Finite Group Databasebeta

← #29688938

Subgroups — #29688938

Order 15616.

1502 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C2×#16839727C212yesmaximal, complemented
3#21446113C212yesmaximal, complemented
4#21446113C212yesmaximal, complemented
5#21446108C212yesmaximal, complemented
6#21446108C212yesmaximal, complemented
7#21445888C212yesmaximal, complemented
8#21445729C211yesmaximal, characteristic, complemented
9C61×#1779C211yesmaximal, characteristic, complemented
10C22×#11758222C2211yescharacteristic
11C22×#11758189C2212yescomplemented
12C22×C8×D61C2212yescomplemented
13#16840273—28no—
14C2×#14519760C412yes—
15C2×#14519756C411yescharacteristic
16C2×#14519756C411yescharacteristic
17C2×#14519751C411yescharacteristic
18C2×#14519751C411yescharacteristic
19C2×#14519746C412yes—
20C2×C4×C22⋊D61C2212yes—
21C2×C4×C22⋊D61C2212yes—
22C2×#14519736C2211yescharacteristic
23#16839727—28no—
24C2×C22⋊#92418C2212yes—
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2212yes—
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519689C2212yescomplemented
29C2×#14519689C2212yescomplemented
30#16839516C2212yescomplemented
31#16839516C2212yescomplemented
32#16839516C2212yescomplemented
33#16839516C2212yescomplemented
34C24×C4×C61C2211yescharacteristic
35C2×C22⋊C8×C61C2212yes—
36C2×C22⋊C8×C61C2211yescharacteristic
37C2×C22⋊C8×C61C2212yes—
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×#11758222—41no—
40C2×#11758222—42no—
41C2×#11758222—41no—
42C2×#11758222D418yes—
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61C2×C412yes—
46C22×C22⋊D61C2×C412yes—
47C22×C22⋊D61C2×C412yes—
48C22×C4×D61C2312yes—
49C2×#11758189—24no—
50C2×#11758189—42no—
51C2×#11758189—42no—
52C22×#92418C2312yes—
53C22×#92418C2312yes—
54C2×C8×D61—24no—
55C2×C8×D61—42no—
56C2×C8×D61—42no—
57#14519760—28no—
58#14519756—24no—
59#14519756—24no—
60#14519751—24no—
61#14519751—24no—
62#14519746—28no—
63C4×C22⋊D61—24no—
64C4×C22⋊D61—24no—
65C4×C22⋊D61—24no—
66C4×C22⋊D61—24no—
67#14519736—24no—
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×#11758196C2×C412yes—
71C2×#11758196C2×C412yes—
72C2×C22⋊Dic61C2×C412yes—
73C2×C22⋊Dic61C2×C412yes—
74C2×C22⋊Dic61C2×C412yes—
75C2×#11758198C2×C412yes—
76C2×#11758198C2×C412yes—
77C2×C4×Dic61C2312yes—
78C22⋊#92418—24no—
79C22⋊#92418—41no—
80C22⋊#92418—42no—
81C22⋊#92418—41no—
82#14519689—24no—
83#14519689—24no—
84C25×C61C2×C411yescharacteristic
85C23×C4×C61—24no—
86C23×C4×C61—42no—
87C23×C4×C61—41no—
88C23×C4×C61—41no—
89C23×C4×C61C2×C411yescharacteristic
90C23×C4×C61C2×C411yescharacteristic
91C23×C4×C61C2×C411yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C22×C8×C61C2312yes—
96C22×C8×C61C2312yes—
97C22⋊C8×C61—24no—
98C22⋊C8×C61—41no—
99C22⋊C8×C61—42no—
100C22⋊C8×C61—41no—
101C24×C61—22no—
102C24×C61—22no—
103C24×C61—22no—
104C24×C61—41no—
105C24×C61—41no—
106C24×C61—41no—
107C24×C61—41no—
108C24×C61C22×C411yescharacteristic
109C24×C61C22×C411yescharacteristic
110C24×C61C22×C411yescharacteristic
111C23×D61C22×C412yes—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—22no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—22no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61—48no—
133C22×C4×C61—48no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C2×D414yes—
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—24no—
140C2×C22⋊D61—24no—
141C2×C22⋊D61—24no—
142C2×C22⋊D61—24no—
143C2×C22⋊D61—42no—
144C2×C22⋊D61—42no—
145C2×C22⋊D61—42no—
146C2×C22⋊D61—42no—
147C2×C22⋊D61C22⋊C418yes—
148C22×Dic61C22×C412yes—
149C22×Dic61C22×C412yes—
150C22×Dic61C22×C412yes—
151#11758222—48no—
152#11758222—48no—
153C2×D244—41no—
154C2×D244—41no—
155C2×D244C22⋊C414yes—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61C2×D414yes—
161C2×C4×D61C2×D414yes—
162C2×Dic122—41no—
163C2×Dic122—41no—
164C2×Dic122C22⋊C414yes—
165C2×C8×C61—22no—
166C2×C8×C61—22no—
167C2×C8×C61—22no—
168C2×C8×C61—22no—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C22⋊Dic61—24no—
172C22⋊Dic61—24no—
173C22⋊Dic61—24no—
174#11758198—24no—
175#11758198—24no—
176C4⋊Dic61—22no—
177C4⋊Dic61—22no—
178#11758196—24no—
179#11758196—24no—
180C4×Dic61—22no—
181C4×Dic61—22no—
182C2×#92418—22no—
183C2×#92418—22no—
184C2×#92418—22no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188#11758189—48no—
189C8×D61—48no—
190C23×C61—21no—
191C23×C61—21no—
192C23×C61—21no—
193C23×C61—21no—
194C23×C61—21no—
195C23×C61—21no—
196C23×C61—21no—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61—21no—
200C23×C61—21no—
201C23×C61—21no—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—44no—
209C23×C61—44no—
210C23×C61—44no—
211C23×C61—44no—
212C23×C61—44no—
213C23×C61—44no—
214C23×C61—44no—
215C23×C61C2×C22⋊C412yes—
216C23×C61#13112yes—
217C23×C61#13112yes—
218C23×C61C23×C411yescharacteristic
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61—22no—
223C22×D61—22no—
224C22×D61—22no—
225C22×D61C2×C22⋊C414yes—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—24no—
229C2×C4×C61—24no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—44no—
237C2×C4×C61—44no—
238C2×C4×C61—44no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61C2×C22⋊C412yes—
244C2×C4×C61C22×D412yes—
245C2×C4×C61H(5,𝔽2)11yescharacteristic
246C2×C4×C61H(5,𝔽2)11yescharacteristic
247C2×C4×C61H(5,𝔽2)12yes—
248C22⋊D61—48no—
249C22⋊D61—48no—
250C22⋊D61—48no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61C2×C22⋊C414yes—
260D244—44no—
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—24no—
264C4×D61—24no—
265Dic122—44no—
266C8×C61—42no—
267C8×C61—42no—
268#92418—42no—
269#92418—42no—
270#21744—611nomaximal, Sylow
271C22×C61—22no—
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—416no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61C22×C22⋊C411yescharacteristic
294C22×C61#51811yescharacteristic
295C22×C61#51811yescharacteristic
296C22×C61C2×#13111yescharacteristic
297C22×C61C2×#13111yescharacteristic
298C22×C61#56811yescharacteristic
299C22×C61#56811yescharacteristic
300C2×D61—24no—
301C2×D61—24no—
302C2×D61—24no—
303C2×D61—42no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—42no—
307C4×C61—22no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61#53412yes—
311C4×C61#53412yes—
312Dic61—24no—
313Dic61—42no—
314Dic61—42no—
315C2×#525—611no—
316C2×#408—612no—
317#1870—612no—
318#1870—612no—
319#1869—612no—
320#1869—612no—
321#1818—612no—
322#1779—611no—
323#1779D6111yescharacteristic, complemented
324C2×C61—42no—
325C2×C61—42no—
326C2×C61—42no—
327C2×C61#230811yescharacteristic
328C2×C61#288011yescharacteristic
329C2×C61#288011yescharacteristic
330C2×C61#297611yescharacteristic
331C2×C61#297611yescharacteristic
332C2×C61#297711yescharacteristic
333C2×C61#297811yescharacteristic
334D61—44no—
335C22×#41—611no—
336C24×C4C2×D6111yescharacteristic
337C22×M16—612no—
338C23×C8—612no—
339#525—1228no—
340C2×#123—612no—
341C2×C22⋊Q8—611no—
342C2×C22⋊Q8—611no—
343C2×#121—611no—
344C2×#121—611no—
345C2×#120—612no—
346C2×C4×D4—612no—
347C2×C4×D4—612no—
348C2×#117—611no—
349#408—1228no—
350C2×C22⋊C8—612no—
351C2×C22⋊C8—612no—
352C2×C22⋊C8—612no—
353C2×C22⋊C8—611no—
354C2×C22⋊C8—612no—
355C2×C22⋊C8—611no—
356C2×C22⋊C8C2×D6112yes—
357C2×C22⋊C8C2×D6111yescharacteristic
358C2×C22⋊C8C2×D6112yes—
359C2×C22⋊C8C2×D6111yescharacteristic
360#336—612no—
361#336—612no—
362#336—612no—
363#336—612no—
364C61#2174411yescharacteristic, complemented, Sylow
365C25C4×D6111yescharacteristic
366C2×#41—618no—
367C2×#41—2441no—
368C2×#41—2442no—
369C2×#41—2441no—
370C22×Q8—611no—
371C22×D4—612no—
372C22×D4—612no—
373C22×D4—612no—
374C22×D4—611no—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4—612no—
380C23×C4C4×D6111yescharacteristic
381C23×C4C4×D6111yescharacteristic
382C23×C4C4×D6111yescharacteristic
383C23×C4C22×D6111yescharacteristic
384C23×C4C22×D6111yescharacteristic
385C23×C4C22×D6111yescharacteristic
386C2×M16—1224no—
387C2×M16—2442no—
388C2×M16—2442no—
389C22×C8—612no—
390C22×C8—612no—
391C22×C8—1224no—
392C22×C8—2442no—
393C22×C8—2442no—
394C22×C8C22×D6112yes—
395C22×C8C22×D6112yes—
396#123—1228no—
397C22⋊Q8—1224no—
398C22⋊Q8—1224no—
399#121—1224no—
400#121—1224no—
401#120—1228no—
402C4×D4—1224no—
403C4×D4—1224no—
404C4×D4—1224no—
405C4×D4—1224no—
406#117—1224no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—612no—
410C2×C4⋊C4—612no—
411C2×C22⋊C4—612no—
412C2×C22⋊C4—612no—
413C2×C22⋊C4—612no—
414C2×C22⋊C4—612no—
415C2×C22⋊C4—612no—
416C2×C42—612no—
417C22⋊C8—24no—
418C22⋊C8—41no—
419C22⋊C8—42no—
420C22⋊C8—41no—
421C22⋊C8—1224no—
422C22⋊C8—1224no—
423C22⋊C8—1224no—
424C22⋊C8—2441no—
425C22⋊C8—2442no—
426C22⋊C8—2441no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—612no—
435C24C2×C4×D6111yescharacteristic
436C24C2×C4×D6111yescharacteristic
437C24C2×C4×D6111yescharacteristic
438#41—2448no—
439#41—2448no—
440C2×Q8—614no—
441C2×Q8—2441no—
442C2×Q8—2441no—
443C2×D4—618no—
444C2×D4—614no—
445C2×D4—1224no—
446C2×D4—1224no—
447C2×D4—1224no—
448C2×D4—1224no—
449C2×D4—2441no—
450C2×D4—2441no—
451C2×D4—2442no—
452C2×D4—2442no—
453C2×D4—2442no—
454C2×D4—2442no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—48no—
476C22×C4—48no—
477C22×C4—612no—
478C22×C4—614no—
479C22×C4—614no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4C2×C4×D6111yescharacteristic
487C22×C4C2×C4×D6111yescharacteristic
488C22×C4C2×C4×D6111yescharacteristic
489C22×C4D4×D6114yes—
490C22×C4C23×D6111yescharacteristic
491M16—2448no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—2448no—
505C4⋊C4—1224no—
506C4⋊C4—1224no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C22⋊C4—1224no—
510C22⋊C4—1224no—
511C22⋊C4—1224no—
512C22⋊C4—1224no—
513C22⋊C4—1224no—
514C42—1222no—
515C42—1222no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—44no—
535C23—44no—
536C23—44no—
537C23—44no—
538C23—44no—
539C23—44no—
540C23—44no—
541C23—614no—
542C23—1222no—
543C23—1222no—
544C23—1222no—
545C23—1222no—
546C23—1222no—
547C23—1222no—
548C23C22⋊C4×D6112yes—
549C23#1451978312yes—
550C23#1451978512yes—
551C23C22×C4×D6111yescharacteristic
552Q8—2444no—
553D4—2444no—
554D4—2448no—
555D4—2448no—
556D4—2448no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—614no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1224no—
580C2×C4—1224no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4C22⋊C4×D6112yes—
588C2×C4C2×D4×D6112yes—
589C2×C4#1451982211yescharacteristic
590C2×C4#1451982211yescharacteristic
591C2×C4#1451982212yes—
592C8—42no—
593C8—42no—
594C8—2442no—
595C8—2442no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—416no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—1224no—
619C22—1224no—
620C22—1224no—
621C22—2442no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22C2×C22⋊C4×D6111yescharacteristic
626C22#1684023511yescharacteristic
627C22#1684023511yescharacteristic
628C22C2×#1451978311yescharacteristic
629C22C2×#1451978511yescharacteristic
630C22#1684052811yescharacteristic
631C22#1684052811yescharacteristic
632C4—22no—
633C4—41no—
634C4—41no—
635C4—1224no—
636C4—2442no—
637C4—2442no—
638C4#1684032212yes—
639C4#1684032212yes—
640C2—42no—
641C2—42no—
642C2—42no—
643C2—2444no—
644C2#2144839511yescharacteristic
645C2#2145426511yescharacteristic
646C2#2145426911yescharacteristic
647C2#2145486411yescharacteristic
648C2#2145486911yescharacteristic
649C2#2145487311yescharacteristic
650C2#2145487911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1779C2
prime radicalC2×#16840273C2
cosocleC22×C4×C61C24
hypercenter#1779D61
hypocenterC61#21744
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#16839727C2semidirect
3. #21446113C2semidirect
4. #21446113C2semidirect
5. #21446108C2semidirect
6. #21446108C2semidirect
7. #21445888C2semidirect
8. #21445729C2semidirect
9. C61×#1779C2semidirect
11. C22×#11758189C22semidirect
12. C22×C8×D61C22semidirect
28. C2×#14519689C22semidirect
29. C2×#14519689C22semidirect
30. #16839516C22semidirect
31. #16839516C22semidirect
32. #16839516C22semidirect
33. #16839516C22semidirect
323. #1779D61semidirect
364. C61#21744semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C2×#168397272
#214461132
#214461082
#214458882
#214457292
C61×#17792
#2174461