Finite Group Databasebeta

← #29571502

Subgroups — #29571502

Order 15616.

1082 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840310C211yesmaximal, characteristic
2#21445796C211yesmaximal, characteristic, complemented
3#21445796C211yesmaximal, characteristic, complemented
4C2×#16839509C211yesmaximal, characteristic, complemented
5C2×#16839507C211yesmaximal, characteristic, complemented
6C2×#16839506C211yesmaximal, characteristic, complemented
7C2×C61×#331C211yesmaximal, characteristic, complemented
8C22×#11758224—21no—
9#16840310—22no—
10#16840310—22no—
11#16840310—22no—
12#16840310—22no—
13C2×#14519777C2211yescharacteristic
14C2×#14519764—21no—
15C2×#14519748—21no—
16C2×#14519748C412yes—
17C2×D4×Dic61—21no—
18C2×D4×Dic61C412yes—
19C2×C42×D61C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519689—21no—
23C2×#14519689—21no—
24#16839516—21no—
25#16839516—21no—
26#16839509—22no—
27#16839507—22no—
28#16839506—22no—
29C2×#127×C61C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C61×#331—22no—
33C2×#11758224—24no—
34C2×#11758224—24no—
35C2×#11758224—42no—
36C2×#11758224—42no—
37C2×#11758224—42no—
38C2×#11758224—42no—
39C22×Dic122—21no—
40C22×C22⋊D61—22no—
41C23×Dic61—22no—
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×#92418—21no—
46C22×#92418—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777D412yes—
50#14519777D412yes—
51#14519764—24no—
52#14519764—24no—
53#14519748—24no—
54#14519748—24no—
55#14519748—24no—
56#14519748—24no—
57D4×Dic61—24no—
58D4×Dic61—24no—
59D4×Dic61—24no—
60D4×Dic61—24no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61C2×C412yes—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—22no—
65C2×C4×Dic61C2×C411yescharacteristic
66C2×C4×Dic61D411yescharacteristic
67C2×C4×Dic61D411yescharacteristic
68C42×D61—21no—
69C42×D61—21no—
70C42×D61—21no—
71C42×D61—21no—
72C4⋊#92418—21no—
73C4⋊#92418—21no—
74C4⋊#92418—21no—
75C4⋊#92418—21no—
76#14519689—42no—
77#14519689—42no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61C2×C412yes—
81C22×C8×C61—21no—
82C22×C8×C61—21no—
83#127×C61—21no—
84#127×C61—21no—
85#127×C61D412yes—
86#127×C61D412yes—
87C2×C42×C61C2311yescharacteristic
88C4⋊C8×C61—21no—
89C4⋊C8×C61—21no—
90C4⋊C8×C61—21no—
91C4⋊C8×C61—21no—
92C24×C61—22no—
93C23×D61C22⋊C411yescharacteristic
94C2×D4×C61—22no—
95C2×D4×C61—22no—
96C2×D4×C61—22no—
97C2×D4×C61—22no—
98C2×D4×C61—22no—
99C2×D4×C61—42no—
100C2×D4×C61—42no—
101C2×D4×C61—41no—
102C2×D4×C61—41no—
103C2×D4×C61—41no—
104C2×D4×C61—41no—
105C2×D4×C61—41no—
106C2×D4×C61—41no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C2×D4×C61C22⋊C414yes—
110C22×C4×C61C22×C411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C2×C22⋊D61—28no—
114C2×C22⋊D61—44no—
115C2×C22⋊D61—44no—
116C22×Dic61—28no—
117C22×Dic61—22no—
118C22×Dic61—44no—
119C22×Dic61—44no—
120C22×Dic61C22⋊C411yescharacteristic
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C22⋊C411yescharacteristic
123#11758224—48no—
124#11758224—48no—
125#11758224—48no—
126#11758224—48no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—41no—
140C2×C4×D61—41no—
141C2×C4×D61D812yes—
142C2×C4×D61SD1612yes—
143C2×Dic122—22no—
144C2×Dic122—22no—
145C2×Dic122—41no—
146C2×Dic122—41no—
147C2×Dic122—41no—
148C2×Dic122—41no—
149C2×C8×C61—41no—
150C2×C8×C61—41no—
151C2×C8×C61—41no—
152C2×C8×C61—41no—
153C2×C8×C61—41no—
154C2×C8×C61—41no—
155C42×C61C2×D411yescharacteristic
156C42×C61C2×D411yescharacteristic
157C42×C61C2×D411yescharacteristic
158C42×C61C2×D411yescharacteristic
159C22⋊Dic61—28no—
160C22⋊Dic61—28no—
161C4⋊Dic61—22no—
162C4⋊Dic61—22no—
163C4⋊Dic61—22no—
164C4⋊Dic61C22⋊C414yes—
165C4×Dic61—21no—
166C4×Dic61—21no—
167C4×Dic61—21no—
168C4×Dic61—21no—
169C4×Dic61—21no—
170C4×Dic61—21no—
171C2×#92418—41no—
172C2×#92418—41no—
173C2×#92418—41no—
174C2×#92418—41no—
175C2×#92418—41no—
176C2×#92418—41no—
177C23×C61—24no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61C2×C22⋊C411yescharacteristic
185C22×D61—21no—
186C22×D61—21no—
187C22×D61—21no—
188C22×D61—21no—
189C22×D61—21no—
190C22×D61—21no—
191C22×D61#10212yes—
192D4×C61—44no—
193D4×C61—44no—
194D4×C61—42no—
195D4×C61—42no—
196D4×C61—42no—
197D4×C61—42no—
198D4×C61—42no—
199D4×C61—42no—
200D4×C61—42no—
201D4×C61—42no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61C2×C22⋊C411yescharacteristic
205C2×C4×C61C2×C22⋊C411yescharacteristic
206C2×C4×C61#12011yescharacteristic
207C2×C4×C61#12011yescharacteristic
208C2×C4×C61#12011yescharacteristic
209C2×C4×C61#12011yescharacteristic
210C2×C4×C61C2×D811yescharacteristic
211C2×C4×C61C2×SD1611yescharacteristic
212C2×C4×C61#13511yescharacteristic
213C2×C4×C61#13511yescharacteristic
214C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
215C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
216C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
217C2×C4×C61#13711yescharacteristic
218C22⋊D61—416no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—24no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—416no—
229C2×Dic61—42no—
230C2×Dic61—42no—
231C2×Dic61#10212yes—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—42no—
237C4×D61—42no—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—41no—
242Dic122—42no—
243Dic122—42no—
244Dic122—42no—
245Dic122—42no—
246C8×C61—81no—
247C8×C61—81no—
248#92418—81no—
249#92418—81no—
250#8341—611nomaximal, Sylow
251C22×C61—44no—
252C22×C61—44no—
253C22×C61—44no—
254C22×C61—82no—
255C22×C61—82no—
256C22×C61—82no—
257C22×C61—82no—
258C22×C61#37911yescharacteristic
259C22×C61#41311yescharacteristic
260C22×C61#41311yescharacteristic
261C22×C61C2×#10211yescharacteristic
262C22×C61#41611yescharacteristic
263C22×C61#41711yescharacteristic
264C22×C61#41811yescharacteristic
265C2×D61—22no—
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—41no—
269C2×D61—41no—
270C2×D61—41no—
271C2×D61—41no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61#44711yescharacteristic
275C4×C61#44711yescharacteristic
276C4×C61#44911yescharacteristic
277C4×C61#44911yescharacteristic
278C4×C61#45011yescharacteristic
279C4×C61#45011yescharacteristic
280C4×C61#45211yescharacteristic
281C4×C61#45211yescharacteristic
282Dic61—22no—
283Dic61—41no—
284Dic61—44no—
285Dic61—41no—
286C2×#532—611no—
287#1797—611no—
288#1797—611no—
289C2×#332—611no—
290C2×#332—611no—
291C2×#331—611no—
292C2×#331D6111yescharacteristic, complemented
293C2×C61—84no—
294C2×C61#154011yescharacteristic
295C2×C61#154711yescharacteristic
296C2×C61#155311yescharacteristic
297C2×C61#155711yescharacteristic
298C2×C61#178511yescharacteristic
299C2×C61#178611yescharacteristic
300C2×C61#178811yescharacteristic
301D61—42no—
302C22×#41—1221no—
303#532—1222no—
304#532—1222no—
305#532—1222no—
306#532—1222no—
307C2×C4⋊Q8—611no—
308C2×#127C2×D6111yescharacteristic
309C2×#124—1221no—
310C2×#121—612no—
311C2×#121—1221no—
312C2×C4×D4—612no—
313C2×C4×D4—1221no—
314C22×C42—611no—
315C2×C4⋊C8—611no—
316C2×C4⋊C8—611no—
317C2×C4⋊C8C2×D6111yescharacteristic
318C2×C4⋊C8C2×D6111yescharacteristic
319C2×C22⋊C8—1221no—
320C2×C22⋊C8—1221no—
321#336—1221no—
322#336—1221no—
323#332—1222no—
324#332—1222no—
325#331—22no—
326#331—1222no—
327C61#834111yescharacteristic, complemented, Sylow
328C2×#41—1224no—
329C2×#41—1224no—
330C2×#41—2442no—
331C2×#41—2442no—
332C2×#41—2442no—
333C2×#41—2442no—
334C22×Q8—1221no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—1222no—
338C22×D4C4×D6112yes—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—1222no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—1221no—
346C22×C8—1221no—
347C4⋊Q8—612no—
348C4⋊Q8—612no—
349C4⋊Q8—1221no—
350C4⋊Q8—1221no—
351#127—21no—
352#127—21no—
353#127D24412yes—
354#127C22⋊D6112yes—
355#124—1224no—
356#124—1224no—
357#121—1224no—
358#121—1224no—
359#121—1224no—
360#121—1224no—
361C4×D4—1224no—
362C4×D4—1224no—
363C4×D4—1224no—
364C4×D4—1224no—
365C2×C4⋊C4—612no—
366C2×C4⋊C4—1221no—
367C2×C22⋊C4—1222no—
368C2×C22⋊C4—1222no—
369C2×C42—611no—
370C2×C42—611no—
371C2×C42—611no—
372C2×C42—1221no—
373C2×C42—1221no—
374C2×C42—1221no—
375C2×C42—1221no—
376C2×C42C22×D6111yescharacteristic
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—1221no—
382C4⋊C8—1221no—
383C4⋊C8—1221no—
384C4⋊C8—1221no—
385C22⋊C8—2442no—
386C22⋊C8—2442no—
387C24—22no—
388C24—611no—
389#41—2448no—
390#41—2448no—
391#41—2448no—
392#41—2448no—
393C2×Q8—1222no—
394C2×Q8—1222no—
395C2×Q8—2441no—
396C2×Q8—2441no—
397C2×Q8—2441no—
398C2×Q8—2441no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—1228no—
415C2×D4—2444no—
416C2×D4—2444no—
417C2×D4#1175819814yes—
418C22×C4—611no—
419C22×C4—612no—
420C22×C4—612no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—1228no—
428C22×C4—1222no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—2441no—
438C22×C4—2441no—
439C22×C4—2444no—
440C22×C4—2444no—
441C22×C4C2×C4×D6111yescharacteristic
442C22×C4D4×D6111yescharacteristic
443C22×C4D4×D6111yescharacteristic
444C2×C8—41no—
445C2×C8—41no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—41no—
449C2×C8—41no—
450C2×C8—2441no—
451C2×C8—2441no—
452C2×C8—2441no—
453C2×C8—2441no—
454C2×C8—2441no—
455C2×C8—2441no—
456C4⋊C4—614no—
457C4⋊C4—1222no—
458C4⋊C4—1222no—
459C4⋊C4—1222no—
460C22⋊C4—1228no—
461C22⋊C4—1228no—
462C42—1221no—
463C42—1221no—
464C42—1221no—
465C42—1221no—
466C42—1221no—
467C42—1221no—
468C42C2×D24411yescharacteristic
469C42D4×D6111yescharacteristic
470C42D4×D6111yescharacteristic
471C42C2×C22⋊D6111yescharacteristic
472C23—24no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—612no—
480C23—1221no—
481C23—1221no—
482C23—1221no—
483C23—1221no—
484C23—1221no—
485C23—1221no—
486C23C22⋊C4×D6111yescharacteristic
487Q8—2442no—
488Q8—2442no—
489Q8—2442no—
490Q8—2442no—
491D4—44no—
492D4—44no—
493D4—42no—
494D4—42no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—24416no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—612no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—1224no—
518C2×C4—2442no—
519C2×C4—2442no—
520C2×C4—24416no—
521C2×C4—2442no—
522C2×C4—2442no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4C22⋊C4×D6111yescharacteristic
528C2×C4C2×#1175819811yescharacteristic
529C2×C4#1451974511yescharacteristic
530C2×C4#1451974511yescharacteristic
531C2×C4#1451974711yescharacteristic
532C2×C4#1451974711yescharacteristic
533C2×C4D8×D6111yescharacteristic
534C2×C4SD16×D6111yescharacteristic
535C2×C4#1451979611yescharacteristic
536C2×C4#1451979811yescharacteristic
537C2×C4#1451980111yescharacteristic
538C2×C4#1451980111yescharacteristic
539C2×C4#1451980411yescharacteristic
540C2×C4#1451980611yescharacteristic
541C8—81no—
542C8—81no—
543C8—4881no—
544C8—4881no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—1222no—
553C22—1222no—
554C22—1222no—
555C22—2441no—
556C22—2441no—
557C22—2441no—
558C22—2441no—
559C22#1683961711yescharacteristic
560C22#1683974311yescharacteristic
561C22#1683974311yescharacteristic
562C22#102×D6111yescharacteristic
563C22#1683975511yescharacteristic
564C22#1683976011yescharacteristic
565C22#1683976511yescharacteristic
566C4—21no—
567C4—21no—
568C4—1222no—
569C4—2441no—
570C4—2444no—
571C4—2441no—
572C4#1683989411yescharacteristic
573C4#1683989711yescharacteristic
574C4#1683990411yescharacteristic
575C4#1683990811yescharacteristic
576C4#1683991111yescharacteristic
577C4#1683991411yescharacteristic
578C4#1683992111yescharacteristic
579C4#1683992511yescharacteristic
580C2—84no—
581C2—2442no—
582C2#2144446511yescharacteristic
583C2#2144449311yescharacteristic
584C2#2144452111yescharacteristic
585C2#2144453811yescharacteristic
586C2#2144574411yescharacteristic
587C2#2144574811yescharacteristic
588C2#2144575611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#331C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#16840310C2
cosocleC2×C42×C61C23
hypercenterC2×#331D61
hypocenterC61#8341
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #21445796C2semidirect
3. #21445796C2semidirect
4. C2×#16839509C2semidirect
5. C2×#16839507C2semidirect
6. C2×#16839506C2semidirect
7. C2×C61×#331C2semidirect
292. C2×#331D61semidirect
327. C61#8341semidirect

Maximal subgroups

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

subgroupindex
C2×#168403102
#214457962
C2×#168395092
C2×#168395072
C2×#168395062
C2×C61×#3312
#834161