Finite Group Databasebeta

← #29568562

Subgroups — #29568562

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445799C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3#21443645C212yesmaximal, complemented
4#21443642C212yesmaximal, complemented
5C61×#2855C211yesmaximal, characteristic
6C2×C4⋊#92418—21no—
7C2×C22⋊#92418—21no—
8C2×C22⋊#92418—21no—
9C2×#14519688—21no—
10#16839517C2212yes—
11#16839517C2212yes—
12C2×C22⋊Q8×C61C411yescharacteristic
13C22×C42×C61C2211yescharacteristic
14C61×#391C411yescharacteristic
15C61×#391C2211yescharacteristic
16C61×#389C411yescharacteristic
17C61×#389C2211yescharacteristic
18C61×#387—21no—
19C61×#387—21no—
20C61×#385—21no—
21C61×#381—21no—
22C61×#380C411yescharacteristic
23C22×#92418—22no—
24C22×#92418—22no—
25C4⋊#92418—42no—
26C22⋊#92418—24no—
27C22⋊#92418—42no—
28#14519688—42no—
29C22×Q8×C61C2×C411yescharacteristic
30C23×C4×C61C2×C411yescharacteristic
31C23×C4×C61D411yescharacteristic
32C23×C4×C61D411yescharacteristic
33C22⋊Q8×C61—42no—
34C2×C4⋊C4×C61—21no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61—21no—
42C2×C42×C61—42no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61C2311yescharacteristic
47#95×C61—21no—
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54C24×C61C22⋊C411yescharacteristic
55C2×Q8×C61—22no—
56C2×Q8×C61—41no—
57C2×Q8×C61—41no—
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—22no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C4⋊C4×C61—22no—
79C4⋊C4×C61—42no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—42no—
86C22⋊C4×C61—42no—
87C42×C61—22no—
88C42×C61—22no—
89C42×C61—41no—
90C42×C61—41no—
91C2×#92418—24no—
92C2×#92418—42no—
93C2×#92418—42no—
94C2×#92418—42no—
95C2×#92418—42no—
96C2×#92418—42no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61#10412yes—
104C23×C61C2×C22⋊C411yescharacteristic
105Q8×C61—82no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—44no—
121C2×C4×C61—44no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
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—41no—
136C2×C4×C61#9912yes—
137C2×C4×C61#13112yes—
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61#13712yes—
140C2×C4×C61#13711yescharacteristic
141#92418—44no—
142#92418—82no—
143#7701—611nomaximal, Sylow
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61#40811yescharacteristic
152C22×C61C2×#9911yescharacteristic
153C22×C61#41311yescharacteristic
154C22×C61#41711yescharacteristic
155C22×C61#41911yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C22×C61#42111yescharacteristic
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—22no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—81no—
166C4×C61—81no—
167C4×C61—81no—
168C4×C61—81no—
169#2855D6111yescharacteristic
170#1797—611no—
171#1749—611no—
172#1272—612no—
173#1271—612no—
174C2×C61—42no—
175C2×C61#146811yescharacteristic
176C2×C61#148311yescharacteristic
177C2×C61#149711yescharacteristic
178C2×C61#150811yescharacteristic
179C2×C61#151311yescharacteristic
180C2×C61#153211yescharacteristic
181C2×C61#155911yescharacteristic
182C2×C22⋊Q8Dic6111yescharacteristic
183C22×C42C2×D6111yescharacteristic
184C2×C4⋊C8—1221no—
185C2×C22⋊C8—1221no—
186C2×C22⋊C8—1221no—
187C2×#97—1221no—
188#391Dic6111yescharacteristic
189#391C2×D6111yescharacteristic
190#389Dic6111yescharacteristic
191#389C2×D6111yescharacteristic
192#387—21no—
193#387—21no—
194#385—21no—
195#381—21no—
196#380Dic6111yescharacteristic
197#336—612no—
198#336—612no—
199C61#770111yescharacteristic, complemented, Sylow
200C22×Q8C2×Dic6111yescharacteristic
201C23×C4C2×Dic6111yescharacteristic
202C23×C4C22⋊D6111yescharacteristic
203C23×C4C22⋊D6111yescharacteristic
204C22×C8—1222no—
205C22×C8—1222no—
206C22⋊Q8—42no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×Dic6111yescharacteristic
211C2×C4⋊C4C2×Dic6111yescharacteristic
212C2×C4⋊C4C2×Dic6111yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C42—42no—
216C2×C42C2×Dic6111yescharacteristic
217C2×C42C22⋊D6111yescharacteristic
218C2×C42C22⋊D6111yescharacteristic
219C2×C42C22×D6111yescharacteristic
220C4⋊C8—2442no—
221C22⋊C8—1224no—
222C22⋊C8—2442no—
223#97—2442no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C24C22⋊Dic6111yescharacteristic
232C2×Q8—22no—
233C2×Q8—41no—
234C2×Q8—41no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4C22⋊Dic6111yescharacteristic
250C22×C4C22⋊Dic6111yescharacteristic
251C22×C4C22⋊Dic6111yescharacteristic
252C22×C4C22×Dic6111yescharacteristic
253C22×C4C2×C22⋊D6111yescharacteristic
254C22×C4C2×C22⋊D6111yescharacteristic
255C2×C8—1224no—
256C2×C8—2442no—
257C2×C8—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C2×C8—2442no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23#1451970412yes—
281C23C2×C22⋊Dic6111yescharacteristic
282Q8—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4#1451969212yes—
314C2×C4#1451978412yes—
315C2×C4#1451980211yescharacteristic
316C2×C4#1451980711yescharacteristic
317C2×C4#1451980812yes—
318C8—4882no—
319C8—2444no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22#1683972911yescharacteristic
328C22C2×#1451969211yescharacteristic
329C22#1683974611yescharacteristic
330C22#1683976311yescharacteristic
331C22#1683977111yescharacteristic
332C22C2×#1451970411yescharacteristic
333C22#1683977911yescharacteristic
334C4—21no—
335C4—21no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C2—42no—
346C2#2144416711yescharacteristic
347C2#2144423211yescharacteristic
348C2#2144429211yescharacteristic
349C2#2144433911yescharacteristic
350C2#2144436211yescharacteristic
351C2#2144443911yescharacteristic
352C2#2144454911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2855C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2855D61
hypocenterC61#7701
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
3. #21443645C2semidirect
4. #21443642C2semidirect
199. C61#7701semidirect

Maximal subgroups

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

subgroupindex
#214457992
#214455812
#214436452
#214436422
C61×#28552
#770161