Finite Group Databasebeta

← #29690549

Subgroups — #29690549

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839814C211yesmaximal, characteristic
2#21448225C211yesmaximal, characteristic
3#21448223C211yesmaximal, characteristic
4#21446589C211yesmaximal, characteristic, complemented
5#21446587C211yesmaximal, characteristic, complemented
6#21446585C211yesmaximal, characteristic, complemented
7#21446021C211yesmaximal, characteristic
8#21446019C211yesmaximal, characteristic
9#21446017C211yesmaximal, characteristic
10#21446015C211yesmaximal, characteristic
11#21445977C211yesmaximal, characteristic, complemented
12#21445974C211yesmaximal, characteristic, complemented
13#21445945C211yesmaximal, characteristic, complemented
14#21445945C211yesmaximal, characteristic, complemented
15C61×#1949C211yesmaximal, characteristic, complemented
16C2×#14519735C2211yescharacteristic
17C2×#14519735C2211yescharacteristic
18C2×#14519734—21no—
19C2×C42×D61C2211yescharacteristic
20#16839814C418yescomplemented
21C2×#14519711C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519709C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×C8×Dic61C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839631C2211yescharacteristic
33#16839631C2211yescharacteristic
34#16839631C2211yescharacteristic
35#16839631C2211yescharacteristic
36#16839628C2211yescharacteristic
37#16839626—21no—
38#16839621—21no—
39#16839621—21no—
40#16839621—21no—
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43C4×#11758196—21no—
44C4×C4⋊Dic61C2211yescharacteristic
45#16839613—21no—
46#16839613—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×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519735—41no—
66#14519735—41no—
67#14519735—41no—
68#14519735—41no—
69#14519734—44no—
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61D411yescharacteristic
90C2×C4×Dic61D411yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C42×D61C2×C414yes—
93C42×D61Q814yes—
94#14519711—41no—
95#14519710—41no—
96#14519710—41no—
97#14519709—41no—
98#14519708—41no—
99#14519708—41no—
100C4⋊#92418C2×C414yes—
101#14519689C2×C414yes—
102#14519689C2×C414yes—
103C8×Dic61C2×C414yes—
104C8×Dic61C2×C414yes—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118#107×C61—41no—
119#106×C61—41no—
120C4⋊C8×C61C2×C414yes—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124C23×D61C2×D411yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2411yescharacteristic
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61C4⋊C414yes—
148C2×C4×D61C4⋊C414yes—
149C2×C4×D61C22×C412yes—
150C2×C4×D61C2×Q812yes—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61C22×C412yes—
156C2×C8×C61C22×C412yes—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C42×C61—42no—
166C42×C61C22×C412yes—
167C42×C61C2×Q812yes—
168#11758198—42no—
169#11758198—42no—
170#11758198—42no—
171#11758198—42no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180#11758196—42no—
181#11758196—42no—
182#11758196—42no—
183#11758196—42no—
184#11758196—42no—
185#11758196—42no—
186#11758196—42no—
187#11758196—42no—
188C4×Dic61—42no—
189C4×Dic61—42no—
190C4×Dic61—42no—
191C4×Dic61C4⋊C414yes—
192C4×Dic61C4⋊C414yes—
193C4×Dic61C22×C412yes—
194C4×Dic61C2×Q812yes—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C22×C412yes—
200C2×#92418C22×C412yes—
201C23×C61C22×D411yescharacteristic
202C22×D61—21no—
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61C2×C4⋊C412yes—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
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×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61C2×C4⋊C412yes—
226C2×C4×C61C2×C4⋊C412yes—
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×Q811yescharacteristic
229C2×C4×C61H(5,𝔽2)11yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C2×C4×C612−1+411yescharacteristic
232C2×C4×C612−1+411yescharacteristic
233C2×Dic61—21no—
234C2×Dic61—21no—
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×Dic61—41no—
247C2×Dic61C2×C4⋊C412yes—
248C2×Dic61C2×C4⋊C412yes—
249C2×Dic61C2×C4⋊C412yes—
250C2×Dic61#13512yes—
251C2×Dic61#13512yes—
252C2×Dic61AGL(1,ℤ/8)12yes—
253C2×Dic61#13712yes—
254C4×D61—22no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—28no—
259C4×D61—28no—
260C8×C61—22no—
261C8×C61—22no—
262#92418—22no—
263#92418—22no—
264#21984—611nomaximal, Sylow
265C22×C61C22×C4⋊C411yescharacteristic
266C22×C61#53511yescharacteristic
267C22×C61#53611yescharacteristic
268C22×C61C2×#13511yescharacteristic
269C22×C61C2×#13511yescharacteristic
270C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C61C2×#13711yescharacteristic
272C2×D61—22no—
273C2×D61—22no—
274C2×D61—22no—
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C4×C61—22no—
280C4×C61—22no—
281C4×C61—81no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61#52011yescharacteristic
286C4×C61#52011yescharacteristic
287C4×C61#54411yescharacteristic
288C4×C61#54411yescharacteristic
289Dic61—22no—
290Dic61—81no—
291Dic61—81no—
292Dic61—81no—
293Dic61—81no—
294Dic61#42714yes—
295Dic61#42814yes—
296C2×#431—611no—
297#2285—611no—
298#2285—611no—
299#1949—611no—
300#1949—611no—
301#1949—611no—
302#1949D6111yescharacteristic, complemented
303#1854—611no—
304#1854—611no—
305#1854—611no—
306#1854—611no—
307#1845—611no—
308#1844—611no—
309#1834—611no—
310#1834—611no—
311C2×C61#231711yescharacteristic
312C2×C61C2×#42711yescharacteristic
313C2×C61C2×#42811yescharacteristic
314C2×C61#320711yescharacteristic
315C2×C61#321011yescharacteristic
316C2×C61#322811yescharacteristic
317C2×C61#323111yescharacteristic
318D61—42no—
319C2×#117—611no—
320C2×#117—611no—
321C2×#117—1221no—
322C22×C42—611no—
323#431—618no—
324C2×#107—611no—
325C2×#107—611no—
326C2×#107—611no—
327C2×#107C2×D6111yescharacteristic
328C2×#106—611no—
329C2×#106—611no—
330C2×#106—611no—
331C2×#106C2×D6111yescharacteristic
332C2×C4⋊C8—611no—
333C2×C4⋊C8C2×D6111yescharacteristic
334C2×C22⋊C8—611no—
335C2×C22⋊C8—611no—
336C2×C4×C8—611no—
337C2×C4×C8—611no—
338#384—611no—
339#384—611no—
340#384—611no—
341#384—611no—
342#382—611no—
343#382—1221no—
344#382C2×D6111yescharacteristic
345#380—611no—
346#380—611no—
347#380—1221no—
348#380—1221no—
349#380—1221no—
350C4×C4⋊C4—611no—
351C4×C4⋊C4—1221no—
352C4×C4⋊C4—1221no—
353C4×C4⋊C4—1221no—
354C4×C4⋊C4C2×D6111yescharacteristic
355#340—611no—
356#340—611no—
357#340—611no—
358#340—611no—
359#340—611no—
360#340—611no—
361#340C2×D6111yescharacteristic
362#340C2×D6111yescharacteristic
363C61#2198411yescharacteristic, complemented, Sylow
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—611no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8C22×D6111yescharacteristic
370C22×C8C22×D6111yescharacteristic
371#117—2444no—
372#117—2441no—
373#117—2441no—
374#117—2441no—
375#117—2441no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4C22×D6111yescharacteristic
389C2×C4⋊C4C22×D6111yescharacteristic
390C2×C4⋊C4C22×D6111yescharacteristic
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C22⋊C4—1221no—
395C2×C22⋊C4—1221no—
396C2×C42—21no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—614no—
401C2×C42—614no—
402C2×C42—1221no—
403C2×C42—1221no—
404C2×C42—1221no—
405C2×C42C22×D6111yescharacteristic
406#107—41no—
407#107—2441no—
408#107—2441no—
409#107—2441no—
410#106—41no—
411#106—2441no—
412#106—2441no—
413#106—2441no—
414C4⋊C8—614no—
415C4⋊C8C4×D6114yes—
416C22⋊C8—614no—
417C22⋊C8—614no—
418C4×C8—614no—
419C4×C8—614no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—1221no—
424#95—1221no—
425#95—1221no—
426#95—1221no—
427#95—1221no—
428C24—611no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—612no—
437C22×C4—612no—
438C22×C4—614no—
439C22×C4—614no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4D4×D6111yescharacteristic
453C22×C4D4×D6111yescharacteristic
454C22×C4C23×D6111yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—612no—
460C2×C8—612no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8C2×C4×D6112yes—
466C2×C8C2×C4×D6112yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—2442no—
484C4⋊C4—2442no—
485C4⋊C4—2442no—
486C4⋊C4—2442no—
487C4⋊C4—2442no—
488C4⋊C4—2442no—
489C4⋊C4—2442no—
490C4⋊C4—2442no—
491C22⋊C4—2442no—
492C22⋊C4—2442no—
493C22⋊C4—2442no—
494C22⋊C4—2442no—
495C42—42no—
496C42—612no—
497C42—612no—
498C42—614no—
499C42—614no—
500C42—2442no—
501C42—2442no—
502C42—2442no—
503C42C2×C4×D6112yes—
504C42Q8×D6112yes—
505C23—612no—
506C23—1221no—
507C23—1221no—
508C23—1221no—
509C23—1221no—
510C23—1221no—
511C23—1221no—
512C23C2×D4×D6111yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—612no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—612no—
534C2×C4—612no—
535C2×C4—612no—
536C2×C4—1228no—
537C2×C4—1228no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1222no—
541C2×C4—1222no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4C4⋊C4×D6112yes—
557C2×C4C4⋊C4×D6112yes—
558C2×C4C22×C4×D6111yescharacteristic
559C2×C4C2×Q8×D6111yescharacteristic
560C2×C4#1451982211yescharacteristic
561C2×C4#1451982311yescharacteristic
562C2×C4#1451982411yescharacteristic
563C2×C4#1451982511yescharacteristic
564C8—22no—
565C8—22no—
566C8—1222no—
567C8—1222no—
568C22—1222no—
569C22—1222no—
570C22—1222no—
571C22—2441no—
572C22—2441no—
573C22—2441no—
574C22—2441no—
575C22C2×C4⋊C4×D6111yescharacteristic
576C22#1684032811yescharacteristic
577C22#1684033511yescharacteristic
578C22#135×D6111yescharacteristic
579C22#135×D6111yescharacteristic
580C22AGL(1,ℤ/8)×D6111yescharacteristic
581C22#137×D6111yescharacteristic
582C4—22no—
583C4—22no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—614no—
589C4—614no—
590C4—1222no—
591C4—4881no—
592C4—4881no—
593C4—4881no—
594C4—4881no—
595C4#1684024111yescharacteristic
596C4#1684024411yescharacteristic
597C4#1684038911yescharacteristic
598C4#1684039211yescharacteristic
599C2—2442no—
600C2#2144844111yescharacteristic
601C2#427×D6111yescharacteristic
602C2#428×D6111yescharacteristic
603C2#2145675111yescharacteristic
604C2#2145677411yescharacteristic
605C2#2145695411yescharacteristic
606C2#2145697711yescharacteristic
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#21984
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. #21445977C2semidirect
12. #21445974C2semidirect
13. #21445945C2semidirect
14. #21445945C2semidirect
15. C61×#1949C2semidirect
20. #16839814C4semidirect
302. #1949D61semidirect
363. C61#21984semidirect

Maximal subgroups

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

subgroupindex
C2×#168398142
#214482252
#214482232
#214465892
#214465872
#214465852
#214460212
#214460192
#214460172
#214460152
#214459772
#214459742
#214459452
C61×#19492
#2198461