Finite Group Databasebeta

← #29590875

Subgroups — #29590875

Order 15616.

446 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451386C211yesmaximal, characteristic
2#21445895C211yesmaximal, characteristic, complemented
3#21444130C211yesmaximal, characteristic, complemented
4#21443843C211yesmaximal, characteristic, complemented
5#21443817C211yesmaximal, characteristic
6#21443815C211yesmaximal, characteristic
7C61×#1352C211yesmaximal, characteristic, complemented
8C2×#14519739C411yescharacteristic, complemented
9C2×#14519733C2211yescharacteristic
10#16839812—21no—
11#16839700C411yescharacteristic, complemented
12#16839680C411yescharacteristic, complemented
13#16839671C2211yescharacteristic
14#16839652—21no—
15#16839639—21no—
16#16839638—21no—
17#16839633—21no—
18#16839629C411yescharacteristic, complemented
19#16839623—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#399C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61D411yescharacteristic
30C22×C4×D61—21no—
31#14519739—41no—
32#14519739—41no—
33#14519733—41no—
34#14519733—41no—
35C2×#11758196C2×C411yescharacteristic
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61D411yescharacteristic
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519706—41no—
46C22⋊#92418—21no—
47C8×Dic61—41no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—41no—
53#14519684—41no—
54#14519684C2×C411yescharacteristic
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61C2×C411yescharacteristic
62C24×C61C2×D411yescharacteristic
63C23×D61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C2×C22⋊D61—42no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C2×C22⋊D61—81no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×D244—41no—
85C2×D244—42no—
86C2×C4×D61—42no—
87C2×C4×D61—81no—
88C2×C4×D61—81no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—81no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C22⋊C4×C61—81no—
96C22⋊Dic61—41no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99#11758198—42no—
100#11758198—42no—
101#11758198—41no—
102#11758198—41no—
103#11758198—81no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C2×#92418—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61#13511yescharacteristic
117C23×C61#13511yescharacteristic
118C22×D61—22no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C22⋊D61—82no—
139C22⋊D61—82no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—81no—
157C2×Dic61—81no—
158C2×Dic61—81no—
159C2×Dic61#9911yescharacteristic
160C2×Dic61#9911yescharacteristic
161D244—42no—
162D244—42no—
163C4×D61—84no—
164C8×C61—81no—
165#92418—81no—
166#11840—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—81no—
176C22×C61C2×#9911yescharacteristic
177C22×C61#41611yescharacteristic
178C22×C61#42111yescharacteristic
179C2×D61—42no—
180C2×D61—42no—
181C2×D61—42no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C2×D61—81no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—81no—
189C4×C61—81no—
190C4×C61—161no—
191Dic61—21no—
192Dic61—21no—
193Dic61—41no—
194Dic61—41no—
195Dic61—41no—
196Dic61—81no—
197Dic61—161no—
198#2598—611no—
199#1820—611no—
200#1458—611no—
201#1352—611no—
202#1352D6111yescharacteristic, complemented
203#1343—611no—
204#1343—611no—
205C2×C61—21no—
206C2×C61—21no—
207C2×C61—41no—
208C2×C61—41no—
209C2×C61#151611yescharacteristic
210C2×C61#212011yescharacteristic
211C2×C61#212811yescharacteristic
212D61—82no—
213C2×C4×D4—611no—
214C2×#117—611no—
215#431—1221no—
216#400—611no—
217#399C2×D6111yescharacteristic
218#394—611no—
219#392—611no—
220#388—1221no—
221#386—1221no—
222#386—1221no—
223#385—1221no—
224#383—611no—
225#381—1221no—
226#342—611no—
227#342—1221no—
228#342C2×D6111yescharacteristic
229#324—1221no—
230#323—611no—
231#323C2×D6111yescharacteristic
232C61#1184011yescharacteristic, complemented, Sylow
233C22×D4—611no—
234C22×D4—1221no—
235C23×C4—611no—
236C23×C4—1221no—
237C4×D4—2441no—
238C4×D4—2441no—
239#117—2441no—
240#117—2441no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4C4×D6111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4C22×D6111yescharacteristic
254C2×C42—611no—
255C2×C42—611no—
256C4⋊C8—2441no—
257C22⋊C8—21no—
258C22⋊C8—1221no—
259C4×C8—2441no—
260#95—611no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265#95—2441no—
266#95—2441no—
267#95C4×D6111yescharacteristic
268C24—1221no—
269C24D4×D6111yescharacteristic
270C2×D4—4881no—
271C2×D4—2441no—
272C2×D4—2442no—
273C2×D4—2442no—
274C2×D4—2441no—
275C2×D4—2441no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—4881no—
289C22×C4—4881no—
290C22×C4—2442no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4C2×C4×D6111yescharacteristic
294C22×C4D4×D6111yescharacteristic
295C2×C8—41no—
296C2×C8—2441no—
297C4⋊C4—41no—
298C4⋊C4—81no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—81no—
305C22⋊C4—4881no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2441no—
313C42—1221no—
314C42—1221no—
315C42—1221no—
316C42—1221no—
317C23—21no—
318C23—21no—
319C23—41no—
320C23—41no—
321C23—1222no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23C22⋊C4×D6111yescharacteristic
329C23#1451979811yescharacteristic
330C23#1451980011yescharacteristic
331D4—4882no—
332D4—4882no—
333D4—2442no—
334D4—2442no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4884no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C8—81no—
371C8—4881no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—4881no—
382C22—4881no—
383C22—4881no—
384C22—4881no—
385C22—2442no—
386C22—2442no—
387C22—2442no—
388C22#99×D6111yescharacteristic
389C22#1683975711yescharacteristic
390C22#1683977711yescharacteristic
391C4—41no—
392C4—41no—
393C4—81no—
394C4—81no—
395C4—161no—
396C4—1221no—
397C4—1221no—
398C4—9761no—
399C4—4881no—
400C4—2441no—
401C4—2441no—
402C4—2441no—
403C2—21no—
404C2—21no—
405C2—41no—
406C2—41no—
407C2—4882no—
408C2#2144437411yescharacteristic
409C2#2144745911yescharacteristic
410C2#2144748911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1352C2
socleC22×C61C2×#99
prime radical#16839671C22
cosocleC2×C22⋊C4×C61C23
hypercenter#1352D61
hypocenterC61#11840
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
2. #21445895C2semidirect
3. #21444130C2semidirect
4. #21443843C2semidirect
7. C61×#1352C2semidirect
8. C2×#14519739C4semidirect
11. #16839700C4semidirect
12. #16839680C4semidirect
18. #16839629C4semidirect
202. #1352D61semidirect
232. C61#11840semidirect

Maximal subgroups

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

subgroupindex
#214513862
#214458952
#214441302
#214438432
#214438172
#214438152
C61×#13522
#1184061