Finite Group Databasebeta

← #29579380

Subgroups — #29579380

Order 15616.

416 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456141C211yesmaximal, characteristic
2#21445689C211yesmaximal, characteristic, complemented
3#21444565C211yesmaximal, characteristic, complemented
4#21444319C211yesmaximal, characteristic, complemented
5#21444314C211yesmaximal, characteristic
6#21444221C211yesmaximal, characteristic, complemented
7C61×#1480C211yesmaximal, 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×#14519687—21no—
19C2×C4×#92418C2211yescharacteristic
20C4×C4⋊Dic61C2211yescharacteristic
21#16839516—21no—
22#16839514—21no—
23#16839512—21no—
24#16839500—22no—
25#16839496—22no—
26#16839492—22no—
27C61×#532C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C61×D4⋊C8—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—
42C2×C4×Dic61—21no—
43C4⋊#92418—21no—
44#14519701—21no—
45#14519701—21no—
46#14519701—21no—
47#14519701—21no—
48#14519698—21no—
49#14519698—21no—
50#14519698—21no—
51#14519698—21no—
52C22⋊#92418—21no—
53#14519687—42no—
54C4×#92418—21no—
55C4×#92418C2×C411yescharacteristic
56C4×#92418C2×C411yescharacteristic
57C4×#92418D411yescharacteristic
58C4×#92418D411yescharacteristic
59#14519684D412yes—
60C2×#41×C61—21no—
61C22×C8×C61—21no—
62C4⋊Q8×C61C2×C411yescharacteristic
63#127×C61C2×C411yescharacteristic
64#124×C61—21no—
65#121×C61—21no—
66#121×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61D412yes—
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75#41×C61—41no—
76#41×C61—41no—
77#41×C61—41no—
78#41×C61—41no—
79C2×Q8×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C22×Dic61—22no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×C8×C61—22no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C22⋊Dic61—41no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—42no—
109#11758196—41no—
110#11758196—41no—
111C4×Dic61—41no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—41no—
119C2×#92418C22⋊C411yescharacteristic
120C2×#92418C22⋊C411yescharacteristic
121C2×#92418C22⋊C411yescharacteristic
122C2×#92418C22⋊C411yescharacteristic
123C23×C61—41no—
124C23×C61#12111yescharacteristic
125Q8×C61—41no—
126Q8×C61—41no—
127D4×C61—41no—
128D4×C61—41no—
129D4×C61—42no—
130D4×C61—81no—
131D4×C61—81no—
132D4×C61—81no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12411yescharacteristic
143C2×C4×C61#12711yescharacteristic
144C2×C4×C61#13511yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153Dic122—42no—
154Dic122—81no—
155C8×C61—42no—
156C8×C61—81no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—21no—
161#92418—81no—
162#9754—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61#39011yescharacteristic
169C22×C61#46311yescharacteristic
170C22×C61#46411yescharacteristic
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—81no—
175C4×C61#41611yescharacteristic
176C4×C61#41711yescharacteristic
177C4×C61#44412yes—
178C4×C61#46311yescharacteristic
179C4×C61#46411yescharacteristic
180Dic61—82no—
181Dic61—81no—
182Dic61—81no—
183#3131—611no—
184#1770—611no—
185#1564—611no—
186#1503—611no—
187#1502—611no—
188#1481—611no—
189#1480D6111yescharacteristic
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—161no—
193C2×C61#197511yescharacteristic
194C2×C61#197611yescharacteristic
195C2×C61#198311yescharacteristic
196#533—611no—
197#532C2×D6111yescharacteristic
198#488—1221no—
199#488—1221no—
200#487—611no—
201#487—611no—
202#486—611no—
203#486—611no—
204#431—611no—
205#431C2×D6111yescharacteristic
206C2×C4⋊C8C2×D6111yescharacteristic
207#416—1221no—
208#416—1221no—
209C2×#97—1221no—
210C2×C4×C8—611no—
211C4×C4⋊C4—611no—
212#336—1221no—
213#335—1221no—
214#334—1221no—
215#328—1222no—
216#327—1222no—
217Q8⋊C8—1222no—
218D4⋊C8—22no—
219C61#975411yescharacteristic, complemented, Sylow
220C2×#41—21no—
221C22×C8—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—1221no—
240C2×C42—1221no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—1221no—
245C4⋊C8C22⋊D6112yes—
246#103—1221no—
247#103—1221no—
248#103—1221no—
249#103—1221no—
250#102—1221no—
251#102—1221no—
252#102—1221no—
253#102—1221no—
254C22⋊C8—21no—
255C22⋊C8—1221no—
256#97—2442no—
257C4×C8—21no—
258C4×C8—611no—
259C4×C8—611no—
260C4×C8—611no—
261C4×C8—611no—
262C4×C8—1221no—
263#95—612no—
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—1222no—
277C22×C4#1175822211yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—2441no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—2442no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—2441no—
305C42—2441no—
306C42—2441no—
307C42—2441no—
308C42C2×C4×D6111yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822411yescharacteristic
311C42C2×C22⋊D6111yescharacteristic
312C23—41no—
313C23#1451975011yescharacteristic
314Q8—41no—
315Q8—41no—
316Q8—4881no—
317Q8—2442no—
318D4—41no—
319D4—41no—
320D4—42no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4C22⋊C4×D6111yescharacteristic
335C2×C4#1451973711yescharacteristic
336C2×C4C4×C22⋊D6111yescharacteristic
337C2×C4#1451974911yescharacteristic
338C2×C4#1451976311yescharacteristic
339C2×C4#1451977311yescharacteristic
340C2×C4#1451979611yescharacteristic
341C2×C4#1451979811yescharacteristic
342C2×C4#1451980111yescharacteristic
343C2×C4#1451980611yescharacteristic
344C8—42no—
345C8—81no—
346C8—1221no—
347C8—1221no—
348C8—1221no—
349C8—1221no—
350C8—4881no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1683966211yescharacteristic
357C22#1683997611yescharacteristic
358C22#1683998311yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—4882no—
364C4—4881no—
365C4—4881no—
366C4#1683975511yescharacteristic
367C4#1683976011yescharacteristic
368C4#1683988212yes—
369C4#1683997511yescharacteristic
370C4#1683998211yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#2144671111yescharacteristic
375C2#2144671611yescharacteristic
376C2#2144675011yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1480C2
socleC22×C61#390
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1480D61
hypocenterC61#9754
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #21445689C2semidirect
3. #21444565C2semidirect
4. #21444319C2semidirect
6. #21444221C2semidirect
11. #16840112C4semidirect
12. #16840112C4semidirect
13. #16840108C4semidirect
14. #16840108C4semidirect
219. C61#9754semidirect

Maximal subgroups

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

subgroupindex
#214561412
#214456892
#214445652
#214443192
#214443142
#214442212
C61×#14802
#975461