Finite Group Databasebeta

← #29783236

Subgroups — #29783236

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451779C211yesmaximal, characteristic
2#21448471C211yesmaximal, characteristic, complemented
3#21447317C211yesmaximal, characteristic, complemented
4#21447199C211yesmaximal, characteristic, complemented
5#21447192C211yesmaximal, characteristic
6#21447137C211yesmaximal, characteristic
7#21446673C211yesmaximal, characteristic
8#21446547C211yesmaximal, characteristic, complemented
9#21446516C211yesmaximal, characteristic
10#21446509C211yesmaximal, characteristic, complemented
11#21446447C211yesmaximal, characteristic
12#21446405C211yesmaximal, characteristic, complemented
13#21446173C211yesmaximal, characteristic
14#21446090C211yesmaximal, characteristic, complemented
15C61×#1768C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×#14519709C2211yescharacteristic
19C2×#14519709C2211yescharacteristic
20C2×#14519709C2211yescharacteristic
21C2×#14519702C2211yescharacteristic
22C2×#14519702C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27#16839691—21no—
28#16839691—21no—
29#16839691—21no—
30#16839686—21no—
31#16839668C2211yescharacteristic
32#16839668C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839660C2211yescharacteristic
41#16839644—21no—
42#16839644—21no—
43#16839629—21no—
44#16839626—21no—
45C4×C4⋊Dic61C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C61×#376C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C22×D244C2311yescharacteristic
61C2×#11758190—22no—
62C2×#11758190—22no—
63C2×#11758190—41no—
64C4×Dic122—22no—
65C4×Dic122—22no—
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86#14519709—22no—
87#14519709—22no—
88#14519709—41no—
89#14519702—22no—
90#14519702—22no—
91#14519702—41no—
92#14519699—22no—
93#14519699—22no—
94#14519699—41no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C42×C61C2311yescharacteristic
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112C4⋊C8×C61—22no—
113C4⋊C8×C61—22no—
114#97×C61—41no—
115C4×C8×C61—41no—
116#95×C61D411yescharacteristic
117#95×C61D411yescharacteristic
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C23×D61—21no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2411yescharacteristic
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×Dic122—21no—
142C2×Dic122—21no—
143C2×Dic122—21no—
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122#4112yes—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61#4112yes—
158C2×C8×C61#4112yes—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—21no—
164C42×C61—21no—
165#11758198—81no—
166#11758198—81no—
167#11758198—81no—
168#11758198—81no—
169#11758198—81no—
170#11758198—81no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61#4112yes—
183#11758196—24no—
184#11758196—81no—
185#11758196—81no—
186#11758196—81no—
187#11758196—81no—
188#11758196—81no—
189C4×Dic61—24no—
190C4×Dic61—81no—
191#11758190—44no—
192C23×C61C22×D411yescharacteristic
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
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—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61C2×#4111yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61H(5,𝔽2)11yescharacteristic
223C2×C4×C612−1+411yescharacteristic
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—41no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
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—
245D244—41no—
246D244—41no—
247D244—41no—
248D244—41no—
249Dic122—22no—
250Dic122—22no—
251Dic122—41no—
252Dic122—41no—
253C8×C61—22no—
254C8×C61—22no—
255C8×C61—41no—
256C8×C61—41no—
257#29442—611nomaximal, Sylow
258C22×C61#52511yescharacteristic
259C22×C61#53211yescharacteristic
260C22×C61#53711yescharacteristic
261C22×C61#57711yescharacteristic
262C22×C61#57711yescharacteristic
263C22×C61#57711yescharacteristic
264C22×C61#57711yescharacteristic
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C2×D61—81no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61#55111yescharacteristic
279C4×C61#55211yescharacteristic
280C4×C61#55311yescharacteristic
281C4×C61#55611yescharacteristic
282Dic61—42no—
283Dic61—42no—
284Dic61—81no—
285Dic61—81no—
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289#2644—611no—
290#2320—611no—
291#2088—611no—
292#2066—611no—
293#2065—611no—
294#2055—611no—
295#1968—611no—
296#1941—611no—
297#1936—611no—
298#1935—611no—
299#1926—611no—
300#1920—611no—
301#1880—611no—
302#1865—611no—
303#1768D6111yescharacteristic, complemented
304C2×C61#260111yescharacteristic
305C2×C61#312511yescharacteristic
306C2×C61#312611yescharacteristic
307C2×C61#317311yescharacteristic
308C2×C61#317411yescharacteristic
309C2×C61#326011yescharacteristic
310C2×C61#326311yescharacteristic
311D61—161no—
312C22×SD16—611no—
313C2×C4×Q8—611no—
314C2×#106—611no—
315C2×#106—611no—
316C2×#106—611no—
317C2×C4⋊C8C2×D6111yescharacteristic
318C2×C4⋊C8C2×D6111yescharacteristic
319C2×#103—611no—
320C2×#103—611no—
321C2×#103—611no—
322C2×#102—611no—
323C2×#102—611no—
324C2×#102—611no—
325C2×#97C2×D6111yescharacteristic
326C2×C4×C8C2×D6111yescharacteristic
327#397—1221no—
328#397—1221no—
329#397—1221no—
330#396—1221no—
331#391—611no—
332#391—611no—
333#390—611no—
334#390—611no—
335#390—611no—
336#389—611no—
337#389—611no—
338#389—611no—
339#389—611no—
340#389—611no—
341#387—1221no—
342#387—1221no—
343#383—1221no—
344#382—1221no—
345C4×C4⋊C4—611no—
346#376C2×D6111yescharacteristic
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#336C2×D6111yescharacteristic
354#336C2×D6111yescharacteristic
355C61#2944211yescharacteristic, complemented, Sylow
356C22×Q8—611no—
357C22×D4—611no—
358C2×SD16—1222no—
359C2×SD16—1222no—
360C2×SD16—2441no—
361C22×C8C22×D6111yescharacteristic
362C22×C8C22×D6111yescharacteristic
363C22×C8C22×D6111yescharacteristic
364C22×C8C22×D6111yescharacteristic
365C4×Q8—1222no—
366C4×Q8—1222no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C42—1221no—
386C2×C42—1221no—
387C2×C42C22×D6111yescharacteristic
388C2×C42C22×D6111yescharacteristic
389C2×C42C22×D6111yescharacteristic
390#106—1222no—
391#106—1222no—
392#106—2441no—
393C4⋊C8—22no—
394C4⋊C8—22no—
395#103—1222no—
396#103—1222no—
397#103—2441no—
398#102—1222no—
399#102—1222no—
400#102—2441no—
401#97—41no—
402C4×C8—41no—
403#95—1221no—
404#95—1221no—
405#95—1221no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95D24411yescharacteristic
414#95D24411yescharacteristic
415#95D24411yescharacteristic
416#95D24411yescharacteristic
417C24—1221no—
418C2×Q8—612no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×D4—1221no—
425C2×D4—1221no—
426C2×D4—1221no—
427C2×D4—1221no—
428C2×D4—1221no—
429C2×D4—1221no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4C2×D24411yescharacteristic
438C22×C4C2×D24411yescharacteristic
439C22×C4C2×D24411yescharacteristic
440C22×C4C2×D24411yescharacteristic
441C22×C4C2×D24411yescharacteristic
442C22×C4C2×D24411yescharacteristic
443C22×C4C23×D6111yescharacteristic
444SD16—2444no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8#1175822212yes—
456C2×C8#1175822212yes—
457C4⋊C4—612no—
458C4⋊C4—1224no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—4881no—
471C4⋊C4—4881no—
472C4⋊C4—4881no—
473C4⋊C4—4881no—
474C4⋊C4—4881no—
475C22⋊C4—4881no—
476C22⋊C4—4881no—
477C22⋊C4—4881no—
478C22⋊C4—4881no—
479C22⋊C4—4881no—
480C22⋊C4—4881no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—1224no—
488C42—4881no—
489C23—2441no—
490C23—2441no—
491C23—2441no—
492C23—2441no—
493C23—2441no—
494C23—2441no—
495C23—2441no—
496C23C22×D24411yescharacteristic
497Q8—1222no—
498Q8—1222no—
499Q8—2441no—
500Q8—2441no—
501D4—2441no—
502D4—2441no—
503D4—2441no—
504D4—2441no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—2441no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4#41×D6111yescharacteristic
545C2×C4#41×D6111yescharacteristic
546C2×C4C2×#1175822211yescharacteristic
547C2×C4C2×#1175822211yescharacteristic
548C2×C4#1451982211yescharacteristic
549C2×C4#1451982511yescharacteristic
550C8—22no—
551C8—22no—
552C8—41no—
553C8—41no—
554C22—4881no—
555C22—4881no—
556C22—4881no—
557C22—4881no—
558C22—4881no—
559C22—4881no—
560C22—4881no—
561C22#1684027411yescharacteristic
562C22#1684031211yescharacteristic
563C22#1684034311yescharacteristic
564C22#1684057411yescharacteristic
565C22#1684057411yescharacteristic
566C22#1684057411yescharacteristic
567C22#1684057411yescharacteristic
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—4881no—
575C4—4881no—
576C4—4881no—
577C4—4881no—
578C4—4881no—
579C4—2442no—
580C4—2442no—
581C4#1684044111yescharacteristic
582C4#1684045311yescharacteristic
583C4#1684046111yescharacteristic
584C4#1684048411yescharacteristic
585C2—9761no—
586C2#2145141011yescharacteristic
587C2#2145609811yescharacteristic
588C2#2145611111yescharacteristic
589C2#2145643611yescharacteristic
590C2#2145644711yescharacteristic
591C2#2145726611yescharacteristic
592C2#2145729011yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1768C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1768D61
hypocenterC61#29442
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
2. #21448471C2semidirect
3. #21447317C2semidirect
4. #21447199C2semidirect
8. #21446547C2semidirect
10. #21446509C2semidirect
12. #21446405C2semidirect
14. #21446090C2semidirect
15. C61×#1768C2semidirect
303. #1768D61semidirect
355. C61#29442semidirect

Maximal subgroups

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

subgroupindex
#214517792
#214484712
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