Finite Group Databasebeta

← #29595746

Subgroups — #29595746

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840579C211yesmaximal, characteristic
2C2×#16839579C211yesmaximal, characteristic, complemented
3C2×#16839570C211yesmaximal, characteristic, complemented
4#21447532C211yesmaximal, characteristic, complemented
5C2×#16839567C211yesmaximal, characteristic, complemented
6#21445883C211yesmaximal, characteristic, complemented
7C2×C61×#350C211yesmaximal, characteristic, complemented
8C2×#14519824—21no—
9#16840579—22no—
10#16840579—22no—
11#16840579—22no—
12#16840579C414yescomplemented
13C2×#14519810—22no—
14C2×#14519810—21no—
15C2×#14519799—21no—
16C2×#14519799C2211yescharacteristic
17C22×Dic244—21no—
18C22×Dic244C2211yescharacteristic
19C2×#14519713C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21#16839763—21no—
22#16839579—22no—
23#16839570—22no—
24#16839567—22no—
25#16839567—21no—
26#16839564—21no—
27#16839530—21no—
28C2×#131×C61C2211yescharacteristic
29C2×M32×C61C2211yescharacteristic
30C22×C16×C61C2211yescharacteristic
31C61×#350—22no—
32#14519824—24no—
33#14519824—24no—
34#14519824—42no—
35#14519824—42no—
36C2×#11758222—22no—
37C2×#11758222—21no—
38C2×#11758224—42no—
39C2×#11758224—41no—
40C22×Dic122—22no—
41C22×Dic122—21no—
42C2×Q8×D61—41no—
43#14519810—24no—
44#14519810—28no—
45#14519810—24no—
46#14519810—28no—
47#14519799—24no—
48#14519799—21no—
49#14519799—21no—
50#14519799—24no—
51#14519799C2×C412yes—
52#14519799D412yes—
53C2×Dic244—22no—
54C2×Dic244—24no—
55C2×Dic244—21no—
56C2×Dic244—21no—
57C2×Dic244—21no—
58C2×Dic244—24no—
59C2×Dic244C2×C412yes—
60C2×Dic244D411yescharacteristic
61C2×Dic244D412yes—
62C2×Dic244D412yes—
63C2×#11758190—22no—
64C2×#11758190—21no—
65C2×D488D411yescharacteristic
66C2×#11758194—21no—
67C2×C4⋊Dic61—21no—
68#14519713—21no—
69#14519713—21no—
70#14519711—21no—
71#14519711—21no—
72#14519701—41no—
73#14519698—41no—
74C2×#41×C61D411yescharacteristic
75#131×C61—21no—
76#131×C61—21no—
77#131×C61C2×C412yes—
78#131×C61D412yes—
79C2×M16×C61—21no—
80C2×M16×C61D411yescharacteristic
81C22×C8×C61—21no—
82C22×C8×C61C2311yescharacteristic
83M32×C61—21no—
84M32×C61—21no—
85C2×C16×C61—21no—
86C2×C16×C61—21no—
87C2×C16×C61—21no—
88C2×C16×C61—21no—
89#41×C61—21no—
90#41×C61—21no—
91#41×C61C22⋊C412yes—
92#41×C61SD1612yes—
93C2×Q8×C61D811yescharacteristic
94C2×D4×C61—21no—
95C2×D4×C61D811yescharacteristic
96C22×C4×C61—21no—
97C22×C4×C61C2×D411yescharacteristic
98C2×C22⋊D61—42no—
99C2×C22⋊D61—41no—
100C22×Dic61—42no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103Q8×D61—44no—
104Q8×D61—44no—
105#11758224—48no—
106#11758224—48no—
107#11758224—44no—
108#11758224—44no—
109#11758222—28no—
110#11758222—22no—
111#11758222—22no—
112#11758222—44no—
113#11758222—41no—
114#11758222—41no—
115C2×D244—21no—
116C2×C4×D61—42no—
117C2×C4×D61—41no—
118C2×Dic122—28no—
119C2×Dic122—22no—
120C2×Dic122—22no—
121C2×Dic122—21no—
122C2×Dic122—22no—
123C2×Dic122—42no—
124C2×Dic122—44no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127C2×Dic122—41no—
128M16×C61—21no—
129M16×C61—22no—
130M16×C61—22no—
131M16×C61C22⋊C412yes—
132C2×C8×C61—21no—
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C2×C8×C61C22×C411yescharacteristic
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2×D411yescharacteristic
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2×D411yescharacteristic
140C2×C8×C61C2×D411yescharacteristic
141C4⋊Dic61—41no—
142C4⋊Dic61—41no—
143#11758194—41no—
144#11758194—41no—
145C2×#92418—41no—
146Dic244—28no—
147Dic244—22no—
148Dic244—22no—
149Dic244—21no—
150Dic244—22no—
151Dic244C22⋊C414yes—
152Dic244C22⋊C412yes—
153D488—21no—
154D488C22⋊C412yes—
155#11758190—28no—
156#11758190—22no—
157#11758190—22no—
158C16×C61—41no—
159C16×C61—41no—
160C23×C61—21no—
161C23×C61AGL(1,ℤ/8)11yescharacteristic
162C22×D61—41no—
163Q8×C61—21no—
164Q8×C61#10212yes—
165D4×C61—22no—
166D4×C61—22no—
167D4×C61—21no—
168D4×C61#10212yes—
169C2×C4×C61—21no—
170C2×C4×C61—22no—
171C2×C4×C61—22no—
172C2×C4×C61C2×C22⋊C411yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12011yescharacteristic
175C2×C4×C61C2×D811yescharacteristic
176C2×C4×C61C2×SD1611yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
178C22⋊D61—48no—
179C22⋊D61—42no—
180C22⋊D61—42no—
181C2×Dic61—48no—
182C2×Dic61—42no—
183C2×Dic61—41no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—81no—
187C2×Dic61—161no—
188D244—22no—
189D244—41no—
190C4×D61—48no—
191C4×D61—42no—
192C4×D61—42no—
193Dic122—24no—
194Dic122—22no—
195Dic122—48no—
196Dic122—42no—
197Dic122—42no—
198Dic122—41no—
199Dic122—42no—
200C8×C61—22no—
201C8×C61C2×C22⋊C411yescharacteristic
202C8×C61C2×C22⋊C411yescharacteristic
203C8×C61#12011yescharacteristic
204C8×C61#12011yescharacteristic
205#92418—81no—
206#12749—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—22no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61#41811yescharacteristic
213C22×C61#44711yescharacteristic
214C22×C61#45011yescharacteristic
215C2×D61—42no—
216C2×D61—81no—
217C2×D61—81no—
218C4×C61—22no—
219C4×C61#37911yescharacteristic
220C4×C61C2×#10211yescharacteristic
221C4×C61#44711yescharacteristic
222C4×C61#45011yescharacteristic
223Dic61—42no—
224Dic61—44no—
225Dic61—161no—
226C2×#578—611no—
227C2×#362—611no—
228C2×#359—611no—
229#2139—611no—
230C2×#358—611no—
231C2×#350D6111yescharacteristic, complemented
232#1816—611no—
233C2×C61—21no—
234C2×C61—21no—
235C2×C61—42no—
236C2×C61#178611yescharacteristic
237C2×C61#219311yescharacteristic
238C2×C61#219511yescharacteristic
239D61—82no—
240C2×2−1+4—1221no—
241#578—614no—
242#578—1222no—
243#578—1222no—
244#578—1222no—
245C2×#137—1222no—
246C2×#137—1221no—
247C2×#135—611no—
248C2×#135—1221no—
249C22×Q16—611no—
250C22×Q16—1221no—
251C2×#131C2×D6111yescharacteristic
252C2×M32C2×D6111yescharacteristic
253C22×C16C2×D6111yescharacteristic
254C2×#108—611no—
255C2×#107—611no—
256#417—1221no—
257#362—1222no—
258#359—1222no—
259#358—1222no—
260#358—1221no—
261#357—1221no—
262#350—22no—
263#343—1221no—
264C61#1274911yescharacteristic, complemented, Sylow
2652−1+4—1224no—
2662−1+4—1224no—
2672−1+4—2442no—
2682−1+4—2442no—
269C2×#41—1222no—
270C2×#41—1221no—
271C2×#41—2442no—
272C2×#41—2441no—
273C2×#41D24411yescharacteristic
274C22×Q8—1222no—
275C22×Q8—1221no—
276C22×Q8—2441no—
277#137—1228no—
278#137—1224no—
279#137—1228no—
280#137—1224no—
281#135—612no—
282#135—612no—
283#135—1224no—
284#135—1224no—
285#135—1221no—
286#135—1221no—
287C2×Q16—612no—
288C2×Q16—612no—
289C2×Q16—612no—
290C2×Q16—611no—
291C2×Q16—1224no—
292C2×Q16—1222no—
293C2×Q16—1224no—
294C2×Q16—1221no—
295C2×Q16—1221no—
296C2×Q16—1221no—
297C2×SD16—1222no—
298C2×SD16—1221no—
299C2×D8—611no—
300#131—21no—
301#131—21no—
302#131C4×D6112yes—
303#131C22⋊D6112yes—
304C2×M16—21no—
305C2×M16—1221no—
306C2×M16D24411yescharacteristic
307C22×C8—21no—
308C22×C8C22×D6111yescharacteristic
309C2×C4⋊C4—1221no—
310M32—21no—
311M32—21no—
312C2×C16—21no—
313C2×C16—21no—
314C2×C16—21no—
315C2×C16—21no—
316#108—1221no—
317#108—1221no—
318#107—1221no—
319#107—1221no—
320#103—2441no—
321#102—2441no—
322#41—21no—
323#41—21no—
324#41—1228no—
325#41—1222no—
326#41—1222no—
327#41—2444no—
328#41—2448no—
329#41—2448no—
330#41—2444no—
331#41—2444no—
332#41—2441no—
333#41—2441no—
334#41#1175819012yes—
335#41#1175819812yes—
336C2×Q8—1228no—
337C2×Q8—1222no—
338C2×Q8—1222no—
339C2×Q8—1221no—
340C2×Q8—1222no—
341C2×Q8—2442no—
342C2×Q8—2444no—
343C2×Q8—2444no—
344C2×Q8—2444no—
345C2×Q8—2441no—
346C2×Q8—2441no—
347C2×Q8—2441no—
348C2×Q8D48811yescharacteristic
349C2×D4—21no—
350C2×D4—1221no—
351C2×D4—2442no—
352C2×D4—2441no—
353C2×D4D48811yescharacteristic
354C22×C4—21no—
355C22×C4—2442no—
356C22×C4—2441no—
357C22×C4—2442no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4C2×D24411yescharacteristic
361Q16—614no—
362Q16—612no—
363Q16—1228no—
364Q16—1222no—
365Q16—1222no—
366Q16—1221no—
367Q16—1222no—
368SD16—1228no—
369SD16—1222no—
370SD16—1222no—
371D8—612no—
372D8—1221no—
373M16—21no—
374M16—22no—
375M16—22no—
376M16—2441no—
377M16—2441no—
378M16#1175819812yes—
379C2×C8—21no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—2441no—
383C2×C8C2×C4×D6111yescharacteristic
384C2×C8D4×D6111yescharacteristic
385C2×C8D4×D6111yescharacteristic
386C2×C8D4×D6111yescharacteristic
387C2×C8D4×D6111yescharacteristic
388C2×C8C2×C22⋊D6111yescharacteristic
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C16—41no—
392C16—41no—
393C23—21no—
394C23—2441no—
395C23#1451980511yescharacteristic
396Q8—21no—
397Q8—1224no—
398Q8—1222no—
399Q8—2448no—
400Q8—2442no—
401Q8—2442no—
402Q8—2441no—
403Q8—2442no—
404Q8#1451969912yes—
405D4—22no—
406D4—22no—
407D4—21no—
408D4—1222no—
409D4—2448no—
410D4—2442no—
411D4—2442no—
412D4—2441no—
413D4#1451969912yes—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—9761no—
418C2×C4—4881no—
419C2×C4—2448no—
420C2×C4—2448no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2441no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4C2×#1175819811yescharacteristic
428C2×C4#1451974711yescharacteristic
429C2×C4#1451974711yescharacteristic
430C2×C4C2×D48811yescharacteristic
431C2×C4C2×#1175819011yescharacteristic
432C2×C4#1451980511yescharacteristic
433C8—22no—
434C8—4881no—
435C8C22⋊C4×D6111yescharacteristic
436C8C22⋊C4×D6111yescharacteristic
437C8#1451974511yescharacteristic
438C8#1451974511yescharacteristic
439C22—21no—
440C22—21no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22—4881no—
445C22—4881no—
446C22—2442no—
447C22#1683976811yescharacteristic
448C22#1683989811yescharacteristic
449C22#1683991511yescharacteristic
450C4—22no—
451C4—9761no—
452C4—2444no—
453C4—2442no—
454C4#1683961711yescharacteristic
455C4C2×#1451969911yescharacteristic
456C4#1683989811yescharacteristic
457C4#1683991511yescharacteristic
458C2—21no—
459C2—21no—
460C2—42no—
461C2—4882no—
462C2#2144575111yescharacteristic
463C2#2144778511yescharacteristic
464C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#350C2
socleC22×C61#447
prime radicalC2×#16840579C2
cosocleC22×C8×C61C23
hypercenterC2×#350D61
hypocenterC61#12749
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C2×#16839579C2semidirect
3. C2×#16839570C2semidirect
4. #21447532C2semidirect
5. C2×#16839567C2semidirect
6. #21445883C2semidirect
7. C2×C61×#350C2semidirect
12. #16840579C4semidirect
231. C2×#350D61semidirect
264. C61#12749semidirect

Maximal subgroups

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

subgroupindex
C2×#168405792
C2×#168395792
C2×#168395702
#214475322
C2×#168395672
#214458832
C2×C61×#3502
#1274961