Finite Group Databasebeta

← #29587284

Subgroups — #29587284

Order 15616.

974 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839810C211yesmaximal, characteristic, complemented
2C2×#16839725C211yesmaximal, characteristic
3C2×#16839725C211yesmaximal, characteristic
4C2×#16839725C211yesmaximal, characteristic
5#21445545C211yesmaximal, characteristic, complemented
6C2×#16839520C211yesmaximal, characteristic, complemented
7C61×#1738C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16839810—22no—
13#16839810—22no—
14C2×#14519712—22no—
15#16839725—22no—
16#16839725—22no—
17#16839725—22no—
18#16839725—22no—
19#16839725—22no—
20#16839725C414yes—
21C2×#14519689—22no—
22C2×#14519689—22no—
23C2×#14519689—22no—
24#16839526—22no—
25#16839520—22no—
26C22×M16×C61C2211yescharacteristic
27C22×M16×C61C2211yescharacteristic
28C22×M16×C61C2211yescharacteristic
29C61×#341—22no—
30C24×D61Q811yescharacteristic
31C23×Dic61Q811yescharacteristic
32C22×C4×D61—21no—
33C22×C4×D61—21no—
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×D61C2×C412yes—
45C22×C4×D61D412yes—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194C2×C412yes—
62C2×#11758194D412yes—
63C2×#11758194D412yes—
64C22×#92418—21no—
65C22×#92418D412yes—
66C22×#92418D412yes—
67#14519712—28no—
68#14519689—28no—
69#14519689—28no—
70#14519689—28no—
71C23×C4×C61C2311yescharacteristic
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
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×C61C2×C412yes—
89C2×M16×C61D412yes—
90C22×C8×C61—21no—
91C22×C8×C61—21no—
92C22×C8×C61D412yes—
93C24×C61C2×Q811yescharacteristic
94C23×D61—21no—
95C23×D61—21no—
96C23×D61—21no—
97C23×D61—21no—
98C23×D61—21no—
99C23×D61—21no—
100C23×D61—44no—
101C23×D61C4⋊C412yes—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×Dic61—21no—
117C22×Dic61—21no—
118C22×Dic61—21no—
119C22×Dic61—21no—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61C4⋊C412yes—
123C2×C4×D61—22no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—22no—
133C2×C4×D61—22no—
134C2×C4×D61—22no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61—41no—
138C2×C4×D61—41no—
139C2×C4×D61—41no—
140C2×C4×D61—41no—
141C2×C4×D61—41no—
142C2×C4×D61—41no—
143C2×C4×D61—41no—
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—
151M16×C61—22no—
152M16×C61—22no—
153M16×C61—22no—
154M16×C61—22no—
155M16×C61—41no—
156M16×C61—41no—
157M16×C61—41no—
158M16×C61—41no—
159M16×C61—41no—
160M16×C61—41no—
161M16×C61—41no—
162M16×C61—41no—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—22no—
167C2×C8×C61—22no—
168C2×C8×C61—41no—
169C2×C8×C61—41no—
170C2×C8×C61—41no—
171C2×C8×C61—41no—
172#11758194—22no—
173#11758194—22no—
174#11758194—22no—
175#11758194—22no—
176#11758194—22no—
177#11758194—22no—
178#11758194—41no—
179#11758194—41no—
180#11758194—41no—
181#11758194—41no—
182#11758194—41no—
183#11758194—41no—
184C2×#92418—22no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—22no—
189C2×#92418—22no—
190C2×#92418—41no—
191C2×#92418—41no—
192C2×#92418C22⋊C414yes—
193C23×C61—42no—
194C23×C61C2×C4⋊C411yescharacteristic
195C23×C61C22⋊Q811yescharacteristic
196C23×C61C22⋊Q811yescharacteristic
197C23×C61C22⋊Q811yescharacteristic
198C23×C61C22⋊Q811yescharacteristic
199C23×C61C22⋊Q811yescharacteristic
200C23×C61C22⋊Q811yescharacteristic
201C22×D61—24no—
202C22×D61—24no—
203C22×D61—24no—
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—44no—
208C22×D61—44no—
209C22×D61—44no—
210C22×D61—44no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61#11711yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C4×D411yescharacteristic
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61#12011yescharacteristic
225C2×C4×C61#12011yescharacteristic
226C2×C4×C61#12011yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12311yescharacteristic
236C2×C4×C61#12311yescharacteristic
237C2×C4×C61#12311yescharacteristic
238C2×C4×C61#12311yescharacteristic
239C2×C4×C61#12311yescharacteristic
240C2×C4×C61#12411yescharacteristic
241C2×C4×C61#12411yescharacteristic
242C2×C4×C61#12411yescharacteristic
243C2×C4×C61#12611yescharacteristic
244C2×C4×C61#12611yescharacteristic
245C2×C4×C61#12711yescharacteristic
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C4×D61—42no—
254C4×D61—42no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—42no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—42no—
261C8×C61—42no—
262C8×C61—42no—
263C8×C61—42no—
264#92418—24no—
265#92418—42no—
266#92418—42no—
267#11101—611nomaximal, Sylow
268C22×C61—22no—
269C22×C61—22no—
270C22×C61—22no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61#38011yescharacteristic
276C22×C61#38511yescharacteristic
277C22×C61#38511yescharacteristic
278C22×C61#39311yescharacteristic
279C22×C61#39611yescharacteristic
280C22×C61#39611yescharacteristic
281C22×C61#39911yescharacteristic
282C2×D61—24no—
283C2×D61—24no—
284C2×D61—24no—
285C2×D61—42no—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—44no—
289C2×D61—44no—
290C2×D61—44no—
291C2×D61—44no—
292C2×D61—42no—
293C4×C61#38611yescharacteristic
294C4×C61#38811yescharacteristic
295C4×C61#38811yescharacteristic
296C4×C61#39011yescharacteristic
297C4×C61#39211yescharacteristic
298C4×C61#39411yescharacteristic
299C4×C61#39411yescharacteristic
300C4×C61#39711yescharacteristic
301Dic61—42no—
302C2×#430—611no—
303C2×#407—611no—
304C2×#407—611no—
305C2×#407—611no—
306#1738—611no—
307#1738D6111yescharacteristic, complemented
308C2×#338—611no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61#143911yescharacteristic
316C2×C61#209112yes—
317D61—44no—
318C24×C4—611no—
319C22×M16—611no—
320C22×M16—611no—
321C22×M16—611no—
322C22×M16C2×D6111yescharacteristic
323C22×M16C2×D6111yescharacteristic
324C22×M16C2×D6111yescharacteristic
325#430—1222no—
326#430—1222no—
327C2×#108—1222no—
328#407—614no—
329#407—1222no—
330#407—1222no—
331#407—1222no—
332#407—1222no—
333#407—1222no—
334C2×C22⋊C8—1222no—
335C2×C22⋊C8—1222no—
336C2×C22⋊C8—1222no—
337#341—22no—
338#341—1222no—
339#338—1222no—
340C61#1110111yescharacteristic, complemented, Sylow
341C25—611no—
342C23×C4—611no—
343C23×C4—612no—
344C23×C4—612no—
345C23×C4—1221no—
346C23×C4—1221no—
347C23×C4—1221no—
348C23×C4—1221no—
349C23×C4—1221no—
350C23×C4—1221no—
351C23×C4—1221no—
352C23×C4—1221no—
353C23×C4—1221no—
354C23×C4—1221no—
355C23×C4—1221no—
356C23×C4—1221no—
357C23×C4C22×D6111yescharacteristic
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—612no—
375C2×M16—612no—
376C2×M16—612no—
377C2×M16—1221no—
378C2×M16—1221no—
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×M16—1221no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16C4×D6112yes—
393C2×M16D24412yes—
394C22×C8—21no—
395C22×C8—21no—
396C22×C8—612no—
397C22×C8—612no—
398C22×C8—1221no—
399C22×C8C22⋊D6112yes—
400#108—1228no—
401C22⋊C8—1228no—
402C22⋊C8—1228no—
403C22⋊C8—1228no—
404C24—612no—
405C24—1221no—
406C24—1221no—
407C24—1221no—
408C24—1221no—
409C24—1221no—
410C24—1221no—
411C24—2444no—
412C24Q8×D6111yescharacteristic
413C22×C4—612no—
414C22×C4—1221no—
415C22×C4—1221no—
416C22×C4—1221no—
417C22×C4—1221no—
418C22×C4—1221no—
419C22×C4—1221no—
420C22×C4—1222no—
421C22×C4—1222no—
422C22×C4—1222no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—2441no—
433C22×C4—2441no—
434C22×C4—2441no—
435C22×C4—2441no—
436C22×C4—2441no—
437C22×C4—2441no—
438C22×C4—2441no—
439C22×C4—2441no—
440C22×C4—2441no—
441C22×C4—2441no—
442C22×C4—2441no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4—2441no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4C2×C4×D6111yescharacteristic
449C22×C4C2×D24411yescharacteristic
450C22×C4#1175822211yescharacteristic
451C22×C4#1175822211yescharacteristic
452C22×C4#1175822211yescharacteristic
453C22×C4#1175822211yescharacteristic
454C22×C4D4×D6111yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4#1175822411yescharacteristic
460C22×C4#1175822611yescharacteristic
461C22×C4C2×C22⋊D6111yescharacteristic
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16—41no—
473M16—41no—
474M16—1222no—
475M16—1222no—
476M16—1222no—
477M16—1222no—
478M16—1222no—
479M16—1222no—
480M16—2441no—
481M16—2441no—
482M16—2441no—
483M16—2441no—
484M16—2441no—
485M16—2441no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—614no—
496C2×C8—1222no—
497C2×C8—1222no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8—2441no—
503C2×C8—2441no—
504C23—42no—
505C23—1224no—
506C23—1224no—
507C23—1224no—
508C23—1222no—
509C23—1222no—
510C23—1222no—
511C23—2442no—
512C23—2442no—
513C23—2442no—
514C23—2444no—
515C23—2444no—
516C23—2444no—
517C23—2444no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23—2441no—
522C23C4⋊C4×D6111yescharacteristic
523C23#1451975311yescharacteristic
524C23#1451975511yescharacteristic
525C23#1451975511yescharacteristic
526C23#1451975511yescharacteristic
527C23#1451975511yescharacteristic
528C23#1451975711yescharacteristic
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4C22⋊C4×D6111yescharacteristic
545C2×C4#1451973411yescharacteristic
546C2×C4#1451973711yescharacteristic
547C2×C4C4×C22⋊D6111yescharacteristic
548C2×C4#1451973911yescharacteristic
549C2×C4C4×D24411yescharacteristic
550C2×C4#1451974511yescharacteristic
551C2×C4#1451974711yescharacteristic
552C2×C4#1451974711yescharacteristic
553C2×C4#1451974911yescharacteristic
554C2×C4#1451975011yescharacteristic
555C2×C4#1451975011yescharacteristic
556C2×C4#1451975011yescharacteristic
557C2×C4#1451975011yescharacteristic
558C2×C4#1451975011yescharacteristic
559C2×C4#1451975111yescharacteristic
560C2×C4#1451975211yescharacteristic
561C2×C4#1451975911yescharacteristic
562C2×C4#1451976011yescharacteristic
563C2×C4#1451976211yescharacteristic
564C2×C4#1451976211yescharacteristic
565C2×C4#1451976211yescharacteristic
566C2×C4#1451976311yescharacteristic
567C2×C4#1451976311yescharacteristic
568C2×C4#1451976511yescharacteristic
569C2×C4#1451977111yescharacteristic
570C2×C4#1451977211yescharacteristic
571C2×C4#1451977311yescharacteristic
572C8—42no—
573C8—42no—
574C8—42no—
575C8—1224no—
576C8—2442no—
577C8—2442no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—1224no—
586C22—1224no—
587C22—1224no—
588C22—2442no—
589C22—2442no—
590C22—2442no—
591C22—2444no—
592C22—2444no—
593C22—2444no—
594C22—2444no—
595C22—2442no—
596C22#1683962111yescharacteristic
597C22#1683963311yescharacteristic
598C22#1683963611yescharacteristic
599C22#1683967511yescharacteristic
600C22#1683968411yescharacteristic
601C22#1683968611yescharacteristic
602C22#1683969711yescharacteristic
603C4—2442no—
604C4#1683964011yescharacteristic
605C4#1683965111yescharacteristic
606C4#1683965311yescharacteristic
607C4#1683966211yescharacteristic
608C4#1683967111yescharacteristic
609C4#1683967711yescharacteristic
610C4#1683968011yescharacteristic
611C4#1683969111yescharacteristic
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—2444no—
619C2#2144406311yescharacteristic
620C2#2144733412yes—
subgroupG/H
centerC2×C4#14519773
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1738C2
socleC22×C61#399
prime radicalC24×D61Q8
cosocleC23×C4×C61C23
hypercenter#1738D61
hypocenterC61#11101
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
1. C2×#16839810C2semidirect
5. #21445545C2semidirect
6. C2×#16839520C2semidirect
7. C61×#1738C2semidirect
307. #1738D61semidirect
340. C61#11101semidirect

Maximal subgroups

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

subgroupindex
C2×#168398102
C2×#168397252
#214455452
C2×#168395202
C61×#17382
#1110161