Finite Group Databasebeta

← #29578985

Subgroups — #29578985

Order 15616.

720 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519773C211yesmaximal, characteristic
2#21445674C211yesmaximal, characteristic, complemented
3C4×#14519706C211yesmaximal, characteristic, complemented
4C2×#16839491C211yesmaximal, characteristic, complemented
5C2×D4⋊#92418C211yesmaximal, characteristic, complemented
6C2×#16839489C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10C2×C4×C22⋊D61—21no—
11C2×C4×C22⋊D61—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×#14519706—21no—
14C2×#14519687—21no—
15C2×C4×#92418C2211yescharacteristic
16#16839665C411yescharacteristic
17#16839663C411yescharacteristic
18#16839662—21no—
19#16839662—21no—
20#16839631C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24#16839491—22no—
25D4⋊#92418—22no—
26#16839489—22no—
27C2×C4×D4×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C22⋊D61—21no—
34C22×C4×D61—21no—
35C22×#92418—21no—
36C22×#92418—21no—
37#14519773—22no—
38#14519773—22no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×C22⋊D61—42no—
44C4×C22⋊D61—42no—
45C4×C22⋊D61—42no—
46C4×C22⋊D61—42no—
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×C4×Dic61C2×C411yescharacteristic
56C2×C4×Dic61C2×C411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61D411yescharacteristic
59C2×C4×Dic61D411yescharacteristic
60C2×C4×Dic61D411yescharacteristic
61C4⋊#92418—21no—
62C4⋊#92418D412yescomplemented
63#14519706—24no—
64#14519687—42no—
65C4×#92418—21no—
66C4×#92418—21no—
67C22×D4×C61C2×C411yescharacteristic
68C23×C4×C61—21no—
69C22×C8×C61—21no—
70C22×C8×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C4×D4×C61—21no—
75C2×C4⋊C4×C61C2×C411yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C42×C61C2311yescharacteristic
78C4⋊C8×C61—21no—
79C4⋊C8×C61D412yescomplemented
80C4×C8×C61—21no—
81C4×C8×C61—21no—
82C24×C61—21no—
83C23×D61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61M1612yes—
90C22×C4×C61—21no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C2×C22⋊D61—24no—
101C2×C22⋊D61—24no—
102C2×C22⋊D61—42no—
103C2×C22⋊D61—42no—
104C2×C22⋊D61—42no—
105C2×C22⋊D61—42no—
106C22×Dic61—21no—
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C22⋊C411yescharacteristic
110C22×Dic61C22⋊C411yescharacteristic
111C2×D244—21no—
112C2×D244—21no—
113C2×D244—21no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244M1612yes—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C8×C61—22no—
124C2×C8×C61—22no—
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—42no—
138C22⋊Dic61—42no—
139#11758198—42no—
140#11758198—41no—
141#11758198—41no—
142#11758198—42no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145#11758196—42no—
146#11758196—42no—
147C4×Dic61—21no—
148C4×Dic61—21no—
149C4×Dic61—21no—
150C4×Dic61—21no—
151C4×Dic61—21no—
152C4×Dic61—21no—
153C4×Dic61—22no—
154C4×Dic61—41no—
155C4×Dic61D812yes—
156C4×Dic61SD1612yes—
157C2×#92418—22no—
158C2×#92418—22no—
159C2×#92418—41no—
160C2×#92418—41no—
161C2×#92418—41no—
162C2×#92418—41no—
163C23×C61—22no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61C2×C22⋊C411yescharacteristic
171C22×D61—22no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61—41no—
178D4×C61—22no—
179D4×C61—22no—
180D4×C61—41no—
181D4×C61—41no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—81no—
188C2×C4×C61—81no—
189C2×C4×C61—81no—
190C2×C4×C61—81no—
191C2×C4×C61C4×D411yescharacteristic
192C2×C4×C61C4×D411yescharacteristic
193C2×C4×C61#12111yescharacteristic
194C2×C4×C61#12111yescharacteristic
195C2×C4×C61#12411yescharacteristic
196C2×C4×C61#12711yescharacteristic
197C2×C4×C61C2×M1611yescharacteristic
198C2×C4×C61C2×M1611yescharacteristic
199C2×C4×C61#13111yescharacteristic
200C2×C4×C61#13111yescharacteristic
201C2×C4×C61C2×D811yescharacteristic
202C2×C4×C61C2×SD1611yescharacteristic
203C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
205C22⋊D61—48no—
206C22⋊D61—48no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—21no—
211C2×Dic61—21no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61—21no—
215C2×Dic61—21no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61#10212yes—
220C2×Dic61#10212yes—
221C2×Dic61#10412yes—
222D244—22no—
223D244—22no—
224D244—41no—
225D244—41no—
226C4×D61—81no—
227C4×D61—81no—
228C4×D61—81no—
229C4×D61—81no—
230C8×C61—42no—
231C8×C61—42no—
232#92418—42no—
233#92418—42no—
234#9678—611nomaximal, Sylow
235C22×C61—42no—
236C22×C61—42no—
237C22×C61—42no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—81no—
241C22×C61—81no—
242C22×C61#39011yescharacteristic
243C22×C61#40711yescharacteristic
244C22×C61#40811yescharacteristic
245C22×C61C2×#10211yescharacteristic
246C22×C61#41811yescharacteristic
247C22×C61C2×#10411yescharacteristic
248C22×C61#42111yescharacteristic
249C2×D61—42no—
250C2×D61—42no—
251C2×D61—42no—
252C2×D61—81no—
253C2×D61—81no—
254C2×D61—81no—
255C2×D61—81no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—81no—
259C4×C61#43511yescharacteristic
260C4×C61#43511yescharacteristic
261C4×C61#43511yescharacteristic
262C4×C61#43511yescharacteristic
263C4×C61#45911yescharacteristic
264C4×C61#45911yescharacteristic
265C4×C61#46011yescharacteristic
266C4×C61#46011yescharacteristic
267Dic61—22no—
268Dic61—22no—
269Dic61—22no—
270Dic61—41no—
271Dic61—81no—
272C4×#127—611no—
273#1767—611no—
274C4×C4⋊C8—611no—
275C2×D4⋊C8—611no—
276C2×D4⋊C8—611no—
277C2×D4⋊C8—611no—
278C2×D4⋊C8D6111yescharacteristic, complemented
279C2×C61—82no—
280C2×C61#148611yescharacteristic
281C2×C61#149011yescharacteristic
282C2×C61#149211yescharacteristic
283C2×C61#149611yescharacteristic
284C2×C61#195511yescharacteristic
285C2×C61#198011yescharacteristic
286C2×C61#198211yescharacteristic
287D61—82no—
288C2×#127—611no—
289C2×C4×D4—611no—
290C2×C4×D4—1221no—
291C2×C4×D4—1221no—
292C2×C4×D4C2×D6111yescharacteristic
293C2×C4⋊C8—611no—
294C2×C4⋊C8—1221no—
295C2×C4⋊C8C2×D6111yescharacteristic
296C2×#97—1221no—
297C2×C4×C8—611no—
298C2×C4×C8C2×D6111yescharacteristic
299#390—611no—
300#390—611no—
301#390—1221no—
302#390—1221no—
303#384—611no—
304C43—611no—
305#336—1221no—
306#336—1221no—
307D4⋊C8—22no—
308D4⋊C8—1222no—
309D4⋊C8—1222no—
310D4⋊C8—1222no—
311C61#967811yescharacteristic, complemented, Sylow
312C22×D4—611no—
313C22×D4—1221no—
314C22×D4—1221no—
315C22×D4C4×D6111yescharacteristic
316C23×C4—21no—
317C23×C4—1221no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—1221no—
321C22×C8—1221no—
322#127—1222no—
323#127—1222no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—1221no—
329C4×D4—1221no—
330C4×D4—1221no—
331C4×D4—1221no—
332C4×D4—2442no—
333C4×D4—2442no—
334C4×D4—2442no—
335C4×D4—2442no—
336C2×C4⋊C4—611no—
337C2×C4⋊C4—1221no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4C4×D6111yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—1221no—
343C2×C22⋊C4—1221no—
344C2×C22⋊C4—1221no—
345C2×C22⋊C4—1221no—
346C2×C42—611no—
347C2×C42—611no—
348C2×C42—611no—
349C2×C42—611no—
350C2×C42—611no—
351C2×C42—611no—
352C2×C42C22×D6111yescharacteristic
353C4⋊C8—21no—
354C4⋊C8—612no—
355C4⋊C8—1224no—
356C4⋊C8—1221no—
357C4⋊C8C22⋊D6112yescomplemented
358#97—2442no—
359C4×C8—21no—
360C4×C8—21no—
361C4×C8—1221no—
362C4×C8—1221no—
363C24—21no—
364C24—1221no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—612no—
371C2×D4—1224no—
372C2×D4—1224no—
373C2×D4—1221no—
374C2×D4—1221no—
375C2×D4—1221no—
376C2×D4—1221no—
377C2×D4—1221no—
378C2×D4—2442no—
379C2×D4—2442no—
380C2×D4—2442no—
381C2×D4—2442no—
382C2×D4#1175818912yes—
383C22×C4—21no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—1221no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4C2×C4×D6111yescharacteristic
402C22×C4D4×D6111yescharacteristic
403C22×C4D4×D6111yescharacteristic
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—1222no—
411C2×C8—1222no—
412C2×C8—2441no—
413C2×C8—2441no—
414C2×C8—2441no—
415C2×C8—2441no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—1221no—
419C4⋊C4—1221no—
420C4⋊C4—2442no—
421C4⋊C4—2442no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—2442no—
425C22⋊C4—2442no—
426C22⋊C4—2442no—
427C22⋊C4—2442no—
428C22⋊C4—2441no—
429C22⋊C4—2441no—
430C42—612no—
431C42—612no—
432C42—1222no—
433C42—1221no—
434C42—1221no—
435C42—1221no—
436C42—1221no—
437C42—1221no—
438C42—1221no—
439C42—2441no—
440C42#1175822211yescharacteristic
441C42D4×D6111yescharacteristic
442C42#1175822411yescharacteristic
443C42C2×C22⋊D6111yescharacteristic
444C23—22no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—1222no—
452C23—2441no—
453C23—2441no—
454C23—2441no—
455C23—2441no—
456C23—2441no—
457C23—2441no—
458C23C22⋊C4×D6111yescharacteristic
459D4—22no—
460D4—22no—
461D4—41no—
462D4—41no—
463D4—1222no—
464D4—1222no—
465D4—2448no—
466D4—2448no—
467D4—2441no—
468D4—2441no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—612no—
479C2×C4—612no—
480C2×C4—612no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—1221no—
485C2×C4—1221no—
486C2×C4—1221no—
487C2×C4—1221no—
488C2×C4—1221no—
489C2×C4—1221no—
490C2×C4—4881no—
491C2×C4—4881no—
492C2×C4—4881no—
493C2×C4—4881no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4#1451973711yescharacteristic
498C2×C4C4×C22⋊D6111yescharacteristic
499C2×C4#1451974911yescharacteristic
500C2×C4#1451975011yescharacteristic
501C2×C4#1451976311yescharacteristic
502C2×C4#1451977311yescharacteristic
503C2×C4M16×D6111yescharacteristic
504C2×C4C2×#1175818911yescharacteristic
505C2×C4#1451978311yescharacteristic
506C2×C4#1451978511yescharacteristic
507C2×C4D8×D6111yescharacteristic
508C2×C4SD16×D6111yescharacteristic
509C2×C4#1451980111yescharacteristic
510C2×C4#1451980411yescharacteristic
511C8—42no—
512C8—42no—
513C8—2442no—
514C8—2442no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—4881no—
523C22—4881no—
524C22—4881no—
525C22—4881no—
526C22—2442no—
527C22—2442no—
528C22—2442no—
529C22#1683966211yescharacteristic
530C22#1683972411yescharacteristic
531C22#1683972711yescharacteristic
532C22#102×D6111yescharacteristic
533C22#1683976511yescharacteristic
534C22#104×D6111yescharacteristic
535C22#1683977711yescharacteristic
536C4—21no—
537C4—21no—
538C4—81no—
539C4—1222no—
540C4—1222no—
541C4—1222no—
542C4—4881no—
543C4—2441no—
544C4#1683983011yescharacteristic
545C4#1683983111yescharacteristic
546C4#1683983311yescharacteristic
547C4#1683983611yescharacteristic
548C4#1683995511yescharacteristic
549C4#1683995611yescharacteristic
550C4#1683996011yescharacteristic
551C4#1683996111yescharacteristic
552C2—82no—
553C2—4882no—
554C2#2144424211yescharacteristic
555C2#2144426011yescharacteristic
556C2#2144426811yescharacteristic
557C2#2144428611yescharacteristic
558C2#2144661511yescharacteristic
559C2#2144673611yescharacteristic
560C2#2144674411yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C42×C61C23
hypercenterC2×D4⋊C8D61
hypocenterC61#9678
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
2. #21445674C2semidirect
3. C4×#14519706C2semidirect
4. C2×#16839491C2semidirect
5. C2×D4⋊#92418C2semidirect
6. C2×#16839489C2semidirect
7. C2×C61×D4⋊C8C2semidirect
62. C4⋊#92418D4semidirect
79. C4⋊C8×C61D4semidirect
278. C2×D4⋊C8D61semidirect
311. C61#9678semidirect
357. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C4×#145197732
#214456742
C4×#145197062
C2×#168394912
C2×D4⋊#924182
C2×#168394892
C2×C61×D4⋊C82
#967861