Finite Group Databasebeta

← #29579398

Subgroups — #29579398

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#21456144C211yesmaximal, characteristic
2#21445981C211yesmaximal, characteristic, complemented
3#21444383C211yesmaximal, characteristic, complemented
4#21444380C211yesmaximal, characteristic
5#21444378C211yesmaximal, characteristic
6#21444112C211yesmaximal, characteristic, complemented
7C61×#1518C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840119—21no—
10#16840119—21no—
11#16840114C411yescharacteristic, complemented
12#16840114C411yescharacteristic, complemented
13#16840110C411yescharacteristic, complemented
14#16840110C411yescharacteristic, complemented
15#16839815C2211yescharacteristic
16C2×#14519710—21no—
17C2×#14519708—21no—
18#16839756—21no—
19#16839756—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839628C2211yescharacteristic
22#16839499—22no—
23#16839497—22no—
24#16839495—22no—
25#16839484—21no—
26#16839483—21no—
27C61×#533C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#382C2211yescharacteristic
30C61×#328—22no—
31C2×#11758222—21no—
32C22×#92418D411yescharacteristic
33C22×#92418D411yescharacteristic
34#14519777C2×C411yescharacteristic
35#14519774C2×C411yescharacteristic
36#14519765—21no—
37#14519751—21no—
38#14519751—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42#14519710—42no—
43#14519708—42no—
44C4⋊#92418—21no—
45#14519700—21no—
46#14519700—21no—
47#14519700—21no—
48#14519700—21no—
49#14519697—21no—
50#14519697—21no—
51#14519697—21no—
52#14519697—21no—
53C22⋊#92418D412yes—
54C4×#92418—21no—
55C4×#92418C2×C411yescharacteristic
56C4×#92418C2×C411yescharacteristic
57C4×#92418D411yescharacteristic
58C4×#92418D411yescharacteristic
59#14519684—21no—
60#14519684—21no—
61C4⋊Q8×C61C2×C411yescharacteristic
62C4⋊Q8×C61C2×C411yescharacteristic
63#125×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68#117×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—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C2×C22⋊D61—41no—
83C22×Dic61—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87#11758222—41no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×C4×D61—41no—
92C2×Dic122—21no—
93C2×C8×C61—22no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C42×C61—41no—
104C42×C61C22×C411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C42×C61#4111yescharacteristic
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112C4⋊Dic61—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#12711yescharacteristic
124C22×D61—41no—
125Q8×C61—81no—
126Q8×C61—81no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12411yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61#13711yescharacteristic
143C2×C4×C61#13711yescharacteristic
144C22⋊D61—81no—
145C22⋊D61—81no—
146C2×Dic61—41no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150D244—41no—
151D244—41no—
152D244—81no—
153D244—81no—
154C4×D61—81no—
155C4×D61—81no—
156Dic122—41no—
157Dic122—41no—
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#39011yescharacteristic
168C22×C61#49611yescharacteristic
169C22×C61#49711yescharacteristic
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—81no—
178C4×C61—81no—
179C4×C61—161no—
180C4×C61#41711yescharacteristic
181C4×C61#41711yescharacteristic
182C4×C61#48911yescharacteristic
183C4×C61#48911yescharacteristic
184Dic61—81no—
185Dic61—161no—
186#3131—611no—
187#1846—611no—
188#1518—611no—
189#1518D6111yescharacteristic, complemented
190#1517—611no—
191#1517—611no—
192#1452—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#195911yescharacteristic
196C2×C61#197611yescharacteristic
197C2×C61#197611yescharacteristic
198D61—161no—
199#533C2×D6111yescharacteristic
200#532—611no—
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—22no—
217#328—1222no—
218#327—1222no—
219#327—1222no—
220#322—1221no—
221#322—1221no—
222C61#975811yescharacteristic, complemented, Sylow
223C2×#41—1221no—
224C22×C8—611no—
225C22×C8—611no—
226C4⋊Q8—611no—
227C4⋊Q8C4×D6111yescharacteristic
228C4⋊Q8C4×D6111yescharacteristic
229#127—611no—
230#125—21no—
231#124—1221no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234#121—1221no—
235#121—1221no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×D4—1221no—
239C4×D4—1221no—
240#117—21no—
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—2441no—
269#41—2441no—
270#41—2441no—
271#41—2441no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—2441no—
279C22×C4—41no—
280C22×C4—2441no—
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—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C22⋊C4—41no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C42—41no—
311C42C2×C4×D6111yescharacteristic
312C42#1175822211yescharacteristic
313C42D4×D6111yescharacteristic
314C42#1175822411yescharacteristic
315C23—2441no—
316C23#1451977311yescharacteristic
317Q8—81no—
318Q8—81no—
319Q8—2441no—
320Q8—2441no—
321D4—4881no—
322D4—4881no—
323D4—4881no—
324D4—4881no—
325D4—2441no—
326D4—2441no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—4881no—
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#1451980411yescharacteristic
347C2×C4#1451980411yescharacteristic
348C2×C4#1451980911yescharacteristic
349C2×C4#1451980911yescharacteristic
350C8—42no—
351C8—1221no—
352C8—1221no—
353C8—1221no—
354C8—1221no—
355C8—2442no—
356C22—21no—
357C22—21no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22#1683966211yescharacteristic
362C22#1684014811yescharacteristic
363C22#1684015511yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—161no—
371C4—9761no—
372C4—4881no—
373C4#1683976211yescharacteristic
374C4#1683976211yescharacteristic
375C4#1684012311yescharacteristic
376C4#1684012311yescharacteristic
377C2—21no—
378C2—21no—
379C2—9761no—
380C2#2144663211yescharacteristic
381C2#2144671411yescharacteristic
382C2#2144671611yescharacteristic
subgroupG/H
centerC22#16839662
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1518C2
socleC22×C61#390
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1518D61
hypocenterC61#9758
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
2. #21445981C2semidirect
3. #21444383C2semidirect
6. #21444112C2semidirect
7. C61×#1518C2semidirect
11. #16840114C4semidirect
12. #16840114C4semidirect
13. #16840110C4semidirect
14. #16840110C4semidirect
189. #1518D61semidirect
222. C61#9758semidirect

Maximal subgroups

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

subgroupindex
#214561442
#214459812
#214443832
#214443802
#214443782
#214441122
C61×#15182
#975861