Finite Group Databasebeta

← #29584397

Subgroups — #29584397

Order 15616.

574 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 95 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#21456567C211yesmaximal, characteristic
2#21446656C211yesmaximal, characteristic, complemented
3#21446654C211yesmaximal, characteristic, complemented
4#21446247C211yesmaximal, characteristic, complemented
5#21445997C211yesmaximal, characteristic, complemented
6#21443686C211yesmaximal, characteristic, complemented
7C61×#1893C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9#16840075—21no—
10#16840073—21no—
11#16839996—21no—
12#16839996—21no—
13#16839896—21no—
14#16839895—21no—
15C2×#14519706—21no—
16C2×#14519699—21no—
17C2×#14519692—21no—
18C2×#14519692—21no—
19C2×#14519691—21no—
20C2×#14519691—21no—
21C2×C22⋊#92418C2211yescharacteristic
22#16839622C2211yescharacteristic
23C4×C22⋊Dic61C2211yescharacteristic
24#16839525—21no—
25#16839516—21no—
26C23×C8×C61C2211yescharacteristic
27C2×#121×C61C2211yescharacteristic
28C2×#102×C61—21no—
29C61×#380C2211yescharacteristic
30C61×#340—21no—
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C2×#11758199—21no—
34C2×#11758199—21no—
35C22×#92418D411yescharacteristic
36C22×#92418D411yescharacteristic
37#14519751—21no—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61D411yescharacteristic
45C2×C22⋊Dic61D411yescharacteristic
46C2×#11758198—21no—
47C2×C4×Dic61—21no—
48#14519710—21no—
49#14519710—21no—
50#14519706—42no—
51#14519699—42no—
52#14519698—21no—
53#14519698—21no—
54#14519697—21no—
55#14519697—21no—
56#14519692—42no—
57#14519692—42no—
58#14519691—42no—
59#14519691—42no—
60C22⋊#92418—21no—
61C22⋊#92418—21no—
62#14519684—21no—
63#14519684—21no—
64C22×D4×C61—21no—
65C22×D4×C61D411yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C22×C8×C61—42no—
71#121×C61—21no—
72#121×C61—21no—
73#121×C61—21no—
74#121×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61D411yescharacteristic
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—21no—
79#102×C61—42no—
80#95×C61—21no—
81C24×C61—21no—
82C24×C61C2×D411yescharacteristic
83C23×D61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C22×C4×C61—21no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61#4111yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×C4×C61#4111yescharacteristic
104C2×C22⋊D61—41no—
105C2×C22⋊D61—41no—
106C2×C22⋊D61—41no—
107C2×C22⋊D61—41no—
108C2×C22⋊D61—41no—
109C2×C22⋊D61—41no—
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—41no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244—41no—
117C2×D244—41no—
118C2×C8×C61—22no—
119C2×C8×C61—22no—
120C2×C8×C61—22no—
121C2×C8×C61—41no—
122C2×C8×C61—41no—
123C2×C8×C61—41no—
124C2×C8×C61—41no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊Dic61—21no—
134C22⋊Dic61—21no—
135C22⋊Dic61—21no—
136C22⋊Dic61—41no—
137C22⋊Dic61—41no—
138C22⋊Dic61D812yescomplemented
139#11758199—81no—
140#11758199—81no—
141#11758198—41no—
142#11758198—41no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147C4×Dic61—41no—
148C4×Dic61—41no—
149C2×#92418—21no—
150C2×#92418—21no—
151C2×#92418—41no—
152C2×#92418—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—81no—
159C23×C61—81no—
160C23×C61#12111yescharacteristic
161C23×C61#12111yescharacteristic
162C23×C61#12111yescharacteristic
163C23×C61C2×D811yescharacteristic
164C23×C61#13511yescharacteristic
165C23×C61AGL(1,ℤ/8)11yescharacteristic
166C23×C61AGL(1,ℤ/8)11yescharacteristic
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—81no—
171C22×D61—81no—
172D4×C61—42no—
173D4×C61—41no—
174D4×C61—41no—
175D4×C61—81no—
176D4×C61—81no—
177D4×C61—81no—
178D4×C61—81no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—81no—
192C2×C4×C61—81no—
193C2×C4×C61—81no—
194C2×C4×C61#12011yescharacteristic
195C2×C4×C61#12311yescharacteristic
196C2×C4×C61#12311yescharacteristic
197C2×C4×C61#12411yescharacteristic
198C22⋊D61—81no—
199C22⋊D61—81no—
200C22⋊D61—81no—
201C22⋊D61—81no—
202C2×Dic61—22no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—81no—
212C2×Dic61—81no—
213C2×Dic61—81no—
214D244—42no—
215D244—41no—
216D244—41no—
217C8×C61—42no—
218#92418—41no—
219#92418—41no—
220#10564—611nomaximal, Sylow
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61—161no—
235C22×C61—161no—
236C22×C61#39411yescharacteristic
237C22×C61#45911yescharacteristic
238C22×C61#45911yescharacteristic
239C22×C61#46311yescharacteristic
240C22×C61#46311yescharacteristic
241C22×C61#46611yescharacteristic
242C22×C61#46911yescharacteristic
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—161no—
247C2×D61—161no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—81no—
252C4×C61—161no—
253C4×C61B(4,𝔽2)11yescharacteristic
254C4×C61#45811yescharacteristic
255Dic61—42no—
256Dic61—81no—
257Dic61—81no—
258Dic61—161no—
259#3186—611no—
260#1964—611no—
261#1964—611no—
262#1893—611no—
263#1893D6111yescharacteristic, complemented
264#1850—611no—
265#1289—611no—
266C2×C61—21no—
267C2×C61—21no—
268C2×C61—21no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—161no—
273C2×C61#204411yescharacteristic
274C2×C61#205311yescharacteristic
275C2×C61#205411yescharacteristic
276D61—161no—
277C23×C8C2×D6111yescharacteristic
278C2×#121—611no—
279C2×#121C2×D6111yescharacteristic
280#480—1221no—
281#480—1221no—
282#466—1221no—
283#466—1221no—
284#447—1221no—
285#447—1221no—
286C2×C4⋊C8—1221no—
287C2×#102—21no—
288C2×#102—1221no—
289C2×#99—1221no—
290C2×#99—1221no—
291C2×#99—1221no—
292C2×#99—1221no—
293C2×C22⋊C8—611no—
294#380—611no—
295#380C2×D6111yescharacteristic
296C4×C22⋊C4—611no—
297#340—21no—
298#340—1221no—
299#336—1221no—
300C61#1056411yescharacteristic, complemented, Sylow
301C22×D4—21no—
302C22×D4—611no—
303C22×D4—1221no—
304C22×D4C22⋊D6111yescharacteristic
305C23×C4C22×D6111yescharacteristic
306C2×D8—1221no—
307C2×D8—1221no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—42no—
312C22×C8—611no—
313C22×C8—611no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—1221no—
319#121—1221no—
320#121—1221no—
321#121—1221no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—611no—
324C2×C4⋊C4—1221no—
325C2×C4⋊C4C22⋊D6111yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—611no—
329C2×C22⋊C4—611no—
330C2×C22⋊C4—1221no—
331C2×C22⋊C4—1221no—
332C2×C42—1221no—
333#107—1221no—
334#107—1221no—
335C4⋊C8—2442no—
336#102—42no—
337#102—1221no—
338#102—1221no—
339#102—1221no—
340#102—1221no—
341#102—2442no—
342#99—2442no—
343#99—2442no—
344#99—2442no—
345#99—2442no—
346C22⋊C8—1221no—
347C22⋊C8—1221no—
348#95—21no—
349#95—1221no—
350#95—1221no—
351C24—21no—
352C24—1221no—
353C24D4×D6111yescharacteristic
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—1221no—
365C2×D4—1221no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2441no—
373C2×D4—2441no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—2441no—
382C22×C4#1175822211yescharacteristic
383C22×C4#1175822211yescharacteristic
384C22×C4D4×D6111yescharacteristic
385C22×C4D4×D6111yescharacteristic
386C22×C4#1175822411yescharacteristic
387C22×C4C2×C22⋊D6111yescharacteristic
388D8—4881no—
389D8—4881no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—1221no—
398C2×C8—1221no—
399C2×C8—2441no—
400C2×C8—2441no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—2441no—
408C4⋊C4—2441no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—612no—
414C22⋊C4—1221no—
415C22⋊C4—1221no—
416C22⋊C4—1221no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C42—2441no—
422C42—2441no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—81no—
429C23—81no—
430C23—4881no—
431C23—4881no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23#1451974911yescharacteristic
436C23#1451975011yescharacteristic
437C23#1451975011yescharacteristic
438C23D8×D6111yescharacteristic
439C23#1451979811yescharacteristic
440C23#1451980111yescharacteristic
441C23#1451980411yescharacteristic
442D4—42no—
443D4—41no—
444D4—41no—
445D4—81no—
446D4—81no—
447D4—81no—
448D4—81no—
449D4—4881no—
450D4—4881no—
451D4—4881no—
452D4—4881no—
453D4—2442no—
454D4—2441no—
455D4—2441no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—1222no—
472C2×C4—4881no—
473C2×C4—4881no—
474C2×C4—4881no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4#1451974511yescharacteristic
484C2×C4#1451975911yescharacteristic
485C2×C4#1451976011yescharacteristic
486C2×C4#1451976311yescharacteristic
487C8—42no—
488C8—2441no—
489C8—2441no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—161no—
504C22—161no—
505C22—9761no—
506C22—9761no—
507C22—4881no—
508C22—4881no—
509C22—4881no—
510C22#1683967711yescharacteristic
511C22#1683995511yescharacteristic
512C22#1683995611yescharacteristic
513C22#1683997611yescharacteristic
514C22#1683997911yescharacteristic
515C22#1683999711yescharacteristic
516C22#1684001411yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—81no—
521C4—161no—
522C4—9761no—
523C4—4881no—
524C4—4881no—
525C4—2442no—
526C4#1683994811yescharacteristic
527C4#1683995111yescharacteristic
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—161no—
535C2—9761no—
536C2#2144706811yescharacteristic
537C2#2144712311yescharacteristic
538C2#2144712811yescharacteristic
subgroupG/H
centerC22#16839677
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1893C2
socleC22×C61#394
prime radical#21456567C2
hypercenter#1893D61
hypocenterC61#10564
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. #21446656C2semidirect
3. #21446654C2semidirect
4. #21446247C2semidirect
5. #21445997C2semidirect
6. #21443686C2semidirect
7. C61×#1893C2semidirect
138. C22⋊Dic61D8semidirect
263. #1893D61semidirect
300. C61#10564semidirect

Maximal subgroups

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

subgroupindex
#214565672
#214466562
#214466542
#214462472
#214459972
#214436862
C61×#18932
#1056461