Finite Group Databasebeta

← #29579395

Subgroups — #29579395

Order 15616.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456141C211yesmaximal, characteristic
2#21445949C211yesmaximal, characteristic, complemented
3#21444384C211yesmaximal, characteristic, complemented
4#21444382C211yesmaximal, characteristic, complemented
5#21444379C211yesmaximal, characteristic
6#21444103C211yesmaximal, characteristic, complemented
7C61×#1517C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840116—21no—
10#16840116—21no—
11#16840112C411yescharacteristic, complemented
12#16840112C411yescharacteristic, complemented
13#16840108C411yescharacteristic, complemented
14#16840108C411yescharacteristic, complemented
15#16839815C2211yescharacteristic
16#16839758—21no—
17#16839758—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839628C2211yescharacteristic
20#16839524—21no—
21#16839524—21no—
22#16839500—22no—
23#16839498—22no—
24#16839496—22no—
25#16839484—21no—
26C8×#92418—21no—
27C61×#532C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#382C2211yescharacteristic
30C61×#327—22no—
31C22×#92418D411yescharacteristic
32C22×#92418D411yescharacteristic
33#14519777C2×C411yescharacteristic
34#14519777C2×C411yescharacteristic
35#14519769—21no—
36#14519756—21no—
37#14519756—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40#14519736—21no—
41C2×C4⋊Dic61—21no—
42C4⋊#92418—21no—
43#14519701—21no—
44#14519701—21no—
45#14519701—21no—
46#14519701—21no—
47#14519698—21no—
48#14519698—21no—
49#14519698—21no—
50#14519698—21no—
51C22⋊#92418D412yes—
52C4×#92418—21no—
53C4×#92418C2×C411yescharacteristic
54C4×#92418C2×C411yescharacteristic
55C4×#92418D411yescharacteristic
56C4×#92418D411yescharacteristic
57#14519684—21no—
58#14519684—21no—
59C2×#41×C61—21no—
60C4⋊Q8×C61C2×C411yescharacteristic
61#127×C61C2×C411yescharacteristic
62#124×C61—21no—
63#121×C61—21no—
64#121×C61—21no—
65C4×D4×C61—21no—
66C4×D4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C22⋊C8×C61D412yes—
71C4×C8×C61—21no—
72#95×C61—21no—
73#95×C61—21no—
74#41×C61—41no—
75#41×C61—41no—
76#41×C61—41no—
77#41×C61—41no—
78C2×Q8×C61—21no—
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×Dic61—41no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×C8×C61—22no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C42×C61C22×C411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102C22⋊Dic61—41no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—41no—
108C4⋊Dic61—41no—
109#11758196—41no—
110#11758196—41no—
111C4×Dic61—41no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—22no—
117C2×#92418C22⋊C411yescharacteristic
118C2×#92418C22⋊C411yescharacteristic
119C2×#92418C22⋊C411yescharacteristic
120C2×#92418C22⋊C411yescharacteristic
121C23×C61—41no—
122C23×C61#12711yescharacteristic
123Q8×C61—41no—
124Q8×C61—41no—
125D4×C61—41no—
126D4×C61—41no—
127D4×C61—81no—
128D4×C61—81no—
129D4×C61—81no—
130D4×C61—81no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12411yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154Dic122—81no—
155Dic122—81no—
156C8×C61—42no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—21no—
161#92418—42no—
162#9757—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61#39011yescharacteristic
169C22×C61#49511yescharacteristic
170C22×C61#49511yescharacteristic
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—81no—
176C4×C61—161no—
177C4×C61#41611yescharacteristic
178C4×C61#41611yescharacteristic
179C4×C61#48811yescharacteristic
180C4×C61#48811yescharacteristic
181Dic61—81no—
182Dic61—81no—
183Dic61—161no—
184#3131—611no—
185#1835—611no—
186#1518—611no—
187#1518—611no—
188#1517—611no—
189#1517D6111yescharacteristic
190#1450—611no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—161no—
194C2×C61#195811yescharacteristic
195C2×C61#197611yescharacteristic
196C2×C61#197611yescharacteristic
197#533—611no—
198#532C2×D6111yescharacteristic
199#488—1221no—
200#488—1221no—
201#487—611no—
202#487—611no—
203#486—611no—
204#486—611no—
205#431—611no—
206#431C2×D6111yescharacteristic
207#416—1221no—
208#416—1221no—
209C2×C4×C8—611no—
210#382—611no—
211#382C2×D6111yescharacteristic
212#340—1221no—
213#340—1221no—
214#328—1222no—
215#328—1222no—
216#327—22no—
217#327—1222no—
218#322—1221no—
219C82—1221no—
220C61#975711yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C22×C8—611no—
223C22×C8—611no—
224C4⋊Q8—611no—
225C4⋊Q8—611no—
226C4⋊Q8C4×D6111yescharacteristic
227#127C4×D6111yescharacteristic
228#125—1221no—
229#124—21no—
230C22⋊Q8—1221no—
231C22⋊Q8—1221no—
232#121—21no—
233#121—21no—
234C4×Q8—1221no—
235C4×Q8—1221no—
236C4×D4—21no—
237C4×D4—21no—
238#117—1221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—1221no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—1221no—
244#103—1221no—
245#103—1221no—
246#103—1221no—
247#103—1221no—
248#102—1221no—
249#102—1221no—
250#102—1221no—
251#102—1221no—
252C22⋊C8—612no—
253C22⋊C8C22⋊D6112yes—
254C4×C8—21no—
255C4×C8—611no—
256C4×C8—611no—
257C4×C8—611no—
258C4×C8—611no—
259C4×C8—1221no—
260#95—21no—
261#95—21no—
262#95—1221no—
263#95—1221no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—1221no—
270C2×Q8—1221no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—2441no—
278C22×C4D4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C22×C4C2×C22⋊D6111yescharacteristic
281C2×C8—22no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1222no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—2441no—
306C42—2441no—
307C42C2×C4×D6111yescharacteristic
308C42#1175822211yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822411yescharacteristic
311C23—41no—
312C23#1451977311yescharacteristic
313Q8—41no—
314Q8—41no—
315Q8—4881no—
316Q8—4881no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4C22⋊C4×D6111yescharacteristic
337C2×C4#1451973711yescharacteristic
338C2×C4C4×C22⋊D6111yescharacteristic
339C2×C4#1451974911yescharacteristic
340C2×C4#1451975011yescharacteristic
341C2×C4#1451976311yescharacteristic
342C2×C4#1451979611yescharacteristic
343C2×C4#1451979611yescharacteristic
344C2×C4#1451979811yescharacteristic
345C2×C4#1451979811yescharacteristic
346C8—42no—
347C8—1221no—
348C8—1221no—
349C8—1221no—
350C8—1221no—
351C8—2442no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1683966211yescharacteristic
358C22#1684014311yescharacteristic
359C22#1684014511yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—161no—
366C4—9761no—
367C4—4881no—
368C4—4881no—
369C4#1683975511yescharacteristic
370C4#1683975511yescharacteristic
371C4#1684011511yescharacteristic
372C4#1684011511yescharacteristic
373C2—21no—
374C2—21no—
375C2—161no—
376C2#2144662911yescharacteristic
377C2#2144671411yescharacteristic
378C2#2144671611yescharacteristic
subgroupG/H
centerC22#16839662
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1517C2
socleC22×C61#390
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1517D61
hypocenterC61#9757
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #21445949C2semidirect
3. #21444384C2semidirect
4. #21444382C2semidirect
6. #21444103C2semidirect
11. #16840112C4semidirect
12. #16840112C4semidirect
13. #16840108C4semidirect
14. #16840108C4semidirect
220. C61#9757semidirect

Maximal subgroups

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

subgroupindex
#214561412
#214459492
#214443842
#214443822
#214443792
#214441032
C61×#15172
#975761