Finite Group Databasebeta

← #29692029

Subgroups — #29692029

Order 15616.

786 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839890C211yesmaximal, characteristic, complemented
2C2×#16839818C211yesmaximal, characteristic
3C4×#14519755C211yesmaximal, characteristic
4#21446757C211yesmaximal, characteristic, complemented
5#21446541C211yesmaximal, characteristic, complemented
6#21446541C211yesmaximal, characteristic, complemented
7#21446538C211yesmaximal, characteristic, complemented
8#21446433C211yesmaximal, characteristic
9#21446432C211yesmaximal, characteristic
10#21446426C211yesmaximal, characteristic
11#21446423C211yesmaximal, characteristic
12#21446373C211yesmaximal, characteristic, complemented
13#21445798C211yesmaximal, characteristic
14#21445690C211yesmaximal, characteristic, complemented
15C61×#1917C211yesmaximal, characteristic, complemented
16C2×#14519755C411yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19#16839890—24no—
20#16839818—24no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33C2×#14519687C2211yescharacteristic
34C2×#14519687C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839666C411yescharacteristic
38#16839657C411yescharacteristic
39#16839648C411yescharacteristic
40#16839644C411yescharacteristic
41#16839636C411yescharacteristic
42#16839633C411yescharacteristic
43#16839621C411yescharacteristic
44C4×#11758196C2211yescharacteristic
45C4×#11758196C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47C4×#11758198C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Dic122C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519755—24no—
70C4×Dic122—22no—
71C4×Dic122—22no—
72C2×C4⋊Dic61C2×C411yescharacteristic
73C2×#11758196C2×C411yescharacteristic
74C2×#11758196C2×C411yescharacteristic
75C2×#11758196C2×C411yescharacteristic
76C2×#11758196C2×C411yescharacteristic
77C2×#11758196C2×C411yescharacteristic
78C2×#11758196C2×C411yescharacteristic
79C2×#11758198C2×C411yescharacteristic
80C2×#11758198C2×C411yescharacteristic
81C2×#11758198C2×C411yescharacteristic
82C2×#11758198C2×C411yescharacteristic
83C2×C4×Dic61C2×C411yescharacteristic
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88C42×D61—22no—
89C42×D61—22no—
90C4⋊#92418—22no—
91C4⋊#92418—22no—
92C4⋊#92418—41no—
93#14519706—22no—
94#14519706—22no—
95#14519706—22no—
96#14519706—41no—
97#14519689—22no—
98#14519689—22no—
99#14519689—41no—
100#14519689—41no—
101#14519687—22no—
102#14519687—41no—
103#14519687D414yes—
104C4×#92418—41no—
105C8×Dic61—22no—
106#14519684C2×C411yescharacteristic
107#14519684C2×C411yescharacteristic
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2×C411yescharacteristic
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C2×C42×C61C2311yescharacteristic
122C2×C42×C61C2311yescharacteristic
123C4⋊C8×C61—22no—
124#97×C61—22no—
125#95×C61C2×C411yescharacteristic
126#95×C61C2×C411yescharacteristic
127C23×D61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C411yescharacteristic
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×Dic122—22no—
155C2×Dic122—22no—
156C2×Dic122—41no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61C2×D412yes—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—22no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177#11758198—22no—
178#11758198—41no—
179#11758198—41no—
180#11758198M1614yes—
181C4⋊Dic61—22no—
182#11758196—22no—
183#11758196—22no—
184#11758196—22no—
185#11758196—22no—
186#11758196—22no—
187#11758196—41no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61C2×D412yes—
195C4×Dic61#4112yes—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C2×D412yes—
208C23×C61C23×C411yescharacteristic
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61C2×M1612yes—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61C2×M1612yes—
233C2×C4×C61#13112yes—
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61H(5,𝔽2)11yescharacteristic
237C2×C4×C612−1+411yescharacteristic
238C2×C4×C612−1+411yescharacteristic
239C2×C4×C612−1+411yescharacteristic
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61C4×D412yes—
259C2×Dic61C4×D412yes—
260C2×Dic61C2×M1612yes—
261C4×D61—44no—
262C4×D61—44no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—41no—
267Dic122—44no—
268C8×C61—22no—
269C8×C61—41no—
270C8×C61—41no—
271C8×C61—41no—
272#92418—22no—
273#92418—41no—
274#92418—41no—
275#92418—41no—
276#22108—611nomaximal, Sylow
277C22×C61C2×C4×D411yescharacteristic
278C22×C61#51911yescharacteristic
279C22×C61#52011yescharacteristic
280C22×C61C22×M1611yescharacteristic
281C22×C61C2×#13111yescharacteristic
282C22×C61#56811yescharacteristic
283C22×C61#56811yescharacteristic
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C4×C61—22no—
292C4×C61—22no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61#53611yescharacteristic
298C4×C61#53711yescharacteristic
299C4×C61#54111yescharacteristic
300C4×C61#54211yescharacteristic
301Dic61—22no—
302Dic61—22no—
303Dic61—22no—
304Dic61—41no—
305Dic61—41no—
306Dic61—41no—
307Dic61—41no—
308C2×#446—611no—
309C2×#432—611no—
310C4×C22⋊Q8—611no—
311#1985—611no—
312#1940—611no—
313#1940—611no—
314#1939—611no—
315#1924—611no—
316#1924—611no—
317#1923—611no—
318#1923—611no—
319#1917D6111yescharacteristic, complemented
320#1916—611no—
321#1797—611no—
322#1771—611no—
323C2×C61#232311yescharacteristic
324C2×C61#293311yescharacteristic
325C2×C61D4×M1611yescharacteristic
326C2×C61#298311yescharacteristic
327C2×C61#298511yescharacteristic
328C2×C61#299011yescharacteristic
329C2×C61#299511yescharacteristic
330D61—42no—
331C2×C22⋊Q8—611no—
332C2×C4×Q8—611no—
333C22×C42—611no—
334#446—1224no—
335#432—1224no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—611no—
340C2×C4⋊C8—611no—
341C2×C4⋊C8—611no—
342C2×C4⋊C8—611no—
343C2×C4⋊C8C2×D6111yescharacteristic
344C2×C22⋊C8—611no—
345C2×C22⋊C8—611no—
346C2×C22⋊C8—611no—
347C2×C22⋊C8—611no—
348C2×#97—611no—
349C2×#97—611no—
350C2×#97—611no—
351C2×#97C2×D6111yescharacteristic
352C2×C4×C8—611no—
353C2×C4×C8—611no—
354#391—611no—
355#389—611no—
356#387—611no—
357#387—611no—
358#385—611no—
359#385—611no—
360#380—611no—
361C4×C4⋊C4—611no—
362C4×C4⋊C4—611no—
363C4×C4⋊C4C2×D6111yescharacteristic
364C4×C22⋊C4—611no—
365C4×C22⋊C4—611no—
366#336—611no—
367#336—611no—
368#336—611no—
369#336—611no—
370#336—611no—
371#336—611no—
372#336C2×D6111yescharacteristic
373#336C2×D6111yescharacteristic
374#336C2×D6111yescharacteristic
375#336C2×D6111yescharacteristic
376C61#2210811yescharacteristic, complemented, Sylow
377C22×Q8—611no—
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C22×C8—611no—
382C22×C8—611no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8C22×D6111yescharacteristic
386C22×C8C22×D6111yescharacteristic
387C22×C8C22×D6111yescharacteristic
388C22×C8C22×D6111yescharacteristic
389C22⋊Q8—1224no—
390C4×Q8—1222no—
391C4×Q8—1222no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4C4×D6111yescharacteristic
400C2×C4⋊C4C4×D6111yescharacteristic
401C2×C22⋊C4—611no—
402C2×C22⋊C4—611no—
403C2×C22⋊C4—611no—
404C2×C22⋊C4—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—1222no—
411C2×C42—1222no—
412C2×C42C22×D6111yescharacteristic
413C2×C42C22×D6111yescharacteristic
414C2×C42C22×D6111yescharacteristic
415C4⋊C8—22no—
416C4⋊C8—1222no—
417C4⋊C8—1222no—
418C4⋊C8—1222no—
419C4⋊C8—1222no—
420C4⋊C8—1222no—
421C4⋊C8—2441no—
422C4⋊C8—2441no—
423C22⋊C8—1222no—
424C22⋊C8—1222no—
425C22⋊C8—2441no—
426C22⋊C8—2441no—
427#97—22no—
428#97—614no—
429#97—1222no—
430#97—2441no—
431C4×C8—1222no—
432C4×C8—2441no—
433#95—611no—
434#95—611no—
435#95—611no—
436#95—611no—
437#95—611no—
438#95—611no—
439#95—611no—
440#95—611no—
441#95C4×D6111yescharacteristic
442#95C4×D6111yescharacteristic
443C24—611no—
444C2×Q8—1222no—
445C2×Q8—1222no—
446C2×Q8—2441no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4—1222no—
464C22×C4—2441no—
465C22×C4—2441no—
466C22×C4C2×C4×D6111yescharacteristic
467C22×C4C2×C4×D6111yescharacteristic
468C22×C4C2×C4×D6111yescharacteristic
469C22×C4C2×C4×D6111yescharacteristic
470C22×C4C2×C4×D6111yescharacteristic
471C22×C4C2×C4×D6111yescharacteristic
472C22×C4C23×D6111yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—612no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8D4×D6112yes—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—2441no—
506C22⋊C4—614no—
507C22⋊C4—1222no—
508C22⋊C4—2441no—
509C22⋊C4—2441no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—612no—
517C42—612no—
518C42—1222no—
519C42—1222no—
520C42—1221no—
521C42—1221no—
522C42—1221no—
523C42—1221no—
524C23—612no—
525C23—1221no—
526C23—1221no—
527C23—1221no—
528C23—1221no—
529C23—1221no—
530C23—1221no—
531C23C22×C4×D6111yescharacteristic
532Q8—2444no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—2444no—
571C2×C4—2444no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4M16×D6112yes—
577C2×C4#1451978512yes—
578C2×C4C2×D4×D6111yescharacteristic
579C2×C4#41×D6111yescharacteristic
580C2×C4#1451982311yescharacteristic
581C2×C4#1451982411yescharacteristic
582C2×C4#1451982411yescharacteristic
583C2×C4#1451982511yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—1222no—
589C8—2441no—
590C8—2441no—
591C8—2441no—
592C22—1222no—
593C22—1222no—
594C22—1222no—
595C22—2441no—
596C22—2441no—
597C22—2441no—
598C22—2441no—
599C22C4×D4×D6111yescharacteristic
600C22#1684023811yescharacteristic
601C22#1684024211yescharacteristic
602C22C2×M16×D6111yescharacteristic
603C22C2×#1451978511yescharacteristic
604C22#1684052711yescharacteristic
605C22#1684052711yescharacteristic
606C4—22no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—1222no—
613C4—1222no—
614C4—1222no—
615C4—2441no—
616C4—2441no—
617C4—2441no—
618C4—2441no—
619C4#1684033411yescharacteristic
620C4#1684034211yescharacteristic
621C4#1684037111yescharacteristic
622C4#1684037811yescharacteristic
623C2—2442no—
624C2#2144850011yescharacteristic
625C2#2145454511yescharacteristic
626C2#2145455511yescharacteristic
627C2#2145490111yescharacteristic
628C2#2145491511yescharacteristic
629C2#2145494611yescharacteristic
630C2#2145498411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1917C2
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1917D61
hypocenterC61#22108
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
1. C2×#16839890C2semidirect
4. #21446757C2semidirect
5. #21446541C2semidirect
6. #21446541C2semidirect
7. #21446538C2semidirect
12. #21446373C2semidirect
14. #21445690C2semidirect
15. C61×#1917C2semidirect
319. #1917D61semidirect
376. C61#22108semidirect

Maximal subgroups

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

subgroupindex
C2×#168398902
C2×#168398182
C4×#145197552
#214467572
#214465412
#214465382
#214464332
#214464322
#214464262
#214464232
#214463732
#214457982
#214456902
C61×#19172
#2210861