Finite Group Databasebeta

← #30619571

Subgroups — #30619571

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461992C211yesmaximal, characteristic, complemented
2#21461991C211yesmaximal, characteristic, complemented
3#21461895C211yesmaximal, characteristic
4#21461895C211yesmaximal, characteristic
5#21461894C211yesmaximal, characteristic
6#21461894C211yesmaximal, characteristic
7#21461878C211yesmaximal, characteristic, complemented
8#21461877C211yesmaximal, characteristic, complemented
9#21461875C211yesmaximal, characteristic, complemented
10#21461873C211yesmaximal, characteristic, complemented
11#21461711C211yesmaximal, characteristic
12#21461619C211yesmaximal, characteristic, complemented
13#21461618C211yesmaximal, characteristic, complemented
14C4×#14519834C211yesmaximal, characteristic
15#21448353C211yesmaximal, characteristic
16C2×#14519844C2211yescharacteristic
17C2×#14519844C2211yescharacteristic
18C2×C4⋊#92420C2211yescharacteristic
19C2×C4⋊#92420C2211yescharacteristic
20C2×#14519834C2211yescharacteristic
21C2×#14519834C2211yescharacteristic
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic
24C2×#14519832C2211yescharacteristic
25C2×#14519832C2211yescharacteristic
26C2×#14519832C2211yescharacteristic
27C2×#14519832C2211yescharacteristic
28C2×C4×#92420C2211yescharacteristic
29C2×C4×#92420C2211yescharacteristic
30#16840628C2211yescharacteristic
31#16840628C2211yescharacteristic
32#16840628C2211yescharacteristic
33#16840628C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44C2×#14519755C411yescharacteristic
45C2×#14519742C2211yescharacteristic
46C2×C42×D61C2211yescharacteristic
47#16839666C411yescharacteristic
48#16839659C411yescharacteristic
49#16839646C411yescharacteristic
50#16839636C411yescharacteristic
51#16839633C411yescharacteristic
52#16839621C411yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54#16839613C2211yescharacteristic
55#16839613C2211yescharacteristic
56#16839609C2211yescharacteristic
57#16839609C2211yescharacteristic
58C61×#387C411yescharacteristic
59C22×#92420C2311yescharacteristic
60C22×#92420C2311yescharacteristic
61C22×#92420C2311yescharacteristic
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67#14519844—22no—
68#14519844—41no—
69C4⋊#92420—22no—
70C4⋊#92420—41no—
71#14519834—22no—
72#14519834—22no—
73#14519834—41no—
74#14519834—41no—
75#14519832—22no—
76#14519832—22no—
77#14519832—41no—
78#14519832—41no—
79C4×#92420—41no—
80C4×#92420—41no—
81C22×Dic122C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61C2311yescharacteristic
85#14519755—24no—
86#14519742—41no—
87#14519742—41no—
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×#11758196C2×C411yescharacteristic
90C2×#11758196C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×#11758198C2×C411yescharacteristic
98C2×#11758198C2×C411yescharacteristic
99C2×C4×Dic61C2×C411yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C42×D61—41no—
107C42×D61—41no—
108#14519684C2×C411yescharacteristic
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114C2×C4⋊C4×C61C2×C411yescharacteristic
115C2×C4⋊C4×C61C2×C411yescharacteristic
116C2×C42×C61C2×C411yescharacteristic
117#95×C61C2×C411yescharacteristic
118#95×C61C2×C411yescharacteristic
119#95×C61C2×C411yescharacteristic
120#95×C61C2×C411yescharacteristic
121C23×D61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×Dic61C22×C411yescharacteristic
130C22×Dic61C22×C411yescharacteristic
131C22×Dic61C22×C411yescharacteristic
132C22×Dic61C22×C411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C2411yescharacteristic
136C2×C4×D61—22no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—41no—
144C2×C4×D61—41no—
145C2×C4×D61—41no—
146C2×C4×D61—41no—
147C2×C4×D61M1614yes—
148C2×Dic122—22no—
149C2×Dic122—41no—
150C2×Dic122—41no—
151C2×#92420—21no—
152C2×#92420—21no—
153C2×#92420—21no—
154C2×#92420—21no—
155C2×#92420—21no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420#4112yes—
174C2×#92420#4112yes—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—41no—
177C42×C61—41no—
178#11758198—22no—
179#11758198—22no—
180#11758198—41no—
181#11758198—41no—
182C4⋊Dic61—22no—
183#11758196—22no—
184#11758196—22no—
185#11758196—22no—
186#11758196—41no—
187#11758196—41no—
188#11758196—41no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—41no—
202C23×C61C23×C411yescharacteristic
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61C2×M1612yes—
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×C61—21no—
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—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61C2×M1612yes—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
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×Dic61C2×M1612yes—
248C2×Dic61#13112yes—
249C2×Dic61C2×#4111yescharacteristic
250C2×Dic61C2×#4111yescharacteristic
251C2×Dic61H(5,𝔽2)11yescharacteristic
252C2×Dic61H(5,𝔽2)11yescharacteristic
253C2×Dic612−1+411yescharacteristic
254C2×Dic612−1+411yescharacteristic
255C4×D61—44no—
256C4×D61—44no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—41no—
261Dic122—44no—
262#92420—22no—
263#92420—22no—
264#92420—41no—
265#92420—41no—
266#92420—41no—
267#92420—41no—
268#92420—41no—
269#92420—41no—
270#22325—611nomaximal, Sylow
271C22×C61C4×#4111yescharacteristic
272C22×C61#51811yescharacteristic
273C22×C61#51911yescharacteristic
274C22×C61C22×M1611yescharacteristic
275C22×C61C2×#13111yescharacteristic
276C22×C61#56811yescharacteristic
277C22×C61#56811yescharacteristic
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—22no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C2×D61—41no—
285C4×C61—22no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—41no—
292Dic61—22no—
293Dic61—22no—
294Dic61—41no—
295Dic61—41no—
296Dic61—41no—
297Dic61—41no—
298Dic61#53911yescharacteristic
299Dic61#53911yescharacteristic
300Dic61#54211yescharacteristic
301Dic61#54211yescharacteristic
302C4×C22⋊Q8—611no—
303#1985—611no—
304#1985—611no—
305#1924—611no—
306#1924—611no—
307#1924—611no—
308#1924—611no—
309#1917—611no—
310#1917—611no—
311#1916—611no—
312#1916—611no—
313#1817—611no—
314#1771—611no—
315#1771—611no—
316C4×C22⋊C8—611no—
317C2×C61#233211yescharacteristic
318C2×C61#296511yescharacteristic
319C2×C61#296711yescharacteristic
320C2×C61#297311yescharacteristic
321C2×C61#297611yescharacteristic
322C2×C61#298311yescharacteristic
323C2×C61#298511yescharacteristic
324D61—42no—
325C2×C22⋊Q8—611no—
326C2×C4×Q8—611no—
327C22×C42—611no—
328C2×C4⋊C8—611no—
329C2×C4⋊C8—611no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C22⋊C8—611no—
333C2×C22⋊C8—611no—
334C2×C22⋊C8—611no—
335C2×C22⋊C8—611no—
336C2×#97—611no—
337C2×#97—611no—
338C2×#97—611no—
339C2×#97—611no—
340C2×C4×C8—611no—
341C2×C4×C8—611no—
342#391—611no—
343#389—611no—
344#387—611no—
345#387#692311yescharacteristic
346#385—611no—
347#385—611no—
348#380—611no—
349C4×C4⋊C4—611no—
350C4×C4⋊C4—611no—
351C4×C4⋊C4—611no—
352C4×C22⋊C4—611no—
353C4×C22⋊C4—611no—
354#336—611no—
355#336—611no—
356#336—611no—
357#336—611no—
358#336—611no—
359#336—611no—
360#336—611no—
361#336—611no—
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368C61#2232511yescharacteristic, complemented, Sylow
369C22×Q8—611no—
370C23×C4—611no—
371C23×C4—611no—
372C23×C4—611no—
373C22×C8—611no—
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8—611no—
381C22⋊Q8—1224no—
382C4×Q8—2441no—
383C4×Q8—2441no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4C2×#692311yescharacteristic
392C2×C4⋊C4C2×#692311yescharacteristic
393C2×C22⋊C4—611no—
394C2×C22⋊C4—611no—
395C2×C22⋊C4—611no—
396C2×C22⋊C4—611no—
397C2×C42—611no—
398C2×C42—611no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—611no—
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—2441no—
405C2×C42—2441no—
406C2×C42C2×#692311yescharacteristic
407C4⋊C8—1222no—
408C4⋊C8—1222no—
409C4⋊C8—2441no—
410C4⋊C8—2441no—
411C22⋊C8—1222no—
412C22⋊C8—1222no—
413C22⋊C8—2441no—
414C22⋊C8—2441no—
415#97—1222no—
416#97—1222no—
417#97—2441no—
418#97—2441no—
419C4×C8—2441no—
420C4×C8—2441no—
421#95—611no—
422#95—611no—
423#95—611no—
424#95—611no—
425#95—611no—
426#95—611no—
427#95C2×#692311yescharacteristic
428#95C2×#692311yescharacteristic
429#95C2×#692311yescharacteristic
430#95C2×#692311yescharacteristic
431C24—611no—
432C2×Q8—1222no—
433C2×Q8—2441no—
434C2×Q8—2441no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—614no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1222no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4—2441no—
454C22×C4C22×#692311yescharacteristic
455C22×C4C22×#692311yescharacteristic
456C22×C4C22×#692311yescharacteristic
457C22×C4C22×#692311yescharacteristic
458C22×C4C22×#692311yescharacteristic
459C22×C4C22×#692311yescharacteristic
460C22×C4C22×#692311yescharacteristic
461C2×C8—612no—
462C2×C8—612no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C4⋊C4—2441no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C22⋊C4—2441no—
497C22⋊C4—2441no—
498C42—41no—
499C42—1221no—
500C42—1221no—
501C42—1221no—
502C42—1221no—
503C42—1221no—
504C42—1221no—
505C42—1221no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—2441no—
512C23—612no—
513C23—1221no—
514C23—1221no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23C23×#692311yescharacteristic
520Q8—2444no—
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—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—612no—
548C2×C4—612no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—2444no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2444no—
571C2×C4D61⋊M1612yes—
572C8—1222no—
573C8—1222no—
574C8—2441no—
575C8—2441no—
576C8—2441no—
577C8—2441no—
578C8—2441no—
579C8—2441no—
580C22—1222no—
581C22—1222no—
582C22—1222no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22#41×#692311yescharacteristic
588C22#1684082911yescharacteristic
589C22#1684083011yescharacteristic
590C22C2×D61⋊M1611yescharacteristic
591C22D61⋊#13111yescharacteristic
592C22#1684084111yescharacteristic
593C22#1684084111yescharacteristic
594C4—22no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—611no—
602C4—611no—
603C4—611no—
604C4—611no—
605C4—1222no—
606C4—1222no—
607C4—2441no—
608C4—2441no—
609C4—2441no—
610C4—2441no—
611C2—2442no—
612C2#2146231511yescharacteristic
613C2#2146263011yescharacteristic
614C2#2146264211yescharacteristic
615C2#2146267111yescharacteristic
616C2#2146268711yescharacteristic
617C2#2146271611yescharacteristic
618C2#2146272611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenter#387#6923
hypocenterC61#22325
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. #21461992C2semidirect
2. #21461991C2semidirect
7. #21461878C2semidirect
8. #21461877C2semidirect
9. #21461875C2semidirect
10. #21461873C2semidirect
12. #21461619C2semidirect
13. #21461618C2semidirect
368. C61#22325semidirect

Maximal subgroups

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

subgroupindex
#214619922
#214619912
#214618952
#214618942
#214618782
#214618772
#214618752
#214618732
#214617112
#214616192
#214616182
C4×#145198342
#214483532
#2232561