Finite Group Databasebeta

← #29685395

Subgroups — #29685395

Order 15616.

1132 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840291C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21446812C211yesmaximal, characteristic, complemented
5#21446811C211yesmaximal, characteristic, complemented
6#21446669C211yesmaximal, characteristic, complemented
7#21446284C212yesmaximal, complemented
8#21446279C212yesmaximal
9#101×Dic61C212yesmaximal, complemented
10#100×Dic61C212yesmaximal, complemented
11C61×#1967C211yesmaximal, characteristic, complemented
12C2×M16×D61C2212yes—
13#16840291—21no—
14#16840291—21no—
15#16840291—21no—
16#16840291—21no—
17#16840291—21no—
18#16840291—21no—
19#16840291—21no—
20#16840291—21no—
21C2×#14519770C412yes—
22C2×#14519769C2211yescharacteristic
23C2×#14519759C412yes—
24C2×#14519753C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C2×#14519737C412yes—
29C2×#14519733C412yes—
30C2×C42×D61C2211yescharacteristic
31#16839818—21no—
32#16839818—21no—
33#16839814—21no—
34#16839814—21no—
35#16839786C2211yescharacteristic
36C2×#14519696C2212yes—
37C2×#14519694C2212yes—
38#16839725C2212yes—
39C4×#11758194C2211yescharacteristic
40#16839714—21no—
41M16×Dic61C2212yes—
42M16×Dic61C2212yes—
43C4×#11758189—21no—
44#97×D61—21no—
45C4×C8×D61—21no—
46#16839530C2212yes—
47#16839530C2212yes—
48#16839530C2212yes—
49#16839530C2212yes—
50C2×#124×C61C2211yescharacteristic
51C61×#423C2211yescharacteristic
52C2×#101×C61C2212yes—
53C2×#100×C61C2212yes—
54C4×M16×C61C2211yescharacteristic
55C22×C22⋊D61C2×C412yes—
56C23×Dic61C2×C412yes—
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758194C2312yes—
61C2×#11758194C2312yes—
62C2×#11758189—22no—
63M16×D61—24no—
64M16×D61—24no—
65C2×C8×D61—22no—
66#14519770—22no—
67#14519770—22no—
68#14519770—22no—
69#14519770—22no—
70#14519769—21no—
71#14519769—21no—
72#14519769—21no—
73#14519769—21no—
74#14519759—22no—
75#14519759—22no—
76#14519759—22no—
77#14519759—22no—
78#14519753—21no—
79#14519753—21no—
80#14519753—21no—
81#14519753—21no—
82#14519748—21no—
83#14519748—21no—
84#14519748—21no—
85#14519748—21no—
86Q8×Dic61—21no—
87Q8×Dic61—21no—
88Q8×Dic61—21no—
89Q8×Dic61—21no—
90D4×Dic61—21no—
91D4×Dic61—21no—
92D4×Dic61—21no—
93D4×Dic61—21no—
94#14519737—22no—
95#14519737—22no—
96#14519737—22no—
97#14519737—22no—
98#14519733—22no—
99#14519733—22no—
100#14519733—22no—
101#14519733—22no—
102C2×C4⋊Dic61C2×C412yes—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196C2×C412yes—
106C2×#11758196C2×C412yes—
107C2×#11758196C2×C412yes—
108C2×C22⋊Dic61C2×C412yes—
109C2×C22⋊Dic61C2×C412yes—
110C2×#11758198C2×C412yes—
111C2×C4×Dic61C2×C412yes—
112C2×C4×Dic61C2×C411yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61D411yescharacteristic
120C42×D61D411yescharacteristic
121C42×D61D411yescharacteristic
122C42×D61D411yescharacteristic
123C4⋊#92418—21no—
124C4⋊#92418—21no—
125#14519696—24no—
126#14519694—24no—
127#14519689—22no—
128#14519689—22no—
129#14519688—21no—
130#14519687—22no—
131#14519687—22no—
132C4×#92418—21no—
133C8×Dic61—22no—
134C8×Dic61—22no—
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C2×M16×C61C2312yes—
138C2×M16×C61C2312yes—
139#124×C61—21no—
140#124×C61—21no—
141#124×C61—21no—
142#124×C61—21no—
143C2×C22⋊C4×C61C2×C412yes—
144C2×C22⋊C4×C61C2×C412yes—
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61—21no—
147C4⋊C8×C61—21no—
148#101×C61—24no—
149#100×C61—24no—
150#97×C61—21no—
151C4×C8×C61—21no—
152C24×C61C22×C412yes—
153C23×D61C22×C411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—22no—
157C2×Q8×C61—22no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—44no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—44no—
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C412yes—
175C22×Dic61C22×C412yes—
176C22×Dic61C22×C411yescharacteristic
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—42no—
180C2×C4×D61—42no—
181C2×C4×D61C22⋊C411yescharacteristic
182C2×C4×D61C22⋊C411yescharacteristic
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22⋊C411yescharacteristic
188C2×C4×D61C22⋊C411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193M16×C61—22no—
194M16×C61—22no—
195M16×C61—22no—
196M16×C61#4114yes—
197C2×C8×C61—22no—
198C2×C8×C61—22no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C42×C61C2×D411yescharacteristic
204C42×C61C2×D411yescharacteristic
205C42×C61C2×D411yescharacteristic
206C42×C61C2×D411yescharacteristic
207C22⋊Dic61—22no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210C22⋊Dic61—22no—
211#11758198—22no—
212#11758198—22no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—22no—
218C4⋊Dic61—22no—
219#11758196—22no—
220#11758196—22no—
221#11758196—22no—
222#11758196—22no—
223#11758196—22no—
224#11758196—22no—
225C4×Dic61—22no—
226C4×Dic61—22no—
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C4×Dic61C22⋊C411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C4×Dic61C2×D411yescharacteristic
237C4×Dic61C2×D411yescharacteristic
238C4×Dic61C2×D411yescharacteristic
239#11758194—22no—
240#11758194—22no—
241#11758194—22no—
242#11758194#4114yes—
243C2×#92418—22no—
244C2×#92418—22no—
245#11758189—28no—
246C8×D61—28no—
247C23×C61—22no—
248C23×C61—24no—
249C23×C61—42no—
250C23×C61—42no—
251C23×C61C23×C411yescharacteristic
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—41no—
255C22×D61C2×C22⋊C411yescharacteristic
256C22×D61C2×C22⋊C411yescharacteristic
257Q8×C61—42no—
258Q8×C61—41no—
259Q8×C61—41no—
260D4×C61—42no—
261D4×C61—41no—
262D4×C61—41no—
263C2×C4×C61—22no—
264C2×C4×C61—24no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61C2×C22⋊C411yescharacteristic
268C2×C4×C61C2×C22⋊C411yescharacteristic
269C2×C4×C61C2×C22⋊C411yescharacteristic
270C2×C4×C61C2×C22⋊C411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C22×D411yescharacteristic
273C2×C4×C61C2×#4112yes—
274C2×C4×C61C2×#4112yes—
275C22⋊D61—44no—
276C22⋊D61—44no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—41no—
282C2×Dic61—44no—
283C2×Dic61—44no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61C2×C22⋊C411yescharacteristic
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296C4×D61—21no—
297C4×D61—21no—
298C4×D61—21no—
299C4×D61—21no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—41no—
303C4×D61—41no—
304C4×D61—41no—
305C4×D61—41no—
306C8×C61—24no—
307C8×C61—42no—
308#92418—24no—
309#92418—42no—
310#21426—611nomaximal, Sylow
311C22×C61—21no—
312C22×C61—21no—
313C22×C61—42no—
314C22×C61—42no—
315C22×C61—42no—
316C22×C61—84no—
317C22×C61C22×C22⋊C411yescharacteristic
318C22×C61C4×#4112yes—
319C2×D61—21no—
320C2×D61—21no—
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—21no—
324C2×D61—44no—
325C2×D61#41312yes—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—21no—
330C4×C61—42no—
331C4×C61#52512yes—
332C4×C61#53211yescharacteristic
333C4×C61#53211yescharacteristic
334Dic61—21no—
335Dic61—21no—
336Dic61—21no—
337Dic61—21no—
338Dic61—21no—
339Dic61—42no—
340Dic61—42no—
341Dic61#41312yes—
342C2×#529—611no—
343#2920—611no—
344C2×C4×M16—611no—
345#1998—611no—
346#1998—611no—
347#1967—611no—
348#1967D6111yescharacteristic, complemented
349#1901—612no—
350#1900—612no—
351C4×#101—612no—
352C4×#100—612no—
353C2×C61—22no—
354C2×C61—82no—
355C2×C61#229711yescharacteristic
356C2×C61C2×#41311yescharacteristic
357C2×C61C2×#41311yescharacteristic
358D61—22no—
359D61—41no—
360C22×M16—612no—
361#529—1221no—
362#529—1221no—
363#529—1221no—
364#529—1221no—
365#529—1221no—
366#529—1221no—
367#529—1221no—
368#529—1221no—
369C2×#126—612no—
370C2×#125—611no—
371C2×#124C2×D6111yescharacteristic
372C2×#123—612no—
373C2×C22⋊Q8—611no—
374C2×#121—611no—
375C2×C4×Q8—611no—
376C2×C4×D4—611no—
377C2×C4×D4—612no—
378C2×#117—612no—
379C22×C42—611no—
380#432—1221no—
381#432—1221no—
382#431—1221no—
383#431—1221no—
384#423—611no—
385#423C2×D6111yescharacteristic
386C2×#101—612no—
387C2×#101C2×D6112yes—
388C2×#100—612no—
389C2×#100C2×D6112yes—
390#407—612no—
391C4×M16—612no—
392C4×M16—612no—
393C4×M16—611no—
394C4×M16—1221no—
395C4×M16—1221no—
396C4×M16C2×D6111yescharacteristic
397C2×#97—1221no—
398C2×C4×C8—1221no—
399#343—612no—
400#343—612no—
401#343—612no—
402#343—612no—
403C61#2142611yescharacteristic, complemented, Sylow
404C22×Q8C22×D6111yescharacteristic
405C22×D4—612no—
406C22×D4C22×D6111yescharacteristic
407C23×C4—611no—
408C23×C4—611no—
409C23×C4—611no—
410C23×C4—612no—
411C2×M16—612no—
412C2×M16—612no—
413C2×M16—1222no—
414C2×M16—1224no—
415C2×M16—1224no—
416C2×M16C22×D6112yes—
417C2×M16C22×D6112yes—
418C22×C8—1222no—
419#126—1222no—
420#126—1222no—
421#126—1222no—
422#126—1222no—
423#125—1221no—
424#125—1221no—
425#125—1221no—
426#125—1221no—
427#124—21no—
428#124—21no—
429#124—21no—
430#124—21no—
431#123—1222no—
432#123—1222no—
433#123—1222no—
434#123—1222no—
435C22⋊Q8—1221no—
436C22⋊Q8—1221no—
437C22⋊Q8—1221no—
438C22⋊Q8—1221no—
439#121—1221no—
440#121—1221no—
441#121—1221no—
442#121—1221no—
443C4×Q8—1221no—
444C4×Q8—1221no—
445C4×Q8—1221no—
446C4×Q8—1221no—
447C4×D4—1221no—
448C4×D4—1221no—
449C4×D4—1221no—
450C4×D4—1221no—
451C4×D4—1222no—
452C4×D4—1222no—
453C4×D4—1222no—
454C4×D4—1222no—
455#117—1222no—
456#117—1222no—
457#117—1222no—
458#117—1222no—
459C2×C4⋊C4—612no—
460C2×C4⋊C4—612no—
461C2×C4⋊C4—612no—
462C2×C4⋊C4—612no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C22⋊C4—612no—
466C2×C22⋊C4—612no—
467C2×C22⋊C4—612no—
468C2×C22⋊C4C4×D6112yes—
469C2×C22⋊C4C4×D6112yes—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—612no—
482C2×C42C22×D6111yescharacteristic
483C4⋊C8—21no—
484C4⋊C8—21no—
485C4⋊C8—1221no—
486C4⋊C8—1221no—
487#101—24no—
488#101—1224no—
489#100—24no—
490#100—1224no—
491C22⋊C8—1222no—
492C22⋊C8—1222no—
493#97—21no—
494#97—1222no—
495#97—1222no—
496#97—1221no—
497C4×C8—21no—
498C4×C8—1222no—
499C4×C8—1222no—
500C4×C8—1221no—
501C24—611no—
502C24C2×C4×D6112yes—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—2444no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—612no—
530C22×C4—612no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—1222no—
534C22×C4—1222no—
535C22×C4—2442no—
536C22×C4—2442no—
537C22×C4—2444no—
538C22×C4C2×C4×D6112yes—
539C22×C4C2×C4×D6111yescharacteristic
540C22×C4C2×C4×D6111yescharacteristic
541C22×C4C23×D6111yescharacteristic
542M16—22no—
543M16—22no—
544M16—22no—
545M16—614no—
546M16—1228no—
547M16—1222no—
548M16—1222no—
549M16—1222no—
550M16#1175822414yes—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—1228no—
554C2×C8—1222no—
555C2×C8—1222no—
556C4⋊C4—1222no—
557C4⋊C4—1222no—
558C4⋊C4—1222no—
559C4⋊C4—1222no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1222no—
565C4⋊C4—1222no—
566C4⋊C4—1222no—
567C4⋊C4—1222no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—1222no—
573C22⋊C4—1222no—
574C22⋊C4—1222no—
575C22⋊C4—1222no—
576C22⋊C4—1222no—
577C22⋊C4—1222no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C42—611no—
585C42—611no—
586C42—611no—
587C42—611no—
588C42—611no—
589C42—611no—
590C42—1222no—
591C42—1222no—
592C42D4×D6111yescharacteristic
593C42D4×D6111yescharacteristic
594C42D4×D6111yescharacteristic
595C42D4×D6111yescharacteristic
596C23—22no—
597C23—24no—
598C23—42no—
599C23—42no—
600C23—611no—
601C23—611no—
602C23—1222no—
603C23—1222no—
604C23—2441no—
605C23C22×C4×D6111yescharacteristic
606Q8—42no—
607Q8—41no—
608Q8—41no—
609D4—42no—
610D4—41no—
611D4—41no—
612D4—2444no—
613D4—2444no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—611no—
619C2×C4—611no—
620C2×C4—611no—
621C2×C4—611no—
622C2×C4—611no—
623C2×C4—611no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1222no—
629C2×C4—1222no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—1221no—
635C2×C4—1221no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2444no—
643C2×C4—2441no—
644C2×C4—2444no—
645C2×C4—2442no—
646C2×C4—2442no—
647C2×C4C22⋊C4×D6111yescharacteristic
648C2×C4C22⋊C4×D6111yescharacteristic
649C2×C4C22⋊C4×D6111yescharacteristic
650C2×C4C22⋊C4×D6111yescharacteristic
651C2×C4C2×D4×D6111yescharacteristic
652C2×C4C2×D4×D6111yescharacteristic
653C2×C4#41×D6112yes—
654C2×C4C2×#1175822412yes—
655C8—24no—
656C8—42no—
657C8—1224no—
658C8—2442no—
659C22—21no—
660C22—21no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—84no—
665C22—612no—
666C22—1221no—
667C22—1221no—
668C22—1221no—
669C22—1221no—
670C22—1221no—
671C22—2444no—
672C22C2×C22⋊C4×D6111yescharacteristic
673C22C4×#1175822412yes—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—21no—
678C4—42no—
679C4—612no—
680C4—1221no—
681C4—1221no—
682C4—1221no—
683C4—1221no—
684C4—1221no—
685C4—2442no—
686C4—2442no—
687C4#1684027212yes—
688C4#1684031011yescharacteristic
689C4#1684031111yescharacteristic
690C2—22no—
691C2—82no—
692C2—1222no—
693C2—2441no—
694C2#2144830611yescharacteristic
695C2#413×D6111yescharacteristic
696C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1967C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519748C22
cosocleC22×C4×C61C24
hypercenter#1967D61
hypocenterC61#21426
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1967

Complements

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

NH ≅ G/Ntype
2. #21454451C2semidirect
3. C4×M16×D61C2semidirect
4. #21446812C2semidirect
5. #21446811C2semidirect
6. #21446669C2semidirect
7. #21446284C2semidirect
9. #101×Dic61C2semidirect
10. #100×Dic61C2semidirect
11. C61×#1967C2semidirect
348. #1967D61semidirect
403. C61#21426semidirect

Maximal subgroups

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

subgroupindex
C2×#168402912
#214544512
C4×M16×D612
#214468122
#214468112
#214466692
#214462842
#214462792
#101×Dic612
#100×Dic612
C61×#19672
#2142661