Finite Group Databasebeta

← #29709098

Subgroups — #29709098

Order 15616.

950 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839803C211yesmaximal, characteristic
2C2×#16839784C211yesmaximal, characteristic
3#21448300C211yesmaximal, characteristic
4#389×D61C211yesmaximal, characteristic
5#21447323C211yesmaximal, characteristic, complemented
6#21447320C211yesmaximal, characteristic, complemented
7#21447319C211yesmaximal, characteristic, complemented
8#21447317C211yesmaximal, characteristic, complemented
9#21447316C211yesmaximal, characteristic, complemented
10#21447313C211yesmaximal, characteristic, complemented
11#21447310C211yesmaximal, characteristic, complemented
12#21445537C211yesmaximal, characteristic
13#21445537C211yesmaximal, characteristic
14#21445537C211yesmaximal, characteristic
15C61×#2086C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×#14519735C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×C4⋊C4×D61—21no—
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×C42×D61C2211yescharacteristic
24#16839803—24no—
25C2×#14519710C2211yescharacteristic
26C2×#14519709C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28#16839784—24no—
29C2×C4⋊#92418C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839661C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839659—21no—
37#16839658C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839657—21no—
40#16839636—21no—
41#16839633—21no—
42C4⋊C4×Dic61—21no—
43#16839613—21no—
44#95×D61—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61—21no—
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C2×#11758189—22no—
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189—22no—
70C2×#11758189—22no—
71C2×#11758189D414yes—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519735—22no—
75#14519735—22no—
76#14519735—22no—
77#14519735Q814yes—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—21no—
90C4⋊C4×D61—22no—
91C4⋊C4×D61—22no—
92C4⋊C4×D61—22no—
93C4⋊C4×D61—44no—
94C4⋊C4×D61Q814yes—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61D411yescharacteristic
100C2×C4×Dic61D411yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C42×D61—22no—
103C42×D61—22no—
104#14519710—22no—
105#14519709—22no—
106#14519708—22no—
107C4⋊#92418—22no—
108#14519706—22no—
109#14519706—22no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125#107×C61—22no—
126C4⋊C8×C61—22no—
127#95×C61—21no—
128#95×C61—21no—
129C23×D61C2×D411yescharacteristic
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2411yescharacteristic
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—24no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61—42no—
152C2×C4×D61—42no—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61C2×D412yes—
157C2×C4×D61C2×Q812yes—
158C2×C4×D61C2×Q812yes—
159C2×C4×D61#4112yes—
160C2×C4×D61#4112yes—
161C2×C4×D61#4112yes—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61C2×D412yes—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—42no—
175C4⋊C4×C61—42no—
176C4⋊C4×C61C2×Q812yes—
177C4⋊C4×C61C2×Q812yes—
178C42×C61—21no—
179C42×C61—21no—
180#11758198—24no—
181#11758198—42no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—42no—
189C4⋊Dic61—42no—
190C4⋊Dic61C2×Q812yes—
191C4⋊Dic61C2×Q812yes—
192#11758196—24no—
193#11758196—42no—
194#11758196—42no—
195#11758196—42no—
196#11758196—42no—
197#11758196—42no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—24no—
203C4×Dic61—42no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418C2×D412yes—
210#11758189—28no—
211#11758189—44no—
212C23×C61C22×D411yescharacteristic
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61#12112yes—
218C22×D61C22⋊Q812yes—
219C22×D61C22⋊Q812yes—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61AGL(1,ℤ/8)12yes—
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×Q811yescharacteristic
240C2×C4×C61C22×Q811yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61#12112yes—
262C2×Dic61C22⋊Q812yes—
263C2×Dic61C22⋊Q812yes—
264C2×Dic61#13712yes—
265C4×D61—44no—
266C4×D61—44no—
267C4×D61—48no—
268C4×D61—84no—
269C4×D61#12314yes—
270C4×D61#12514yes—
271C4×D61#12514yes—
272C4×D61C4⋊Q814yes—
273C8×C61—22no—
274C8×C61—41no—
275#92418—22no—
276#92418—41no—
277#23670—611nomaximal, Sylow
278C22×C61C2×#12111yescharacteristic
279C22×C61C2×C22⋊Q811yescharacteristic
280C22×C61C2×C22⋊Q811yescharacteristic
281C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C61C2×#13711yescharacteristic
283C22×C61#57511yescharacteristic
284C22×C61#57511yescharacteristic
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—22no—
290C2×D61—22no—
291C2×D61#39814yes—
292C4×C61—22no—
293C4×C61—42no—
294C4×C61—42no—
295C4×C61—41no—
296C4×C61—81no—
297C4×C61—81no—
298C4×C61C2×#12311yescharacteristic
299C4×C61C2×#12511yescharacteristic
300C4×C61C2×#12511yescharacteristic
301C4×C61C2×C4⋊Q811yescharacteristic
302Dic61—22no—
303Dic61—42no—
304Dic61—42no—
305Dic61—41no—
306Dic61—81no—
307Dic61—81no—
308Dic61#39814yes—
309C2×#428—611no—
310C2×#423—611no—
311#2296—611no—
312C2×#389—611no—
313#2088—611no—
314#2088—611no—
315#2088—611no—
316#2088—611no—
317#2087—611no—
318#2087—611no—
319#2086—611no—
320#2086D6111yescharacteristic, complemented
321#1736—611no—
322#1736—611no—
323#1736—611no—
324C2×C61C2×#39811yescharacteristic
325C2×C61#305511yescharacteristic
326C2×C61#305611yescharacteristic
327C2×C61#307711yescharacteristic
328C2×C61#307811yescharacteristic
329C2×C61#307911yescharacteristic
330C2×C61#308011yescharacteristic
331D61—24no—
332C22×M16—611no—
333C22×M16—611no—
334C2×#117—611no—
335C2×#117—611no—
336C22×C4⋊C4—611no—
337C22×C4⋊C4—611no—
338C22×C4⋊C4—1221no—
339C22×C42—611no—
340#428—1224no—
341C2×#107—611no—
342C2×#107C2×D6111yescharacteristic
343C2×#106—611no—
344C2×#106—611no—
345#423—1224no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8—611no—
349C2×C4⋊C8C2×D6111yescharacteristic
350#389—611no—
351#389—611no—
352#389—611no—
353#389—611no—
354#389—611no—
355#389—611no—
356#389—1221no—
357#389—1221no—
358#389C2×D6111yescharacteristic
359#389C2×D6111yescharacteristic
360#385—1221no—
361#385—1221no—
362C4×C4⋊C4—1221no—
363C4×C4⋊C4—1221no—
364C2×#95—1221no—
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340C2×D6111yescharacteristic
375#340C2×D6111yescharacteristic
376#340C2×D6111yescharacteristic
377C61#2367011yescharacteristic, complemented, Sylow
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—1221no—
382C23×C4—1221no—
383C2×M16—614no—
384C2×M16—1222no—
385C2×M16—1222no—
386C2×M16—1222no—
387C2×M16—1222no—
388C2×M16—1222no—
389C22×C8—611no—
390C22×C8—611no—
391C22×C8C22×D6111yescharacteristic
392C22×C8C22×D6111yescharacteristic
393#117—614no—
394#117—1222no—
395#117—1222no—
396#117—1222no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—614no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1222no—
406C2×C4⋊C4—1222no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—2444no—
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—1222no—
426C2×C42—1222no—
427C2×C42—1221no—
428C2×C42—1221no—
429C2×C42C22×D6111yescharacteristic
430#107—22no—
431#107—1222no—
432#106—1222no—
433#106—1222no—
434C4⋊C8—22no—
435C4⋊C8—1222no—
436C4⋊C8—1222no—
437C4⋊C8—1222no—
438#95—21no—
439#95—21no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445#95—1221no—
446C24—611no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—611no—
452C22×C4—612no—
453C22×C4—612no—
454C22×C4—612no—
455C22×C4—612no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1224no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1222no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—2441no—
470C22×C4—2441no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4D4×D6111yescharacteristic
477C22×C4D4×D6111yescharacteristic
478C22×C4C23×D6111yescharacteristic
479M16—1228no—
480M16—2444no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—612no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8D4×D6112yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—612no—
502C4⋊C4—612no—
503C4⋊C4—1224no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C4⋊C4—2442no—
513C4⋊C4—2442no—
514C4⋊C4—2442no—
515C4⋊C4—2442no—
516C4⋊C4—2442no—
517C4⋊C4Q8×D6112yes—
518C4⋊C4Q8×D6112yes—
519C22⋊C4—1224no—
520C22⋊C4—2442no—
521C42—21no—
522C42—21no—
523C42—1222no—
524C42—1222no—
525C42—1224no—
526C42—1221no—
527C42—1221no—
528C42—2442no—
529C23—612no—
530C23—612no—
531C23—612no—
532C23—1221no—
533C23—1221no—
534C23—1221no—
535C23—1221no—
536C23C2×D4×D6111yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—612no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—614no—
558C2×C4—614no—
559C2×C4—614no—
560C2×C4—614no—
561C2×C4—612no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—4884no—
570C2×C4—2444no—
571C2×C4—2444no—
572C2×C4—2448no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4#1451980112yes—
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4C2×Q8×D6111yescharacteristic
586C2×C4C2×Q8×D6111yescharacteristic
587C2×C4#41×D6111yescharacteristic
588C2×C4#41×D6111yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C8—22no—
591C8—41no—
592C8—1222no—
593C8—2441no—
594C22—614no—
595C22—1222no—
596C22—1222no—
597C22—1222no—
598C22—1222no—
599C22—1222no—
600C22—1222no—
601C22#121×D6111yescharacteristic
602C22C22⋊Q8×D6111yescharacteristic
603C22C22⋊Q8×D6111yescharacteristic
604C22C2×#1451980111yescharacteristic
605C22#137×D6111yescharacteristic
606C22#1684055911yescharacteristic
607C22#1684056111yescharacteristic
608C4—22no—
609C4—42no—
610C4—41no—
611C4—42no—
612C4—81no—
613C4—81no—
614C4—614no—
615C4—1222no—
616C4—4881no—
617C4—4881no—
618C4—2442no—
619C4—2441no—
620C4—2442no—
621C4#123×D6111yescharacteristic
622C4#125×D6111yescharacteristic
623C4#125×D6111yescharacteristic
624C4C4⋊Q8×D6111yescharacteristic
625C2—1224no—
626C2#398×D6111yescharacteristic
627C2#2145543511yescharacteristic
628C2#2145544811yescharacteristic
629C2#2145561111yescharacteristic
630C2#2145562211yescharacteristic
631C2#2145562711yescharacteristic
632C2#2145563811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2086C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2086D61
hypocenterC61#23670
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2086

Complements

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

NH ≅ G/Ntype
5. #21447323C2semidirect
6. #21447320C2semidirect
7. #21447319C2semidirect
8. #21447317C2semidirect
9. #21447316C2semidirect
10. #21447313C2semidirect
11. #21447310C2semidirect
15. C61×#2086C2semidirect
320. #2086D61semidirect
377. C61#23670semidirect

Maximal subgroups

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

subgroupindex
C2×#168398032
C2×#168397842
#214483002
#389×D612
#214473232
#214473202
#214473192
#214473172
#214473162
#214473132
#214473102
#214455372
C61×#20862
#2367061