Finite Group Databasebeta

← #29731937

Subgroups — #29731937

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic
2C2×#16839893C211yesmaximal, characteristic, complemented
3#21451177C211yesmaximal, characteristic
4#21447321C211yesmaximal, characteristic, complemented
5#21447310C211yesmaximal, characteristic, complemented
6#21447204C211yesmaximal, characteristic
7#21447190C211yesmaximal, characteristic
8#21446785C211yesmaximal, characteristic, complemented
9#21446587C211yesmaximal, characteristic, complemented
10#21446559C211yesmaximal, characteristic, complemented
11#21446554C211yesmaximal, characteristic, complemented
12#21446515C211yesmaximal, characteristic
13#21446515C211yesmaximal, characteristic
14C4×#14519697C211yesmaximal, characteristic
15C61×#2584C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17#16840059—24no—
18#16839893—24no—
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519688C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839697—21no—
34#16839673—21no—
35#16839664C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839633—21no—
40#16839633—21no—
41#16839628C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C2×C4×Q8×C61C2211yescharacteristic
52C61×#398—21no—
53C61×#395—21no—
54C61×#389—21no—
55C61×#389—21no—
56C61×#389C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#389C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C4×D244—22no—
68C4×D244—22no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79#14519710—22no—
80#14519710—22no—
81#14519708—22no—
82#14519708—22no—
83C4⋊#92418—22no—
84C4⋊#92418—22no—
85C4⋊#92418D414yes—
86#14519697—22no—
87#14519697—22no—
88#14519697—22no—
89#14519697Q814yescomplemented
90#14519688—22no—
91#14519688—22no—
92C4×#92418—22no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97C22×Q8×C61D411yescharacteristic
98#125×C61—22no—
99#125×C61—22no—
100C4×Q8×C61—22no—
101C4×Q8×C61—22no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124C23×D61—21no—
125C2×Q8×C61—22no—
126C2×Q8×C61—41no—
127C2×Q8×C61—41no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244C2×Q812yes—
148C2×C4×D61—42no—
149C2×C4×D61—81no—
150C2×C4×D61—81no—
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—42no—
161C4⋊C4×C61—42no—
162C4⋊C4×C61—42no—
163C4⋊C4×C61—42no—
164C4⋊C4×C61—81no—
165C4⋊C4×C61—81no—
166C4⋊C4×C61C2×Q812yes—
167C4⋊C4×C61#4112yes—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—81no—
173C42×C61C2×D412yes—
174C42×C61#4112yes—
175#11758198—42no—
176#11758198—42no—
177#11758198—42no—
178#11758198—81no—
179#11758198—81no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186#11758196—81no—
187#11758196—81no—
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—21no—
197C2×#92418C2×D412yes—
198C2×#92418C2×D412yes—
199C2×#92418C2×Q812yes—
200C23×C61C22×D411yescharacteristic
201C22×D61—22no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208Q8×C61—44no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—22no—
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—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
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—41no—
236C2×C4×C61—41no—
237C2×C4×C61#12112yes—
238C2×C4×C61#12112yes—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×Q811yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C612−1+411yescharacteristic
244C2×C4×C612−1+411yescharacteristic
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254D244—22no—
255D244—22no—
256D244—41no—
257D244—41no—
258C4×D61—84no—
259#92418—22no—
260#92418—22no—
261#92418—22no—
262#92418—41no—
263#25475—611nomaximal, Sylow
264C22×C61C2×#12111yescharacteristic
265C22×C61#54811yescharacteristic
266C22×C61D4×Q811yescharacteristic
267C22×C61#57511yescharacteristic
268C22×C61#57511yescharacteristic
269C22×C61#57611yescharacteristic
270C22×C61#57711yescharacteristic
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—81no—
275C2×D61—81no—
276C2×D61—81no—
277C2×D61—81no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—42no—
281C4×C61—42no—
282C4×C61—41no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61—81no—
287C4×C61—81no—
288C4×C61#53311yescharacteristic
289C4×C61#54111yescharacteristic
290C4×C61#54711yescharacteristic
291C4×C61D4×Q811yescharacteristic
292Dic61—81no—
293Dic61—81no—
294Dic61—81no—
295C2×#478—611no—
296C2×#446—611no—
297#2584D6111yescharacteristic, complemented
298#2580—611no—
299#2088—611no—
300#2086—611no—
301#2067—611no—
302#2065—611no—
303#1991—611no—
304#1949—611no—
305#1944—611no—
306#1943—611no—
307#1936—611no—
308#1936—611no—
309C4×#102—611no—
310C2×C61#242911yescharacteristic
311C2×C61#305411yescharacteristic
312C2×C61#306211yescharacteristic
313C2×C61#337011yescharacteristic
314C2×C61#337111yescharacteristic
315C2×C61#338811yescharacteristic
316C2×C61#338911yescharacteristic
317D61—82no—
318C2×#125C2×D6111yescharacteristic
319C2×C4×Q8C2×D6111yescharacteristic
320C2×C4×D4—611no—
321#478—1224no—
322#446—1224no—
323C2×#107—611no—
324C2×#107—611no—
325C2×#106—611no—
326C2×#106—611no—
327C2×C4⋊C8—611no—
328C2×C4⋊C8—611no—
329C2×C4⋊C8—611no—
330C2×#102—611no—
331C2×#102—611no—
332C2×#102—611no—
333C2×#102—611no—
334C2×#97—611no—
335C2×#97—611no—
336C2×C4×C8—611no—
337#399—1221no—
338#398—21no—
339#395—21no—
340#393—1221no—
341#390—611no—
342#390—611no—
343#389—21no—
344#389—21no—
345#389—611no—
346#389—611no—
347#389C2×D6111yescharacteristic
348#389C2×D6111yescharacteristic
349#389C2×D6111yescharacteristic
350#389C2×D6111yescharacteristic
351#385—1221no—
352#385—1221no—
353#382—611no—
354C4×C4⋊C4C2×D6111yescharacteristic
355#340—611no—
356#340—611no—
357#340—611no—
358#340—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363C61#2547511yescharacteristic, complemented, Sylow
364C22×Q8C22⋊D6111yescharacteristic
365C22×D4—611no—
366C23×C4—1221no—
367C22×C8—611no—
368C22×C8—611no—
369C22×C8—611no—
370C22×C8—611no—
371#125—22no—
372#125—22no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×D4—1222no—
376C4×D4—1222no—
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—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
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×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C4⋊C4C22×D6111yescharacteristic
395C2×C22⋊C4—1221no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4—1221no—
398C2×C22⋊C4—1221no—
399C2×C22⋊C4—1221no—
400C2×C42—21no—
401C2×C42C22×D6111yescharacteristic
402C2×C42C22×D6111yescharacteristic
403C2×C42C22×D6111yescharacteristic
404#107—1222no—
405#107—1222no—
406#106—1222no—
407#106—1222no—
408C4⋊C8—614no—
409C4⋊C8—1222no—
410C4⋊C8—1222no—
411#102—614no—
412#102—1222no—
413#102—1222no—
414#102—1222no—
415#97—1222no—
416#97—1222no—
417C4×C8—1222no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—1221no—
424#95—1221no—
425#95—1221no—
426#95—1221no—
427C24—1221no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×D4—612no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4—1221no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—4881no—
445C22×C4—4881no—
446C22×C4—2442no—
447C22×C4C2×C22⋊D6111yescharacteristic
448C22×C4C2×C22⋊D6111yescharacteristic
449C22×C4C2×C22⋊D6111yescharacteristic
450C22×C4C2×C22⋊D6111yescharacteristic
451C22×C4C2×C22⋊D6111yescharacteristic
452C22×C4C2×C22⋊D6111yescharacteristic
453C22×C4C23×D6111yescharacteristic
454C2×C8—612no—
455C2×C8—612no—
456C2×C8—612no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—4881no—
488C4⋊C4—4881no—
489C4⋊C4Q8×D6112yes—
490C4⋊C4#1175822612yes—
491C22⋊C4—4881no—
492C22⋊C4—4881no—
493C22⋊C4—2442no—
494C22⋊C4—2442no—
495C22⋊C4—2442no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—81no—
501C42D4×D6112yes—
502C42#1175822412yes—
503C23—1222no—
504C23—2441no—
505C23—2441no—
506C23—2441no—
507C23—2441no—
508C23—2441no—
509C23—2441no—
510C23C22×C22⋊D6111yescharacteristic
511Q8—44no—
512D4—1222no—
513D4—1222no—
514D4—2441no—
515D4—2441no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—4884no—
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#1451974912yes—
555C2×C4#1451974912yes—
556C2×C4C2×D4×D6111yescharacteristic
557C2×C4C2×Q8×D6111yescharacteristic
558C2×C4C2×#1175822411yescharacteristic
559C2×C4C2×#1175822611yescharacteristic
560C2×C4#1451982511yescharacteristic
561C2×C4#1451982511yescharacteristic
562C8—1222no—
563C8—1222no—
564C8—1222no—
565C8—2441no—
566C22—4881no—
567C22—4881no—
568C22—4881no—
569C22—4881no—
570C22—2442no—
571C22—2442no—
572C22—2442no—
573C22C2×#1451974911yescharacteristic
574C22#1684042311yescharacteristic
575C22Q8×C22⋊D6111yescharacteristic
576C22#1684056011yescharacteristic
577C22#1684056011yescharacteristic
578C22#1684056511yescharacteristic
579C22#1684057011yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—42no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—4881no—
591C4—4881no—
592C4—4881no—
593C4#1684031711yescharacteristic
594C4#1684037311yescharacteristic
595C4#1684041511yescharacteristic
596C4#1684042711yescharacteristic
597C2—4882no—
598C2#2144942111yescharacteristic
599C2#2145542511yescharacteristic
600C2#2145550111yescharacteristic
601C2#2145857211yescharacteristic
602C2#2145858711yescharacteristic
603C2#2145875811yescharacteristic
604C2#2145877311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2584C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2584D61
hypocenterC61#25475
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2584

Complements

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

NH ≅ G/Ntype
2. C2×#16839893C2semidirect
4. #21447321C2semidirect
5. #21447310C2semidirect
8. #21446785C2semidirect
9. #21446587C2semidirect
10. #21446559C2semidirect
11. #21446554C2semidirect
15. C61×#2584C2semidirect
89. #14519697Q8semidirect
297. #2584D61semidirect
363. C61#25475semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C2×#168398932
#214511772
#214473212
#214473102
#214472042
#214471902
#214467852
#214465872
#214465592
#214465542
#214465152
C4×#145196972
C61×#25842
#2547561