22no—
186C2×D61—42no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—42no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—42no—
193C4×C61—84no—
194C4×C61—81no—
195Dic61—24no—
196Dic61—42no—
197Dic61—84no—
198Dic61—81no—
199Dic61#34212yes—
200Dic61#34212yes—
201C2×#410—612no—
202#2297—611no—
203#1393—612no—
204#1393—611no—
205#1393D6111yescharacteristic, complemented
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—42no—
209C2×C61—42no—
210C2×C61C2×#34211yescharacteristic
211C2×C61#212611yescharacteristic
212C2×C61#212611yescharacteristic
213D61—42no—
214C22×#41—611no—
215C2×#117—611no—
216C2×#117—1222no—
217C22×C42—611no—
218#410—618no—
219#410—1224no—
220C2×#99—612no—
221C2×#99—1222no—
222C2×#99C2×D6112yes—
223#391—611no—
224#391—611no—
225#390—611no—
226#390C2×D6111yescharacteristic
227#386—1222no—
228C4×C22⋊C4—1222no—
229C61#1258111yescharacteristic, complemented, Sylow
230C2×#41—614no—
231C2×#41—612no—
232C2×#41—612no—
233C2×#41—2442no—
234C2×#41—2441no—
235C2×#41—2441no—
236C22×Q8—611no—
237C22×D4—612no—
238C22×D4C22×D6111yescharacteristic
239C23×C4—612no—
240C23×C4—611no—
241C23×C4—1221no—
242#117—1228no—
243#117—2444no—
244#117—2441no—
245#117—2441no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—2442no—
248C2×C4⋊C4C4×D6111yescharacteristic
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—1222no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1222no—
254C2×C42—611no—
255C2×C42—1221no—
256C2×C42—1221no—
257C2×C42—2442no—
258C2×C42—2442no—
259C2×C42C4×D6111yescharacteristic
260#99—22no—
261#99—614no—
262#99—1228no—
263#99—1222no—
264#99C4×D6114yescomplemented
265#95—1222no—
266#95—1222no—
267C24—611no—
268C24D4×D6112yes—
269#41—2442no—
270#41—2444no—
271#41—2442no—
272#41—2444no—
273#41—2442no—
274#41—2442no—
275C2×Q8—612no—
276C2×Q8—612no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—614no—
282C2×D4—614no—
283C2×D4—2442no—
284C2×D4—2442no—
285C2×D4C2×C4×D6112yes—
286C2×D4D4×D6111yescharacteristic
287C2×D4Q8×D6111yescharacteristic
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—611no—
292C22×C4—614no—
293C22×C4—612no—
294C22×C4—614no—
295C22×C4—612no—
296C22×C4—612no—
297C22×C4—1222no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1222no—
301C22×C4—1222no—
302C22×C4—1224no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—2442no—
306C22×C4—2442no—
307C22×C4—2442no—
308C22×C4—2442no—
309C22×C4C2×C4×D6111yescharacteristic
310C4⋊C4—41no—
311C4⋊C4—2441no—
312C4⋊C4—2448no—
313C22⋊C4—24no—
314C22⋊C4—44no—
315C22⋊C4—42no—
316C22⋊C4—1224no—
317C22⋊C4—2442no—
318C22⋊C4—2444no—
319C22⋊C4—2442no—
320C42—41no—
321C42—2441no—
322C42—2442no—
323C42—2441no—
324C42—2441no—
325C42—2448no—
326C23—22no—
327C23—22no—
328C23—42no—
329C23—42no—
330C23—612no—
331C23—1221no—
332C23—1221no—
333C23—2441no—
334C23—2441no—
335C23C22⋊C4×D6112yes—
336C23C22⋊C4×D6111yescharacteristic
337C23C4⋊C4×D6112yes—
338Q8—2442no—
339Q8—2442no—
340D4—42no—
341D4—41no—
342D4—41no—
343D4—2444no—
344D4—2444no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—612no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—612no—
359C2×C4—614no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—1224no—
365C2×C4—1224no—
366C2×C4—1224no—
367C2×C4—1224no—
368C2×C4—1222no—
369C2×C4—1222no—
370C2×C4—1222no—
371C2×C4—4882no—
372C2×C4—4882no—
373C2×C4—2448no—
374C2×C4—2444no—
375C2×C4—2442no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4C42×D6111yescharacteristic
380C2×C4C4⋊C4×D6111yescharacteristic
381C22—21no—
382C22—21no—
383C22—22no—
384C22—22no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—82no—
390C22—1222no—
391C22—2442no—
392C22—2442no—
393C22—2441no—
394C22—2441no—
395C22#95×D6111yescharacteristic
396C22#99×D6111yescharacteristic
397C22#99×D6111yescharacteristic
398C4—21no—
399C4—21no—
400C4—42no—
401C4—84no—
402C4—81no—
403C4—612no—
404C4—612no—
405C4—1224no—
406C4—4884no—
407C4—4881no—
408C4—2442no—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—42no—
413C2—2442no—
414C2#342×D6111yescharacteristic
415C2#2144748111yescharacteristic
416C2#2144748311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C2×C42
FrattiniC22×D4C22×D61
FittingC61×#1393C2
socleC22×C61C2×#99
prime radicalC22×#11758224C22
cosocleC22×D4×C61C23
hypercenter#1393D61
hypocenterC61#12581
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
3. #21443944C2semidirect
4. #21443943C2semidirect
5. C61×#1393C2semidirect
7. C2×#14519735C4semidirect
9. C2×C42×D61C4semidirect
11. #16839734C4semidirect
14. #16839668C4semidirect
15. #16839667C4semidirect
47. #14519692C2×C4semidirect
57. #99×C61C2×C4semidirect
205. #1393D61semidirect
229. C61#12581semidirect
264. #99C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397342
#214483062
#214439442
#214439432
C61×#13932
#1258161