Finite Group Databasebeta

← #29574643

Subgroups — #29574643

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454937C211yesmaximal, characteristic
2C4×#14519810C211yesmaximal, characteristic
3#21446754C211yesmaximal, characteristic, complemented
4#21444215C211yesmaximal, characteristic, complemented
5#21444199C211yesmaximal, characteristic
6#21443657C211yesmaximal, characteristic, complemented
7C61×#1283C211yesmaximal, characteristic, complemented
8C2×#14519810C411yescharacteristic
9C4×#11758222C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16839889—21no—
12#16839870—21no—
13#16839864—21no—
14C4×Dic244—21no—
15C4×#11758190—21no—
16#16839839—21no—
17#16839833—22no—
18#16839818—21no—
19#16839815C2211yescharacteristic
20#16839804C411yescharacteristic
21#16839784—21no—
22#16839772C411yescharacteristic
23#16839764C411yescharacteristic
24C2×C4×#92418C2211yescharacteristic
25#16839516—22no—
26#16839494—21no—
27#16839494—21no—
28#16839492—21no—
29#16839489—21no—
30C61×#431C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C4×M16×C61C2211yescharacteristic
33C2×#11758222C2×C411yescharacteristic
34C22×Dic122C2×C411yescharacteristic
35#14519810—22no—
36#14519810—22no—
37C2×Dic244—21no—
38C2×#11758190—21no—
39C2×#11758189—22no—
40C22×#92418—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C4×Dic122D411yescharacteristic
46C4×Dic122D411yescharacteristic
47C4×D244D411yescharacteristic
48C4×D244D411yescharacteristic
49C4×C22⋊D61—21no—
50C4×C22⋊D61—21no—
51#14519736C2×C411yescharacteristic
52#14519734—21no—
53C2×C4⋊Dic61C2×C411yescharacteristic
54C2×#11758196—21no—
55C2×C4×Dic61—21no—
56C42×D61—21no—
57#14519711—21no—
58#14519709—21no—
59C4⋊#92418D411yescharacteristic
60C4⋊#92418D411yescharacteristic
61#14519706—22no—
62#14519702—21no—
63#14519702—21no—
64#14519702—21no—
65#14519699—21no—
66C22⋊#92418—21no—
67#14519689—22no—
68#14519687—22no—
69C4×#92418—21no—
70C4×#92418—21no—
71C4×#92418—21no—
72C2×M16×C61C2×C411yescharacteristic
73C2×M16×C61C2×C411yescharacteristic
74C22×C8×C61D412yes—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80#97×C61—21no—
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61#4111yescharacteristic
86C2×C22⋊D61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89#11758222—21no—
90#11758222—21no—
91#11758222—21no—
92#11758222—21no—
93C2×D244C22⋊C411yescharacteristic
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×Dic122—21no—
98C2×Dic122—21no—
99C2×Dic122—21no—
100C2×Dic122—21no—
101C2×Dic122—21no—
102C2×Dic122C22⋊C411yescharacteristic
103C2×Dic122M1612yescomplemented
104M16×C61—21no—
105M16×C61—21no—
106M16×C61—21no—
107M16×C61M1612yescomplemented
108C2×C8×C61—21no—
109C2×C8×C61—21no—
110C2×C8×C61—22no—
111C2×C8×C61—42no—
112C2×C8×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C22⋊Dic61—21no—
118#11758198—21no—
119#11758198—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61C22⋊C411yescharacteristic
123C4⋊Dic61C22⋊C411yescharacteristic
124#11758196—21no—
125#11758196—21no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—41no—
132C4×Dic61—41no—
133C2×#92418—22no—
134C2×#92418—21no—
135C2×#92418—21no—
136C2×#92418—41no—
137C2×#92418—41no—
138Dic244—24no—
139#11758190—24no—
140#11758189—82no—
141C23×C61C4×D411yescharacteristic
142C22×D61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61C2×M1611yescharacteristic
153C2×C4×C61C2×M1611yescharacteristic
154C2×C4×C61#13111yescharacteristic
155C2×C4×C61#13111yescharacteristic
156C22⋊D61—41no—
157C22⋊D61—41no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—22no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—42no—
165C2×Dic61—41no—
166D244—21no—
167D244—21no—
168C4×D61—41no—
169C4×D61—41no—
170C4×D61—41no—
171C4×D61—41no—
172C4×D61—81no—
173Dic122—22no—
174Dic122—21no—
175Dic122—21no—
176Dic122—22no—
177Dic122—41no—
178Dic122—41no—
179C8×C61—22no—
180C8×C61—41no—
181C8×C61—42no—
182C8×C61—81no—
183#92418—42no—
184#92418—41no—
185#92418—41no—
186#8955—611nomaximal, Sylow
187C22×C61—21no—
188C22×C61—21no—
189C22×C61#38611yescharacteristic
190C22×C61#43511yescharacteristic
191C22×C61#43611yescharacteristic
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C4×C61—21no—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61#40711yescharacteristic
199C4×C61#40811yescharacteristic
200C4×C61#43511yescharacteristic
201C4×C61#43611yescharacteristic
202C4×C61#45511yescharacteristic
203C4×C61#45611yescharacteristic
204Dic61—42no—
205Dic61—41no—
206Dic61—41no—
207Dic61—41no—
208Dic61—81no—
209#2989—611no—
210C4×#137—611no—
211#1984—611no—
212#1479—611no—
213#1476—611no—
214#1283D6111yescharacteristic, complemented
215#1278—611no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61#187011yescharacteristic
219C2×C61#188111yescharacteristic
220C2×C61#188211yescharacteristic
221D61—81no—
222C2×#137—611no—
223C4×#41—611no—
224C2×C4×Q8—611no—
225#446—1221no—
226#441—1221no—
227#440—1221no—
228C4×Q16—1221no—
229C4×SD16—1221no—
230#436—1221no—
231#435—1222no—
232#432—1221no—
233#431—611no—
234#431C2×D6111yescharacteristic
235#428—611no—
236#423—1221no—
237C2×C4⋊C8C2×D6111yescharacteristic
238#419—611no—
239#417—611no—
240C4×M16C2×D6111yescharacteristic
241C2×C4×C8—611no—
242#336—1222no—
243Q8⋊C8—1221no—
244Q8⋊C8—1221no—
245Q8⋊C8—1221no—
246D4⋊C8—1221no—
247C61#895511yescharacteristic, complemented, Sylow
248C2×#41—611no—
249C22×Q8—611no—
250#137—1222no—
251#137—1222no—
252C2×Q16—1221no—
253C2×SD16—1221no—
254C2×M16—1222no—
255C2×M16C4×D6111yescharacteristic
256C2×M16C4×D6111yescharacteristic
257C22×C8—1221no—
258C22×C8D24412yes—
259C4×Q8—611no—
260C4×Q8—611no—
261C4×Q8—1221no—
262C4×Q8—1221no—
263C4×Q8—1221no—
264C4×Q8—1221no—
265C4×D4—611no—
266C4×D4—611no—
267C4×D4—1221no—
268C4×D4—1221no—
269#117—611no—
270#117—1221no—
271C2×C4⋊C4—611no—
272C2×C4⋊C4—1221no—
273C2×C42—1221no—
274C2×C42—1221no—
275C2×C42C22×D6111yescharacteristic
276#107—1221no—
277#106—1221no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—611no—
282C4⋊C8—611no—
283C4⋊C8—1222no—
284#103—1221no—
285#103—1221no—
286#103—1221no—
287#102—1221no—
288C22⋊C8—21no—
289C22⋊C8—1222no—
290C22⋊C8—1221no—
291#97—21no—
292#97—1222no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—1221no—
296C4×C8—1221no—
297C4×C8—1221no—
298#41—1221no—
299#41—1221no—
300#41—1221no—
301#41—1221no—
302C2×Q8—611no—
303C2×Q8—612no—
304C2×Q8—1221no—
305C2×Q8—1221no—
306C2×Q8—1221no—
307C2×Q8—1221no—
308C2×Q8—1221no—
309C2×D4—611no—
310C2×D4—1221no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4C2×C4×D6111yescharacteristic
317C22×C4C2×D24411yescharacteristic
318C22×C4#1175822211yescharacteristic
319Q16—1224no—
320SD16—1224no—
321M16—21no—
322M16—21no—
323M16—21no—
324M16—4882no—
325M16#1175818912yescomplemented
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—42no—
330C2×C8—41no—
331C2×C8—1222no—
332C2×C8—1221no—
333C2×C8—1221no—
334C2×C8—2441no—
335C2×C8—2441no—
336C4⋊C4—611no—
337C4⋊C4—611no—
338C4⋊C4—1221no—
339C4⋊C4—1221no—
340C4⋊C4—1221no—
341C4⋊C4—1221no—
342C4⋊C4—2441no—
343C4⋊C4—2441no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C42—1221no—
348C42—1221no—
349C42—1221no—
350C42—2441no—
351C42—2441no—
352C42D4×D6111yescharacteristic
353C42D4×D6111yescharacteristic
354C42D4×D6111yescharacteristic
355C42#1175822611yescharacteristic
356C23—1221no—
357C23C4×D24411yescharacteristic
358Q8—1222no—
359Q8—1221no—
360Q8—1221no—
361Q8—1222no—
362Q8—2441no—
363Q8—2441no—
364D4—1221no—
365D4—1221no—
366D4—2441no—
367D4—2441no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—1222no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—4881no—
376C2×C4—2442no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4C22⋊C4×D6111yescharacteristic
385C2×C4#1451973911yescharacteristic
386C2×C4#1451974711yescharacteristic
387C2×C4#1451975011yescharacteristic
388C2×C4#1451975211yescharacteristic
389C2×C4#1451976211yescharacteristic
390C2×C4M16×D6111yescharacteristic
391C2×C4C2×#1175818911yescharacteristic
392C2×C4#1451978311yescharacteristic
393C2×C4#1451978511yescharacteristic
394C8—22no—
395C8—42no—
396C8—41no—
397C8—81no—
398C8—2442no—
399C8—2441no—
400C8—2441no—
401C22—21no—
402C22—21no—
403C22—2441no—
404C22—2441no—
405C22—2441no—
406C22#1683964011yescharacteristic
407C22#1683983511yescharacteristic
408C22#1683984111yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—4881no—
413C4—2441no—
414C4—2441no—
415C4—2441no—
416C4—2442no—
417C4#1683972411yescharacteristic
418C4#1683972711yescharacteristic
419C4#1683983211yescharacteristic
420C4#1683983911yescharacteristic
421C4#1683994211yescharacteristic
422C4#1683994711yescharacteristic
423C2—21no—
424C2—21no—
425C2—4881no—
426C2#2144611511yescharacteristic
427C2#2144618011yescharacteristic
428C2#2144618711yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1283C2
socleC22×C61#386
prime radicalC2×#11758222C2×C4
cosocleC2×C42×C61C23
hypercenter#1283D61
hypocenterC61#8955
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
3. #21446754C2semidirect
4. #21444215C2semidirect
6. #21443657C2semidirect
7. C61×#1283C2semidirect
103. C2×Dic122M16semidirect
107. M16×C61M16semidirect
214. #1283D61semidirect
247. C61#8955semidirect
325. M16#11758189semidirect

Maximal subgroups

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

subgroupindex
#214549372
C4×#145198102
#214467542
#214442152
#214441992
#214436572
C61×#12832
#895561