Finite Group Databasebeta

← #29590792

Subgroups — #29590792

Order 15616.

464 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 79 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#21451703C211yesmaximal, characteristic
2#21444160C211yesmaximal, characteristic, complemented
3#21443842C212yesmaximal, complemented
4#21443815C212yesmaximal, complemented
5C61×#1799C211yesmaximal, characteristic, complemented
6C2×#14519751C411yescharacteristic, complemented
7#16839819—21no—
8#16839701C411yescharacteristic, complemented
9#16839698C2211yescharacteristic
10#16839679C411yescharacteristic, complemented
11#16839677—21no—
12#16839671C2211yescharacteristic
13#16839670—21no—
14#16839653—21no—
15#16839641—21no—
16#16839625C411yescharacteristic, complemented
17#16839486—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C61×#380—21no—
22C61×#342C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C22×C22⋊D61—21no—
26#14519751—41no—
27#14519751—41no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×#11758196—21no—
30C2×C22⋊Dic61—21no—
31C2×C22⋊Dic61—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C4⋊#92418—41no—
37C22⋊#92418—22no—
38#14519688—41no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C22×D4×C61D411yescharacteristic
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C4×D4×C61—41no—
48C4×D4×C61—41no—
49C2×C4⋊C4×C61—41no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61C2311yescharacteristic
54C2×C42×C61D411yescharacteristic
55#99×C61—42no—
56#95×C61—41no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—42no—
69C22×C4×C61—81no—
70C22×C4×C61—81no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—42no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—81no—
80C2×C22⋊D61—81no—
81C2×C22⋊D61—81no—
82C2×C22⋊D61—81no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C2×D244—41no—
87C2×D244—81no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—82no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—42no—
93C22⋊C4×C61—42no—
94C42×C61—21no—
95C42×C61—21no—
96C22⋊Dic61—81no—
97C22⋊Dic61—81no—
98#11758198—42no—
99#11758198—41no—
100#11758198—41no—
101#11758198—81no—
102#11758198—81no—
103C4⋊Dic61—41no—
104#11758196—81no—
105C2×#92418—42no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61AGL(1,ℤ/8)11yescharacteristic
117C23×C61#13711yescharacteristic
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125D4×C61—42no—
126D4×C61—42no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61—82no—
142C2×C4×C61—82no—
143C2×C4×C61—82no—
144C2×C4×C61#9911yescharacteristic
145C2×C4×C61#9911yescharacteristic
146C22⋊D61—82no—
147C22⋊D61—82no—
148C22⋊D61—84no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158D244—82no—
159#92418—82no—
160#11824—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61C2×#9911yescharacteristic
176C22×C61#41711yescharacteristic
177C22×C61#42111yescharacteristic
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61—81no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61—162no—
192Dic61—81no—
193Dic61—81no—
194Dic61—81no—
195#2635—611no—
196#1799D6111yescharacteristic, complemented
197#1466—611no—
198#1352—612no—
199#1343—612no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61—41no—
203C2×C61—41no—
204C2×C61—81no—
205C2×C61#151311yescharacteristic
206C2×C61#212111yescharacteristic
207C2×C61#212811yescharacteristic
208D61—161no—
209C2×#121—611no—
210C2×C4×D4C2×D6111yescharacteristic
211#432—1221no—
212C2×#99—21no—
213#400—611no—
214#399—611no—
215#394—611no—
216#394—1221no—
217#392—611no—
218#392—1221no—
219#388—1221no—
220#386—1221no—
221#381—611no—
222#380—21no—
223#342C2×D6112yes—
224#323—612no—
225#323—1221no—
226C61#1182411yescharacteristic, complemented, Sylow
227C22×D4—611no—
228C22×D4—1221no—
229C22×D4—1221no—
230C22×D4C22⋊D6111yescharacteristic
231C23×C4C4×D6111yescharacteristic
232C23×C4C22⋊D6111yescharacteristic
233#121—2441no—
234#121—2441no—
235C4×D4—41no—
236C4×D4—41no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C4×D6111yescharacteristic
241C2×C22⋊C4—22no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4D24411yescharacteristic
249C2×C22⋊C4C22×D6111yescharacteristic
250C2×C42D24411yescharacteristic
251C4⋊C8—2441no—
252#99—42no—
253C22⋊C8—1222no—
254#97—2441no—
255#95—41no—
256#95—611no—
257#95—611no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261C24—1221no—
262C24#1175819811yescharacteristic
263C24C2×C22⋊D6111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—4881no—
269C2×D4—4881no—
270C2×D4—4881no—
271C2×D4—4881no—
272C2×D4—4881no—
273C2×D4—2441no—
274C2×D4—2442no—
275C2×D4—2441no—
276C2×D4—2441no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—42no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4#1175819811yescharacteristic
288C22×C4#1175819811yescharacteristic
289C22×C4#1175819811yescharacteristic
290C22×C4C2×C4×D6111yescharacteristic
291C22×C4C2×D24411yescharacteristic
292C2×C8—2442no—
293C4⋊C4—41no—
294C4⋊C4—82no—
295C4⋊C4—4881no—
296C4⋊C4—2441no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C22⋊C4—4881no—
302C22⋊C4—4881no—
303C22⋊C4—4881no—
304C22⋊C4—4881no—
305C22⋊C4—2442no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C42—21no—
309C42—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23C2×#1175819811yescharacteristic
327C23#1451980311yescharacteristic
328C23#1451980811yescharacteristic
329D4—42no—
330D4—42no—
331D4—4882no—
332D4—4882no—
333D4—4882no—
334D4—4884no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4#1451969111yescharacteristic
362C2×C4#1451969111yescharacteristic
363C8—4882no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—4881no—
379C22—4881no—
380C22—4881no—
381C22—4881no—
382C22—4881no—
383C22—4881no—
384C22—4881no—
385C22C2×#1451969111yescharacteristic
386C22#1683976111yescharacteristic
387C22#1683978011yescharacteristic
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—162no—
395C4—4881no—
396C4—4881no—
397C4—4881no—
398C2—21no—
399C2—21no—
400C2—41no—
401C2—41no—
402C2—81no—
403C2—9761no—
404C2#2144436011yescharacteristic
405C2#2144746311yescharacteristic
406C2#2144749011yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1799C2
socleC22×C61C2×#99
prime radical#21451703C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1799D61
hypocenterC61#11824
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21444160C2semidirect
3. #21443842C2semidirect
4. #21443815C2semidirect
5. C61×#1799C2semidirect
6. C2×#14519751C4semidirect
8. #16839701C4semidirect
10. #16839679C4semidirect
16. #16839625C4semidirect
196. #1799D61semidirect
226. C61#11824semidirect

Maximal subgroups

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

subgroupindex
#214517032
#214441602
#214438422
#214438152
C61×#17992
#1182461