Finite Group Databasebeta

← #29590471

Subgroups — #29590471

Order 15616.

500 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 71 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
1#21451378C211yesmaximal, characteristic
2#21445550C211yesmaximal, characteristic, complemented
3#21444150C211yesmaximal, characteristic, complemented
4#21443844C211yesmaximal, characteristic, complemented
5#21443842C211yesmaximal, characteristic, complemented
6#21443816C211yesmaximal, characteristic
7C61×#1343C211yesmaximal, characteristic
8C2×D4×Dic61C411yescharacteristic, complemented
9C2×#14519733—21no—
10C2×#14519733C2211yescharacteristic
11#16839816—21no—
12#16839702C411yescharacteristic, complemented
13#16839698C2211yescharacteristic
14#16839676C411yescharacteristic, complemented
15#16839656—21no—
16#16839642—21no—
17#16839642—21no—
18#16839634—21no—
19#16839629C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#392C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C23×Dic61—21no—
28C23×Dic61D411yescharacteristic
29D4×Dic61—41no—
30D4×Dic61—41no—
31#14519733—24no—
32#14519733—41no—
33#14519733—41no—
34#14519733—42no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—41no—
38C2×#11758196C2×C411yescharacteristic
39C2×#11758196D411yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61D411yescharacteristic
46C2×C4×Dic61—41no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50C22⋊#92418—21no—
51#14519687—41no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C22×D4×C61—21no—
58C22×D4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63#95×C61C2×C411yescharacteristic
64C24×C61—21no—
65C24×C61C2×D411yescharacteristic
66C2×D4×C61—41no—
67C2×D4×C61—42no—
68C2×D4×C61—42no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—81no—
72C22×C4×C61—21no—
73C22×C4×C61—41no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—22no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—42no—
84C22×Dic61—41no—
85C22×Dic61—81no—
86C22×Dic61—81no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C2×C8×C61—41no—
92C22⋊C4×C61—22no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—81no—
96C22⋊Dic61—22no—
97C22⋊Dic61—41no—
98C22⋊Dic61—42no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102C22⋊Dic61—42no—
103C22⋊Dic61—81no—
104C4⋊Dic61—41no—
105#11758196—41no—
106#11758196—41no—
107#11758196—44no—
108#11758196—81no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61—44no—
114C2×#92418—41no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—22no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61C2×C22⋊C411yescharacteristic
127C23×C61AGL(1,ℤ/8)11yescharacteristic
128C23×C61#13711yescharacteristic
129D4×C61—42no—
130D4×C61—42no—
131D4×C61—82no—
132D4×C61—82no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—81no—
142C2×C4×C61—81no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—84no—
163C2×Dic61—81no—
164C2×Dic61—81no—
165C2×Dic61#9911yescharacteristic
166C2×Dic61#9911yescharacteristic
167C2×Dic61#10412yes—
168C8×C61—81no—
169#92418—81no—
170#11754—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—42no—
178C22×C61—42no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—42no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61C2×#9911yescharacteristic
188C22×C61#41711yescharacteristic
189C22×C61C2×#10411yescharacteristic
190C4×C61—41no—
191C4×C61—41no—
192C4×C61—81no—
193C4×C61—82no—
194Dic61—21no—
195Dic61—21no—
196Dic61—22no—
197Dic61—41no—
198Dic61—41no—
199Dic61—81no—
200Dic61—82no—
201Dic61—81no—
202#2598—611no—
203#1740—611no—
204#1464—611no—
205#1352—611no—
206#1352—611no—
207#1343—611no—
208#1343D6111yescharacteristic
209C2×C61—21no—
210C2×C61—21no—
211C2×C61—41no—
212C2×C61—41no—
213C2×C61—82no—
214C2×C61#150411yescharacteristic
215C2×C61#212011yescharacteristic
216C2×C61#212811yescharacteristic
217C2×C4×D4—611no—
218C2×#117—611no—
219C2×#117—1221no—
220#432—1221no—
221#400—611no—
222#399—611no—
223#394—611no—
224#392C2×D6111yescharacteristic
225#388—1221no—
226#386—1221no—
227#386—1221no—
228#385—1221no—
229#383—611no—
230#342—611no—
231#342—1221no—
232#342C2×D6111yescharacteristic
233#324—1221no—
234#323—611no—
235#323C2×D6111yescharacteristic
236C61#1175411yescharacteristic, complemented, Sylow
237C22×D4—21no—
238C22×D4C4×D6111yescharacteristic
239C23×C4—611no—
240C23×C4—1221no—
241C4×D4—2441no—
242C4×D4—2441no—
243#117—1224no—
244#117—2441no—
245#117—2441no—
246#117—2442no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—2441no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4C22×D6111yescharacteristic
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—2441no—
264C4⋊C8—2441no—
265C22⋊C8—21no—
266C22⋊C8—1221no—
267#97—2441no—
268#95—611no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272#95—1221no—
273#95C4×D6111yescharacteristic
274C24—21no—
275C24D4×D6111yescharacteristic
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—81no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1222no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—4881no—
296C22×C4—4881no—
297C22×C4—2442no—
298C22×C4—2441no—
299C22×C4C2×C4×D6111yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C2×C8—41no—
302C2×C8—2441no—
303C4⋊C4—4881no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2444no—
308C22⋊C4—22no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—81no—
312C22⋊C4—1222no—
313C22⋊C4—4881no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2442no—
317C22⋊C4—2441no—
318C22⋊C4—2442no—
319C22⋊C4—2441no—
320C42—1221no—
321C42—1221no—
322C42—1221no—
323C42—1221no—
324C42—2444no—
325C23—21no—
326C23—21no—
327C23—22no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23C22⋊C4×D6111yescharacteristic
337C23#1451980111yescharacteristic
338C23#1451980611yescharacteristic
339D4—42no—
340D4—42no—
341D4—82no—
342D4—82no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—612no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—4881no—
367C2×C4—4881no—
368C2×C4—4884no—
369C2×C4—2442no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C8—81no—
379C8—4881no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—42no—
387C22—42no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#99×D6111yescharacteristic
397C22#1683976011yescharacteristic
398C22#104×D6111yescharacteristic
399C4—41no—
400C4—41no—
401C4—81no—
402C4—82no—
403C4—1221no—
404C4—1221no—
405C4—1222no—
406C4—4881no—
407C4—4882no—
408C4—4881no—
409C4—2441no—
410C4—2441no—
411C2—21no—
412C2—21no—
413C2—41no—
414C2—41no—
415C2—82no—
416C2#2144432011yescharacteristic
417C2#2144745711yescharacteristic
418C2#2144748911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1343C2
socleC22×C61C2×#99
prime radicalC61×#392C22
cosocleC2×C22⋊C4×C61C23
hypercenter#1343D61
hypocenterC61#11754
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #21445550C2semidirect
3. #21444150C2semidirect
4. #21443844C2semidirect
5. #21443842C2semidirect
8. C2×D4×Dic61C4semidirect
12. #16839702C4semidirect
14. #16839676C4semidirect
19. #16839629C4semidirect
236. C61#11754semidirect

Maximal subgroups

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

subgroupindex
#214513782
#214455502
#214441502
#214438442
#214438422
#214438162
C61×#13432
#1175461