Finite Group Databasebeta

← #29709113

Subgroups — #29709113

Order 15616.

874 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
1C2×#16839803C211yesmaximal, characteristic
2C2×#16839787C211yesmaximal, characteristic
3#21448441C211yesmaximal, characteristic
4#21448434C211yesmaximal, characteristic
5#21447323C211yesmaximal, characteristic, complemented
6#21447320C211yesmaximal, characteristic, complemented
7#21447319C211yesmaximal, characteristic, complemented
8#21447317C211yesmaximal, characteristic, complemented
9#21447316C211yesmaximal, characteristic, complemented
10#21447310C211yesmaximal, characteristic, complemented
11#21447308C211yesmaximal, characteristic, complemented
12#21445537C211yesmaximal, characteristic
13#21445534C211yesmaximal, characteristic
14#340×D61C211yesmaximal, characteristic
15C61×#2087C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519735C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839803—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27#16839787—24no—
28C2×C4⋊#92418C2211yescharacteristic
29C2×#14519706C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31#16839661C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839659—21no—
36#16839658C2211yescharacteristic
37#16839658C2211yescharacteristic
38#16839657—21no—
39#16839636—21no—
40#16839633—21no—
41#16839631—21no—
42#16839626—21no—
43#16839621—21no—
44#16839619—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×D61C2311yescharacteristic
64C2×#11758189—22no—
65C2×#11758189—22no—
66C2×#11758189D414yes—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C2×C8×D61—22no—
70C2×C8×D61—22no—
71C2×C8×D61—22no—
72#14519735—22no—
73#14519735—22no—
74#14519735—22no—
75#14519735Q814yes—
76#14519734—22no—
77#14519734—22no—
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—
90C2×#11758196D411yescharacteristic
91C2×#11758196D411yescharacteristic
92C4⋊C4×D61—22no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C4⋊C4×D61Q814yes—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198D411yescharacteristic
99C2×#11758198D411yescharacteristic
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102C2×C4×Dic61C2311yescharacteristic
103#14519710—22no—
104#14519709—22no—
105#14519708—22no—
106C4⋊#92418—22no—
107#14519706—22no—
108#14519706—22no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124#107×C61—22no—
125C4⋊C8×C61—22no—
126#95×C61—21no—
127#95×C61—21no—
128C23×D61C2×D411yescharacteristic
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C2×C4×D61—24no—
144C2×C4×D61—42no—
145C2×C4×D61—81no—
146C2×C4×D61—81no—
147C2×C4×D61—81no—
148C2×C4×D61—81no—
149C2×C4×D61C2×D412yes—
150C2×C4×D61C2×Q812yes—
151C2×C4×D61C2×Q812yes—
152C2×C4×D61#4112yes—
153C2×C4×D61#4112yes—
154C2×C4×D61#4112yes—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61C2×D412yes—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—81no—
168C4⋊C4×C61—81no—
169C4⋊C4×C61C2×Q812yes—
170C4⋊C4×C61C2×Q812yes—
171C42×C61—21no—
172C42×C61—21no—
173#11758198—22no—
174#11758198—22no—
175#11758198—24no—
176#11758198—42no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—81no—
184C4⋊Dic61—81no—
185C4⋊Dic61C2×Q812yes—
186C4⋊Dic61C2×Q812yes—
187#11758196—22no—
188#11758196—22no—
189#11758196—24no—
190#11758196—42no—
191#11758196—81no—
192#11758196—81no—
193#11758196—81no—
194#11758196—81no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—24no—
198C4×Dic61—42no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D412yes—
205#11758189—28no—
206C8×D61—44no—
207C23×C61C22×D411yescharacteristic
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61#12112yes—
213C22×D61C22⋊Q812yes—
214C22×D61C22⋊Q812yes—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
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×C61C22×D411yescharacteristic
234C2×C4×C61C22×Q811yescharacteristic
235C2×C4×C61C22×Q811yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61#12112yes—
258C2×Dic61C22⋊Q812yes—
259C2×Dic61C22⋊Q812yes—
260C4×D61—84no—
261C4×D61—84no—
262C4×D61#12314yes—
263C4×D61#12514yes—
264C4×D61#12514yes—
265C4×D61C4⋊Q814yes—
266C8×C61—22no—
267C8×C61—41no—
268#92418—22no—
269#92418—41no—
270#23671—611nomaximal, Sylow
271C22×C61C2×#12111yescharacteristic
272C22×C61C2×C22⋊Q811yescharacteristic
273C22×C61C2×C22⋊Q811yescharacteristic
274C22×C61#57611yescharacteristic
275C22×C61#57711yescharacteristic
276C22×C61#57711yescharacteristic
277C22×C61#57811yescharacteristic
278C2×D61—22no—
279C2×D61—22no—
280C2×D61—22no—
281C2×D61—22no—
282C2×D61—22no—
283C2×D61—22no—
284C2×D61#39814yes—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—81no—
290C4×C61—81no—
291C4×C61C2×#12311yescharacteristic
292C4×C61C2×#12511yescharacteristic
293C4×C61C2×#12511yescharacteristic
294C4×C61C2×C4⋊Q811yescharacteristic
295Dic61—42no—
296Dic61—42no—
297Dic61—41no—
298Dic61—41no—
299Dic61—81no—
300Dic61—81no—
301Dic61#39814yes—
302C2×#428—611no—
303C2×#424—611no—
304#2317—611no—
305#2316—611no—
306#2088—611no—
307#2088—611no—
308#2088—611no—
309#2088—611no—
310#2087—611no—
311#2087D6111yescharacteristic, complemented
312#2086—611no—
313#2086—611no—
314#1736—611no—
315#1735—611no—
316C2×#340—611no—
317C2×C61C2×#39811yescharacteristic
318C2×C61#306211yescharacteristic
319C2×C61#306311yescharacteristic
320C2×C61#308111yescharacteristic
321C2×C61#308211yescharacteristic
322C2×C61#308311yescharacteristic
323C2×C61#308411yescharacteristic
324D61—24no—
325C22×M16—611no—
326C23×C8—611no—
327C2×#117—611no—
328C2×#117—611no—
329C2×#117—611no—
330C22×C4⋊C4—611no—
331C22×C4⋊C4—611no—
332#428—1224no—
333C2×#107—611no—
334C2×#107C2×D6111yescharacteristic
335C2×#106—611no—
336C2×#106—611no—
337#424—1224no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—611no—
340C2×C4⋊C8—611no—
341C2×C4⋊C8C2×D6111yescharacteristic
342#389—611no—
343#389—611no—
344#389—611no—
345#389—611no—
346#389—611no—
347#389—611no—
348#389—1221no—
349#389—1221no—
350#389C2×D6111yescharacteristic
351#389C2×D6111yescharacteristic
352#385—1221no—
353#385—1221no—
354#384—1221no—
355#382—1221no—
356#380—1221no—
357#380—1221no—
358#340—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340C2×D6111yescharacteristic
368#340C2×D6111yescharacteristic
369#340C2×D6111yescharacteristic
370C61#2367111yescharacteristic, complemented, Sylow
371C23×C4—611no—
372C23×C4—1221no—
373C23×C4—1221no—
374C2×M16—614no—
375C2×M16—1222no—
376C2×M16—1222no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—1222no—
380C22×C8—1222no—
381C22×C8—1222no—
382C22×C8C22×D6111yescharacteristic
383C22×C8C22×D6111yescharacteristic
384#117—614no—
385#117—1222no—
386#117—1222no—
387#117—1222no—
388#117—1222no—
389#117—1222no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—614no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
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⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C4⋊C4C22×D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C22⋊C4—611no—
415C2×C22⋊C4—611no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C42—611no—
419C2×C42—1221no—
420C2×C42—1221no—
421C2×C42C22×D6111yescharacteristic
422#107—22no—
423#107—1222no—
424#106—1222no—
425#106—1222no—
426C4⋊C8—22no—
427C4⋊C8—1222no—
428C4⋊C8—1222no—
429C4⋊C8—1222no—
430#95—21no—
431#95—21no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436#95—1221no—
437#95—1221no—
438C24—611no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—611no—
444C22×C4—612no—
445C22×C4—612no—
446C22×C4—612no—
447C22×C4—612no—
448C22×C4—612no—
449C22×C4—612no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—1224no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—4881no—
458C22×C4—4881no—
459C22×C4—4881no—
460C22×C4—4881no—
461C22×C4—2442no—
462C22×C4D4×D6111yescharacteristic
463C22×C4D4×D6111yescharacteristic
464C22×C4C23×D6111yescharacteristic
465M16—1228no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—612no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—2444no—
478C2×C8D4×D6112yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—612no—
488C4⋊C4—612no—
489C4⋊C4—1224no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—4881no—
499C4⋊C4—4881no—
500C4⋊C4—4881no—
501C4⋊C4—4881no—
502C4⋊C4—4881no—
503C4⋊C4—4881no—
504C4⋊C4—2442no—
505C4⋊C4Q8×D6112yes—
506C4⋊C4Q8×D6112yes—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1224no—
510C22⋊C4—2442no—
511C42—21no—
512C42—21no—
513C42—1224no—
514C42—1221no—
515C42—1221no—
516C42—2442no—
517C23—612no—
518C23—612no—
519C23—612no—
520C23—1221no—
521C23—1221no—
522C23—1221no—
523C23—1221no—
524C23C2×D4×D6111yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—612no—
544C2×C4—612no—
545C2×C4—612no—
546C2×C4—614no—
547C2×C4—614no—
548C2×C4—614no—
549C2×C4—614no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—4884no—
559C2×C4—4884no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4C2×D4×D6111yescharacteristic
571C2×C4C2×Q8×D6111yescharacteristic
572C2×C4C2×Q8×D6111yescharacteristic
573C2×C4#41×D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4#41×D6111yescharacteristic
576C8—22no—
577C8—41no—
578C8—1222no—
579C8—2441no—
580C22—614no—
581C22—1222no—
582C22—1222no—
583C22—1222no—
584C22—1222no—
585C22—1222no—
586C22—1222no—
587C22#121×D6111yescharacteristic
588C22C22⋊Q8×D6111yescharacteristic
589C22C22⋊Q8×D6111yescharacteristic
590C22#1684056611yescharacteristic
591C22#1684056911yescharacteristic
592C22#1684057211yescharacteristic
593C22#1684057511yescharacteristic
594C4—42no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—614no—
601C4—4881no—
602C4—4881no—
603C4—2442no—
604C4—2442no—
605C4—2441no—
606C4—2441no—
607C4#123×D6111yescharacteristic
608C4#125×D6111yescharacteristic
609C4#125×D6111yescharacteristic
610C4C4⋊Q8×D6111yescharacteristic
611C2—1224no—
612C2#398×D6111yescharacteristic
613C2#2145549611yescharacteristic
614C2#2145550911yescharacteristic
615C2#2145564911yescharacteristic
616C2#2145565611yescharacteristic
617C2#2145566711yescharacteristic
618C2#2145568211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2087C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#2087D61
hypocenterC61#23671
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2087

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. #21447310C2semidirect
11. #21447308C2semidirect
15. C61×#2087C2semidirect
311. #2087D61semidirect
370. C61#23671semidirect

Maximal subgroups

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

subgroupindex
C2×#168398032
C2×#168397872
#214484412
#214484342
#214473232
#214473202
#214473192
#214473172
#214473162
#214473102
#214473082
#214455372
#214455342
#340×D612
C61×#20872
#2367161