Finite Group Databasebeta

← #29581080

Subgroups — #29581080

Order 15616.

746 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839954C211yesmaximal, characteristic
2#21450993C211yesmaximal, characteristic, complemented
3#21446747C211yesmaximal, characteristic, complemented
4C2×#16839511C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C2×C61×#492C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×C4×D244C2211yescharacteristic
10#16839954—22no—
11#16839954—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519698—21no—
15C2×#14519698—22no—
16#16839673—22no—
17#16839663—21no—
18#16839627—21no—
19#16839619—22no—
20C4×C4⋊Dic61C2211yescharacteristic
21#16839511—22no—
22#16839491—22no—
23C22×SD16×C61—22no—
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×#127×C61C2211yescharacteristic
26C61×#492—22no—
27C61×#492—22no—
28C2×C4×C8×C61C2211yescharacteristic
29C22×D244D411yescharacteristic
30C22×C4×D61—21no—
31C2×#11758199—24no—
32C2×#11758199—42no—
33C2×#11758199—42no—
34C22×#92418—21no—
35C22×#92418—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D412yes—
42C2×#11758198—21no—
43C2×#11758198—24no—
44C2×C4×Dic61—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418D412yes—
49#14519698—24no—
50#14519698—44no—
51#14519684—24no—
52#14519684—21no—
53C22×Q8×C61D412yes—
54C22×D4×C61—21no—
55C22×D4×C61—21no—
56C22×D4×C61—21no—
57C2×SD16×C61—28no—
58C2×SD16×C61—48no—
59C22×C8×C61—21no—
60C4⋊Q8×C61—21no—
61C4⋊Q8×C61—21no—
62C4⋊Q8×C61—21no—
63C4⋊Q8×C61—21no—
64#127×C61—21no—
65#127×C61—21no—
66#127×C61—21no—
67#127×C61D412yes—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4×C8×C61—21no—
72C4×C8×C61D412yes—
73C24×C61—41no—
74C23×D61—21no—
75C2×Q8×C61—22no—
76C2×Q8×C61—22no—
77C2×Q8×C61—44no—
78C2×D4×C61—22no—
79C2×D4×C61—22no—
80C2×D4×C61—22no—
81C2×D4×C61—44no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—42no—
88C2×D4×C61—42no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C22×C4×C61—22no—
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×Dic61—21no—
96C22×Dic61—22no—
97C2×D244—21no—
98C2×D244—21no—
99C2×D244—21no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244SD1612yescomplemented
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107SD16×C61—416no—
108C2×C8×C61—24no—
109C2×C8×C61—22no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61C2×D411yescharacteristic
117C42×C61#4111yescharacteristic
118#11758199—48no—
119#11758198—41no—
120#11758198—41no—
121#11758198—84no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61—22no—
125C4⋊Dic61—22no—
126C4×Dic61—41no—
127C4×Dic61—41no—
128C2×#92418—22no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—42no—
133C23×C61—42no—
134C23×C61—81no—
135C23×C61—81no—
136C23×C61—82no—
137C23×C61—82no—
138C23×C61#12011yescharacteristic
139C22×D61—22no—
140C22×D61—41no—
141C22×D61—42no—
142C22×D61—41no—
143C22×D61—42no—
144Q8×C61—44no—
145Q8×C61—82no—
146D4×C61—44no—
147D4×C61—42no—
148D4×C61—42no—
149D4×C61—44no—
150D4×C61—82no—
151D4×C61—81no—
152D4×C61—81no—
153D4×C61—81no—
154D4×C61—81no—
155C2×C4×C61—22no—
156C2×C4×C61—42no—
157C2×C4×C61—44no—
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12011yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×C4×C61#12111yescharacteristic
162C2×C4×C61#12111yescharacteristic
163C2×C4×C61#12711yescharacteristic
164C2×C4×C61C2×SD1611yescharacteristic
165C2×C4×C61#13511yescharacteristic
166C2×C4×C61#13512yes—
167C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C61AGL(1,ℤ/8)12yes—
169C2×C4×C61#13711yescharacteristic
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175D244—22no—
176D244—22no—
177D244—41no—
178D244—41no—
179C4×D61—82no—
180C4×D61—81no—
181C4×D61—81no—
182C8×C61—24no—
183#92418—42no—
184#92418—81no—
185#10048—611nomaximal, Sylow
186C22×C61—82no—
187C22×C61—82no—
188C22×C61—82no—
189C22×C61—162no—
190C22×C61—162no—
191C22×C61#39211yescharacteristic
192C22×C61#44811yescharacteristic
193C22×C61#44912yes—
194C22×C61#44911yescharacteristic
195C22×C61#45312yes—
196C2×D61—44no—
197C2×D61—42no—
198C2×D61—82no—
199C2×D61—81no—
200C2×D61—81no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—82no—
204C4×C61#45011yescharacteristic
205C4×C61#45211yescharacteristic
206C4×C61#46312yes—
207C4×C61#46511yescharacteristic
208C4×C61#46811yescharacteristic
209C4×C61#49511yescharacteristic
210C4×C61#49611yescharacteristic
211Dic61—82no—
212Dic61—81no—
213C2×#492D6111yescharacteristic, complemented
214C2×#459—611no—
215#2563—611no—
216#1982—611no—
217C2×#333—611no—
218C2×D4⋊C8—611no—
219#1279—611no—
220C2×C61—162no—
221C2×C61#162212yes—
222C2×C61#162412yes—
223C2×C61#200011yescharacteristic
224C2×C61#200211yescharacteristic
225C2×C61#201211yescharacteristic
226D61—82no—
227C22×SD16—22no—
228C22×D8—1221no—
229C2×C4⋊Q8C2×D6111yescharacteristic
230C2×#127C2×D6111yescharacteristic
231C2×C4×D4—611no—
232#492—22no—
233#492—22no—
234#459—1222no—
235#459—1222no—
236C2×C4⋊C8—611no—
237C2×C4⋊C8—611no—
238C2×#102—1221no—
239C2×#102—1222no—
240C2×C4×C8C2×D6111yescharacteristic
241#393—1222no—
242#390—1221no—
243#382—1221no—
244#380—1222no—
245C4×C4⋊C4—611no—
246#333—1222no—
247D4⋊C8—1222no—
248C61#1004811yescharacteristic, complemented, Sylow
249C22×Q8C22⋊D6112yes—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—611no—
254C23×C4—1221no—
255C2×SD16—28no—
256C2×SD16—48no—
257C2×D8—1224no—
258C2×D8—2442no—
259C2×D8—2442no—
260C22×C8—21no—
261C22×C8—1221no—
262C22×C8—1221no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267#127—21no—
268#127—21no—
269#127—21no—
270#127C22⋊D6112yes—
271C4×D4—1221no—
272C4×D4—1221no—
273C4×D4—1221no—
274C4×D4—1221no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—612no—
279C2×C22⋊C4—1224no—
280C2×C22⋊C4—1221no—
281C2×C42—1221no—
282C2×C42C22×D6111yescharacteristic
283C4⋊C8—612no—
284C4⋊C8—1221no—
285C4⋊C8—1221no—
286C4⋊C8—1221no—
287#102—1224no—
288#102—2444no—
289C4×C8—21no—
290C4×C8C22⋊D6112yes—
291#95—1224no—
292#95—1221no—
293C24—41no—
294C24—1221no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—44no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—44no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—41no—
308C2×D4—42no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—612no—
312C2×D4—1221no—
313C2×D4—1221no—
314C2×D4—1221no—
315C2×D4—1221no—
316C2×D4—1221no—
317C22×C4—22no—
318C22×C4—1221no—
319C22×C4—1222no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2442no—
323C22×C4—2442no—
324C22×C4D4×D6111yescharacteristic
325C22×C4D4×D6111yescharacteristic
326C22×C4C2×C22⋊D6111yescharacteristic
327SD16—416no—
328D8—2448no—
329C2×C8—24no—
330C2×C8—22no—
331C2×C8—1222no—
332C2×C8—2441no—
333C2×C8—2442no—
334C2×C8—2441no—
335C2×C8—2441no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—1222no—
343C4⋊C4—1222no—
344C22⋊C4—4884no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C42—2441no—
348C42—2441no—
349C42D4×D6111yescharacteristic
350C42#1175822411yescharacteristic
351C42C2×C22⋊D6111yescharacteristic
352C42C2×C22⋊D6111yescharacteristic
353C23—42no—
354C23—81no—
355C23—81no—
356C23—82no—
357C23—82no—
358C23—1222no—
359C23—2442no—
360C23—2441no—
361C23—2441no—
362C23—2442no—
363C23#1451974511yescharacteristic
364Q8—44no—
365Q8—82no—
366D4—44no—
367D4—44no—
368D4—42no—
369D4—42no—
370D4—82no—
371D4—81no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—1222no—
376D4—1222no—
377D4—2441no—
378D4—2441no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—44no—
382C2×C4—4882no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—2442no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2441no—
389C2×C4—2442no—
390C2×C4#1451974511yescharacteristic
391C2×C4#1451974611yescharacteristic
392C2×C4#1451974811yescharacteristic
393C2×C4#1451974911yescharacteristic
394C2×C4#1451974911yescharacteristic
395C2×C4#1451977311yescharacteristic
396C2×C4SD16×D6111yescharacteristic
397C2×C4#1451979812yes—
398C2×C4#1451979811yescharacteristic
399C2×C4#1451980412yes—
400C2×C4#1451980411yescharacteristic
401C2×C4#1451980611yescharacteristic
402C8—24no—
403C8—4881no—
404C8—2442no—
405C22—82no—
406C22—82no—
407C22—82no—
408C22—162no—
409C22—162no—
410C22—4882no—
411C22—4881no—
412C22—4881no—
413C22—2444no—
414C22—2442no—
415C22#1683967011yescharacteristic
416C22#1683989911yescharacteristic
417C22#1683990612yes—
418C22#1683990611yescharacteristic
419C22#1683992912yes—
420C4—21no—
421C4—21no—
422C4—82no—
423C4—4882no—
424C4—4881no—
425C4#1683991111yescharacteristic
426C4#1683992111yescharacteristic
427C4#1683997912yes—
428C4#1683998811yescharacteristic
429C4#1684000511yescharacteristic
430C4#1684014311yescharacteristic
431C4#1684014811yescharacteristic
432C2—162no—
433C2—4882no—
434C2#2144488812yes—
435C2#2144490012yes—
436C2#2144681911yescharacteristic
437C2#2144683411yescharacteristic
438C2#2144689311yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#492C2
socleC23×C61#120
prime radicalC2×#16839954C2
hypercenterC2×#492D61
hypocenterC61#10048
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
2. #21450993C2semidirect
3. #21446747C2semidirect
4. C2×#16839511C2semidirect
5. C2×#16839491C2semidirect
6. #21443659C2semidirect
7. C2×C61×#492C2semidirect
102. C2×D244SD16semidirect
213. C2×#492D61semidirect
248. C61#10048semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
#214509932
#214467472
C2×#168395112
C2×#168394912
#214436592
C2×C61×#4922
#1004861