Finite Group Databasebeta

← #29579382

Subgroups — #29579382

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#21445688C211yesmaximal, characteristic, complemented
3#21444565C211yesmaximal, characteristic, complemented
4#21444317C211yesmaximal, characteristic, complemented
5#21444223C211yesmaximal, characteristic, complemented
6#21444218C211yesmaximal, characteristic
7C61×#1502C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840116—21no—
10#16840116—21no—
11#16840112C411yescharacteristic, complemented
12#16840112C411yescharacteristic, complemented
13#16840108C411yescharacteristic, complemented
14#16840108C411yescharacteristic, complemented
15#16839815C2211yescharacteristic
16C2×C4⋊#92418C2211yescharacteristic
17#16839758—21no—
18#16839758—21no—
19C2×#14519688—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839517—21no—
22#16839514—21no—
23#16839512—21no—
24#16839498—22no—
25#16839494—22no—
26D4⋊#92418—22no—
27C61×#532C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#327—22no—
31C22×#92418—21no—
32C22×#92418D411yescharacteristic
33C22×#92418D411yescharacteristic
34#14519777C2×C411yescharacteristic
35#14519777C2×C411yescharacteristic
36#14519769—21no—
37#14519756—21no—
38#14519756—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41#14519736—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418D412yes—
45#14519701—21no—
46#14519701—21no—
47#14519701—21no—
48#14519701—21no—
49#14519698—21no—
50#14519698—21no—
51#14519698—21no—
52#14519698—21no—
53C22⋊#92418—21no—
54#14519688—42no—
55C4×#92418—21no—
56C4×#92418C2×C411yescharacteristic
57C4×#92418C2×C411yescharacteristic
58C4×#92418D411yescharacteristic
59C4×#92418D411yescharacteristic
60C2×#41×C61—21no—
61C4⋊Q8×C61C2×C411yescharacteristic
62#127×C61C2×C411yescharacteristic
63#124×C61—21no—
64#121×C61—21no—
65#121×C61—21no—
66C4×D4×C61—21no—
67C4×D4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C42×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C4×C8×C61—21no—
74#95×C61D412yes—
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—22no—
85C22×C4×C61—41no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×C8×C61—41no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—42no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C42×C61—41no—
98C42×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—
108#11758196—41no—
109#11758196—41no—
110C4×Dic61—41no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—22no—
116C2×#92418—41no—
117C2×#92418—41no—
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—42no—
136C2×C4×C61—42no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12411yescharacteristic
146C2×C4×C61#12711yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61#13711yescharacteristic
151C2×Dic61—41no—
152C2×Dic61—41no—
153Dic122—42no—
154Dic122—81no—
155C8×C61—81no—
156#92418—21no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—42no—
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—82no—
175C4×C61—81no—
176C4×C61#41611yescharacteristic
177C4×C61#41711yescharacteristic
178C4×C61#44412yes—
179C4×C61#46311yescharacteristic
180C4×C61#46411yescharacteristic
181Dic61—81no—
182Dic61—81no—
183#3131—611no—
184#1770—611no—
185#1564—611no—
186#1503—611no—
187#1502D6111yescharacteristic
188#1481—611no—
189#1480—611no—
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⋊C8—611no—
207#416—1221no—
208#416—1221no—
209C2×#97—1221no—
210C2×C4×C8—611no—
211C4×C4⋊C4C2×D6111yescharacteristic
212#336—1221no—
213#335—1221no—
214#334—1221no—
215#328—1222no—
216#327—22no—
217Q8⋊C8—1222no—
218D4⋊C8—1222no—
219C61#975411yescharacteristic, complemented, Sylow
220C2×#41—21no—
221C22×C8—611no—
222C22×C8—611no—
223C22×C8—1221no—
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×C42—21no—
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—612no—
244C4⋊C8—1221no—
245C4⋊C8—1221no—
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#95C22⋊D6112yes—
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—22no—
276C22×C4—41no—
277C22×C4D4×D6111yescharacteristic
278C22×C4#1175822411yescharacteristic
279C22×C4C2×C22⋊D6111yescharacteristic
280C2×C8—41no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—1221no—
289C2×C8—1222no—
290C2×C8—2441no—
291C2×C8—2441no—
292C2×C8—2441no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—42no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—2441no—
305C42—41no—
306C42—41no—
307C42—2441no—
308C42C2×C4×D6111yescharacteristic
309C42#1175822211yescharacteristic
310C42D4×D6111yescharacteristic
311C42D4×D6111yescharacteristic
312C23—41no—
313C23#1451974911yescharacteristic
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—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4C22⋊C4×D6111yescharacteristic
335C2×C4#1451973711yescharacteristic
336C2×C4C4×C22⋊D6111yescharacteristic
337C2×C4#1451975011yescharacteristic
338C2×C4#1451976311yescharacteristic
339C2×C4#1451977311yescharacteristic
340C2×C4#1451979611yescharacteristic
341C2×C4#1451979811yescharacteristic
342C2×C4#1451980111yescharacteristic
343C2×C4#1451980611yescharacteristic
344C8—81no—
345C8—1221no—
346C8—1221no—
347C8—1221no—
348C8—1221no—
349C8—4881no—
350C8—2442no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1683966211yescharacteristic
357C22#1683997511yescharacteristic
358C22#1683998211yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—4881no—
365C4—4881no—
366C4#1683975511yescharacteristic
367C4#1683976011yescharacteristic
368C4#1683988112yes—
369C4#1683997611yescharacteristic
370C4#1683998311yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#2144670911yescharacteristic
375C2#2144671411yescharacteristic
376C2#2144675011yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1502C2
socleC22×C61#390
prime radicalC61×#532C22
cosocleC2×C42×C61C23
hypercenter#1502D61
hypocenterC61#9754
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #21445688C2semidirect
3. #21444565C2semidirect
4. #21444317C2semidirect
5. #21444223C2semidirect
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
#214456882
#214445652
#214443172
#214442232
#214442182
C61×#15022
#975461