Finite Group Databasebeta

← C4×#16840577 #30544256

Subgroups — C4×#16840577 #30544256

Order 15616.

2658 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840577C211yesmaximal, characteristic
2C4×#14519824C211yesmaximal, characteristic, complemented
3#21454692C213yesmaximal, complemented
4#21454685C213yesmaximal, complemented
5#21454662C213yesmaximal, complemented
6#21454658C213yesmaximal, complemented
7C4×#14519808C213yesmaximal, complemented
8C4×#14519807C213yesmaximal, complemented
9C4×#14519797C213yesmaximal, complemented
10C2×C4×#11758202C213yesmaximal, complemented
11#21454417C211yesmaximal, characteristic, complemented
12#21454352C211yesmaximal, characteristic, complemented
13#21454349C211yesmaximal, characteristic, complemented
14C4×#14519784C211yesmaximal, characteristic, complemented
15C4×2−1+4×C61C211yesmaximal, characteristic, complemented
16C2×#14519824C2211yescharacteristic
17#16840577C4116yesdirect product factor
18C2×#14519808C2213yes—
19C2×#14519807C2213yes—
20C2×#14519797C2213yes—
21C22×#11758202C2213yes—
22C2×#14519784C2211yescharacteristic
23C2×#14519784C2211yescharacteristic
24#16840245C2211yescharacteristic
25#16840242C2213yes—
26#16840241—23no—
27#16840239C2213yes—
28#16840238—21no—
29C4×#11758222C2213yes—
30C4×#11758224—23no—
31C2×C4×Dic122C2213yes—
32C4×Q8×D61—21no—
33#16839867C2216yes—
34#16839867C2216yes—
35#16839862C2216yes—
36#16839860C2216yes—
37C4×#11758202C2216yes—
38C4×#11758202C2216yes—
39C4×#11758202C2213yes—
40C4×#11758202C2216yes—
41C4×#11758202C2213yes—
42C4×#11758201C2213yes—
43C4×#11758201C2213yes—
44C4×#11758200C2213yes—
45C4×#11758200C2213yes—
46C4×#11758199C2213yes—
47C4×#11758199C2211yescharacteristic
48#16839805C2213yes—
49#16839802C2213yes—
50#16839798C2213yes—
51C2×#14519710C2213yes—
52#16839771C2213yes—
53#16839770C2213yes—
54#16839763C2213yes—
55#16839761C2213yes—
56#16839758C2213yes—
57#16839756C2213yes—
58C2×#14519701C2213yes—
59C2×#14519700C2213yes—
60#16839718C2213yes—
61#16839718C2213yes—
62C4×#11758194C2213yes—
63C2×C4×#92418C2213yes—
64C2×2−1+4×C61C2211yescharacteristic
65C61×#520—23no—
66C61×#520C2213yes—
67C61×#520C2211yescharacteristic
68C61×#519—21no—
69C61×#519C2213yes—
70C4×#41×C61—23no—
71C4×#41×C61C2213yes—
72C4×#41×C61C2211yescharacteristic
73C2×C4×Q8×C61—21no—
74C2×C4×Q8×C61C2213yes—
75#14519824—24no—
76#14519824C2×C418yescomplemented
77C2×#11758222C2313yes—
78C2×#11758224—23no—
79C22×Dic122C2313yes—
80C2×Q8×D61—21no—
81#14519808C2×C4124yescomplemented
82#14519807C2×C4124yescomplemented
83#14519797C2×C4124yescomplemented
84C2×#11758202C2×C4124yescomplemented
85C2×#11758202C2313yes—
86C2×#11758202C2316yes—
87C2×#11758200C2313yes—
88C2×#11758201C2313yes—
89C2×#11758199C2311yescharacteristic
90#14519784—24no—
91#14519784C2×C418yescomplemented
92C2×#11758194C2313yes—
93C2×#11758194C2313yes—
94C22×#92418C2313yes—
95C22×#92418C2313yes—
96Q8×Dic61—21no—
97C4×Dic122—23no—
98C4×Dic122—23no—
99C4×Dic122C2313yes—
100C4×Dic122C2316yes—
101C4×Dic122C2313yes—
102#14519742—23no—
103#14519742—23no—
104C4×D244C2311yescharacteristic
105C4×D244C2313yes—
106D4×Dic61—23no—
107C4×C22⋊D61—23no—
108C4×C22⋊D61—23no—
109#14519737—26no—
110#14519736C2313yes—
111#14519735—23no—
112#14519734—23no—
113#14519733—26no—
114C2×C4⋊Dic61C2313yes—
115C2×#11758196—23no—
116C4⋊C4×D61—23no—
117C2×C4×Dic61—23no—
118C42×D61—23no—
119#14519710C2313yes—
120#14519710C2316yes—
121#14519710C2311yescharacteristic
122#14519708C2313yes—
123#14519708C2313yes—
124#14519701C2313yes—
125#14519701C2316yes—
126#14519701C2313yes—
127#14519700C2313yes—
128#14519700C2316yes—
129#14519700C2313yes—
130#14519698C2311yescharacteristic
131#14519698C2313yes—
132#14519697C2311yescharacteristic
133#14519697C2313yes—
134#14519688C2316yes—
135C4×#92418C2311yescharacteristic
136C4×#92418C2313yes—
137C4×#92418C2313yes—
138C4×#92418C2313yes—
1392−1+4×C61—24no—
1402−1+4×C61C2×C418yescomplemented
141C2×#41×C61—23no—
142C2×#41×C61C2313yes—
143C2×#41×C61C2311yescharacteristic
144C22×Q8×C61—21no—
145C22×Q8×C61C2313yes—
146C4×Q8×C61—21no—
147C4×Q8×C61—23no—
148C4×Q8×C61—23no—
149C4×Q8×C61—23no—
150C4×Q8×C61—23no—
151C4×Q8×C61D411yescharacteristic
152C4×Q8×C61D411yescharacteristic
153C4×Q8×C61C2313yes—
154C4×Q8×C61C2313yes—
155C4×Q8×C61C2316yes—
156C4×D4×C61—23no—
157C4×D4×C61—23no—
158C4×D4×C61—23no—
159C4×D4×C61—26no—
160C4×D4×C61D413yes—
161C4×D4×C61D413yes—
162C4×D4×C61C2311yescharacteristic
163C4×D4×C61C2313yes—
164#117×C61—23no—
165#117×C61—26no—
166#117×C61—23no—
167#117×C61C2313yes—
168#117×C61C2313yes—
169C2×C4⋊C4×C61—23no—
170C2×C4⋊C4×C61—23no—
171C2×C4⋊C4×C61C2313yes—
172C2×C42×C61—23no—
173C2×C42×C61—23no—
174C2×C42×C61C2313yes—
175#41×C61—224no—
176#41×C61—26no—
177#41×C61C22×C4112yes—
178#41×C61C22×C414yes—
179#41×C61#4114yes—
180C2×Q8×C61—28no—
181C2×Q8×C61—23no—
182C2×Q8×C61—26no—
183C2×Q8×C61C22×C4112yes—
184C2×Q8×C61C2×D411yescharacteristic
185C2×Q8×C61C2413yes—
186C2×D4×C61—23no—
187C2×D4×C61C2×D413yes—
188C2×D4×C61C2411yescharacteristic
189C22×C4×C61—23no—
190C22×C4×C61—23no—
191C22×C4×C61—23no—
192C22×C4×C61—21no—
193C22×C4×C61—23no—
194C22×C4×C61C2×D413yes—
195C22×C4×C61C2×D413yes—
196C22×C4×C61C2413yes—
197C2×C22⋊D61—23no—
198C22×Dic61—23no—
199C22×Dic61—23no—
200Q8×D61—28no—
201#11758224—224no—
202#11758222—26no—
203#11758222C22×C4112yes—
204C2×D244C2411yescharacteristic
205C2×C4×D61—23no—
206C2×C4×D61—21no—
207C2×C4×D61—23no—
208C2×Dic122—23no—
209C2×Dic122—26no—
210C2×Dic122C22×C4112yes—
211C2×Dic122C2413yes—
212C4⋊C4×C61—26no—
213C4⋊C4×C61—23no—
214C4⋊C4×C61—23no—
215C4⋊C4×C61—23no—
216C4⋊C4×C61C2×D413yes—
217C4⋊C4×C61C2×D413yes—
218C4⋊C4×C61C2413yes—
219C4⋊C4×C61C2411yescharacteristic
220C22⋊C4×C61—23no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61—23no—
223C22⋊C4×C61C2×D416yes—
224C42×C61—23no—
225C42×C61—23no—
226C42×C61—26no—
227C42×C61—23no—
228C42×C61C2×D413yes—
229C42×C61C2×D413yes—
230C42×C61C2411yescharacteristic
231C42×C61C2413yes—
232C22⋊Dic61—23no—
233#11758202C22×C4124yes—
234#11758202C22×C4112yes—
235#11758201C22×C4112yes—
236#11758200C22×C4112yes—
237#11758199C22×C414yes—
238#11758198—21no—
239#11758198—23no—
240C4⋊Dic61—23no—
241C4⋊Dic61C2411yescharacteristic
242C4⋊Dic61C2413yes—
243#11758196—26no—
244#11758196—23no—
245#11758196—23no—
246C4×Dic61—23no—
247C4×Dic61—23no—
248C4×Dic61—23no—
249C4×Dic61—26no—
250#11758194—26no—
251#11758194C22×C4112yes—
252C2×#92418—26no—
253C2×#92418C22×C4112yes—
254C2×#92418C2411yescharacteristic
255C2×#92418C2413yes—
256C2×#92418C2411yescharacteristic
257C2×#92418C2413yes—
258C23×C61—21no—
259C23×C61C22×D413yes—
260C22×D61—21no—
261Q8×C61—212no—
262Q8×C61—23no—
263Q8×C61C4×D414yes—
264Q8×C61C23×C416yes—
265D4×C61—212no—
266D4×C61—21no—
267D4×C61C4×D4112yes—
268D4×C61C23×C412yes—
269C2×C4×C61—212no—
270C2×C4×C61—23no—
271C2×C4×C61—212no—
272C2×C4×C61—26no—
273C2×C4×C61—21no—
274C2×C4×C61—23no—
275C2×C4×C61—43no—
276C2×C4×C61—42no—
277C2×C4×C61—83no—
278C2×C4×C61—83no—
279C2×C4×C61C23×C416yes—
280C2×C4×C61C22×D413yes—
281C2×C4×C61C22×D413yes—
282C2×C4×C61C22×D411yescharacteristic
283C2×C4×C61C22×D413yes—
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C2×#4116yes—
286C2×C4×C61C2511yescharacteristic
287C22⋊D61—212no—
288C2×Dic61—212no—
289C2×Dic61—23no—
290C2×Dic61—21no—
291C2×Dic61—23no—
292C2×Dic61—83no—
293D244—21no—
294D244C23×C412yes—
295C4×D61—212no—
296C4×D61—42no—
297C4×D61—83no—
298Dic122—212no—
299Dic122—23no—
300Dic122C23×C416yes—
301#92418—21no—
302#92418—23no—
303#92418C23×C412yes—
304#92418C23×C416yes—
305C4×#578—611nomaximal, Sylow
306C22×C61—23no—
307C22×C61—23no—
308C22×C61—22no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61C2×C4×D416yes—
312C22×C61C23×D411yescharacteristic
313C2×D61—22no—
314C2×D61—41no—
315C2×D61—41no—
316C4×C61—23no—
317C4×C61—21no—
318C4×C61—26no—
319C4×C61—23no—
320C4×C61—43no—
321C4×C61—41no—
322C4×C61C2×C4×D416yes—
323C4×C61#57812yescomplemented
324C4×C61C24×C411yescharacteristic
325C4×C61C22×#4111yescharacteristic
326Dic61—26no—
327Dic61—43no—
328Dic61—41no—
329C2×#578—611no—
330C4×2−1+4—611no—
331C4×2−1+4D6111yescharacteristic, complemented
332#2951—613no—
333#2950—613no—
334#2947—613no—
335#2947—613no—
336C4×#137—613no—
337C4×#137—613no—
338C4×#135—613no—
339C2×C4×Q16—613no—
340#2913—611no—
341#2898—611no—
342#2898—611no—
343C4×#131—611no—
344C2×C61—26no—
345C2×C61—42no—
346C2×C61C22×C4×D411yescharacteristic
347C2×C61C2×#57811yescharacteristic
348C2×C61#358411yescharacteristic
349D61—42no—
350C2×2−1+4—611no—
351C2×2−1+4C2×D6111yescharacteristic
352#578—6116no—
353C2×#137—613no—
354C2×#137—613no—
355C2×#135—613no—
356C22×Q16—613no—
357C2×#131—611no—
358C2×#131—611no—
359#520—23no—
360#520—611no—
361#520—613no—
362#520—1223no—
363#520C2×D6113yes—
364#520C2×D6111yescharacteristic
365#519—21no—
366#519—613no—
367#519—1221no—
368#519C2×D6113yes—
369C4×#41—23no—
370C4×#41—613no—
371C4×#41—1223no—
372C4×#41C2×D6113yes—
373C4×#41C2×D6111yescharacteristic
374C2×C4×Q8—21no—
375C2×C4×Q8—613no—
376C2×C4×Q8—1221no—
377C2×C4×Q8C2×D6113yes—
378#441—616no—
379#441—616no—
380#440—616no—
381#440—616no—
382C4×Q16—613no—
383C4×Q16—616no—
384C4×Q16—616no—
385C4×Q16—616no—
386C4×Q16—613no—
387C4×SD16—613no—
388C4×SD16—613no—
389C4×SD16—613no—
390C4×SD16—613no—
391C4×D8—611no—
392C4×D8—613no—
393#428—613no—
394#428—613no—
395#427—613no—
396C2×#107—613no—
397#419—613no—
398#419—613no—
399#417—613no—
400#417—613no—
401#416—613no—
402#416—613no—
403C2×#103—613no—
404C2×#103—613no—
405#405—613no—
406#405—613no—
407C4×M16—613no—
408C2×C4×C8—613no—
409C61C4×#57811yescharacteristic, complemented, Sylow
4102−1+4—24no—
4112−1+4—618no—
4122−1+4—1224no—
4132−1+4C4×D6118yescomplemented
414C2×#41—23no—
415C2×#41—613no—
416C2×#41—1223no—
417C2×#41C22×D6113yes—
418C2×#41C22×D6111yescharacteristic
419C22×Q8—21no—
420C22×Q8—613no—
421C22×Q8—1221no—
422C22×Q8C22×D6113yes—
423#137—6124no—
424#137—6124no—
425#135—6124no—
426C2×Q16—6124no—
427C2×Q16—613no—
428C2×Q16—616no—
429C2×SD16—613no—
430C2×SD16—613no—
431C2×D8—611no—
432#131—618no—
433#131—1224no—
434C2×M16—613no—
435C2×M16—613no—
436C22×C8—613no—
437C22×C8—613no—
438C4×Q8—21no—
439C4×Q8—23no—
440C4×Q8—23no—
441C4×Q8—23no—
442C4×Q8—23no—
443C4×Q8—613no—
444C4×Q8—616no—
445C4×Q8—613no—
446C4×Q8—1221no—
447C4×Q8—1223no—
448C4×Q8—1223no—
449C4×Q8—1223no—
450C4×Q8—1223no—
451C4×Q8C22⋊D6111yescharacteristic
452C4×Q8C22⋊D6111yescharacteristic
453C4×Q8C22×D6113yes—
454C4×Q8C22×D6116yes—
455C4×Q8C22×D6113yes—
456C4×D4—23no—
457C4×D4—23no—
458C4×D4—23no—
459C4×D4—26no—
460C4×D4—611no—
461C4×D4—613no—
462C4×D4—1223no—
463C4×D4—1223no—
464C4×D4—1223no—
465C4×D4—1226no—
466C4×D4C22⋊D6113yes—
467C4×D4C22⋊D6113yes—
468C4×D4C22×D6111yescharacteristic
469C4×D4C22×D6113yes—
470#117—23no—
471#117—26no—
472#117—23no—
473#117—613no—
474#117—1223no—
475#117—1226no—
476#117—1223no—
477#117C22×D6113yes—
478#117C22×D6113yes—
479C2×C4⋊C4—23no—
480C2×C4⋊C4—23no—
481C2×C4⋊C4—613no—
482C2×C4⋊C4—1223no—
483C2×C4⋊C4—1223no—
484C2×C4⋊C4C22×D6113yes—
485C2×C42—23no—
486C2×C42—23no—
487C2×C42—1223no—
488C2×C42—1223no—
489C2×C42C22×D6113yes—
490#107—613no—
491#107—616no—
492#107—611no—
493#106—613no—
494#106—613no—
495#103—613no—
496#103—616no—
497#103—613no—
498#103—613no—
499#103—616no—
500#103—613no—
501#102—611no—
502#102—613no—
503#102—611no—
504#102—613no—
505#97—616no—
506C4×C8—611no—
507C4×C8—613no—
508C4×C8—613no—
509C4×C8—613no—
510#41—224no—
511#41—26no—
512#41—6112no—
513#41—12224no—
514#41—1226no—
515#41C2×C4×D61112yes—
516#41C2×C4×D6114yes—
517#41#1175822214yes—
518C2×Q8—28no—
519C2×Q8—23no—
520C2×Q8—26no—
521C2×Q8—6112no—
522C2×Q8—613no—
523C2×Q8—1228no—
524C2×Q8—1223no—
525C2×Q8—1226no—
526C2×Q8C2×C4×D61112yes—
527C2×Q8C2×C22⋊D6111yescharacteristic
528C2×Q8C23×D6113yes—
529C2×D4—23no—
530C2×D4—611no—
531C2×D4—1223no—
532C2×D4C2×C22⋊D6113yes—
533C2×D4C23×D6111yescharacteristic
534C22×C4—23no—
535C22×C4—23no—
536C22×C4—23no—
537C22×C4—21no—
538C22×C4—23no—
539C22×C4—1223no—
540C22×C4—1223no—
541C22×C4—1223no—
542C22×C4—1223no—
543C22×C4—1221no—
544C22×C4C2×C22⋊D6113yes—
545C22×C4C2×C22⋊D6113yes—
546C22×C4C23×D6113yes—
547Q16—6112no—
548Q16—6124no—
549SD16—6112no—
550SD16—6112no—
551D8—614no—
552M16—6112no—
553M16—1226no—
554C2×C8—6112no—
555C2×C8—611no—
556C2×C8—613no—
557C2×C8—611no—
558C2×C8—613no—
559C2×C8—1226no—
560C4⋊C4—26no—
561C4⋊C4—23no—
562C4⋊C4—23no—
563C4⋊C4—23no—
564C4⋊C4—611no—
565C4⋊C4—613no—
566C4⋊C4—1223no—
567C4⋊C4—1226no—
568C4⋊C4—1223no—
569C4⋊C4—1223no—
570C4⋊C4C2×C22⋊D6113yes—
571C4⋊C4C2×C22⋊D6113yes—
572C4⋊C4C23×D6111yescharacteristic
573C4⋊C4C23×D6113yes—
574C22⋊C4—23no—
575C22⋊C4—21no—
576C22⋊C4—23no—
577C22⋊C4—1223no—
578C22⋊C4—1221no—
579C22⋊C4—1223no—
580C22⋊C4C2×C22⋊D6116yes—
581C42—23no—
582C42—26no—
583C42—23no—
584C42—23no—
585C42—1223no—
586C42—1223no—
587C42—1226no—
588C42—1223no—
589C42C2×C22⋊D6113yes—
590C42C2×C22⋊D6113yes—
591C42C23×D6113yes—
592C42C23×D6111yescharacteristic
593C23—21no—
594C23—1221no—
595C23C22×C22⋊D6113yes—
596Q8—212no—
597Q8—23no—
598Q8—616no—
599Q8—12212no—
600Q8—1223no—
601Q8C4×C22⋊D6114yes—
602Q8C22×C4×D6116yes—
603D4—212no—
604D4—21no—
605D4—612no—
606D4—12212no—
607D4—1221no—
608D4C4×C22⋊D61112yes—
609D4C22×C4×D6112yes—
610C2×C4—212no—
611C2×C4—23no—
612C2×C4—212no—
613C2×C4—26no—
614C2×C4—21no—
615C2×C4—23no—
616C2×C4—43no—
617C2×C4—42no—
618C2×C4—83no—
619C2×C4—83no—
620C2×C4—12212no—
621C2×C4—1223no—
622C2×C4—12212no—
623C2×C4—1221no—
624C2×C4—1223no—
625C2×C4—4883no—
626C2×C4—4883no—
627C2×C4—2442no—
628C2×C4C22×C4×D6116yes—
629C2×C4C22×C22⋊D6113yes—
630C2×C4C22×C22⋊D6113yes—
631C2×C4C22×C22⋊D6111yescharacteristic
632C2×C4C22×C22⋊D6113yes—
633C2×C4C22×C22⋊D6111yescharacteristic
634C2×C4C2×#1175822216yes—
635C2×C4C24×D6111yescharacteristic
636C8—612no—
637C8—616no—
638C8—1221no—
639C8—1223no—
640C22—23no—
641C22—23no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—1222no—
646C22—2441no—
647C22—2441no—
648C22C2×C4×C22⋊D6116yes—
649C22C23×C22⋊D6111yescharacteristic
650C4—26no—
651C4—23no—
652C4—21no—
653C4—23no—
654C4—41no—
655C4—43no—
656C4—1226no—
657C4—2441no—
658C4—2443no—
659C4C2×C4×C22⋊D6116yes—
660C4#1684057712yesdirect product factor
661C4C23×C4×D6111yescharacteristic
662C4C22×#1175822211yescharacteristic
663C2—26no—
664C2—42no—
665C2—2442no—
666C2C22×C4×C22⋊D6111yescharacteristic
667C2C2×#1684057711yescharacteristic
668C2#2146059011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC4×2−1+4×C61C2
socleC22×C61C23×D4
prime radicalC2×#16840577C2
cosocleC2×C4×C61C25
hypercenterC4×2−1+4D61
hypocenterC61C4×#578
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. C4×#14519824C2semidirect
3. #21454692C2semidirect
4. #21454685C2semidirect
5. #21454662C2semidirect
6. #21454658C2semidirect
7. C4×#14519808C2semidirect
8. C4×#14519807C2semidirect
9. C4×#14519797C2semidirect
10. C2×C4×#11758202C2semidirect
11. #21454417C2semidirect
12. #21454352C2semidirect
13. #21454349C2semidirect
14. C4×#14519784C2semidirect
15. C4×2−1+4×C61C2semidirect
17. #16840577C4direct (N × H)
76. #14519824C2×C4semidirect
81. #14519808C2×C4semidirect
82. #14519807C2×C4semidirect
83. #14519797C2×C4semidirect
84. C2×#11758202C2×C4semidirect
91. #14519784C2×C4semidirect
140. 2−1+4×C61C2×C4semidirect
323. C4×C61#578semidirect
331. C4×2−1+4D61semidirect
409. C61C4×#578semidirect
413. 2−1+4C4×D61semidirect
660. C4#16840577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405772
C4×#145198242
#214546922
#214546852
#214546622
#214546582
C4×#145198082
C4×#145198072
C4×#145197972
C2×C4×#117582022
#214544172
#214543522
#214543492
C4×#145197842
C4×2−1+4×C612
C4×#57861