Finite Group Databasebeta

← #30621830

Subgroups — #30621830

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840792C211yesmaximal, characteristic
2C2×#16840781C211yesmaximal, characteristic, complemented
3#21461921C211yesmaximal, characteristic, complemented
4#21461894C211yesmaximal, characteristic, complemented
5#21461890C211yesmaximal, characteristic, complemented
6#21461876C211yesmaximal, characteristic, complemented
7#21461874C211yesmaximal, characteristic, complemented
8#21461795C211yesmaximal, characteristic
9#21461765C211yesmaximal, characteristic, complemented
10#21461764C211yesmaximal, characteristic, complemented
11#21461618C211yesmaximal, characteristic, complemented
12#21461560C211yesmaximal, characteristic, complemented
13#21461557C211yesmaximal, characteristic, complemented
14#21461480C211yesmaximal, characteristic, complemented
15#21448340C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19#16840792—24no—
20#16840781—24no—
21C2×#14519844C2211yescharacteristic
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×C4⋊#92420C2211yescharacteristic
25C2×C4⋊#92420C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519832C2211yescharacteristic
32C2×#14519832C2211yescharacteristic
33C2×#14519832C2211yescharacteristic
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×#14519762C411yescharacteristic
47C2×#14519739C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839654C411yescharacteristic
50#16839653C411yescharacteristic
51#16839643C411yescharacteristic
52#16839640C411yescharacteristic
53#16839636C411yescharacteristic
54#16839624C411yescharacteristic
55C4⋊C4×Dic61C2211yescharacteristic
56#16839613C2211yescharacteristic
57#16839609C2211yescharacteristic
58#16839609C2211yescharacteristic
59#16839609C2211yescharacteristic
60C61×#387C411yescharacteristic
61C2×#11758213—22no—
62C2×#11758213—22no—
63C2×#11758213—41no—
64C2×D61⋊C8—22no—
65C2×D61⋊C8—22no—
66C2×D61⋊C8—22no—
67C2×D61⋊C8—22no—
68C2×D61⋊C8—41no—
69C2×D61⋊C8—41no—
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78#14519844—22no—
79#14519844—41no—
80C4⋊#92420—22no—
81C4⋊#92420—22no—
82C4⋊#92420—22no—
83#14519834—22no—
84#14519834—22no—
85#14519834—22no—
86#14519834—41no—
87#14519834D414yes—
88#14519832—22no—
89#14519832—22no—
90#14519832—41no—
91C4×#92420—22no—
92C4×#92420—22no—
93C22×D244C2×C411yescharacteristic
94C22×C4×D61C2×C411yescharacteristic
95C22×C4×D61C2×C411yescharacteristic
96C22×C4×D61C2311yescharacteristic
97C22×C4×D61C2311yescharacteristic
98#14519762—24no—
99#14519739—22no—
100#14519739—22no—
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×C4×Dic61C2×C411yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C42×D61—22no—
119C42×D61—22no—
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125#14519684C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C42×C61C2×C411yescharacteristic
129#95×C61C2×C411yescharacteristic
130#95×C61C2×C411yescharacteristic
131#95×C61C2×C411yescharacteristic
132#95×C61C2×C411yescharacteristic
133C23×D61C22×C411yescharacteristic
134C23×D61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C2411yescharacteristic
148C2×D244—22no—
149C2×D244—22no—
150C2×D244—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—41no—
166C2×C4×D61M1614yescomplemented
167C2×C4×D61C2×D412yes—
168C2×C4×D61#4112yes—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—21no—
185C2×#92420—21no—
186C2×#92420—21no—
187C2×#92420—21no—
188C2×#92420—21no—
189C2×#92420C2×D412yes—
190C2×#92420C2×D412yes—
191C2×#92420#4112yes—
192C2×#92420#4112yes—
193#11758213—44no—
194D61⋊C8—44no—
195D61⋊C8—44no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C42×C61—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205#11758198—22no—
206#11758198—41no—
207C4⋊Dic61—41no—
208#11758196—22no—
209#11758196—22no—
210C4×Dic61—22no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C23×C61C23×C411yescharacteristic
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61C4×D412yes—
234C22×D61C2×M1612yes—
235C22×D61#13112yes—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61C4×D412yes—
255C2×C4×C61C2×M1612yes—
256C2×C4×C61#13112yes—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61C2×M1612yes—
272C2×Dic61C22×D411yescharacteristic
273C2×Dic61C2×#4111yescharacteristic
274C2×Dic61C2×#4111yescharacteristic
275C2×Dic61C2×#4111yescharacteristic
276C2×Dic61H(5,𝔽2)11yescharacteristic
277C2×Dic612−1+411yescharacteristic
278D244—44no—
279C4×D61—28no—
280C4×D61—22no—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—44no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289#92420—22no—
290#92420—22no—
291#92420—22no—
292#92420—22no—
293#92420—41no—
294#92420—41no—
295#92420—41no—
296#92420—41no—
297#22902—611nomaximal, Sylow
298C22×C61C2×C4×D411yescharacteristic
299C22×C61C4×#4111yescharacteristic
300C22×C61#52011yescharacteristic
301C22×C61C22×M1611yescharacteristic
302C22×C61C2×#13111yescharacteristic
303C22×C61C2×#13111yescharacteristic
304C22×C61#56811yescharacteristic
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—22no—
309C2×D61—22no—
310C2×D61—22no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C2×D61—41no—
318C2×D61#43514yes—
319C4×C61—22no—
320C4×C61—22no—
321C4×C61—22no—
322C4×C61—41no—
323C4×C61—41no—
324C4×C61—41no—
325C4×C61—41no—
326Dic61—22no—
327Dic61—41no—
328Dic61—41no—
329Dic61—41no—
330Dic61—41no—
331Dic61#54611yescharacteristic
332Dic61#54711yescharacteristic
333Dic61#55111yescharacteristic
334Dic61#55211yescharacteristic
335C2×#435—611no—
336C2×#431—611no—
337C4×#123—611no—
338#1940—611no—
339#1924—611no—
340#1923—611no—
341#1917—611no—
342#1916—611no—
343#1869—611no—
344#1851—611no—
345#1850—611no—
346#1771—611no—
347#1753—611no—
348#1752—611no—
349C2×#336—611no—
350C2×C61#235911yescharacteristic
351C2×C61C2×#43511yescharacteristic
352C2×C61#293311yescharacteristic
353C2×C61#296511yescharacteristic
354C2×C61#296811yescharacteristic
355C2×C61#298911yescharacteristic
356C2×C61#299411yescharacteristic
357D61—24no—
358D61—81no—
359C22×M16—611no—
360C23×C8—611no—
361C23×C8—611no—
362C2×#123—611no—
363C2×C4×D4—611no—
364C22×C42—611no—
365#435—1224no—
366#431—1224no—
367C2×C4⋊C8—611no—
368C2×C4⋊C8—611no—
369C2×C4⋊C8—611no—
370C2×C4⋊C8—611no—
371C2×C4⋊C8—611no—
372C2×C22⋊C8—611no—
373C2×C22⋊C8—611no—
374C2×C22⋊C8—611no—
375C2×C22⋊C8—611no—
376C2×C22⋊C8—611no—
377C2×#97—611no—
378C2×#97—611no—
379C2×#97—611no—
380C2×C4×C8—611no—
381C2×C4×C8—611no—
382#388—611no—
383#388—611no—
384#387—611no—
385#387#692311yescharacteristic
386#386—611no—
387#385—611no—
388#381—611no—
389C4×C4⋊C4—611no—
390C4×C4⋊C4—611no—
391C4×C22⋊C4—611no—
392C4×C22⋊C4—611no—
393C4×C22⋊C4—611no—
394#336—611no—
395#336—611no—
396#336—611no—
397#336—611no—
398#336—611no—
399#336—611no—
400#336—611no—
401#336—611no—
402#336—611no—
403#336—611no—
404C61#2290211yescharacteristic, complemented, Sylow
405C22×D4—611no—
406C23×C4—611no—
407C23×C4—611no—
408C23×C4—611no—
409C23×C4—611no—
410C2×M16—1222no—
411C2×M16—1222no—
412C2×M16—2441no—
413C22×C8—611no—
414C22×C8—611no—
415C22×C8—611no—
416C22×C8—611no—
417C22×C8—611no—
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—611no—
421C22×C8—1222no—
422C22×C8—1222no—
423C22×C8—1222no—
424C22×C8—1222no—
425C22×C8—2441no—
426C22×C8—2441no—
427#123—1224no—
428C4×D4—1222no—
429C4×D4—1222no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4C2×#692311yescharacteristic
434C2×C4⋊C4C2×#692311yescharacteristic
435C2×C22⋊C4—611no—
436C2×C22⋊C4—611no—
437C2×C22⋊C4—611no—
438C2×C22⋊C4—611no—
439C2×C22⋊C4—611no—
440C2×C22⋊C4—611no—
441C2×C22⋊C4—611no—
442C2×C22⋊C4—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—611no—
449C2×C42—1222no—
450C2×C42—1222no—
451C2×C42C2×#692311yescharacteristic
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454C4⋊C8—1222no—
455C4⋊C8—1222no—
456C4⋊C8—2441no—
457C22⋊C8—614no—
458C22⋊C8—1222no—
459C22⋊C8—1222no—
460C22⋊C8—1222no—
461C22⋊C8—2441no—
462#97—1222no—
463#97—1222no—
464#97—2441no—
465C4×C8—1222no—
466C4×C8—1222no—
467#95—611no—
468#95—611no—
469#95—611no—
470#95—611no—
471#95—611no—
472#95—611no—
473#95C2×#692311yescharacteristic
474#95C2×#692311yescharacteristic
475#95C2×#692311yescharacteristic
476#95C2×#692311yescharacteristic
477C24—611no—
478C24—611no—
479C2×D4—1222no—
480C2×D4—1222no—
481C2×D4—1222no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—614no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—2441no—
506C22×C4C22×#692311yescharacteristic
507C22×C4C22×#692311yescharacteristic
508C22×C4C22×#692311yescharacteristic
509C22×C4C22×#692311yescharacteristic
510C22×C4C22×#692311yescharacteristic
511C22×C4C22×#692311yescharacteristic
512C22×C4C22×#692311yescharacteristic
513M16—2444no—
514C2×C8—612no—
515C2×C8—612no—
516C2×C8—612no—
517C2×C8—612no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8—2444no—
539C2×C8—2444no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—1222no—
543C4⋊C4—1222no—
544C4⋊C4—2441no—
545C22⋊C4—1222no—
546C22⋊C4—1222no—
547C22⋊C4—1222no—
548C22⋊C4—1222no—
549C22⋊C4—1222no—
550C22⋊C4—1222no—
551C22⋊C4—1222no—
552C22⋊C4—2441no—
553C42—22no—
554C42—1221no—
555C42—1221no—
556C42—1221no—
557C42—1221no—
558C42—1221no—
559C42—1221no—
560C42—1221no—
561C42—1221no—
562C42—1221no—
563C42—1221no—
564C42—1222no—
565C23—612no—
566C23—612no—
567C23—612no—
568C23—1221no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23—1221no—
573C23—1221no—
574C23—1221no—
575C23—1221no—
576C23—1221no—
577C23—1221no—
578C23—1221no—
579C23C23×#692311yescharacteristic
580D4—2444no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—611no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—611no—
605C2×C4—612no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1222no—
609C2×C4—1222no—
610C2×C4—1228no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—2444no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4D4×#692312yes—
631C2×C4D61⋊M1612yes—
632C2×C4#1451986512yes—
633C8—1222no—
634C8—1222no—
635C8—1222no—
636C8—1222no—
637C8—2441no—
638C8—2441no—
639C8—2441no—
640C8—2441no—
641C22—614no—
642C22—1222no—
643C22—1222no—
644C22—1222no—
645C22—1222no—
646C22—1222no—
647C22—1222no—
648C22—2441no—
649C22—2441no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22—2441no—
654C22—2441no—
655C22C2×D4×#692311yescharacteristic
656C22#41×#692311yescharacteristic
657C22#1684083111yescharacteristic
658C22C2×D61⋊M1611yescharacteristic
659C22D61⋊#13111yescharacteristic
660C22C2×#1451986511yescharacteristic
661C22#1684084111yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—611no—
670C4—611no—
671C4—611no—
672C4—611no—
673C4—1222no—
674C4—2441no—
675C4—2441no—
676C4—2441no—
677C4—2441no—
678C2—1224no—
679C2—4881no—
680C2#2146234211yescharacteristic
681C2D61⋊#43511yescharacteristic
682C2#2146255211yescharacteristic
683C2#2146262711yescharacteristic
684C2#2146264911yescharacteristic
685C2#2146274111yescharacteristic
686C2#2146277111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#387C4
prime radicalC22×D244C2×C4
cosocleC22×Dic61C24
hypercenter#387#6923
hypocenterC61#22902
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×#16840781C2semidirect
3. #21461921C2semidirect
4. #21461894C2semidirect
5. #21461890C2semidirect
6. #21461876C2semidirect
7. #21461874C2semidirect
9. #21461765C2semidirect
10. #21461764C2semidirect
11. #21461618C2semidirect
12. #21461560C2semidirect
13. #21461557C2semidirect
14. #21461480C2semidirect
166. C2×C4×D61M16semidirect
404. C61#22902semidirect

Maximal subgroups

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

subgroupindex
C2×#168407922
C2×#168407812
#214619212
#214618942
#214618902
#214618762
#214618742
#214617952
#214617652
#214617642
#214616182
#214615602
#214615572
#214614802
#214483402
#2290261