Finite Group Databasebeta

← #29587608

Subgroups — #29587608

Order 15616.

826 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×#16839780C211yesmaximal, characteristic
2C2×#16839761C211yesmaximal, characteristic
3C2×#16839744C211yesmaximal, characteristic
4C2×#16839532C211yesmaximal, characteristic, complemented
5C2×#16839531C211yesmaximal, characteristic, complemented
6#21445545C211yesmaximal, characteristic, complemented
7C61×#1736C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16839780—22no—
13#16839780—22no—
14C2×#14519705—22no—
15#16839761—22no—
16#16839761—22no—
17C2×#14519700—21no—
18C2×#14519697—21no—
19#16839744—22no—
20#16839744C414yescomplemented
21C2×#14519695—21no—
22C2×#14519693—21no—
23#16839532—22no—
24#16839531—22no—
25#16839526—22no—
26C22×M16×C61C2211yescharacteristic
27C2×#117×C61C2211yescharacteristic
28C22×C4⋊C4×C61C2211yescharacteristic
29C61×#340—22no—
30C2×#11758222—21no—
31C2×#11758222—21no—
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×#11758222C2×C412yes—
41C2×#11758222D412yes—
42C22×Dic122D411yescharacteristic
43C22×D244D411yescharacteristic
44C22×C22⋊D61—21no—
45C22×C4×D61—21no—
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×#92418—21no—
66C22×#92418—21no—
67#14519705—28no—
68#14519700—24no—
69#14519697—24no—
70#14519695—24no—
71#14519693—24no—
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61C2×C412yes—
80C22×C8×C61—21no—
81#117×C61—21no—
82#117×C61—21no—
83#117×C61—21no—
84#117×C61D412yes—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61D412yes—
92C2×C22⋊C4×C61—21no—
93C2×C42×C61—21no—
94C24×C61#4111yescharacteristic
95C23×D61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—82no—
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C2×C22⋊D61—22no—
116C2×C22⋊D61—22no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C22×Dic61—21no—
122#11758222—22no—
123#11758222—22no—
124#11758222—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—41no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244C22⋊C412yes—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—41no—
147C2×C4×D61—41no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122C22⋊C412yes—
156M16×C61—22no—
157M16×C61—22no—
158M16×C61—41no—
159M16×C61—41no—
160C2×C8×C61—22no—
161C2×C8×C61—41no—
162C2×C8×C61—41no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61—41no—
169C22⋊C4×C61—22no—
170C22⋊C4×C61—41no—
171C42×C61—22no—
172C42×C61—41no—
173#11758194—22no—
174#11758194—22no—
175#11758194—22no—
176#11758194—22no—
177#11758194—22no—
178#11758194—22no—
179#11758194—41no—
180#11758194—41no—
181#11758194—41no—
182#11758194—41no—
183#11758194—41no—
184#11758194—41no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—41no—
189C2×#92418—41no—
190C2×#92418—41no—
191C2×#92418—41no—
192C2×#92418—41no—
193C2×#92418—41no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61#11711yescharacteristic
197C23×C61#12111yescharacteristic
198C23×C61#12311yescharacteristic
199C23×C61#12311yescharacteristic
200C23×C61#12311yescharacteristic
201C23×C61#12411yescharacteristic
202C23×C61#12611yescharacteristic
203C22×D61—22no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—81no—
207C22×D61—81no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—81no—
211C2×C4×C61—81no—
212C2×C4×C61—82no—
213C2×C4×C61—82no—
214C2×C4×C61—82no—
215C2×C4×C61C2×C22⋊C411yescharacteristic
216C2×C4×C61#11711yescharacteristic
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12011yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12311yescharacteristic
231C2×C4×C61#12311yescharacteristic
232C2×C4×C61#12311yescharacteristic
233C2×C4×C61#12311yescharacteristic
234C2×C4×C61#12311yescharacteristic
235C2×C4×C61#12311yescharacteristic
236C2×C4×C61#12311yescharacteristic
237C2×C4×C61#12411yescharacteristic
238C2×C4×C61#12411yescharacteristic
239C2×C4×C61#12411yescharacteristic
240C2×C4×C61#12611yescharacteristic
241C2×C4×C61#12611yescharacteristic
242C2×C4×C61#12611yescharacteristic
243C22⋊D61—42no—
244C22⋊D61—42no—
245C22⋊D61—42no—
246C22⋊D61—42no—
247C2×Dic61—22no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250D244—22no—
251D244—22no—
252D244—41no—
253D244—41no—
254C4×D61—42no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—42no—
258Dic122—22no—
259Dic122—22no—
260Dic122—41no—
261Dic122—41no—
262C8×C61—42no—
263#92418—42no—
264#92418—42no—
265#92418—42no—
266#11152—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61#38111yescharacteristic
278C22×C61#38811yescharacteristic
279C22×C61#38811yescharacteristic
280C22×C61#39411yescharacteristic
281C22×C61#39411yescharacteristic
282C22×C61#39711yescharacteristic
283C22×C61#39711yescharacteristic
284C2×D61—42no—
285C2×D61—82no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—82no—
289C4×C61—82no—
290C4×C61—82no—
291C4×C61#38611yescharacteristic
292C4×C61#38611yescharacteristic
293C4×C61#38811yescharacteristic
294C4×C61#38811yescharacteristic
295C4×C61#39411yescharacteristic
296C4×C61#39411yescharacteristic
297C4×C61#39711yescharacteristic
298C4×C61#39711yescharacteristic
299Dic61—42no—
300C2×#421—611no—
301C2×#417—611no—
302C2×#413—611no—
303C2×#344—611no—
304C2×#343—611no—
305#1738—611no—
306#1736D6111yescharacteristic, complemented
307C2×C61—21no—
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61#144011yescharacteristic
314C2×C61#204811yescharacteristic
315C2×C61#204911yescharacteristic
316D61—82no—
317C22×#41—611no—
318C22×M16—611no—
319C22×M16—611no—
320C22×M16—611no—
321C22×M16C2×D6111yescharacteristic
322C2×#117C2×D6111yescharacteristic
323C22×C4⋊C4C2×D6111yescharacteristic
324#421—1222no—
325#421—1222no—
326C2×#104—1222no—
327#417—1222no—
328#417—1222no—
329C2×#103—1221no—
330C2×#102—1221no—
331#413—614no—
332#413—1222no—
333C2×#101—1221no—
334C2×#100—1221no—
335#344—1222no—
336#343—1222no—
337#341—1222no—
338#340—22no—
339C61#1115211yescharacteristic, complemented, Sylow
340C2×#41—612no—
341C2×#41—612no—
342C2×#41—1221no—
343C2×#41—1221no—
344C2×#41—1221no—
345C2×#41—1221no—
346C2×#41—1221no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C22×Q8—611no—
353C22×D4—611no—
354C22×D4—1221no—
355C23×C4—21no—
356C23×C4—1221no—
357C23×C4C22×D6111yescharacteristic
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—612no—
364C2×M16—612no—
365C2×M16—612no—
366C2×M16—1221no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—1221no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16C4×D6112yes—
382C22×C8—21no—
383C22×C8—1221no—
384C22×C8—1221no—
385C22×C8—1221no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117D24412yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4C22⋊D6112yes—
397C2×C22⋊C4—21no—
398C2×C42—21no—
399#104—1228no—
400#103—1224no—
401#102—1224no—
402#101—1224no—
403#100—1224no—
404C24—1221no—
405C24#1175822411yescharacteristic
406#41—1222no—
407#41—1222no—
408#41—1222no—
409#41—1222no—
410#41—1222no—
411#41—1222no—
412#41—1222no—
413#41—1222no—
414#41—2441no—
415#41—2441no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419#41—2441no—
420#41—2441no—
421#41—2441no—
422C2×Q8—612no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×D4—612no—
429C2×D4—1222no—
430C2×D4—1222no—
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4—2441no—
437C2×D4—2441no—
438C2×D4—2441no—
439C2×D4—2441no—
440C22×C4—22no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—82no—
445C22×C4—1221no—
446C22×C4—1222no—
447C22×C4—1222no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4C2×C4×D6111yescharacteristic
453C22×C4C2×D24411yescharacteristic
454C22×C4#1175822211yescharacteristic
455C22×C4#1175822211yescharacteristic
456C22×C4#1175822211yescharacteristic
457C22×C4#1175822211yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4D4×D6111yescharacteristic
460C22×C4D4×D6111yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4#1175822411yescharacteristic
463C22×C4#1175822611yescharacteristic
464C22×C4#1175822611yescharacteristic
465C22×C4C2×C22⋊D6111yescharacteristic
466M16—22no—
467M16—22no—
468M16—41no—
469M16—41no—
470M16—1222no—
471M16—1222no—
472M16—1222no—
473M16—1222no—
474M16—1222no—
475M16—1222no—
476M16—2441no—
477M16—2441no—
478M16—2441no—
479M16—2441no—
480M16—2441no—
481M16—2441no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—1222no—
486C2×C8—1222no—
487C2×C8—1222no—
488C2×C8—2441no—
489C2×C8—2441no—
490C2×C8—2441no—
491C2×C8—2441no—
492C2×C8—2441no—
493C2×C8—2441no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C22⋊C4—22no—
501C22⋊C4—41no—
502C42—22no—
503C42—41no—
504C23—41no—
505C23—41no—
506C23—1222no—
507C23—4881no—
508C23—4881no—
509C23—2441no—
510C23—2441no—
511C23#1451973511yescharacteristic
512C23#1451974911yescharacteristic
513C23#1451975911yescharacteristic
514C23#1451975911yescharacteristic
515C23#1451976111yescharacteristic
516C23#1451976311yescharacteristic
517C23#1451977211yescharacteristic
518Q8—1222no—
519Q8—1222no—
520Q8—2441no—
521Q8—2441no—
522D4—1222no—
523D4—1222no—
524D4—2442no—
525D4—2442no—
526D4—2442no—
527D4—2442no—
528D4—2441no—
529D4—2441no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—1222no—
538C2×C4—2441no—
539C2×C4—2441no—
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#1451974811yescharacteristic
553C2×C4#1451975011yescharacteristic
554C2×C4#1451975011yescharacteristic
555C2×C4#1451975011yescharacteristic
556C2×C4#1451975111yescharacteristic
557C2×C4#1451975211yescharacteristic
558C2×C4#1451975211yescharacteristic
559C2×C4#1451975911yescharacteristic
560C2×C4#1451976011yescharacteristic
561C2×C4#1451976211yescharacteristic
562C2×C4#1451976211yescharacteristic
563C2×C4#1451976211yescharacteristic
564C2×C4#1451976211yescharacteristic
565C2×C4#1451976211yescharacteristic
566C2×C4#1451976311yescharacteristic
567C2×C4#1451976511yescharacteristic
568C2×C4#1451976611yescharacteristic
569C2×C4#1451977111yescharacteristic
570C2×C4#1451977211yescharacteristic
571C2×C4#1451977211yescharacteristic
572C8—42no—
573C8—2442no—
574C8—2442no—
575C8—2442no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—4882no—
587C22—4882no—
588C22—4881no—
589C22—4881no—
590C22—2442no—
591C22#1683962411yescharacteristic
592C22#1683965211yescharacteristic
593C22#1683965411yescharacteristic
594C22#1683967711yescharacteristic
595C22#1683967811yescharacteristic
596C22#1683968911yescharacteristic
597C22#1683969111yescharacteristic
598C4—82no—
599C4—82no—
600C4—2442no—
601C4#1683963811yescharacteristic
602C4#1683964011yescharacteristic
603C4#1683965111yescharacteristic
604C4#1683965311yescharacteristic
605C4#1683967911yescharacteristic
606C4#1683968011yescharacteristic
607C4#1683968811yescharacteristic
608C4#1683969111yescharacteristic
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—4882no—
616C2#2144406711yescharacteristic
617C2#2144709011yescharacteristic
618C2#2144709711yescharacteristic
subgroupG/H
centerC22#16839677
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1736C2
socleC22×C61#394
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#1736D61
hypocenterC61#11152
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#16839532C2semidirect
5. C2×#16839531C2semidirect
6. #21445545C2semidirect
7. C61×#1736C2semidirect
20. #16839744C4semidirect
306. #1736D61semidirect
339. C61#11152semidirect

Maximal subgroups

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

subgroupindex
C2×#168397802
C2×#168397612
C2×#168397442
C2×#168395322
C2×#168395312
#214455452
C61×#17362
#1115261