Finite Group Databasebeta

← #30602550

Subgroups — #30602550

Order 15616.

1254 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
1C2×#16840761C212yesmaximal
2#21461524C211yesmaximal, characteristic, complemented
3#21461518C211yesmaximal, characteristic, complemented
4#21461506C212yesmaximal, complemented
5C2×#16840244C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840761—24no—
9#16840761C418yescomplemented
10C2×#14519842—24no—
11#16840642—21no—
12#16840642—21no—
13#16840640—21no—
14#16840640—21no—
15#16840635—24no—
16C22×#11758226C2211yescharacteristic
17#16840244—24no—
18#16840244—24no—
19C2×Q8×Dic61C411yescharacteristic, complemented
20C2×C4×D244—21no—
21C2×C4×D244C411yescharacteristic, complemented
22C2×#14519739—21no—
23C2×#14519739C411yescharacteristic, complemented
24C2×#14519734—21no—
25C2×#14519734C2211yescharacteristic
26C2×C4⋊C4×D61—21no—
27C2×C4⋊C4×D61C2211yescharacteristic
28C2×C4×Q8×C61C411yescharacteristic, complemented
29C2×#11758213—22no—
30D61⋊M16—22no—
31D61⋊M16—22no—
32D61⋊M16—22no—
33D61⋊M16C2×C414yescomplemented
34C2×#11758217—22no—
35C2×D61⋊C8—22no—
36#14519856—22no—
37#14519856—22no—
38#14519856—22no—
39#14519856C2×C414yescomplemented
40C2×C4⋊#6923—22no—
41C2×C22⋊#6923—22no—
42C2×C4×#6923—22no—
43#14519842—216no—
44C2×#11758226—22no—
45C2×#11758226—22no—
46C2×#11758226—21no—
47C2×#11758226—21no—
48C2×#11758226C2×C414yes—
49C2×#11758226D414yes—
50C2×#11758226D412yes—
51C2×#11758226Q812yes—
52C22×D244—21no—
53C22×D244C2×C411yescharacteristic
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—21no—
57C22×C4×D61—21no—
58C22×C4×D61C2311yescharacteristic
59Q8×Dic61—22no—
60Q8×Dic61—22no—
61C4×D244—28no—
62C4×D244—22no—
63C4×D244—22no—
64#14519739—28no—
65#14519739—22no—
66#14519739—22no—
67#14519734—28no—
68#14519734—22no—
69#14519734—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×#11758196—21no—
73C2×#11758196D411yescharacteristic
74C2×#11758196D411yescharacteristic
75C4⋊C4×D61—28no—
76C4⋊C4×D61—22no—
77C4⋊C4×D61D414yes—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198D411yescharacteristic
81C2×#11758198D411yescharacteristic
82C2×C4×Dic61—21no—
83C2×C4×Dic61C2×C411yescharacteristic
84C22×Q8×C61C2×C411yescharacteristic
85C4×Q8×C61—22no—
86C4×Q8×C61—22no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61C2×C411yescharacteristic
89C2×C42×C61—21no—
90C2×C42×C61C2×C411yescharacteristic
91C23×D61—21no—
92C23×D61C2×D411yescharacteristic
93C22×#6923—42no—
94C2×Q8×C61—21no—
95C2×Q8×C61—21no—
96C2×Q8×C61—21no—
97C2×Q8×C61C4212yes—
98C2×Q8×C61C22⋊C412yes—
99C2×Q8×C61C4⋊C412yes—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C22⋊C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C22×Dic61—21no—
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C2×D411yescharacteristic
109#11758226—24no—
110#11758226—24no—
111#11758226—24no—
112#11758226—24no—
113#11758226—24no—
114#11758226—24no—
115#11758226C22⋊C418yes—
116#11758226C4⋊C418yes—
117C2×D244—24no—
118C2×D244—24no—
119C2×D244—22no—
120C2×D244—22no—
121C2×D244—21no—
122C2×D244—21no—
123C2×D244—21no—
124C2×D244C4212yes—
125C2×D244C22⋊C412yes—
126C2×D244C4⋊C412yes—
127C2×C4×D61—24no—
128C2×C4×D61—24no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—24no—
132C2×C4×D61—24no—
133C2×C4×D61—24no—
134C2×C4×D61—82no—
135C2×C4×D61—82no—
136C2×C4×D61—82no—
137C2×C4×D61C22×C412yes—
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×D412yes—
140C2×C4×D61C2×D412yes—
141C2×C4×D61C2×Q811yescharacteristic
142C2×C4×D61#4111yescharacteristic
143C2×C4×D61#4111yescharacteristic
144C2×C4×D61#4112yes—
145C22⋊#6923—24no—
146C22⋊#6923—42no—
147#11758217—24no—
148#11758217—42no—
149C2×#92420—42no—
150C4⋊#6923—24no—
151C4⋊#6923—42no—
152C4×#6923—24no—
153C4×#6923—42no—
154#11758213—24no—
155#11758213—42no—
156D61⋊C8—24no—
157D61⋊C8—42no—
158C4⋊C4×C61—24no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61C22⋊C412yes—
161C42×C61—24no—
162C42×C61—21no—
163C42×C61—21no—
164#11758198—24no—
165#11758198—24no—
166#11758198—22no—
167#11758198—22no—
168C4⋊Dic61—24no—
169C4⋊Dic61—21no—
170C4⋊Dic61C22⋊C412yes—
171#11758196—22no—
172#11758196—24no—
173#11758196—22no—
174C4×Dic61—24no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C23×C61C2×C22⋊C411yescharacteristic
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—22no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—42no—
184C22×D61—42no—
185C22×D61C4×D412yes—
186C22×D61#12012yes—
187C22×D61#12111yescharacteristic
188C22×D61C22⋊Q811yescharacteristic
189C2×#6923—44no—
190C2×#6923—82no—
191C2×#6923—82no—
192Q8×C61—22no—
193Q8×C61—22no—
194Q8×C61—22no—
195Q8×C61#9514yes—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—22no—
202C2×C4×C61—42no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61C2×C4211yescharacteristic
206C2×C4×C61C2×C22⋊C411yescharacteristic
207C2×C4×C61C2×C22⋊C411yescharacteristic
208C2×C4×C61C2×C4⋊C411yescharacteristic
209C2×C4×C61#11711yescharacteristic
210C2×C4×C61#11711yescharacteristic
211C2×Dic61—21no—
212C2×Dic61—21no—
213C2×Dic61—22no—
214C2×Dic61—42no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61C4×D412yes—
218C2×Dic61#12012yes—
219C2×Dic61#12111yescharacteristic
220C2×Dic61C22⋊Q811yescharacteristic
221D244—28no—
222D244—28no—
223D244—22no—
224D244—22no—
225D244—22no—
226D244#9514yes—
227C4×D61—28no—
228C4×D61—28no—
229C4×D61—84no—
230C4×D61—84no—
231C4×D61—84no—
232C4×D61C2×C22⋊C412yes—
233C4×D61C2×C4⋊C412yes—
234C4×D61C4×D412yes—
235C4×D61C4×D412yes—
236C4×D61#12112yes—
237C4×D61C22⋊Q812yes—
238C4×D61#12312yes—
239C4×D61#12312yes—
240#92420—44no—
241#10775—611nomaximal, Sylow
242C22×C61—21no—
243C22×C61—21no—
244C22×C61C4×C22⋊C411yescharacteristic
245C22×C61#37911yescharacteristic
246C22×C61#38011yescharacteristic
247C2×D61—22no—
248C2×D61—22no—
249C2×D61—24no—
250C2×D61—42no—
251C2×D61—41no—
252C2×D61—41no—
253C2×D61—44no—
254C2×D61—44no—
255C2×D61—42no—
256C2×D61—42no—
257C2×D61#38512yes—
258C2×D61#38612yes—
259#6923—84no—
260C4×C61—24no—
261C4×C61—41no—
262C4×C61—42no—
263C4×C61—41no—
264C4×C61C2×#9511yescharacteristic
265C4×C61C4×C22⋊C411yescharacteristic
266C4×C61#38011yescharacteristic
267C4×C61#38111yescharacteristic
268Dic61—41no—
269Dic61—42no—
270Dic61—41no—
271Dic61#38512yes—
272Dic61#38612yes—
273C2×#520—611no—
274C2×#421—612no—
275#1742—611no—
276#1740—611no—
277#1736—612no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61C22⋊#9511yescharacteristic
281C2×C61#179511yescharacteristic
282C2×C61#179611yescharacteristic
283D61—22no—
284D61—22no—
285D61—44no—
286C22×#41—611no—
287C22×M16—612no—
288#520—1224no—
289#520—1224no—
290C2×C4×Q8—611no—
291C2×C4×Q8#692311yescharacteristic, complemented
292C2×C4×D4—611no—
293C2×C4×D4—611no—
294C2×C4×D4—1221no—
295C2×C4×D4—1221no—
296C2×#117—611no—
297C2×#117—612no—
298C2×#117—1221no—
299C22×C4⋊C4—611no—
300C22×C4⋊C4—1221no—
301#421—618no—
302#421—1224no—
303C2×#104—1224no—
304#343—1221no—
305#343—1221no—
306#342—1221no—
307#342—1221no—
308#340—1224no—
309C61#1077511yescharacteristic, complemented, Sylow
310C2×#41—614no—
311C2×#41—612no—
312C2×#41—612no—
313C2×#41—614no—
314C2×#41—1222no—
315C2×#41—1221no—
316C2×#41—1222no—
317C2×#41—1221no—
318C22×Q8C2×#692311yescharacteristic
319C22×D4—611no—
320C22×D4—1221no—
321C23×C4—611no—
322C23×C4—1221no—
323C23×C4—1221no—
324C23×C4—1221no—
325C23×C4—1221no—
326C2×M16—614no—
327C2×M16—1222no—
328C2×M16—1222no—
329C2×M16—1222no—
330C2×M16—1222no—
331C2×M16—1222no—
332C22×C8—1222no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—1222no—
336C4×Q8—1222no—
337C4×D4—1222no—
338C4×D4—1222no—
339C4×D4—1228no—
340C4×D4—1222no—
341C4×D4—1228no—
342C4×D4—1222no—
343#117—614no—
344#117—1222no—
345#117—1222no—
346#117—1228no—
347#117—1222no—
348#117—1222no—
349#117—1222no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—611no—
352C2×C4⋊C4—614no—
353C2×C4⋊C4—611no—
354C2×C4⋊C4—611no—
355C2×C4⋊C4—1222no—
356C2×C4⋊C4—1228no—
357C2×C4⋊C4—1221no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1222no—
360C2×C4⋊C4C2×#692311yescharacteristic
361C2×C22⋊C4—611no—
362C2×C22⋊C4—611no—
363C2×C22⋊C4—1221no—
364C2×C22⋊C4—1221no—
365C2×C22⋊C4—1222no—
366C2×C42—21no—
367C2×C42—611no—
368C2×C42—1221no—
369C2×C42—1222no—
370C2×C42C2×#692311yescharacteristic
371#104—12216no—
372C24—611no—
373C24—1221no—
374#41—618no—
375#41—618no—
376#41—1224no—
377#41—1224no—
378#41—1224no—
379#41—1224no—
380#41—1224no—
381#41—1224no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8C4×#692312yes—
386C2×Q8C4⋊#692312yes—
387C2×Q8C22⋊#692312yes—
388C2×D4—612no—
389C2×D4—612no—
390C2×D4—612no—
391C2×D4—1224no—
392C2×D4—1222no—
393C2×D4—1222no—
394C2×D4—1224no—
395C2×D4—1221no—
396C2×D4—1221no—
397C2×D4—1221no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—611no—
401C22×C4—612no—
402C22×C4—612no—
403C22×C4—612no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—612no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—1224no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—1224no—
415C22×C4—1224no—
416C22×C4—1224no—
417C22×C4—1224no—
418C22×C4—1221no—
419C22×C4—4882no—
420C22×C4—4882no—
421C22×C4—4882no—
422C22×C4—2442no—
423C22×C4C22⋊#692311yescharacteristic
424C22×C4C22⋊#692311yescharacteristic
425C22×C4C22×#692311yescharacteristic
426M16—1224no—
427M16—1224no—
428M16—2442no—
429M16—2442no—
430C2×C8—1224no—
431C2×C8—2442no—
432C2×C8—2442no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—612no—
436C4⋊C4—1222no—
437C4⋊C4—1224no—
438C4⋊C4—1222no—
439C4⋊C4—1224no—
440C4⋊C4—1224no—
441C4⋊C4—1221no—
442C4⋊C4—2442no—
443C4⋊C4C22⋊#692312yes—
444C22⋊C4—1222no—
445C22⋊C4—1222no—
446C22⋊C4—1224no—
447C22⋊C4—1224no—
448C22⋊C4—1224no—
449C22⋊C4—2442no—
450C42—24no—
451C42—21no—
452C42—21no—
453C42—1224no—
454C42—1224no—
455C42—1221no—
456C42—1221no—
457C42—2442no—
458C23—612no—
459C23—611no—
460C23—611no—
461C23—612no—
462C23—1222no—
463C23—1222no—
464C23—1222no—
465C23—2441no—
466C23—2441no—
467C23—2442no—
468C23—2442no—
469C23C2×C22⋊#692311yescharacteristic
470Q8—22no—
471Q8—22no—
472Q8—22no—
473Q8(C2×#6923)⋊C414yes—
474D4—614no—
475D4—1228no—
476D4—1228no—
477D4—1222no—
478D4—1222no—
479D4—1222no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—611no—
490C2×C4—611no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—612no—
494C2×C4—612no—
495C2×C4—612no—
496C2×C4—612no—
497C2×C4—612no—
498C2×C4—612no—
499C2×C4—612no—
500C2×C4—612no—
501C2×C4—1228no—
502C2×C4—1228no—
503C2×C4—1221no—
504C2×C4—1222no—
505C2×C4—1221no—
506C2×C4—4884no—
507C2×C4—4884no—
508C2×C4—4884no—
509C2×C4—4882no—
510C2×C4—4882no—
511C2×C4—2444no—
512C2×C4—2442no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4C2×C4×#692311yescharacteristic
516C2×C4C2×C22⋊#692311yescharacteristic
517C2×C4C2×C22⋊#692311yescharacteristic
518C2×C4C2×C4⋊#692311yescharacteristic
519C2×C4#1451985611yescharacteristic
520C2×C4#1451985611yescharacteristic
521C8—2444no—
522C22—21no—
523C22—21no—
524C22—612no—
525C22—612no—
526C22—1222no—
527C22—1222no—
528C22—1224no—
529C22—2441no—
530C22—2441no—
531C22—2442no—
532C22—2444no—
533C22—2444no—
534C22—2442no—
535C22—2442no—
536C22C4×C22⋊#692311yescharacteristic
537C22#1684070311yescharacteristic
538C22#1684070411yescharacteristic
539C4—24no—
540C4—42no—
541C4—41no—
542C4—41no—
543C4—612no—
544C4—612no—
545C4—4884no—
546C4—2441no—
547C4—2442no—
548C4—2441no—
549C4C2×(C2×#6923)⋊C411yescharacteristic
550C4C4×C22⋊#692311yescharacteristic
551C4#1684070411yescharacteristic
552C4#1684070511yescharacteristic
553C2—21no—
554C2—21no—
555C2—1222no—
556C2—1222no—
557C2—2444no—
558C2#2146099311yescharacteristic
559C2#2146167011yescharacteristic
560C2#2146167111yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61#379
prime radicalC22×#11758226C22
cosocleC22×C4×D61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#10775
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #21461524C2semidirect
3. #21461518C2semidirect
4. #21461506C2semidirect
9. #16840761C4semidirect
19. C2×Q8×Dic61C4semidirect
21. C2×C4×D244C4semidirect
23. C2×#14519739C4semidirect
28. C2×C4×Q8×C61C4semidirect
33. D61⋊M16C2×C4semidirect
39. #14519856C2×C4semidirect
291. C2×C4×Q8#6923semidirect
309. C61#10775semidirect

Maximal subgroups

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

subgroupindex
C2×#168407612
#214615242
#214615182
#214615062
C2×#168402442
#1077561