Finite Group Databasebeta

← #29590842

Subgroups — #29590842

Order 15616.

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

normal subgroups only

This group has 400 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#21451736C211yesmaximal, characteristic
2#21444157C211yesmaximal, characteristic
3#21443848C212yesmaximal, complemented
4#21443824C212yesmaximal, complemented
5C61×#1800C211yesmaximal, characteristic
6C2×#14519756C411yescharacteristic
7#16839726—21no—
8#16839692C2211yescharacteristic
9#16839690—21no—
10#16839687C411yescharacteristic
11#16839682C2211yescharacteristic
12#16839676—21no—
13#16839674C411yescharacteristic
14#16839646—21no—
15#16839635—21no—
16#16839625C411yescharacteristic
17#16839488C2212yes—
18#16839486—21no—
19C2×C4×D4×C61C2211yescharacteristic
20C61×#423—21no—
21C2×#100×C61—21no—
22C61×#343C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C2×#11758194—41no—
25#14519756—41no—
26#14519756—41no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C22⋊#92418—22no—
36C22⋊#92418—41no—
37#14519684—21no—
38#14519684—21no—
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
47C2×M16×C61—22no—
48C4×D4×C61—41no—
49C4×D4×C61—41no—
50C2×C4⋊C4×C61C2311yescharacteristic
51C2×C22⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C4⋊C8×C61—41no—
55C4⋊C8×C61—41no—
56#100×C61—42no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C22⋊C411yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—81no—
68C22×C4×C61—81no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C2×Dic122—41no—
79C2×Dic122—81no—
80M16×C61—42no—
81M16×C61—42no—
82C2×C8×C61—42no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C42×C61—21no—
87C42×C61—21no—
88C22⋊Dic61—42no—
89C22⋊Dic61—42no—
90C22⋊Dic61—81no—
91C22⋊Dic61—81no—
92C4⋊Dic61—41no—
93#11758196—41no—
94#11758196—41no—
95#11758196—41no—
96#11758196—41no—
97#11758196—81no—
98#11758194—82no—
99C2×#92418—42no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111D4×C61—42no—
112D4×C61—42no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61#9911yescharacteristic
127C2×C4×C61#9911yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142Dic122—82no—
143C8×C61—82no—
144#92418—82no—
145#11834—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—42no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61C2×#9911yescharacteristic
159C22×C61#41711yescharacteristic
160C22×C61#42111yescharacteristic
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168Dic61—81no—
169Dic61—81no—
170Dic61—81no—
171Dic61—81no—
172#2638—611no—
173#1800D6111yescharacteristic
174#1465—611no—
175#1354—612no—
176#1346—612no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—81no—
180C2×C61—81no—
181C2×C61#151311yescharacteristic
182C2×C61#212111yescharacteristic
183C2×C61#213511yescharacteristic
184C2×C22⋊Q8—611no—
185C2×C4×D4C2×D6111yescharacteristic
186#423—21no—
187C2×#100—21no—
188#407—1221no—
189#398—611no—
190#397—611no—
191#397—1221no—
192#395—611no—
193#394—1221no—
194#393—611no—
195#387—1221no—
196#385—1221no—
197#381—611no—
198#343C2×D6112yes—
199#324—612no—
200#323—1221no—
201C61#1183411yescharacteristic, complemented, Sylow
202C22×Q8—611no—
203C22×D4C22⋊D6111yescharacteristic
204C23×C4C4×D6111yescharacteristic
205C23×C4D24411yescharacteristic
206C2×M16—22no—
207C2×M16—2441no—
208C22⋊Q8—2441no—
209C22⋊Q8—2441no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4C22×D6111yescharacteristic
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4C4×D6111yescharacteristic
222C2×C22⋊C4D24411yescharacteristic
223C2×C42C22⋊D6111yescharacteristic
224C4⋊C8—41no—
225C4⋊C8—41no—
226#100—42no—
227C22⋊C8—1222no—
228C22⋊C8—2441no—
229#95—611no—
230#95—611no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236C24#1175819811yescharacteristic
237C24#1175819811yescharacteristic
238C2×Q8—4881no—
239C2×Q8—2441no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—41no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4#1175819811yescharacteristic
255C22×C4#1175819811yescharacteristic
256C22×C4C2×C4×D6111yescharacteristic
257C22×C4C2×D24411yescharacteristic
258C22×C4C2×C22⋊D6111yescharacteristic
259M16—42no—
260M16—42no—
261M16—4882no—
262C2×C8—42no—
263C2×C8—2442no—
264C4⋊C4—41no—
265C4⋊C4—4881no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—4881no—
274C22⋊C4—4881no—
275C22⋊C4—2442no—
276C22⋊C4—2442no—
277C42—21no—
278C42—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×#1175819811yescharacteristic
290Q8—4882no—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4#1451969111yescharacteristic
319C2×C4#1451969111yescharacteristic
320C2×C4#1451980311yescharacteristic
321C2×C4#1451980811yescharacteristic
322C8—82no—
323C8—4882no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×#1451969111yescharacteristic
337C22#1683976111yescharacteristic
338C22#1683978011yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—4881no—
347C4—4881no—
348C4—4881no—
349C4—4881no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—81no—
354C2#2144436011yescharacteristic
355C2#2144746611yescharacteristic
356C2#2144751311yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1800C2
socleC22×C61C2×#99
prime radicalC22×D4×C61D4
cosocleC2×C4⋊C4×C61C23
hypercenter#1800D61
hypocenterC61#11834
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #21443848C2semidirect
4. #21443824C2semidirect
201. C61#11834semidirect

Maximal subgroups

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

subgroupindex
#214517362
#214441572
#214438482
#214438242
C61×#18002
#1183461