Finite Group Databasebeta

← #30610457

Subgroups — #30610457

Order 15616.

1214 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#21462497C211yesmaximal, characteristic
2#21462496C211yesmaximal, characteristic
3#21461163C212yesmaximal, complemented
4#21461161C212yesmaximal, complemented
5#21461148C214yesmaximal, complemented
6#21461122C214yesmaximal, complemented
7C2×C4×Q8×D61C211yesmaximal, characteristic
8#16840785—21no—
9#16840784—21no—
10#16840784—21no—
11#16840783C2212yes—
12#16840781C2212yes—
13#16840781C2212yes—
14#16840780C2212yes—
15#16840778—21no—
16#16840766C2212yes—
17#16840765—21no—
18#16840734—21no—
19#16840733—21no—
20C4×#11758213—21no—
21C4×#11758217C2212yes—
22#16840612C2218yescomplemented
23Q8⋊#92420C2218yescomplemented
24C22×Q8×D61C411yescharacteristic
25C2×Q8×Dic61C2211yescharacteristic
26C2×C4×Dic122—21no—
27C2×C4×Dic122C411yescharacteristic
28C2×#14519742—21no—
29C2×#14519742C2211yescharacteristic
30C4×Q8×D61—21no—
31C4×Q8×D61—21no—
32C4×Q8×D61—21no—
33C4×Q8×D61—21no—
34C4×Q8×D61C412yes—
35C4×Q8×D61C412yes—
36C4×Q8×D61C2212yes—
37C4×Q8×D61C2212yes—
38C2×C4⋊C4×D61—21no—
39C2×C4⋊C4×D61C411yescharacteristic
40C2×C42×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44C2×#11758217—22no—
45#14519844—22no—
46C4⋊#92420—22no—
47C4⋊#92420—22no—
48C4⋊#92420C2314yes—
49#14519834—22no—
50#14519834—22no—
51#14519834—22no—
52C22⋊#92420—22no—
53#14519832—22no—
54#14519832—22no—
55C4×#92420—22no—
56C4×#92420C2314yes—
57C22×Dic122—21no—
58C22×Dic122C2×C411yescharacteristic
59C2×Q8×D61—28no—
60C2×Q8×D61—21no—
61C2×Q8×D61—21no—
62C2×Q8×D61C2×C412yes—
63C2×Q8×D61C2×C412yes—
64C22×C4×D61—21no—
65C22×C4×D61—21no—
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69Q8×Dic61—21no—
70Q8×Dic61—21no—
71Q8×Dic61C2×C412yes—
72Q8×Dic61C2312yes—
73C4×Dic122—21no—
74C4×Dic122—21no—
75C4×Dic122—22no—
76C4×Dic122—22no—
77C4×Dic122—22no—
78C4×Dic122—22no—
79C4×Dic122C2×C412yes—
80C4×Dic122C2×C412yes—
81#14519742—22no—
82#14519742—22no—
83#14519742—21no—
84#14519742—21no—
85#14519742—22no—
86#14519742—22no—
87#14519742C2×C412yes—
88#14519742C2312yes—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—22no—
99C4⋊C4×D61—22no—
100C4⋊C4×D61C2×C412yes—
101C4⋊C4×D61C2×C412yes—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C42×D61—22no—
109C42×D61—22no—
110C42×D61—22no—
111C42×D61—22no—
112C42×D61C2×C411yescharacteristic
113C42×D61C2×C411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61C2311yescharacteristic
119C42×D61C2311yescharacteristic
120C22×Q8×C61C2×C411yescharacteristic
121C4×Q8×C61—21no—
122C4×Q8×C61—21no—
123C4×Q8×C61C2×C412yes—
124C4×Q8×C61C2×C412yes—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C42×C61—21no—
128C2×C42×C61C2×C411yescharacteristic
129C23×D61C22⋊C411yescharacteristic
130C2×Q8×C61—24no—
131C2×Q8×C61—21no—
132C2×Q8×C61C22×C412yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61C22⋊C411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143Q8×D61—28no—
144Q8×D61—28no—
145Q8×D61—24no—
146Q8×D61—24no—
147Q8×D61—24no—
148Q8×D61M1618yescomplemented
149C2×C4×D61—28no—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—24no—
153C2×C4×D61—24no—
154C2×C4×D61—22no—
155C2×C4×D61—22no—
156C2×C4×D61—42no—
157C2×C4×D61—44no—
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C22×C411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×Dic122—28no—
171C2×Dic122—21no—
172C2×Dic122—22no—
173C2×Dic122—22no—
174C2×Dic122—24no—
175C2×Dic122C22×C412yes—
176#11758217—44no—
177C2×#92420—24no—
178C2×#92420—24no—
179#11758213—44no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61C22×C412yes—
184C42×C61—22no—
185C42×C61—22no—
186C42×C61C22⋊C411yescharacteristic
187C42×C61C22⋊C411yescharacteristic
188C42×C61C22×C411yescharacteristic
189C42×C61C22×C411yescharacteristic
190C4⋊Dic61—21no—
191C4⋊Dic61—22no—
192C4⋊Dic61—22no—
193C4⋊Dic61C22×C412yes—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61C22⋊C411yescharacteristic
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22×C411yescharacteristic
211C4×Dic61C2×D411yescharacteristic
212C4×Dic61C2×D411yescharacteristic
213C4×Dic61C2×D411yescharacteristic
214C4×Dic61C2×D411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2411yescharacteristic
218C23×C61C2×C22⋊C411yescharacteristic
219C22×D61—22no—
220C22×D61—22no—
221C22×D61—22no—
222C22×D61C2×C22⋊C411yescharacteristic
223C22×D61C2×C22⋊C411yescharacteristic
224Q8×C61—24no—
225Q8×C61—22no—
226Q8×C61C2×M1614yes—
227C2×C4×C61—24no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—42no—
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C23×C411yescharacteristic
240C2×Dic61—24no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—42no—
247C2×Dic61C2×C22⋊C411yescharacteristic
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×C22⋊C411yescharacteristic
250C2×Dic61C2×C22⋊C411yescharacteristic
251C2×Dic61C22×D411yescharacteristic
252C2×Dic61C22×D411yescharacteristic
253C4×D61—28no—
254C4×D61—28no—
255C4×D61—22no—
256C4×D61—22no—
257C4×D61—22no—
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—41no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—44no—
266C4×D61—44no—
267C4×D61C2×M1614yes—
268C4×D61#13714yes—
269Dic122—28no—
270Dic122—24no—
271Dic122—22no—
272Dic122—28no—
273Dic122C2×M1614yes—
274#92420—44no—
275#92420—44no—
276#17449—611nomaximal, Sylow
277C22×C61—21no—
278C22×C61—21no—
279C22×C61#42112yes—
280C22×C61C22×C22⋊C411yescharacteristic
281C2×D61—28no—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—21no—
286C2×D61#40712yes—
287C2×D61#41912yes—
288C4×C61—24no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—42no—
294C4×C61#41912yes—
295C4×C61C22×M1612yes—
296Dic61—21no—
297Dic61—24no—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301Dic61—42no—
302Dic61#40712yes—
303Dic61C2×#13712yes—
304C22×C4×Q8—611no—
305#2920—611no—
306#2920—611no—
307#1491—612no—
308#1491—612no—
309#1487—614no—
310#1479—614no—
311C2×C61—22no—
312C2×C61C2×#40711yescharacteristic
313C2×C61C2×#41911yescharacteristic
314C2×C61C2×#42111yescharacteristic
315D61—22no—
316D61—22no—
317C23×Q8—611no—
318C2×C4×Q8—611no—
319C2×C4×Q8—612no—
320C2×C4×Q8—612no—
321C2×C4×Q8—612no—
322C2×C4×Q8—612no—
323C2×C4×Q8—611no—
324C2×C4×Q8—611no—
325C2×C4×Q8—1221no—
326C2×C4×Q8—1221no—
327C2×C4×Q8—1221no—
328C2×C4×Q8—1221no—
329C2×C4×Q8—1221no—
330C2×C4×Q8—1221no—
331C2×C4×Q8#692311yescharacteristic
332C22×C4⋊C4—611no—
333C22×C4⋊C4—1221no—
334C22×C42—611no—
335C22×C42—1221no—
336#432—612no—
337#432—1221no—
338#432—1221no—
339#432—1221no—
340#431—612no—
341#431—612no—
342#431—612no—
343#431—1221no—
344#423—612no—
345#423—1221no—
346#407—1221no—
347#407—1221no—
348C4×M16—612no—
349C4×M16—1221no—
350Q8⋊C8—618no—
351Q8⋊C8—618no—
352C61#1744911yescharacteristic, complemented, Sylow
353C22×Q8—612no—
354C22×Q8—612no—
355C22×Q8—611no—
356C22×Q8—1221no—
357C22×Q8—1221no—
358C22×Q8—1221no—
359C22×Q8—1228no—
360C22×Q8C2×#692311yescharacteristic
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—611no—
364C23×C4—1221no—
365C23×C4—1221no—
366C2×M16—1222no—
367C2×M16—1222no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—612no—
371C4×Q8—612no—
372C4×Q8—612no—
373C4×Q8—612no—
374C4×Q8—612no—
375C4×Q8—612no—
376C4×Q8—1222no—
377C4×Q8—1222no—
378C4×Q8—1222no—
379C4×Q8—1222no—
380C4×Q8—1222no—
381C4×Q8—1221no—
382C4×Q8—1221no—
383C4×Q8—1222no—
384C4×Q8—1222no—
385C4×Q8—1222no—
386C4×Q8—1221no—
387C4×Q8—1221no—
388C4×Q8—1221no—
389C4×Q8—1221no—
390C4×Q8C2×#692312yes—
391C4×Q8C2×#692312yes—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—612no—
395C2×C4⋊C4—612no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1222no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4—1222no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4C2×#692311yescharacteristic
407C2×C42—21no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—1222no—
420C2×C42—1222no—
421C2×C42—1222no—
422C2×C42—1222no—
423C2×C42—1221no—
424C2×C42—1221no—
425C2×C42—1221no—
426C2×C42C2×#692311yescharacteristic
427C4⋊C8—614no—
428C4⋊C8—1222no—
429C4⋊C8—1222no—
430C4⋊C8—1222no—
431C22⋊C8—1222no—
432C22⋊C8—1222no—
433C22⋊C8—1222no—
434C22⋊C8—1222no—
435#97—1222no—
436#97—1222no—
437C4×C8—614no—
438C4×C8—1222no—
439C24—611no—
440C2×Q8—24no—
441C2×Q8—21no—
442C2×Q8—618no—
443C2×Q8—612no—
444C2×Q8—1222no—
445C2×Q8—1222no—
446C2×Q8—1224no—
447C2×Q8—1228no—
448C2×Q8—1224no—
449C2×Q8—1224no—
450C2×Q8—1228no—
451C2×Q8—1228no—
452C2×Q8—1224no—
453C2×Q8—1221no—
454C2×Q8C22×#692312yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—1224no—
473C22×C4—1224no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—1228no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—2442no—
482C22×C4—2444no—
483C22×C4C22⋊#692311yescharacteristic
484C22×C4C22⋊#692311yescharacteristic
485C22×C4C22×#692311yescharacteristic
486M16—2444no—
487M16—2444no—
488C2×C8—1224no—
489C2×C8—1224no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—612no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1221no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4C22×#692312yes—
504C42—22no—
505C42—22no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42—611no—
515C42—611no—
516C42—611no—
517C42—611no—
518C42—1222no—
519C42—1222no—
520C42—1222no—
521C42—1222no—
522C42—1222no—
523C42—1222no—
524C42C22⋊#692311yescharacteristic
525C42C22⋊#692311yescharacteristic
526C42C22×#692311yescharacteristic
527C42C22×#692311yescharacteristic
528C23—611no—
529C23—611no—
530C23—1222no—
531C23—1222no—
532C23—1222no—
533C23C2×C22⋊#692311yescharacteristic
534Q8—24no—
535Q8—22no—
536Q8—614no—
537Q8—1228no—
538Q8—1228no—
539Q8—1224no—
540Q8—1222no—
541Q8D61⋊M1614yes—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—42no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—614no—
552C2×C4—614no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—1222no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1228no—
562C2×C4—1228no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1224no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1222no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2444no—
576C2×C4—2444no—
577C2×C4—2442no—
578C2×C4C2×C22⋊#692311yescharacteristic
579C2×C4C2×C22⋊#692311yescharacteristic
580C2×C4C2×C22⋊#692311yescharacteristic
581C2×C4C2×C22⋊#692311yescharacteristic
582C2×C4C2×C22⋊#692311yescharacteristic
583C2×C4C23×#692311yescharacteristic
584C8—2444no—
585C8—2444no—
586C22—21no—
587C22—21no—
588C22—612no—
589C22—612no—
590C22—1228no—
591C22—1221no—
592C22—1221no—
593C22—1221no—
594C22—1221no—
595C22#1684075912yes—
596C22C22×C22⋊#692311yescharacteristic
597C4—24no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—42no—
603C4—612no—
604C4—612no—
605C4—1221no—
606C4—1224no—
607C4—1221no—
608C4—1221no—
609C4—1221no—
610C4—2442no—
611C4#1684075512yes—
612C4C2×D61⋊M1612yes—
613C2—22no—
614C2—1222no—
615C2—1222no—
616C2D61⋊#40711yescharacteristic
617C2C2×#1684075511yescharacteristic
618C2C2×#1684075911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17449
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461163C2semidirect
4. #21461161C2semidirect
5. #21461148C2semidirect
6. #21461122C2semidirect
22. #16840612C22semidirect
23. Q8⋊#92420C22semidirect
148. Q8×D61M16semidirect
352. C61#17449semidirect

Maximal subgroups

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

subgroupindex
#214624972
#214624962
#214611632
#214611612
#214611482
#214611222
C2×C4×Q8×D612
#1744961