Finite Group Databasebeta

← #29575366

Subgroups — #29575366

Order 15616.

690 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×#14519748C211yesmaximal, characteristic
3#21445796C211yesmaximal, characteristic, complemented
4C2×D4⋊#92418C211yesmaximal, characteristic, complemented
5#21443659C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#14519748C411yescharacteristic
9C2×C4×C22⋊D61—21no—
10C2×C42×D61C2211yescharacteristic
11#16839813—22no—
12#16839813—22no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519706—21no—
15C2×#14519689—21no—
16C2×#14519689—21no—
17C2×C4×#92418C2211yescharacteristic
18#16839665C411yescharacteristic
19#16839658C411yescharacteristic
20#16839650—21no—
21#16839638—21no—
22#16839619C411yescharacteristic
23C4×C4⋊Dic61C2211yescharacteristic
24C4×C22⋊Dic61—21no—
25#16839516—21no—
26D4⋊#92418—22no—
27C2×C4×D4×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×C22⋊D61—21no—
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×#92418—21no—
36C22×#92418—21no—
37#14519748—22no—
38#14519748—22no—
39C4×C22⋊D61—42no—
40C4×C22⋊D61—42no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C42×D61—21no—
53C42×D61—21no—
54C42×D61—21no—
55C42×D61—21no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58#14519706—24no—
59#14519689—24no—
60#14519689—42no—
61C4×#92418—21no—
62C4×#92418D412yescomplemented
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66C22×D4×C61C2×C411yescharacteristic
67C23×C4×C61—21no—
68C22×C8×C61—21no—
69C22×C8×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C2×C4⋊C4×C61C2×C411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C2×C42×C61C2311yescharacteristic
77C4⋊C8×C61—21no—
78C4⋊C8×C61—21no—
79C4×C8×C61—21no—
80C4×C8×C61D412yescomplemented
81C24×C61—21no—
82C23×D61C22⋊C411yescharacteristic
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61M1612yes—
89C22×C4×C61—21no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C2×C22⋊D61—24no—
100C2×C22⋊D61—42no—
101C2×C22⋊D61—42no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
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—21no—
114C2×C4×D61—21no—
115C2×C4×D61—21no—
116C2×C4×D61—21no—
117C2×C4×D61—21no—
118C2×C4×D61—21no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61D812yes—
122C2×C4×D61SD1612yes—
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—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61#4111yescharacteristic
136C42×C61#4111yescharacteristic
137C22⋊Dic61—24no—
138C22⋊Dic61—42no—
139C22⋊Dic61—42no—
140#11758198—42no—
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61M1612yes—
145#11758196—42no—
146C4×Dic61—21no—
147C4×Dic61—21no—
148C4×Dic61—21no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C4×Dic61—21no—
152C4×Dic61—41no—
153C4×Dic61—41no—
154C2×#92418—22no—
155C2×#92418—41no—
156C2×#92418—41no—
157C2×#92418—41no—
158C2×#92418—41no—
159C2×#92418—41no—
160C23×C61—22no—
161C23×C61—41no—
162C23×C61—41no—
163C23×C61—41no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61C2×C22⋊C411yescharacteristic
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—21no—
172C22×D61—21no—
173C22×D61—21no—
174C22×D61#10212yes—
175D4×C61—22no—
176D4×C61—22no—
177D4×C61—41no—
178D4×C61—41no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—81no—
185C2×C4×C61—81no—
186C2×C4×C61—81no—
187C2×C4×C61—81no—
188C2×C4×C61C4×D411yescharacteristic
189C2×C4×C61C4×D411yescharacteristic
190C2×C4×C61#12011yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61#12111yescharacteristic
193C2×C4×C61#12311yescharacteristic
194C2×C4×C61C2×M1611yescharacteristic
195C2×C4×C61C2×M1611yescharacteristic
196C2×C4×C61#13111yescharacteristic
197C2×C4×C61#13111yescharacteristic
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C2×SD1611yescharacteristic
200C2×C4×C61#13511yescharacteristic
201C2×C4×C61#13511yescharacteristic
202C22⋊D61—48no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—22no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61#10212yes—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—42no—
223C4×D61—42no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—41no—
227C4×D61—41no—
228C8×C61—42no—
229C8×C61—81no—
230#92418—42no—
231#92418—81no—
232#9076—611nomaximal, Sylow
233C22×C61—42no—
234C22×C61—42no—
235C22×C61—42no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61#38611yescharacteristic
241C22×C61#40711yescharacteristic
242C22×C61#40811yescharacteristic
243C22×C61C2×#10211yescharacteristic
244C22×C61#41611yescharacteristic
245C22×C61#42111yescharacteristic
246C22×C61#42111yescharacteristic
247C2×D61—22no—
248C2×D61—22no—
249C2×D61—22no—
250C2×D61—41no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—41no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—81no—
257C4×C61#43511yescharacteristic
258C4×C61#43511yescharacteristic
259C4×C61#43611yescharacteristic
260C4×C61#43611yescharacteristic
261C4×C61#46511yescharacteristic
262C4×C61#46511yescharacteristic
263C4×C61#46611yescharacteristic
264C4×C61#46611yescharacteristic
265Dic61—22no—
266Dic61—41no—
267Dic61—41no—
268Dic61—42no—
269Dic61—81no—
270C2×#431—611no—
271C4×#121—611no—
272#1797—611no—
273C2×D4⋊C8—611no—
274C2×D4⋊C8D6111yescharacteristic, complemented
275#1279—611no—
276#1279—611no—
277C2×C61—82no—
278C2×C61#148011yescharacteristic
279C2×C61#148211yescharacteristic
280C2×C61#148611yescharacteristic
281C2×C61#148811yescharacteristic
282C2×C61#187011yescharacteristic
283C2×C61#189311yescharacteristic
284C2×C61#189711yescharacteristic
285D61—42no—
286C2×#121—611no—
287C2×C4×D4—1221no—
288C2×C4×D4C2×D6111yescharacteristic
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⋊C4—611no—
305C4×C22⋊C4—1221no—
306#336—1221no—
307D4⋊C8—22no—
308D4⋊C8—1222no—
309C61#907611yescharacteristic, complemented, Sylow
310C22×D4—1221no—
311C22×D4C4×D6111yescharacteristic
312C23×C4—21no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—611no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—1221no—
319C22×C8—1221no—
320#121—1222no—
321#121—1222no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—2442no—
327C4×D4—2442no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—611no—
330C2×C4⋊C4—1221no—
331C2×C4⋊C4C4×D6111yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C42—611no—
338C2×C42—611no—
339C2×C42—611no—
340C2×C42—1221no—
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×C8C22⋊D6112yescomplemented
357#95—1221no—
358#95—1221no—
359#95—1221no—
360C24—21no—
361C24—611no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—1224no—
368C2×D4—2442no—
369C2×D4—2442no—
370C2×D4#1175818912yes—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—611no—
379C22×C4—612no—
380C22×C4—612no—
381C22×C4—611no—
382C22×C4—611no—
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—1221no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—1221no—
396C22×C4—1221no—
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—612no—
417C4⋊C4—1221no—
418C4⋊C4—1221no—
419C4⋊C4—1221no—
420C4⋊C4—2442no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—1224no—
424C22⋊C4—2442no—
425C22⋊C4—2442no—
426C22⋊C4—2442no—
427C42—1221no—
428C42—1221no—
429C42—1221no—
430C42—1221no—
431C42—1221no—
432C42—1221no—
433C42—2441no—
434C42—2441no—
435C42#1175822211yescharacteristic
436C42D4×D6111yescharacteristic
437C42#1175822411yescharacteristic
438C42C2×C22⋊D6111yescharacteristic
439C23—22no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23—612no—
447C23—1221no—
448C23—1221no—
449C23—1221no—
450C23—1221no—
451C23—1221no—
452C23—1221no—
453C23C22⋊C4×D6111yescharacteristic
454D4—22no—
455D4—22no—
456D4—41no—
457D4—41no—
458D4—2448no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—612no—
469C2×C4—1221no—
470C2×C4—1221no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1221no—
476C2×C4—1222no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4#1451973711yescharacteristic
494C2×C4C4×C22⋊D6111yescharacteristic
495C2×C4#1451974511yescharacteristic
496C2×C4#1451974811yescharacteristic
497C2×C4#1451975011yescharacteristic
498C2×C4#1451975911yescharacteristic
499C2×C4M16×D6111yescharacteristic
500C2×C4C2×#1175818911yescharacteristic
501C2×C4#1451978311yescharacteristic
502C2×C4#1451978511yescharacteristic
503C2×C4D8×D6111yescharacteristic
504C2×C4SD16×D6111yescharacteristic
505C2×C4#1451979611yescharacteristic
506C2×C4#1451979811yescharacteristic
507C8—42no—
508C8—81no—
509C8—4881no—
510C8—2442no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—1222no—
519C22—1222no—
520C22—1222no—
521C22—2441no—
522C22—2441no—
523C22—2441no—
524C22—2441no—
525C22#1683963811yescharacteristic
526C22#1683972411yescharacteristic
527C22#1683972711yescharacteristic
528C22#102×D6111yescharacteristic
529C22#1683975511yescharacteristic
530C22#1683977711yescharacteristic
531C22#1683977711yescharacteristic
532C4—21no—
533C4—21no—
534C4—81no—
535C4—1222no—
536C4—4881no—
537C4—2441no—
538C4—2442no—
539C4—2441no—
540C4#1683983011yescharacteristic
541C4#1683983311yescharacteristic
542C4#1683983711yescharacteristic
543C4#1683983811yescharacteristic
544C4#1683998811yescharacteristic
545C4#1683999011yescharacteristic
546C4#1683999511yescharacteristic
547C4#1683999711yescharacteristic
548C2—82no—
549C2—2442no—
550C2#2144421611yescharacteristic
551C2#2144422411yescharacteristic
552C2#2144424211yescharacteristic
553C2#2144425011yescharacteristic
554C2#2144611311yescharacteristic
555C2#2144624411yescharacteristic
556C2#2144626411yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C42×C61C23
hypercenterC2×D4⋊C8D61
hypocenterC61#9076
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#16839813C2semidirect
3. #21445796C2semidirect
4. C2×D4⋊#92418C2semidirect
5. #21443659C2semidirect
6. #21443658C2semidirect
7. C2×C61×D4⋊C8C2semidirect
62. C4×#92418D4semidirect
80. C4×C8×C61D4semidirect
274. C2×D4⋊C8D61semidirect
309. C61#9076semidirect
356. C4×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398132
C4×#145197482
#214457962
C2×D4⋊#924182
#214436592
#214436582
C2×C61×D4⋊C82
#907661