Finite Group Databasebeta

← #29658787

Subgroups — #29658787

Order 15616.

1192 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic122C211yesmaximal, characteristic, complemented
2#21456937C211yesmaximal, characteristic, complemented
3#21455287C211yesmaximal, characteristic, complemented
4#21445067C214yesmaximal, complemented
5#21444921C214yesmaximal, complemented
6#21444490C211yesmaximal, characteristic, complemented
7#21444244C211yesmaximal, characteristic, complemented
8#21444213C211yesmaximal, characteristic, complemented
9C61×#3100C211yesmaximal, characteristic
10C23×Dic122—21no—
11C2×#14519807—21no—
12D4×Dic122—22no—
13D4×Dic122—22no—
14D4×Dic122—22no—
15D4×Dic122C2214yes—
16C2×#14519777C2211yescharacteristic
17C2×#14519776—21no—
18C2×#14519756—21no—
19C2×#14519754—22no—
20C2×C4×Dic122C2211yescharacteristic
21C2×D4×Dic61—21no—
22#16840165C2212yescomplemented
23#16840108C2212yescomplemented
24#16840073—22no—
25#16840042—22no—
26#16839981—22no—
27#16839969C2212yescomplemented
28#16839959C2212yescomplemented
29#16839815C2211yescharacteristic
30#16839786C2211yescharacteristic
31#16839763—21no—
32#16839507C2214yescomplemented
33#16839492C2214yescomplemented
34D4⋊#92418C2214yes—
35C61×#532C2211yescharacteristic
36C2×C4×D4×C61C2211yescharacteristic
37C61×#480—21no—
38C61×#474C2212yes—
39C61×#459C2212yes—
40C61×#447—21no—
41C4×D8×C61—22no—
42C61×#431C2211yescharacteristic
43C22×Dic122—22no—
44C22×Dic122—24no—
45C22×Dic122—21no—
46C22×Dic122—24no—
47C22×Dic122—44no—
48C22×Dic122—44no—
49C22×Dic122D411yescharacteristic
50C23×Dic61—22no—
51#14519807—44no—
52C2×#11758202—22no—
53C2×#11758200—22no—
54C2×#11758194—21no—
55#14519777—21no—
56#14519777—21no—
57#14519777D412yes—
58#14519777C2312yes—
59#14519776—24no—
60#14519776—24no—
61#14519756—24no—
62#14519756—24no—
63#14519754—28no—
64#14519754—28no—
65C4×Dic122—21no—
66C4×Dic122—21no—
67C4×Dic122D412yes—
68C4×Dic122C2312yes—
69D4×Dic61—24no—
70D4×Dic61—24no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D411yescharacteristic
73C2×C4⋊Dic61D412yes—
74C2×#11758196—22no—
75C2×#11758196—21no—
76C2×C22⋊Dic61—22no—
77C2×C4×Dic61—21no—
78#14519710—24no—
79C4⋊#92418—21no—
80C4⋊#92418—21no—
81C4⋊#92418C2312yes—
82#14519701—22no—
83#14519698—22no—
84#14519698—24no—
85C22⋊#92418—21no—
86C4×#92418C2312yes—
87C2×#41×C61—21no—
88C22×D4×C61D411yescharacteristic
89C23×C4×C61—21no—
90C2×D8×C61—22no—
91C4⋊Q8×C61C2311yescharacteristic
92#127×C61C2311yescharacteristic
93#124×C61—21no—
94#121×C61—21no—
95#121×C61—21no—
96C4×D4×C61—21no—
97C4×D4×C61—21no—
98C4×D4×C61—21no—
99C4×D4×C61—21no—
100C4×D4×C61D412yes—
101C4×D4×C61C2312yes—
102C2×C4⋊C4×C61D411yescharacteristic
103C2×C22⋊C4×C61—21no—
104C2×C42×C61C2311yescharacteristic
105#107×C61—22no—
106C4⋊C8×C61C2312yes—
107#102×C61—22no—
108#102×C61—22no—
109C22⋊C8×C61—21no—
110C4×C8×C61—21no—
111C24×C61—21no—
112#41×C61—42no—
113#41×C61—42no—
114C2×Q8×C61—21no—
115C2×D4×C61—24no—
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61—41no—
121C2×D4×C61C2×D412yes—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—42no—
126C22×C4×C61—42no—
127C22×C4×C61—41no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—28no—
133C22×Dic61—22no—
134C22×Dic61—21no—
135C22×Dic61—48no—
136C2×Dic122—21no—
137C2×Dic122—22no—
138C2×Dic122—28no—
139C2×Dic122—22no—
140C2×Dic122—22no—
141C2×Dic122—48no—
142C2×Dic122—416no—
143C2×Dic122—48no—
144C2×Dic122—42no—
145C2×Dic122—42no—
146C2×Dic122—48no—
147C2×Dic122D814yescomplemented
148C2×Dic122C2×D412yes—
149D8×C61—44no—
150C2×C8×C61—22no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61C2×D412yes—
155C22⋊C4×C61—22no—
156C22⋊C4×C61—22no—
157C22⋊C4×C61—41no—
158C22⋊C4×C61—41no—
159C42×C61C2×D411yescharacteristic
160C42×C61C2×D411yescharacteristic
161C42×C61C2×D411yescharacteristic
162C42×C61C2411yescharacteristic
163C22⋊Dic61—28no—
164#11758202—44no—
165#11758200—44no—
166C4⋊Dic61—22no—
167C4⋊Dic61—21no—
168C4⋊Dic61—22no—
169C4⋊Dic61—22no—
170C4⋊Dic61C2×D412yes—
171C4⋊Dic61C2×D414yes—
172#11758196—28no—
173#11758196—22no—
174#11758196—22no—
175C4×Dic61—22no—
176C4×Dic61—22no—
177#11758194—42no—
178C2×#92418—22no—
179C2×#92418—22no—
180C23×C61—24no—
181C23×C61—22no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—41no—
185C23×C61#12011yescharacteristic
186Q8×C61—41no—
187Q8×C61—41no—
188D4×C61—24no—
189D4×C61—22no—
190D4×C61—42no—
191D4×C61—41no—
192D4×C61—41no—
193D4×C61—42no—
194D4×C61—82no—
195D4×C61#13714yescomplemented
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—41no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61—44no—
203C2×C4×C61—41no—
204C2×C4×C61—82no—
205C2×C4×C61#12011yescharacteristic
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61#12011yescharacteristic
208C2×C4×C61C2×D812yes—
209C2×C4×C61AGL(1,ℤ/8)12yes—
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C22×D411yescharacteristic
213C2×Dic61—22no—
214C2×Dic61—24no—
215C2×Dic61—22no—
216C2×Dic61—24no—
217C2×Dic61—416no—
218C2×Dic61—42no—
219C2×Dic61—44no—
220Dic122—22no—
221Dic122—24no—
222Dic122—416no—
223Dic122—42no—
224Dic122—42no—
225Dic122—44no—
226Dic122C2×D814yes—
227C8×C61—42no—
228#92418—42no—
229#92418—42no—
230#18776—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—24no—
234C22×C61—48no—
235C22×C61—42no—
236C22×C61—42no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61#44712yes—
241C22×C61C2×#12011yescharacteristic
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—42no—
246C4×C61—81no—
247C4×C61#44712yes—
248C4×C61C22×D811yescharacteristic
249C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
250C4×C61C2×#13712yes—
251Dic61—24no—
252Dic61—44no—
253Dic61—42no—
254C2×D4×Q8—611no—
255#3226—611no—
256#3100D6111yescharacteristic
257#3037—611no—
258#1649—614no—
259#1627—614no—
260#1546—611no—
261#1486—611no—
262#1479—611no—
263C2×C61—22no—
264C2×C61—44no—
265C2×C61—161no—
266C2×C61C2×#44711yescharacteristic
267C2×C61#300411yescharacteristic
268C2×C61#302011yescharacteristic
269C23×Q8—1221no—
270C2×#137—1221no—
271D4×Q8—614no—
272D4×Q8—1222no—
273D4×Q8—1222no—
274D4×Q8—1222no—
275#532C2×D6111yescharacteristic
276C2×C4⋊Q8—611no—
277C2×C4⋊Q8—1221no—
278C2×C22⋊Q8—1222no—
279C2×C22⋊Q8—1221no—
280C2×C4×Q8—611no—
281C2×C4×D4—1221no—
282C2×C4×D4C2×D6111yescharacteristic
283#500—612no—
284#486—612no—
285#480—21no—
286#480—1222no—
287#474—1222no—
288#474C2×D6112yes—
289#464—1222no—
290#462—612no—
291#460—612no—
292#459C2×D6112yes—
293#447—21no—
294C4×D8—22no—
295#431—611no—
296#431C2×D6111yescharacteristic
297#423—611no—
298#417—1221no—
299#332—614no—
300Q8⋊C8—614no—
301D4⋊C8—614no—
302C61#1877611yescharacteristic, complemented, Sylow
303C2×#41—21no—
304C22×Q8—611no—
305C22×Q8—1224no—
306C22×Q8—1222no—
307C22×Q8—1224no—
308C22×Q8—1221no—
309C22×Q8—2444no—
310C22×Q8—2444no—
311C22×D4C22⋊D6111yescharacteristic
312C23×C4—21no—
313C23×C4—1222no—
314#137—2444no—
315C2×Q16—1222no—
316C2×SD16—1222no—
317C2×D8—22no—
318C2×M16—1221no—
319C4⋊Q8—612no—
320C4⋊Q8—612no—
321C4⋊Q8—1224no—
322C4⋊Q8—1224no—
323C4⋊Q8—1221no—
324C4⋊Q8—1221no—
325C4⋊Q8C22×D6111yescharacteristic
326#127C22×D6111yescharacteristic
327#124—21no—
328C22⋊Q8—1228no—
329C22⋊Q8—1228no—
330C22⋊Q8—1224no—
331C22⋊Q8—1224no—
332#121—21no—
333#121—21no—
334C4×Q8—612no—
335C4×Q8—612no—
336C4×Q8—1221no—
337C4×Q8—1221no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—1224no—
343C4×D4—1224no—
344C4×D4C22⋊D6112yes—
345C4×D4C22×D6112yes—
346C2×C4⋊C4—611no—
347C2×C4⋊C4—612no—
348C2×C4⋊C4—1222no—
349C2×C4⋊C4—1221no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4C22⋊D6111yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—1222no—
354C2×C42—1221no—
355C2×C42C22×D6111yescharacteristic
356#107—22no—
357#107—1224no—
358C4⋊C8—612no—
359C4⋊C8—1221no—
360C4⋊C8—1221no—
361C4⋊C8C22×D6112yes—
362#103—1222no—
363#102—22no—
364#102—22no—
365#102—1222no—
366#102—1224no—
367C22⋊C8—21no—
368C22⋊C8—1221no—
369C4×C8—21no—
370C4×C8—612no—
371C24—21no—
372#41—42no—
373#41—42no—
374C2×Q8—21no—
375C2×Q8—612no—
376C2×Q8—614no—
377C2×Q8—1228no—
378C2×Q8—1222no—
379C2×Q8—1221no—
380C2×Q8—1222no—
381C2×Q8—1222no—
382C2×Q8—2448no—
383C2×Q8—2448no—
384C2×Q8—2448no—
385C2×Q8—24416no—
386C2×Q8—2442no—
387C2×Q8—2442no—
388C2×D4—24no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4C2×C22⋊D6112yes—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—41no—
401C22×C4—1221no—
402C22×C4—1228no—
403C22×C4—1221no—
404C22×C4—1222no—
405C22×C4—2448no—
406C22×C4D4×D6111yescharacteristic
407C22×C4D4×D6111yescharacteristic
408C22×C4C2×C22⋊D6111yescharacteristic
409Q16—2444no—
410SD16—2444no—
411D8—44no—
412M16—2442no—
413C2×C8—22no—
414C2×C8—1222no—
415C2×C8—1222no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—612no—
420C4⋊C4—614no—
421C4⋊C4—1228no—
422C4⋊C4—1222no—
423C4⋊C4—1222no—
424C4⋊C4—1221no—
425C4⋊C4—1222no—
426C4⋊C4—1222no—
427C4⋊C4—1222no—
428C4⋊C4C2×C22⋊D6112yes—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—1228no—
434C42—1222no—
435C42—1222no—
436C42D4×D6111yescharacteristic
437C42D4×D6111yescharacteristic
438C42C2×C22⋊D6111yescharacteristic
439C42C23×D6111yescharacteristic
440C23—24no—
441C23—22no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23#1451974511yescharacteristic
446Q8—41no—
447Q8—41no—
448Q8—614no—
449Q8—1222no—
450Q8—1224no—
451Q8—24416no—
452Q8—2442no—
453Q8—2442no—
454Q8—2444no—
455D4—24no—
456D4—22no—
457D4—42no—
458D4—41no—
459D4—41no—
460D4—42no—
461D4—82no—
462D4#1451980714yescomplemented
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—1222no—
473C2×C4—1224no—
474C2×C4—1222no—
475C2×C4—1224no—
476C2×C4—24416no—
477C2×C4—2442no—
478C2×C4—2444no—
479C2×C4#1451974511yescharacteristic
480C2×C4#1451974511yescharacteristic
481C2×C4#1451974511yescharacteristic
482C2×C4D8×D6112yes—
483C2×C4#1451980112yes—
484C2×C4C2×D4×D6111yescharacteristic
485C2×C4C2×D4×D6111yescharacteristic
486C2×C4C22×C22⋊D6111yescharacteristic
487C8—42no—
488C8—2442no—
489C8—2442no—
490C22—21no—
491C22—21no—
492C22—24no—
493C22—48no—
494C22—42no—
495C22—42no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22#1683989412yes—
500C22C2×#1451974511yescharacteristic
501C4—21no—
502C4—21no—
503C4—21no—
504C4—42no—
505C4—81no—
506C4—1224no—
507C4—2442no—
508C4—2444no—
509C4#1683989412yes—
510C4C2×D8×D6111yescharacteristic
511C4C2×#1451980111yescharacteristic
512C4C2×#1451980712yes—
513C2—22no—
514C2—44no—
515C2—161no—
516C2C2×#1683989411yescharacteristic
517C2#2145505211yescharacteristic
518C2#2145518111yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3100C2
socleC22×C61C2×#120
hypercenter#3100D61
hypocenterC61#18776
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic122C2semidirect
2. #21456937C2semidirect
3. #21455287C2semidirect
4. #21445067C2semidirect
5. #21444921C2semidirect
6. #21444490C2semidirect
7. #21444244C2semidirect
8. #21444213C2semidirect
22. #16840165C22semidirect
23. #16840108C22semidirect
27. #16839969C22semidirect
28. #16839959C22semidirect
32. #16839507C22semidirect
33. #16839492C22semidirect
147. C2×Dic122D8semidirect
195. D4×C61#137semidirect
302. C61#18776semidirect
462. D4#14519807semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1222
#214569372
#214552872
#214450672
#214449212
#214444902
#214442442
#214442132
C61×#31002
#1877661