Finite Group Databasebeta

← #29690542

Subgroups — #29690542

Order 15616.

834 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839814C211yesmaximal, characteristic
2#21448215C211yesmaximal, characteristic
3#382×D61C211yesmaximal, characteristic
4#21446589C211yesmaximal, characteristic, complemented
5#21446587C211yesmaximal, characteristic, complemented
6#21446585C211yesmaximal, characteristic, complemented
7#21446013C211yesmaximal, characteristic
8#21446010C211yesmaximal, characteristic
9#21446008C211yesmaximal, characteristic
10#21446005C211yesmaximal, characteristic
11#21445982C211yesmaximal, characteristic, complemented
12#21445980C211yesmaximal, characteristic, complemented
13#21445948C211yesmaximal, characteristic, complemented
14#21445948C211yesmaximal, characteristic, complemented
15C61×#1949C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D61C2211yescharacteristic
17C2×C4⋊C4×D61C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19#16839814C418yescomplemented
20C2×#14519711C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31#16839629—21no—
32#16839628C2211yescharacteristic
33#16839627C2211yescharacteristic
34#16839627C2211yescharacteristic
35#16839627C2211yescharacteristic
36#16839627C2211yescharacteristic
37#16839626—21no—
38#16839626—21no—
39#16839624—21no—
40#16839619C2211yescharacteristic
41#16839619C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×#11758198—21no—
44#16839608—21no—
45#95×D61—21no—
46#95×D61—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×#11758196—21no—
72C2×#11758196—21no—
73C4⋊C4×D61—41no—
74C4⋊C4×D61—41no—
75C4⋊C4×D61—41no—
76C4⋊C4×D61—41no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×C4×Dic61—21no—
80C2×C4×Dic61D411yescharacteristic
81C2×C4×Dic61D411yescharacteristic
82C2×C4×Dic61C2311yescharacteristic
83C42×D61C2×C414yes—
84C42×D61Q814yes—
85#14519711—41no—
86#14519710—41no—
87#14519710—41no—
88#14519709—41no—
89#14519708—41no—
90#14519708—41no—
91C4⋊#92418C2×C414yescomplemented
92#14519689C2×C414yes—
93#14519689C2×C414yes—
94C8×Dic61C2×C414yescomplemented
95C8×Dic61C2×C414yescomplemented
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117#107×C61—41no—
118#106×C61—41no—
119C4⋊C8×C61C2×C414yescomplemented
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123C23×D61C2×D411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—41no—
145C2×C4×D61—41no—
146C2×C4×D61—42no—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61—42no—
152C2×C4×D61C4⋊C414yes—
153C2×C4×D61C4⋊C414yes—
154C2×C4×D61C22×C412yes—
155C2×C4×D61C2×Q812yes—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61C22×C412yes—
161C2×C8×C61C22×C412yes—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C42×C61—42no—
171C42×C61C22×C412yes—
172C42×C61C2×Q812yes—
173#11758198—42no—
174#11758198—42no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183#11758196—42no—
184#11758196—42no—
185C4×Dic61—42no—
186C4×Dic61C4⋊C414yes—
187C4×Dic61C4⋊C414yes—
188C4×Dic61C22×C412yes—
189C4×Dic61C2×Q812yes—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418C22×C412yes—
195C2×#92418C22×C412yes—
196C23×C61C22×D411yescharacteristic
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C22×D61C2×C4⋊C412yes—
202C22×D61#13512yes—
203C22×D61#13512yes—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61C2×C4⋊C412yes—
221C2×C4×C61C2×C4⋊C412yes—
222C2×C4×C61C23×C411yescharacteristic
223C2×C4×C61C22×Q811yescharacteristic
224C2×C4×C61H(5,𝔽2)11yescharacteristic
225C2×C4×C61H(5,𝔽2)11yescharacteristic
226C2×C4×C612−1+411yescharacteristic
227C2×C4×C612−1+411yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61C2×C4⋊C412yes—
247C2×Dic61C2×C4⋊C412yes—
248C2×Dic61C2×C4⋊C412yes—
249C4×D61—28no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—22no—
253C4×D61—22no—
254C4×D61—44no—
255C4×D61—84no—
256C4×D61—84no—
257C8×C61—22no—
258C8×C61—22no—
259#92418—22no—
260#92418—22no—
261#21983—611nomaximal, Sylow
262C22×C61C22×C4⋊C411yescharacteristic
263C22×C61#53511yescharacteristic
264C22×C61#53611yescharacteristic
265C22×C61C2×#13511yescharacteristic
266C22×C61C2×#13511yescharacteristic
267C22×C61#57511yescharacteristic
268C22×C61#57511yescharacteristic
269C2×D61—22no—
270C2×D61—22no—
271C2×D61—22no—
272C2×D61—22no—
273C2×D61—22no—
274C2×D61—22no—
275C2×D61#42714yes—
276C4×C61—22no—
277C4×C61—22no—
278C4×C61—81no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61#52011yescharacteristic
283C4×C61#52011yescharacteristic
284C4×C61#54411yescharacteristic
285C4×C61#54411yescharacteristic
286Dic61—22no—
287Dic61—22no—
288Dic61—22no—
289Dic61—81no—
290Dic61—81no—
291Dic61—81no—
292Dic61—81no—
293C2×#431—611no—
294#2283—611no—
295C2×#382—611no—
296#1949—611no—
297#1949—611no—
298#1949—611no—
299#1949D6111yescharacteristic, complemented
300#1853—611no—
301#1853—611no—
302#1852—611no—
303#1852—611no—
304#1846—611no—
305#1846—611no—
306#1835—611no—
307#1835—611no—
308C2×C61#231711yescharacteristic
309C2×C61C2×#42711yescharacteristic
310C2×C61#291111yescharacteristic
311C2×C61#321111yescharacteristic
312C2×C61#321111yescharacteristic
313C2×C61#323211yescharacteristic
314C2×C61#323211yescharacteristic
315D61—24no—
316C22×C4⋊C4—611no—
317C22×C4⋊C4—611no—
318C22×C42—611no—
319#431—618no—
320C2×#107—611no—
321C2×#107—611no—
322C2×#107—611no—
323C2×#107C2×D6111yescharacteristic
324C2×#106—611no—
325C2×#106—611no—
326C2×#106—611no—
327C2×#106C2×D6111yescharacteristic
328C2×C4⋊C8—611no—
329C2×C4⋊C8C2×D6111yescharacteristic
330C2×C22⋊C8—611no—
331C2×C22⋊C8—611no—
332C2×C4×C8—611no—
333C2×C4×C8—611no—
334#383—1221no—
335#382—611no—
336#382—611no—
337#382—611no—
338#382—611no—
339#382—611no—
340#382—1221no—
341#382—1221no—
342#382C2×D6111yescharacteristic
343#381—1221no—
344#380—611no—
345#380—611no—
346C4×C4⋊C4—611no—
347C4×C4⋊C4C2×D6111yescharacteristic
348C4×C22⋊C4—1221no—
349#376—1221no—
350C2×#95—1221no—
351C2×#95—1221no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357#340—611no—
358#340C2×D6111yescharacteristic
359#340C2×D6111yescharacteristic
360C61#2198311yescharacteristic, complemented, Sylow
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—611no—
364C23×C4—1221no—
365C23×C4—1221no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8C22×D6111yescharacteristic
369C22×C8C22×D6111yescharacteristic
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—2441no—
377C2×C4⋊C4—2441no—
378C2×C4⋊C4—2441no—
379C2×C4⋊C4—2441no—
380C2×C4⋊C4C22×D6111yescharacteristic
381C2×C4⋊C4C22×D6111yescharacteristic
382C2×C4⋊C4C22×D6111yescharacteristic
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C42—21no—
387C2×C42—611no—
388C2×C42—611no—
389C2×C42—611no—
390C2×C42—614no—
391C2×C42—614no—
392C2×C42—1221no—
393C2×C42C22×D6111yescharacteristic
394#107—41no—
395#107—2441no—
396#107—2441no—
397#107—2441no—
398#106—41no—
399#106—2441no—
400#106—2441no—
401#106—2441no—
402C4⋊C8—614no—
403C4⋊C8C4×D6114yescomplemented
404C22⋊C8—614no—
405C22⋊C8—614no—
406C4×C8—614no—
407C4×C8—614no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423#95—1221no—
424C24—611no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—612no—
433C22×C4—612no—
434C22×C4—614no—
435C22×C4—614no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4—2442no—
449C22×C4—2442no—
450C22×C4—2442no—
451C22×C4—2442no—
452C22×C4—2442no—
453C22×C4—2442no—
454C22×C4D4×D6111yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4C23×D6111yescharacteristic
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—612no—
462C2×C8—612no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8C2×C4×D6112yes—
468C2×C8C2×C4×D6112yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—2442no—
486C4⋊C4—2442no—
487C22⋊C4—2442no—
488C22⋊C4—2442no—
489C42—42no—
490C42—612no—
491C42—612no—
492C42—614no—
493C42—614no—
494C42—2442no—
495C42C2×C4×D6112yes—
496C42Q8×D6112yes—
497C23—612no—
498C23—612no—
499C23—612no—
500C23—1221no—
501C23—1221no—
502C23—1221no—
503C23—1221no—
504C23C2×D4×D6111yescharacteristic
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—1228no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—4884no—
536C2×C4—4884no—
537C2×C4—2444no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4C4⋊C4×D6112yes—
551C2×C4C4⋊C4×D6112yes—
552C2×C4C22×C4×D6111yescharacteristic
553C2×C4C2×Q8×D6111yescharacteristic
554C2×C4#1451982211yescharacteristic
555C2×C4#1451982311yescharacteristic
556C2×C4#1451982411yescharacteristic
557C2×C4#1451982511yescharacteristic
558C8—22no—
559C8—22no—
560C8—1222no—
561C8—1222no—
562C22—614no—
563C22—1222no—
564C22—1222no—
565C22—1222no—
566C22—1222no—
567C22—1222no—
568C22—1222no—
569C22C2×C4⋊C4×D6111yescharacteristic
570C22#1684032811yescharacteristic
571C22#1684033511yescharacteristic
572C22#135×D6111yescharacteristic
573C22#135×D6111yescharacteristic
574C22#1684055811yescharacteristic
575C22#1684056111yescharacteristic
576C4—22no—
577C4—22no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—1222no—
583C4—1222no—
584C4—1222no—
585C4—4881no—
586C4—4881no—
587C4—4881no—
588C4—4881no—
589C4#1684024111yescharacteristic
590C4#1684024411yescharacteristic
591C4#1684038911yescharacteristic
592C4#1684039211yescharacteristic
593C2—1224no—
594C2#2144844111yescharacteristic
595C2#427×D6111yescharacteristic
596C2#2145440611yescharacteristic
597C2#2145678211yescharacteristic
598C2#2145678811yescharacteristic
599C2#2145698511yescharacteristic
600C2#2145699111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1949C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1949D61
hypocenterC61#21983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #21446589C2semidirect
5. #21446587C2semidirect
6. #21446585C2semidirect
11. #21445982C2semidirect
12. #21445980C2semidirect
13. #21445948C2semidirect
14. #21445948C2semidirect
15. C61×#1949C2semidirect
19. #16839814C4semidirect
91. C4⋊#92418C2×C4semidirect
94. C8×Dic61C2×C4semidirect
95. C8×Dic61C2×C4semidirect
119. C4⋊C8×C61C2×C4semidirect
299. #1949D61semidirect
360. C61#21983semidirect
403. C4⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398142
#214482152
#382×D612
#214465892
#214465872
#214465852
#214460132
#214460102
#214460082
#214460052
#214459822
#214459802
#214459482
C61×#19492
#2198361