Finite Group Databasebeta

← #30620486

Subgroups — #30620486

Order 15616.

1314 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462620C212yesmaximal, complemented
2#21461961C212yesmaximal, complemented
3#21461961C214yesmaximal, complemented
4#21461684C212yesmaximal, complemented
5#21461683C211yesmaximal, characteristic, complemented
6#21461569C212yesmaximal, complemented
7C4×#14519837C211yesmaximal, characteristic, complemented
8C2×#16840430C211yesmaximal, characteristic
9#16840814—24no—
10#16840812—22no—
11#16840811—22no—
12#16840765C2212yes—
13#16840765C2214yes—
14C2×#14519837C2212yes—
15C2×#14519837C2214yes—
16C2×#14519837C2212yes—
17C2×#14519837C2214yes—
18C4×#11758217C2212yes—
19C4×#11758217C2214yes—
20#16840642C2211yescharacteristic
21#16840642C2211yescharacteristic
22#16840642C2212yes—
23C22×#11758222C411yescharacteristic
24C22×#11758224C411yescharacteristic
25#16840430—22no—
26#16840430—22no—
27#16840430—24no—
28C2×#14519773C2212yes—
29C2×#14519773C2211yescharacteristic
30C2×#14519752C411yescharacteristic
31C2×#14519750C412yes—
32C2×#14519749C412yes—
33C2×#14519742C2211yescharacteristic
34C2×C4×C22⋊D61C2211yescharacteristic
35C2×#14519737C2212yes—
36C2×#121×C61C411yescharacteristic
37C2×#11758217C2312yes—
38C2×#11758217C2314yes—
39C2×#11758217C2312yes—
40#14519844—24no—
41#14519844—22no—
42C4⋊#92420—22no—
43C4⋊#92420—24no—
44#14519837—24no—
45#14519837—28no—
46#14519837—42no—
47#14519837—44no—
48#14519832—24no—
49#14519832—22no—
50C4×#92420—22no—
51C4×#92420—24no—
52C2×#11758222—21no—
53C2×#11758222—22no—
54C2×#11758222—21no—
55C2×#11758222—44no—
56C2×#11758224—21no—
57C2×#11758224—22no—
58C2×#11758224—21no—
59C2×#11758224—44no—
60C22×Dic122C2×C411yescharacteristic
61C22×D244C2×C411yescharacteristic
62C22×D244C2×C412yes—
63C22×C22⋊D61C2×C412yes—
64C22×C22⋊D61C2×C412yes—
65C22×C22⋊D61C2×C412yes—
66C22×C22⋊D61C2312yes—
67C22×C22⋊D61C2311yescharacteristic
68C23×Dic61C2×C412yes—
69C22×C4×D61C2×C412yes—
70C22×C4×D61C2×C411yescharacteristic
71#14519773—22no—
72#14519773—24no—
73#14519773—24no—
74#14519773—22no—
75#14519752—22no—
76#14519752—22no—
77#14519750—24no—
78#14519750—24no—
79#14519749—24no—
80#14519749—24no—
81#14519742D412yes—
82#14519742D412yes—
83#14519742D414yes—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86#14519737—24no—
87#14519737—24no—
88C2×#11758196C2×C412yes—
89C2×#11758196C2311yescharacteristic
90C2×C22⋊Dic61C2×C411yescharacteristic
91C2×#11758198C2×C412yes—
92C2×#11758198C2×C411yescharacteristic
93C2×C4×Dic61C2312yes—
94C2×C4×Dic61C2311yescharacteristic
95C22×D4×C61C2×C411yescharacteristic
96C22×D4×C61C2×C412yes—
97C23×C4×C61C2×C411yescharacteristic
98#121×C61—22no—
99#121×C61—22no—
100C2×C4⋊C4×C61C2×C411yescharacteristic
101C2×C22⋊C4×C61C2×C412yes—
102C24×C61C22×C412yes—
103C24×C61C22×C411yescharacteristic
104C23×D61C22×C412yes—
105C23×D61C22×C411yescharacteristic
106C2×D4×C61—21no—
107C2×D4×C61—21no—
108C2×D4×C61—24no—
109C2×D4×C61—42no—
110C2×D4×C61—82no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—42no—
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C22×C411yescharacteristic
116C22×C4×C61C22×C412yes—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—22no—
119C2×C22⋊D61—22no—
120C2×C22⋊D61—22no—
121C2×C22⋊D61—24no—
122C2×C22⋊D61—24no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61—24no—
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61—21no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—21no—
130C2×C22⋊D61—44no—
131C2×C22⋊D61—44no—
132C2×C22⋊D61—82no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—44no—
136C22×Dic61C22×C412yes—
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C2411yescharacteristic
140#11758224—44no—
141#11758224—48no—
142#11758224—44no—
143#11758222—44no—
144#11758222—48no—
145#11758222—44no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—24no—
149C2×D244—42no—
150C2×D244—82no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—22no—
154C2×C4×D61—22no—
155C2×C4×D61—44no—
156C2×C4×D61—42no—
157C2×Dic122—24no—
158C2×Dic122C22⋊C411yescharacteristic
159C2×Dic122C22⋊C412yes—
160C2×Dic122C22⋊C411yescharacteristic
161#11758217—22no—
162#11758217—22no—
163#11758217—24no—
164#11758217—24no—
165#11758217—22no—
166#11758217#4114yescomplemented
167C2×#92420—22no—
168C2×#92420—22no—
169C2×#92420—24no—
170C4⋊C4×C61C22⋊C412yes—
171C4⋊C4×C61C22⋊C412yes—
172C22⋊C4×C61—24no—
173C22⋊Dic61—22no—
174#11758198—24no—
175#11758198—22no—
176#11758196—22no—
177#11758196C22⋊C414yes—
178#11758196C22⋊C414yes—
179C4×Dic61C2×D412yes—
180C4×Dic61C2×D414yes—
181C4×Dic61C2×D414yes—
182C4×Dic61C2×D412yes—
183C23×C61—21no—
184C23×C61—22no—
185C23×C61—22no—
186C23×C61—21no—
187C23×C61—22no—
188C23×C61—21no—
189C23×C61—42no—
190C23×C61—41no—
191C23×C61—42no—
192C23×C61—41no—
193C23×C61C23×C411yescharacteristic
194C22×D61—22no—
195C22×D61—21no—
196C22×D61—22no—
197C22×D61—21no—
198C22×D61—22no—
199C22×D61—21no—
200C22×D61—42no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—42no—
204D4×C61—42no—
205D4×C61—42no—
206D4×C61—84no—
207C2×C4×C61—22no—
208C2×C4×C61—21no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—41no—
213C2×C4×C61C2×C22⋊C414yes—
214C2×C4×C61C2×C22⋊C411yescharacteristic
215C2×C4×C61C2×C22⋊C411yescharacteristic
216C22⋊D61—44no—
217C22⋊D61—44no—
218C22⋊D61—44no—
219C22⋊D61—42no—
220C22⋊D61—44no—
221C22⋊D61—42no—
222C22⋊D61—44no—
223C22⋊D61—44no—
224C22⋊D61—84no—
225C2×Dic61—24no—
226C2×Dic61—21no—
227C2×Dic61—41no—
228C2×Dic61—44no—
229C2×Dic61—44no—
230C2×Dic61—41no—
231C2×Dic61C2×C22⋊C412yes—
232C2×Dic61C2×C22⋊C412yes—
233C2×Dic61C2×C22⋊C412yes—
234C2×Dic61C22×D412yes—
235C2×Dic61C2×#4112yes—
236C2×Dic61H(5,𝔽2)11yescharacteristic
237C2×Dic612−1+411yescharacteristic
238D244—42no—
239D244—42no—
240D244—84no—
241C4×D61—44no—
242C4×D61—42no—
243C4×D61—42no—
244C4×D61—44no—
245Dic122—22no—
246Dic122—24no—
247Dic122#10014yescomplemented
248#92420—24no—
249#92420—42no—
250#92420—44no—
251#22536—611nomaximal, Sylow
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—41no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—41no—
258C22×C61—42no—
259C22×C61—41no—
260C22×C61—82no—
261C22×C61—81no—
262C22×C61—82no—
263C22×C61—81no—
264C22×C61C22×C22⋊C411yescharacteristic
265C22×C61C4×#4111yescharacteristic
266C22×C61#52011yescharacteristic
267C2×D61—42no—
268C2×D61—41no—
269C2×D61—42no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—42no—
273C2×D61—82no—
274C2×D61—81no—
275C2×D61—82no—
276C2×D61—81no—
277C4×C61—21no—
278C4×C61—24no—
279C4×C61—41no—
280C4×C61C2×#10012yes—
281Dic61—22no—
282Dic61—22no—
283Dic61—41no—
284Dic61C2×#10014yes—
285Dic61#54812yes—
286Dic61#55012yes—
287C2×#550—611no—
288Q8×M16—612no—
289#1965—612no—
290#1965—614no—
291#1800—611no—
292#1800—612no—
293C4×#100—611no—
294C4×#100—612no—
295C2×C61—21no—
296C2×C61—21no—
297C2×C61—82no—
298C2×C61—81no—
299C2×C61#234111yescharacteristic
300C2×C61C22×#10011yescharacteristic
301C2×C61#288811yescharacteristic
302D61—82no—
303D61—81no—
304C22×#41—611no—
305C22×#41—611no—
306#550—1222no—
307#550—1224no—
308#550—1222no—
309C2×#127—611no—
310C2×#127—612no—
311C2×#121—612no—
312C2×#121—611no—
313C2×#121—612no—
314C2×#121#692311yescharacteristic
315C2×C4×Q8—611no—
316C2×C4×D4—611no—
317C2×C4×D4—612no—
318#446—1222no—
319#446—1224no—
320C8×Q8—1222no—
321#423—612no—
322#423—614no—
323C2×#100—612no—
324C2×#100—614no—
325C2×#100—612no—
326C2×#100—614no—
327C4×M16—612no—
328C4×M16—614no—
329#343—612no—
330#343—611no—
331#343—611no—
332C61#2253611yescharacteristic, complemented, Sylow
333C2×#41—1221no—
334C2×#41—1222no—
335C2×#41—1221no—
336C2×#41—1221no—
337C2×#41—1222no—
338C2×#41—1221no—
339C2×#41—2444no—
340C2×#41—2444no—
341C22×Q8—611no—
342C22×D4—611no—
343C22×D4—612no—
344C22×D4—612no—
345C22×D4—612no—
346C22×D4—612no—
347C22×D4—612no—
348C22×D4—611no—
349C22×D4C2×#692311yescharacteristic
350C22×D4C2×#692312yes—
351C23×C4—612no—
352C23×C4—612no—
353C23×C4—611no—
354C23×C4C2×#692311yescharacteristic
355C2×M16—612no—
356C2×M16—614no—
357C2×M16—612no—
358#127—1222no—
359#127—1224no—
360#127—1222no—
361#127—1224no—
362#121—22no—
363#121—22no—
364#121—1224no—
365#121—1224no—
366#121—1224no—
367#121—1224no—
368#121—1222no—
369#121—1222no—
370C4×Q8—612no—
371C4×Q8—612no—
372C4×Q8—614no—
373C4×D4—1224no—
374C4×D4—1224no—
375C4×D4—1222no—
376C4×D4—1222no—
377C2×C4⋊C4—612no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4C2×#692311yescharacteristic
380C2×C22⋊C4—611no—
381C2×C22⋊C4—611no—
382C2×C22⋊C4—612no—
383C2×C22⋊C4C2×#692312yes—
384C2×C42—612no—
385C2×C42—611no—
386C4⋊C8—1222no—
387C4⋊C8—1224no—
388C4⋊C8—1224no—
389C4⋊C8—1222no—
390#100—1224no—
391#100—1228no—
392#100—2442no—
393#100—2444no—
394#97—1224no—
395#97—1222no—
396C4×C8—1222no—
397C4×C8—1224no—
398C24—612no—
399C24—611no—
400C24C22×#692311yescharacteristic
401C24C22×#692312yes—
402#41—2444no—
403#41—2448no—
404#41—2444no—
405#41—2444no—
406#41—2448no—
407#41—2444no—
408C2×Q8—611no—
409C2×Q8—612no—
410C2×Q8—611no—
411C2×Q8—1224no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—24no—
415C2×D4—42no—
416C2×D4—82no—
417C2×D4—1224no—
418C2×D4—1222no—
419C2×D4—1224no—
420C2×D4—1221no—
421C2×D4—1222no—
422C2×D4—1224no—
423C2×D4—1222no—
424C2×D4—1222no—
425C2×D4—1222no—
426C2×D4—1222no—
427C2×D4—1222no—
428C2×D4—1221no—
429C2×D4—1222no—
430C2×D4—1224no—
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—4882no—
434C2×D4—4882no—
435C2×D4—2442no—
436C2×D4—2444no—
437C2×D4—2444no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—611no—
442C22×C4—612no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—2442no—
452C22×C4—2444no—
453C22×C4—2444no—
454C22×C4C22×#692311yescharacteristic
455C22×C4C22×#692311yescharacteristic
456C22×C4C22×#692312yes—
457M16—614no—
458M16—1222no—
459M16—1224no—
460M16—1222no—
461M16—1224no—
462M16—1222no—
463C2×C8—1222no—
464C2×C8—1224no—
465C2×C8—1222no—
466C4⋊C4—614no—
467C4⋊C4—614no—
468C4⋊C4—1222no—
469C4⋊C4C22⋊#692312yes—
470C4⋊C4C22⋊#692312yes—
471C22⋊C4—24no—
472C22⋊C4—1222no—
473C22⋊C4—1222no—
474C22⋊C4—1224no—
475C42—614no—
476C42—612no—
477C42—612no—
478C42—614no—
479C23—22no—
480C23—21no—
481C23—21no—
482C23—22no—
483C23—21no—
484C23—22no—
485C23—41no—
486C23—42no—
487C23—41no—
488C23—42no—
489C23—1222no—
490C23—1221no—
491C23—1222no—
492C23—1221no—
493C23—1221no—
494C23—1222no—
495C23—2442no—
496C23—2441no—
497C23—2441no—
498C23—2442no—
499C23C23×#692311yescharacteristic
500Q8—614no—
501Q8—1224no—
502Q8—1222no—
503D4—42no—
504D4—42no—
505D4—84no—
506D4—4884no—
507D4—4884no—
508D4—2442no—
509D4—2444no—
510D4—2442no—
511D4—2444no—
512D4—2442no—
513D4—2444no—
514D4—2444no—
515D4—2444no—
516D4—2444no—
517D4—2442no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—612no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—612no—
530C2×C4—612no—
531C2×C4—1224no—
532C2×C4—1221no—
533C2×C4—2442no—
534C2×C4—2444no—
535C2×C4—2444no—
536C2×C4—2444no—
537C2×C4—2441no—
538C2×C4—2444no—
539C2×C4—2442no—
540C2×C4—2441no—
541C2×C4C2×C22⋊#692314yes—
542C2×C4C2×C22⋊#692311yescharacteristic
543C2×C4C2×C22⋊#692311yescharacteristic
544C8—1224no—
545C8—2444no—
546C8—2442no—
547C22—21no—
548C22—21no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—42no—
553C22—41no—
554C22—42no—
555C22—81no—
556C22—82no—
557C22—81no—
558C22—82no—
559C22—4882no—
560C22—4881no—
561C22—4882no—
562C22—4881no—
563C22—2441no—
564C22—2442no—
565C22—2441no—
566C22—2442no—
567C22—2441no—
568C22—2442no—
569C22C22×C22⋊#692311yescharacteristic
570C22#41×#692311yescharacteristic
571C22#1684083111yescharacteristic
572C4—21no—
573C4—24no—
574C4—41no—
575C4—612no—
576C4—612no—
577C4—614no—
578C4—1222no—
579C4—1222no—
580C4—2441no—
581C4D61⋊#10012yes—
582C2—21no—
583C2—21no—
584C2—81no—
585C2—82no—
586C2—4881no—
587C2—4882no—
588C2#2146232411yescharacteristic
589C2C2×D61⋊#10011yescharacteristic
590C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#121×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840430C2
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#22536
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21462620C2semidirect
2. #21461961C2semidirect
3. #21461961C2semidirect
4. #21461684C2semidirect
5. #21461683C2semidirect
6. #21461569C2semidirect
7. C4×#14519837C2semidirect
166. #11758217#41semidirect
247. Dic122#100semidirect
332. C61#22536semidirect

Maximal subgroups

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

subgroupindex
#214626202
#214619612
#214616842
#214616832
#214615692
C4×#145198372
C2×#168404302
#2253661