Finite Group Databasebeta

← #29579400

Subgroups — #29579400

Order 15616.

408 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456141C211yesmaximal, characteristic
2#21445981C211yesmaximal, characteristic, complemented
3#21444384C211yesmaximal, characteristic, complemented
4#21444382C211yesmaximal, characteristic, complemented
5#21444379C211yesmaximal, characteristic
6#21444112C211yesmaximal, 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
16C2×#14519710—21no—
17C2×#14519708—21no—
18#16839758—21no—
19#16839758—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839628C2211yescharacteristic
22#16839500—22no—
23#16839498—22no—
24#16839496—22no—
25#16839484—21no—
26#16839483—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—
42#14519710—42no—
43#14519708—42no—
44C4⋊#92418—21no—
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⋊#92418D412yes—
54C4×#92418—21no—
55C4×#92418C2×C411yescharacteristic
56C4×#92418C2×C411yescharacteristic
57C4×#92418D411yescharacteristic
58C4×#92418D411yescharacteristic
59#14519684—21no—
60#14519684—21no—
61C2×#41×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×C4⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61D412yes—
73C4×C8×C61—21no—
74#95×C61—21no—
75#95×C61—21no—
76#41×C61—41no—
77#41×C61—41no—
78#41×C61—41no—
79#41×C61—41no—
80C2×Q8×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×Dic61—41no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×C8×C61—22no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C42×C61C22×C411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104C22⋊Dic61—41no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111#11758196—41no—
112#11758196—41no—
113C4×Dic61—41no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—22no—
119C2×#92418C22⋊C411yescharacteristic
120C2×#92418C22⋊C411yescharacteristic
121C2×#92418C22⋊C411yescharacteristic
122C2×#92418C22⋊C411yescharacteristic
123C23×C61—41no—
124C23×C61#12711yescharacteristic
125Q8×C61—41no—
126Q8×C61—41no—
127D4×C61—41no—
128D4×C61—41no—
129D4×C61—81no—
130D4×C61—81no—
131D4×C61—81no—
132D4×C61—81no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
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#12111yescharacteristic
146C2×C4×C61#12411yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C61#13711yescharacteristic
150C2×C4×C61#13711yescharacteristic
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155C2×Dic61—81no—
156Dic122—81no—
157Dic122—81no—
158C8×C61—42no—
159#92418—21no—
160#92418—21no—
161#92418—21no—
162#92418—21no—
163#92418—42no—
164#9758—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61#39011yescharacteristic
171C22×C61#49611yescharacteristic
172C22×C61#49711yescharacteristic
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—81no—
178C4×C61—161no—
179C4×C61#41711yescharacteristic
180C4×C61#41711yescharacteristic
181C4×C61#48911yescharacteristic
182C4×C61#48911yescharacteristic
183Dic61—81no—
184Dic61—81no—
185Dic61—161no—
186#3131—611no—
187#1846—611no—
188#1518—611no—
189#1518—611no—
190#1517—611no—
191#1517D6111yescharacteristic
192#1452—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—161no—
196C2×C61#195911yescharacteristic
197C2×C61#197611yescharacteristic
198C2×C61#197611yescharacteristic
199#533—611no—
200#532C2×D6111yescharacteristic
201#488—1221no—
202#488—1221no—
203#487—611no—
204#487—611no—
205#486—611no—
206#486—611no—
207#431—611no—
208#431C2×D6111yescharacteristic
209C2×#107—1221no—
210C2×#106—1221no—
211#416—1221no—
212#416—1221no—
213C2×C4×C8—611no—
214#382—611no—
215#382C2×D6111yescharacteristic
216#328—1222no—
217#328—1222no—
218#327—22no—
219#327—1222no—
220#322—1221no—
221#322—1221no—
222C61#975811yescharacteristic, complemented, Sylow
223C2×#41—21no—
224C22×C8—611no—
225C22×C8—611no—
226C4⋊Q8—611no—
227C4⋊Q8—611no—
228C4⋊Q8C4×D6111yescharacteristic
229#127C4×D6111yescharacteristic
230#125—1221no—
231#124—21no—
232C22⋊Q8—1221no—
233C22⋊Q8—1221no—
234#121—21no—
235#121—21no—
236C4×Q8—1221no—
237C4×Q8—1221no—
238C4×D4—21no—
239C4×D4—21no—
240#117—1221no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—1221no—
243C2×C42C22×D6111yescharacteristic
244#107—2442no—
245#106—2442no—
246C4⋊C8—21no—
247C4⋊C8—1221no—
248#103—1221no—
249#103—1221no—
250#103—1221no—
251#103—1221no—
252#102—1221no—
253#102—1221no—
254#102—1221no—
255#102—1221no—
256C22⋊C8—612no—
257C22⋊C8C22⋊D6112yes—
258C4×C8—21no—
259C4×C8—611no—
260C4×C8—611no—
261C4×C8—611no—
262C4×C8—611no—
263C4×C8—1221no—
264#95—21no—
265#95—21no—
266#95—1221no—
267#95—1221no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272C2×Q8—21no—
273C2×Q8—1221no—
274C2×Q8—1221no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—2441no—
282C22×C4D4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4C2×C22⋊D6111yescharacteristic
285C2×C8—22no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8—1221no—
291C2×C8—1221no—
292C2×C8—1221no—
293C2×C8—1221no—
294C2×C8—1222no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—2441no—
310C42—2441no—
311C42C2×C4×D6111yescharacteristic
312C42#1175822211yescharacteristic
313C42D4×D6111yescharacteristic
314C42#1175822411yescharacteristic
315C23—41no—
316C23#1451977311yescharacteristic
317Q8—41no—
318Q8—41no—
319Q8—4881no—
320Q8—4881no—
321D4—41no—
322D4—41no—
323D4—81no—
324D4—81no—
325D4—81no—
326D4—81no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4C22⋊C4×D6111yescharacteristic
341C2×C4#1451973711yescharacteristic
342C2×C4C4×C22⋊D6111yescharacteristic
343C2×C4#1451974911yescharacteristic
344C2×C4#1451975011yescharacteristic
345C2×C4#1451976311yescharacteristic
346C2×C4#1451980111yescharacteristic
347C2×C4#1451980111yescharacteristic
348C2×C4#1451980611yescharacteristic
349C2×C4#1451980611yescharacteristic
350C8—42no—
351C8—1221no—
352C8—1221no—
353C8—1221no—
354C8—1221no—
355C8—2442no—
356C22—21no—
357C22—21no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22#1683966211yescharacteristic
362C22#1684015011yescharacteristic
363C22#1684015311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—161no—
370C4—9761no—
371C4—4881no—
372C4—4881no—
373C4#1683976011yescharacteristic
374C4#1683976011yescharacteristic
375C4#1684012011yescharacteristic
376C4#1684012011yescharacteristic
377C2—21no—
378C2—21no—
379C2—161no—
380C2#2144663411yescharacteristic
381C2#2144671411yescharacteristic
382C2#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#9758
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. #21445981C2semidirect
3. #21444384C2semidirect
4. #21444382C2semidirect
6. #21444112C2semidirect
11. #16840112C4semidirect
12. #16840112C4semidirect
13. #16840108C4semidirect
14. #16840108C4semidirect
222. C61#9758semidirect

Maximal subgroups

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

subgroupindex
#214561412
#214459812
#214443842
#214443822
#214443792
#214441122
C61×#15172
#975861