Finite Group Databasebeta

← #29587237

Subgroups — #29587237

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839788C211yesmaximal, characteristic, complemented
2#21454336C211yesmaximal, characteristic
3C2×#16839759C211yesmaximal, characteristic
4C2×#16839735C211yesmaximal, characteristic
5#21445552C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C61×#1735C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839788—22no—
13#16839788—22no—
14C2×#14519706—22no—
15#16839770—21no—
16#16839766—21no—
17#16839761—22no—
18#16839759—22no—
19#16839759—22no—
20#16839756—22no—
21C2×#14519702—21no—
22C2×#14519699—21no—
23#16839735—22no—
24#16839735C414yescomplemented
25C2×#14519691—22no—
26#16839529—22no—
27#16839518—22no—
28C23×C8×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C61×#340—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—
54C22×#92418D412yes—
55#14519736—21no—
56#14519736—21no—
57#14519736—21no—
58#14519736—21no—
59#14519736—21no—
60#14519736C2×C412yes—
61#14519736D412yes—
62#14519736D412yes—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C22⋊Dic61—21no—
66C2×C22⋊Dic61D412yes—
67C2×C4×Dic61—21no—
68C2×C4×Dic61—21no—
69#14519706—28no—
70#14519702—24no—
71#14519700—24no—
72#14519699—24no—
73#14519697—24no—
74#14519691—28no—
75C23×C4×C61C2311yescharacteristic
76C22×C8×C61—21no—
77C22×C8×C61—21no—
78C22×C8×C61—21no—
79C22×C8×C61—21no—
80C22×C8×C61—21no—
81C22×C8×C61—21no—
82C22×C8×C61D412yes—
83#117×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×C61C2×C412yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61D412yes—
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—21no—
95C2×C42×C61—21no—
96C2×C42×C61—21no—
97C24×C61C2×D411yescharacteristic
98C23×D61—21no—
99C22×C4×C61—22no—
100C22×C4×C61—41no—
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×C61C2×Q811yescharacteristic
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—
122C22×Dic61—22no—
123C22×Dic61—41no—
124#11758222—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244C4⋊C412yes—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C4⋊C412yes—
158C2×C8×C61—22no—
159C2×C8×C61—22no—
160C2×C8×C61—22no—
161C2×C8×C61—41no—
162C2×C8×C61—41no—
163C2×C8×C61—41no—
164C2×C8×C61—41no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—41no—
169C22⋊C4×C61—22no—
170C22⋊C4×C61—41no—
171C22⋊C4×C61—41no—
172C22⋊C4×C61—41no—
173C42×C61—22no—
174C42×C61—41no—
175C42×C61—41no—
176C42×C61—41no—
177C22⋊Dic61—22no—
178C22⋊Dic61—22no—
179C22⋊Dic61—41no—
180C22⋊Dic61C22⋊C414yes—
181C4⋊Dic61—22no—
182C4⋊Dic61—22no—
183C4⋊Dic61—22no—
184C4⋊Dic61—41no—
185C4×Dic61—22no—
186C4×Dic61—22no—
187C4×Dic61—22no—
188C4×Dic61—41no—
189#11758194—41no—
190#11758194—41no—
191#11758194—41no—
192#11758194—41no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—22no—
196C23×C61—42no—
197C23×C61C2×C22⋊C411yescharacteristic
198C23×C61#12111yescharacteristic
199C23×C61#12111yescharacteristic
200C23×C61#12111yescharacteristic
201C23×C61#12111yescharacteristic
202C23×C61#12111yescharacteristic
203C23×C61C22⋊Q811yescharacteristic
204C22×D61—22no—
205C22×D61—41no—
206C22×D61—41no—
207C22×D61—82no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—82no—
211C2×C4×C61—82no—
212C2×C4×C61C2×C4⋊C411yescharacteristic
213C2×C4×C61#11711yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61#12011yescharacteristic
219C2×C4×C61#12011yescharacteristic
220C2×C4×C61#12011yescharacteristic
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61C22⋊Q811yescharacteristic
225C2×C4×C61C22⋊Q811yescharacteristic
226C2×C4×C61C22⋊Q811yescharacteristic
227C2×C4×C61C22⋊Q811yescharacteristic
228C2×C4×C61C22⋊Q811yescharacteristic
229C2×C4×C61#12311yescharacteristic
230C2×C4×C61#12311yescharacteristic
231C2×C4×C61#12311yescharacteristic
232C2×C4×C61#12311yescharacteristic
233C2×C4×C61#12311yescharacteristic
234C2×C4×C61#12411yescharacteristic
235C2×C4×C61#12411yescharacteristic
236C2×C4×C61#12411yescharacteristic
237C2×C4×C61#12611yescharacteristic
238C2×C4×C61#12611yescharacteristic
239C2×C4×C61#12711yescharacteristic
240C22⋊D61—42no—
241C22⋊D61—42no—
242C22⋊D61—42no—
243C22⋊D61—42no—
244C2×Dic61—22no—
245C2×Dic61—24no—
246C2×Dic61—44no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—42no—
250C2×Dic61—82no—
251D244—22no—
252D244—22no—
253D244—41no—
254D244—41no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—42no—
258C4×D61—42no—
259Dic122—22no—
260Dic122—22no—
261Dic122—41no—
262Dic122—41no—
263C8×C61—42no—
264#92418—42no—
265#11092—611nomaximal, Sylow
266C22×C61—22no—
267C22×C61—22no—
268C22×C61—22no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61#38011yescharacteristic
274C22×C61#38611yescharacteristic
275C22×C61#39011yescharacteristic
276C22×C61#39411yescharacteristic
277C22×C61#39411yescharacteristic
278C22×C61#39611yescharacteristic
279C22×C61#39611yescharacteristic
280C2×D61—42no—
281C2×D61—82no—
282C2×D61—82no—
283C2×D61—82no—
284C4×C61—82no—
285C4×C61—82no—
286C4×C61#38511yescharacteristic
287C4×C61#38511yescharacteristic
288C4×C61#38811yescharacteristic
289C4×C61#38811yescharacteristic
290C4×C61#39211yescharacteristic
291C4×C61#39311yescharacteristic
292C4×C61#39711yescharacteristic
293C4×C61#39911yescharacteristic
294Dic61—44no—
295Dic61—42no—
296Dic61—82no—
297C2×#424—611no—
298#2896—611no—
299C2×#416—611no—
300C2×#410—611no—
301#1740—611no—
302#1735D6111yescharacteristic, complemented
303C2×H(3,ℤ/4)—611no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61—21no—
309C2×C61—21no—
310C2×C61#143911yescharacteristic
311C2×C61#205312yes—
312D61—82no—
313C22×#41—611no—
314C22×M16—611no—
315C23×C8C2×D6111yescharacteristic
316C2×#117—611no—
317C2×#117—611no—
318C2×#117C2×D6111yescharacteristic
319C2×#117C2×D6111yescharacteristic
320#424—1222no—
321#424—1222no—
322C2×C4⋊C8—1222no—
323#419—1221no—
324#418—1221no—
325#417—1222no—
326#416—1222no—
327#416—1222no—
328#416—1222no—
329C2×#103—1221no—
330C2×#102—1221no—
331#410—614no—
332#410—1222no—
333C2×#99—1222no—
334#342—1222no—
335#340—22no—
336H(3,ℤ/4)—1222no—
337C61#1109211yescharacteristic, complemented, Sylow
338C2×#41—612no—
339C2×#41—612no—
340C2×#41—1221no—
341C2×#41—1221no—
342C2×#41—1221no—
343C2×#41—1221no—
344C2×#41—1221no—
345C2×#41—1221no—
346C2×#41—1221no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1221no—
350C22×Q8—611no—
351C22×D4—611no—
352C22×D4—1221no—
353C23×C4—1221no—
354C23×C4C22×D6111yescharacteristic
355C2×M16—1221no—
356C2×M16—1221no—
357C2×M16—1221no—
358C2×M16—1221no—
359C2×M16—1221no—
360C2×M16—1221no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—612no—
368C22×C8D24412yes—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—612no—
377#117—612no—
378#117—612no—
379#117—1221no—
380#117—1221no—
381#117—1221no—
382#117—1221no—
383#117—1221no—
384#117C4×D6112yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4C22⋊D6112yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—612no—
392C2×C22⋊C4—1221no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—1221no—
396C2×C42—1221no—
397C4⋊C8—1228no—
398#103—1224no—
399#103—1224no—
400#102—1224no—
401#102—1224no—
402#99—1228no—
403C24—1221no—
404C24D4×D6111yescharacteristic
405#41—1222no—
406#41—1222no—
407#41—1222no—
408#41—1222no—
409#41—1222no—
410#41—1222no—
411#41—1222no—
412#41—1222no—
413#41—2441no—
414#41—2441no—
415#41—2441no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419#41—2441no—
420#41—2441no—
421C2×Q8—612no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×D4—612no—
428C2×D4—1222no—
429C2×D4—1222no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—2441no—
436C2×D4—2441no—
437C2×D4—2441no—
438C2×D4—2441no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—1222no—
442C22×C4—1221no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—2441no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4C2×C4×D6111yescharacteristic
451C22×C4C2×D24411yescharacteristic
452C22×C4#1175822211yescharacteristic
453C22×C4#1175822211yescharacteristic
454C22×C4#1175822211yescharacteristic
455C22×C4#1175822211yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4D4×D6111yescharacteristic
460C22×C4#1175822411yescharacteristic
461C22×C4Q8×D6111yescharacteristic
462C22×C4#1175822611yescharacteristic
463C22×C4C2×C22⋊D6111yescharacteristic
464M16—2441no—
465M16—2441no—
466M16—2441no—
467M16—2441no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—1222no—
476C2×C8—1222no—
477C2×C8—1222no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—41no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—2441no—
486C22⋊C4—22no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—614no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—2441no—
494C42—22no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42—1222no—
499C42—1222no—
500C42—1222no—
501C42—2441no—
502C23—42no—
503C23—1222no—
504C23—4882no—
505C23—2441no—
506C23—2441no—
507C23C22⋊C4×D6111yescharacteristic
508C23#1451974911yescharacteristic
509C23#1451975011yescharacteristic
510C23#1451975011yescharacteristic
511C23#1451975011yescharacteristic
512C23#1451975211yescharacteristic
513C23#1451975511yescharacteristic
514Q8—1222no—
515Q8—1222no—
516Q8—2441no—
517Q8—2441no—
518D4—1222no—
519D4—1222no—
520D4—2442no—
521D4—2442no—
522D4—2442no—
523D4—2442no—
524D4—2441no—
525D4—2441no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—1222no—
531C2×C4—1224no—
532C2×C4—4882no—
533C2×C4—2442no—
534C2×C4—2444no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2442no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4C4⋊C4×D6111yescharacteristic
542C2×C4#1451973411yescharacteristic
543C2×C4#1451973711yescharacteristic
544C2×C4C4×C22⋊D6111yescharacteristic
545C2×C4#1451973911yescharacteristic
546C2×C4C4×D24411yescharacteristic
547C2×C4#1451974511yescharacteristic
548C2×C4#1451974711yescharacteristic
549C2×C4#1451974711yescharacteristic
550C2×C4#1451975011yescharacteristic
551C2×C4#1451975011yescharacteristic
552C2×C4#1451975111yescharacteristic
553C2×C4#1451975311yescharacteristic
554C2×C4#1451975511yescharacteristic
555C2×C4#1451975511yescharacteristic
556C2×C4#1451975511yescharacteristic
557C2×C4#1451975711yescharacteristic
558C2×C4#1451975911yescharacteristic
559C2×C4#1451976011yescharacteristic
560C2×C4#1451976211yescharacteristic
561C2×C4#1451976211yescharacteristic
562C2×C4#1451976211yescharacteristic
563C2×C4#1451976311yescharacteristic
564C2×C4#1451976311yescharacteristic
565C2×C4#1451976511yescharacteristic
566C2×C4#1451977111yescharacteristic
567C2×C4#1451977211yescharacteristic
568C2×C4#1451977311yescharacteristic
569C8—42no—
570C8—2442no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—4882no—
579C22—4882no—
580C22—4882no—
581C22—2442no—
582C22#1683962111yescharacteristic
583C22#1683964011yescharacteristic
584C22#1683966211yescharacteristic
585C22#1683967711yescharacteristic
586C22#1683968011yescharacteristic
587C22#1683968411yescharacteristic
588C22#1683968611yescharacteristic
589C4—82no—
590C4—82no—
591C4—4882no—
592C4—2444no—
593C4—2442no—
594C4#1683963311yescharacteristic
595C4#1683963611yescharacteristic
596C4#1683965111yescharacteristic
597C4#1683965311yescharacteristic
598C4#1683967111yescharacteristic
599C4#1683967511yescharacteristic
600C4#1683969111yescharacteristic
601C4#1683969711yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—4882no—
609C2#2144406311yescharacteristic
610C2#2144712312yes—
subgroupG/H
centerC2×C4#14519763
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1735C2
socleC22×C61#394
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#1735D61
hypocenterC61#11092
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
1. C2×#16839788C2semidirect
5. #21445552C2semidirect
6. C2×#16839518C2semidirect
7. C61×#1735C2semidirect
24. #16839735C4semidirect
302. #1735D61semidirect
337. C61#11092semidirect

Maximal subgroups

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

subgroupindex
C2×#168397882
#214543362
C2×#168397592
C2×#168397352
#214455522
C2×#168395182
C61×#17352
#1109261