Finite Group Databasebeta

← #29575358

Subgroups — #29575358

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839813C211yesmaximal, characteristic, complemented
2C4×#14519752C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic, complemented
4C2×#16839491C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1279C211yesmaximal, characteristic, complemented
8C2×#14519752C411yescharacteristic
9C2×C4×D244—21no—
10C2×C4×D244C2211yescharacteristic
11C2×C42×D61C2211yescharacteristic
12#16839813—22no—
13#16839813—22no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519706—21no—
16C2×#14519689—21no—
17C2×#14519689—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839663C411yescharacteristic
20#16839661C411yescharacteristic
21#16839654—21no—
22#16839640—21no—
23#16839619C411yescharacteristic
24C4×#11758198—21no—
25#16839516—21no—
26#16839491—22no—
27#16839489—22no—
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C22×D244—21no—
32C22×D244C2×C411yescharacteristic
33C22×C4×D61—21no—
34C22×C4×D61C2×C411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×#92418—21no—
38C22×#92418—21no—
39#14519752—22no—
40#14519752C814yescomplemented
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—42no—
46C4×D244—42no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×C4×Dic61C2×C411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C42×D61—21no—
58C42×D61—21no—
59C42×D61—21no—
60C42×D61—21no—
61C4⋊#92418—21no—
62C4⋊#92418—21no—
63#14519706—24no—
64#14519689—24no—
65#14519689—42no—
66C4×#92418—21no—
67C4×#92418D412yescomplemented
68#14519684—21no—
69#14519684—21no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C4⋊C4×C61C2×C411yescharacteristic
74C2×C42×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61—21no—
78C4×C8×C61—21no—
79C4×C8×C61D412yescomplemented
80#95×C61—21no—
81C23×D61—21no—
82C23×D61C22⋊C411yescharacteristic
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61C22×C411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×Dic61—21no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C2×D244—21no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244—24no—
97C2×D244—21no—
98C2×D244—42no—
99C2×D244—42no—
100C2×D244C2×C812yes—
101C2×C4×D61—21no—
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×C4×D61—21no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—21no—
109C2×C4×D61—21no—
110C2×C4×D61—21no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61C2×C812yes—
122C2×C4×D61M1612yes—
123C2×C8×C61—22no—
124C2×C8×C61—41no—
125C2×C8×C61—41no—
126C2×C8×C61—41no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61C2×C812yes—
133C42×C61—41no—
134C42×C61—41no—
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138C42×C61#4111yescharacteristic
139#11758198—24no—
140#11758198—42no—
141#11758198—42no—
142#11758198—42no—
143#11758198—41no—
144#11758198—41no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—42no—
148C4×Dic61—21no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C4×Dic61—21no—
152C4×Dic61—21no—
153C4×Dic61—21no—
154C2×#92418—22no—
155C2×#92418—41no—
156C2×#92418—41no—
157C2×#92418—41no—
158C2×#92418—41no—
159C2×#92418—41no—
160C23×C61C2×C22⋊C411yescharacteristic
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—22no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61C22⋊C812yes—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—22no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61C4×D411yescharacteristic
184C2×C4×C61C4×D411yescharacteristic
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61#12311yescharacteristic
189C2×C4×C61C22×C811yescharacteristic
190C2×C4×C61C2×M1611yescharacteristic
191C2×C4×C61#13111yescharacteristic
192C2×C4×C61#13111yescharacteristic
193C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C61#13711yescharacteristic
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61C22⋊C812yes—
209D244—22no—
210D244—22no—
211D244—48no—
212D244—41no—
213D244—41no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—42no—
219C4×D61—42no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—81no—
225C4×D61—81no—
226C4×D61—81no—
227C4×D61—81no—
228C8×C61—42no—
229C8×C61—81no—
230#92418—42no—
231#92418—81no—
232#9074—611nomaximal, Sylow
233C22×C61#38611yescharacteristic
234C22×C61C2×C22⋊C811yescharacteristic
235C22×C61#40811yescharacteristic
236C22×C61#41711yescharacteristic
237C22×C61#41811yescharacteristic
238C22×C61#42111yescharacteristic
239C22×C61#42111yescharacteristic
240C2×D61—22no—
241C2×D61—22no—
242C2×D61—22no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—42no—
250C2×D61—81no—
251C2×D61—81no—
252C2×D61—81no—
253C2×D61—81no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—42no—
257C4×C61—81no—
258C4×C61C8×D411yescharacteristic
259C4×C61C8×D411yescharacteristic
260C4×C61#43511yescharacteristic
261C4×C61#43511yescharacteristic
262C4×C61#46811yescharacteristic
263C4×C61#46811yescharacteristic
264C4×C61#46911yescharacteristic
265C4×C61#46911yescharacteristic
266Dic61—22no—
267Dic61—41no—
268Dic61—41no—
269Dic61—81no—
270C2×#431—611no—
271C4×#121—611no—
272#1797—611no—
273C2×D4⋊C8—611no—
274C2×D4⋊C8—611no—
275#1279—611no—
276#1279D6111yescharacteristic, complemented
277C2×C61#147711yescharacteristic
278C2×C61#147811yescharacteristic
279C2×C61#149511yescharacteristic
280C2×C61#149611yescharacteristic
281C2×C61#186911yescharacteristic
282C2×C61#189511yescharacteristic
283C2×C61#189711yescharacteristic
284D61—42no—
285D61—82no—
286C2×#121—611no—
287C2×C4×D4—611no—
288C2×C4×D4—1221no—
289C22×C42—611no—
290#431—1222no—
291#431—1222no—
292C2×C4⋊C8—611no—
293C2×C4⋊C8—1221no—
294C2×C4⋊C8C2×D6111yescharacteristic
295C2×C22⋊C8—1221no—
296C2×C22⋊C8—1221no—
297C2×C4×C8—611no—
298C2×C4×C8C2×D6111yescharacteristic
299#390—611no—
300#389—611no—
301#388—1221no—
302#386—1221no—
303#380—611no—
304C4×C4⋊C4C2×D6111yescharacteristic
305C4×C22⋊C4—1221no—
306#336—1221no—
307D4⋊C8—1222no—
308D4⋊C8—1222no—
309C61#907411yescharacteristic, complemented, Sylow
310C22×D4—611no—
311C22×D4—1221no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—1221no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—1221no—
319C22×C8—1221no—
320#121—614no—
321#121—1222no—
322C4×D4—1221no—
323C4×D4—1221no—
324C4×D4—1221no—
325C4×D4—1221no—
326C4×D4—2442no—
327C4×D4—2442no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—1221no—
330C2×C4⋊C4C4×D6111yescharacteristic
331C2×C4⋊C4C4×D6111yescharacteristic
332C2×C22⋊C4—1221no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C42—21no—
338C2×C42—611no—
339C2×C42—611no—
340C2×C42—611no—
341C2×C42—1221no—
342C2×C42—1221no—
343C2×C42—1221no—
344C2×C42—1221no—
345C2×C42C22×D6111yescharacteristic
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—1224no—
349C4⋊C8—1221no—
350C4⋊C8—1221no—
351C22⋊C8—1224no—
352C22⋊C8—2442no—
353C4×C8—21no—
354C4×C8—612no—
355C4×C8—1221no—
356C4×C8D24412yescomplemented
357#95—21no—
358#95—1221no—
359#95—1221no—
360C24—611no—
361C24—1221no—
362C2×D4—612no—
363C2×D4—1224no—
364C2×D4—1221no—
365C2×D4—1221no—
366C2×D4—1221no—
367C2×D4—1221no—
368C2×D4—1221no—
369C2×D4—2442no—
370C2×D4—2442no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—611no—
374C22×C4—612no—
375C22×C4—612no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—1221no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—2441no—
392C22×C4—2441no—
393C22×C4—2441no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4C2×C4×D6111yescharacteristic
400C22×C4D4×D6111yescharacteristic
401C22×C4D4×D6111yescharacteristic
402C2×C8—22no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—1222no—
409C2×C8—2441no—
410C2×C8—2441no—
411C2×C8—2441no—
412C2×C8—2441no—
413C2×C8—2441no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—1221no—
418C4⋊C4—1221no—
419C4⋊C4—2442no—
420C4⋊C4C8×D6112yes—
421C22⋊C4—1224no—
422C22⋊C4—2442no—
423C22⋊C4—2442no—
424C22⋊C4—2442no—
425C22⋊C4—2441no—
426C22⋊C4—2441no—
427C42—41no—
428C42—41no—
429C42—1221no—
430C42—1221no—
431C42—1221no—
432C42—1221no—
433C42—1221no—
434C42—1221no—
435C42C2×D24411yescharacteristic
436C42#1175822211yescharacteristic
437C42D4×D6111yescharacteristic
438C42#1175822611yescharacteristic
439C23—612no—
440C23—1221no—
441C23—1221no—
442C23—1221no—
443C23—1221no—
444C23—1221no—
445C23—1221no—
446C23—1222no—
447C23—2441no—
448C23—2441no—
449C23—2441no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23C22⋊C4×D6111yescharacteristic
454D4—1222no—
455D4—1222no—
456D4—2448no—
457D4—2441no—
458D4—2441no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—612no—
468C2×C4—1221no—
469C2×C4—1221no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1222no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—4881no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4#1451973911yescharacteristic
494C2×C4C4×D24411yescharacteristic
495C2×C4#1451974711yescharacteristic
496C2×C4#1451975011yescharacteristic
497C2×C4#1451975211yescharacteristic
498C2×C4#1451976211yescharacteristic
499C2×C4C2×C8×D6111yescharacteristic
500C2×C4M16×D6111yescharacteristic
501C2×C4#1451978311yescharacteristic
502C2×C4#1451978511yescharacteristic
503C2×C4#1451980111yescharacteristic
504C2×C4#1451980411yescharacteristic
505C2×C4#1451980411yescharacteristic
506C2×C4#1451980911yescharacteristic
507C8—42no—
508C8—81no—
509C8—4881no—
510C8—2442no—
511C22—1222no—
512C22—1222no—
513C22—1222no—
514C22—4881no—
515C22—4881no—
516C22—4881no—
517C22—4881no—
518C22—2442no—
519C22—2442no—
520C22—2442no—
521C22—2441no—
522C22—2441no—
523C22—2441no—
524C22—2441no—
525C22#1683964011yescharacteristic
526C22C22⋊C8×D6111yescharacteristic
527C22#1683972711yescharacteristic
528C22#1683976211yescharacteristic
529C22#1683976511yescharacteristic
530C22#1683977711yescharacteristic
531C22#1683977711yescharacteristic
532C4—21no—
533C4—21no—
534C4—42no—
535C4—81no—
536C4—1222no—
537C4—4881no—
538C4—2441no—
539C4—2441no—
540C4#1683982711yescharacteristic
541C4C8×D24411yescharacteristic
542C4#1683983211yescharacteristic
543C4#1683983511yescharacteristic
544C4#1684000911yescharacteristic
545C4#1684001111yescharacteristic
546C4#1684001411yescharacteristic
547C4#1684001611yescharacteristic
548C2—4882no—
549C2—2442no—
550C2#2144420511yescharacteristic
551C2#2144420811yescharacteristic
552C2#2144428311yescharacteristic
553C2#2144428611yescharacteristic
554C2#2144611011yescharacteristic
555C2#2144625611yescharacteristic
556C2#2144626611yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1279C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C42×C61C23
hypercenter#1279D61
hypocenterC61#9074
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
1. C2×#16839813C2semidirect
3. #21445796C2semidirect
4. C2×#16839491C2semidirect
5. C2×#16839489C2semidirect
6. #21443660C2semidirect
7. C61×#1279C2semidirect
40. #14519752C8semidirect
67. C4×#92418D4semidirect
79. C4×C8×C61D4semidirect
276. #1279D61semidirect
309. C61#9074semidirect
356. C4×C8D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168398132
C4×#145197522
#214457962
C2×#168394912
C2×#168394892
#214436602
C61×#12792
#907461