Finite Group Databasebeta

← #29580748

Subgroups — #29580748

Order 15616.

622 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455815C211yesmaximal, characteristic
2#21450724C211yesmaximal, characteristic, complemented
3#21444379C211yesmaximal, characteristic, complemented
4#21444243C211yesmaximal, characteristic, complemented
5#21444214C211yesmaximal, characteristic, complemented
6#21443679C211yesmaximal, characteristic, complemented
7C61×#3037C211yesmaximal, characteristic, complemented
8C2×#14519753—21no—
9C2×C4×D244C2211yescharacteristic
10#16840073—21no—
11#16840039—21no—
12#16839954—21no—
13#16839895—21no—
14C4×#11758199—22no—
15#16839815C2211yescharacteristic
16#16839815C2211yescharacteristic
17#16839692—21no—
18#16839679—21no—
19#16839653—22no—
20#16839628C2211yescharacteristic
21#16839619—21no—
22#16839496—22no—
23Q8⋊#92418—22no—
24#16839489—22no—
25C2×#137×C61—21no—
26C61×#532C2211yescharacteristic
27C2×C4×Q8×C61C2211yescharacteristic
28C61×#464—22no—
29C61×#462—21no—
30C61×#460—21no—
31C61×#423C2211yescharacteristic
32C61×#417—21no—
33C22×D244D411yescharacteristic
34C22×C4×D61—21no—
35C2×#11758199—22no—
36#14519753—42no—
37#14519753—42no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—22no—
45C2×#11758198—22no—
46C2×#11758198—22no—
47C2×#11758198—21no—
48#14519710—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51#14519698—22no—
52#14519697—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C4×#92418—21no—
56C4×#92418D412yes—
57#14519684—22no—
58#14519684—21no—
59#14519684D412yes—
60C2×#41×C61—21no—
61C22×Q8×C61D411yescharacteristic
62#137×C61—42no—
63#137×C61—42no—
64C2×Q16×C61—22no—
65C2×SD16×C61—22no—
66C2×M16×C61—21no—
67C4⋊Q8×C61D411yescharacteristic
68#127×C61D411yescharacteristic
69#124×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72C4×Q8×C61—21no—
73C4×Q8×C61—21no—
74C4×Q8×C61—21no—
75C4×Q8×C61—21no—
76C4×D4×C61—21no—
77C4×D4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61D411yescharacteristic
80C2×C42×C61—21no—
81C2×C42×C61C2311yescharacteristic
82C4⋊C8×C61—21no—
83C4⋊C8×C61D412yes—
84#103×C61—22no—
85#102×C61—22no—
86C23×D61—21no—
87#41×C61—41no—
88#41×C61—41no—
89#41×C61—41no—
90#41×C61—41no—
91C2×Q8×C61—21no—
92C2×Q8×C61—21no—
93C2×Q8×C61—21no—
94C2×Q8×C61—21no—
95C2×Q8×C61—21no—
96C2×Q8×C61—21no—
97C2×Q8×C61D812yescomplemented
98C2×D4×C61—21no—
99C2×D4×C61—21no—
100C2×D4×C61—21no—
101C2×D4×C61—41no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—41no—
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×Dic61—21no—
109C22×Dic61—22no—
110C2×D244—21no—
111C2×D244—21no—
112C2×D244—42no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119Q16×C61—44no—
120SD16×C61—44no—
121M16×C61—41no—
122M16×C61—41no—
123C2×C8×C61—22no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C42×C61—41no—
133C42×C61—41no—
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138#11758199—44no—
139#11758198—44no—
140#11758198—44no—
141#11758198—41no—
142#11758198—41no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147#11758196—44no—
148C2×#92418—22no—
149C2×#92418—41no—
150C23×C61—41no—
151C23×C61#12011yescharacteristic
152C22×D61—22no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159Q8×C61—22no—
160Q8×C61—22no—
161Q8×C61—41no—
162Q8×C61—41no—
163Q8×C61—41no—
164Q8×C61—41no—
165D4×C61—42no—
166D4×C61—41no—
167D4×C61—41no—
168D4×C61—81no—
169D4×C61—81no—
170D4×C61—81no—
171C2×C4×C61—22no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—42no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—81no—
180C2×C4×C61—81no—
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61#12011yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12711yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61#13511yescharacteristic
189C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—42no—
196C2×Dic61—41no—
197D244—22no—
198D244—22no—
199D244—41no—
200D244—41no—
201C4×D61—81no—
202C4×D61—81no—
203C4×D61—81no—
204C4×D61—81no—
205C8×C61—42no—
206#92418—42no—
207#92418—81no—
208#9997—611nomaximal, Sylow
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61#39211yescharacteristic
215C22×C61#44711yescharacteristic
216C22×C61#44911yescharacteristic
217C2×D61—42no—
218C2×D61—42no—
219C2×D61—42no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61—81no—
223C2×D61—81no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—42no—
229C4×C61—81no—
230C4×C61—81no—
231C4×C61#44711yescharacteristic
232C4×C61#44911yescharacteristic
233C4×C61#46611yescharacteristic
234C4×C61#46911yescharacteristic
235Dic61—82no—
236Dic61—81no—
237#3100—611no—
238#3037D6111yescharacteristic, complemented
239#2536—611no—
240#1517—611no—
241#1486—611no—
242#1479—611no—
243#1286—611no—
244C2×C61—21no—
245C2×C61—21no—
246C2×C61—161no—
247C2×C61#199911yescharacteristic
248C2×C61#200911yescharacteristic
249C2×C61#201011yescharacteristic
250D61—82no—
251C2×#137—21no—
252#532C2×D6111yescharacteristic
253C2×C22⋊Q8—1221no—
254C2×C4×Q8C2×D6111yescharacteristic
255C2×C4×D4—611no—
256#480—1221no—
257#474—1221no—
258#464—22no—
259#462—21no—
260#460—21no—
261#459—1221no—
262#447—1221no—
263C4×D8—1222no—
264#431—611no—
265#431—611no—
266#423C2×D6111yescharacteristic
267#417—21no—
268#398—1221no—
269#394—1221no—
270#388—1222no—
271#382—611no—
272#380—1221no—
273#327—1222no—
274Q8⋊C8—1222no—
275D4⋊C8—1222no—
276C61#999711yescharacteristic, complemented, Sylow
277C2×#41—21no—
278C22×Q8C22⋊D6111yescharacteristic
279C22×D4—611no—
280C23×C4—1221no—
281#137—42no—
282#137—42no—
283C2×Q16—22no—
284C2×SD16—22no—
285C2×D8—1222no—
286C2×M16—21no—
287C4⋊Q8C22⋊D6111yescharacteristic
288#127C22⋊D6111yescharacteristic
289#124—21no—
290C22⋊Q8—2442no—
291C22⋊Q8—2442no—
292#121—21no—
293#121—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—1221no—
301C4×D4—1221no—
302C4×D4—1221no—
303C4×D4—1221no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—1222no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4C22⋊D6111yescharacteristic
309C2×C22⋊C4—1222no—
310C2×C22⋊C4—1222no—
311C2×C22⋊C4—1221no—
312C2×C42—21no—
313C2×C42C22×D6111yescharacteristic
314#107—1222no—
315C4⋊C8—21no—
316C4⋊C8—1221no—
317C4⋊C8—1221no—
318C4⋊C8C22⋊D6112yes—
319#103—22no—
320#102—22no—
321#102—1222no—
322#102—1222no—
323C22⋊C8—1221no—
324C22⋊C8—1221no—
325C4×C8—612no—
326C4×C8—1221no—
327#95—612no—
328#95—1222no—
329#95—1221no—
330C24—1221no—
331#41—41no—
332#41—41no—
333#41—41no—
334#41—41no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8#1175819912yescomplemented
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—41no—
346C2×D4—1221no—
347C2×D4—1221no—
348C2×D4—2442no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—1222no—
353C22×C4—1221no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4D4×D6111yescharacteristic
361C22×C4D4×D6111yescharacteristic
362C22×C4C2×C22⋊D6111yescharacteristic
363Q16—44no—
364SD16—44no—
365D8—2444no—
366M16—41no—
367M16—41no—
368C2×C8—22no—
369C2×C8—1222no—
370C2×C8—2441no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—2444no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—2444no—
385C22⋊C4—2444no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C42—41no—
389C42—41no—
390C42D4×D6111yescharacteristic
391C42#1175822411yescharacteristic
392C42C2×C22⋊D6111yescharacteristic
393C42C2×C22⋊D6111yescharacteristic
394C23—41no—
395C23—1222no—
396C23—2441no—
397C23—2441no—
398C23—2441no—
399C23—2441no—
400C23—2441no—
401C23—2441no—
402C23#1451974511yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409D4—42no—
410D4—41no—
411D4—41no—
412D4—81no—
413D4—81no—
414D4—81no—
415D4—1222no—
416D4—1222no—
417D4—2441no—
418D4—2441no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—4881no—
430C2×C4—4881no—
431C2×C4—4881no—
432C2×C4—4881no—
433C2×C4—2442no—
434C2×C4—2442no—
435C2×C4—2442no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4—2441no—
439C2×C4#1451974511yescharacteristic
440C2×C4#1451974611yescharacteristic
441C2×C4#1451974811yescharacteristic
442C2×C4#1451974911yescharacteristic
443C2×C4#1451974911yescharacteristic
444C2×C4#1451977311yescharacteristic
445C2×C4C2×#1175819911yescharacteristic
446C2×C4#1451979711yescharacteristic
447C2×C4#1451980211yescharacteristic
448C2×C4#1451980311yescharacteristic
449C8—42no—
450C8—4881no—
451C8—2442no—
452C22—21no—
453C22—21no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—4881no—
458C22—4881no—
459C22—4881no—
460C22—4881no—
461C22—2442no—
462C22—2442no—
463C22—2442no—
464C22#1683967011yescharacteristic
465C22#1683989511yescharacteristic
466C22#1683990511yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—81no—
473C4—81no—
474C4—4882no—
475C4—4881no—
476C4#1683989611yescharacteristic
477C4#1683990711yescharacteristic
478C4#1683999611yescharacteristic
479C4#1684001311yescharacteristic
480C2—21no—
481C2—21no—
482C2—161no—
483C2—4882no—
484C2#2144681511yescharacteristic
485C2#2144687711yescharacteristic
486C2#2144688311yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3037C2
socleC22×C61#392
prime radical#21455815C2
hypercenter#3037D61
hypocenterC61#9997
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. #21450724C2semidirect
3. #21444379C2semidirect
4. #21444243C2semidirect
5. #21444214C2semidirect
6. #21443679C2semidirect
7. C61×#3037C2semidirect
97. C2×Q8×C61D8semidirect
238. #3037D61semidirect
276. C61#9997semidirect
341. C2×Q8#11758199semidirect

Maximal subgroups

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

subgroupindex
#214558152
#214507242
#214443792
#214442432
#214442142
#214436792
C61×#30372
#999761