Finite Group Databasebeta

← #30602427

Subgroups — #30602427

Order 15616.

1334 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3C2×#16840644C214yesmaximal, complemented
4C2×#16839724C211yesmaximal, characteristic
5C22×#11758213—21no—
6C2×D61⋊M16—28no—
7C2×D61⋊M16—21no—
8C2×D61⋊M16—21no—
9C2×D61⋊M16C412yescomplemented
10C2×D61⋊M16C2212yes—
11C22×#11758217C412yescomplemented
12C22×D61⋊C8—21no—
13C2×#14519856C2212yes—
14#16840705C412yes—
15#16840704—21no—
16#16840704—21no—
17#16840703C412yes—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923—21no—
20#16840644—28no—
21C23×C4×D61C2211yescharacteristic
22C22×#11758189C2212yes—
23#16839724—21no—
24#16839724—21no—
25#16839724—21no—
26#16839724—21no—
27C2×C22⋊#92418C411yescharacteristic, complemented
28C2×#14519689C412yescomplemented
29C2×C22⋊C8×C61C411yescharacteristic, complemented
30C2×#11758213—28no—
31C2×#11758213—22no—
32C2×#11758213—22no—
33D61⋊M16—28no—
34D61⋊M16—28no—
35D61⋊M16—24no—
36D61⋊M16—28no—
37D61⋊M16D418yes—
38C2×#11758217—22no—
39C2×#11758217—28no—
40C2×#11758217C2×C414yes—
41C2×D61⋊C8—28no—
42C2×D61⋊C8—22no—
43C2×D61⋊C8—22no—
44C22×#92420—22no—
45#14519856—24no—
46#14519856—24no—
47C2×C4⋊#6923—22no—
48C2×C22⋊#6923—22no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923C2×C414yes—
51C2×C4×#6923—22no—
52(C2×#6923)⋊C4—22no—
53(C2×#6923)⋊C4—22no—
54C24×D61C2×C411yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61Q811yescharacteristic
68C22×C4×D61Q811yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C2×#11758189—22no—
71C2×#11758189—22no—
72C2×#11758189—24no—
73C2×#11758189—24no—
74C22×#92418C2×C412yes—
75C22⋊#92418—21no—
76C22⋊#92418—21no—
77#14519689—22no—
78#14519689—22no—
79C23×C4×C61C2×C411yescharacteristic
80C22×C8×C61C2×C412yes—
81C22⋊C8×C61—21no—
82C22⋊C8×C61—21no—
83C24×C61C4211yescharacteristic
84C23×D61—24no—
85C23×D61—42no—
86C23×D61—42no—
87C23×D61C4211yescharacteristic
88C23×D61C22⋊C411yescharacteristic
89C23×D61C22⋊C411yescharacteristic
90C23×D61C4⋊C411yescharacteristic
91C23×D61C4⋊C411yescharacteristic
92C23×D61C22×C411yescharacteristic
93C22×#6923—24no—
94C22×C4×C61—24no—
95C22×C4×C61C4211yescharacteristic
96C22×C4×C61C22⋊C411yescharacteristic
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C4⋊C411yescharacteristic
99C22×C4×C61C4⋊C411yescharacteristic
100C22×C4×C61C22×C411yescharacteristic
101C22×Dic61—22no—
102C22×Dic61—22no—
103C22×Dic61C4211yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C4⋊C411yescharacteristic
107C22×Dic61C4⋊C411yescharacteristic
108C22×Dic61C22×C411yescharacteristic
109C2×C4×D61—24no—
110C2×C4×D61—24no—
111C2×C4×D61—22no—
112C2×C4×D61—22no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—24no—
118C2×C4×D61—24no—
119C2×C4×D61—24no—
120C2×C4×D61—24no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61C22⋊C411yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C4⋊C411yescharacteristic
132C2×C4×D61C4⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C4⋊C411yescharacteristic
137C2×C4×D61C2×D414yes—
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×D411yescharacteristic
140C2×C4×D61C2×D411yescharacteristic
141C2×C4×D61C2×Q811yescharacteristic
142C2×C4×D61#4114yes—
143C22⋊#6923—28no—
144C22⋊#6923—44no—
145C22⋊#6923—44no—
146#11758217—28no—
147#11758217—24no—
148#11758217C22⋊C418yescomplemented
149C2×#92420—28no—
150C2×#92420—24no—
151C4⋊#6923—42no—
152C4⋊#6923—42no—
153C4×#6923—44no—
154#11758213—28no—
155#11758213—28no—
156D61⋊C8—28no—
157D61⋊C8—28no—
158C2×C8×C61—22no—
159C2×C8×C61—24no—
160C2×#92418—22no—
161C2×#92418—24no—
162#11758189—42no—
163#11758189—44no—
164#11758189—42no—
165C23×C61—22no—
166C23×C61—22no—
167C23×C61—41no—
168C23×C61#9511yescharacteristic
169C23×C61#9511yescharacteristic
170C23×C61C2×C4211yescharacteristic
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—22no—
181C22×D61—41no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—416no—
189C22×D61#9511yescharacteristic
190C22×D61#9511yescharacteristic
191C22×D61C2×C22⋊C411yescharacteristic
192C22×D61C2×C4⋊C411yescharacteristic
193C22×D61C4×D414yes—
194C2×#6923—44no—
195C2×#6923—44no—
196C2×#6923—44no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61#9511yescharacteristic
203C2×C4×C61#9511yescharacteristic
204C2×C4×C61C2×C22⋊C411yescharacteristic
205C2×C4×C61C2×C4⋊C411yescharacteristic
206C2×C4×C61C4×D414yes—
207C2×Dic61—22no—
208C2×Dic61—21no—
209C2×Dic61—21no—
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—21no—
213C2×Dic61—21no—
214C2×Dic61#9511yescharacteristic
215C2×Dic61#9511yescharacteristic
216C2×Dic61C2×C22⋊C412yes—
217C2×Dic61C2×C22⋊C411yescharacteristic
218C2×Dic61C2×C4⋊C411yescharacteristic
219C2×Dic61#11712yes—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—22no—
223C4×D61—22no—
224C4×D61—22no—
225C4×D61—22no—
226C4×D61—22no—
227C4×D61—22no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—22no—
231C4×D61—22no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61#12012yes—
235C4×D61#12012yes—
236C4×D61#12114yes—
237C4×D61C22⋊Q814yes—
238C4×D61#12312yes—
239C4×D61#12312yes—
240#92420—28no—
241C8×C61—42no—
242#92418—42no—
243#10737—611nomaximal, Sylow
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—44no—
252C22×C61#34412yescomplemented
253C22×C61C2×#9511yescharacteristic
254C22×C61C4×C22⋊C412yes—
255C2×D61—28no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—44no—
266C2×D61—44no—
267C2×D61—44no—
268C2×D61—44no—
269C2×D61—44no—
270C2×D61#34412yescomplemented
271C2×D61#38512yes—
272C2×D61#38612yes—
273#6923—84no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61#38512yes—
277C4×C61#38612yes—
278Dic61—21no—
279Dic61—21no—
280Dic61#37911yescharacteristic
281Dic61#38012yes—
282Dic61#38111yescharacteristic
283C23×M16—611no—
284C2×#407—611no—
285#2280—611no—
286C2×#344—614no—
287C2×C61—22no—
288C2×C61—22no—
289C2×C61—41no—
290C2×C61C22⋊#9511yescharacteristic
291C2×C61C2×#34411yescharacteristic
292C2×C61C2×#34411yescharacteristic
293D61—22no—
294D61—22no—
295D61—22no—
296D61—41no—
297C24×C4—611no—
298C22×M16—612no—
299C22×M16—612no—
300C22×M16—612no—
301C22×M16—612no—
302C22×M16—1228no—
303C22×M16—1221no—
304C22×M16—1221no—
305C22×M16—1221no—
306C23×C8—1221no—
307C2×#117—612no—
308#407—1221no—
309#407—1221no—
310#407—1221no—
311#407—1221no—
312C2×C22⋊C8—611no—
313C2×C22⋊C8—612no—
314C2×C22⋊C8#692311yescharacteristic, complemented
315#381—612no—
316#380—1221no—
317#380—1221no—
318#379—612no—
319C4×C22⋊C4—1221no—
320C4×C22⋊C4—1221no—
321#344—1228no—
322C61#1073711yescharacteristic, complemented, Sylow
323C25—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—611no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—611no—
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—1224no—
338C23×C4—1224no—
339C23×C4C2×#692311yescharacteristic
340C2×M16—614no—
341C2×M16—618no—
342C2×M16—1224no—
343C2×M16—1222no—
344C2×M16—1222no—
345C2×M16—1224no—
346C2×M16—1228no—
347C2×M16—1228no—
348C2×M16—1222no—
349C2×M16—1224no—
350C2×M16—1222no—
351C2×M16—1222no—
352C2×M16—1228no—
353C2×M16—1228no—
354C2×M16—1228no—
355C22×C8—612no—
356C22×C8—1222no—
357C22×C8—1222no—
358C22×C8—1222no—
359C22×C8—1228no—
360C22×C8C2×#692312yes—
361#117—1224no—
362#117—1224no—
363C2×C4⋊C4—1222no—
364C2×C22⋊C4—614no—
365C2×C22⋊C4—1222no—
366C2×C22⋊C4—1222no—
367C2×C42—1222no—
368C22⋊C8—21no—
369C22⋊C8—21no—
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372C22⋊C8—1221no—
373C22⋊C8—1221no—
374#95—1222no—
375#95—1222no—
376C24—611no—
377C24—611no—
378C24—611no—
379C24—611no—
380C24—611no—
381C24—611no—
382C24—1224no—
383C24—2442no—
384C24—2442no—
385C24C4×#692311yescharacteristic
386C22×C4—24no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—614no—
393C22×C4—614no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—1222no—
412C22×C4—1222no—
413C22×C4—1222no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1222no—
417C22×C4—1224no—
418C22×C4—1224no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1224no—
422C22×C4—1224no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1224no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1224no—
429C22×C4—1224no—
430C22×C4C4×#692311yescharacteristic
431C22×C4C4⋊#692311yescharacteristic
432C22×C4C4⋊#692311yescharacteristic
433C22×C4C22⋊#692311yescharacteristic
434C22×C4C22⋊#692311yescharacteristic
435C22×C4C22×#692311yescharacteristic
436M16—618no—
437M16—1228no—
438M16—1224no—
439M16—1228no—
440M16—1228no—
441M16—2442no—
442M16—2444no—
443M16—2442no—
444C2×C8—22no—
445C2×C8—24no—
446C2×C8—1228no—
447C2×C8—1224no—
448C2×C8—1228no—
449C2×C8—1228no—
450C2×C8—1222no—
451C2×C8—1224no—
452C4⋊C4—2442no—
453C4⋊C4—2442no—
454C22⋊C4—1228no—
455C22⋊C4—2444no—
456C22⋊C4—2444no—
457C42—2444no—
458C23—22no—
459C23—22no—
460C23—41no—
461C23—611no—
462C23—611no—
463C23—611no—
464C23—614no—
465C23—611no—
466C23—1222no—
467C23—1222no—
468C23—1222no—
469C23—1222no—
470C23—1222no—
471C23—1222no—
472C23—1222no—
473C23—1222no—
474C23—1222no—
475C23—1222no—
476C23—2441no—
477C23—2441no—
478C23—2441no—
479C23—2441no—
480C23—2441no—
481C23—2441no—
482C23—2441no—
483C23—24416no—
484C23(C2×#6923)⋊C411yescharacteristic
485C23(C2×#6923)⋊C411yescharacteristic
486C23C2×C4×#692311yescharacteristic
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—611no—
493C2×C4—611no—
494C2×C4—612no—
495C2×C4—612no—
496C2×C4—612no—
497C2×C4—614no—
498C2×C4—612no—
499C2×C4—612no—
500C2×C4—614no—
501C2×C4—612no—
502C2×C4—611no—
503C2×C4—611no—
504C2×C4—1221no—
505C2×C4—1221no—
506C2×C4—1222no—
507C2×C4—1222no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—1222no—
513C2×C4—1222no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—2444no—
526C2×C4—2444no—
527C2×C4—2444no—
528C2×C4(C2×#6923)⋊C411yescharacteristic
529C2×C4(C2×#6923)⋊C411yescharacteristic
530C2×C4C2×C22⋊#692311yescharacteristic
531C2×C4C2×C4⋊#692311yescharacteristic
532C2×C4D4×#692314yes—
533C8—42no—
534C8—1228no—
535C8—2442no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—44no—
544C22—612no—
545C22—612no—
546C22—612no—
547C22—1228no—
548C22—1221no—
549C22—1221no—
550C22—1221no—
551C22—1221no—
552C22—1221no—
553C22—1221no—
554C22—1221no—
555C22—1221no—
556C22—1221no—
557C22—2444no—
558C22—2444no—
559C22—2444no—
560C22—2444no—
561C22—2444no—
562C22#1684064412yescomplemented
563C22C2×(C2×#6923)⋊C411yescharacteristic
564C22C22⋊C4×#692312yes—
565C4—21no—
566C4—21no—
567C4—611no—
568C4—612no—
569C4—611no—
570C4—1221no—
571C4—1221no—
572C4—4884no—
573C4#1684070912yes—
574C4#1684071012yes—
575C2—22no—
576C2—22no—
577C2—41no—
578C2—1222no—
579C2—1222no—
580C2—1222no—
581C2—2441no—
582C2#2146099211yescharacteristic
583C2C2×#1684064411yescharacteristic
584C2#2146152911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#10737
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#16840644C2semidirect
9. C2×D61⋊M16C4semidirect
11. C22×#11758217C4semidirect
27. C2×C22⋊#92418C4semidirect
28. C2×#14519689C4semidirect
29. C2×C22⋊C8×C61C4semidirect
148. #11758217C22⋊C4semidirect
252. C22×C61#344semidirect
270. C2×D61#344semidirect
314. C2×C22⋊C8#6923semidirect
322. C61#10737semidirect
562. C22#16840644semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
#214622632
C2×#168406442
C2×#168397242
#1073761