Finite Group Databasebeta

← #29699240

Subgroups — #29699240

Order 15616.

830 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839849C211yesmaximal, characteristic
2#21448788C211yesmaximal, characteristic
3#21448738C211yesmaximal, characteristic, complemented
4#21446517C211yesmaximal, characteristic
5#21446515C211yesmaximal, characteristic
6#21446406C211yesmaximal, characteristic, complemented
7#21446175C211yesmaximal, characteristic
8#21446173C211yesmaximal, characteristic
9#21445948C211yesmaximal, characteristic, complemented
10#21445833C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic
12#21445685C211yesmaximal, characteristic, complemented
13#21445652C211yesmaximal, characteristic, complemented
14#21445648C211yesmaximal, characteristic, complemented
15C61×#1920C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×#14519742C2211yescharacteristic
19C2×#14519742C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21#16839849C418yescomplemented
22C2×#14519706C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31C2×C8×Dic61C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839663C2211yescharacteristic
34#16839661C2211yescharacteristic
35#16839659—21no—
36#16839657—21no—
37#16839653—21no—
38#16839651—21no—
39#16839627C2211yescharacteristic
40#16839627C2211yescharacteristic
41#16839626—21no—
42#16839624—21no—
43C4⋊C4×Dic61—21no—
44C4⋊C4×Dic61C2211yescharacteristic
45C4×#11758196C2211yescharacteristic
46C4×#11758198—21no—
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×Dic122C2311yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C2×#11758190—22no—
64C2×#11758190—22no—
65C2×#11758190C2×C414yes—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C4×Dic122—22no—
69C4×Dic122—41no—
70#14519742—22no—
71#14519742—22no—
72#14519742—41no—
73#14519742C2×C414yes—
74#14519739—22no—
75#14519739C2×C414yes—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196D411yescharacteristic
83C2×#11758196D411yescharacteristic
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519706—22no—
96#14519702—22no—
97#14519700—22no—
98#14519700C2×C414yes—
99#14519699—41no—
100#14519697—41no—
101#14519697C2×C414yes—
102#14519688—41no—
103#14519687—41no—
104C8×Dic61C2×C414yes—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684D411yescharacteristic
112#14519684D411yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#106×C61C2×C414yes—
123#95×C61—21no—
124#95×C61—21no—
125C23×D61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244C22×C412yes—
146C2×C4×D61—24no—
147C2×C4×D61—81no—
148C2×C4×D61—81no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122C22×C412yes—
153C2×Dic122#4112yes—
154C2×Dic122#4112yes—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61C22×C412yes—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—42no—
168C4⋊C4×C61C22×C412yes—
169C4⋊C4×C61C22×C412yes—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—81no—
173#11758198—24no—
174#11758198—42no—
175#11758198—42no—
176#11758198—81no—
177#11758198—81no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—42no—
183#11758196—24no—
184#11758196—41no—
185#11758196—41no—
186#11758196—42no—
187#11758196—42no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—24no—
191C4×Dic61—42no—
192C4×Dic61—42no—
193C4×Dic61—81no—
194C4×Dic61C22×C412yes—
195C4×Dic61#4112yes—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C22×C412yes—
202#11758190—28no—
203C23×C61C22×D411yescharacteristic
204C22×D61—22no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61C23×C411yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61H(5,𝔽2)11yescharacteristic
234C2×C4×C612−1+411yescharacteristic
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—21no—
239C2×Dic61—21no—
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—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61C4×D412yes—
255C2×Dic61C4×D412yes—
256D244—22no—
257D244—22no—
258D244—41no—
259D244—41no—
260C4×D61—84no—
261Dic122—22no—
262Dic122—22no—
263Dic122—22no—
264Dic122#11714yes—
265C8×C61—22no—
266C8×C61—41no—
267#92418—22no—
268#92418—41no—
269#22765—611nomaximal, Sylow
270C22×C61C2×C4×D411yescharacteristic
271C22×C61#54611yescharacteristic
272C22×C61#54811yescharacteristic
273C22×C61#57511yescharacteristic
274C22×C61#57511yescharacteristic
275C22×C61#57711yescharacteristic
276C22×C61#57711yescharacteristic
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—81no—
281C2×D61—81no—
282C2×D61—81no—
283C2×D61—81no—
284C4×C61—42no—
285C4×C61—42no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—81no—
289C4×C61—81no—
290C4×C61C2×#11711yescharacteristic
291C4×C61#52011yescharacteristic
292C4×C61#55211yescharacteristic
293C4×C61#55311yescharacteristic
294Dic61—24no—
295Dic61—22no—
296Dic61—22no—
297Dic61—41no—
298Dic61—41no—
299Dic61—81no—
300Dic61—81no—
301C2×C4×SD16—611no—
302#2357—611no—
303#2351—611no—
304#1936—611no—
305#1936—611no—
306#1920—611no—
307#1920D6111yescharacteristic, complemented
308#1880—611no—
309#1880—611no—
310#1835—611no—
311#1805—611no—
312#1804—611no—
313#1770—611no—
314#1763—611no—
315#1763—611no—
316C2×C61#235211yescharacteristic
317C2×C61#294311yescharacteristic
318C2×C61#294911yescharacteristic
319C2×C61#332611yescharacteristic
320C2×C61#332611yescharacteristic
321C2×C61#337111yescharacteristic
322C2×C61#337111yescharacteristic
323D61—82no—
324C22×SD16—611no—
325C2×C4×Q8—611no—
326C2×C4×Q8—611no—
327C2×C4×Q8—611no—
328C2×C4×D4—611no—
329C4×SD16—618no—
330C2×#106C2×D6111yescharacteristic
331C2×C4⋊C8—611no—
332C2×#103—611no—
333C2×#103—611no—
334C2×#103—611no—
335C2×#102—611no—
336C2×#102—611no—
337C2×#102—611no—
338C2×#97—611no—
339C2×#97—611no—
340C2×C4×C8—611no—
341#390—611no—
342#390—611no—
343#389—611no—
344#389—1221no—
345#389—1221no—
346#389C2×D6111yescharacteristic
347#388—1221no—
348#388—1221no—
349#382—611no—
350#382—611no—
351#382—1221no—
352#381—1221no—
353C4×C4⋊C4—611no—
354C4×C4⋊C4—611no—
355C4×C4⋊C4—1221no—
356C4×C4⋊C4C2×D6111yescharacteristic
357C4×C22⋊C4—1221no—
358#340—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340C2×D6111yescharacteristic
364#340C2×D6111yescharacteristic
365#340C2×D6111yescharacteristic
366#336—611no—
367#336C2×D6111yescharacteristic
368C61#2276511yescharacteristic, complemented, Sylow
369C22×Q8—611no—
370C22×D4—611no—
371C23×C4—1221no—
372C2×SD16—614no—
373C2×SD16—1222no—
374C2×SD16—1222no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8C22×D6111yescharacteristic
378C22×C8C22×D6111yescharacteristic
379C4×Q8—614no—
380C4×Q8—1222no—
381C4×Q8—1222no—
382C4×Q8—1222no—
383C4×Q8—2441no—
384C4×Q8—2441no—
385C4×D4—614no—
386C4×D4—1222no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C42—21no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—1221no—
409C2×C42—1221no—
410C2×C42—1221no—
411C2×C42—1221no—
412C2×C42C22×D6111yescharacteristic
413#106C4×D6114yes—
414C4⋊C8—1222no—
415#103—614no—
416#103—1222no—
417#103—1222no—
418#102—614no—
419#102—2441no—
420#102—2441no—
421#97—2441no—
422#97—2441no—
423C4×C8—614no—
424#95—21no—
425#95—21no—
426#95—611no—
427#95—611no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434C24—1221no—
435C2×Q8—612no—
436C2×Q8—612no—
437C2×Q8—612no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×D4—612no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—1224no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—4881no—
460C22×C4—4881no—
461C22×C4D4×D6111yescharacteristic
462C22×C4D4×D6111yescharacteristic
463C22×C4C23×D6111yescharacteristic
464SD16—1228no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—612no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8C2×C4×D6112yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—1224no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—2441no—
490C4⋊C4—2441no—
491C4⋊C4—2442no—
492C4⋊C4—2442no—
493C4⋊C4—2442no—
494C4⋊C4C2×C4×D6112yes—
495C4⋊C4C2×C4×D6112yes—
496C22⋊C4—1224no—
497C22⋊C4—4881no—
498C22⋊C4—4881no—
499C22⋊C4—2442no—
500C22⋊C4—2442no—
501C42—21no—
502C42—21no—
503C42—81no—
504C42—612no—
505C42—612no—
506C42—1224no—
507C42—1221no—
508C42—1221no—
509C42—4881no—
510C42—2442no—
511C42—2442no—
512C23—1222no—
513C23—2441no—
514C23—2441no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23—2441no—
519C23C2×D4×D6111yescharacteristic
520Q8—614no—
521Q8—1222no—
522Q8—1222no—
523Q8—1222no—
524D4—1222no—
525D4—1222no—
526D4—2441no—
527D4—2441no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
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—41no—
545C2×C4—41no—
546C2×C4—612no—
547C2×C4—612no—
548C2×C4—1222no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—4884no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4C22×C4×D6111yescharacteristic
569C2×C4#41×D6111yescharacteristic
570C2×C4#41×D6111yescharacteristic
571C2×C4#41×D6111yescharacteristic
572C2×C4#1451982311yescharacteristic
573C2×C4#1451982511yescharacteristic
574C8—22no—
575C8—41no—
576C8—1222no—
577C8—2441no—
578C22—4881no—
579C22—4881no—
580C22—4881no—
581C22—4881no—
582C22—2442no—
583C22—2442no—
584C22—2442no—
585C22C4×D4×D6111yescharacteristic
586C22#1684040411yescharacteristic
587C22#1684042211yescharacteristic
588C22#1684055811yescharacteristic
589C22#1684056111yescharacteristic
590C22#1684056811yescharacteristic
591C22#1684056911yescharacteristic
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4—1222no—
599C4—1224no—
600C4—1222no—
601C4—4881no—
602C4—4881no—
603C4—2441no—
604C4—2441no—
605C4#117×D6111yescharacteristic
606C4#1684024411yescharacteristic
607C4#1684044411yescharacteristic
608C4#1684046311yescharacteristic
609C2—4882no—
610C2#2144874311yescharacteristic
611C2#2145461411yescharacteristic
612C2#2145467311yescharacteristic
613C2#2145807011yescharacteristic
614C2#2145807511yescharacteristic
615C2#2145859011yescharacteristic
616C2#2145859411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1920C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenter#1920D61
hypocenterC61#22765
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
3. #21448738C2semidirect
6. #21446406C2semidirect
9. #21445948C2semidirect
10. #21445833C2semidirect
12. #21445685C2semidirect
13. #21445652C2semidirect
14. #21445648C2semidirect
15. C61×#1920C2semidirect
21. #16839849C4semidirect
307. #1920D61semidirect
368. C61#22765semidirect

Maximal subgroups

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

subgroupindex
C2×#168398492
#214487882
#214487382
#214465172
#214465152
#214464062
#214461752
#214461732
#214459482
#214458332
#214458282
#214456852
#214456522
#214456482
C61×#19202
#2276561