Finite Group Databasebeta

← #29587140

Subgroups — #29587140

Order 15616.

990 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
1C22×#14519705C211yesmaximal, characteristic
2C2×#16839761C211yesmaximal, characteristic
3#21448412C211yesmaximal, characteristic
4C2×#16839531C211yesmaximal, characteristic, complemented
5#21445538C211yesmaximal, characteristic, complemented
6C2×#16839522C211yesmaximal, characteristic, complemented
7C2×C61×#382C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12C2×#14519705—22no—
13C2×#14519705—22no—
14C2×#14519705C414yescomplemented
15#16839761—22no—
16#16839761—22no—
17C2×#14519700—21no—
18C2×#14519697—21no—
19#16839667—21no—
20#16839663—21no—
21#16839641—22no—
22#16839619—22no—
23#16839531—22no—
24#16839524—22no—
25#16839522—22no—
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C22×C42×C61C2211yescharacteristic
29C61×#382—22no—
30C61×#382—22no—
31C2×#95×C61—22no—
32C2×#11758222—21no—
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222C2×C412yes—
43C2×#11758222Q812yes—
44C22×Dic122D411yescharacteristic
45C22×D244D411yescharacteristic
46C22×C22⋊D61—21no—
47C22×C4×D61—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×#11758194C2×C412yes—
59C2×#11758194D412yes—
60C22×#92418—21no—
61C22×#92418—21no—
62#14519736—21no—
63#14519736—21no—
64#14519736—21no—
65#14519736—21no—
66C2×C4⋊Dic61D412yes—
67C2×C22⋊Dic61—21no—
68C2×#11758198—24no—
69C2×C4×Dic61—21no—
70#14519705—28no—
71#14519700—24no—
72#14519697—24no—
73#14519684—24no—
74C23×C4×C61—21no—
75C23×C4×C61—21no—
76C23×C4×C61D412yes—
77C23×C4×C61C2311yescharacteristic
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61D412yes—
90C2×C42×C61—21no—
91C2×C42×C61—21no—
92C2×C42×C61—21no—
93C2×C42×C61C2×C412yes—
94C2×C42×C61D412yes—
95C2×C42×C61D412yes—
96#95×C61—28no—
97C24×C61C2×D411yescharacteristic
98C23×D61—21no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—42no—
107C22×C4×C61—42no—
108C22×C4×C61—44no—
109C22×C4×C61—44no—
110C22×C4×C61—41no—
111C22×C4×C61—41no—
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×Q811yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61#4111yescharacteristic
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—41no—
129C2×C22⋊D61—41no—
130C2×C22⋊D61—41no—
131C2×C22⋊D61—41no—
132C22×Dic61—21no—
133C22×Dic61—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—22no—
137#11758222—22no—
138#11758222—22no—
139#11758222—22no—
140#11758222—22no—
141#11758222—22no—
142#11758222—41no—
143#11758222—41no—
144#11758222—41no—
145#11758222—41no—
146#11758222—41no—
147#11758222—41no—
148#11758222—41no—
149#11758222—41no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244C4⋊C412yes—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—41no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×C4×D61—41no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122C4⋊C412yes—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C42×C61—22no—
177C42×C61—22no—
178C42×C61—22no—
179C42×C61C22⋊C414yescomplemented
180C22⋊Dic61—41no—
181C22⋊Dic61—41no—
182#11758198—84no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4×Dic61—41no—
186C4×Dic61—41no—
187#11758194—22no—
188#11758194—22no—
189#11758194—22no—
190#11758194—22no—
191#11758194—41no—
192#11758194—41no—
193#11758194—41no—
194#11758194—41no—
195C2×#92418—22no—
196C2×#92418—22no—
197C2×#92418—41no—
198C2×#92418—41no—
199C2×#92418—41no—
200C2×#92418—41no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61C4×D411yescharacteristic
204C23×C61#12011yescharacteristic
205C23×C61#12011yescharacteristic
206C23×C61#12111yescharacteristic
207C23×C61#12111yescharacteristic
208C23×C61C22⋊Q811yescharacteristic
209C23×C61#12411yescharacteristic
210C22×D61—22no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—42no—
214C22×D61—42no—
215C2×C4×C61—24no—
216C2×C4×C61—44no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—44no—
220C2×C4×C61—44no—
221C2×C4×C61—44no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—44no—
225C2×C4×C61—82no—
226C2×C4×C61—82no—
227C2×C4×C61—82no—
228C2×C4×C61C2×C22⋊C411yescharacteristic
229C2×C4×C61C2×C4⋊C411yescharacteristic
230C2×C4×C61#11711yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61#12011yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61C22⋊Q811yescharacteristic
242C2×C4×C61C22⋊Q811yescharacteristic
243C2×C4×C61C22⋊Q811yescharacteristic
244C2×C4×C61C22⋊Q811yescharacteristic
245C2×C4×C61C22⋊Q811yescharacteristic
246C2×C4×C61#12311yescharacteristic
247C2×C4×C61#12311yescharacteristic
248C2×C4×C61#12311yescharacteristic
249C2×C4×C61#12311yescharacteristic
250C2×C4×C61#12311yescharacteristic
251C2×C4×C61#12411yescharacteristic
252C2×C4×C61#12411yescharacteristic
253C2×C4×C61#12611yescharacteristic
254C2×C4×C61#12611yescharacteristic
255C2×C4×C61#12711yescharacteristic
256C22⋊D61—42no—
257C22⋊D61—42no—
258C22⋊D61—42no—
259C22⋊D61—42no—
260C2×Dic61—22no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—42no—
264C2×Dic61—42no—
265C2×Dic61—42no—
266D244—22no—
267D244—22no—
268D244—41no—
269D244—41no—
270C4×D61—42no—
271C4×D61—42no—
272C4×D61—42no—
273C4×D61—42no—
274Dic122—22no—
275Dic122—22no—
276Dic122—41no—
277Dic122—41no—
278#92418—42no—
279#92418—42no—
280#11079—611nomaximal, Sylow
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—22no—
288C22×C61—22no—
289C22×C61#38511yescharacteristic
290C22×C61#38611yescharacteristic
291C22×C61#38811yescharacteristic
292C22×C61#39211yescharacteristic
293C22×C61#39311yescharacteristic
294C22×C61#39411yescharacteristic
295C22×C61#39611yescharacteristic
296C22×C61#45412yes—
297C22×C61#45512yes—
298C2×D61—44no—
299C2×D61—42no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61—82no—
303C4×C61—44no—
304C4×C61—82no—
305C4×C61—82no—
306C4×C61#38011yescharacteristic
307C4×C61#38511yescharacteristic
308C4×C61#38811yescharacteristic
309C4×C61#39011yescharacteristic
310C4×C61#39411yescharacteristic
311C4×C61#39611yescharacteristic
312C4×C61#39711yescharacteristic
313C4×C61#39911yescharacteristic
314Dic61—42no—
315Dic61—82no—
316C22×#104—611no—
317C2×#417—611no—
318#2311—611no—
319C2×#382D6111yescharacteristic, complemented
320C2×#343—611no—
321#1736—611no—
322C2×#339—611no—
323C2×C61—21no—
324C2×C61—21no—
325C2×C61—21no—
326C2×C61—21no—
327C2×C61#143911yescharacteristic
328C2×C61#186012yes—
329C2×C61#200311yescharacteristic
330C2×C61#200411yescharacteristic
331C2×C61#204012yes—
332D61—82no—
333C22×#41—611no—
334C22×M16—611no—
335C22×M16—611no—
336C2×#117—611no—
337C22×C4⋊C4C2×D6111yescharacteristic
338C22×C4⋊C4C2×D6111yescharacteristic
339C22×C42C2×D6111yescharacteristic
340C2×#104—614no—
341C2×#104—1222no—
342C2×#104—1222no—
343#417—1222no—
344#417—1222no—
345C2×#103—1221no—
346C2×#102—1221no—
347#391—1221no—
348#390—1221no—
349#386—1222no—
350#382—22no—
351#382—22no—
352#380—1222no—
353C2×#95—22no—
354#343—1222no—
355#340—1222no—
356#339—1222no—
357C61#1107911yescharacteristic, complemented, Sylow
358C2×#41—612no—
359C2×#41—612no—
360C2×#41—1221no—
361C2×#41—1221no—
362C2×#41—1221no—
363C2×#41—1221no—
364C2×#41—1221no—
365C2×#41—1221no—
366C2×#41—1221no—
367C2×#41—1221no—
368C2×#41—1221no—
369C2×#41—1221no—
370C22×Q8—611no—
371C22×D4—611no—
372C22×D4—1221no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—1221no—
376C23×C4C22⋊D6112yes—
377C23×C4C22×D6111yescharacteristic
378C2×M16—612no—
379C2×M16—612no—
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—
390C22×C8—1221no—
391C22×C8—1221no—
392#117—1221no—
393#117—1221no—
394#117—1221no—
395#117—1221no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—612no—
408C2×C4⋊C4C22⋊D6112yes—
409C2×C22⋊C4—1224no—
410C2×C22⋊C4—1221no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—1221no—
415C2×C42C4×D6112yes—
416C2×C42D24412yes—
417C2×C42C22⋊D6112yes—
418#104—1228no—
419#103—1224no—
420#102—1224no—
421#95—28no—
422#95—1224no—
423C24—1221no—
424C24C2×C22⋊D6111yescharacteristic
425#41—1222no—
426#41—1222no—
427#41—1222no—
428#41—1222no—
429#41—1222no—
430#41—1222no—
431#41—1222no—
432#41—1222no—
433#41—2441no—
434#41—2441no—
435#41—2441no—
436#41—2441no—
437#41—2441no—
438#41—2441no—
439#41—2441no—
440#41—2441no—
441C2×Q8—612no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×D4—612no—
448C2×D4—1222no—
449C2×D4—1222no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—2441no—
456C2×D4—2441no—
457C2×D4—2441no—
458C2×D4—2441no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—1221no—
473C22×C4—1222no—
474C22×C4—1222no—
475C22×C4—1222no—
476C22×C4—2441no—
477C22×C4—2441no—
478C22×C4—2441no—
479C22×C4—2441no—
480C22×C4C2×C4×D6111yescharacteristic
481C22×C4C2×D24411yescharacteristic
482C22×C4#1175822211yescharacteristic
483C22×C4#1175822211yescharacteristic
484C22×C4D4×D6111yescharacteristic
485C22×C4D4×D6111yescharacteristic
486C22×C4D4×D6111yescharacteristic
487C22×C4#1175822411yescharacteristic
488C22×C4Q8×D6111yescharacteristic
489C22×C4#1175822611yescharacteristic
490C22×C4#1175822611yescharacteristic
491C22×C4#1175822611yescharacteristic
492C22×C4C2×C22⋊D6111yescharacteristic
493C22×C4C2×C22⋊D6111yescharacteristic
494M16—1222no—
495M16—1222no—
496M16—1222no—
497M16—1222no—
498M16—2441no—
499M16—2441no—
500M16—2441no—
501M16—2441no—
502C2×C8—1222no—
503C2×C8—1222no—
504C2×C8—2441no—
505C2×C8—2441no—
506C2×C8—2441no—
507C2×C8—2441no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C22⋊C4—4884no—
519C22⋊C4—2441no—
520C22⋊C4—2441no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—2441no—
525C42—2441no—
526C42#1175819814yescomplemented
527C23—22no—
528C23—22no—
529C23—1222no—
530C23—2442no—
531C23—2441no—
532C23—2442no—
533C23—2441no—
534C23C4×C22⋊D6111yescharacteristic
535C23#1451974511yescharacteristic
536C23#1451974611yescharacteristic
537C23#1451974911yescharacteristic
538C23#1451975111yescharacteristic
539C23#1451975311yescharacteristic
540C23#1451976611yescharacteristic
541Q8—1222no—
542Q8—1222no—
543Q8—2441no—
544Q8—2441no—
545D4—1222no—
546D4—1222no—
547D4—2442no—
548D4—2442no—
549D4—2442no—
550D4—2442no—
551D4—2441no—
552D4—2441no—
553C2×C4—24no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—1222no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4C2×#1175819811yescharacteristic
577C2×C4C4⋊C4×D6111yescharacteristic
578C2×C4#1451973511yescharacteristic
579C2×C4C4×C22⋊D6111yescharacteristic
580C2×C4#1451973911yescharacteristic
581C2×C4#1451973911yescharacteristic
582C2×C4#1451974511yescharacteristic
583C2×C4#1451974811yescharacteristic
584C2×C4#1451974911yescharacteristic
585C2×C4#1451975111yescharacteristic
586C2×C4#1451975211yescharacteristic
587C2×C4#1451975211yescharacteristic
588C2×C4#1451975211yescharacteristic
589C2×C4#1451975311yescharacteristic
590C2×C4#1451975311yescharacteristic
591C2×C4#1451975511yescharacteristic
592C2×C4#1451975511yescharacteristic
593C2×C4#1451975711yescharacteristic
594C2×C4#1451976011yescharacteristic
595C2×C4#1451976211yescharacteristic
596C2×C4#1451976211yescharacteristic
597C2×C4#1451976211yescharacteristic
598C2×C4#1451976211yescharacteristic
599C2×C4#1451976611yescharacteristic
600C2×C4#1451976611yescharacteristic
601C2×C4#1451977211yescharacteristic
602C2×C4#1451977211yescharacteristic
603C2×C4#1451977311yescharacteristic
604C8—2442no—
605C8—2442no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—4882no—
615C22—4881no—
616C22—4881no—
617C22—2444no—
618C22—2442no—
619C22#1683963311yescharacteristic
620C22#1683964111yescharacteristic
621C22#1683965211yescharacteristic
622C22#1683967011yescharacteristic
623C22#1683967311yescharacteristic
624C22#1683967911yescharacteristic
625C22#1683968411yescharacteristic
626C22#1683993412yes—
627C22#1683993912yes—
628C4—44no—
629C4—82no—
630C4—82no—
631C4—4882no—
632C4—2442no—
633C4#1683961911yescharacteristic
634C4#1683963311yescharacteristic
635C4#1683965211yescharacteristic
636C4#1683966311yescharacteristic
637C4#1683967911yescharacteristic
638C4#1683968411yescharacteristic
639C4#1683968811yescharacteristic
640C4#1683969711yescharacteristic
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—4882no—
646C2#2144406111yescharacteristic
647C2#2144605112yes—
648C2#2144684111yescharacteristic
649C2#2144684811yescharacteristic
650C2#2144704812yes—
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#382C2
socleC23×C61#120
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#382D61
hypocenterC61#11079
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
4. C2×#16839531C2semidirect
5. #21445538C2semidirect
6. C2×#16839522C2semidirect
7. C2×C61×#382C2semidirect
14. C2×#14519705C4semidirect
179. C42×C61C22⋊C4semidirect
319. C2×#382D61semidirect
357. C61#11079semidirect
526. C42#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197052
C2×#168397612
#214484122
C2×#168395312
#214455382
C2×#168395222
C2×C61×#3822
#1107961