Finite Group Databasebeta

← #29587279

Subgroups — #29587279

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454408C211yesmaximal, characteristic, complemented
2C2×#16839725C211yesmaximal, characteristic
3#21448198C211yesmaximal, characteristic
4#21448198C211yesmaximal, characteristic
5#21445530C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C61×#1733C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839805—22no—
13#16839802—22no—
14#16839798—22no—
15#16839725—22no—
16#16839725C414yescomplemented
17C2×#14519689—22no—
18#16839623—21no—
19#16839623—21no—
20#16839619—22no—
21#16839619—22no—
22#16839617—21no—
23#16839617—21no—
24C4×#11758198—22no—
25C4×#11758198—22no—
26#16839523—22no—
27#16839518—22no—
28C22×M16×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C61×#339—22no—
32C24×D61D411yescharacteristic
33C23×Dic61D411yescharacteristic
34C22×C4×D61—21no—
35C22×C4×D61—21no—
36C22×C4×D61—21no—
37C22×C4×D61—21no—
38C22×C4×D61—21no—
39C22×C4×D61—21no—
40C22×C4×D61—21no—
41C22×C4×D61—21no—
42C22×C4×D61—21no—
43C22×C4×D61—21no—
44C22×C4×D61—21no—
45C22×C4×D61—21no—
46C22×C4×D61C2×C412yes—
47C22×C4×D61Q812yes—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194C2×C412yes—
53C2×#11758194D412yes—
54C22×#92418D412yes—
55#14519736—21no—
56#14519736—21no—
57#14519736—21no—
58#14519736—21no—
59#14519736—21no—
60#14519736—21no—
61#14519736—21no—
62#14519736—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61D412yes—
65C2×C22⋊Dic61—21no—
66C2×C22⋊Dic61—21no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61D412yes—
71#14519710—24no—
72#14519708—24no—
73#14519689—28no—
74#14519684—24no—
75#14519684—24no—
76C23×C4×C61C2311yescharacteristic
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61C2×C412yes—
83C22×C8×C61—21no—
84#117×C61—21no—
85#117×C61—21no—
86#117×C61—21no—
87#117×C61—21no—
88#117×C61—21no—
89#117×C61—21no—
90#117×C61—21no—
91#117×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61D412yes—
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61D412yes—
98C24×C61C2×D411yescharacteristic
99C23×D61—21no—
100C23×D61—21no—
101C23×D61—21no—
102C23×D61—21no—
103C23×D61—21no—
104C23×D61—21no—
105C23×D61—44no—
106C23×D61C4⋊C412yes—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×Q811yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61C4⋊C412yes—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—41no—
145C2×C4×D61—41no—
146C2×C4×D61—41no—
147C2×C4×D61—41no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C4×D61—41no—
156C2×C4×D61—41no—
157C2×C4×D61—41no—
158C2×C4×D61—41no—
159C2×C4×D61—41no—
160M16×C61—22no—
161M16×C61—22no—
162M16×C61—41no—
163M16×C61—41no—
164C2×C8×C61—22no—
165C2×C8×C61—41no—
166C2×C8×C61—41no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C22⋊C4×C61—41no—
172C22⋊C4×C61—41no—
173C22⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C42×C61—22no—
176C42×C61—22no—
177C42×C61—41no—
178C42×C61—41no—
179C22⋊Dic61—41no—
180C22⋊Dic61—41no—
181C22⋊Dic61—41no—
182C22⋊Dic61—41no—
183#11758198—48no—
184#11758198—48no—
185C4⋊Dic61—22no—
186C4⋊Dic61—22no—
187C4⋊Dic61—41no—
188C4⋊Dic61—41no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C4×Dic61—41no—
192C4×Dic61—41no—
193#11758194—22no—
194#11758194—22no—
195#11758194—22no—
196#11758194—22no—
197C2×#92418—22no—
198C2×#92418—22no—
199C2×#92418C22⋊C414yescomplemented
200C23×C61—42no—
201C23×C61C2×C4⋊C411yescharacteristic
202C23×C61#12011yescharacteristic
203C23×C61#12011yescharacteristic
204C23×C61#12111yescharacteristic
205C23×C61#12111yescharacteristic
206C23×C61#12311yescharacteristic
207C23×C61#12311yescharacteristic
208C22×D61—24no—
209C22×D61—24no—
210C22×D61—24no—
211C22×D61—22no—
212C22×D61—22no—
213C22×D61—22no—
214C22×D61—44no—
215C22×D61—44no—
216C22×D61—44no—
217C22×D61—44no—
218C22×D61—42no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C2×C4×C61—44no—
226C2×C4×C61—44no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61#11711yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61#12011yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61C22⋊Q811yescharacteristic
243C2×C4×C61C22⋊Q811yescharacteristic
244C2×C4×C61C22⋊Q811yescharacteristic
245C2×C4×C61C22⋊Q811yescharacteristic
246C2×C4×C61C22⋊Q811yescharacteristic
247C2×C4×C61C22⋊Q811yescharacteristic
248C2×C4×C61#12311yescharacteristic
249C2×C4×C61#12311yescharacteristic
250C2×C4×C61#12311yescharacteristic
251C2×C4×C61#12411yescharacteristic
252C2×C4×C61#12411yescharacteristic
253C2×C4×C61#12411yescharacteristic
254C2×C4×C61#12611yescharacteristic
255C2×C4×C61#12611yescharacteristic
256C2×C4×C61#12711yescharacteristic
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—44no—
265C2×Dic61—44no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C4×D61—42no—
269C4×D61—42no—
270C4×D61—42no—
271C4×D61—42no—
272C4×D61—42no—
273C4×D61—42no—
274C4×D61—42no—
275C4×D61—42no—
276C8×C61—42no—
277#92418—24no—
278#11100—611nomaximal, Sylow
279C22×C61—22no—
280C22×C61—22no—
281C22×C61—22no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61#38011yescharacteristic
287C22×C61#38511yescharacteristic
288C22×C61#38511yescharacteristic
289C22×C61#39211yescharacteristic
290C22×C61#39411yescharacteristic
291C22×C61#39411yescharacteristic
292C22×C61#39711yescharacteristic
293C2×D61—24no—
294C2×D61—24no—
295C2×D61—24no—
296C2×D61—44no—
297C2×D61—44no—
298C2×D61—42no—
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—44no—
302C2×D61—42no—
303C2×D61—44no—
304C4×C61—82no—
305C4×C61—82no—
306C4×C61#38611yescharacteristic
307C4×C61#38811yescharacteristic
308C4×C61#38811yescharacteristic
309C4×C61#39011yescharacteristic
310C4×C61#39311yescharacteristic
311C4×C61#39611yescharacteristic
312C4×C61#39611yescharacteristic
313C4×C61#39911yescharacteristic
314Dic61—42no—
315Dic61—82no—
316Dic61—82no—
317#2911—611no—
318C2×#407—611no—
319#2280—611no—
320#2280—611no—
321#1733—611no—
322#1733D6111yescharacteristic, complemented
323C2×H(3,ℤ/4)—611no—
324C2×C61—21no—
325C2×C61—21no—
326C2×C61—21no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61—21no—
330C2×C61#143911yescharacteristic
331C2×C61#201012yes—
332D61—44no—
333C24×C4—611no—
334C22×M16—611no—
335C22×M16C2×D6111yescharacteristic
336C2×#117—611no—
337C2×#117—611no—
338C2×#117C2×D6111yescharacteristic
339C2×#117C2×D6111yescharacteristic
340#428—1222no—
341#428—1222no—
342#427—1222no—
343#407—614no—
344#407—1222no—
345C2×C22⋊C8—1222no—
346#381—1221no—
347#381—1221no—
348#380—1222no—
349#380—1222no—
350#379—1221no—
351#379—1221no—
352C4×C22⋊C4—1222no—
353C4×C22⋊C4—1222no—
354#339—22no—
355#339—1222no—
356H(3,ℤ/4)—1222no—
357C61#1110011yescharacteristic, complemented, Sylow
358C25—611no—
359C23×C4—611no—
360C23×C4—612no—
361C23×C4—612no—
362C23×C4—1221no—
363C23×C4—1221no—
364C23×C4—1221no—
365C23×C4—1221no—
366C23×C4—1221no—
367C23×C4—1221no—
368C23×C4—1221no—
369C23×C4—1221no—
370C23×C4—1221no—
371C23×C4—1221no—
372C23×C4—1221no—
373C23×C4—1221no—
374C23×C4C22×D6111yescharacteristic
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—612no—
381C2×M16—612no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16C4×D6112yes—
387C22×C8—21no—
388C22×C8—612no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—1221no—
398#117—1221no—
399#117—1221no—
400#117—1221no—
401#117—1221no—
402#117—1221no—
403#117—1221no—
404#117—1221no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—612no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4D24412yes—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—1224no—
412C2×C22⋊C4—1224no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C42—21no—
416C2×C42—612no—
417C2×C42—1221no—
418C2×C42C22⋊D6112yes—
419#107—1224no—
420#106—1224no—
421C22⋊C8—1228no—
422#95—1224no—
423#95—1224no—
424C24—612no—
425C24—1221no—
426C24—1221no—
427C24—1221no—
428C24—1221no—
429C24—1221no—
430C24—1221no—
431C24—2444no—
432C24D4×D6111yescharacteristic
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—612no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—2441no—
457C22×C4—2441no—
458C22×C4—2441no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4—2441no—
463C22×C4—2441no—
464C22×C4—2441no—
465C22×C4—2441no—
466C22×C4—2441no—
467C22×C4—2441no—
468C22×C4—2441no—
469C22×C4—2441no—
470C22×C4—2441no—
471C22×C4—2441no—
472C22×C4C2×C4×D6111yescharacteristic
473C22×C4C2×D24411yescharacteristic
474C22×C4#1175822211yescharacteristic
475C22×C4#1175822211yescharacteristic
476C22×C4#1175822211yescharacteristic
477C22×C4#1175822211yescharacteristic
478C22×C4D4×D6111yescharacteristic
479C22×C4D4×D6111yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4D4×D6111yescharacteristic
482C22×C4#1175822411yescharacteristic
483C22×C4Q8×D6111yescharacteristic
484C22×C4#1175822611yescharacteristic
485C22×C4C2×C22⋊D6111yescharacteristic
486M16—22no—
487M16—22no—
488M16—41no—
489M16—41no—
490M16—1222no—
491M16—1222no—
492M16—1222no—
493M16—1222no—
494C2×C8—22no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—614no—
498C2×C8—1222no—
499C2×C8—1222no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—2441no—
507C4⋊C4—2441no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—2448no—
513C22⋊C4—2448no—
514C22⋊C4—2441no—
515C22⋊C4—2441no—
516C22⋊C4—2441no—
517C22⋊C4—2441no—
518C42—22no—
519C42—22no—
520C42—41no—
521C42—41no—
522C42—1222no—
523C42—1222no—
524C42—2441no—
525C42—2441no—
526C23—42no—
527C23—1224no—
528C23—1224no—
529C23—1224no—
530C23—1222no—
531C23—1222no—
532C23—1222no—
533C23—2442no—
534C23—2442no—
535C23—2442no—
536C23—2444no—
537C23—2444no—
538C23—2444no—
539C23—2444no—
540C23—2441no—
541C23—2441no—
542C23—2441no—
543C23—2441no—
544C23C4⋊C4×D6111yescharacteristic
545C23#1451974511yescharacteristic
546C23#1451974711yescharacteristic
547C23#1451975011yescharacteristic
548C23#1451975011yescharacteristic
549C23#1451975911yescharacteristic
550C23#1451976211yescharacteristic
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—2444no—
559C2×C4—2444no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4C22⋊C4×D6111yescharacteristic
575C2×C4#1451973411yescharacteristic
576C2×C4#1451973711yescharacteristic
577C2×C4C4×C22⋊D6111yescharacteristic
578C2×C4#1451973911yescharacteristic
579C2×C4C4×D24411yescharacteristic
580C2×C4#1451974711yescharacteristic
581C2×C4#1451974911yescharacteristic
582C2×C4#1451975011yescharacteristic
583C2×C4#1451975011yescharacteristic
584C2×C4#1451975011yescharacteristic
585C2×C4#1451975111yescharacteristic
586C2×C4#1451975211yescharacteristic
587C2×C4#1451975311yescharacteristic
588C2×C4#1451975511yescharacteristic
589C2×C4#1451975511yescharacteristic
590C2×C4#1451975511yescharacteristic
591C2×C4#1451975511yescharacteristic
592C2×C4#1451975711yescharacteristic
593C2×C4#1451976011yescharacteristic
594C2×C4#1451976211yescharacteristic
595C2×C4#1451976211yescharacteristic
596C2×C4#1451976311yescharacteristic
597C2×C4#1451976311yescharacteristic
598C2×C4#1451976511yescharacteristic
599C2×C4#1451977111yescharacteristic
600C2×C4#1451977211yescharacteristic
601C2×C4#1451977311yescharacteristic
602C8—42no—
603C8—1224no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—1224no—
612C22—1224no—
613C22—1224no—
614C22—2444no—
615C22—2444no—
616C22—2442no—
617C22—2442no—
618C22—2442no—
619C22—2444no—
620C22—2442no—
621C22—2444no—
622C22#1683962111yescharacteristic
623C22#1683963311yescharacteristic
624C22#1683963611yescharacteristic
625C22#1683967111yescharacteristic
626C22#1683967711yescharacteristic
627C22#1683968011yescharacteristic
628C22#1683969111yescharacteristic
629C4—82no—
630C4—82no—
631C4—4882no—
632C4—4882no—
633C4—2442no—
634C4#1683964011yescharacteristic
635C4#1683965111yescharacteristic
636C4#1683965311yescharacteristic
637C4#1683966211yescharacteristic
638C4#1683967511yescharacteristic
639C4#1683968411yescharacteristic
640C4#1683968611yescharacteristic
641C4#1683969711yescharacteristic
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—21no—
648C2—2444no—
649C2#2144406311yescharacteristic
650C2#2144688512yes—
subgroupG/H
centerC2×C4#14519773
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1733C2
socleC22×C61#392
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1733D61
hypocenterC61#11100
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
1. #21454408C2semidirect
5. #21445530C2semidirect
6. C2×#16839518C2semidirect
7. C61×#1733C2semidirect
16. #16839725C4semidirect
199. C2×#92418C22⋊C4semidirect
322. #1733D61semidirect
357. C61#11100semidirect

Maximal subgroups

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

subgroupindex
#214544082
C2×#168397252
#214481982
#214455302
C2×#168395182
C61×#17332
#1110061