Finite Group Databasebeta

← #29572055

Subgroups — #29572055

Order 15616.

760 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic122C211yesmaximal, characteristic
2C4×#14519700C211yesmaximal, characteristic, complemented
3#21444317C211yesmaximal, characteristic, complemented
4#21444273C211yesmaximal, characteristic, complemented
5#21444247C211yesmaximal, characteristic, complemented
6#21444201C211yesmaximal, characteristic
7C61×#1806C211yesmaximal, characteristic
8Q8×Dic122C411yescharacteristic, complemented
9#16840491C411yescharacteristic, complemented
10#16840488—21no—
11#16840471—22no—
12#16840471—21no—
13#16840469—21no—
14#16840469C411yescharacteristic, complemented
15D4×Dic122—21no—
16D4×Dic122C411yescharacteristic, complemented
17#16840319—21no—
18#16840319C2211yescharacteristic
19#16840315—22no—
20#16840315—21no—
21#41×Dic61—21no—
22C2×C4×Dic122—21no—
23C2×C4×Dic122C2211yescharacteristic
24#16839815C2211yescharacteristic
25C2×#14519700—21no—
26C2×C4×#92418C2211yescharacteristic
27#16839524—21no—
28#16839498—22no—
29Q8⋊#92418—21no—
30#16839492—21no—
31#16839492—21no—
32#16839492—22no—
33D4⋊#92418—21no—
34C4×#41×C61C2211yescharacteristic
35C61×#423C2211yescharacteristic
36C2×#104×C61—21no—
37C4×C4⋊C4×C61C2211yescharacteristic
38C61×#339—21no—
39C22×Dic122—21no—
40C22×Dic122D411yescharacteristic
41C22×#92418—21no—
42#14519777—21no—
43#14519777—21no—
44#14519777C2×C411yescharacteristic
45#14519777C2×C411yescharacteristic
46#14519776—22no—
47#14519776—22no—
48#14519776—21no—
49#14519776—21no—
50#14519769—22no—
51#14519769—21no—
52#14519768—22no—
53#14519768—21no—
54#14519768—21no—
55#14519768—22no—
56#14519756—22no—
57#14519756—21no—
58#14519756—21no—
59#14519756—21no—
60#14519756D412yes—
61#14519754—22no—
62#14519754—22no—
63#14519754—22no—
64#14519754—22no—
65#14519754—22no—
66#14519754—22no—
67Q8×Dic61—21no—
68Q8×Dic61—21no—
69C4×Dic122—22no—
70C4×Dic122—22no—
71C4×Dic122—22no—
72C4×Dic122—21no—
73C4×Dic122—21no—
74C4×Dic122—21no—
75C4×Dic122—21no—
76C4×Dic122—21no—
77C4×Dic122C2×C411yescharacteristic
78C4×Dic122C2×C411yescharacteristic
79C4×Dic122D411yescharacteristic
80C4×Dic122D411yescharacteristic
81C4×Dic122D412yes—
82D4×Dic61—22no—
83D4×Dic61—22no—
84D4×Dic61—21no—
85D4×Dic61—21no—
86#14519736—22no—
87#14519736—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61D411yescharacteristic
90C2×#11758196—22no—
91C2×#11758196—21no—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—21no—
94C4⋊#92418—21no—
95#14519700—24no—
96C22⋊#92418—21no—
97C4×#92418—21no—
98C4×#92418—21no—
99C4×#92418—21no—
100C2×#41×C61D411yescharacteristic
101C2×M16×C61—21no—
102C4×Q8×C61C2×C411yescharacteristic
103C4×Q8×C61D411yescharacteristic
104C4×D4×C61—21no—
105C4×D4×C61—21no—
106C4×D4×C61C2×C411yescharacteristic
107C4×D4×C61D411yescharacteristic
108#117×C61—21no—
109#117×C61D411yescharacteristic
110C2×C4⋊C4×C61—21no—
111C2×C42×C61—21no—
112C2×C42×C61—21no—
113C2×C42×C61C2311yescharacteristic
114C4⋊C8×C61—21no—
115C4⋊C8×C61—21no—
116#104×C61—42no—
117#95×C61—21no—
118#41×C61—21no—
119#41×C61—21no—
120#41×C61SD1612yes—
121#41×C61Q1612yes—
122C2×Q8×C61C22⋊C411yescharacteristic
123C2×D4×C61—21no—
124C2×D4×C61C22⋊C411yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—41no—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×Dic61—22no—
133C22×Dic61—21no—
134C22×Dic61—22no—
135C22×Dic61—21no—
136C2×Dic122—22no—
137C2×Dic122—22no—
138C2×Dic122—21no—
139C2×Dic122—21no—
140C2×Dic122—22no—
141C2×Dic122—41no—
142C2×Dic122—42no—
143C2×Dic122—42no—
144C2×Dic122C22⋊C411yescharacteristic
145C2×Dic122C22⋊C411yescharacteristic
146C2×Dic122C22⋊C412yes—
147M16×C61—41no—
148M16×C61—41no—
149C2×C8×C61—41no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61C22⋊C411yescharacteristic
155C4⋊C4×C61C22⋊C411yescharacteristic
156C22⋊C4×C61—21no—
157C22⋊C4×C61—21no—
158C22⋊C4×C61—21no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—41no—
163C42×C61—41no—
164C42×C61C22×C411yescharacteristic
165C42×C61C2×D411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C22⋊Dic61—22no—
169C22⋊Dic61—22no—
170C22⋊Dic61—22no—
171C4⋊Dic61—22no—
172C4⋊Dic61—22no—
173C4⋊Dic61—22no—
174C4⋊Dic61—22no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61C22⋊C411yescharacteristic
180C4⋊Dic61C22⋊C411yescharacteristic
181C4⋊Dic61C22⋊C412yes—
182#11758196—22no—
183#11758196—22no—
184#11758196—22no—
185#11758196—22no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—22no—
190#11758196—21no—
191#11758196—22no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—22no—
198C4×Dic61—21no—
199C2×#92418—22no—
200C2×#92418—41no—
201C2×#92418—41no—
202C2×#92418—41no—
203C23×C61—21no—
204C23×C61#12011yescharacteristic
205Q8×C61—21no—
206Q8×C61#10312yescomplemented
207D4×C61—22no—
208D4×C61—22no—
209D4×C61—21no—
210D4×C61#10312yescomplemented
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—42no—
222C2×C4×C61—81no—
223C2×C4×C61—81no—
224C2×C4×C61—81no—
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C22⋊C411yescharacteristic
227C2×C4×C61C2×C22⋊C411yescharacteristic
228C2×C4×C61#12011yescharacteristic
229C2×C4×C61#12011yescharacteristic
230C2×C4×C61#12011yescharacteristic
231C2×C4×C61C2×SD1611yescharacteristic
232C2×C4×C61C2×Q1611yescharacteristic
233C2×C4×C61#13711yescharacteristic
234C2×C4×C61#13711yescharacteristic
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—22no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—22no—
241C2×Dic61—42no—
242C2×Dic61—44no—
243C2×Dic61—81no—
244C2×Dic61—82no—
245Dic122—21no—
246Dic122—21no—
247Dic122—21no—
248Dic122—42no—
249Dic122—44no—
250Dic122—41no—
251Dic122—41no—
252Dic122—42no—
253Dic122—82no—
254Dic122#10412yescomplemented
255C8×C61—81no—
256#92418—42no—
257#92418—81no—
258#8439—611nomaximal, Sylow
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61#37911yescharacteristic
265C22×C61#44811yescharacteristic
266C22×C61#45111yescharacteristic
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—22no—
270C4×C61—21no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—82no—
274C4×C61C2×#10311yescharacteristic
275C4×C61#41911yescharacteristic
276C4×C61C2×#10411yescharacteristic
277C4×C61#42111yescharacteristic
278C4×C61#44811yescharacteristic
279C4×C61#45111yescharacteristic
280Dic61—22no—
281Dic61—42no—
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285Dic61—42no—
286Q8×#41—611no—
287#1806D6111yescharacteristic
288C4×#103—611no—
289#1503—611no—
290#1493—611no—
291#1487—611no—
292#1476—611no—
293C2×C61—21no—
294C2×C61—21no—
295C2×C61—42no—
296C2×C61#178711yescharacteristic
297C2×C61#178911yescharacteristic
298C2×C61#179411yescharacteristic
299Q82—611no—
300#557—611no—
301#557—1221no—
302#554—611no—
303#554—1221no—
304#554—1222no—
305#554—1221no—
306D4×Q8—611no—
307D4×Q8—1221no—
308#533—611no—
309#533—1221no—
310#533—1222no—
311#533—1221no—
312C4×#41—1221no—
313C4×#41C2×D6111yescharacteristic
314C2×C4×Q8—611no—
315C2×C4×Q8—1221no—
316#431—611no—
317#423C2×D6111yescharacteristic
318C2×#104—21no—
319C2×#103—1221no—
320C2×C4×C8—611no—
321C4×C4⋊C4C2×D6111yescharacteristic
322#340—1221no—
323#339—21no—
324#328—1222no—
325Q8⋊C8—1221no—
326Q8⋊C8—1221no—
327Q8⋊C8—1222no—
328Q8⋊C8—1221no—
329D4⋊C8—1221no—
330C61#843911yescharacteristic, complemented, Sylow
331C2×#41C22⋊D6111yescharacteristic
332C22×Q8—611no—
333C22×Q8—1221no—
334C2×M16—21no—
335C22×C8—1221no—
336C4⋊Q8—611no—
337C4⋊Q8—611no—
338C4⋊Q8—1221no—
339C4⋊Q8—1221no—
340C4⋊Q8—1222no—
341C4⋊Q8—1222no—
342C4⋊Q8—1221no—
343C4⋊Q8—1221no—
344#125—1222no—
345#125—1222no—
346#125—1222no—
347#125—1221no—
348#125—1221no—
349#125—1221no—
350C22⋊Q8—612no—
351C22⋊Q8—1222no—
352C22⋊Q8—1222no—
353C22⋊Q8—1222no—
354C22⋊Q8—1222no—
355C22⋊Q8—1222no—
356C22⋊Q8—1222no—
357C22⋊Q8—1221no—
358C22⋊Q8—1221no—
359C22⋊Q8—1222no—
360C22⋊Q8—1221no—
361C4×Q8—611no—
362C4×Q8—611no—
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—612no—
366C4×Q8—1221no—
367C4×Q8—1221no—
368C4×Q8—1222no—
369C4×Q8—1222no—
370C4×Q8—1222no—
371C4×Q8—1221no—
372C4×Q8—1221no—
373C4×Q8—1221no—
374C4×Q8—1221no—
375C4×Q8—1221no—
376C4×Q8C4×D6111yescharacteristic
377C4×Q8D24411yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—1222no—
381C4×D4—1222no—
382C4×D4—1221no—
383C4×D4—1221no—
384C4×D4C4×D6111yescharacteristic
385C4×D4D24411yescharacteristic
386#117—21no—
387#117—1222no—
388#117—1221no—
389#117C22⋊D6111yescharacteristic
390C2×C4⋊C4—21no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1222no—
394C2×C4⋊C4—1221no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—1222no—
398C2×C42—1221no—
399C2×C42C22×D6111yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—1221no—
403#104—42no—
404#103—1224no—
405C22⋊C8—1221no—
406C4×C8—1221no—
407C4×C8—1221no—
408C4×C8—1221no—
409#95—21no—
410#41—21no—
411#41—21no—
412#41#1175820012yes—
413#41#1175820212yes—
414C2×Q8—611no—
415C2×Q8—611no—
416C2×Q8—612no—
417C2×Q8—1222no—
418C2×Q8—1222no—
419C2×Q8—1222no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—2441no—
423C2×Q8—2442no—
424C2×Q8—2442no—
425C2×Q8#1175819811yescharacteristic
426C2×D4—21no—
427C2×D4#1175819811yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—1222no—
433C22×C4—1221no—
434C22×C4—1222no—
435C22×C4—1221no—
436C22×C4D4×D6111yescharacteristic
437C22×C4D4×D6111yescharacteristic
438C22×C4C2×C22⋊D6111yescharacteristic
439M16—41no—
440M16—41no—
441C2×C8—41no—
442C2×C8—1222no—
443C2×C8—2441no—
444C2×C8—2441no—
445C2×C8—2441no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—41no—
450C4⋊C4—611no—
451C4⋊C4—611no—
452C4⋊C4—612no—
453C4⋊C4—1222no—
454C4⋊C4—1222no—
455C4⋊C4—1222no—
456C4⋊C4—1222no—
457C4⋊C4—1222no—
458C4⋊C4—1222no—
459C4⋊C4—1222no—
460C4⋊C4—1222no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1222no—
470C4⋊C4—1222no—
471C4⋊C4#1175819811yescharacteristic
472C4⋊C4#1175819811yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—1222no—
477C22⋊C4—1222no—
478C22⋊C4—1222no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42—1222no—
485C42—1222no—
486C42—1221no—
487C42—1221no—
488C42—1221no—
489C42—1222no—
490C42—1221no—
491C42C2×C4×D6111yescharacteristic
492C42C2×D24411yescharacteristic
493C42D4×D6111yescharacteristic
494C42D4×D6111yescharacteristic
495C23—21no—
496C23#1451974511yescharacteristic
497Q8—21no—
498Q8—612no—
499Q8—1221no—
500Q8—1221no—
501Q8—1221no—
502Q8—4882no—
503Q8—2442no—
504Q8—2442no—
505Q8—2444no—
506Q8—2441no—
507Q8—2441no—
508Q8#1451970012yescomplemented
509D4—22no—
510D4—22no—
511D4—21no—
512D4#1451970012yescomplemented
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—81no—
525C2×C4—81no—
526C2×C4—81no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1222no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1222no—
533C2×C4—4881no—
534C2×C4—4882no—
535C2×C4—2442no—
536C2×C4—2444no—
537C2×C4C22⋊C4×D6111yescharacteristic
538C2×C4C22⋊C4×D6111yescharacteristic
539C2×C4C2×#1175819811yescharacteristic
540C2×C4#1451974511yescharacteristic
541C2×C4#1451974711yescharacteristic
542C2×C4#1451974711yescharacteristic
543C2×C4C2×#1175820011yescharacteristic
544C2×C4C2×#1175820211yescharacteristic
545C2×C4#1451980711yescharacteristic
546C2×C4#1451980711yescharacteristic
547C8—81no—
548C8—4881no—
549C8—2442no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22#1683961711yescharacteristic
556C22#1683990011yescharacteristic
557C22#1683991711yescharacteristic
558C4—22no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—82no—
565C4—1222no—
566C4—2441no—
567C4—2442no—
568C4—2441no—
569C4—2441no—
570C4—2442no—
571C4C2×#1451970011yescharacteristic
572C4#1683977011yescharacteristic
573C4#104×D6111yescharacteristic
574C4#1683977711yescharacteristic
575C4#1683990011yescharacteristic
576C4#1683991711yescharacteristic
577C2—21no—
578C2—21no—
579C2—42no—
580C2#2144575311yescharacteristic
581C2#2144576111yescharacteristic
582C2#2144578111yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1806C2
socleC22×C61#379
prime radicalC2×#41×C61D4
cosocleC2×C42×C61C23
hypercenter#1806D61
hypocenterC61#8439
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. C4×#14519700C2semidirect
3. #21444317C2semidirect
4. #21444273C2semidirect
5. #21444247C2semidirect
8. Q8×Dic122C4semidirect
9. #16840491C4semidirect
14. #16840469C4semidirect
16. D4×Dic122C4semidirect
206. Q8×C61#103semidirect
210. D4×C61#103semidirect
254. Dic122#104semidirect
330. C61#8439semidirect
508. Q8#14519700semidirect
512. D4#14519700semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1222
C4×#145197002
#214443172
#214442732
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C61×#18062
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