Finite Group Databasebeta

← #29586337

Subgroups — #29586337

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839726C211yesmaximal, characteristic
2#21454237C211yesmaximal, characteristic, complemented
3#21448202C211yesmaximal, characteristic
4C2×#16839534C211yesmaximal, characteristic, complemented
5C2×#16839533C211yesmaximal, characteristic, complemented
6#21445557C211yesmaximal, characteristic, complemented
7C2×C61×#407C211yesmaximal, characteristic
8C22×#11758194C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839726—22no—
13#16839726C414yescomplemented
14C2×C22⋊#92418—22no—
15#16839720—22no—
16#16839717—22no—
17M16×Dic61—22no—
18#16839625C412yes—
19#16839622—22no—
20#16839618C412yes—
21C4×C22⋊Dic61—22no—
22#16839534—22no—
23#16839533—22no—
24#16839530—22no—
25C24×C4×C61C2211yescharacteristic
26C22×M16×C61C2211yescharacteristic
27C22×M16×C61C2211yescharacteristic
28C61×#407—22no—
29C61×#407C414yescomplemented
30C2×C22⋊C8×C61—22no—
31C2×#11758194—21no—
32C2×#11758194—21no—
33C2×#11758194—21no—
34C2×#11758194—21no—
35C2×#11758194—21no—
36C2×#11758194—21no—
37C2×#11758194—21no—
38C2×#11758194—21no—
39C2×#11758194—21no—
40C2×#11758194C2×C412yes—
41C2×#11758194C2×C412yes—
42C2×#11758194D412yes—
43C22×#92418—21no—
44C22×#92418D412yes—
45#14519736—21no—
46#14519736—21no—
47#14519736—21no—
48#14519736—21no—
49#14519736—21no—
50#14519736—21no—
51#14519736—21no—
52#14519736—21no—
53C2×C4⋊Dic61—21no—
54C2×C4⋊Dic61D412yes—
55C2×C22⋊Dic61—24no—
56C2×C22⋊Dic61C2×C412yes—
57C2×C22⋊Dic61C2×C412yes—
58C2×C4×Dic61—21no—
59C2×C4×Dic61D412yes—
60C22⋊#92418—28no—
61#14519687—24no—
62C8×Dic61—24no—
63#14519684—24no—
64C25×C61C2×C411yescharacteristic
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C23×C4×C61—21no—
68C23×C4×C61—21no—
69C23×C4×C61—21no—
70C23×C4×C61—21no—
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61—21no—
74C23×C4×C61—21no—
75C23×C4×C61—21no—
76C23×C4×C61—21no—
77C23×C4×C61C2×C411yescharacteristic
78C23×C4×C61C2×C412yes—
79C23×C4×C61C2×C412yes—
80C23×C4×C61C2311yescharacteristic
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61—21no—
87C2×M16×C61—21no—
88C2×M16×C61—21no—
89C2×M16×C61—21no—
90C2×M16×C61C2×C412yes—
91C2×M16×C61C2×C412yes—
92C2×M16×C61D412yes—
93C22×C8×C61—21no—
94C22×C8×C61D412yes—
95C22⋊C8×C61—28no—
96C24×C61—21no—
97C24×C61—21no—
98C24×C61—21no—
99C24×C61—21no—
100C24×C61—21no—
101C24×C61—21no—
102C24×C61—44no—
103C24×C61C4212yes—
104C24×C61C22×C411yescharacteristic
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—41no—
124C22×C4×C61—41no—
125C22×C4×C61—41no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61—41no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61—41no—
134C22×C4×C61—41no—
135C22×C4×C61—41no—
136C22×C4×C61—41no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61C4212yes—
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C22×C4×C61#4111yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C22×Dic61—22no—
155C22×Dic61C22⋊C414yes—
156M16×C61—22no—
157M16×C61—22no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—22no—
162M16×C61—41no—
163M16×C61—41no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—22no—
167C2×C8×C61—41no—
168C2×C8×C61—41no—
169C2×C8×C61C22⋊C414yescomplemented
170C22⋊Dic61—22no—
171C22⋊Dic61—22no—
172C22⋊Dic61—22no—
173C22⋊Dic61—22no—
174C22⋊Dic61—48no—
175C4⋊Dic61—22no—
176C4⋊Dic61—22no—
177C4⋊Dic61—41no—
178C4⋊Dic61—41no—
179C4×Dic61—22no—
180C4×Dic61—22no—
181C4×Dic61—41no—
182C4×Dic61—41no—
183#11758194—22no—
184#11758194—22no—
185#11758194—22no—
186#11758194—22no—
187#11758194—22no—
188#11758194—22no—
189#11758194—41no—
190#11758194—41no—
191C2×#92418—22no—
192C2×#92418—22no—
193C2×#92418—22no—
194C2×#92418—41no—
195C2×#92418—41no—
196C2×#92418C22⋊C414yescomplemented
197C23×C61—24no—
198C23×C61—24no—
199C23×C61—24no—
200C23×C61—22no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61—44no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—42no—
207C23×C61—42no—
208C23×C61—44no—
209C23×C61—44no—
210C23×C61—44no—
211C23×C61—41no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61C2×C4211yescharacteristic
216C23×C61C2×C22⋊C411yescharacteristic
217C23×C61#11711yescharacteristic
218C23×C61C4×D411yescharacteristic
219C23×C61C4×D411yescharacteristic
220C23×C61C4×D411yescharacteristic
221C23×C61C4×D411yescharacteristic
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61C2×C22⋊C411yescharacteristic
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61#11711yescharacteristic
240C2×C4×C61#11711yescharacteristic
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C4×D411yescharacteristic
244C2×C4×C61C4×D411yescharacteristic
245C2×C4×C61C4×D411yescharacteristic
246C2×C4×C61C4×D411yescharacteristic
247C2×C4×C61C4×D411yescharacteristic
248C2×C4×C61C4×D411yescharacteristic
249C2×C4×C61#12011yescharacteristic
250C2×C4×C61#12111yescharacteristic
251C2×C4×C61#12111yescharacteristic
252C2×C4×C61#12111yescharacteristic
253C2×C4×C61#12111yescharacteristic
254C2×C4×C61#12111yescharacteristic
255C2×C4×C61#12111yescharacteristic
256C2×C4×C61#12311yescharacteristic
257C2×C4×C61#12311yescharacteristic
258C2×C4×C61#12311yescharacteristic
259C2×C4×C61#12411yescharacteristic
260C2×C4×C61#12411yescharacteristic
261C2×C4×C61#12411yescharacteristic
262C2×C4×C61#12611yescharacteristic
263C2×C4×C61#12611yescharacteristic
264C2×C4×C61#12711yescharacteristic
265C2×Dic61—24no—
266C2×Dic61—44no—
267C2×Dic61—44no—
268C2×Dic61—42no—
269C8×C61—24no—
270C8×C61—42no—
271#92418—24no—
272#92418—42no—
273#10937—611nomaximal, Sylow
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—24no—
278C22×C61—24no—
279C22×C61—24no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—44no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—44no—
289C22×C61—44no—
290C22×C61—44no—
291C22×C61—42no—
292C22×C61C4×C22⋊C411yescharacteristic
293C22×C61C4×C22⋊C411yescharacteristic
294C22×C61C4×C22⋊C411yescharacteristic
295C22×C61#38611yescharacteristic
296C22×C61#38811yescharacteristic
297C22×C61#38811yescharacteristic
298C22×C61#39011yescharacteristic
299C4×C61—42no—
300C4×C61#38611yescharacteristic
301C4×C61#38611yescharacteristic
302C4×C61#38811yescharacteristic
303C4×C61#38811yescharacteristic
304C4×C61#38811yescharacteristic
305C4×C61#38811yescharacteristic
306C4×C61#39011yescharacteristic
307C4×C61#39011yescharacteristic
308Dic61—44no—
309Dic61—82no—
310C2×#407—611no—
311C2×#407D6111yescharacteristic
312#2873—611no—
313#2280—611no—
314C2×#344—611no—
315C2×#344—611no—
316#1742—611no—
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—44no—
324C2×C61#143711yescharacteristic
325C2×C61#189112yes—
326C24×C4C2×D6111yescharacteristic
327C22×M16—611no—
328C22×M16—611no—
329C22×M16C2×D6111yescharacteristic
330C22×M16C2×D6111yescharacteristic
331C2×#117—611no—
332C2×#117—611no—
333#407—22no—
334#407—614no—
335#407—1222no—
336#407Dic6114yescomplemented
337C2×C22⋊C8—22no—
338C2×C22⋊C8—1222no—
339#405—1222no—
340#405—1222no—
341C4×M16—1222no—
342#381—612no—
343#380—1222no—
344#379—612no—
345C4×C22⋊C4—1222no—
346#344—1222no—
347#344—1222no—
348#343—1222no—
349C61#1093711yescharacteristic, complemented, Sylow
350C25C4×D6111yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C4×D6111yescharacteristic
364C23×C4C4×D6112yes—
365C23×C4C2×Dic6112yes—
366C23×C4C22×D6111yescharacteristic
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—612no—
377C2×M16—612no—
378C2×M16—612no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16—1221no—
387C2×M16—1221no—
388C2×M16C2×Dic6112yes—
389C2×M16C2×Dic6112yes—
390C2×M16C22⋊D6112yes—
391C22×C8—21no—
392C22×C8—612no—
393C22×C8—1221no—
394C22×C8C22⋊D6112yes—
395#117—1221no—
396#117—1221no—
397#117—1221no—
398#117—1221no—
399#117—1221no—
400#117—1221no—
401#117—1221no—
402#117—1221no—
403C2×C4⋊C4—612no—
404C2×C4⋊C4—1221no—
405C2×C22⋊C4—612no—
406C2×C22⋊C4—612no—
407C2×C22⋊C4—1224no—
408C2×C42—612no—
409C2×C42—1221no—
410C22⋊C8—28no—
411C22⋊C8—1228no—
412#97—1224no—
413C4×C8—1224no—
414#95—1224no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—44no—
422C24C4×Dic6112yes—
423C24C2×C4×D6111yescharacteristic
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—614no—
459C22×C4—1222no—
460C22×C4C4×Dic6112yes—
461C22×C4C2×C4×D6111yescharacteristic
462C22×C4#1175822211yescharacteristic
463C22×C4#1175822211yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C22×C4D4×D6111yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4D4×D6111yescharacteristic
468C22×C4#1175822411yescharacteristic
469C22×C4#1175822411yescharacteristic
470C22×C4#1175822411yescharacteristic
471C22×C4#1175822411yescharacteristic
472C22×C4C22×Dic6111yescharacteristic
473C22×C4C2×C22⋊D6111yescharacteristic
474C22×C4C2×C22⋊D6111yescharacteristic
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—1222no—
484M16—1222no—
485M16—1222no—
486M16—1222no—
487M16—1222no—
488M16—1222no—
489M16—2441no—
490M16—2441no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—614no—
497C2×C8—1222no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—2441no—
501C2×C8—2441no—
502C2×C8C22⋊Dic6114yescomplemented
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—2441no—
506C4⋊C4—2441no—
507C22⋊C4—1222no—
508C22⋊C4—1222no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C22⋊C4—2448no—
512C42—1222no—
513C42—1222no—
514C42—2441no—
515C42—2441no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—44no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C2×C4×Dic6111yescharacteristic
535C23C22⋊C4×D6111yescharacteristic
536C23#1451973311yescharacteristic
537C23#1451973711yescharacteristic
538C23#1451973711yescharacteristic
539C23C4×C22⋊D6111yescharacteristic
540C23C4×C22⋊D6111yescharacteristic
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—1224no—
557C2×C4—2444no—
558C2×C4—2442no—
559C2×C4—2444no—
560C2×C4C22⋊C4×D6111yescharacteristic
561C2×C4C2×C22⋊Dic6111yescharacteristic
562C2×C4#1451973311yescharacteristic
563C2×C4#1451973611yescharacteristic
564C2×C4#1451973711yescharacteristic
565C2×C4#1451973711yescharacteristic
566C2×C4C4×C22⋊D6111yescharacteristic
567C2×C4C4×C22⋊D6111yescharacteristic
568C2×C4D4×Dic6111yescharacteristic
569C2×C4D4×Dic6111yescharacteristic
570C2×C4D4×Dic6111yescharacteristic
571C2×C4D4×Dic6111yescharacteristic
572C2×C4#1451974511yescharacteristic
573C2×C4#1451974811yescharacteristic
574C2×C4#1451974811yescharacteristic
575C2×C4#1451974911yescharacteristic
576C2×C4#1451974911yescharacteristic
577C2×C4#1451975011yescharacteristic
578C2×C4#1451975011yescharacteristic
579C2×C4#1451975811yescharacteristic
580C2×C4#1451975911yescharacteristic
581C2×C4#1451975911yescharacteristic
582C2×C4#1451976311yescharacteristic
583C2×C4#1451976311yescharacteristic
584C2×C4#1451976411yescharacteristic
585C2×C4#1451977011yescharacteristic
586C2×C4#1451977011yescharacteristic
587C2×C4#1451977311yescharacteristic
588C8—24no—
589C8—42no—
590C8—1224no—
591C8—2442no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—24no—
596C22—24no—
597C22—24no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—44no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—42no—
610C22C4×C22⋊Dic6111yescharacteristic
611C22C22⋊C4×Dic6111yescharacteristic
612C22C22⋊C4×Dic6111yescharacteristic
613C22#1683963811yescharacteristic
614C22#1683965011yescharacteristic
615C22#1683965611yescharacteristic
616C22#1683966211yescharacteristic
617C4—42no—
618C4—4882no—
619C4—2444no—
620C4#1683963811yescharacteristic
621C4#1683964211yescharacteristic
622C4#1683965011yescharacteristic
623C4#1683965511yescharacteristic
624C4#1683965511yescharacteristic
625C4#1683965611yescharacteristic
626C4#1683966211yescharacteristic
627C4#1683966511yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—44no—
635C2#2144405611yescharacteristic
636C2#2144623412yes—
subgroupG/H
centerC2×C4#14519745
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC2×C61×#407C2
socleC22×C61#386
prime radicalC25×C61C2×C4
cosocleC23×C4×C61C23
hypercenterC2×#407D61
hypocenterC61#10937
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #21454237C2semidirect
4. C2×#16839534C2semidirect
5. C2×#16839533C2semidirect
6. #21445557C2semidirect
13. #16839726C4semidirect
29. C61×#407C4semidirect
169. C2×C8×C61C22⋊C4semidirect
196. C2×#92418C22⋊C4semidirect
336. #407Dic61semidirect
349. C61#10937semidirect
502. C2×C8C22⋊Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397262
#214542372
#214482022
C2×#168395342
C2×#168395332
#214455572
C2×C61×#4072
#1093761