Finite Group Databasebeta

← #29574232

Subgroups — #29574232

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×D244C211yesmaximal, characteristic
2#21446577C211yesmaximal, characteristic, complemented
3#21445947C211yesmaximal, characteristic, complemented
4#21445820C211yesmaximal, characteristic
5C2×#16839491C211yesmaximal, characteristic
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D244—21no—
9C2×C4×D244C2211yescharacteristic
10C2×C4⋊C4×D61—21no—
11C2×#14519710—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519699—21no—
14#16839660—21no—
15#16839636—22no—
16#16839632C2211yescharacteristic
17#16839632C2211yescharacteristic
18#16839619—21no—
19#16839525—22no—
20#16839525—21no—
21#16839524—21no—
22#16839491C414yescomplemented
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4×C8×C61C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C22×D244D411yescharacteristic
27C22×C4×D61—21no—
28C22×C4×D61—22no—
29C22×#92418—21no—
30C4×D244—21no—
31C4×D244—21no—
32C4×D244—42no—
33C4×D244—42no—
34C4×D244C2×C412yes—
35C4×D244Q812yes—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D412yes—
43C2×#11758196—22no—
44C4⋊C4×D61—42no—
45C4⋊C4×D61—42no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48#14519710—42no—
49C4⋊#92418—21no—
50C4⋊#92418C2×C412yescomplemented
51#14519699—42no—
52#14519684—22no—
53C22×C8×C61—21no—
54C22×C8×C61—21no—
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C42×C61—21no—
58C2×C42×C61C2311yescharacteristic
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4×C8×C61—21no—
62C4×C8×C61C2×C412yescomplemented
63#95×C61—21no—
64C23×D61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—22no—
72C22×Dic61—41no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244C4⋊C412yes—
77C2×D244D812yes—
78C2×D244Q1612yes—
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—44no—
86C2×C4×D61—44no—
87C2×C4×D61—82no—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C2×C8×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61SD1612yes—
98C42×C61—41no—
99C42×C61—41no—
100C42×C61C22×C411yescharacteristic
101C42×C61C2×Q811yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104#11758198—22no—
105#11758198—22no—
106#11758198—44no—
107C4⋊Dic61—21no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61—42no—
113C4⋊Dic61—42no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61—41no—
117C4⋊Dic61—41no—
118C4⋊Dic61C4⋊C412yes—
119#11758196—44no—
120C2×#92418—22no—
121C2×#92418—41no—
122C2×#92418—41no—
123C23×C61#12011yescharacteristic
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—22no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61C2×C4⋊C411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C22⋊Q811yescharacteristic
143C2×C4×C61C22⋊Q811yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61C2×D811yescharacteristic
146C2×C4×C61C2×SD1611yescharacteristic
147C2×C4×C61C2×Q1611yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—22no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—81no—
160C2×Dic61—81no—
161C2×Dic61—81no—
162D244—22no—
163D244—22no—
164D244—22no—
165D244#10714yescomplemented
166C4×D61—42no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—42no—
170C4×D61—88no—
171C8×C61—42no—
172C8×C61—81no—
173#92418—42no—
174#8890—611nomaximal, Sylow
175C22×C61#38511yescharacteristic
176C22×C61#44711yescharacteristic
177C22×C61#44911yescharacteristic
178C22×C61#45011yescharacteristic
179C22×C61#45111yescharacteristic
180C22×C61#45411yescharacteristic
181C22×C61#45511yescharacteristic
182C2×D61—24no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—42no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—42no—
192C4×C61—81no—
193C4×C61C2×#10711yescharacteristic
194C4×C61#42811yescharacteristic
195C4×C61C4×SD1611yescharacteristic
196C4×C61#44211yescharacteristic
197C4×C61#47611yescharacteristic
198C4×C61#47811yescharacteristic
199C4×C61#48011yescharacteristic
200C4×C61#48411yescharacteristic
201Dic61—42no—
202Dic61—82no—
203Dic61—161no—
204D4×C4⋊C4—611no—
205#1947—611no—
206#1834—611no—
207#1802—611no—
208C2×D4⋊C8—611no—
209#1296—611no—
210#1279D6111yescharacteristic, complemented
211C2×C61#162511yescharacteristic
212C2×C61#163711yescharacteristic
213C2×C61#163911yescharacteristic
214C2×C61#164411yescharacteristic
215C2×C61#185211yescharacteristic
216C2×C61#186011yescharacteristic
217C2×C61#186411yescharacteristic
218D61—44no—
219C2×C4×D4—611no—
220C2×C4×D4—1221no—
221C22×C4⋊C4—1221no—
222C2×#107—1221no—
223C2×C4⋊C8—611no—
224C2×C4⋊C8C2×D6111yescharacteristic
225C2×#102—1221no—
226C2×C4×C8C2×D6111yescharacteristic
227#389—1221no—
228#385—1222no—
229#384—611no—
230#384—611no—
231#380—1221no—
232C4×C4⋊C4C2×D6111yescharacteristic
233#340—1221no—
234#340—1222no—
235#340—1221no—
236D4⋊C8—614no—
237C61#889011yescharacteristic, complemented, Sylow
238C22×D4—611no—
239C23×C4—1222no—
240C23×C4—1221no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—1221no—
244C4×D4—612no—
245C4×D4—612no—
246C4×D4—1221no—
247C4×D4—1221no—
248C4×D4—2442no—
249C4×D4—2442no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—612no—
252C2×C4⋊C4—1222no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—2442no—
259C2×C4⋊C4—2442no—
260C2×C4⋊C4D24411yescharacteristic
261C2×C4⋊C4D24411yescharacteristic
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1222no—
264C2×C42—21no—
265C2×C42C22×D6111yescharacteristic
266#107—2442no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—612no—
270C4⋊C8—1221no—
271#102—2442no—
272C4×C8—21no—
273C4×C8C4×D6112yescomplemented
274#95—21no—
275#95—1222no—
276C24—1221no—
277C2×D4—612no—
278C2×D4—612no—
279C2×D4—612no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—1221no—
286C22×C4—1222no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—4882no—
290C22×C4—2444no—
291C22×C4—2444no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4C2×D24411yescharacteristic
298C22×C4D4×D6111yescharacteristic
299C22×C4D4×D6111yescharacteristic
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—1222no—
307C2×C8—2441no—
308C2×C8—2441no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—612no—
313C4⋊C4—1221no—
314C4⋊C4—2442no—
315C4⋊C4—2442no—
316C4⋊C4—2444no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C4⋊C4#1175819012yes—
326C22⋊C4—1222no—
327C22⋊C4—1222no—
328C22⋊C4—2444no—
329C42—41no—
330C42—41no—
331C42C2×C4×D6111yescharacteristic
332C42#1175822211yescharacteristic
333C42#1175822411yescharacteristic
334C42Q8×D6111yescharacteristic
335C23—1222no—
336C23—1222no—
337C23—1222no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23—2441no—
342C23#1451974711yescharacteristic
343D4—614no—
344D4—1222no—
345D4—1222no—
346D4—1222no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—1222no—
356C2×C4—4888no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2442no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4C4⋊C4×D6111yescharacteristic
370C2×C4#1451973711yescharacteristic
371C2×C4C4×D24411yescharacteristic
372C2×C4#1451975511yescharacteristic
373C2×C4#1451975711yescharacteristic
374C2×C4#1451975911yescharacteristic
375C2×C4D8×D6111yescharacteristic
376C2×C4C2×#1175819011yescharacteristic
377C2×C4Q16×D6111yescharacteristic
378C2×C4#1451979911yescharacteristic
379C2×C4#1451980411yescharacteristic
380C2×C4#1451980511yescharacteristic
381C2×C4#1451980511yescharacteristic
382C2×C4#1451980611yescharacteristic
383C8—42no—
384C8—81no—
385C8—2442no—
386C22—1224no—
387C22—2442no—
388C22—2442no—
389C22—2442no—
390C22—2442no—
391C22—2442no—
392C22—2442no—
393C22#1683963611yescharacteristic
394C22#1683989711yescharacteristic
395C22#1683990911yescharacteristic
396C22#1683991511yescharacteristic
397C22#1683991911yescharacteristic
398C22#1683993611yescharacteristic
399C22#1683994111yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—81no—
404C4—9761no—
405C4—4882no—
406C4—2442no—
407C4#107×D6111yescharacteristic
408C4#1683980111yescharacteristic
409C4C4×#1175819011yescharacteristic
410C4#1683987511yescharacteristic
411C4#1684005311yescharacteristic
412C4#1684006311yescharacteristic
413C4#1684007411yescharacteristic
414C4#1684009611yescharacteristic
415C2—2444no—
416C2#2144491111yescharacteristic
417C2#2144498611yescharacteristic
418C2#2144500111yescharacteristic
419C2#2144503511yescharacteristic
420C2#2144600811yescharacteristic
421C2#2144605311yescharacteristic
422C2#2144608311yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61#120
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#8890
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #21446577C2semidirect
3. #21445947C2semidirect
6. #21443703C2semidirect
7. C61×#1279C2semidirect
22. #16839491C4semidirect
50. C4⋊#92418C2×C4semidirect
62. C4×C8×C61C2×C4semidirect
165. D244#107semidirect
210. #1279D61semidirect
237. C61#8890semidirect
273. C4×C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D2442
#214465772
#214459472
#214458202
C2×#168394912
#214437032
C61×#12792
#889061