Finite Group Databasebeta

← #29590508

Subgroups — #29590508

Order 15616.

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

normal subgroups only

This group has 484 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#21451388C211yesmaximal, characteristic
2#21445556C211yesmaximal, characteristic, complemented
3#21444152C211yesmaximal, characteristic, complemented
4#21443846C211yesmaximal, characteristic, complemented
5#21443823C211yesmaximal, characteristic, complemented
6#21443821C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519739C411yescharacteristic
10C2×#14519735C2211yescharacteristic
11#16839816—21no—
12#16839697C411yescharacteristic
13#16839679C2211yescharacteristic
14#16839672C411yescharacteristic
15#16839651—21no—
16#16839640—21no—
17#16839640—21no—
18#16839636—21no—
19#16839629C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839485—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×D244—21no—
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×#11758189—41no—
33M16×D61—24no—
34M16×D61—42no—
35C2×C8×D61—41no—
36#14519739—41no—
37#14519739—41no—
38#14519735—41no—
39#14519735—41no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198C2×C411yescharacteristic
48C2×#11758198D411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519706—41no—
52C22⋊#92418—21no—
53#14519687—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61—21no—
65C23×D61C22⋊C411yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×D244—41no—
76C2×D244—42no—
77C2×D244—42no—
78C2×D244—42no—
79C2×D244—81no—
80C2×C4×D61—22no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—42no—
86C2×C4×D61—81no—
87C2×C4×D61—81no—
88M16×C61—22no—
89M16×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94#11758198—41no—
95#11758198—41no—
96#11758198—42no—
97#11758198—41no—
98#11758198—41no—
99#11758198—41no—
100#11758198—41no—
101#11758198—81no—
102#11758198—81no—
103C4⋊Dic61—41no—
104#11758196—81no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109#11758194—22no—
110#11758194—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113#11758189—44no—
114C8×D61—44no—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—22no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61#10412yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61#13711yescharacteristic
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61#9911yescharacteristic
152C2×Dic61#9911yescharacteristic
153D244—42no—
154D244—42no—
155D244—84no—
156C4×D61—22no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—84no—
161C8×C61—42no—
162C8×C61—81no—
163#92418—42no—
164#92418—81no—
165#11761—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61C2×#9911yescharacteristic
169C22×C61#41711yescharacteristic
170C22×C61C2×#10411yescharacteristic
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—42no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61—42no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—81no—
188C4×C61—81no—
189Dic61—21no—
190Dic61—21no—
191Dic61—41no—
192Dic61—41no—
193Dic61—81no—
194#2598—611no—
195#1742—611no—
196#1464—611no—
197#1353—611no—
198#1353D6111yescharacteristic, complemented
199#1345—611no—
200#1345—611no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61#150411yescharacteristic
204C2×C61#212011yescharacteristic
205C2×C61#213411yescharacteristic
206D61—42no—
207D61—82no—
208C22×M16—1221no—
209C2×C4×D4—611no—
210C2×#117—611no—
211#432—1221no—
212#400C2×D6111yescharacteristic
213#399—611no—
214#394—611no—
215#392—611no—
216#388—1221no—
217#386—1221no—
218#386—1221no—
219#385—1221no—
220#383—611no—
221#343—611no—
222#343—1221no—
223#343C2×D6111yescharacteristic
224#324—611no—
225#324C2×D6111yescharacteristic
226#323—1221no—
227C61#1176111yescharacteristic, complemented, Sylow
228C22×D4—611no—
229C22×D4—1221no—
230C23×C4—611no—
231C23×C4—1221no—
232C2×M16—21no—
233C2×M16—1224no—
234C2×M16—1221no—
235C2×M16—2441no—
236C2×M16—2442no—
237C22×C8—2441no—
238C4×D4—2441no—
239C4×D4—2441no—
240#117—2441no—
241#117—2441no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4C4×D6111yescharacteristic
245C2×C4⋊C4C22×D6111yescharacteristic
246C2×C22⋊C4—611no—
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×C42—611no—
254C2×C42—611no—
255C4⋊C8—2441no—
256C22⋊C8—21no—
257C22⋊C8—1221no—
258#97—2441no—
259#95—21no—
260#95—21no—
261#95—611no—
262#95—1221no—
263#95—1221no—
264#95C4×D6111yescharacteristic
265C24—611no—
266C24—1221no—
267C2×D4—4881no—
268C2×D4—2441no—
269C2×D4—2442no—
270C2×D4—2442no—
271C2×D4—2442no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1222no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—4881no—
284C22×C4—4881no—
285C22×C4—2442no—
286C22×C4C2×C4×D6111yescharacteristic
287C22×C4D4×D6111yescharacteristic
288C22×C4D4×D6111yescharacteristic
289M16—22no—
290M16—41no—
291M16—1222no—
292M16—2444no—
293M16—2441no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—2444no—
297C2×C8—2441no—
298C2×C8—2441no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—4881no—
302C4⋊C4—2441no—
303C22⋊C4—4881no—
304C22⋊C4—4881no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2442no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C42—1221no—
313C42—1221no—
314C42—1221no—
315C42—1221no—
316C23—612no—
317C23—1222no—
318C23—1221no—
319C23—1221no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23—2441no—
326C23—2441no—
327C23—2441no—
328C23C22⋊C4×D6111yescharacteristic
329D4—4884no—
330D4—2442no—
331D4—2442no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—4884no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4#1451980411yescharacteristic
361C2×C4#1451980911yescharacteristic
362C8—42no—
363C8—81no—
364C8—4881no—
365C8—2442no—
366C22—21no—
367C22—21no—
368C22—1222no—
369C22—4881no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—2442no—
375C22—2442no—
376C22—2442no—
377C22—2442no—
378C22—2441no—
379C22—2441no—
380C22#99×D6111yescharacteristic
381C22#1683976211yescharacteristic
382C22#104×D6111yescharacteristic
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—81no—
389C4—1221no—
390C4—1221no—
391C4—4881no—
392C4—2441no—
393C4—2441no—
394C2—21no—
395C2—21no—
396C2—4882no—
397C2—2442no—
398C2#2144432211yescharacteristic
399C2#2144745911yescharacteristic
400C2#2144750911yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radical#16839672C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61#11761
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
2. #21445556C2semidirect
3. #21444152C2semidirect
4. #21443846C2semidirect
5. #21443823C2semidirect
6. #21443821C2semidirect
7. C61×#1353C2semidirect
198. #1353D61semidirect
227. C61#11761semidirect

Maximal subgroups

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

subgroupindex
#214513882
#214455562
#214441522
#214438462
#214438232
#214438212
C61×#13532
#1176161