Finite Group Databasebeta

← #29737612

Subgroups — #29737612

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448686C211yesmaximal, characteristic
2#21447376C211yesmaximal, characteristic, complemented
3#21447310C211yesmaximal, characteristic, complemented
4#21447310C211yesmaximal, characteristic, complemented
5#21447144C211yesmaximal, characteristic, complemented
6#21446772C211yesmaximal, characteristic, complemented
7#21446575C211yesmaximal, characteristic, complemented
8#21446387C211yesmaximal, characteristic, complemented
9#21446387C211yesmaximal, characteristic, complemented
10#21446007C211yesmaximal, characteristic
11#21445999C211yesmaximal, characteristic
12#21445903C211yesmaximal, characteristic
13#21445846C211yesmaximal, characteristic
14C2×#16839524C211yesmaximal, characteristic
15C61×#2440C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519733—21no—
18C22×C4⋊Dic61C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26#16839660C2211yescharacteristic
27#16839660C2211yescharacteristic
28#16839647—21no—
29#16839647—21no—
30#16839623—21no—
31#16839622C2211yescharacteristic
32C4×C4⋊Dic61C2211yescharacteristic
33C4×C4⋊Dic61C2211yescharacteristic
34#16839524C2211yescharacteristic
35#16839524C2211yescharacteristic
36#16839524C2211yescharacteristic
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4⋊Q8×C61C2211yescharacteristic
49C2×C22⋊Q8×C61—21no—
50C22×C4⋊C4×C61C2211yescharacteristic
51C61×#398—21no—
52C61×#395—21no—
53C61×#389C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C61×#385—21no—
56C61×#384C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C23×Dic61—21no—
60C22×#92418—22no—
61C22×#92418—22no—
62C22×#92418—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519733—44no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61Q814yescomplemented
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×C22⋊Dic61—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61—21no—
80#14519710—22no—
81#14519710—22no—
82#14519710—41no—
83#14519710—41no—
84C4⋊#92418—22no—
85C4⋊#92418—41no—
86C22⋊#92418—22no—
87#14519684—21no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92C22×Q8×C61—21no—
93C23×C4×C61—21no—
94C23×C4×C61C2311yescharacteristic
95C4⋊Q8×C61—22no—
96C4⋊Q8×C61—41no—
97C22⋊Q8×C61—44no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—41no—
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C22⋊C4×C61D411yescharacteristic
113C2×C42×C61C2311yescharacteristic
114C2×C42×C61C2311yescharacteristic
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C24×C61C2×D411yescharacteristic
121C2×Q8×C61—42no—
122C2×Q8×C61—42no—
123C2×Q8×C61—81no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—42no—
133C22×C4×C61—42no—
134C22×C4×C61—81no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×Q812yes—
141C22×C4×C61#4112yes—
142C22×C4×C61C2411yescharacteristic
143C22×Dic61—24no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—42no—
149C22×Dic61—42no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—42no—
158C4⋊C4×C61—42no—
159C4⋊C4×C61—42no—
160C4⋊C4×C61—42no—
161C4⋊C4×C61—42no—
162C4⋊C4×C61—81no—
163C4⋊C4×C61#4112yes—
164C22⋊C4×C61—22no—
165C22⋊C4×C61—42no—
166C22⋊C4×C61D814yes—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C22⋊Dic61—42no—
172C4⋊Dic61—24no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61C2×Q812yes—
180C4⋊Dic61C2×Q812yes—
181#11758196—42no—
182#11758196—42no—
183C4×Dic61—42no—
184C4×Dic61—42no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—44no—
197C2×#92418#4112yes—
198C23×C61—21no—
199C23×C61—21no—
200C23×C61—21no—
201C23×C61—21no—
202C23×C61C22⋊Q812yes—
203C23×C61C2×D812yes—
204C23×C61#13712yes—
205C23×C61C22×D411yescharacteristic
206Q8×C61—84no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—21no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—84no—
236C2×C4×C61C22⋊Q812yes—
237C2×C4×C61C2×D812yes—
238C2×C4×C61C2×D812yes—
239C2×C4×C61C22×Q811yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61H(5,𝔽2)11yescharacteristic
244C2×C4×C612−1+411yescharacteristic
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—48no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258#92418—22no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#25988—611nomaximal, Sylow
263C22×C61—22no—
264C22×C61—22no—
265C22×C61—22no—
266C22×C61—22no—
267C22×C61—22no—
268C22×C61—22no—
269C22×C61#47414yes—
270C22×C61C2×C22⋊Q811yescharacteristic
271C22×C61#54611yescharacteristic
272C22×C61#54711yescharacteristic
273C22×C61C22×D811yescharacteristic
274C22×C61C2×#13711yescharacteristic
275C22×C61#57711yescharacteristic
276C22×C61#57811yescharacteristic
277C4×C61—22no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—41no—
281C4×C61—42no—
282C4×C61—41no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61—81no—
286C4×C61#53311yescharacteristic
287C4×C61#54411yescharacteristic
288C4×C61#55111yescharacteristic
289C4×C61#55211yescharacteristic
290Dic61—42no—
291Dic61—42no—
292Dic61—81no—
293Dic61—81no—
294#2440D6111yescharacteristic
295#2344—611no—
296#2099—611no—
297#2086—611no—
298#2086—611no—
299#2057—611no—
300#1988—611no—
301#1947—611no—
302#1918—611no—
303#1918—611no—
304#1852—611no—
305#1850—611no—
306#1823—611no—
307#1808—611no—
308C2×#340—611no—
309C2×C61—24no—
310C2×C61#243811yescharacteristic
311C2×C61C2×#47411yescharacteristic
312C2×C61#308211yescharacteristic
313C2×C61#329411yescharacteristic
314C2×C61#331211yescharacteristic
315C2×C61#333411yescharacteristic
316C2×C61#334411yescharacteristic
317C23×C8—611no—
318C2×C4⋊Q8C2×D6111yescharacteristic
319C2×C22⋊Q8—21no—
320C2×#117—1221no—
321C22×C4⋊C4—611no—
322C22×C4⋊C4C2×D6111yescharacteristic
323C2×#107—611no—
324C2×#107—611no—
325C2×#107—611no—
326C2×#107—611no—
327C2×C4⋊C8—611no—
328C2×C4⋊C8—611no—
329C2×C22⋊C8—611no—
330#398—21no—
331#395—21no—
332#389—611no—
333#389—611no—
334#389C2×D6111yescharacteristic
335#389C2×D6111yescharacteristic
336#387—1221no—
337#387—1221no—
338#385—21no—
339#384C2×D6111yescharacteristic
340#381—1221no—
341#380—611no—
342#380C2×D6111yescharacteristic
343C4×C4⋊C4—611no—
344C4×C4⋊C4—611no—
345C4×C22⋊C4C2×D6111yescharacteristic
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357#340—611no—
358#336—611no—
359#336—611no—
360C61#2598811yescharacteristic, complemented, Sylow
361C22×Q8—21no—
362C23×C4—21no—
363C23×C4—1221no—
364C23×C4C22×D6111yescharacteristic
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8—1222no—
370C22×C8—1222no—
371C22×C8—2441no—
372C4⋊Q8—22no—
373C4⋊Q8—41no—
374C22⋊Q8—44no—
375#117—2444no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—614no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1222no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C4⋊C4C22×D6111yescharacteristic
395C2×C4⋊C4C22×D6111yescharacteristic
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4C22⋊D6111yescharacteristic
400C2×C22⋊C4C22⋊D6111yescharacteristic
401C2×C42—1221no—
402C2×C42—1221no—
403C2×C42C22×D6111yescharacteristic
404C2×C42C22×D6111yescharacteristic
405#107—1222no—
406#107—1222no—
407#107—2441no—
408#107—2441no—
409C4⋊C8—1222no—
410C4⋊C8—2441no—
411C22⋊C8—1222no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420#95C22⋊D6111yescharacteristic
421#95C22⋊D6111yescharacteristic
422C24C2×C22⋊D6111yescharacteristic
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8—81no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—81no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1224no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4Q8×D6112yes—
445C22×C4#1175822612yes—
446C22×C4C2×C22⋊D6111yescharacteristic
447C22×C4C2×C22⋊D6111yescharacteristic
448C22×C4C2×C22⋊D6111yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450C22×C4C2×C22⋊D6111yescharacteristic
451C22×C4C23×D6111yescharacteristic
452C2×C8—612no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—2444no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4—612no—
479C4⋊C4—612no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1224no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—2442no—
488C4⋊C4—2442no—
489C4⋊C4#1175822412yes—
490C22⋊C4—22no—
491C22⋊C4—42no—
492C22⋊C4—2442no—
493C22⋊C4#1175819914yes—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—2442no—
499C42—2442no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23#1451975312yes—
505C23C2×#1175819912yes—
506C23#1451980812yes—
507C23C22×C22⋊D6111yescharacteristic
508Q8—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4—1222no—
539C2×C4—1222no—
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—2448no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4#1451975312yes—
552C2×C4C2×#1175819912yes—
553C2×C4C2×#1175819912yes—
554C2×C4C2×Q8×D6111yescharacteristic
555C2×C4#41×D6111yescharacteristic
556C2×C4C2×#1175822411yescharacteristic
557C2×C4C2×#1175822611yescharacteristic
558C2×C4#1451982211yescharacteristic
559C2×C4#1451982411yescharacteristic
560C8—1222no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#1684003914yes—
571C22C2×#1451975311yescharacteristic
572C22#1684040611yescharacteristic
573C22#1684041111yescharacteristic
574C22C22×#1175819911yescharacteristic
575C22C2×#1451980811yescharacteristic
576C22#1684057311yescharacteristic
577C22#1684057711yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—41no—
582C4—41no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—4881no—
588C4—4881no—
589C4—2442no—
590C4—2442no—
591C4#1684031411yescharacteristic
592C4#1684039111yescharacteristic
593C4#1684043911yescharacteristic
594C4#1684045411yescharacteristic
595C2—24no—
596C2#2144949111yescharacteristic
597C2C2×#1684003911yescharacteristic
598C2#2145565511yescharacteristic
599C2#2145763211yescharacteristic
600C2#2145787011yescharacteristic
601C2#2145816211yescharacteristic
602C2#2145826811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2440C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2440D61
hypocenterC61#25988
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
2. #21447376C2semidirect
3. #21447310C2semidirect
4. #21447310C2semidirect
5. #21447144C2semidirect
6. #21446772C2semidirect
7. #21446575C2semidirect
8. #21446387C2semidirect
9. #21446387C2semidirect
70. C2×C4⋊Dic61Q8semidirect
360. C61#25988semidirect

Maximal subgroups

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

subgroupindex
#214486862
#214473762
#214473102
#214471442
#214467722
#214465752
#214463872
#214460072
#214459992
#214459032
#214458462
C2×#168395242
C61×#24402
#2598861